# Finite nilpotent groups

Let $$G$$ be a finite nilpotent nonabelian group. Is it true that for every natural number $$k$$ there exists a finite group $$G_k$$ such $$G_k$$ is not isomorphic to a subgroup of a direct power of $$G$$ while every $$k$$-generated subgroup of $$G_k$$ is isomorphic to such a subgroup.

I know that for abelian groups this is not possible.