Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
4399 conjugacy classes of subgroups; only the 903 normal subgroups are shown.
This group has 4399 conjugacy classes of subgroups — too many to draw. Only its 903 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C25 | C23 |
| commutator, Frattini, cosocle | C23 | C25 |
| prime radical | C24×D4 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C25 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×C4⋊C4 | C2 | semidirect |
| 3. C23×C22⋊C4 | C2 | semidirect |
| 4. C23×C22⋊C4 | C2 | semidirect |
| 5. C2×#394 | C2 | direct (N × H) |
| 6. C22×#95 | C2 | semidirect |
| 16. C22×C4⋊C4 | C22 | semidirect |
| 19. C22×C22⋊C4 | C22 | semidirect |
| 20. C22×C22⋊C4 | C22 | semidirect |
| 21. #394 | C22 | direct (N × H) |
| 22. C2×#95 | C22 | semidirect |
| 45. C23×C4 | D4 | semidirect |
| 51. C2×C4⋊C4 | C23 | semidirect |
| 54. C2×C22⋊C4 | C23 | semidirect |
| 55. C2×C22⋊C4 | C23 | semidirect |
| 56. #95 | C23 | semidirect |
| 94. C22×C4 | C2×D4 | semidirect |
| 142. C2×C4 | C22×D4 | semidirect |
| 151. C22 | #394 | direct (N × H) |
| 167. C2 | C2×#394 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D4 | 2 |
| C23×C4⋊C4 | 2 |
| C23×C22⋊C4 | 2 |
| C2×#394 | 2 |
| C22×#95 | 2 |