Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
4417 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 |
|---|---|
| #59963 | 2 |
| #59828 | 2 |
| #59766 | 2 |
| #59467 | 2 |
| #59443 | 2 |
| #45154 | 2 |
| #44672 | 2 |
| #40215 | 2 |
| #40082 | 2 |
| #39762 | 2 |
| #39170 | 2 |
| #36598 | 2 |
| #36560 | 2 |
| #36313 | 2 |
| #36285 | 2 |
| #35870 | 2 |
| #34951 | 2 |
| #34337 | 2 |
| #34328 | 2 |
| C4×#557 | 2 |