gap> Q:=List(L,QuasiIsomorph);;
gap> M:=[];;

gap> for q in Q do
> bool:=true;;
> for m in M do
> if not IsomorphismCatOneGroups(m,q)=fail then bool:=false; break; fi;
> od;
> if bool then Add(M,q); fi;
> od;

gap> Length(M);
51
