The selection of "carrier" ships in Star Citizen is extremely limited.
So far, the only "carrier" ships in the game right now are the 890 Jump (can fit most small ships in the front hangar, has room for 1-3 small ships in the front hangar at once), the Carrack (can fit a few small ships in the top hangar but only 1), and the newly added Hercules Star Lifter (which can fit about half of the small ships, about 2-3 ships can fit in at once). However, as mentioned earlier, the game servers are unstable, so the game is set to delete any ships if its owner is more than a few kilometers away and there is no one else on board, so you can't leave your 890 Jump/Carrack/Star Lifter in orbit over a planet while you fly around in your smaller mining ship or a combat fighter or a passenger ship going to pick someone up.
IIRC the only other carrier ships that are planned are the Kraken (small, mobile spacestation with landing pads and hangars and player owned shops), the Idris (is ingame as an NPC ship, cannot be flown by players ATM, can carry multiple small ships in its hangar), and the Bengal (can carry multiple small ships, is ingame but cannot be flown by players ATM). However, given the current state of the game, I doubt that any of those three ships will ever be flyable by players (despite the Kraken and the Idris having been sold to backers for thousands of dollars).