Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
343 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 343 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
| prime radical | C2×#493 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ C2×C4×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. #3170 | C2 | semidirect |
| 3. #2248 | C2 | semidirect |
| 4. #2240 | C2 | semidirect |
| 5. #2207 | C2 | semidirect |
| 6. #2187 | C2 | semidirect |
| 7. #2162 | C2 | semidirect |
| 12. C2×SD32 | C22 | semidirect |
| 13. #500 | C22 | semidirect |
| 14. #494 | C22 | semidirect |
| 23. C4×Q16 | C22 | semidirect |
| 25. C4⋊C16 | C22 | semidirect |
| 26. #357 | C22 | semidirect |
| 28. C4×C16 | C22 | semidirect |
| 126. C2×C4 | SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3170 | 2 |
| C2×#493 | 2 |
| #2248 | 2 |
| #2240 | 2 |
| #2207 | 2 |
| #2187 | 2 |
| #2162 | 2 |