Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
222 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D29 |
| commutator, socle, cosocle | C22×C29 | C24 |
| Fitting | C29×C22⋊Q8 | C2 |
| prime radical | C23×C29 | C23 |
| hypercenter | C22⋊Q8 | D29 |
| hypocenter | C29 | #533 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q8×Dic29 | C2 | semidirect |
| 3. #11745306 | C2 | semidirect |
| 6. #11745251 | C2 | semidirect |
| 7. #11745250 | C2 | semidirect |
| 8. #11745249 | C2 | semidirect |
| 9. #11745249 | C2 | semidirect |
| 43. C2×Dic29 | Q8 | semidirect |
| 82. C29 | #533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×C22⋊Q8 | 2 |
| Q8×Dic29 | 2 |
| #11745306 | 2 |
| #11745286 | 2 |
| C2×C4×Dic29 | 2 |
| #11745251 | 2 |
| #11745250 | 2 |
| #11745249 | 2 |
| #11745240 | 2 |
| #11745239 | 2 |
| #533 | 29 |