Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
2149 conjugacy classes of subgroups; only the 575 normal subgroups are shown.
This group has 2149 conjugacy classes of subgroups — too many to draw. Only its 575 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 | C25 |
| 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. C2×#534 | C2 | semidirect |
| 2. C22×#121 | C2 | semidirect |
| 3. #2856 | C2 | semidirect |
| 4. #2656 | C2 | semidirect |
| 5. #2539 | C2 | semidirect |
| 6. #2501 | C2 | semidirect |
| 7. #2433 | C2 | semidirect |
| 8. C2×C4×C22⋊C4 | C2 | semidirect |
| 10. C23×D4 | C22 | semidirect |
| 13. C2×#127 | C22 | semidirect |
| 14. C2×#123 | C22 | semidirect |
| 18. C2×#121 | C22 | semidirect |
| 19. C2×#121 | C22 | semidirect |
| 20. C2×#121 | C22 | semidirect |
| 21. C2×#120 | C22 | semidirect |
| 22. C22×C4⋊C4 | C22 | semidirect |
| 24. C22×C22⋊C4 | C22 | semidirect |
| 25. C22×C42 | C22 | semidirect |
| 26. #399 | C22 | semidirect |
| 27. #392 | C22 | semidirect |
| 28. #390 | C22 | semidirect |
| 29. #390 | C22 | semidirect |
| 30. #384 | C22 | semidirect |
| 31. C4×C22⋊C4 | C22 | semidirect |
| 32. C4×C22⋊C4 | C22 | semidirect |
| 33. C2×#95 | C22 | semidirect |
| 46. C23×C4 | D4 | semidirect |
| 66. C2×C22⋊C4 | D4 | semidirect |
| 112. C22×C4 | C2×D4 | semidirect |
| 124. C22⋊C4 | C2×D4 | semidirect |
| 142. C23 | #127 | semidirect |
| 192. C4 | #534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#534 | 2 |
| C22×#121 | 2 |
| #2856 | 2 |
| #2656 | 2 |
| #2539 | 2 |
| #2501 | 2 |
| #2433 | 2 |
| C2×C4×C22⋊C4 | 2 |