Suppose $G$ is a finite group. The socle over solvable radical of $G$, denoted $\operatorname{Soc}^*(G)$, is defined as the unique subgroup $H$ of $G$ such that $H$ contains the solvable radical $\operatorname{Rad}(G)$ of $G$ and the quotient group $H/\operatorname{Rad}(G)$ is the socle of the quotient group $G/\operatorname{Rad}(G)$.
If $H$ is the socle over solvable radical of $G$, then $\operatorname{Rad}(H) = \operatorname{Rad}(G)$ and $H/\operatorname{Rad}(H)$ is a direct product of simple non-abelian groups.