What determines fleet size?

I have a hostile neighbor whose fleet's are more powerful than any of mine. The problem isn't that I don't have good enough ships, but that my fleet sizes are too small.

With my best ships I can only merge two at a time into a fleet.

Is there a way to increase the size of a fleet?

Fleet size is determined by Command Points Cap, found on the left (Diplomacy and Trading) branch of the tech tree.

Clicking on a fleet and looking at the number next to the satellite dish icon is a quick way to see the fleet size limts. Here 16 of 16 slots are used.

Note: Researching Quantum Communications unlocks C3 Systems which gives you +2 cap for each new ship class acquired (ship classes are unlocked in the bottom tree, Exploration and Expansion).