Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1076 conjugacy classes of subgroups.
The subgroup lattice has 633 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10596189 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10593906 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#5073 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#5072 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10591486 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10591484 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10591435 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10591433 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10590355 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C4×#3714 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #10590254 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #81778 | — | 3 | 1 | no | maximal |
| 13 | #80324 | — | 3 | 1 | no | maximal |
| 14 | C2×#3830 | — | 2 | 1 | no | — |
| 15 | C2×#3795 | — | 2 | 1 | no | — |
| 16 | C32×#127 | C22 | 1 | 1 | yes | characteristic |
| 17 | #64149 | C22 | 1 | 2 | yes | — |
| 18 | #64148 | — | 2 | 2 | no | — |
| 19 | #64147 | — | 2 | 1 | no | — |
| 20 | D4×C3⋊Dic3 | C22 | 1 | 2 | yes | — |
| 21 | C4×C4⋊(C3⋊D3) | C22 | 1 | 1 | yes | characteristic |
| 22 | C4×#634 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×C3×#213 | C22 | 1 | 2 | yes | — |
| 24 | C2×C3×#213 | C22 | 1 | 2 | yes | — |
| 25 | C2×C3×#213 | C22 | 1 | 2 | yes | — |
| 26 | C3×#874 | C22 | 1 | 1 | yes | characteristic |
| 27 | C3×C4×D12 | C22 | 1 | 1 | yes | characteristic |
| 28 | #63914 | C22 | 1 | 2 | yes | — |
| 29 | #63908 | — | 2 | 1 | no | — |
| 30 | #63898 | C22 | 1 | 2 | yes | — |
| 31 | #63885 | — | 2 | 2 | no | — |
| 32 | C2×#3714 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×#3714 | C22 | 1 | 2 | yes | — |
| 34 | C3×#832 | C22 | 1 | 2 | yes | — |
| 35 | C3×C4⋊(C3⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 36 | C3×C4×C3⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 37 | #63575 | C22 | 1 | 1 | yes | characteristic |
| 38 | #63572 | C22 | 1 | 2 | yes | — |
| 39 | #63564 | C22 | 1 | 1 | yes | characteristic |
| 40 | #63563 | C22 | 1 | 1 | yes | characteristic |
| 41 | #63563 | C22 | 1 | 2 | yes | — |
| 42 | #63553 | C22 | 1 | 2 | yes | — |
| 43 | #5718 | — | 3 | 1 | no | — |
| 44 | #5718 | — | 3 | 1 | no | — |
| 45 | #5718 | — | 3 | 1 | no | — |
| 46 | #5718 | — | 6 | 1 | no | — |
| 47 | #5553 | — | 3 | 1 | no | — |
| 48 | C3×#493 | — | 3 | 1 | no | — |
| 49 | C3×#459 | — | 3 | 1 | no | — |
| 50 | #5151 | — | 3 | 2 | no | — |
| 51 | #5151 | — | 3 | 2 | no | — |
| 52 | #5150 | — | 3 | 2 | no | — |
| 53 | #5150 | — | 3 | 2 | no | — |
| 54 | #5150 | — | 3 | 2 | no | — |
| 55 | Dic3×D8 | — | 3 | 2 | no | — |
| 56 | #5073 | D3 | 1 | 1 | yes | characteristic, complemented |
| 57 | #5072 | — | 3 | 1 | no | — |
| 58 | #5072 | D3 | 1 | 1 | yes | characteristic, complemented |
| 59 | C4×#213 | — | 3 | 1 | no | — |
| 60 | #4843 | — | 3 | 1 | no | — |
| 61 | #4830 | — | 3 | 1 | no | — |
| 62 | #4786 | — | 3 | 2 | no | — |
| 63 | #4756 | — | 3 | 2 | no | — |
| 64 | C4×D24 | — | 3 | 1 | no | — |
| 65 | C8×Dic6 | — | 3 | 1 | no | — |
| 66 | C2×C32×D4 | — | 2 | 1 | no | — |
| 67 | C2×C32×D4 | — | 2 | 1 | no | — |
| 68 | C2×C32×D4 | C23 | 1 | 2 | yes | — |
| 69 | C2×#638 | — | 2 | 2 | no | — |
| 70 | C2×#638 | — | 2 | 2 | no | — |
| 71 | C22×C3⋊Dic3 | — | 2 | 2 | no | — |
