Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
9999 conjugacy classes of subgroups; only the 3695 normal subgroups are shown.
This group has 9999 conjugacy classes of subgroups — too many to draw. Only its 3695 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 | C22 | C26 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C25 ◁ G | |
| LECS | G ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×D4 | C2 | semidirect |
| 2. C24×D4 | C2 | semidirect |
| 3. C25×C4 | C2 | semidirect |
| 4. C22×#121 | C2 | direct (N × H) |
| 5. C23×C4⋊C4 | C2 | semidirect |
| 6. C23×C22⋊C4 | C2 | semidirect |
| 11. C23×D4 | C22 | semidirect |
| 12. C23×D4 | C22 | semidirect |
| 17. C24×C4 | C22 | semidirect |
| 18. C2×#121 | C22 | direct (N × H) |
| 19. C22×C4⋊C4 | C22 | semidirect |
| 20. C22×C22⋊C4 | C22 | semidirect |
| 26. C25 | D4 | semidirect |
| 32. C22×D4 | C23 | semidirect |
| 33. C22×D4 | C23 | semidirect |
| 37. C23×C4 | D4 | semidirect |
| 41. C23×C4 | C23 | semidirect |
| 42. #121 | C23 | direct (N × H) |
| 43. C2×C4⋊C4 | C23 | semidirect |
| 44. C2×C22⋊C4 | C23 | semidirect |
| 54. C24 | C2×D4 | semidirect |
| 61. C2×D4 | C24 | semidirect |
| 62. C2×D4 | C24 | semidirect |
| 66. C22×C4 | C2×D4 | semidirect |
| 70. C22×C4 | C24 | semidirect |
| 71. C4⋊C4 | C24 | semidirect |
| 72. C22⋊C4 | C24 | semidirect |
| 80. C23 | #121 | direct (N × H) |
| 83. C23 | C22×D4 | semidirect |
| 93. C2×C4 | C22×D4 | semidirect |
| 104. C22 | C2×#121 | direct (N × H) |
| 107. C22 | C23×D4 | semidirect |
| 112. C4 | C23×D4 | semidirect |
| 115. C2 | C22×#121 | 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 |
| C25×C4 | 2 |
| C22×#121 | 2 |
| C23×C4⋊C4 | 2 |
| C23×C22⋊C4 | 2 |