Terminology for military spacecraft tends to hinge on metaphorical words such as "battleship" and "air wing". That's fine, of course, but here's an attempt at doing something else.
First, terms for what sort of vessel you're looking at:
Now, what one would tend to call a fleet:
A Flagship of any group is that group's COORDINATOR. Its deputy is the BACKUP COORDINATOR. A Coordinator that is also the Coordinator of a larger group than the one currently being referred to is a PRIME COORDINATOR.
Now, combatant vessels (more specific roles generally just appended as adjectives or symbol suffixes):
And support craft (each can be of any size, in which case their symbol is prefixed with the letter for that size). One can expect one of each of these in each Asterism, though some may omit some types in favor of more gneralized craft:
Now, strike craft (shuttles and boarding craft generally labeled completely separately, though some may be marked like "MBG-58132" or "XB-143"):
Strike craft are divided into three main groups: Anti-light craft/interdictor, Anti-heavy craft/attack, and support/non-combatant.
Examples follow:
This is the City Of Tarroved, a Cherask-series superprimary. As the coordinator for Constellation Epsilon, it also serves as coordinator for its namesake Tarroved Cluster, Tarroved Asterism, and the 1st Prime Combatant System and Section of that Asterism.
The system CarGru 1 of the US Navy consists of coordinator USS Carl Vinson, a nuclear-powered attack supercarrier of the Nimitz-class and Nimitz-series. It is accompanied by USS Lake Champlain, an AEGIS guided missile cruiser of the Spruance-class, Ticonderoga-series, and Bunker Hill-model; as well as the section DesRon 1. DesRon 1 consists of four Arleigh Burke-class AEGIS guided missile destroyers of the Oscar Austin/Flight IIA-series, which are all McCampbell-model vessels. In proper parlance these instead be a Primary Patrol Carrier, a Supertertiary, and four Fleet Tertiaries.
This is the Charrimash Kelato, a Terali-series LFT/C (light fleet tertiary/command) of the Karravos-class and Panek-model. It heads a system of similar ships, LFT-Y13(-T1) of defense asterism 7, as the system coordinator. Its backup system coordinator is the Ithrallar-model LFT/S (light fleet tertiary/screening) Beruk Kelato of the same class and series. Trailing the system is its support section, consisting of two tenders and one military cargo vessel.
The asterism "Tensak Dyllath" (Dyllath's Fighters) is one of the Unified Republics Stellar Military's primary combat asterisms. Its setup is typical of that military, and is as follows:
System "Yikal Dyllath" (Dyllath's Court), a formation of 7 fleet primaries with the superprimary (Chesod-class, Persul anti-superprimary series) Dyllath as prime coordinator (that is, coordinator of both the system and its surrounding asterism) and the fleet primaries (Pasak-class, Talur command series) Ikkal and Mashak as backup prime coordinator and backup coordinator (each themselves in command of one 3-ship section) respectively. These perform the primary actions of the fleet.
System "Pelas Kiv Danet" (roughly "blue stinging wasps"), a group of 15 fleet secondaries with the large fleet secondary (Tekul-class, Maroth large command series) Temsul, Dersav, and Shendl as coordinator and backup coordinators- each is in control of a section of 5 satellites, including four other Yarast-class fleet secondaries of varying series. These are usually sent in to confront enemy forward formations or to scout ahead.
System "Dyllath-Berusa" (Berusa-class satellites belonging to Dyllath), a group of 3 sections each consisting of one supertertiary and six fleet tertiaries. All are of the Yash Berusa (great Berusa) or Berusa classes, and all named along the lines of their prime coordinator Issola Yash Berusa. These serve as screening satellites for the larger craft.
System "Mersola Irusatval" (hive 137), a group of 3 sections each consisting of one tertiary carrier of the Seshem-class and three fleet quartaries of the Sallav-class Opol spinal gun series. These provide long-range support.
TCF Carriers of the Seshem class, while relatively small, operate 12 onboard Sections (though, as these are deployed vessels, they are usually instead Groups) of up to 7 spacecraft each. The usual arrangement is: 2x7 MII, 2x7 MIS, 3x7 MID, 2x4 MAH, 2x4 MAL, 1x2 MNS. In addition, non-carrier vessels of tertiary size and larger often carry anywhere from a short Group (on tertiaries) to 6 full Groups (on independent-operation primaries) of onboard spacecraft, usually multirole craft such as MIR, MAF, and MNS; as well as at least one Senary and several "shuttle" or "runabout" craft intermediate between Septaries and Senaries.
The integrated supply chain consists of System "Ano Kalav" (nectar and nourishment), a collection of support craft consisting of several sections. The first, Tender Section, contains five secondary-scale tenders each designed to accomodate six tertiaries or two secondaries; each tender also carries three Fleet Quinaries for defense. The second, Spares Section, contains a single primary-scale replacement ship which carries five fleet quartaries and three groups of defense interceptors. The third, Supply Section, contains three primary-scale tankers and two primary-scale cargo ships, which each carry the same defensive setup as Spares Section. The fourth and final section is a single primary-scale hospital/repair satellite, with fore drydock and rear habitation space, which carries along four fleet quartaries and one group of defense interceptors.
In total, Tensak Dyllath consists of:
The Primary Combat Carrier Rossevol, of the Kaldiat-class and Pemdur independent operation series, carries its entire fleet with it. Said fleet contains not only strike craft, but also several relatively large vessels: a full section of one Supertertiary and six Tertiaries, another 5 Patrol Quartaries for picket and scouting work, 15 multirole Quinaries, and a full complement of 30 Senaries with duties from patrol to shuttling. Its strike craft complement consists of a dazzling 100 groups: 5x7 MIR, 10x7 MII, 25x7 MIS, 10x7 MID, 10x4 MAH, 10x4 MAL, 15x6 MAF, 5x2 MNR, and 10x2 MNS. It also carries many noncombatant vessels (for crew transfer, rescue, and mining), including 10 Senary-sized shuttles, 15 intermediate-sized shuttles, and 40 Septenary-sized shuttles as well as a functional Secondary Tender for its carried craft. Said carried craft bring with them a further 5x7 MID and 5x1 MAF.