Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2058 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×2−1+6 | C3 | 1 | 1 | yes | maximal, characteristic |
| 2 | #63703 | — | 4 | 12 | no | maximal |
| 3 | C22⋊(Q8⋊C9) | — | 4 | 9 | no | maximal |
| 4 | C3×#585 | — | 3 | 12 | no | — |
| 5 | C2×C3×2−1+4 | — | 3 | 9 | no | — |
| 6 | 2−1+6 | C9 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 7 | C3×2−1+4 | — | 3 | 72 | no | — |
| 8 | C3×H(5,𝔽2) | — | 3 | 36 | no | — |
| 9 | C3×H(5,𝔽2) | A4 | 1 | 12 | yes | — |
| 10 | C2×C3×#41 | — | 3 | 36 | no | — |
| 11 | C2×C3×#41 | — | 3 | 54 | no | — |
| 12 | C22×C3×Q8 | — | 3 | 12 | no | — |
| 13 | C22×C3×Q8 | A4 | 1 | 9 | yes | — |
| 14 | C2×C22⋊C9 | — | 16 | 9 | no | — |
| 15 | Q8⋊C9 | — | 16 | 12 | no | — |
| 16 | #585 | — | 3 | 12 | no | — |
| 17 | C2×2−1+4 | — | 3 | 9 | no | — |
| 18 | C3×#41 | — | 3 | 216 | no | — |
| 19 | C3×#41 | — | 3 | 24 | no | — |
| 20 | C2×C3×Q8 | — | 3 | 54 | no | — |
| 21 | C2×C3×Q8 | — | 3 | 36 | no | — |
| 22 | C2×C3×D4 | — | 3 | 54 | no | — |
| 23 | C2×C3×D4 | — | 3 | 36 | no | — |
| 24 | C22×C3×C4 | — | 3 | 36 | no | — |
| 25 | C22×C3×C4 | — | 3 | 9 | no | — |
| 26 | C22⋊C9 | — | 16 | 9 | no | — |
| 27 | 2−1+4 | — | 3 | 72 | no | — |
| 28 | H(5,𝔽2) | — | 3 | 36 | no | — |
| 29 | H(5,𝔽2) | C22⋊C9 | 1 | 12 | yes | complemented |
| 30 | C2×#41 | — | 3 | 36 | no | — |
| 31 | C2×#41 | — | 3 | 54 | no | — |
| 32 | C22×Q8 | — | 3 | 12 | no | — |
| 33 | C22×Q8 | C22⋊C9 | 1 | 9 | yes | complemented |
| 34 | C23×C3 | — | 3 | 12 | no | — |
| 35 | C23×C3 | C22⋊A4 | 1 | 9 | yes | — |
| 36 | C3×Q8 | — | 3 | 36 | no | — |
| 37 | C3×Q8 | C22⋊A4 | 1 | 12 | yes | — |
| 38 | C3×D4 | — | 3 | 72 | no | — |
| 39 | C2×C3×C4 | — | 3 | 36 | no | — |
| 40 | C2×C3×C4 | — | 3 | 54 | no | — |
| 41 | C2×C9 | — | 64 | 1 | no | — |
| 42 | #41 | — | 3 | 216 | no | — |
| 43 | #41 | — | 3 | 24 | no | — |
| 44 | C2×Q8 | — | 3 | 54 | no | — |
| 45 | C2×Q8 | — | 3 | 36 | no | — |
| 46 | C2×D4 | — | 3 | 54 | no | — |
| 47 | C2×D4 | — | 3 | 36 | no | — |
| 48 | C22×C4 | — | 3 | 36 | no | — |
| 49 | C22×C4 | — | 3 | 9 | no | — |
| 50 | C22×C3 | — | 3 | 9 | no | — |
| 51 | C22×C3 | — | 4 | 9 | no | — |
| 52 | C22×C3 | — | 12 | 12 | no | — |
| 53 | C3×C4 | — | 3 | 12 | no | — |
| 54 | C9 | — | 64 | 1 | no | Sylow |
| 55 | C23 | — | 3 | 12 | no | — |
| 56 | C23 | C22⋊(C22⋊C9) | 1 | 9 | yes | — |
| 57 | Q8 | — | 3 | 36 | no | — |
| 58 | Q8 | C22⋊(C22⋊C9) | 1 | 12 | yes | — |
| 59 | D4 | — | 3 | 72 | no | — |
| 60 | C2×C4 | — | 3 | 36 | no | — |
| 61 | C2×C4 | — | 3 | 54 | no | — |
| 62 | C2×C3 | — | 6 | 9 | no | — |
| 63 | C2×C3 | C22⋊(C22⋊A4) | 1 | 1 | yes | characteristic |
| 64 | C22 | — | 3 | 9 | no | — |
| 65 | C22 | — | 4 | 9 | no | — |
| 66 | C22 | — | 12 | 12 | no | — |
| 67 | C4 | — | 3 | 12 | no | — |
| 68 | C3 | #87551 | 1 | 1 | yes | characteristic |
| 69 | C2 | — | 6 | 9 | no | — |
| 70 | C2 | C22⋊(C22⋊(C22⋊C9)) | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C2×C3 | C22⋊(C22⋊A4) |
| commutator, hypocenter | 2−1+6 | C9 |
| Fitting, prime radical, cosocle | C3×2−1+6 | C3 |
| LCS | G ▷ 2−1+6 | |
| UCS | C1 ◁ C2×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. 2−1+6 | C9 | semidirect |
| 29. H(5,𝔽2) | C22⋊C9 | semidirect |
| 33. C22×Q8 | C22⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×2−1+6 | 3 |
| #63703 | 4 |
| C22⋊(Q8⋊C9) | 4 |