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!