Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
990 conjugacy classes of subgroups.
The subgroup lattice has 616 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10593902 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10593900 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10592542 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#4843 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#4830 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10590880 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10590765 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10590753 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10590745 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10590350 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C4×#3714 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #80324 | — | 3 | 1 | no | maximal |
| 13 | #79910 | — | 3 | 1 | no | maximal |
| 14 | C2×#3799 | — | 2 | 1 | no | — |
| 15 | C2×#3796 | — | 2 | 1 | no | — |
| 16 | C2×#3745 | C22 | 1 | 2 | yes | — |
| 17 | #64083 | C22 | 1 | 1 | yes | characteristic |
| 18 | C4×C4⋊(C3⋊D3) | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×C3×D24 | C22 | 1 | 2 | yes | — |
| 20 | C3×#874 | C22 | 1 | 1 | yes | characteristic |
| 21 | C3×C4×D12 | C22 | 1 | 1 | yes | characteristic |
| 22 | C3×C4×Dic6 | C22 | 1 | 1 | yes | characteristic |
| 23 | #63916 | — | 2 | 1 | no | — |
| 24 | #63911 | C22 | 1 | 2 | yes | — |
| 25 | #63911 | C22 | 1 | 2 | yes | — |
| 26 | #63910 | — | 2 | 2 | no | — |
| 27 | #63909 | — | 2 | 1 | no | — |
| 28 | #63894 | C22 | 1 | 2 | yes | — |
| 29 | Dic3×D12 | C22 | 1 | 2 | yes | — |
| 30 | #63886 | — | 2 | 2 | no | — |
| 31 | C2×#3714 | C22 | 1 | 2 | yes | — |
| 32 | C2×#3714 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×#3714 | C22 | 1 | 2 | yes | — |
| 34 | C32×C4⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 35 | #63648 | C22 | 1 | 2 | yes | — |
| 36 | C3×#821 | C22 | 1 | 2 | yes | — |
| 37 | C3×Dic3⋊C8 | C22 | 1 | 2 | yes | — |
| 38 | C3×C8×Dic3 | C22 | 1 | 2 | yes | — |
| 39 | C3×C4×C3⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 40 | #63575 | C22 | 1 | 1 | yes | characteristic |
| 41 | #63564 | C22 | 1 | 1 | yes | characteristic |
| 42 | #63563 | C22 | 1 | 1 | yes | characteristic |
| 43 | #5718 | — | 3 | 1 | no | — |
| 44 | #5577 | — | 3 | 1 | no | — |
| 45 | #5577 | — | 3 | 1 | no | — |
| 46 | #5553 | — | 3 | 1 | no | — |
| 47 | C3×#459 | — | 3 | 1 | no | — |
| 48 | C3×C8×Q8 | — | 3 | 1 | no | — |
| 49 | #5151 | — | 3 | 2 | no | — |
| 50 | #5150 | — | 3 | 2 | no | — |
| 51 | #5073 | — | 3 | 1 | no | — |
| 52 | C4×#213 | — | 3 | 1 | no | — |
| 53 | #4843 | — | 3 | 2 | no | — |
| 54 | #4843 | — | 3 | 1 | no | — |
| 55 | #4843 | — | 3 | 1 | no | — |
| 56 | #4843 | — | 3 | 2 | no | — |
| 57 | #4843 | — | 6 | 1 | no | — |
| 58 | #4843 | D3 | 1 | 1 | yes | characteristic, complemented |
| 59 | #4830 | D3 | 1 | 1 | yes | characteristic, complemented |
