  We study algebraic and topological properties of subsemigroups of the
hyperspace exp(G) of non-empty compact subsets of a topological group G endowed
with the Vietoris topology and the natural semigroup operation. On this base we
prove that a compact Clifford topological semigroup S is topologically
isomorphic to a subsemigroup of exp(G) for a suitable topological group G if
and only if S is a topological inverse semigroup with zero-dimensional
idempotent semilattice.