| 72 | #3830 | — | 4 | 4 | no | — |
| 73 | C2×C4⋊(C3⋊D3) | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 75 | C2×#634 | D4 | 1 | 1 | yes | characteristic |
| 76 | C2×C3×D12 | — | 2 | 1 | no | — |
| 77 | C2×C3×D12 | — | 2 | 1 | no | — |
| 78 | C2×C3×D12 | C23 | 1 | 2 | yes | — |
| 79 | C2×C3×D12 | C23 | 1 | 1 | yes | characteristic |
| 80 | C2×C3×C4×D3 | — | 2 | 1 | no | — |
| 81 | C2×#625 | — | 2 | 2 | no | — |
| 82 | C2×#625 | — | 2 | 2 | no | — |
| 83 | C2×D3×Dic3 | — | 2 | 2 | no | — |
| 84 | #3795 | — | 4 | 4 | no | — |
| 85 | C32×C42 | C23 | 1 | 1 | yes | characteristic |
| 86 | #3757 | — | 2 | 2 | no | — |
| 87 | #3752 | — | 2 | 1 | no | — |
| 88 | C4⋊(C3⋊Dic3) | D4 | 1 | 1 | yes | characteristic |
| 89 | C4⋊(C3⋊Dic3) | C23 | 1 | 1 | yes | characteristic |
| 90 | #3750 | D4 | 1 | 2 | yes | — |
| 91 | C4×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 92 | C3×#213 | — | 2 | 4 | no | — |
| 93 | C3×#213 | — | 4 | 2 | no | — |
| 94 | C3×#213 | — | 4 | 2 | no | — |
| 95 | C3×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 96 | C3×C4⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 97 | C2×C3×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 98 | C2×C3×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 99 | C2×C3×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 100 | (C2×D3)⋊Dic3 | — | 2 | 2 | no | — |
| 101 | #3714 | — | 2 | 2 | no | — |
| 102 | #3714 | — | 4 | 2 | no | — |
| 103 | #3391 | — | 9 | 1 | no | Sylow |
| 104 | C2×#237 | — | 6 | 1 | no | — |
| 105 | C2×#237 | — | 6 | 1 | no | — |
| 106 | C2×#237 | — | 6 | 1 | no | — |
| 107 | C2×#237 | — | 6 | 2 | no | — |
| 108 | C2×#235 | — | 6 | 1 | no | — |
| 109 | C2×C3×D8 | — | 3 | 2 | no | — |
| 110 | C2×C3×D8 | — | 3 | 2 | no | — |
| 111 | C2×C3×D8 | — | 3 | 2 | no | — |
| 112 | C3×#127 | — | 2 | 1 | no | — |
| 113 | C3×#127 | — | 3 | 1 | no | — |
| 114 | C3×#127 | C2×D3 | 1 | 1 | yes | characteristic |
| 115 | C3×#127 | C2×D3 | 1 | 1 | yes | characteristic |
| 116 | C3×C4×D4 | — | 3 | 1 | no | — |
| 117 | #940 | — | 3 | 2 | no | — |
| 118 | #940 | — | 3 | 2 | no | — |
| 119 | #940 | — | 3 | 2 | no | — |
| 120 | #940 | — | 3 | 2 | no | — |
| 121 | #940 | — | 6 | 2 | no | — |
| 122 | #939 | — | 6 | 2 | no | — |
| 123 | #939 | — | 6 | 2 | no | — |
| 124 | #939 | — | 6 | 2 | no | — |
| 125 | #939 | — | 6 | 4 | no | — |
| 126 | #938 | — | 6 | 1 | no | — |
| 127 | #938 | — | 6 | 1 | no | — |
| 128 | #938 | — | 6 | 1 | no | — |
| 129 | #938 | — | 6 | 2 | no | — |
| 130 | D4×Dic3 | — | 3 | 2 | no | — |
| 131 | D4×Dic3 | — | 3 | 2 | no | — |
| 132 | D4×Dic3 | — | 3 | 2 | no | — |
| 133 | D4×Dic3 | — | 6 | 2 | no | — |
| 134 | C2×#213 | — | 3 | 1 | no | — |
| 135 | C2×#213 | — | 3 | 2 | no | — |
| 136 | C2×#213 | C2×D3 | 1 | 2 | yes | — |
| 137 | C2×#213 | C2×D3 | 1 | 2 | yes | — |
| 138 | C2×#213 | C2×D3 | 1 | 2 | yes | — |
| 139 | #930 | — | 6 | 1 | no | — |
| 140 | C2×D24 | — | 3 | 1 | no | — |
| 141 | C2×D24 | — | 3 | 2 | no | — |
| 142 | #893 | — | 3 | 2 | no | — |
| 143 | #884 | — | 6 | 2 | no | — |
| 144 | #874 | C2×D3 | 1 | 1 | yes | characteristic |
| 145 | C4×D12 | — | 3 | 1 | no | — |
| 146 | C4×D12 | — | 3 | 1 | no | — |
| 147 | C4×D12 | — | 6 | 1 | no | — |
| 148 | C4×D12 | C2×D3 | 1 | 1 | yes | characteristic |
| 149 | C4×Dic6 | — | 3 | 1 | no | — |
| 150 | C4×Dic6 | — | 3 | 1 | no | — |
| 151 | C4×Dic6 | — | 6 | 1 | no | — |
| 152 | C3×C4⋊C8 | — | 3 | 1 | no | — |
