Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
355 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 355 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24 |
| socle | C22 | C22×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ 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×#508 | C2 | semidirect |
| 2. C23×C16 | C2 | semidirect |
| 3. #3050 | C2 | semidirect |
| 4. #2217 | C2 | semidirect |
| 5. #2216 | C2 | semidirect |
| 6. #2215 | C2 | semidirect |
| 7. #2158 | C2 | semidirect |
| 8. #2138 | C2 | semidirect |
| 13. C2×Q32 | C22 | semidirect |
| 14. C2×SD32 | C22 | semidirect |
| 15. C2×D16 | C22 | semidirect |
| 26. #367 | C22 | semidirect |
| 27. #366 | C22 | semidirect |
| 28. #358 | C22 | semidirect |
| 29. #357 | C22 | semidirect |
| 55. C2×C16 | D4 | semidirect |
| 134. C22 | #508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#508 | 2 |
| C23×C16 | 2 |
| #3050 | 2 |
| #2217 | 2 |
| #2216 | 2 |
| #2215 | 2 |
| #2158 | 2 |
| #2138 | 2 |