For each finite solvable
group G, there is a minimal positive integer ram(G) (resp. ramt(G)) such that G
appears as the Galois group of an extension of ℚ (resp. a tamely ramified extension
of ℚ) ramified at only ram(G) (resp. ramt(G)) finite primes. We obtain bounds for
ram(G) and ramt(G), where G is either a nilpotent group of odd order or a
generalized dihedral group.