Finite Group DatabasebetaFinite Group DatabasebetaOrder 1984.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D4×D31 |
| commutator, cosocle | C4×C31 | C24 |
| Frattini | C4 | C23×D31 |
| Fitting | C2×D8×C31 | C2 |
| socle | C2×C31 | C22×D4 |
| hypercenter | C2×D8 | D31 |
| hypocenter | C31 | #576 |
| LCS | G ▷ C4×C31 ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×D8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11758561 | C2 | semidirect |
| 2. C2×D8×C31 | C2 | semidirect |
| 3. #11758509 | C2 | semidirect |
| 4. #11758489 | C2 | semidirect |
| 5. #11758488 | C2 | semidirect |
| 6. D8×D31 | C2 | semidirect |
| 7. #11758481 | C2 | semidirect |
| 8. #11758478 | C2 | semidirect |
| 9. C2×D4×C31 | C22 | semidirect |
| 12. #92497 | C22 | semidirect |
| 14. D4×D31 | C22 | semidirect |
| 16. #92495 | C22 | semidirect |
| 17. D8×C31 | C22 | semidirect |
| 18. D8×C31 | C22 | semidirect |
| 19. C2×C8×C31 | C22 | semidirect |
| 20. #92480 | C22 | semidirect |
| 21. #92479 | C22 | semidirect |
| 22. #92474 | C22 | semidirect |
| 23. Dic124 | C22 | semidirect |
| 24. D248 | C22 | semidirect |
| 25. #92470 | C22 | semidirect |
| 26. #92469 | C22 | semidirect |
| 27. C8×D31 | C22 | semidirect |
| 69. C2×D8 | D31 | semidirect |
| 71. C31 | #576 | semidirect |
| 79. C2×D4 | C2×D31 | semidirect |
| 85. D8 | C2×D31 | semidirect |
| 86. D8 | C2×D31 | semidirect |
| 90. C2×C8 | C2×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11758561 | 2 |
| C2×D8×C31 | 2 |
| #11758509 | 2 |
| #11758489 | 2 |
| #11758488 | 2 |
| D8×D31 | 2 |
| #11758481 | 2 |
| #11758478 | 2 |
| #576 | 31 |