Finite Group DatabasebetaFinite Group DatabasebetaOrder 10388.
28 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C7⋊D371 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C72×C53 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 3 | D371 | — | 14 | 4 | no | — |
| 4 | C7×C53 | — | 2 | 4 | no | — |
| 5 | #6157 | — | 49 | 1 | no | maximal, Hall |
| 6 | #5997 | — | 53 | 1 | no | maximal, Hall |
| 7 | D53 | — | 49 | 1 | no | — |
| 8 | C7⋊D7 | — | 53 | 1 | no | — |
| 9 | C53 | #5997 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 10 | C72 | #6157 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 11 | D7 | — | 742 | 4 | no | — |
| 12 | C7 | — | 2 | 4 | no | — |
| 13 | C4 | — | 2597 | 1 | no | Sylow |
| 14 | C2 | — | 2597 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C53 | C4 |
| prime radical, cosocle | C7⋊D371 | C2 |
| LCS | G ▷ C72×C53 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C72×C53 | C4 | semidirect |
| 9. C53 | #5997 | semidirect |
| 10. C72 | #6157 | semidirect |