Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
280 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 115 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×C4⋊Q8 | C2 |
| prime radical | C2×D116 | C22 |
| hypercenter | C4⋊Q8 | D29 |
| hypocenter | C29 | D4×Q8 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×D29 | C2 | semidirect |
| 2. C29×C4⋊Q8 | C2 | semidirect |
| 3. #11745308 | C2 | semidirect |
| 4. #11745258 | C2 | semidirect |
| 6. #11745250 | C2 | semidirect |
| 8. C4×Dic58 | C2 | semidirect |
| 35. D116 | Q8 | semidirect |
| 39. Dic58 | D4 | semidirect |
| 43. C2×D29 | C2×Q8 | semidirect |
| 47. C4×C29 | C2×Q8 | semidirect |
| 58. C4⋊Q8 | D29 | semidirect |
| 64. C29 | D4×Q8 | semidirect |
| 106. C4 | Q8×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D29 | 2 |
| C29×C4⋊Q8 | 2 |
| #11745308 | 2 |
| #11745258 | 2 |
| #11745255 | 2 |
| #11745250 | 2 |
| C4×D116 | 2 |
| C4×Dic58 | 2 |
| D4×Q8 | 29 |