Finite Group DatabasebetaFinite Group DatabasebetaOrder 23604.
24 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×C7×D281 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C7×#11765499 | C3 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 3 | C3×C7×C281 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C7×D281 | C2×C3 | 1 | 1 | yes | characteristic |
| 5 | C3×#11765499 | C7 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 6 | C7×C281 | C3×C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 7 | C3×D281 | C2×C7 | 1 | 1 | yes | characteristic |
| 8 | #11765499 | C3×C7 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 9 | C3×C281 | C4×C7 | 1 | 1 | yes | characteristic, complemented, Hall |
| 10 | D281 | C2×C3×C7 | 1 | 1 | yes | characteristic |
| 11 | C281 | C3×C4×C7 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | C3×C4×C7 | — | 281 | 1 | no | maximal, Hall |
| 13 | C2×C3×C7 | — | 281 | 1 | no | — |
| 14 | C4×C7 | — | 281 | 1 | no | Hall |
| 15 | C3×C7 | #11765499 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 16 | C2×C7 | — | 281 | 1 | no | — |
| 17 | C3×C4 | — | 281 | 1 | no | Hall |
| 18 | C7 | C3×#11765499 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 19 | C2×C3 | — | 281 | 1 | no | — |
| 20 | C4 | — | 281 | 1 | no | Sylow |
| 21 | C3 | C7×#11765499 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 22 | C2 | — | 281 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | #11765499 |
| commutator, hypocenter | C281 | C3×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C281 | C4 |
| prime radical | C3×C7×D281 | C2 |
| cosocle | D281 | C2×C3×C7 |
| LCS | G ▷ C281 | |
| UCS | C1 ◁ C3×C7 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×#11765499 | C3 | direct (N × H) |
| 3. C3×C7×C281 | C4 | semidirect |
| 5. C3×#11765499 | C7 | direct (N × H) |
| 6. C7×C281 | C3×C4 | semidirect |
| 8. #11765499 | C3×C7 | direct (N × H) |
| 9. C3×C281 | C4×C7 | semidirect |
| 11. C281 | C3×C4×C7 | semidirect |
| 15. C3×C7 | #11765499 | direct (N × H) |
| 18. C7 | C3×#11765499 | direct (N × H) |
| 21. C3 | C7×#11765499 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×D281 | 2 |
| C7×#11765499 | 3 |
| C3×#11765499 | 7 |
| C3×C4×C7 | 281 |