Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
224 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | Q82×C11 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10622708 | C2 | 1 | 3 | yes | maximal |
| 3 | #10622186 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #67040 | C22 | 1 | 1 | yes | characteristic |
| 5 | C11×C4⋊Q8 | — | 2 | 3 | no | — |
| 6 | C11×C4⋊Q8 | C22 | 1 | 3 | yes | — |
| 7 | C4×Q8×C11 | — | 2 | 3 | no | — |
| 8 | #66995 | — | 2 | 3 | no | — |
| 9 | #66900 | C22 | 1 | 3 | yes | — |
| 10 | #66869 | — | 2 | 3 | no | — |
| 11 | C2×Q8×C11 | — | 2 | 1 | no | — |
| 12 | C2×Q8×C11 | — | 2 | 1 | no | — |
| 13 | C2×Q8×C11 | D4 | 1 | 3 | yes | — |
| 14 | C2×Q8×C11 | C23 | 1 | 1 | yes | characteristic |
| 15 | #4343 | — | 4 | 1 | no | — |
| 16 | Q8×D11 | — | 4 | 1 | no | — |
| 17 | #4339 | — | 2 | 3 | no | — |
| 18 | C11×C4⋊C4 | — | 2 | 3 | no | — |
| 19 | C11×C4⋊C4 | — | 2 | 6 | no | — |
| 20 | C42×C11 | — | 2 | 3 | no | — |
| 21 | C42×C11 | D4 | 1 | 3 | yes | — |
| 22 | #4326 | — | 4 | 3 | no | — |
| 23 | #4325 | — | 4 | 3 | no | — |
| 24 | #4318 | — | 2 | 3 | no | — |
| 25 | #2205 | — | 11 | 1 | no | maximal, Sylow |
| 26 | Q8×C11 | — | 2 | 4 | no | — |
| 27 | Q8×C11 | — | 4 | 1 | no | — |
| 28 | Q8×C11 | — | 4 | 3 | no | — |
| 29 | Q8×C11 | — | 8 | 1 | no | — |
| 30 | C2×C4×C11 | — | 2 | 3 | no | — |
| 31 | C2×C4×C11 | — | 2 | 3 | no | — |
| 32 | C2×C4×C11 | C2×D4 | 1 | 3 | yes | — |
| 33 | C22⋊D11 | — | 4 | 1 | no | — |
| 34 | D44 | — | 2 | 3 | no | — |
| 35 | C4×D11 | — | 4 | 3 | no | — |
| 36 | Dic22 | — | 2 | 3 | no | — |
| 37 | C11⋊C8 | — | 4 | 3 | no | — |
| 38 | Q82 | D11 | 1 | 1 | yes | characteristic, complemented |
| 39 | #456 | — | 11 | 3 | no | — |
| 40 | #356 | — | 11 | 3 | no | — |
| 41 | C22×C11 | #120 | 1 | 1 | yes | characteristic |
| 42 | C2×D11 | — | 4 | 1 | no | — |
| 43 | C4×C11 | — | 2 | 6 | no | — |
| 44 | C4×C11 | — | 2 | 3 | no | — |
| 45 | C4×C11 | — | 4 | 3 | no | — |
| 46 | Dic11 | — | 4 | 1 | no | — |
| 47 | 2−1+4 | — | 11 | 1 | no | — |
| 48 | #137 | — | 22 | 3 | no | — |
| 49 | C4⋊Q8 | — | 2 | 3 | no | — |
| 50 | C4⋊Q8 | C2×D11 | 1 | 3 | yes | — |
| 51 | C4×Q8 | — | 2 | 3 | no | — |
| 52 | #104 | — | 22 | 3 | no | — |
| 53 | #101 | — | 11 | 3 | no | — |
| 54 | C2×C11 | — | 2 | 1 | no | — |
| 55 | C2×C11 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 56 | D11 | — | 8 | 1 | no | — |
| 57 | #41 | — | 22 | 3 | no | — |
| 58 | #41 | — | 44 | 1 | no | — |
| 59 | C2×Q8 | — | 2 | 1 | no | — |
| 60 | C2×Q8 | — | 2 | 1 | no | — |
| 61 | C2×Q8 | — | 44 | 1 | no | — |
| 62 | C2×Q8 | C22⋊D11 | 1 | 3 | yes | — |
| 63 | C2×Q8 | C22×D11 | 1 | 1 | yes | characteristic |
| 64 | Q16 | — | 44 | 3 | no | — |
| 65 | SD16 | — | 44 | 3 | no | — |
| 66 | M16 | — | 22 | 3 | no | — |
| 67 | C4⋊C4 | — | 2 | 3 | no | — |
| 68 | C4⋊C4 | — | 2 | 6 | no | — |
| 69 | C42 | — | 2 | 3 | no | — |
| 70 | C42 | C22⋊D11 | 1 | 3 | yes | — |
| 71 | C11 | #2205 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 72 | Q8 | — | 2 | 4 | no | — |
| 73 | Q8 | — | 4 | 1 | no | — |
| 74 | Q8 | — | 4 | 3 | no | — |
| 75 | Q8 | — | 8 | 1 | no | — |
| 76 | Q8 | — | 22 | 3 | no | — |
| 77 | D4 | — | 22 | 3 | no | — |
| 78 | D4 | — | 44 | 1 | no | — |
| 79 | C2×C4 | — | 2 | 3 | no | — |
| 80 | C2×C4 | — | 2 | 3 | no | — |
| 81 | C2×C4 | — | 44 | 3 | no | — |
| 82 | C2×C4 | C2×C22⋊D11 | 1 | 3 | yes | — |
| 83 | C8 | — | 44 | 3 | no | — |
| 84 | C22 | — | 44 | 1 | no | — |
| 85 | C22 | #67006 | 1 | 1 | yes | characteristic |
| 86 | C4 | — | 2 | 6 | no | — |
| 87 | C4 | — | 2 | 3 | no | — |
| 88 | C4 | — | 4 | 3 | no | — |
| 89 | C4 | — | 44 | 1 | no | — |
| 90 | C2 | — | 2 | 1 | no | — |
| 91 | C2 | — | 88 | 1 | no | — |
| 92 | C2 | #10622857 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q82×C11 | C2 | semidirect |
| 3. #10622186 | C2 | semidirect |
| 38. Q82 | D11 | semidirect |
| 71. C11 | #2205 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q82×C11 | 2 |
| #10622708 | 2 |
| #10622186 | 2 |
| #2205 | 11 |