Let \(G\) be a semisimple Lie group with finite center and \(S\subseteq G\) a subsemigroup with non-empty interior. The authors show that if \(S\) is generated by one-parameter semigroups, then there exists a compact subgroup of \(G\) whose homotopy groups are precisely the homotopy groups of \(S\). This generalizes the well-known fact that the homotopy type of a semisimple Lie group with finite center is completely determined by its maximal compact subgroups. The semigroup case, however, is much more delicate since in general no analog of the Iwasawa or Cartan decomposition is available. The proofs are based on San Martin's theory of invariant control sets and the techniques provide further interesting results. So for instance the authors show that all orbits of the interior of \(S\) in the Riemannian symmetric space associated with \(G\) are contractible.