Finite Group DatabasebetaFinite Group DatabasebetaOrder 59176.
24 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | Dic7397 | C2 | 1 | 2 | yes | maximal |
| 2 | C4×C13×C569 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×C13×C569 | C22 | 1 | 1 | yes | characteristic |
| 4 | C13×C569 | Q8 | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | Dic1138 | — | 13 | 1 | no | maximal, Hall |
| 6 | C4×C569 | D13 | 1 | 1 | yes | characteristic |
| 7 | Dic569 | — | 13 | 2 | no | — |
| 8 | C2×C569 | C2×D13 | 1 | 1 | yes | characteristic |
| 9 | C569 | Dic26 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 10 | Dic26 | — | 569 | 1 | no | maximal, Hall |
| 11 | C4×C13 | D569 | 1 | 1 | yes | characteristic |
| 12 | Dic13 | — | 569 | 2 | no | — |
| 13 | C2×C13 | C2×D569 | 1 | 1 | yes | characteristic |
| 14 | C13 | Dic1138 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 15 | Q8 | — | 7397 | 1 | no | Sylow |
| 16 | C4 | — | 7397 | 2 | no | — |
| 17 | C4 | D7397 | 1 | 1 | yes | characteristic |
| 18 | C2 | C2×D7397 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D7397 |
| commutator, socle, prime radical, cosocle | C2×C13×C569 | C22 |
| Fitting | C4×C13×C569 | C2 |
| hypercenter | C4 | D7397 |
| hypocenter | C13×C569 | Q8 |
| LCS | G ▷ C2×C13×C569 ▷ C13×C569 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C13×C569 | Q8 | semidirect |
| 9. C569 | Dic26 | semidirect |
| 14. C13 | Dic1138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic7397 | 2 |
| C4×C13×C569 | 2 |
| Dic1138 | 13 |
| Dic26 | 569 |