Is a periodic group of automorphisms of an artinian locally nilpotent group (group satisfying min condition on subgroups) artinian?

Question

Let $G$ be a locally nilpotent group satisfying the minimal condition on subgroups (Min), and let $H$ be a subgroup of $Aut(G)$ which is periodic. Do you know if one can say that $H$ satisfies Min itself?
Thank you for reading and answering, pg