Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
559 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 559 conjugacy classes of subgroups — too many to draw. Only its 199 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 | C2×#121 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| prime radical | C23×D4 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2911 | C2 | semidirect |
| 5. #2873 | C2 | semidirect |
| 6. #1931 | C2 | semidirect |
| 7. #1742 | C2 | semidirect |
| 8. #1738 | C2 | semidirect |
| 17. #428 | C22 | semidirect |
| 25. C2×#100 | C4 | semidirect |
| 28. #405 | C22 | semidirect |
| 30. #343 | C22 | semidirect |
| 31. #341 | C22 | semidirect |
| 82. #100 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2911 | 2 |
| C2×#418 | 2 |
| C22×#100 | 2 |
| #2873 | 2 |
| #1931 | 2 |
| #1742 | 2 |
| #1738 | 2 |