Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
298 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 105 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 ◁ C2×C42 ◁ C2×C4×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. #3169 | C2 | semidirect |
| 2. C4×#135 | C2 | semidirect |
| 3. #2234 | C2 | semidirect |
| 4. #2227 | C2 | semidirect |
| 5. #2226 | C2 | semidirect |
| 6. #2207 | C2 | semidirect |
| 7. #2206 | C2 | semidirect |
| 8. #2186 | C2 | semidirect |
| 9. C4×SD32 | C2 | semidirect |
| 10. C4×D16 | C2 | semidirect |
| 11. #2162 | C2 | semidirect |
| 109. Q16 | #41 | semidirect |
| 115. D8 | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3169 | 2 |
| C4×#135 | 2 |
| #2234 | 2 |
| #2227 | 2 |
| #2226 | 2 |
| #2207 | 2 |
| #2206 | 2 |
| #2186 | 2 |
| C4×SD32 | 2 |
| C4×D16 | 2 |
| #2162 | 2 |