Normal closure of finite subgroups of $\mathrm{A}\mathrm{u}\mathrm{t}(F_n)$ and $\mathrm{O}\mathrm{u}\mathrm{t}(F_n)$

For $n\ge 3$, let $G$ be a nontrivial finite subgroup of $\mathrm{A}\mathrm{u}\mathrm{t}(F_n)$ with $\mathrm{\mid }G\mathrm{\mid }$ not a power of $2$. We prove that the normal closure $N(G)$ is $\mathrm{S}\mathrm{A}\mathrm{u}\mathrm{t}(F_n)$ if $G\subset \mathrm{S}\mathrm{A}\mathrm{u}\mathrm{t}(F_n)$ and $N(G)$ is $\mathrm{A}\mathrm{u}\mathrm{t}(F_n)$ otherwise. When $\mathrm{\mid }G\mathrm{\mid }$ is a power of $2$, we have a partial theorem. Similarly, let $G^{\mathrm{\prime }}$ be a nontrivial finite subgroup of $\mathrm{O}\mathrm{u}\mathrm{t}(F_n)$ with $\mathrm{\mid }{G}^{\mathrm{\prime }}\mathrm{\mid }$ not a power of $2$. Then the normal closure $N(G^{\mathrm{\prime }})$ is $\mathrm{S}\mathrm{O}\mathrm{u}\mathrm{t}(F_n)$ if $G^{\mathrm{\prime }}\subset \mathrm{S}\mathrm{O}\mathrm{u}\mathrm{t}(F_n)$ and $N(G^{\mathrm{\prime }})$ is $\mathrm{O}\mathrm{u}\mathrm{t}(F_n)$ otherwise. When $\mathrm{\mid }{G}^{\mathrm{\prime }}\mathrm{\mid }$ is a power of $2$, we have a partial theorem as well.