Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1005 conjugacy classes of subgroups; only the 447 normal subgroups are shown.
This group has 1005 conjugacy classes of subgroups — too many to draw. Only its 447 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C2×#117 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#540 | C2 | semidirect |
| 2. #3259 | C2 | direct (N × H) |
| 3. C2×#478 | C2 | semidirect |
| 4. C2×#469 | C2 | semidirect |
| 5. C2×#466 | C2 | semidirect |
| 6. C2×#459 | C2 | semidirect |
| 7. C2×#424 | C2 | semidirect |
| 13. #540 | C22 | semidirect |
| 21. #478 | C22 | semidirect |
| 22. #469 | C22 | semidirect |
| 23. #466 | C22 | semidirect |
| 24. #459 | C22 | semidirect |
| 27. #424 | C22 | semidirect |
| 154. C2 | #3259 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#540 | 2 |
| #3259 | 2 |
| C2×#478 | 2 |
| C2×#469 | 2 |
| C2×#466 | 2 |
| C2×#459 | 2 |
| C2×#424 | 2 |