Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
4982 conjugacy classes of subgroups.
The subgroup lattice has 405 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C23 | C26 |
| prime radical | C25 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #35627 | C2 | semidirect |
| 2. #35555 | C2 | semidirect |
| 3. #35543 | C2 | semidirect |
| 4. #35181 | C2 | semidirect |
| 5. #35159 | C2 | semidirect |
| 19. #2571 | C22 | semidirect |
| 20. #2571 | C22 | semidirect |
| 21. #2570 | C22 | semidirect |
| 22. #2570 | C22 | semidirect |
| 23. #2552 | C22 | semidirect |
| 24. #2552 | C22 | semidirect |
| 25. #2509 | C22 | semidirect |
| 26. #2508 | C22 | semidirect |
| 27. #2507 | C22 | semidirect |
| 28. #2506 | C22 | semidirect |
| 265. C22×C4 | #125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #35627 | 2 |
| #35555 | 2 |
| #35543 | 2 |
| #35181 | 2 |
| #35159 | 2 |
| #34994 | 2 |
| #34052 | 2 |
| C2×#2317 | 2 |
| C2×#2274 | 2 |