| 60 | #4786 | — | 3 | 2 | no | — |
| 61 | #4756 | — | 3 | 2 | no | — |
| 62 | #4695 | — | 3 | 2 | no | — |
| 63 | #4695 | — | 3 | 1 | no | — |
| 64 | C4×D24 | — | 3 | 1 | no | — |
| 65 | C4×D24 | — | 3 | 2 | no | — |
| 66 | C2×C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 67 | C2×C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 68 | C2×C4⋊(C3⋊D3) | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×C4⋊(C3⋊D3) | C23 | 1 | 2 | yes | — |
| 70 | C2×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 71 | C2×C3×D12 | — | 2 | 1 | no | — |
| 72 | C2×C3×D12 | — | 2 | 1 | no | — |
| 73 | C2×C3×D12 | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×C3×D12 | C23 | 1 | 2 | yes | — |
| 75 | C2×C3×C4×D3 | — | 2 | 1 | no | — |
| 76 | C2×C3×Dic6 | D4 | 1 | 1 | yes | characteristic |
| 77 | C2×#626 | — | 2 | 2 | no | — |
| 78 | C2×#626 | — | 2 | 2 | no | — |
| 79 | C2×#626 | — | 2 | 2 | no | — |
| 80 | C2×#626 | — | 2 | 2 | no | — |
| 81 | C2×#624 | — | 2 | 2 | no | — |
| 82 | C2×D3×Dic3 | — | 2 | 2 | no | — |
| 83 | #3799 | — | 4 | 4 | no | — |
| 84 | #3796 | — | 4 | 4 | no | — |
| 85 | C2×C32×C8 | C23 | 1 | 2 | yes | — |
| 86 | C32×C42 | C23 | 1 | 1 | yes | characteristic |
| 87 | #3752 | — | 2 | 1 | no | — |
| 88 | C4⋊(C3⋊Dic3) | C23 | 1 | 1 | yes | characteristic |
| 89 | #3745 | — | 4 | 2 | no | — |
| 90 | C3×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 91 | C3×C4⋊Dic3 | D4 | 1 | 1 | yes | characteristic |
| 92 | C3×C4⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 93 | C3×Dic3⋊C4 | D4 | 1 | 2 | yes | — |
| 94 | C3×C4×Dic3 | C23 | 1 | 2 | yes | — |
| 95 | C2×C3×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 96 | C2×C3×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 97 | C3×D24 | — | 4 | 2 | no | — |
| 98 | #3722 | — | 2 | 2 | no | — |
| 99 | (C2×D3)⋊Dic3 | — | 2 | 2 | no | — |
| 100 | #3714 | — | 2 | 4 | no | — |
| 101 | #3714 | — | 2 | 2 | no | — |
| 102 | #3714 | — | 4 | 2 | no | — |
| 103 | #3391 | — | 9 | 1 | no | Sylow |
| 104 | C2×#239 | — | 6 | 1 | no | — |
| 105 | C2×#239 | — | 6 | 1 | no | — |
| 106 | C2×#237 | — | 6 | 1 | no | — |
| 107 | C2×#235 | — | 6 | 1 | no | — |
| 108 | C2×C3×D8 | — | 3 | 2 | no | — |
| 109 | C3×#127 | — | 3 | 1 | no | — |
| 110 | C3×C4×Q8 | — | 3 | 1 | no | — |
| 111 | C3×C4×D4 | — | 3 | 1 | no | — |
| 112 | #940 | — | 3 | 2 | no | — |
| 113 | #940 | — | 3 | 2 | no | — |
| 114 | #939 | — | 6 | 2 | no | — |
| 115 | #938 | — | 6 | 1 | no | — |
| 116 | D4×Dic3 | — | 3 | 2 | no | — |
| 117 | C2×#213 | — | 3 | 1 | no | — |
| 118 | C2×#213 | — | 3 | 2 | no | — |
| 119 | C2×#213 | — | 3 | 2 | no | — |
| 120 | #930 | — | 6 | 1 | no | — |
| 121 | C2×D24 | — | 3 | 1 | no | — |
| 122 | C2×D24 | — | 3 | 2 | no | — |
| 123 | C2×D24 | — | 3 | 2 | no | — |
| 124 | C2×D24 | — | 3 | 2 | no | — |
| 125 | C2×D24 | — | 3 | 2 | no | — |
| 126 | C2×D24 | — | 6 | 2 | no | — |
| 127 | C2×D24 | C2×D3 | 1 | 2 | yes | — |
