It seems the biggest / last class a ship can be is a Collossal Galaxy Destroyer.
Will it go further?
Galaxy Carrier Class
You will now have a set number of drone fighters per your level, that will add to your
defense, and you will have to maintain. Research and outfitting still apply.
or
You will now have to recruit and outfit small fighters, that will add to your
defense, and you will have to maintain. Research and outfitting still apply.
Pilots will be a set number per your level that you will be able to train under a pilot
tech tree.