Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
854 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 854 conjugacy classes of subgroups — too many to draw. Only its 183 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 |
| prime radical | #2847 | C2 |
| 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. C24×C8 | C2 | semidirect |
| 2. C2×#465 | C2 | semidirect |
| 3. #2848 | C2 | semidirect |
| 5. #1893 | C2 | semidirect |
| 6. #1892 | C2 | semidirect |
| 7. #1807 | C2 | semidirect |
| 9. C22×SD16 | C22 | semidirect |
| 17. C2×#106 | C22 | semidirect |
| 18. C2×#103 | C22 | semidirect |
| 19. C2×#102 | C22 | semidirect |
| 25. #340 | C22 | semidirect |
| 39. C22×C8 | D4 | semidirect |
| 62. C24 | SD16 | semidirect |
| 131. C8 | #120 | semidirect |
| 140. C22 | #465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C8 | 2 |
| C2×#465 | 2 |
| #2848 | 2 |
| #2847 | 2 |
| #1893 | 2 |
| #1892 | 2 |
| #1807 | 2 |