Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
258 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×D29 |
| commutator, socle | C2×C29 | C23×C4 |
| Fitting | C2×M16×C29 | C2 |
| prime radical | C2×#90805 | C2 |
| cosocle | C4×C29 | C24 |
| hypercenter | C2×M16 | D29 |
| hypocenter | C29 | #568 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C4 ◁ C2×M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×M16×C29 | C2 | semidirect |
| 3. C2×#90777 | C2 | semidirect |
| 4. #11745269 | C2 | semidirect |
| 5. M16×D29 | C2 | semidirect |
| 6. #11745263 | C2 | semidirect |
| 17. M16×C29 | C22 | semidirect |
| 18. C2×C8×C29 | C22 | semidirect |
| 20. #90777 | C22 | semidirect |
| 21. C2×#6597 | C22 | semidirect |
| 22. #90772 | C22 | semidirect |
| 23. C8×D29 | C22 | semidirect |
| 65. C2×M16 | D29 | semidirect |
| 66. C29 | #568 | semidirect |
| 80. M16 | C2×D29 | semidirect |
| 83. C2×C8 | C2×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90805 | 2 |
| C2×M16×C29 | 2 |
| C2×#90777 | 2 |
| #11745269 | 2 |
| M16×D29 | 2 |
| #11745263 | 2 |
| #568 | 29 |