Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
206 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | AGL(1,𝔽9)⋊Q8 | C2 | 1 | 2 | yes | maximal |
| 2 | #10596404 | C2 | 1 | 2 | yes | maximal |
| 3 | #10593535 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #10593295 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #10593251 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | C4⋊PSU(3,𝔽2) | C22 | 1 | 2 | yes | — |
| 7 | #64228 | — | 2 | 1 | no | — |
| 8 | #64222 | C22 | 1 | 1 | yes | characteristic |
| 9 | #64222 | C22 | 1 | 1 | yes | characteristic |
| 10 | C4×AGL(1,𝔽9) | C22 | 1 | 2 | yes | — |
| 11 | AGL(1,𝔽9)⋊C4 | — | 2 | 4 | no | — |
| 12 | PSU(3,𝔽2)⋊C4 | — | 2 | 4 | no | — |
| 13 | #63802 | — | 2 | 1 | no | — |
| 14 | #63768 | — | 2 | 1 | no | — |
| 15 | C8×#157 | C22 | 1 | 1 | yes | characteristic |
| 16 | #63745 | — | 2 | 1 | no | — |
| 17 | C2×PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 18 | C2×AGL(1,𝔽9) | D4 | 1 | 4 | yes | — |
| 19 | #3797 | — | 2 | 1 | no | — |
| 20 | #3797 | — | 2 | 1 | no | — |
| 21 | C4⋊#157 | — | 2 | 2 | no | — |
| 22 | C4×#157 | C23 | 1 | 1 | yes | characteristic |
| 23 | #3787 | D4 | 1 | 1 | yes | characteristic |
| 24 | #3777 | — | 2 | 2 | no | — |
| 25 | #3776 | — | 4 | 2 | no | — |
| 26 | #3773 | — | 2 | 2 | no | — |
| 27 | #3773 | — | 2 | 2 | no | — |
| 28 | C8×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 29 | C3×Dic12 | — | 4 | 1 | no | — |
| 30 | #3718 | — | 4 | 1 | no | — |
| 31 | #1716 | — | 9 | 1 | no | maximal, Sylow |
| 32 | D3×Q16 | — | 12 | 1 | no | — |
| 33 | C2×#157 | — | 4 | 2 | no | — |
| 34 | C2×#157 | C2×D4 | 1 | 2 | yes | — |
| 35 | PSU(3,𝔽2) | — | 4 | 4 | no | — |
| 36 | AGL(1,𝔽9) | — | 2 | 4 | no | — |
| 37 | C4×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 38 | C3×Dic6 | — | 4 | 1 | no | — |
| 39 | C3×Dic6 | — | 4 | 1 | no | — |
| 40 | #627 | — | 4 | 1 | no | — |
| 41 | #627 | — | 4 | 1 | no | — |
| 42 | #624 | — | 4 | 1 | no | — |
| 43 | #624 | — | 4 | 1 | no | — |
| 44 | #622 | SD16 | 1 | 2 | yes | — |
| 45 | C32×C8 | SD16 | 1 | 1 | yes | characteristic |
| 46 | C3⋊(C3⋊C8) | SD16 | 1 | 1 | yes | characteristic |
| 47 | #498 | — | 9 | 2 | no | — |
| 48 | #498 | — | 9 | 1 | no | — |
| 49 | #494 | — | 9 | 1 | no | — |
| 50 | #487 | — | 9 | 2 | no | — |
| 51 | #322 | — | 9 | 1 | no | — |
| 52 | D3×Q8 | — | 12 | 1 | no | — |
| 53 | D3×Q8 | — | 12 | 1 | no | — |
| 54 | C3×Q16 | — | 12 | 1 | no | — |
| 55 | #216 | — | 12 | 1 | no | — |
| 56 | #216 | — | 12 | 1 | no | — |
| 57 | Dic12 | — | 4 | 1 | no | — |
| 58 | D3×C8 | — | 12 | 1 | no | — |
| 59 | C2×C3⋊D3 | #127 | 1 | 1 | yes | characteristic |
| 60 | #157 | — | 8 | 2 | no | — |
| 61 | #157 | #137 | 1 | 4 | yes | — |
| 62 | C32×C4 | C2×SD16 | 1 | 1 | yes | characteristic |
| 63 | C3⋊Dic3 | C2×SD16 | 1 | 1 | yes | characteristic |
| 64 | C3×Dic3 | — | 8 | 1 | no | — |
| 65 | C3×Dic3 | — | 8 | 1 | no | — |
