Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
2591 conjugacy classes of subgroups; only the 1039 normal subgroups are shown.
This group has 2591 conjugacy classes of subgroups — too many to draw. Only its 1039 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 | C24 |
| commutator | C22 | C24×C4 |
| Frattini, cosocle | C23 | C25 |
| prime radical | C26 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #2315 | C2 | direct (N × H) |
| 4. C2×#385 | C2 | semidirect |
| 5. C2×#380 | C2 | semidirect |
| 9. C22×C4⋊C4 | C22 | semidirect |
| 11. C22×C22⋊C4 | C4 | semidirect |
| 17. #385 | C22 | semidirect |
| 18. #380 | C22 | semidirect |
| 19. C2×#95 | C22 | semidirect |
| 30. C23×C4 | C2×C4 | semidirect |
| 36. C2×C4⋊C4 | C23 | semidirect |
| 40. C2×C22⋊C4 | C2×C4 | semidirect |
| 41. C2×C22⋊C4 | C2×C4 | semidirect |
| 45. #95 | C23 | semidirect |
| 52. C24 | C4⋊C4 | semidirect |
| 74. C22×C4 | C22×C4 | semidirect |
| 80. C22⋊C4 | C22×C4 | semidirect |
| 95. C23 | C2×C4⋊C4 | semidirect |
| 138. C2 | #2315 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊C4 | 2 |
| #2315 | 2 |
| C2×#385 | 2 |
| C2×#380 | 2 |