Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
348 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 109 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 ◁ C4×D4 ◁ C8×D4 ◁ 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. #3287 | C2 | semidirect |
| 3. #2246 | C2 | semidirect |
| 4. #2215 | C2 | semidirect |
| 5. #2207 | C2 | semidirect |
| 6. #2186 | C2 | semidirect |
| 7. C4×Q32 | C2 | semidirect |
| 8. D4×C16 | C2 | semidirect |
| 44. Q32 | D4 | semidirect |
| 125. C4 | #508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#508 | 2 |
| #3287 | 2 |
| #2246 | 2 |
| #2215 | 2 |
| #2207 | 2 |
| #2186 | 2 |
| C4×Q32 | 2 |
| D4×C16 | 2 |