| 66 | C2×Q16 | — | 18 | 1 | no | — |
| 67 | C2×Q16 | — | 18 | 1 | no | — |
| 68 | C4⋊Q8 | — | 9 | 1 | no | — |
| 69 | C4⋊Q8 | — | 9 | 1 | no | — |
| 70 | C4⋊Q8 | — | 9 | 2 | no | — |
| 71 | #106 | — | 18 | 1 | no | — |
| 72 | #106 | — | 18 | 1 | no | — |
| 73 | #106 | — | 18 | 4 | no | — |
| 74 | #103 | — | 18 | 4 | no | — |
| 75 | C4×C8 | — | 9 | 1 | no | — |
| 76 | C4×C8 | — | 9 | 2 | no | — |
| 77 | C3×Q8 | — | 12 | 1 | no | — |
| 78 | C3×Q8 | — | 12 | 1 | no | — |
| 79 | C4×D3 | — | 12 | 1 | no | — |
| 80 | C4×D3 | — | 24 | 1 | no | — |
| 81 | C4×D3 | — | 24 | 1 | no | — |
| 82 | Dic6 | — | 4 | 1 | no | — |
| 83 | Dic6 | — | 4 | 1 | no | — |
| 84 | Dic6 | — | 24 | 1 | no | — |
| 85 | Dic6 | — | 24 | 1 | no | — |
| 86 | C3×C8 | — | 4 | 1 | no | — |
| 87 | C3⋊C8 | — | 12 | 1 | no | — |
| 88 | C2×C32 | #492 | 1 | 1 | yes | characteristic |
| 89 | C3⋊D3 | #497 | 1 | 2 | yes | — |
| 90 | C2×Q8 | — | 18 | 1 | no | — |
| 91 | C2×Q8 | — | 18 | 1 | no | — |
| 92 | C2×Q8 | — | 18 | 2 | no | — |
| 93 | Q16 | — | 12 | 1 | no | — |
| 94 | Q16 | — | 36 | 1 | no | — |
| 95 | Q16 | — | 36 | 2 | no | — |
| 96 | C2×C8 | — | 9 | 1 | no | — |
| 97 | C2×C8 | — | 9 | 1 | no | — |
| 98 | C2×C8 | — | 9 | 4 | no | — |
| 99 | C4⋊C4 | — | 18 | 2 | no | — |
| 100 | C4⋊C4 | — | 18 | 2 | no | — |
| 101 | C4⋊C4 | — | 18 | 2 | no | — |
| 102 | C4⋊C4 | — | 18 | 2 | no | — |
| 103 | C42 | — | 9 | 1 | no | — |
| 104 | C2×D3 | — | 12 | 1 | no | — |
| 105 | C3×C4 | — | 4 | 1 | no | — |
| 106 | C3×C4 | — | 24 | 1 | no | — |
| 107 | C3×C4 | — | 24 | 1 | no | — |
| 108 | Dic3 | — | 8 | 1 | no | — |
| 109 | Dic3 | — | 8 | 1 | no | — |
| 110 | Dic3 | — | 12 | 1 | no | — |
| 111 | C32 | #1716 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 112 | Q8 | — | 12 | 1 | no | — |
| 113 | Q8 | — | 12 | 1 | no | — |
| 114 | Q8 | — | 36 | 1 | no | — |
| 115 | Q8 | — | 36 | 1 | no | — |
| 116 | Q8 | — | 36 | 4 | no | — |
| 117 | C2×C4 | — | 9 | 2 | no | — |
| 118 | C2×C4 | — | 9 | 1 | no | — |
| 119 | C2×C4 | — | 36 | 1 | no | — |
| 120 | C2×C4 | — | 36 | 1 | no | — |
| 121 | C2×C4 | — | 36 | 2 | no | — |
| 122 | C8 | — | 9 | 2 | no | — |
| 123 | C8 | — | 9 | 1 | no | — |
| 124 | C8 | — | 18 | 4 | no | — |
| 125 | C8 | AΓL(1,𝔽9) | 1 | 1 | yes | characteristic |
| 126 | C2×C3 | — | 4 | 1 | no | — |
| 127 | D3 | — | 12 | 2 | no | — |
| 128 | C22 | — | 9 | 1 | no | — |
| 129 | C4 | — | 9 | 4 | no | — |
| 130 | C4 | — | 9 | 1 | no | — |
| 131 | C4 | — | 24 | 1 | no | — |
| 132 | C4 | — | 24 | 1 | no | — |
| 133 | C4 | — | 72 | 2 | no | — |
| 134 | C4 | C2×AΓL(1,𝔽9) | 1 | 1 | yes | characteristic |
| 135 | C3 | — | 4 | 1 | no | — |
| 136 | C2 | — | 9 | 2 | no | — |
| 137 | C2 | #10596408 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 111. C32 | #1716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| AGL(1,𝔽9)⋊Q8 | 2 |
| #10596404 | 2 |
| #10593535 | 2 |
| #10593295 | 2 |
| #10593251 | 2 |
| #1716 | 9 |