Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
341 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 159 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 | C8 | C23×C4 |
| Frattini, cosocle | C2×C8 | C24 |
| socle | C22 | C22×D8 |
| prime radical | C2×#508 | C2 |
| LCS | G ▷ 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 |
|---|---|---|
| 2. C4×#135 | C2 | semidirect |
| 3. #2177 | C2 | semidirect |
| 4. #2176 | C2 | semidirect |
| 5. #2175 | C2 | semidirect |
| 6. #2158 | C2 | semidirect |
| 7. #2138 | C2 | semidirect |
| 8. C2×#346 | C2 | semidirect |
| 11. #508 | C4 | semidirect |
| 31. #135 | C2×C4 | semidirect |
| 44. Q32 | C2×C4 | semidirect |
| 45. SD32 | C2×C4 | semidirect |
| 46. D16 | C2×C4 | semidirect |
| 48. C2×C16 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#508 | 2 |
| C4×#135 | 2 |
| #2177 | 2 |
| #2176 | 2 |
| #2175 | 2 |
| #2158 | 2 |
| #2138 | 2 |
| C2×#346 | 2 |