Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
923 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 923 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. #2737 | C2 | semidirect |
| 3. #2736 | C2 | semidirect |
| 4. #2599 | C2 | semidirect |
| 5. #2483 | C2 | semidirect |
| 6. #2458 | C2 | semidirect |
| 8. #2312 | C2 | semidirect |
| 12. C2×C4×Q8 | C22 | semidirect |
| 15. #398 | C22 | semidirect |
| 17. #397 | C22 | semidirect |
| 18. #395 | C22 | semidirect |
| 21. #393 | C22 | semidirect |
| 22. #393 | C22 | semidirect |
| 25. #388 | C22 | semidirect |
| 26. #388 | C22 | semidirect |
| 27. #388 | C22 | semidirect |
| 28. #387 | C22 | semidirect |
| 29. #387 | C22 | semidirect |
| 32. #385 | C22 | semidirect |
| 33. #383 | C22 | semidirect |
| 34. #381 | C22 | semidirect |
| 35. #380 | 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 |
| #2737 | 2 |
| #2736 | 2 |
| #2599 | 2 |
| #2483 | 2 |
| #2458 | 2 |
| #2405 | 2 |
| #2312 | 2 |
| #2309 | 2 |