Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
9310 conjugacy classes of subgroups; only the 6366 normal subgroups are shown.
This group has 9310 conjugacy classes of subgroups — too many to draw. Only its 6366 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 | C24 |
| commutator, Frattini, cosocle | C22 | C26×C11 |
| prime radical | C26×C11 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C11×#543 | C2 | direct (N × H) |
| 2. C22×C11×C22⋊Q8 | C2 | semidirect |
| 5. C23×Q8×C11 | C22 | semidirect |
| 7. C11×#543 | C22 | direct (N × H) |
| 8. C2×C11×C22⋊Q8 | C22 | semidirect |
| 9. C22×C11×C4⋊C4 | C22 | semidirect |
| 13. C25×C11 | Q8 | semidirect |
| 17. C22×Q8×C11 | C23 | semidirect |
| 21. C11×C22⋊Q8 | C23 | semidirect |
| 22. C2×C11×C4⋊C4 | C23 | semidirect |
| 25. C22×#543 | C11 | direct (N × H) |
| 30. C24×C11 | C2×Q8 | semidirect |
| 35. C2×Q8×C11 | C24 | semidirect |
| 40. C11×C4⋊C4 | C24 | semidirect |
| 42. C2×#543 | C2×C11 | direct (N × H) |
| 43. C22×C22⋊Q8 | C2×C11 | semidirect |
| 51. C23×C11 | C22×Q8 | semidirect |
| 60. C23×Q8 | C22×C11 | semidirect |
| 62. #543 | C22×C11 | direct (N × H) |
| 63. C2×C22⋊Q8 | C22×C11 | semidirect |
| 64. C22×C4⋊C4 | C22×C11 | semidirect |
| 70. C22×C11 | #543 | direct (N × H) |
| 77. C25 | Q8×C11 | semidirect |
| 81. C22×Q8 | C23×C11 | semidirect |
| 85. C22⋊Q8 | C23×C11 | semidirect |
| 86. C2×C4⋊C4 | C23×C11 | semidirect |
| 90. C2×C11 | C2×#543 | direct (N × H) |
| 97. C24 | C2×Q8×C11 | semidirect |
| 102. C2×Q8 | C24×C11 | semidirect |
| 107. C4⋊C4 | C24×C11 | semidirect |
| 109. C11 | C22×#543 | direct (N × H) |
| 116. C23 | C22×Q8×C11 | semidirect |
| 127. C22 | C11×#543 | direct (N × H) |
| 134. C2 | C2×C11×#543 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11×#543 | 2 |
| C22×C11×C22⋊Q8 | 2 |
| C23×C11×C22⋊C4 | 2 |
| C22×#543 | 11 |