Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
3277 conjugacy classes of subgroups; only the 2847 normal subgroups are shown.
This group has 3277 conjugacy classes of subgroups — too many to draw. Only its 2847 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 | C24 |
| commutator, Frattini, cosocle | C22 | C26 |
| socle | C23 | C25 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3531 | C2 | direct (N × H) |
| 2. C2×#564 | C2 | semidirect |
| 3. C2×#563 | C2 | semidirect |
| 4. C2×#562 | C2 | semidirect |
| 5. C2×#533 | C2 | semidirect |
| 6. C2×#529 | C2 | semidirect |
| 7. #564 | C22 | semidirect |
| 8. #563 | C22 | semidirect |
| 9. #562 | C22 | semidirect |
| 10. #533 | C22 | semidirect |
| 12. #529 | C22 | semidirect |
| 104. C2 | #3531 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3531 | 2 |
| C2×#564 | 2 |
| C2×#563 | 2 |
| C2×#562 | 2 |
| C2×#533 | 2 |
| C2×#529 | 2 |