Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
294 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#1181 |
| commutator, socle | C2×C29 | C23×C4 |
| Fitting | #41×C29 | C4 |
| prime radical | #41×D29 | C2 |
| cosocle | C2×D29 | C24 |
| hypercenter | #41 | #1181 |
| hypocenter | C29 | #520 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C2 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q8×#1181 | C2 | semidirect |
| 3. D4×#1181 | C2 | semidirect |
| 4. #11745345 | C2 | semidirect |
| 5. C2×C4⋊#1181 | C2 | semidirect |
| 7. #41×C29 | C4 | semidirect |
| 8. #90809 | C4 | semidirect |
| 10. #90807 | C4 | semidirect |
| 12. #90805 | C4 | semidirect |
| 23. Q8×C29 | C2×C4 | semidirect |
| 24. D4×C29 | C2×C4 | semidirect |
| 25. C2×C4×C29 | C2×C4 | semidirect |
| 26. C22⋊D29 | C2×C4 | semidirect |
| 27. C2×Dic29 | C2×C4 | semidirect |
| 28. D116 | C2×C4 | semidirect |
| 29. C4×D29 | C2×C4 | semidirect |
| 30. C4×D29 | C2×C4 | semidirect |
| 33. Dic58 | C2×C4 | semidirect |
| 56. C29 | #520 | semidirect |
| 60. #41 | #1181 | semidirect |
| 72. Q8 | C2×#1181 | semidirect |
| 75. D4 | C2×#1181 | semidirect |
| 84. C2×C4 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D29 | 2 |
| Q8×#1181 | 2 |
| D4×#1181 | 2 |
| #11745345 | 2 |
| C2×C4⋊#1181 | 2 |
| #520 | 29 |