Fusion Subcategories of Representation Categories of Twisted Quantum Doubles of Finite Groups

We describe all fusion subcategories of the representation category Rep(D-omega(G)) of a twisted quantum double D-omega(G), where G is a finite group and omega is a 3-cocycle on G. In view of the fact that every group-theoretical braided fusion category can be embedded into some Rep(D-omega(G)), this gives a complete description of all group-theoretical braided fusion categories. We describe the lattice and give formulas for some invariants of the fusion subcategories of Rep(D-omega(G)). We also give a characterization of group-theoretical braided fusion categories as equivariantizations of pointed categories.