Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
688 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C11×#466 | C2 | semidirect |
| 2. C11×#2233 | C2 | semidirect |
| 3. C11×#2218 | C2 | semidirect |
| 4. C11×#2184 | C2 | semidirect |
| 5. C11×#2112 | C2 | semidirect |
| 6. C22×C11×D8 | C22 | semidirect |
| 9. C2×C11×D16 | C22 | semidirect |
| 10. C2×C11×M32 | C22 | semidirect |
| 14. C11×#466 | C22 | semidirect |
| 15. C2×C11×#107 | C22 | semidirect |
| 17. C11×#367 | C22 | semidirect |
| 18. C11×#357 | C22 | semidirect |
| 19. C11×C22⋊C16 | C22 | semidirect |
| 44. #33758 | C11 | direct (N × H) |
| 75. C2×#466 | C2×C11 | semidirect |
| 76. #2233 | C2×C11 | semidirect |
| 77. #2218 | C2×C11 | semidirect |
| 78. #2184 | C2×C11 | semidirect |
| 79. #2112 | C2×C11 | semidirect |
| 107. C22×D8 | C22×C11 | semidirect |
| 110. C2×D16 | C22×C11 | semidirect |
| 111. C2×M32 | C22×C11 | semidirect |
| 115. #466 | C22×C11 | semidirect |
| 116. C2×#107 | C22×C11 | semidirect |
| 118. #367 | C22×C11 | semidirect |
| 119. #357 | C22×C11 | semidirect |
| 120. C22⋊C16 | C22×C11 | semidirect |
| 196. C11 | #33758 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11×#466 | 2 |
| C11×#2233 | 2 |
| C11×#2218 | 2 |
| C11×#2184 | 2 |
| C11×#2112 | 2 |
| #33758 | 11 |