Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
5956 conjugacy classes of subgroups; only the 3205 normal subgroups are shown.
This group has 5956 conjugacy classes of subgroups — too many to draw. Only its 3205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C24×D89 |
| commutator, cosocle | C2×C89 | C26 |
| Frattini | C2 | C25×D89 |
| Fitting | C2×H(5,𝔽2)×C89 | C2 |
| socle | C22×C89 | C25 |
| hypercenter | C2×H(5,𝔽2) | D89 |
| hypocenter | C89 | C2×#585 |
| LCS | G ▷ C2×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ C2×H(5,𝔽2) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19152433 | C2 | direct (N × H) |
| 2. C2×#15668059 | C2 | semidirect |
| 3. C2×#15668057 | C2 | semidirect |
| 4. C22×#13083573 | C2 | semidirect |
| 5. C2×#41×D89 | C2 | semidirect |
| 6. C2×H(5,𝔽2)×C89 | C2 | semidirect |
| 7. #15668059 | C22 | semidirect |
| 8. #15668057 | C22 | semidirect |
| 9. C2×#13083575 | C22 | semidirect |
| 10. C2×#13083574 | C22 | semidirect |
| 11. C2×#13083573 | C22 | semidirect |
| 12. C2×#13083573 | C22 | semidirect |
| 13. C2×#13083573 | C22 | semidirect |
| 14. #41×D89 | C22 | semidirect |
| 15. C22×Dic178 | C22 | semidirect |
| 16. C2×Q8×D89 | C22 | semidirect |
| 17. C22×C22⋊D89 | C22 | semidirect |
| 18. C2×D4×D89 | C22 | semidirect |
| 19. C23×Dic89 | C22 | semidirect |
| 20. C22×C4×D89 | C22 | semidirect |
| 21. H(5,𝔽2)×C89 | C22 | semidirect |
| 22. C2×#41×C89 | C22 | semidirect |
| 23. C22×D4×C89 | C22 | semidirect |
| 25. #13083575 | C23 | semidirect |
| 26. #13083574 | C23 | semidirect |
| 27. #13083573 | C23 | semidirect |
| 28. #13083573 | C23 | semidirect |
| 30. C2×Dic178 | C23 | semidirect |
| 31. Q8×D89 | C23 | semidirect |
| 34. C2×C22⋊D89 | C23 | semidirect |
| 35. D4×D89 | C23 | semidirect |
| 38. C22×Dic89 | C23 | semidirect |
| 41. C2×C4×D89 | C23 | semidirect |
| 43. #41×C89 | C23 | semidirect |
| 46. C2×D4×C89 | C23 | semidirect |
| 78. C2×C89 | #585 | semidirect |
| 82. C89 | C2×#585 | semidirect |
| 86. C2×H(5,𝔽2) | D89 | semidirect |
| 91. H(5,𝔽2) | C2×D89 | semidirect |
| 98. C2×#41 | C2×D89 | semidirect |
| 103. C22×D4 | C2×D89 | semidirect |
| 112. #41 | C22×D89 | semidirect |
| 122. C2×D4 | C22×D89 | semidirect |
| 161. C2 | #19152433 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152433 | 2 |
| C2×#15668059 | 2 |
| C2×#15668057 | 2 |
| C22×#13083573 | 2 |
| C2×#41×D89 | 2 |
| C2×H(5,𝔽2)×C89 | 2 |
| C2×#585 | 89 |