Finite Group DatabasebetaFinite Group DatabasebetaOrder 31168.
428 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 115 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×D487 |
| commutator, socle, cosocle | C22×C487 | C24 |
| Fitting | #120×C487 | C2 |
| hypercenter | #120 | D487 |
| hypocenter | C487 | D42 |
| LCS | G ▷ C22×C487 ▷ C487 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C22⋊D487 | C2 | semidirect |
| 2. C2×D4×D487 | C2 | semidirect |
| 3. #29510211 | C2 | semidirect |
| 4. #29510188 | C2 | semidirect |
| 5. #29510187 | C2 | semidirect |
| 6. #29510185 | C2 | semidirect |
| 7. #29510183 | C2 | semidirect |
| 8. (C22⋊D487)⋊C4 | C2 | semidirect |
| 9. #120×C487 | C2 | semidirect |
| 10. C23×D487 | C22 | semidirect |
| 11. C23×D487 | C22 | semidirect |
| 12. C2×D1948 | C22 | semidirect |
| 13. C2×D1948 | C22 | semidirect |
| 16. C2×C22⋊D487 | C22 | semidirect |
| 17. C2×C22⋊D487 | C22 | semidirect |
| 18. C2×C22⋊D487 | C22 | semidirect |
| 19. C2×C22⋊D487 | C22 | semidirect |
| 21. C22×Dic487 | C22 | semidirect |
| 22. C2×C4×D487 | C22 | semidirect |
| 23. Dic487⋊C4 | C22 | semidirect |
| 24. C22⋊Dic487 | C22 | semidirect |
| 25. (C2×D487)⋊C4 | C22 | semidirect |
| 26. (C2×D487)⋊C4 | C22 | semidirect |
| 27. C4×Dic487 | C22 | semidirect |
| 28. C24×C487 | C22 | semidirect |
| 29. C2×D4×C487 | C22 | semidirect |
| 30. C2×D4×C487 | C22 | semidirect |
| 31. C22⋊C4×C487 | C22 | semidirect |
| 32. C22⋊C4×C487 | C22 | semidirect |
| 46. C22⋊D487 | D4 | semidirect |
| 67. C22×C487 | C2×D4 | semidirect |
| 76. C2×D487 | C2×D4 | semidirect |
| 80. Dic487 | C2×D4 | semidirect |
| 88. C487 | D42 | semidirect |
| 97. #120 | D487 | semidirect |
| 101. C24 | C2×D487 | semidirect |
| 111. C2×D4 | C2×D487 | semidirect |
| 112. C2×D4 | C2×D487 | semidirect |
| 119. C22⋊C4 | C2×D487 | semidirect |
| 120. C22⋊C4 | C2×D487 | semidirect |
| 164. C22 | D4×D487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D487 | 2 |
| C2×D4×D487 | 2 |
| #29510211 | 2 |
| #29510188 | 2 |
| #29510187 | 2 |
| #29510185 | 2 |
| #29510183 | 2 |
| (C22⋊D487)⋊C4 | 2 |
| #120×C487 | 2 |
| D42 | 487 |