| 128 | #895 | — | 6 | 2 | no | — |
| 129 | #895 | — | 6 | 1 | no | — |
| 130 | #895 | — | 6 | 2 | no | — |
| 131 | #895 | — | 6 | 1 | no | — |
| 132 | #893 | — | 3 | 2 | no | — |
| 133 | #884 | — | 6 | 2 | no | — |
| 134 | #874 | — | 3 | 2 | no | — |
| 135 | #874 | — | 3 | 2 | no | — |
| 136 | #874 | — | 3 | 1 | no | — |
| 137 | #874 | — | 3 | 1 | no | — |
| 138 | #874 | — | 6 | 1 | no | — |
| 139 | #874 | C2×D3 | 1 | 1 | yes | characteristic |
| 140 | C4×D12 | — | 3 | 2 | no | — |
| 141 | C4×D12 | — | 3 | 1 | no | — |
| 142 | C4×D12 | — | 3 | 1 | no | — |
| 143 | C4×D12 | — | 3 | 2 | no | — |
| 144 | C4×D12 | — | 6 | 1 | no | — |
| 145 | C4×D12 | C2×D3 | 1 | 1 | yes | characteristic |
| 146 | C4×Dic6 | C2×D3 | 1 | 1 | yes | characteristic |
| 147 | C3×C4⋊C8 | — | 2 | 1 | no | — |
| 148 | C3×C4⋊C8 | — | 3 | 2 | no | — |
| 149 | C3×C4⋊C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 150 | C3×C4⋊C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 151 | C3×#102 | — | 3 | 2 | no | — |
| 152 | C3×C4×C8 | — | 3 | 2 | no | — |
| 153 | C3×C4×C8 | — | 3 | 1 | no | — |
| 154 | #832 | — | 3 | 1 | no | — |
| 155 | #821 | — | 3 | 1 | no | — |
| 156 | #821 | — | 3 | 2 | no | — |
| 157 | #821 | — | 3 | 2 | no | — |
| 158 | #821 | — | 3 | 1 | no | — |
| 159 | #821 | — | 6 | 2 | no | — |
| 160 | #821 | C2×D3 | 1 | 2 | yes | — |
| 161 | #818 | — | 3 | 1 | no | — |
| 162 | Dic3⋊C8 | C2×D3 | 1 | 2 | yes | — |
| 163 | C8×Dic3 | C2×D3 | 1 | 2 | yes | — |
| 164 | #809 | — | 3 | 1 | no | — |
| 165 | #807 | — | 3 | 1 | no | — |
| 166 | C4×C3⋊C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 167 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 168 | C22×C3⋊D3 | — | 2 | 1 | no | — |
| 169 | C22×C3×D3 | — | 2 | 2 | no | — |
| 170 | C22×C3×D3 | — | 2 | 1 | no | — |
| 171 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 172 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 174 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 175 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 176 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 177 | C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 178 | C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 179 | C4⋊(C3⋊D3) | — | 4 | 2 | no | — |
| 180 | C4⋊(C3⋊D3) | — | 8 | 1 | no | — |
| 181 | C4×C3⋊D3 | — | 4 | 2 | no | — |
| 182 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 183 | C2×C3×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 184 | C2×C3×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 185 | C3×D12 | — | 2 | 1 | no | — |
| 186 | C3×D12 | — | 2 | 2 | no | — |
| 187 | C3×D12 | — | 2 | 2 | no | — |
| 188 | C3×D12 | — | 2 | 1 | no | — |
| 189 | C3×D12 | — | 4 | 2 | no | — |
| 190 | C3×D12 | — | 8 | 1 | no | — |
| 191 | C3×C4×D3 | — | 4 | 2 | no | — |
| 192 | C3×Dic6 | D8 | 1 | 4 | yes | complemented |
| 193 | #626 | — | 4 | 4 | no | — |
| 194 | #626 | — | 4 | 4 | no | — |
| 195 | #626 | — | 8 | 2 | no | — |
| 196 | #626 | — | 8 | 2 | no | — |
