Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
6823 conjugacy classes of subgroups; only the 983 normal subgroups are shown.
This group has 6823 conjugacy classes of subgroups — too many to draw. Only its 983 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 |
| 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 |
|---|---|---|
| 1. C24×D4 | C2 | semidirect |
| 2. C23×C22⋊C4 | C2 | semidirect |
| 3. C2×#392 | C2 | direct (N × H) |
| 4. C22×#95 | C2 | semidirect |
| 8. C23×D4 | C22 | semidirect |
| 12. C22×C22⋊C4 | C22 | semidirect |
| 13. #392 | C22 | direct (N × H) |
| 14. C2×#95 | C22 | semidirect |
| 19. C25 | D4 | semidirect |
| 25. C22×D4 | C23 | semidirect |
| 28. C23×C4 | D4 | semidirect |
| 32. C2×C22⋊C4 | C23 | semidirect |
| 33. #95 | C23 | semidirect |
| 45. C24 | C2×D4 | semidirect |
| 56. C22×C4 | C2×D4 | semidirect |
| 75. C23 | C22×D4 | semidirect |
| 83. C2×C4 | C22×D4 | semidirect |
| 90. C22 | #392 | direct (N × H) |
| 100. C2 | C2×#392 | 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×C22⋊C4 | 2 |
| C2×#392 | 2 |
| C22×#95 | 2 |