Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
8094 conjugacy classes of subgroups; only the 1123 normal subgroups are shown.
This group has 8094 conjugacy classes of subgroups — too many to draw. Only its 1123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D11 |
| commutator, socle, cosocle | C23×C11 | C25 |
| Fitting | C11×#2867 | C2 |
| hypercenter | #2867 | D11 |
| hypocenter | C11 | C2×#2867 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #2867 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D11×#127 | C2 | semidirect |
| 2. #13077011 | C2 | semidirect |
| 3. #13077010 | C2 | semidirect |
| 4. C43×D11 | C2 | semidirect |
| 5. C11×#2867 | C2 | semidirect |
| 7. C2×C11×#127 | C22 | semidirect |
| 8. C2×#66993 | C22 | semidirect |
| 10. C2×#66927 | C22 | semidirect |
| 12. C43×C11 | C22 | semidirect |
| 13. C42×Dic11 | C22 | semidirect |
| 25. C42×D11 | D4 | semidirect |
| 38. C42×C11 | C2×D4 | semidirect |
| 39. C4×Dic11 | C2×D4 | semidirect |
| 43. #2867 | D11 | direct (N × H) |
| 55. C4×D11 | #127 | semidirect |
| 60. C2×#127 | C2×D11 | semidirect |
| 63. C43 | C2×D11 | semidirect |
| 69. C4×C11 | C2×#127 | semidirect |
| 70. Dic11 | C2×#127 | semidirect |
| 86. D11 | #2867 | direct (N × H) |
| 99. C42 | D4×D11 | semidirect |
| 100. C11 | C2×#2867 | semidirect |
| 118. C4 | D11×#127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D11×#127 | 2 |
| #13077011 | 2 |
| #13077010 | 2 |
| C43×D11 | 2 |
| C11×#2867 | 2 |
| C2×#2867 | 11 |