Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1007 conjugacy classes of subgroups; only the 479 normal subgroups are shown.
This group has 1007 conjugacy classes of subgroups — too many to draw. Only its 479 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25 |
| prime radical | C22×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ 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. #3458 | C2 | semidirect |
| 3. #3140 | C2 | semidirect |
| 4. #3139 | C2 | semidirect |
| 5. #3137 | C2 | semidirect |
| 7. C2×#419 | C2 | semidirect |
| 8. #2873 | C2 | semidirect |
| 13. #544 | C22 | semidirect |
| 25. #491 | C22 | semidirect |
| 26. #489 | C22 | semidirect |
| 27. #488 | C22 | semidirect |
| 28. #487 | C22 | semidirect |
| 31. #419 | C22 | semidirect |
| 35. C2×#103 | C22 | semidirect |
| 36. #405 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3458 | 2 |
| C2×#536 | 2 |
| #3140 | 2 |
| #3139 | 2 |
| #3137 | 2 |
| #2896 | 2 |
| C2×#419 | 2 |
| #2873 | 2 |