Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
451 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 451 conjugacy classes of subgroups — too many to draw. Only its 98 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 | #10592775 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×#5070 | C2 | 1 | 2 | yes | maximal |
| 3 | #10590309 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10590287 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C3⋊C82 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #71181 | — | 3 | 2 | no | maximal |
| 7 | C32×#127 | C22 | 1 | 1 | yes | characteristic |
| 8 | C2×#3754 | — | 2 | 2 | no | — |
| 9 | #64078 | C22 | 1 | 1 | yes | characteristic |
| 10 | C3×#869 | C22 | 1 | 2 | yes | — |
| 11 | C4×C3⋊(C3⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 12 | C3×#832 | — | 2 | 4 | no | — |
| 13 | C3×C4×C3⋊C8 | C22 | 1 | 2 | yes | — |
| 14 | #63574 | — | 2 | 2 | no | — |
| 15 | #63566 | — | 2 | 4 | no | — |
| 16 | C3×#486 | — | 3 | 2 | no | — |
| 17 | #5080 | — | 3 | 2 | no | — |
| 18 | #5079 | — | 3 | 2 | no | — |
| 19 | #5076 | — | 3 | 2 | no | — |
| 20 | #5076 | — | 6 | 1 | no | — |
| 21 | #5070 | D3 | 1 | 2 | yes | — |
| 22 | #4681 | — | 3 | 2 | no | — |
| 23 | C8×C3⋊C8 | — | 3 | 2 | no | — |
| 24 | C2×C32×D4 | — | 2 | 1 | no | — |
| 25 | C2×C32×D4 | — | 2 | 2 | no | — |
| 26 | C2×#634 | — | 2 | 1 | no | — |
| 27 | C2×C3×Dic6 | — | 2 | 2 | no | — |
| 28 | C32×C42 | C23 | 1 | 1 | yes | characteristic |
| 29 | #3754 | — | 4 | 4 | no | — |
| 30 | C4⋊(C3⋊Dic3) | — | 2 | 2 | no | — |
| 31 | C2×C3⋊(C3⋊C8) | D4 | 1 | 2 | yes | — |
| 32 | C3×C4⋊Dic3 | — | 2 | 2 | no | — |
| 33 | C3×C4⋊Dic3 | — | 2 | 2 | no | — |
| 34 | C2×C3×C3⋊C8 | D4 | 1 | 4 | yes | — |
| 35 | #1708 | — | 9 | 1 | no | Sylow |
| 36 | C3×C4⋊Q8 | — | 3 | 2 | no | — |
| 37 | C3×#127 | — | 2 | 1 | no | — |
| 38 | C3×#127 | C2×D3 | 1 | 2 | yes | — |
| 39 | C2×#214 | — | 6 | 4 | no | — |
| 40 | C2×#214 | — | 6 | 4 | no | — |
| 41 | #869 | — | 3 | 2 | no | — |
| 42 | #869 | — | 6 | 1 | no | — |
| 43 | #869 | C2×D3 | 1 | 2 | yes | — |
| 44 | C3×#102 | — | 6 | 4 | no | — |
| 45 | C3×C4×C8 | — | 3 | 2 | no | — |
| 46 | #835 | — | 6 | 4 | no | — |
| 47 | #832 | — | 2 | 4 | no | — |
| 48 | #816 | — | 6 | 4 | no | — |
| 49 | #808 | — | 6 | 4 | no | — |
| 50 | C4×C3⋊C8 | — | 3 | 2 | no | — |
| 51 | C4×C3⋊C8 | — | 6 | 1 | no | — |
| 52 | C4×C3⋊C8 | C2×D3 | 1 | 2 | yes | — |
| 53 | C23×C32 | — | 4 | 1 | no | — |
| 54 | C32×D4 | — | 4 | 2 | no | — |
| 55 | C32×D4 | — | 4 | 4 | no | — |
| 56 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 57 | C2×C32×C4 | C2×D4 | 1 | 2 | yes | — |
| 58 | C2×C3⋊Dic3 | — | 4 | 1 | no | — |
| 59 | #634 | — | 4 | 2 | no | — |
| 60 | C2×C3×Dic3 | — | 4 | 2 | no | — |
| 61 | C3×Dic6 | — | 4 | 4 | no | — |
