Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1170 conjugacy classes of subgroups; only the 429 normal subgroups are shown.
This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 429 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C24 |
| commutator, Frattini, socle, cosocle | C23 | C25 |
| prime radical | #2679 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2804 | C2 | semidirect |
| 2. #2782 | C2 | semidirect |
| 3. #2684 | C2 | semidirect |
| 5. #2398 | C2 | semidirect |
| 6. C4×#124 | C2 | semidirect |
| 7. C4×#120 | C2 | semidirect |
| 8. C24×C4 | C22 | semidirect |
| 11. C2×C4×Q8 | C22 | semidirect |
| 14. #400 | C22 | semidirect |
| 15. #400 | C22 | semidirect |
| 16. #397 | C22 | semidirect |
| 19. #393 | C22 | semidirect |
| 20. #391 | C22 | semidirect |
| 22. #388 | C22 | semidirect |
| 25. #385 | C22 | semidirect |
| 26. #385 | C22 | semidirect |
| 27. #382 | C22 | semidirect |
| 28. #379 | C22 | semidirect |
| 29. C4×C22⋊C4 | C22 | semidirect |
| 30. C4×C22⋊C4 | C22 | semidirect |
| 31. #376 | C22 | semidirect |
| 32. C43 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2804 | 2 |
| #2782 | 2 |
| #2684 | 2 |
| #2679 | 2 |
| #2398 | 2 |
| C4×#124 | 2 |
| C4×#120 | 2 |