Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
254 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 103 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 | #2218 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #405 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3175 | C2 | semidirect |
| 2. #2254 | C2 | semidirect |
| 3. #2249 | C2 | semidirect |
| 4. #2243 | C2 | semidirect |
| 5. #2219 | C2 | semidirect |
| 7. #2217 | C2 | semidirect |
| 8. #2177 | C2 | semidirect |
| 9. #2176 | C2 | semidirect |
| 10. C4×SD32 | C2 | semidirect |
| 11. #2108 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3175 | 2 |
| #2254 | 2 |
| #2249 | 2 |
| #2243 | 2 |
| #2219 | 2 |
| #2218 | 2 |
| #2217 | 2 |
| #2177 | 2 |
| #2176 | 2 |
| C4×SD32 | 2 |
| #2108 | 2 |