Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
4388 conjugacy classes of subgroups; only the 2854 normal subgroups are shown.
This group has 4388 conjugacy classes of subgroups — too many to draw. Only its 2854 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C23 | C26 |
| prime radical | C26 | C23 |
| 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. #48950 | C2 | semidirect |
| 2. #36057 | C2 | semidirect |
| 4. #2790 | C22 | semidirect |
| 5. #2787 | C22 | semidirect |
| 6. #2770 | C22 | semidirect |
| 7. #2722 | C22 | semidirect |
| 8. #2652 | C22 | semidirect |
| 9. #2587 | C22 | semidirect |
| 10. #2577 | C22 | semidirect |
| 11. #2530 | C22 | semidirect |
| 12. #2496 | C22 | semidirect |
| 17. #2401 | C22 | semidirect |
| 18. #2383 | C22 | semidirect |
| 19. #2373 | C22 | semidirect |
| 28. #401 | C23 | semidirect |
| 29. #401 | C23 | semidirect |
| 30. #400 | C23 | semidirect |
| 31. #400 | C23 | semidirect |
| 32. #398 | C23 | semidirect |
| 33. #398 | C23 | semidirect |
| 40. #389 | C23 | semidirect |
| 41. #389 | C23 | semidirect |
| 46. #387 | C23 | semidirect |
| 47. #387 | C23 | semidirect |
| 48. #387 | C23 | semidirect |
| 49. #387 | C23 | semidirect |
| 54. #384 | C23 | semidirect |
| 55. #383 | C23 | semidirect |
| 60. C4×C4⋊C4 | C23 | semidirect |
| 63. #376 | C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #48950 | 2 |
| #36057 | 2 |
| #35369 | 2 |