Superfluous subgroups or small subgroup

Question

The basic characterization of superfluous subgroups of an abelian group is the following one.

Let $A≤G$. Then $A\ll G$ if and only if $A\subseteq \operatorname{Rad}(G)$ and $A$ has no divisible quotient groups.

Now my question: Is there characterization of superfluous subgroups for non-abelian group?