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We study algebraic and topological properties of subsemigroups of thehyperspace exp(G) of non-empty compact subsets of a topological group G endowedwith the Vietoris topology and the natural semigroup operation. On this base weprove that a compact Clifford topological semigroup S is topologicallyisomorphic to a subsemigroup of exp(G) for a suitable topological group G ifand only if S is a topological inverse semigroup with zero-dimensionalidempotent semilattice.

Embedding topological semigroups into the hyperspaces over topological groups