  The quotient process of M\"uger and Brugui\`eres is used to construct modular
categories and TQFTs out of closed subsets of the Weyl alcove of a simple Lie
algebra. In particular it is determined at which levels closed subsets
associated to nonsimply-connected groups lead to TQFTs. Many of these TQFTs are
shown to decompose into a tensor product of TQFTs coming from smaller subsets.
The "prime" subsets among these are classified, and apart from some giving
TQFTs depending on homology as described by Murakami, Ohtsuki and Okada, they
are shown to be in one-to-one correspondence with the TQFTs predicted by
Dijkgraaf and Witten to be associated to Chern-Simons theory with a
nonsimply-connected Lie group. Thus in particular a rigorous construction of
the Dijkgraaf-Witten TQFTs is given. As a byproduct, a purely quantum groups
proof of the modularity of the full Weyl alcove for arbitrary quantum groups at
arbitrary levels is given.
