Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
929 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 929 conjugacy classes of subgroups — too many to draw. Only its 403 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 | C23×D4 | C22 |
| 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. #2840 | C2 | semidirect |
| 2. #2764 | C2 | semidirect |
| 3. #2687 | C2 | semidirect |
| 4. #2572 | C2 | semidirect |
| 5. #2561 | C2 | semidirect |
| 6. #2483 | C2 | semidirect |
| 8. #2312 | C2 | semidirect |
| 12. C2×C22⋊Q8 | C22 | semidirect |
| 15. #400 | C22 | semidirect |
| 16. #398 | C22 | semidirect |
| 18. #397 | C22 | semidirect |
| 21. #393 | C22 | semidirect |
| 22. #393 | C22 | semidirect |
| 23. #391 | C22 | semidirect |
| 25. #388 | C22 | semidirect |
| 26. #388 | C22 | semidirect |
| 30. #385 | C22 | semidirect |
| 31. #383 | C22 | semidirect |
| 33. #381 | C22 | semidirect |
| 34. #381 | C22 | semidirect |
| 35. #380 | C22 | semidirect |
| 40. C4×C22⋊C4 | C22 | semidirect |
| 41. C4×C22⋊C4 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2840 | 2 |
| #2764 | 2 |
| #2687 | 2 |
| #2572 | 2 |
| #2561 | 2 |
| #2483 | 2 |
| #2405 | 2 |
| #2312 | 2 |
| #2308 | 2 |