Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
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×D29 |
| commutator, cosocle | C4×C29 | C24 |
| Frattini | C4 | C23×D29 |
| Fitting | C2×D8×C29 | C2 |
| socle | C2×C29 | C22×D4 |
| hypercenter | C2×D8 | D29 |
| hypocenter | C29 | #576 |
| LCS | G ▷ C4×C29 ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×D8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11745359 | C2 | semidirect |
| 2. C2×D8×C29 | C2 | semidirect |
| 3. #11745294 | C2 | semidirect |
| 4. #11745274 | C2 | semidirect |
| 5. #11745273 | C2 | semidirect |
| 6. D8×D29 | C2 | semidirect |
| 7. #11745266 | C2 | semidirect |
| 8. #11745263 | C2 | semidirect |
| 9. C2×D4×C29 | C22 | semidirect |
| 12. #90807 | C22 | semidirect |
| 14. D4×D29 | C22 | semidirect |
| 16. #90805 | C22 | semidirect |
| 17. D8×C29 | C22 | semidirect |
| 18. D8×C29 | C22 | semidirect |
| 19. C2×C8×C29 | C22 | semidirect |
| 20. #90783 | C22 | semidirect |
| 21. #90782 | C22 | semidirect |
| 22. #90777 | C22 | semidirect |
| 23. Dic116 | C22 | semidirect |
| 24. D232 | C22 | semidirect |
| 25. #90773 | C22 | semidirect |
| 26. #90772 | C22 | semidirect |
| 27. C8×D29 | C22 | semidirect |
| 69. C2×D8 | D29 | semidirect |
| 71. C29 | #576 | semidirect |
| 79. C2×D4 | C2×D29 | semidirect |
| 85. D8 | C2×D29 | semidirect |
| 86. D8 | C2×D29 | semidirect |
| 90. C2×C8 | C2×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11745359 | 2 |
| C2×D8×C29 | 2 |
| #11745294 | 2 |
| #11745274 | 2 |
| #11745273 | 2 |
| D8×D29 | 2 |
| #11745266 | 2 |
| #11745263 | 2 |
| #576 | 29 |