Fleet Sizes

It's controlled by your "logistics" capability -- this is a set total sum of ship logistic sizes that can be in one fleet. To put two fleets in one, drive them to the same square and then click on the "manage" button to the lower left. Then you can click, shift-click a,d etc., on ships to put in the same fleet.

So can something be researched to increase this. My enemy seems to be able to field far larger fleets.

What would be your tips on having the biggest fleet?

Take a race that has organized or make a custom race with organized. Then take all of the logistics techs + take the logistics specializations. I believe this gives you a maximum of +40 from logistics +10 base +10 from organized for 60 total. I may be missing one more +10 tech so it's either 60 or 70 logistics.

I have 61 logistics and do not think I have all posible points available.

Have you built the Hyperion Logistics System? The level bonus also grants additional logistics (+1 per level).

You can massively reduce the logistic cost of ships in a fleet with the hyperion logistic system