| 153 | C3×#102 | — | 3 | 2 | no | — |
| 154 | C3×C4×C8 | — | 3 | 1 | no | — |
| 155 | #832 | — | 3 | 2 | no | — |
| 156 | #832 | — | 3 | 1 | no | — |
| 157 | #832 | C2×D3 | 1 | 2 | yes | — |
| 158 | #821 | — | 3 | 1 | no | — |
| 159 | #821 | — | 3 | 2 | no | — |
| 160 | #821 | — | 3 | 1 | no | — |
| 161 | #818 | — | 3 | 1 | no | — |
| 162 | Dic3⋊C8 | — | 3 | 2 | no | — |
| 163 | Dic3⋊C8 | — | 3 | 2 | no | — |
| 164 | C8×Dic3 | — | 3 | 2 | no | — |
| 165 | C8×Dic3 | — | 3 | 2 | no | — |
| 166 | #809 | — | 3 | 1 | no | — |
| 167 | #807 | — | 3 | 1 | no | — |
| 168 | C4⋊(C3⋊C8) | C2×D3 | 1 | 1 | yes | characteristic |
| 169 | C4×C3⋊C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 170 | C23×C32 | — | 2 | 2 | no | — |
| 171 | C22×C3⋊D3 | — | 2 | 1 | no | — |
| 172 | C22×C3×D3 | — | 2 | 2 | no | — |
| 173 | C22×C3×D3 | — | 2 | 1 | no | — |
| 174 | C32×D4 | — | 2 | 2 | no | — |
| 175 | C32×D4 | — | 2 | 2 | no | — |
| 176 | C32×D4 | — | 4 | 2 | no | — |
| 177 | C32×D4 | — | 8 | 1 | no | — |
| 178 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 179 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 180 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 181 | #638 | — | 4 | 4 | no | — |
| 182 | #638 | — | 8 | 2 | no | — |
| 183 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 184 | C2×C3⋊Dic3 | — | 4 | 4 | no | — |
| 185 | C2×C3⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 186 | C2×C3⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 187 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 188 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 189 | C4×C3⋊D3 | — | 4 | 2 | no | — |
| 190 | #634 | D8 | 1 | 4 | yes | complemented |
| 191 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 192 | C3×D12 | — | 2 | 1 | no | — |
| 193 | C3×D12 | — | 2 | 2 | no | — |
| 194 | C3×D12 | — | 2 | 2 | no | — |
| 195 | C3×D12 | — | 2 | 1 | no | — |
| 196 | C3×D12 | — | 4 | 2 | no | — |
| 197 | C3×D12 | — | 8 | 1 | no | — |
| 198 | C3×C4×D3 | — | 4 | 2 | no | — |
| 199 | #625 | — | 4 | 4 | no | — |
| 200 | #625 | — | 8 | 2 | no | — |
| 201 | D3×Dic3 | — | 4 | 4 | no | — |
| 202 | C3×C3⋊C8 | — | 2 | 2 | no | — |
| 203 | C3×C3⋊C8 | — | 2 | 1 | no | — |
| 204 | C3×C3⋊C8 | #41 | 1 | 2 | yes | complemented |
| 205 | #550 | — | 9 | 1 | no | — |
| 206 | #550 | — | 9 | 1 | no | — |
| 207 | #493 | — | 3 | 1 | no | — |
| 208 | #493 | — | 9 | 2 | no | — |
| 209 | #459 | — | 3 | 1 | no | — |
| 210 | #459 | — | 9 | 2 | no | — |
| 211 | #459 | — | 9 | 1 | no | — |
| 212 | #459 | — | 9 | 2 | no | — |
| 213 | C8×Q8 | — | 9 | 1 | no | — |
| 214 | C4×D8 | — | 9 | 1 | no | — |
| 215 | C4×D8 | — | 9 | 2 | no | — |
| 216 | C2×C3×D4 | — | 2 | 2 | no | — |
| 217 | C2×C3×D4 | — | 2 | 2 | no | — |
| 218 | C2×C3×D4 | — | 2 | 1 | no | — |
| 219 | C2×C3×D4 | — | 2 | 1 | no | — |
| 220 | C2×C3×D4 | — | 2 | 1 | no | — |
| 221 | C2×C3×D4 | — | 2 | 1 | no | — |
| 222 | C2×C3×D4 | — | 2 | 2 | no | — |
| 223 | C2×C3×D4 | — | 3 | 2 | no | — |
| 224 | C2×C3×D4 | — | 3 | 1 | no | — |
| 225 | C2×C3×D4 | — | 6 | 1 | no | — |
| 226 | C2×C3×D4 | — | 6 | 1 | no | — |
| 227 | C2×C3×D4 | C22×D3 | 1 | 2 | yes | — |
| 228 | C2×C3×D4 | C22×D3 | 1 | 2 | yes | — |
| 229 | C22×C3×C4 | — | 6 | 1 | no | — |
| 230 | C2×#67 | — | 6 | 2 | no | — |
| 231 | C2×#67 | — | 6 | 2 | no | — |
| 232 | C2×#67 | — | 6 | 2 | no | — |
| 233 | C2×#67 | — | 6 | 2 | no | — |