| 197 | #624 | — | 4 | 4 | no | — |
| 198 | D3×Dic3 | — | 4 | 4 | no | — |
| 199 | C32×C8 | — | 2 | 2 | no | — |
| 200 | C3×C3⋊C8 | — | 2 | 1 | no | — |
| 201 | C3×C3⋊C8 | #41 | 1 | 2 | yes | complemented |
| 202 | #550 | — | 9 | 1 | no | — |
| 203 | #550 | — | 9 | 1 | no | — |
| 204 | #493 | — | 9 | 1 | no | — |
| 205 | #493 | — | 9 | 2 | no | — |
| 206 | #459 | — | 3 | 1 | no | — |
| 207 | #459 | — | 9 | 2 | no | — |
| 208 | #459 | — | 9 | 2 | no | — |
| 209 | #459 | — | 9 | 1 | no | — |
| 210 | C8×Q8 | — | 3 | 1 | no | — |
| 211 | C4×D8 | — | 9 | 2 | no | — |
| 212 | C4×D8 | — | 9 | 1 | no | — |
| 213 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 214 | C2×C3×D4 | — | 3 | 1 | no | — |
| 215 | C2×C3×D4 | — | 3 | 2 | no | — |
| 216 | C2×C3×D4 | — | 6 | 1 | no | — |
| 217 | C2×C3×D4 | — | 6 | 1 | no | — |
| 218 | C22×C3×C4 | — | 6 | 1 | no | — |
| 219 | C2×#67 | — | 6 | 2 | no | — |
| 220 | C2×#67 | — | 6 | 2 | no | — |
| 221 | C2×#67 | — | 6 | 2 | no | — |
| 222 | C2×#67 | — | 6 | 2 | no | — |
| 223 | C22×Dic3 | — | 6 | 2 | no | — |
| 224 | #239 | — | 12 | 4 | no | — |
| 225 | #239 | — | 12 | 4 | no | — |
| 226 | #237 | — | 12 | 4 | no | — |
| 227 | #235 | — | 12 | 4 | no | — |
| 228 | C2×D12 | — | 2 | 1 | no | — |
| 229 | C2×D12 | — | 2 | 1 | no | — |
| 230 | C2×D12 | — | 3 | 1 | no | — |
| 231 | C2×D12 | — | 3 | 2 | no | — |
| 232 | C2×D12 | — | 3 | 1 | no | — |
| 233 | C2×D12 | — | 3 | 2 | no | — |
| 234 | C2×D12 | — | 6 | 1 | no | — |
| 235 | C2×D12 | — | 6 | 2 | no | — |
| 236 | C2×D12 | — | 6 | 2 | no | — |
| 237 | C2×D12 | — | 6 | 2 | no | — |
| 238 | C2×D12 | — | 6 | 1 | no | — |
| 239 | C2×D12 | — | 6 | 1 | no | — |
| 240 | C2×D12 | — | 6 | 2 | no | — |
| 241 | C2×D12 | — | 6 | 2 | no | — |
| 242 | C2×D12 | — | 6 | 1 | no | — |
| 243 | C2×D12 | — | 6 | 1 | no | — |
| 244 | C2×D12 | — | 12 | 1 | no | — |
| 245 | C2×D12 | — | 12 | 1 | no | — |
| 246 | C2×D12 | C22×D3 | 1 | 1 | yes | characteristic |
| 247 | C2×D12 | C22×D3 | 1 | 2 | yes | — |
| 248 | C2×C4×D3 | — | 2 | 1 | no | — |
| 249 | C2×C4×D3 | — | 6 | 2 | no | — |
| 250 | C2×C4×D3 | — | 6 | 2 | no | — |
| 251 | C2×C4×D3 | — | 6 | 1 | no | — |
| 252 | C2×C4×D3 | — | 6 | 1 | no | — |
| 253 | C2×C4×D3 | — | 6 | 2 | no | — |
| 254 | C2×C4×D3 | — | 12 | 1 | no | — |
| 255 | C2×Dic6 | D12 | 1 | 1 | yes | characteristic |
| 256 | C3×D8 | — | 12 | 2 | no | — |
| 257 | C2×C3×C8 | — | 2 | 2 | no | — |
| 258 | C2×C3×C8 | — | 3 | 1 | no | — |
| 259 | C2×C3×C8 | — | 3 | 1 | no | — |
| 260 | C2×C3×C8 | C22×D3 | 1 | 2 | yes | — |
| 261 | C2×C3×C8 | C22×D3 | 1 | 2 | yes | — |
| 262 | C3×C4⋊C4 | — | 3 | 2 | no | — |
| 263 | C3×C4⋊C4 | — | 3 | 1 | no | — |
| 264 | C3×C4⋊C4 | — | 3 | 1 | no | — |
| 265 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 266 | C3×C42 | — | 2 | 1 | no | — |
| 267 | C3×C42 | — | 3 | 2 | no | — |
| 268 | C3×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 269 | C3×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 270 | #217 | — | 6 | 2 | no | — |
