Finite Group DatabasebetaFinite Group DatabasebetaOrder 10404.
64 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×(C17⋊D17)⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3⋊#11923883 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11923883⋊C3 | — | 3 | 1 | no | maximal |
| 4 | C3×C172⋊C3 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | C3×C17⋊D17 | C2×C3 | 1 | 1 | yes | characteristic |
| 6 | (C17⋊D17)⋊C3 | — | 2 | 1 | no | — |
| 7 | (C17⋊D17)⋊C3 | D3 | 1 | 1 | yes | characteristic |
| 8 | #11923883 | — | 3 | 1 | no | Hall |
| 9 | C3×C172 | C3×C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | C172⋊C3 | — | 2 | 1 | no | — |
| 11 | C172⋊C3 | Dic3 | 1 | 1 | yes | characteristic, complemented |
| 12 | C17⋊D17 | C3×D3 | 1 | 1 | yes | characteristic |
| 13 | C172 | C3×Dic3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | C3⋊#595 | — | 51 | 6 | no | — |
| 15 | C3×D17 | — | 51 | 6 | no | — |
| 16 | #595 | — | 153 | 6 | no | — |
| 17 | C3×C17 | — | 3 | 6 | no | — |
| 18 | C3×Dic3 | — | 289 | 1 | no | maximal, Hall |
| 19 | D17 | — | 51 | 6 | no | — |
| 20 | C2×C32 | — | 289 | 1 | no | — |
| 21 | C17 | — | 3 | 6 | no | — |
| 22 | C3×C4 | — | 867 | 1 | no | — |
| 23 | Dic3 | — | 289 | 1 | no | — |
| 24 | C32 | — | 289 | 1 | no | Sylow |
| 25 | C2×C3 | — | 289 | 1 | no | — |
| 26 | C2×C3 | — | 289 | 1 | no | — |
| 27 | C2×C3 | — | 578 | 1 | no | — |
| 28 | C4 | — | 867 | 1 | no | Sylow |
| 29 | C3 | — | 289 | 1 | no | — |
| 30 | C3 | — | 578 | 1 | no | — |
| 31 | C3 | #11923883⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 32 | C2 | — | 289 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C172 | C3×C4 |
| prime radical | C3×(C17⋊D17)⋊C3 | C2 |
| cosocle | C3×C17⋊D17 | C2×C3 |
| LCS | G ▷ C3×C172 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3⋊#11923883 | C3 | semidirect |
| 4. C3×C172⋊C3 | C4 | semidirect |
| 9. C3×C172 | C3×C4 | semidirect |
| 11. C172⋊C3 | Dic3 | semidirect |
| 13. C172 | C3×Dic3 | semidirect |
| 31. C3 | #11923883⋊C3 | semidirect |