| 234 | C2×#67 | — | 6 | 2 | no | — |
| 235 | C2×#67 | — | 6 | 2 | no | — |
| 236 | C2×#67 | — | 6 | 2 | no | — |
| 237 | C2×#67 | — | 6 | 2 | no | — |
| 238 | C2×#67 | — | 6 | 4 | no | — |
| 239 | C2×#67 | — | 6 | 4 | no | — |
| 240 | C22×Dic3 | — | 6 | 2 | no | — |
| 241 | C22×Dic3 | — | 6 | 2 | no | — |
| 242 | C22×Dic3 | — | 6 | 2 | no | — |
| 243 | C22×Dic3 | — | 6 | 4 | no | — |
| 244 | #237 | — | 12 | 4 | no | — |
| 245 | #237 | — | 12 | 4 | no | — |
| 246 | #237 | — | 12 | 4 | no | — |
| 247 | #237 | — | 12 | 8 | no | — |
| 248 | #235 | — | 12 | 4 | no | — |
| 249 | C2×D12 | — | 2 | 1 | no | — |
| 250 | C2×D12 | — | 2 | 1 | no | — |
| 251 | C2×D12 | — | 3 | 1 | no | — |
| 252 | C2×D12 | — | 3 | 1 | no | — |
| 253 | C2×D12 | — | 6 | 1 | no | — |
| 254 | C2×D12 | C22×D3 | 1 | 1 | yes | characteristic |
| 255 | C2×D12 | C22×D3 | 1 | 2 | yes | — |
| 256 | C2×C4×D3 | — | 2 | 1 | no | — |
| 257 | C2×C4×D3 | — | 6 | 2 | no | — |
| 258 | C2×C4×D3 | — | 6 | 2 | no | — |
| 259 | C2×C4×D3 | — | 6 | 1 | no | — |
| 260 | C2×C4×D3 | — | 6 | 1 | no | — |
| 261 | C2×Dic6 | — | 3 | 1 | no | — |
| 262 | C2×Dic6 | — | 3 | 1 | no | — |
| 263 | C2×Dic6 | — | 6 | 1 | no | — |
| 264 | C3×D8 | — | 6 | 4 | no | — |
| 265 | C3×D8 | — | 12 | 2 | no | — |
| 266 | C3×D8 | — | 12 | 2 | no | — |
| 267 | C2×C3×C8 | — | 3 | 1 | no | — |
| 268 | C2×C3×C8 | — | 3 | 2 | no | — |
| 269 | C2×C3×C8 | — | 3 | 1 | no | — |
| 270 | C3×C4⋊C4 | — | 3 | 1 | no | — |
| 271 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 272 | C3×C42 | — | 2 | 1 | no | — |
| 273 | C3×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 274 | C3×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 275 | #217 | — | 6 | 2 | no | — |
| 276 | #217 | — | 6 | 2 | no | — |
| 277 | #217 | — | 6 | 2 | no | — |
| 278 | #217 | — | 6 | 4 | no | — |
| 279 | #213 | — | 2 | 4 | no | — |
| 280 | #213 | — | 4 | 2 | no | — |
| 281 | #213 | — | 4 | 2 | no | — |
| 282 | #213 | — | 6 | 2 | no | — |
| 283 | #213 | — | 12 | 2 | no | — |
| 284 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 285 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 286 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 287 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 288 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 289 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 290 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 291 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 292 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 293 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 294 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 295 | C4⋊Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 296 | Dic3⋊C4 | — | 3 | 2 | no | — |
| 297 | Dic3⋊C4 | — | 3 | 2 | no | — |
| 298 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 299 | C4×Dic3 | — | 3 | 2 | no | — |
| 300 | C4×Dic3 | — | 3 | 2 | no | — |
| 301 | C4×Dic3 | — | 6 | 2 | no | — |
| 302 | C2×C3⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 303 | C2×C3⋊C8 | C22×D3 | 1 | 2 | yes | — |
| 304 | C2×C3⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 305 | D24 | — | 6 | 2 | no | — |
| 306 | D24 | — | 12 | 2 | no | — |
| 307 | C22×C32 | — | 4 | 2 | no | — |
| 308 | C22×C32 | — | 4 | 2 | no | — |
| 309 | C22×C32 | — | 4 | 2 | no | — |
