Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
811 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 811 conjugacy classes of subgroups — too many to draw. Only its 255 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| socle | C23 | C22×D4 |
| prime radical | C22×#135 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#427 | C2 | semidirect |
| 3. C2×#416 | C2 | semidirect |
| 4. C22×C4×C8 | C2 | semidirect |
| 5. #2297 | C2 | semidirect |
| 6. #1970 | C2 | semidirect |
| 7. #1969 | C2 | semidirect |
| 8. #1968 | C2 | semidirect |
| 12. C2×#135 | C4 | semidirect |
| 48. C2×Q16 | C2×C4 | semidirect |
| 51. C2×SD16 | C2×C4 | semidirect |
| 54. C2×D8 | C2×C4 | semidirect |
| 124. C2×C8 | C22⋊C4 | semidirect |
| 174. C2×C4 | #135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#135 | 2 |
| C2×#427 | 2 |
| C2×#416 | 2 |
| C22×C4×C8 | 2 |
| #2297 | 2 |
| #1970 | 2 |
| #1969 | 2 |
| #1968 | 2 |