  Let $\Out(F_n)$ denote the outer automorphism group of the free group $F_n$
with $n>3$. We prove that for any finite index subgroup $\Gamma<\Out(F_n)$, the
group $\Aut(\Gamma)$ is isomorphic to the normalizer of $\Gamma$ in
$\Out(F_n)$. We prove that $\Gamma$ is {\em co-Hopfian} : every injective
homomorphism $\Gamma\to \Gamma$ is surjective. Finally, we prove that the
abstract commensurator $\Comm(\Out(F_n))$ is isomorphic to $\Out(F_n)$.