| 310 | C22×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 311 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 312 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 313 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 314 | C2×C3×D3 | — | 4 | 2 | no | — |
| 315 | C2×C3×D3 | — | 4 | 1 | no | — |
| 316 | C2×C3×D3 | — | 4 | 2 | no | — |
| 317 | C2×C3×D3 | — | 4 | 1 | no | — |
| 318 | C2×C3×D3 | — | 4 | 1 | no | — |
| 319 | C2×C3×D3 | — | 4 | 2 | no | — |
| 320 | C32×C4 | — | 2 | 1 | no | — |
| 321 | C32×C4 | C2×D8 | 1 | 2 | yes | — |
| 322 | C32×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 323 | C32×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 324 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 325 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 326 | C3⋊Dic3 | C2×D8 | 1 | 4 | yes | — |
| 327 | C3×Dic3 | — | 4 | 1 | no | — |
| 328 | C2×#41 | — | 18 | 1 | no | — |
| 329 | C2×#41 | — | 18 | 1 | no | — |
| 330 | C2×D8 | — | 3 | 2 | no | — |
| 331 | C2×D8 | — | 3 | 2 | no | — |
| 332 | C2×D8 | — | 3 | 2 | no | — |
| 333 | C2×D8 | — | 9 | 1 | no | — |
| 334 | C2×D8 | — | 9 | 2 | no | — |
| 335 | #127 | — | 3 | 1 | no | — |
| 336 | #127 | — | 9 | 2 | no | — |
| 337 | #127 | — | 9 | 2 | no | — |
| 338 | #127 | D32 | 1 | 1 | yes | characteristic |
| 339 | #121 | — | 18 | 2 | no | — |
| 340 | #121 | — | 18 | 1 | no | — |
| 341 | #121 | — | 18 | 1 | no | — |
| 342 | #121 | — | 18 | 2 | no | — |
| 343 | C4×Q8 | — | 9 | 1 | no | — |
| 344 | C4×D4 | — | 3 | 1 | no | — |
| 345 | C4×D4 | — | 9 | 2 | no | — |
| 346 | C4×D4 | — | 9 | 2 | no | — |
| 347 | C4×D4 | — | 9 | 1 | no | — |
| 348 | #107 | — | 9 | 1 | no | — |
| 349 | C4⋊C8 | — | 3 | 1 | no | — |
| 350 | C4⋊C8 | — | 9 | 2 | no | — |
| 351 | #102 | — | 3 | 2 | no | — |
| 352 | #102 | — | 9 | 1 | no | — |
| 353 | #102 | — | 9 | 1 | no | — |
| 354 | #102 | — | 9 | 2 | no | — |
| 355 | C4×C8 | — | 3 | 1 | no | — |
| 356 | C4×C8 | — | 9 | 2 | no | — |
| 357 | C23×C3 | — | 2 | 4 | no | — |
| 358 | C23×C3 | — | 2 | 2 | no | — |
| 359 | C23×C3 | — | 2 | 2 | no | — |
| 360 | C23×C3 | — | 6 | 2 | no | — |
| 361 | C23×C3 | — | 6 | 1 | no | — |
| 362 | C22×D3 | — | 2 | 1 | no | — |
| 363 | C22×D3 | — | 2 | 2 | no | — |
| 364 | C22×D3 | — | 6 | 2 | no | — |
| 365 | C22×D3 | — | 6 | 1 | no | — |
| 366 | C22×D3 | — | 6 | 1 | no | — |
| 367 | C3×D4 | — | 2 | 2 | no | — |
| 368 | C3×D4 | — | 2 | 2 | no | — |
| 369 | C3×D4 | — | 2 | 2 | no | — |
| 370 | C3×D4 | — | 2 | 2 | no | — |
| 371 | C3×D4 | — | 4 | 2 | no | — |
| 372 | C3×D4 | — | 4 | 2 | no | — |
| 373 | C3×D4 | — | 4 | 4 | no | — |
| 374 | C3×D4 | — | 4 | 2 | no | — |
| 375 | C3×D4 | — | 4 | 2 | no | — |
| 376 | C3×D4 | — | 6 | 1 | no | — |
| 377 | C3×D4 | — | 6 | 2 | no | — |
| 378 | C3×D4 | — | 6 | 1 | no | — |
| 379 | C3×D4 | — | 6 | 2 | no | — |
| 380 | C3×D4 | — | 8 | 1 | no | — |
| 381 | C3×D4 | — | 8 | 1 | no | — |
| 382 | C3×D4 | — | 8 | 2 | no | — |
| 383 | C3×D4 | — | 12 | 2 | no | — |
| 384 | C3×D4 | — | 24 | 1 | no | — |
| 385 | C2×C3×C4 | — | 2 | 1 | no | — |
| 386 | C2×C3×C4 | — | 2 | 1 | no | — |
| 387 | C2×C3×C4 | — | 2 | 1 | no | — |
| 388 | C2×C3×C4 | — | 6 | 1 | no | — |
| 389 | C2×C3×C4 | — | 12 | 2 | no | — |
| 390 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 391 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 392 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 393 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 394 | C2×C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 395 | C2×C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 396 | #67 | — | 12 | 4 | no | — |
