In light of updates, some of the data in the manual is inaccurate (for example, the Sova supports a maximum of 6 squadrons, manual says 7).
The SoaSE Wiki gives the initial number of squadrons, plus how many the capital gains per level. However, keep in mind that you must round down the number given to find the actual number of squadrons. For example, the Radiance is listed as having 0.8 squadrons at level 1, gaining 0.2 squadrons per level. This means it starts off with no squadrons (0.8 rounded down is 0), but at level 2, it has one squadron (0.8 + 0.2 = 1.0). It gains its 2nd and final squadron at level 7. However, data for some capitals is missing, though you can look at equivalents for other races (all capitals of the same type carry the same number of squadrons, e.g. all battleships carry 2 squadrons at level 10, all colonizers carry 3 squadrons at level 10, etc.)