Superlocals in Symmetric and Alternating Groups

On Aschbacher's definition, a subgroup $N$ of a finite group $G$ is called a $p$-superlocal for a prime $p$ if $N=N_G(O_p(N))$. We describe the $p$-superlocals in symmetric and alternating groups, thereby resolving part way Problem 11.3 in the Kourovka Notebook [3].