Finite Group DatabasebetaFinite Group DatabasebetaOrder 11584.
248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D181 |
| commutator, socle, cosocle | C22×C181 | C24 |
| Fitting | C4×D4×C181 | C2 |
| prime radical | #19153784 | C2 |
| hypercenter | C4×D4 | D181 |
| hypocenter | C181 | #551 |
| LCS | G ▷ C22×C181 ▷ C181 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19153811 | C2 | semidirect |
| 2. #19153810 | C2 | semidirect |
| 3. #19153802 | C2 | semidirect |
| 4. #19153799 | C2 | semidirect |
| 5. #19153798 | C2 | semidirect |
| 6. #19153797 | C2 | semidirect |
| 7. #19153795 | C2 | semidirect |
| 8. #19153794 | C2 | semidirect |
| 10. C4×C22⋊D181 | C2 | semidirect |
| 11. #19153773 | C2 | semidirect |
| 12. #19153772 | C2 | semidirect |
| 13. C2×#15668426 | C2 | semidirect |
| 14. C22⋊C4×D181 | C2 | semidirect |
| 15. C4×D4×C181 | C2 | semidirect |
| 17. C2×Dic362 | C22 | semidirect |
| 23. C4⋊Dic181 | C22 | semidirect |
| 24. #15668428 | C22 | semidirect |
| 25. #15668428 | C22 | semidirect |
| 26. #15668428 | C22 | semidirect |
| 27. #15668428 | C22 | semidirect |
| 28. #15668428 | C22 | semidirect |
| 29. #15668428 | C22 | semidirect |
| 32. C22⋊Dic181 | C22 | semidirect |
| 33. C22⋊Dic181 | C22 | semidirect |
| 42. C4×Dic181 | C22 | semidirect |
| 43. C4×Dic181 | C22 | semidirect |
| 46. C22×C4×C181 | C22 | semidirect |
| 47. C4⋊C4×C181 | C22 | semidirect |
| 49. C22⋊C4×C181 | C22 | semidirect |
| 50. C42×C181 | C22 | semidirect |
| 110. C181 | #551 | semidirect |
| 122. C4×D4 | D181 | semidirect |
| 136. C22×C4 | C2×D181 | semidirect |
| 144. C4⋊C4 | C2×D181 | semidirect |
| 158. C22⋊C4 | C2×D181 | semidirect |
| 161. C42 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19153811 | 2 |
| #19153810 | 2 |
| #19153802 | 2 |
| #19153799 | 2 |
| #19153798 | 2 |
| #19153797 | 2 |
| #19153795 | 2 |
| #19153794 | 2 |
| #19153784 | 2 |
| C4×C22⋊D181 | 2 |
| #19153773 | 2 |
| #19153772 | 2 |
| C2×#15668426 | 2 |
| C22⋊C4×D181 | 2 |
| C4×D4×C181 | 2 |
| #551 | 181 |