Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
829 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 829 conjugacy classes of subgroups — too many to draw. Only its 163 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×M16 | C2 | semidirect |
| 2. C2×#469 | C2 | semidirect |
| 3. C2×#466 | C2 | semidirect |
| 4. #2847 | C2 | semidirect |
| 5. #1895 | C2 | semidirect |
| 6. #1893 | C2 | semidirect |
| 7. #1809 | C2 | semidirect |
| 8. #1807 | C2 | semidirect |
| 10. C22×D8 | C22 | semidirect |
| 22. C2×#107 | C22 | semidirect |
| 23. C2×#106 | C22 | semidirect |
| 24. C2×#102 | C22 | semidirect |
| 25. C2×#102 | C22 | semidirect |
| 30. #340 | C22 | semidirect |
| 31. #340 | C22 | semidirect |
| 52. C2×M16 | D4 | semidirect |
| 56. C22×C8 | D4 | semidirect |
| 187. C8 | #120 | semidirect |
| 202. C22 | #469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×M16 | 2 |
| C2×#469 | 2 |
| C2×#466 | 2 |
| #2847 | 2 |
| #1895 | 2 |
| #1893 | 2 |
| #1809 | 2 |
| #1807 | 2 |