Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
4413 conjugacy classes of subgroups.
The subgroup lattice has 1024 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, prime radical, cosocle | C23 | C26 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #59875 | 2 |
| #59766 | 2 |
| #59681 | 2 |
| #59447 | 2 |
| #59443 | 2 |
| #45344 | 2 |
| #43744 | 2 |
| #40024 | 2 |
| #39769 | 2 |
| #39241 | 2 |
| #39170 | 2 |
| #36600 | 2 |
| #36598 | 2 |
| #36593 | 2 |
| #36560 | 2 |
| #36313 | 2 |
| #36285 | 2 |
| #35870 | 2 |
| #34951 | 2 |
| #34328 | 2 |
| C4×#557 | 2 |