  Let $G$ denote the projective special linear group $\text{PSL}(2,q)$, for a
prime power $q$. It is shown that a finite 2-subgroup of the group
$V(\mathbb{Z}G)$ of augmentation 1 units in the integral group ring
$\mathbb{Z}G$ of $G$ is isomorphic to a subgroup of $G$. Furthermore, it is
shown that a composition factor of a finite subgroup of $V(\mathbb{Z}G)$ is
isomorphic to a subgroup of $G$.
