Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
2071 conjugacy classes of subgroups; only the 495 normal subgroups are shown.
This group has 2071 conjugacy classes of subgroups — too many to draw. Only its 495 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 |
| prime radical | C22×#120 | C2 |
| 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 |
|---|---|---|
| 2. C2×#518 | C2 | semidirect |
| 3. #2482 | C2 | semidirect |
| 4. #2418 | C2 | semidirect |
| 5. #2405 | C2 | semidirect |
| 6. #2315 | C2 | semidirect |
| 7. #2308 | C2 | semidirect |
| 8. C2×#379 | C2 | semidirect |
| 12. C2×#123 | C22 | semidirect |
| 16. C2×C4×D4 | C22 | semidirect |
| 17. C2×#117 | C22 | semidirect |
| 22. C22×C22⋊C4 | C22 | semidirect |
| 23. C22×C22⋊C4 | C22 | semidirect |
| 24. #399 | C22 | semidirect |
| 25. #397 | C22 | semidirect |
| 26. #394 | C22 | semidirect |
| 27. #388 | C22 | semidirect |
| 28. #386 | C22 | semidirect |
| 29. #386 | C22 | semidirect |
| 30. #385 | C22 | semidirect |
| 31. #385 | C22 | semidirect |
| 32. #381 | C22 | semidirect |
| 33. #380 | C22 | semidirect |
| 35. #379 | C22 | semidirect |
| 36. #379 | C22 | semidirect |
| 54. C23×C4 | C23 | semidirect |
| 59. C2×C4⋊C4 | C23 | semidirect |
| 60. C2×C4⋊C4 | C23 | semidirect |
| 75. C2×C22⋊C4 | C23 | semidirect |
| 76. C2×C22⋊C4 | C23 | semidirect |
| 77. C2×C42 | C23 | semidirect |
| 78. #95 | C23 | semidirect |
| 79. #95 | C23 | semidirect |
| 160. C23 | #123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#120 | 2 |
| C2×#518 | 2 |
| #2482 | 2 |
| #2418 | 2 |
| #2405 | 2 |
| #2315 | 2 |
| #2308 | 2 |
| C2×#379 | 2 |