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This online calculator generates all combinations of teams, so that everyone can play with, and against everyone. Technically, it is the Set partitions generator with restrictions. You should input number of players and size of a team, and it generates a list of all combinations.
Note that number of players is limited to 12. This is because of a combinatorial explosion. If you want to get all combinations of teams of 2 players for 12 players, you will get 10395 combinations. I believe it is beyond any practical usage.