Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
347 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 347 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#466 | C2 | semidirect |
| 2. #2232 | C2 | semidirect |
| 3. #2215 | C2 | semidirect |
| 4. #2184 | C2 | semidirect |
| 5. C2×C22⋊C16 | C2 | semidirect |
| 6. C22×D8 | C22 | semidirect |
| 9. C2×D16 | C22 | semidirect |
| 10. C22×C16 | C22 | semidirect |
| 14. #466 | C22 | semidirect |
| 15. C2×#107 | C22 | semidirect |
| 17. #366 | C22 | semidirect |
| 18. #357 | C22 | semidirect |
| 19. C22⋊C16 | C22 | semidirect |
| 80. C23 | D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#466 | 2 |
| #2232 | 2 |
| #2215 | 2 |
| #2184 | 2 |
| C2×C22⋊C16 | 2 |