| 397 | #67 | — | 12 | 4 | no | — |
| 398 | #67 | — | 12 | 4 | no | — |
| 399 | #67 | — | 12 | 4 | no | — |
| 400 | #67 | — | 12 | 8 | no | — |
| 401 | #67 | — | 24 | 2 | no | — |
| 402 | #67 | — | 24 | 2 | no | — |
| 403 | #67 | — | 24 | 2 | no | — |
| 404 | #67 | — | 24 | 2 | no | — |
| 405 | #67 | — | 24 | 4 | no | — |
| 406 | C2×Dic3 | — | 2 | 1 | no | — |
| 407 | C2×Dic3 | — | 3 | 2 | no | — |
| 408 | C2×Dic3 | — | 3 | 2 | no | — |
| 409 | C2×Dic3 | — | 3 | 2 | no | — |
| 410 | C2×Dic3 | — | 3 | 2 | no | — |
| 411 | C2×Dic3 | — | 6 | 2 | no | — |
| 412 | C2×Dic3 | — | 6 | 2 | no | — |
| 413 | C2×Dic3 | — | 6 | 2 | no | — |
| 414 | C2×Dic3 | — | 6 | 1 | no | — |
| 415 | C2×Dic3 | — | 6 | 1 | no | — |
| 416 | C2×Dic3 | — | 12 | 4 | no | — |
| 417 | C2×Dic3 | — | 12 | 4 | no | — |
| 418 | C2×Dic3 | — | 12 | 4 | no | — |
| 419 | C2×Dic3 | — | 12 | 8 | no | — |
| 420 | D12 | — | 2 | 2 | no | — |
| 421 | D12 | — | 2 | 2 | no | — |
| 422 | D12 | — | 2 | 1 | no | — |
| 423 | D12 | — | 2 | 1 | no | — |
| 424 | D12 | — | 4 | 2 | no | — |
| 425 | D12 | — | 6 | 1 | no | — |
| 426 | D12 | — | 6 | 1 | no | — |
| 427 | D12 | — | 6 | 1 | no | — |
| 428 | D12 | — | 6 | 1 | no | — |
| 429 | D12 | — | 8 | 1 | no | — |
| 430 | D12 | — | 12 | 1 | no | — |
| 431 | D12 | — | 12 | 1 | no | — |
| 432 | C4×D3 | — | 4 | 2 | no | — |
| 433 | C4×D3 | — | 12 | 4 | no | — |
| 434 | C4×D3 | — | 12 | 4 | no | — |
| 435 | C4×D3 | — | 12 | 2 | no | — |
| 436 | C4×D3 | — | 12 | 2 | no | — |
| 437 | Dic6 | — | 3 | 4 | no | — |
| 438 | Dic6 | — | 3 | 4 | no | — |
| 439 | Dic6 | — | 6 | 4 | no | — |
| 440 | C3×C8 | — | 3 | 2 | no | — |
| 441 | C3×C8 | — | 6 | 2 | no | — |
| 442 | C3×C8 | — | 6 | 1 | no | — |
| 443 | C3⋊C8 | — | 2 | 1 | no | — |
| 444 | C3⋊C8 | — | 2 | 2 | no | — |
| 445 | C3⋊C8 | #237 | 1 | 2 | yes | complemented |
| 446 | C2×C32 | — | 8 | 2 | no | — |
| 447 | C2×C32 | #550 | 1 | 1 | yes | characteristic |
| 448 | C2×C32 | C22×D8 | 1 | 1 | yes | characteristic |
| 449 | C2×C32 | #576 | 1 | 1 | yes | characteristic |
| 450 | C3⋊D3 | — | 8 | 1 | no | — |
| 451 | C3×D3 | — | 8 | 2 | no | — |
| 452 | C3×D3 | — | 8 | 1 | no | — |
| 453 | #41 | — | 36 | 4 | no | — |
| 454 | #41 | — | 36 | 4 | no | — |
| 455 | C2×Q8 | — | 9 | 1 | no | — |
| 456 | C2×D4 | — | 2 | 1 | no | — |
| 457 | C2×D4 | — | 2 | 1 | no | — |
| 458 | C2×D4 | — | 3 | 1 | no | — |
| 459 | C2×D4 | — | 3 | 2 | no | — |
| 460 | C2×D4 | — | 6 | 1 | no | — |
| 461 | C2×D4 | — | 6 | 1 | no | — |
| 462 | C2×D4 | — | 9 | 1 | no | — |
| 463 | C2×D4 | — | 18 | 2 | no | — |
| 464 | C2×D4 | — | 18 | 2 | no | — |
| 465 | C2×D4 | — | 18 | 2 | no | — |
| 466 | C2×D4 | — | 18 | 2 | no | — |
| 467 | C2×D4 | C2×D32 | 1 | 2 | yes | — |
| 468 | C22×C4 | — | 6 | 1 | no | — |
| 469 | C22×C4 | — | 18 | 2 | no | — |
| 470 | C22×C4 | — | 18 | 2 | no | — |
| 471 | C22×C4 | — | 18 | 1 | no | — |
| 472 | D8 | — | 6 | 4 | no | — |
| 473 | D8 | — | 12 | 2 | no | — |
| 474 | D8 | — | 12 | 2 | no | — |
| 475 | D8 | — | 18 | 2 | no | — |
| 476 | D8 | — | 36 | 2 | no | — |
| 477 | C2×C8 | — | 3 | 1 | no | — |
| 478 | C2×C8 | — | 3 | 1 | no | — |
| 479 | C2×C8 | — | 3 | 2 | no | — |
| 480 | C4⋊C4 | — | 3 | 1 | no | — |
| 481 | C4⋊C4 | — | 9 | 2 | no | — |
| 482 | C4⋊C4 | — | 9 | 1 | no | — |
| 483 | C4⋊C4 | — | 9 | 1 | no | — |
| 484 | C22⋊C4 | — | 6 | 1 | no | — |
