Finite Group DatabasebetaFinite Group DatabasebetaOrder 33396.
40 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C23×C112⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C11×Dic253 | — | 3 | 1 | no | maximal, Hall |
| 3 | C23×C112⋊C3 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C2×C112×C23 | D3 | 1 | 1 | yes | characteristic |
| 5 | C112×C23 | Dic3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | #13089712 | — | 23 | 1 | no | maximal, Hall |
| 7 | Dic253 | — | 3 | 1 | no | — |
| 8 | C11×Dic23 | — | 33 | 1 | no | — |
| 9 | C2×C112⋊C3 | D23 | 1 | 1 | yes | characteristic |
| 10 | C2×C11×C23 | — | 3 | 1 | no | — |
| 11 | C2×C11×C23 | — | 3 | 1 | no | — |
| 12 | C2×C11×C23 | — | 6 | 1 | no | — |
| 13 | C11×Dic11 | — | 69 | 1 | no | Hall |
| 14 | C112⋊C3 | Dic23 | 1 | 1 | yes | characteristic, complemented, Hall |
| 15 | Dic69 | — | 121 | 1 | no | maximal, Hall |
| 16 | C11×C23 | — | 3 | 1 | no | — |
| 17 | C11×C23 | — | 3 | 1 | no | — |
| 18 | C11×C23 | — | 6 | 1 | no | — |
| 19 | C2×C112 | D69 | 1 | 1 | yes | characteristic |
| 20 | C2×C3×C23 | — | 121 | 1 | no | — |
| 21 | C112 | Dic69 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 22 | Dic23 | — | 33 | 1 | no | Hall |
| 23 | C3×C23 | — | 121 | 1 | no | Hall |
| 24 | C2×C23 | #10624391 | 1 | 1 | yes | characteristic |
| 25 | C4×C11 | — | 759 | 1 | no | — |
| 26 | Dic11 | — | 69 | 1 | no | — |
| 27 | C23 | #13089712 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 28 | C2×C11 | — | 3 | 1 | no | — |
| 29 | C2×C11 | — | 3 | 1 | no | — |
| 30 | C2×C11 | — | 6 | 1 | no | — |
| 31 | Dic3 | — | 2783 | 1 | no | Hall |
| 32 | C11 | — | 3 | 1 | no | — |
| 33 | C11 | — | 3 | 1 | no | — |
| 34 | C11 | — | 6 | 1 | no | — |
| 35 | C2×C3 | — | 121 | 1 | no | — |
| 36 | C4 | — | 759 | 1 | no | Sylow |
| 37 | C3 | — | 121 | 1 | no | Sylow |
| 38 | C2 | C23⋊#10624391 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C23⋊#10624391 |
| commutator, hypocenter | C23×C112⋊C3 | C4 |
| Fitting, socle | C2×C112×C23 | D3 |
| prime radical, cosocle | C2×C23×C112⋊C3 | C2 |
| LCS | G ▷ C23×C112⋊C3 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C23×C112⋊C3 | C4 | semidirect |
| 5. C112×C23 | Dic3 | semidirect |
| 14. C112⋊C3 | Dic23 | semidirect |
| 21. C112 | Dic69 | semidirect |
| 27. C23 | #13089712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C23×C112⋊C3 | 2 |
| C11×Dic253 | 3 |
| #13089712 | 23 |
| Dic69 | 121 |