Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
8094 conjugacy classes of subgroups; only the 1243 normal subgroups are shown.
This group has 8094 conjugacy classes of subgroups — too many to draw. Only its 1243 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D11 |
| commutator, cosocle | C23×C11 | C25 |
| Frattini | C23 | C24×D11 |
| Fitting | C22×C11×#127 | C2 |
| socle | C24×C11 | C24 |
| hypercenter | C22×#127 | D11 |
| hypocenter | C11 | C2×#2867 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C24 ◁ C22×#127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#66927 | C2 | semidirect |
| 2. C22×#66993 | C2 | semidirect |
| 3. #13077010 | C2 | direct (N × H) |
| 4. C2×C42×Dic11 | C2 | semidirect |
| 5. C22×C11×#127 | C2 | semidirect |
| 10. C2×C11×#127 | C22 | semidirect |
| 13. C2×#66993 | C22 | semidirect |
| 16. C2×#66927 | C22 | semidirect |
| 17. C42×Dic11 | C22 | semidirect |
| 31. C2×C42×C11 | D4 | semidirect |
| 34. C2×C4×Dic11 | D4 | semidirect |
| 58. C42×C11 | C2×D4 | semidirect |
| 59. C4×Dic11 | C2×D4 | semidirect |
| 62. C22×#127 | D11 | semidirect |
| 77. C2×C4×C11 | #127 | semidirect |
| 81. C2×Dic11 | #127 | semidirect |
| 92. C2×#127 | C2×D11 | semidirect |
| 106. C4×C11 | C2×#127 | semidirect |
| 107. Dic11 | C2×#127 | semidirect |
| 125. C2×C42 | C22⋊D11 | semidirect |
| 128. C2×C11 | #2867 | semidirect |
| 153. C42 | C2×C22⋊D11 | semidirect |
| 154. C11 | C2×#2867 | semidirect |
| 171. C2×C4 | #66993 | semidirect |
| 185. C4 | C2×#66993 | semidirect |
| 188. C2 | #13077010 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#66927 | 2 |
| C22×#66993 | 2 |
| #13077010 | 2 |
| C2×C42×Dic11 | 2 |
| C22×C11×#127 | 2 |
| C2×#2867 | 11 |