| 485 | C22⋊C4 | — | 18 | 2 | no | — |
| 486 | C22⋊C4 | — | 18 | 2 | no | — |
| 487 | C22⋊C4 | — | 18 | 1 | no | — |
| 488 | C42 | — | 9 | 2 | no | — |
| 489 | C42 | C2×D32 | 1 | 1 | yes | characteristic |
| 490 | C22×C3 | — | 2 | 1 | no | — |
| 491 | C22×C3 | — | 4 | 4 | no | — |
| 492 | C22×C3 | — | 4 | 4 | no | — |
| 493 | C22×C3 | — | 4 | 4 | no | — |
| 494 | C22×C3 | — | 4 | 2 | no | — |
| 495 | C22×C3 | — | 4 | 2 | no | — |
| 496 | C22×C3 | — | 4 | 2 | no | — |
| 497 | C22×C3 | — | 4 | 2 | no | — |
| 498 | C22×C3 | — | 4 | 2 | no | — |
| 499 | C22×C3 | — | 4 | 2 | no | — |
| 500 | C22×C3 | — | 12 | 1 | no | — |
| 501 | C22×C3 | — | 12 | 2 | no | — |
| 502 | C22×C3 | — | 12 | 1 | no | — |
| 503 | C22×C3 | — | 12 | 1 | no | — |
| 504 | C22×C3 | — | 12 | 2 | no | — |
| 505 | C22×C3 | — | 12 | 2 | no | — |
| 506 | C22×C3 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 507 | C22×C3 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 508 | C2×D3 | — | 4 | 2 | no | — |
| 509 | C2×D3 | — | 4 | 1 | no | — |
| 510 | C2×D3 | — | 4 | 2 | no | — |
| 511 | C2×D3 | — | 4 | 2 | no | — |
| 512 | C2×D3 | — | 4 | 1 | no | — |
| 513 | C2×D3 | — | 4 | 1 | no | — |
| 514 | C2×D3 | — | 12 | 2 | no | — |
| 515 | C2×D3 | — | 12 | 2 | no | — |
| 516 | C2×D3 | — | 12 | 2 | no | — |
| 517 | C2×D3 | — | 12 | 1 | no | — |
| 518 | C2×D3 | — | 12 | 1 | no | — |
| 519 | C2×D3 | — | 12 | 1 | no | — |
| 520 | C2×D3 | — | 12 | 1 | no | — |
| 521 | C2×D3 | — | 12 | 1 | no | — |
| 522 | C2×D3 | — | 12 | 1 | no | — |
| 523 | C3×C4 | — | 2 | 1 | no | — |
| 524 | C3×C4 | — | 2 | 1 | no | — |
| 525 | C3×C4 | — | 2 | 1 | no | — |
| 526 | C3×C4 | — | 2 | 1 | no | — |
| 527 | C3×C4 | — | 2 | 2 | no | — |
| 528 | C3×C4 | — | 4 | 1 | no | — |
| 529 | C3×C4 | — | 12 | 1 | no | — |
| 530 | C3×C4 | D3×D8 | 1 | 2 | yes | — |
| 531 | C3×C4 | D3×D8 | 1 | 2 | yes | — |
| 532 | C3×C4 | C2×#237 | 1 | 1 | yes | characteristic |
| 533 | C3×C4 | #1004 | 1 | 1 | yes | characteristic |
| 534 | C3×C4 | #1004 | 1 | 1 | yes | characteristic |
| 535 | C3×C4 | D3×#41 | 1 | 1 | yes | characteristic |
| 536 | Dic3 | — | 3 | 4 | no | — |
| 537 | Dic3 | — | 3 | 4 | no | — |
| 538 | Dic3 | — | 4 | 1 | no | — |
| 539 | Dic3 | — | 6 | 4 | no | — |
| 540 | Dic3 | — | 6 | 2 | no | — |
| 541 | Dic3 | — | 6 | 2 | no | — |
| 542 | Dic3 | — | 12 | 2 | no | — |
| 543 | Dic3 | — | 12 | 2 | no | — |
| 544 | Dic3 | — | 12 | 1 | no | — |
| 545 | Dic3 | — | 12 | 1 | no | — |
| 546 | C32 | #3391 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 547 | C23 | — | 2 | 2 | no | — |
| 548 | C23 | — | 6 | 1 | no | — |
| 549 | C23 | — | 6 | 2 | no | — |
| 550 | C23 | — | 18 | 1 | no | — |
| 551 | Q8 | — | 9 | 4 | no | — |
| 552 | D4 | — | 2 | 2 | no | — |
| 553 | D4 | — | 2 | 2 | no | — |
| 554 | D4 | — | 4 | 2 | no | — |
| 555 | D4 | — | 6 | 2 | no | — |
| 556 | D4 | — | 6 | 1 | no | — |
| 557 | D4 | — | 6 | 1 | no | — |
| 558 | D4 | — | 6 | 2 | no | — |
| 559 | D4 | — | 8 | 1 | no | — |
| 560 | D4 | — | 12 | 2 | no | — |
| 561 | D4 | — | 18 | 1 | no | — |
| 562 | D4 | — | 18 | 1 | no | — |
| 563 | D4 | — | 24 | 1 | no | — |
| 564 | D4 | — | 36 | 4 | no | — |
| 565 | D4 | — | 36 | 4 | no | — |
| 566 | D4 | — | 72 | 2 | no | — |
| 567 | D4 | — | 72 | 2 | no | — |
| 568 | C2×C4 | — | 6 | 1 | no | — |
| 569 | C2×C4 | — | 9 | 2 | no | — |
| 570 | C2×C4 | — | 9 | 2 | no | — |
| 571 | C2×C4 | — | 12 | 2 | no | — |
