Let $\Gamma$ be a finite subgroup of $\mathrm{SO}(4)$ acting freely on $\mathbb{S}^3$. It is known that all such $\Gamma$ can be classified.

Is there any characterization of $\Gamma$ such that $\Gamma$ is conjugate in $\mathrm{O}(4)$ to a subgroup of $\mathrm{U}(2)$?