Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
890 conjugacy classes of subgroups; only the 455 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 455 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D431 |
| commutator, cosocle | C2×C431 | C25 |
| Frattini | C2 | C24×D431 |
| Fitting | C2×#41×C431 | C2 |
| socle | C22×C431 | C24 |
| hypercenter | C2×#41 | D431 |
| hypocenter | C431 | C22×#41 |
| LCS | G ▷ C2×C431 ▷ C431 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#20293801 | C2 | semidirect |
| 2. C2×#20293800 | C2 | semidirect |
| 3. C2×#20293799 | C2 | semidirect |
| 4. #41×D431 | C2 | direct (N × H) |
| 5. C2×Q8×D431 | C2 | semidirect |
| 6. C2×D4×D431 | C2 | semidirect |
| 7. C22×C4×D431 | C2 | semidirect |
| 8. C2×#41×C431 | C2 | semidirect |
| 10. #20293801 | C22 | semidirect |
| 11. #20293800 | C22 | semidirect |
| 12. #20293799 | C22 | semidirect |
| 13. C2×Dic862 | C22 | semidirect |
| 14. Q8×D431 | C22 | semidirect |
| 15. C2×D1724 | C22 | semidirect |
| 16. C2×C22⋊D431 | C22 | semidirect |
| 17. D4×D431 | C22 | semidirect |
| 18. C22×Dic431 | C22 | semidirect |
| 21. C2×C4×D431 | C22 | semidirect |
| 22. C2×C4×D431 | C22 | semidirect |
| 23. C2×C4×D431 | C22 | semidirect |
| 24. #41×C431 | C22 | semidirect |
| 25. C2×Q8×C431 | C22 | semidirect |
| 26. C2×D4×C431 | C22 | semidirect |
| 27. C22×C4×C431 | C22 | semidirect |
| 32. Dic862 | C23 | semidirect |
| 33. D1724 | C23 | semidirect |
| 34. C22⋊D431 | C23 | semidirect |
| 37. C2×Dic431 | C23 | semidirect |
| 40. C4×D431 | C23 | semidirect |
| 41. C4×D431 | C23 | semidirect |
| 43. Q8×C431 | C23 | semidirect |
| 44. D4×C431 | C23 | semidirect |
| 47. C2×C4×C431 | C23 | semidirect |
| 53. C2×D431 | #41 | direct (N × H) |
| 61. C2×C431 | C2×#41 | semidirect |
| 64. D431 | C2×#41 | direct (N × H) |
| 65. C431 | C22×#41 | semidirect |
| 71. C2×#41 | D431 | direct (N × H) |
| 79. #41 | C2×D431 | direct (N × H) |
| 82. C2×Q8 | C2×D431 | semidirect |
| 86. C2×D4 | C2×D431 | semidirect |
| 93. C22×C4 | C2×D431 | semidirect |
| 100. Q8 | C22×D431 | semidirect |
| 103. D4 | C22×D431 | semidirect |
| 113. C2×C4 | C22×D431 | semidirect |
| 129. C2 | #41×D431 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20293801 | 2 |
| C2×#20293800 | 2 |
| C2×#20293799 | 2 |
| #41×D431 | 2 |
| C2×Q8×D431 | 2 |
| C2×D4×D431 | 2 |
| C22×C4×D431 | 2 |
| C2×#41×C431 | 2 |
| C22×#41 | 431 |