Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
917 conjugacy classes of subgroups; only the 343 normal subgroups are shown.
This group has 917 conjugacy classes of subgroups — too many to draw. Only its 343 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 | C22×C22⋊C4 |
| commutator | C22 | C22×C42 |
| Frattini, cosocle | C24 | C24 |
| prime radical | C23×D4 | C22 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C22⋊C4 ◁ G | |
| LECS | G ▷ C24 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #2273 | C2 | semidirect |
| 4. C4×#99 | C2 | semidirect |
| 5. C2×#342 | C2 | semidirect |
| 8. C2×C4×D4 | C4 | semidirect |
| 10. C2×#117 | C4 | semidirect |
| 11. C22×C22⋊C4 | C4 | semidirect |
| 15. C2×#99 | C4 | semidirect |
| 18. C4×C22⋊C4 | C22 | semidirect |
| 19. #342 | C22 | semidirect |
| 30. C23×C4 | C2×C4 | semidirect |
| 35. C2×C4⋊C4 | C2×C4 | semidirect |
| 43. C2×C22⋊C4 | C2×C4 | semidirect |
| 44. C2×C22⋊C4 | C2×C4 | semidirect |
| 49. C2×C42 | C2×C4 | semidirect |
| 50. #99 | C2×C4 | semidirect |
| 56. C24 | C42 | semidirect |
| 70. C2×D4 | C42 | semidirect |
| 82. C22×C4 | C42 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#518 | 2 |
| C22×#99 | 2 |
| #2273 | 2 |
| C4×#99 | 2 |
| C2×#342 | 2 |