  We prove that if $X$ is a rationally connected threefold and $G$ is a
$p$-subgroup in the group of birational selfmaps of $X$, then $G$ is an abelian
group generated by at most $3$ elements provided that $p\ge 17$. We also prove
a similar result for $p\ge 11$ under an assumption that $G$ acts on a
(Gorenstein) $G$-Fano threefold, and show that the same holds for $p\ge 5$
under an assumption that $G$ acts on a $G$-Mori fiber space.
