I am given a set of sets:

{{a,b}, {a,b,c}, {a,c},{a,c,f}} 

I would like to have a data structure to index those sets such that the following "lookup" is executed fast: find all supersets of a given set.

For example, given the set {a,c} the structure would return

{{a,b,c},{a,c,f}, {a,c} 

but not {a,b}.

Any suggestions? Could this be done with a smart trie-like data structure?