| 62 | C3⋊(C3⋊C8) | SD16 | 1 | 4 | yes | — |
| 63 | C3×C3⋊C8 | — | 2 | 4 | no | — |
| 64 | #498 | — | 9 | 1 | no | — |
| 65 | #492 | — | 9 | 1 | no | — |
| 66 | #487 | — | 9 | 2 | no | — |
| 67 | #486 | — | 3 | 2 | no | — |
| 68 | C82 | — | 9 | 1 | no | — |
| 69 | C2×C3×Q8 | — | 6 | 2 | no | — |
| 70 | C2×C3×D4 | — | 2 | 2 | no | — |
| 71 | C2×C3×D4 | — | 2 | 2 | no | — |
| 72 | C2×C3×D4 | — | 2 | 2 | no | — |
| 73 | C2×C3×D4 | — | 2 | 2 | no | — |
| 74 | C2×C3×D4 | — | 4 | 2 | no | — |
| 75 | C2×Dic6 | — | 2 | 2 | no | — |
| 76 | C2×Dic6 | — | 6 | 2 | no | — |
| 77 | C2×Dic6 | — | 6 | 2 | no | — |
| 78 | C2×C3×C8 | — | 3 | 4 | no | — |
| 79 | C3×C4⋊C4 | — | 6 | 2 | no | — |
| 80 | C3×C4⋊C4 | — | 6 | 2 | no | — |
| 81 | C3×C42 | — | 2 | 1 | no | — |
| 82 | C3×C42 | C22×D3 | 1 | 2 | yes | — |
| 83 | #214 | — | 12 | 8 | no | — |
| 84 | #214 | — | 12 | 8 | no | — |
| 85 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 86 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 87 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 88 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 89 | C4⋊Dic3 | — | 12 | 2 | no | — |
| 90 | C2×C3⋊C8 | — | 3 | 4 | no | — |
| 91 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 92 | C2×C3⋊C8 | #67 | 1 | 4 | yes | — |
| 93 | C22×C32 | — | 8 | 1 | no | — |
| 94 | C22×C32 | — | 8 | 2 | no | — |
| 95 | C22×C32 | #127 | 1 | 1 | yes | characteristic |
| 96 | C32×C4 | C2×SD16 | 1 | 2 | yes | — |
| 97 | C32×C4 | #135 | 1 | 4 | yes | — |
| 98 | C3⋊Dic3 | — | 8 | 1 | no | — |
| 99 | C3×Dic3 | — | 8 | 2 | no | — |
| 100 | C2×SD16 | — | 18 | 2 | no | — |
| 101 | C4⋊Q8 | — | 3 | 2 | no | — |
| 102 | C4⋊Q8 | — | 9 | 1 | no | — |
| 103 | #127 | D32 | 1 | 1 | yes | characteristic |
| 104 | #106 | — | 18 | 2 | no | — |
| 105 | #103 | — | 18 | 4 | no | — |
| 106 | #102 | — | 6 | 4 | no | — |
| 107 | C4×C8 | — | 3 | 2 | no | — |
| 108 | C4×C8 | — | 9 | 1 | no | — |
| 109 | C23×C3 | — | 4 | 2 | no | — |
| 110 | C23×C3 | — | 4 | 2 | no | — |
| 111 | C3×Q8 | — | 12 | 4 | no | — |
| 112 | C3×D4 | — | 4 | 4 | no | — |
| 113 | C3×D4 | — | 4 | 4 | no | — |
| 114 | C3×D4 | — | 4 | 4 | no | — |
| 115 | C3×D4 | — | 4 | 4 | no | — |
| 116 | C3×D4 | — | 8 | 4 | no | — |
| 117 | C2×C3×C4 | — | 2 | 2 | no | — |
| 118 | C2×C3×C4 | — | 2 | 1 | no | — |
| 119 | C2×C3×C4 | — | 12 | 2 | no | — |
| 120 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 121 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 122 | C2×C3×C4 | C2×#67 | 1 | 2 | yes | — |
| 123 | C2×Dic3 | — | 4 | 2 | no | — |
| 124 | C2×Dic3 | — | 12 | 2 | no | — |
| 125 | C2×Dic3 | — | 12 | 2 | no | — |
| 126 | Dic6 | — | 4 | 4 | no | — |
| 127 | Dic6 | — | 12 | 4 | no | — |
| 128 | Dic6 | — | 12 | 4 | no | — |
| 129 | C3×C8 | — | 6 | 4 | no | — |
| 130 | C3⋊C8 | — | 2 | 4 | no | — |
| 131 | C3⋊C8 | — | 3 | 8 | no | — |
