Rigid points of $\mathrm{Co}_0$

Question

Let the rigid points of a matrix group refer to subgroups of it that stabilize a nonzero vector and are maximal among such subgroups.

How many conjugacy classes of rigid points are there under the automorphism group $\mathrm{Co}_0$ of the Leech lattice, and what are they?

I am already aware of the following classes:

• $\mathrm{Co}_2$
• $\mathrm{Co}_3$
• $\mathrm{M}_{24}$
• $2^{11}:\mathrm{M}_{23}$
• $\mathrm{P}\Gamma\mathrm{U}_6(2)$
• $3^6:(2\times\mathrm{M}_{11})$