| 271 | #213 | — | 6 | 2 | no | — |
| 272 | #213 | — | 6 | 4 | no | — |
| 273 | #213 | — | 12 | 2 | no | — |
| 274 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 275 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 276 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 277 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 278 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 279 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 280 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 281 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 282 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 283 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 284 | C4⋊Dic3 | D12 | 1 | 1 | yes | characteristic |
| 285 | C4⋊Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 286 | Dic3⋊C4 | D12 | 1 | 2 | yes | — |
| 287 | C4×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 288 | C2×C3⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 289 | C2×C3⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 290 | D24 | — | 4 | 2 | no | — |
| 291 | D24 | — | 6 | 2 | no | — |
| 292 | D24 | — | 6 | 4 | no | — |
| 293 | D24 | — | 12 | 2 | no | — |
| 294 | D24 | — | 12 | 2 | no | — |
| 295 | D24 | — | 12 | 4 | no | — |
| 296 | D24 | — | 12 | 2 | no | — |
| 297 | C22×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 298 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 299 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 300 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 301 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 302 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 303 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 304 | C2×C3×D3 | — | 4 | 2 | no | — |
| 305 | C2×C3×D3 | — | 4 | 1 | no | — |
| 306 | C2×C3×D3 | — | 4 | 2 | no | — |
| 307 | C2×C3×D3 | — | 4 | 1 | no | — |
| 308 | C2×C3×D3 | — | 4 | 1 | no | — |
| 309 | C2×C3×D3 | — | 4 | 2 | no | — |
| 310 | C32×C4 | — | 2 | 1 | no | — |
| 311 | C32×C4 | C2×D8 | 1 | 2 | yes | — |
| 312 | C32×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 313 | C32×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 314 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 315 | C3×Dic3 | — | 2 | 2 | no | — |
| 316 | C3×Dic3 | — | 4 | 1 | no | — |
| 317 | C3×Dic3 | C2×D8 | 1 | 4 | yes | — |
| 318 | C2×#41 | — | 18 | 1 | no | — |
| 319 | C2×#41 | — | 18 | 1 | no | — |
| 320 | C2×D8 | — | 3 | 2 | no | — |
| 321 | C2×D8 | — | 9 | 2 | no | — |
| 322 | C2×D8 | — | 9 | 1 | no | — |
| 323 | C2×D8 | — | 9 | 2 | no | — |
| 324 | C2×D8 | — | 9 | 2 | no | — |
| 325 | #127 | — | 3 | 1 | no | — |
| 326 | #127 | — | 9 | 2 | no | — |
| 327 | #127 | — | 9 | 2 | no | — |
| 328 | #127 | — | 9 | 1 | no | — |
| 329 | #121 | — | 18 | 2 | no | — |
| 330 | #121 | — | 18 | 1 | no | — |
| 331 | #121 | — | 18 | 1 | no | — |
| 332 | #121 | — | 18 | 2 | no | — |
