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

We describe all fusion subcategories of the representation category ${\mathrm Rep}(D^\omega(G))$ 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 ${\mathrm Rep}(D^\omega(G))$, 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 ${\mathrm Rep}(D^\omega(G))$. We also give a characterization of group-theoretical braided fusion categories as equivariantizations of pointed categories.