Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
635 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 635 conjugacy classes of subgroups — too many to draw. Only its 207 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24 |
| prime radical | C25 | D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#106 | C2 | semidirect |
| 5. #2077 | C2 | direct (N × H) |
| 6. C2×#340 | C2 | semidirect |
| 7. C2×#340 | C2 | semidirect |
| 8. C2×#340 | C2 | semidirect |
| 19. C2×#106 | C22 | semidirect |
| 28. #340 | C22 | semidirect |
| 29. #340 | C22 | semidirect |
| 30. #340 | C22 | semidirect |
| 245. C2 | #2077 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#106 | 2 |
| C22×C22⋊C8 | 2 |
| C2×#380 | 2 |
| #2077 | 2 |
| C2×#340 | 2 |