Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
293 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 293 conjugacy classes of subgroups — too many to draw. Only its 61 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #405 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#509 | C2 | semidirect |
| 2. C22×D16 | C2 | semidirect |
| 3. #3155 | C2 | semidirect |
| 4. C2×#361 | C2 | semidirect |
| 5. C2×#359 | C2 | semidirect |
| 6. #1978 | C2 | semidirect |
| 7. #1379 | C2 | semidirect |
| 56. C2×D8 | D4 | semidirect |
| 69. M32 | D4 | semidirect |
| 73. C2×C16 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#509 | 2 |
| C22×D16 | 2 |
| #3155 | 2 |
| C2×#361 | 2 |
| C2×#359 | 2 |
| #1978 | 2 |
| #1379 | 2 |