Thanks for your answer!
I made seperate carrier and battleship fleets. And I have to say, carrier fleets really kick ass! A fleet without carriers really takes a beating against them, as it should be...

Since Japan has a lot of carriers I will hold my BB fleets back or send them against the german fleet for now.
My older Carrier Fleet is already making a lot of damage. Soon 2 brand new will be ready!
I have another question though, regarding Army composition:
I know I get a combined arms bonus when I group tanks and motorised infantry 2:1 or 1:2.
What would be the recomended ratio? More tanks than Mot.Inf so the army has more punch, but with less armies because of tank cost
or more Mot.Inf to get more Armies with tanks in them out of the IC ?
Also, should I combine tanks and mech.Inf or keep the mech.Inf in sperate armies since they don't get comb.arms bonus (I think) and then rather build pure tank armies?