| 572 | C2×C4 | — | 18 | 1 | no | — |
| 573 | C2×C4 | — | 36 | 4 | no | — |
| 574 | C2×C4 | — | 36 | 4 | no | — |
| 575 | C2×C4 | — | 36 | 2 | no | — |
| 576 | C2×C4 | #3811 | 1 | 1 | yes | characteristic |
| 577 | C2×C4 | #3811 | 1 | 1 | yes | characteristic |
| 578 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 579 | C8 | — | 3 | 2 | no | — |
| 580 | C8 | — | 6 | 1 | no | — |
| 581 | C8 | — | 6 | 2 | no | — |
| 582 | C2×C3 | — | 2 | 1 | no | — |
| 583 | C2×C3 | — | 2 | 1 | no | — |
| 584 | C2×C3 | — | 2 | 1 | no | — |
| 585 | C2×C3 | — | 8 | 4 | no | — |
| 586 | C2×C3 | — | 8 | 2 | no | — |
| 587 | C2×C3 | — | 8 | 2 | no | — |
| 588 | C2×C3 | — | 24 | 1 | no | — |
| 589 | C2×C3 | — | 24 | 2 | no | — |
| 590 | C2×C3 | #5599 | 1 | 1 | yes | characteristic |
| 591 | C2×C3 | #5718 | 1 | 1 | yes | characteristic |
| 592 | C2×C3 | C2×D3×D8 | 1 | 1 | yes | characteristic |
| 593 | C2×C3 | C2×D3×D8 | 1 | 1 | yes | characteristic |
| 594 | C2×C3 | #5757 | 1 | 1 | yes | characteristic |
| 595 | C2×C3 | #5774 | 1 | 1 | yes | characteristic |
| 596 | D3 | — | 8 | 2 | no | — |
| 597 | D3 | — | 8 | 1 | no | — |
| 598 | D3 | — | 24 | 2 | no | — |
| 599 | D3 | — | 24 | 1 | no | — |
| 600 | D3 | — | 24 | 1 | no | — |
| 601 | C22 | — | 4 | 2 | no | — |
| 602 | C22 | — | 4 | 2 | no | — |
| 603 | C22 | — | 4 | 2 | no | — |
| 604 | C22 | — | 12 | 1 | no | — |
| 605 | C22 | — | 12 | 2 | no | — |
| 606 | C22 | — | 12 | 2 | no | — |
| 607 | C22 | — | 12 | 1 | no | — |
| 608 | C22 | — | 12 | 2 | no | — |
| 609 | C22 | — | 12 | 1 | no | — |
| 610 | C22 | — | 36 | 1 | no | — |
| 611 | C22 | — | 36 | 1 | no | — |
| 612 | C22 | — | 36 | 1 | no | — |
| 613 | C22 | C2×#3811 | 1 | 1 | yes | characteristic |
| 614 | C4 | — | 2 | 1 | no | — |
| 615 | C4 | — | 9 | 4 | no | — |
| 616 | C4 | — | 12 | 1 | no | — |
| 617 | C4 | — | 18 | 2 | no | — |
| 618 | C4 | — | 36 | 1 | no | — |
| 619 | C4 | #63926 | 1 | 2 | yes | — |
| 620 | C4 | D3×#237 | 1 | 1 | yes | characteristic |
| 621 | C4 | #64313 | 1 | 1 | yes | characteristic |
| 622 | C3 | — | 2 | 1 | no | — |
| 623 | C3 | #80324 | 1 | 1 | yes | characteristic, complemented |
| 624 | C3 | #81778 | 1 | 1 | yes | characteristic, complemented |
| 625 | C2 | — | 8 | 2 | no | — |
| 626 | C2 | — | 24 | 1 | no | — |
| 627 | C2 | — | 24 | 2 | no | — |
| 628 | C2 | — | 72 | 1 | no | — |
| 629 | C2 | C2×#63926 | 1 | 1 | yes | characteristic |
| 630 | C2 | #10595102 | 1 | 1 | yes | characteristic |
| 631 | C2 | #10595164 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10596189 | C2 | semidirect |
| 2. #10593906 | C2 | semidirect |
| 3. C3×#5073 | C2 | semidirect |
| 4. C3×#5072 | C2 | semidirect |
| 5. #10591486 | C2 | semidirect |
| 6. #10591484 | C2 | semidirect |
| 7. #10591435 | C2 | semidirect |
| 8. #10591433 | C2 | semidirect |
| 9. #10590355 | C2 | semidirect |
| 10. C4×#3714 | C2 | semidirect |
| 11. #10590254 | C2 | semidirect |
| 56. #5073 | D3 | semidirect |
| 58. #5072 | D3 | semidirect |
| 190. #634 | D8 | semidirect |
| 204. C3×C3⋊C8 | #41 | semidirect |
| 445. C3⋊C8 | #237 | semidirect |
| 546. C32 | #3391 | semidirect |
| 623. C3 | #80324 | semidirect |
| 624. C3 | #81778 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596189 | 2 |
| #10593906 | 2 |
| C3×#5073 | 2 |
| C3×#5072 | 2 |
| #10591486 | 2 |
| #10591484 | 2 |
| #10591435 | 2 |
| #10591433 | 2 |
| #10590355 | 2 |
| C4×#3714 | 2 |
| #10590254 | 2 |
| #81778 | 3 |
| #80324 | 3 |