Finite Group DatabasebetaFinite Group DatabasebetaOrder 3520.
1620 conjugacy classes of subgroups; only the 818 normal subgroups are shown.
This group has 1620 conjugacy classes of subgroups — too many to draw. Only its 818 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×AGL(1,𝔽11) |
| commutator, socle, cosocle | C2×C11 | C25×C5 |
| Fitting | C11×H(5,𝔽2) | C2×C5 |
| hypercenter | H(5,𝔽2) | AGL(1,𝔽11) |
| hypocenter | C11 | C5×#585 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. H(5,𝔽2)×C11⋊C5 | C2 | semidirect |
| 2. #67043⋊C5 | C2 | semidirect |
| 3. #41×AGL(1,𝔽11) | C2 | semidirect |
| 4. #67037⋊C5 | C2 | semidirect |
| 5. C2×#4341⋊C5 | C2 | semidirect |
| 6. #41×C11⋊C5 | C22 | semidirect |
| 7. C2×D4×C11⋊C5 | C22 | semidirect |
| 8. C2×C22⋊AGL(1,𝔽11) | C22 | semidirect |
| 9. C22×Dic11⋊C5 | C22 | semidirect |
| 10. #4343⋊C5 | C22 | semidirect |
| 11. Q8×AGL(1,𝔽11) | C22 | semidirect |
| 12. #4341⋊C5 | C22 | semidirect |
| 13. #4341⋊C5 | C22 | semidirect |
| 14. D4×AGL(1,𝔽11) | C22 | semidirect |
| 15. #4339⋊C5 | C22 | semidirect |
| 16. C2×C4×AGL(1,𝔽11) | C22 | semidirect |
| 17. C2×(C11⋊C5)⋊Q8 | C22 | semidirect |
| 18. #10623455 | C5 | semidirect |
| 31. C11×H(5,𝔽2) | C2×C5 | semidirect |
| 32. #67043 | C2×C5 | semidirect |
| 33. #41×D11 | C2×C5 | semidirect |
| 34. #67037 | C2×C5 | semidirect |
| 35. C2×#4341 | C2×C5 | semidirect |
| 44. C11×#41 | C22×C5 | semidirect |
| 45. C2×D4×C11 | C22×C5 | semidirect |
| 46. C2×C22⋊D11 | C22×C5 | semidirect |
| 47. C22×Dic11 | C22×C5 | semidirect |
| 48. #4343 | C22×C5 | semidirect |
| 49. Q8×D11 | C22×C5 | semidirect |
| 50. #4341 | C22×C5 | semidirect |
| 51. #4341 | C22×C5 | semidirect |
| 52. D4×D11 | C22×C5 | semidirect |
| 53. #4339 | C22×C5 | semidirect |
| 54. C2×C4×D11 | C22×C5 | semidirect |
| 55. C2×Dic22 | C22×C5 | semidirect |
| 89. C11⋊C5 | #585 | semidirect |
| 111. H(5,𝔽2) | AGL(1,𝔽11) | semidirect |
| 128. #41 | C2×AGL(1,𝔽11) | semidirect |
| 133. C2×D4 | C2×AGL(1,𝔽11) | semidirect |
| 136. C11 | C5×#585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(5,𝔽2)×C11⋊C5 | 2 |
| #67043⋊C5 | 2 |
| #41×AGL(1,𝔽11) | 2 |
| #67037⋊C5 | 2 |
| C2×#4341⋊C5 | 2 |
| #10623455 | 5 |
| C5×#585 | 11 |