I'm trying to classify compact manifolds $M^{16}$ with a metric which is locally conformal to a (local) metric with holonomy (included in) Spin(9)$\subset$SO(16). To do this, I would need a complete list of finite subgroups of Spin(9) acting freely on $S^{15}$.
Any hint on finite subgroups of Spin(9) (even not acting freely) would be very helpful!



Finite subgroups of Spin(9)
Although there exists an algorithm which will list all finite subgroups of $Spin(9)$ I suspect it is not effective. For background and references see


[The finite subgroups of SU(n)](https://mathoverflow.net/questions/17072)


I don't know if imposing the condition that the group acts freely on $S^{15}$ improves the situation. 


