Finite Group DatabasebetaFinite Group DatabasebetaOrder 25016.
24 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | Dic3127 | C2 | 1 | 2 | yes | maximal |
| 2 | C4×C53×C59 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×C53×C59 | C22 | 1 | 1 | yes | characteristic |
| 4 | C53×C59 | Q8 | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | Dic118 | — | 53 | 1 | no | maximal, Hall |
| 6 | Dic106 | — | 59 | 1 | no | maximal, Hall |
| 7 | C4×C59 | D53 | 1 | 1 | yes | characteristic |
| 8 | Dic59 | — | 53 | 2 | no | — |
| 9 | C4×C53 | D59 | 1 | 1 | yes | characteristic |
| 10 | Dic53 | — | 59 | 2 | no | — |
| 11 | C2×C59 | C2×D53 | 1 | 1 | yes | characteristic |
| 12 | C2×C53 | C2×D59 | 1 | 1 | yes | characteristic |
| 13 | C59 | Dic106 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | C53 | Dic118 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 15 | Q8 | — | 3127 | 1 | no | Sylow |
| 16 | C4 | — | 3127 | 2 | no | — |
| 17 | C4 | D3127 | 1 | 1 | yes | characteristic |
| 18 | C2 | C2×D3127 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D3127 |
| commutator, socle, prime radical, cosocle | C2×C53×C59 | C22 |
| Fitting | C4×C53×C59 | C2 |
| hypercenter | C4 | D3127 |
| hypocenter | C53×C59 | Q8 |
| LCS | G ▷ C2×C53×C59 ▷ C53×C59 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C53×C59 | Q8 | semidirect |
| 13. C59 | Dic106 | semidirect |
| 14. C53 | Dic118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic3127 | 2 |
| C4×C53×C59 | 2 |
| Dic118 | 53 |
| Dic106 | 59 |