| 132 | C3⋊C8 | — | 6 | 4 | no | — |
| 133 | C2×C32 | — | 16 | 1 | no | — |
| 134 | C2×C32 | #492 | 1 | 1 | yes | characteristic |
| 135 | C2×C32 | #495 | 1 | 2 | yes | — |
| 136 | C2×Q8 | — | 6 | 2 | no | — |
| 137 | C2×Q8 | — | 18 | 1 | no | — |
| 138 | C2×D4 | — | 2 | 2 | no | — |
| 139 | C2×D4 | — | 2 | 1 | no | — |
| 140 | SD16 | — | 36 | 4 | no | — |
| 141 | C2×C8 | — | 3 | 4 | no | — |
| 142 | C2×C8 | — | 9 | 2 | no | — |
| 143 | C4⋊C4 | — | 6 | 2 | no | — |
| 144 | C4⋊C4 | — | 6 | 2 | no | — |
| 145 | C4⋊C4 | — | 18 | 2 | no | — |
| 146 | C42 | C2×D32 | 1 | 1 | yes | characteristic |
| 147 | C22×C3 | — | 2 | 1 | no | — |
| 148 | C22×C3 | — | 8 | 2 | no | — |
| 149 | C22×C3 | — | 8 | 4 | no | — |
| 150 | C22×C3 | — | 8 | 2 | no | — |
| 151 | C22×C3 | — | 8 | 2 | no | — |
| 152 | C22×C3 | — | 8 | 2 | no | — |
| 153 | C22×C3 | #940 | 1 | 2 | yes | — |
| 154 | C3×C4 | — | 2 | 2 | no | — |
| 155 | C3×C4 | — | 2 | 4 | no | — |
| 156 | C3×C4 | — | 24 | 2 | no | — |
| 157 | C3×C4 | #912 | 1 | 4 | yes | — |
| 158 | C3×C4 | D3×SD16 | 1 | 4 | yes | — |
| 159 | C3×C4 | #950 | 1 | 4 | yes | — |
| 160 | Dic3 | — | 8 | 2 | no | — |
| 161 | Dic3 | — | 24 | 2 | no | — |
| 162 | Dic3 | — | 24 | 2 | no | — |
| 163 | C32 | #1708 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 164 | C23 | — | 4 | 1 | no | — |
| 165 | Q8 | — | 12 | 4 | no | — |
| 166 | Q8 | — | 36 | 2 | no | — |
| 167 | D4 | — | 4 | 2 | no | — |
| 168 | D4 | — | 4 | 4 | no | — |
| 169 | C2×C4 | — | 12 | 2 | no | — |
| 170 | C2×C4 | — | 36 | 1 | no | — |
| 171 | C2×C4 | D3×#67 | 1 | 2 | yes | — |
| 172 | C2×C4 | #3811 | 1 | 1 | yes | characteristic |
| 173 | C8 | — | 6 | 4 | no | — |
| 174 | C8 | — | 9 | 4 | no | — |
| 175 | C2×C3 | — | 2 | 1 | no | — |
| 176 | C2×C3 | — | 2 | 2 | no | — |
| 177 | C2×C3 | — | 16 | 2 | no | — |
| 178 | C2×C3 | — | 16 | 2 | no | — |
| 179 | C2×C3 | #5059 | 1 | 2 | yes | — |
| 180 | C2×C3 | #5155 | 1 | 2 | yes | — |
| 181 | C2×C3 | #5175 | 1 | 2 | yes | — |
| 182 | C22 | — | 8 | 1 | no | — |
| 183 | C22 | — | 8 | 2 | no | — |
| 184 | C22 | #63979 | 1 | 1 | yes | characteristic |
| 185 | C4 | — | 24 | 2 | no | — |
| 186 | C4 | — | 72 | 1 | no | — |
| 187 | C4 | #63930 | 1 | 2 | yes | — |
| 188 | C4 | #63933 | 1 | 4 | yes | — |
| 189 | C3 | — | 2 | 1 | no | — |
| 190 | C3 | #71181 | 1 | 2 | yes | complemented |
| 191 | C2 | — | 16 | 1 | no | — |
| 192 | C2 | #10591470 | 1 | 2 | yes | — |
| 193 | C2 | #10591492 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #10590309 | C2 | semidirect |
| 4. #10590287 | C2 | semidirect |
| 5. C3⋊C82 | C2 | semidirect |
| 163. C32 | #1708 | semidirect |
| 190. C3 | #71181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592775 | 2 |
| C3×#5070 | 2 |
| #10590309 | 2 |
| #10590287 | 2 |
| C3⋊C82 | 2 |
| #71181 | 3 |