Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
2025 conjugacy classes of subgroups; only the 495 normal subgroups are shown.
This group has 2025 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 |
|---|---|---|
| 1. C2×#543 | C2 | semidirect |
| 3. #2561 | C2 | semidirect |
| 4. #2472 | C2 | semidirect |
| 5. #2435 | C2 | semidirect |
| 6. #2308 | C2 | semidirect |
| 7. C2×#379 | C2 | semidirect |
| 8. #2273 | C2 | semidirect |
| 13. C2×#124 | C22 | semidirect |
| 14. C2×C22⋊Q8 | C22 | semidirect |
| 15. C2×C22⋊Q8 | C22 | semidirect |
| 22. C22×C22⋊C4 | C22 | semidirect |
| 23. #397 | C22 | semidirect |
| 24. #394 | C22 | semidirect |
| 25. #393 | C22 | semidirect |
| 26. #390 | C22 | semidirect |
| 27. #388 | C22 | semidirect |
| 28. #386 | C22 | semidirect |
| 29. #386 | C22 | semidirect |
| 30. #381 | C22 | semidirect |
| 32. #379 | C22 | semidirect |
| 33. #379 | C22 | semidirect |
| 34. C4×C22⋊C4 | C22 | semidirect |
| 35. C4×C22⋊C4 | C22 | semidirect |
| 43. C22×Q8 | C23 | semidirect |
| 58. C2×C4⋊C4 | C23 | semidirect |
| 59. C2×C4⋊C4 | C23 | semidirect |
| 73. C2×C22⋊C4 | C23 | semidirect |
| 74. C2×C42 | C23 | semidirect |
| 75. #95 | C23 | semidirect |
| 76. #95 | C23 | semidirect |
| 157. C23 | #124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#543 | 2 |
| C22×#120 | 2 |
| #2561 | 2 |
| #2472 | 2 |
| #2435 | 2 |
| #2308 | 2 |
| C2×#379 | 2 |
| #2273 | 2 |