Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
471 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 471 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 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#469 | C2 | semidirect |
| 2. #3006 | C2 | semidirect |
| 3. #2879 | C2 | semidirect |
| 4. #2079 | C2 | semidirect |
| 5. #2051 | C2 | semidirect |
| 6. #2018 | C2 | semidirect |
| 7. #1900 | C2 | semidirect |
| 8. #1811 | C2 | semidirect |
| 11. C22×D8 | C22 | semidirect |
| 20. C2×#108 | C22 | semidirect |
| 21. C2×#106 | C22 | semidirect |
| 23. C2×#102 | C22 | semidirect |
| 24. C2×#100 | C22 | semidirect |
| 30. #343 | C22 | semidirect |
| 31. #341 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#469 | 2 |
| #3006 | 2 |
| #2879 | 2 |
| #2079 | 2 |
| #2051 | 2 |
| #2018 | 2 |
| #1900 | 2 |
| #1811 | 2 |