Finite Group DatabasebetaFinite Group DatabasebetaOrder 36300.
68 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | (C11⋊D11)⋊(C52⋊C3) | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #27130990 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | C52⋊(C112⋊C3) | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C52×C11⋊D11 | C2×C3 | 1 | 1 | yes | characteristic |
| 5 | C52×C112 | C3×C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | #14559102 | — | 15 | 2 | no | — |
| 7 | #92150⋊C3 | — | 25 | 1 | no | maximal, Hall |
| 8 | C5×C11⋊D11 | — | 3 | 2 | no | — |
| 9 | (C11⋊D11)⋊C3 | — | 50 | 1 | no | — |
| 10 | C5×C112 | — | 3 | 2 | no | — |
| 11 | C52×D11 | — | 66 | 2 | no | — |
| 12 | #92150 | — | 25 | 1 | no | Hall |
| 13 | C112⋊C3 | — | 50 | 1 | no | Hall |
| 14 | #1039⋊C3 | — | 121 | 1 | no | maximal, Hall |
| 15 | C52×C11 | — | 6 | 2 | no | — |
| 16 | C11⋊D11 | (C5⋊D5)⋊C3 | 1 | 1 | yes | characteristic |
| 17 | C2×C52⋊C3 | — | 121 | 1 | no | — |
| 18 | C112 | #1039⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 19 | C5×D11 | — | 66 | 12 | no | — |
| 20 | #1039 | — | 121 | 1 | no | Hall |
| 21 | C52⋊C3 | — | 484 | 1 | no | Hall |
| 22 | C5×C11 | — | 6 | 12 | no | — |
| 23 | C2×C52 | — | 121 | 1 | no | — |
| 24 | C52 | #92150⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 25 | D11 | — | 66 | 2 | no | — |
| 26 | Dic5 | — | 1815 | 2 | no | — |
| 27 | C3×C4 | — | 3025 | 1 | no | Hall |
| 28 | C11 | — | 6 | 2 | no | — |
| 29 | C2×C5 | — | 363 | 2 | no | — |
| 30 | C2×C3 | — | 6050 | 1 | no | — |
| 31 | C5 | — | 3 | 2 | no | — |
| 32 | C4 | — | 3025 | 1 | no | Sylow |
| 33 | C3 | — | 12100 | 1 | no | Sylow |
| 34 | C2 | — | 121 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C112 | C3×C4 |
| prime radical | (C11⋊D11)⋊(C52⋊C3) | C2 |
| cosocle | C52×C11⋊D11 | C2×C3 |
| LCS | G ▷ C52×C112 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #27130990 | C3 | semidirect |
| 3. C52⋊(C112⋊C3) | C4 | semidirect |
| 5. C52×C112 | C3×C4 | semidirect |
| 18. C112 | #1039⋊C3 | semidirect |
| 24. C52 | #92150⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C11⋊D11)⋊(C52⋊C3) | 2 |
| #27130990 | 3 |
| #92150⋊C3 | 25 |
| #1039⋊C3 | 121 |