Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
2590 conjugacy classes of subgroups; only the 1054 normal subgroups are shown.
This group has 2590 conjugacy classes of subgroups — too many to draw. Only its 1054 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×C11 | D8 |
| commutator, Frattini, cosocle | C8 | C25×C11 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C11×D8 | C2 | semidirect |
| 2. C22×C11×D16 | C2 | direct (N × H) |
| 3. C23×C11×C16 | C2 | semidirect |
| 6. C22×C11×D8 | C22 | semidirect |
| 8. C2×C11×D16 | C22 | direct (N × H) |
| 9. C22×C11×C16 | C22 | semidirect |
| 15. C2×C11×D8 | C23 | semidirect |
| 18. C11×D16 | C23 | direct (N × H) |
| 19. C2×C11×C16 | C23 | semidirect |
| 20. C23×D16 | C11 | direct (N × H) |
| 29. C11×D8 | C24 | semidirect |
| 32. C11×C16 | C24 | semidirect |
| 33. C23×D8 | C2×C11 | semidirect |
| 34. C22×D16 | C2×C11 | direct (N × H) |
| 35. C23×C16 | C2×C11 | semidirect |
| 38. C23×C11 | D16 | direct (N × H) |
| 48. C22×D8 | C22×C11 | semidirect |
| 50. C2×D16 | C22×C11 | direct (N × H) |
| 51. C22×C16 | C22×C11 | semidirect |
| 54. C22×C11 | C2×D16 | direct (N × H) |
| 63. C2×D8 | C23×C11 | semidirect |
| 66. D16 | C23×C11 | direct (N × H) |
| 67. C2×C16 | C23×C11 | semidirect |
| 69. C2×C11 | C22×D16 | direct (N × H) |
| 79. D8 | C24×C11 | semidirect |
| 82. C16 | C24×C11 | semidirect |
| 83. C11 | C23×D16 | direct (N × H) |
| 86. C23 | C11×D16 | direct (N × H) |
| 96. C22 | C2×C11×D16 | direct (N × H) |
| 101. C2 | C22×C11×D16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C11×D8 | 2 |
| C22×C11×D16 | 2 |
| C23×C11×C16 | 2 |
| C23×D16 | 11 |