| 333 | C4×Q8 | — | 3 | 1 | no | — |
| 334 | C4×D4 | — | 3 | 1 | no | — |
| 335 | C4×D4 | — | 9 | 2 | no | — |
| 336 | C4×D4 | — | 9 | 2 | no | — |
| 337 | C4×D4 | — | 9 | 1 | no | — |
| 338 | #107 | — | 9 | 1 | no | — |
| 339 | C4⋊C8 | — | 3 | 2 | no | — |
| 340 | C4⋊C8 | D32 | 1 | 1 | yes | characteristic |
| 341 | #102 | — | 3 | 2 | no | — |
| 342 | #102 | — | 9 | 1 | no | — |
| 343 | #102 | — | 9 | 1 | no | — |
| 344 | #102 | — | 9 | 2 | no | — |
| 345 | C4×C8 | — | 3 | 2 | no | — |
| 346 | C4×C8 | — | 3 | 1 | no | — |
| 347 | C23×C3 | — | 6 | 2 | no | — |
| 348 | C23×C3 | — | 6 | 1 | no | — |
| 349 | C22×D3 | — | 2 | 1 | no | — |
| 350 | C22×D3 | — | 2 | 2 | no | — |
| 351 | C22×D3 | — | 6 | 2 | no | — |
| 352 | C22×D3 | — | 6 | 1 | no | — |
| 353 | C22×D3 | — | 6 | 2 | no | — |
| 354 | C22×D3 | — | 6 | 1 | no | — |
| 355 | C22×D3 | — | 12 | 1 | no | — |
| 356 | C22×D3 | — | 12 | 2 | no | — |
| 357 | C3×Q8 | — | 3 | 4 | no | — |
| 358 | C3×D4 | — | 6 | 1 | no | — |
| 359 | C3×D4 | — | 6 | 2 | no | — |
| 360 | C3×D4 | — | 6 | 2 | no | — |
| 361 | C3×D4 | — | 6 | 1 | no | — |
| 362 | C3×D4 | — | 12 | 2 | no | — |
| 363 | C3×D4 | — | 24 | 1 | no | — |
| 364 | C2×C3×C4 | — | 2 | 1 | no | — |
| 365 | C2×C3×C4 | — | 2 | 1 | no | — |
| 366 | C2×C3×C4 | — | 2 | 1 | no | — |
| 367 | C2×C3×C4 | — | 3 | 2 | no | — |
| 368 | C2×C3×C4 | — | 3 | 2 | no | — |
| 369 | C2×C3×C4 | — | 6 | 1 | no | — |
| 370 | C2×C3×C4 | — | 12 | 2 | no | — |
| 371 | C2×C3×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 372 | C2×C3×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 373 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 374 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 375 | C2×C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 376 | C2×C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 377 | #67 | — | 12 | 4 | no | — |
| 378 | #67 | — | 12 | 4 | no | — |
| 379 | #67 | — | 24 | 2 | no | — |
| 380 | #67 | — | 24 | 2 | no | — |
| 381 | C2×Dic3 | — | 2 | 1 | no | — |
| 382 | C2×Dic3 | — | 6 | 1 | no | — |
| 383 | C2×Dic3 | — | 6 | 1 | no | — |
| 384 | C2×Dic3 | — | 12 | 1 | no | — |
| 385 | C2×Dic3 | — | 12 | 4 | no | — |
| 386 | C2×Dic3 | C2×D12 | 1 | 2 | yes | — |
| 387 | C2×Dic3 | C2×D12 | 1 | 2 | yes | — |
| 388 | D12 | — | 2 | 1 | no | — |
| 389 | D12 | — | 2 | 2 | no | — |
| 390 | D12 | — | 2 | 1 | no | — |
| 391 | D12 | — | 2 | 2 | no | — |
| 392 | D12 | — | 4 | 2 | no | — |
| 393 | D12 | — | 6 | 2 | no | — |
| 394 | D12 | — | 6 | 1 | no | — |
| 395 | D12 | — | 6 | 2 | no | — |
| 396 | D12 | — | 6 | 1 | no | — |
| 397 | D12 | — | 6 | 2 | no | — |
| 398 | D12 | — | 6 | 1 | no | — |
| 399 | D12 | — | 6 | 2 | no | — |
| 400 | D12 | — | 6 | 1 | no | — |
| 401 | D12 | — | 6 | 2 | no | — |
| 402 | D12 | — | 8 | 1 | no | — |
| 403 | D12 | — | 12 | 1 | no | — |
| 404 | D12 | — | 12 | 2 | no | — |
| 405 | D12 | — | 12 | 2 | no | — |
| 406 | D12 | — | 12 | 4 | no | — |
| 407 | D12 | — | 12 | 4 | no | — |
| 408 | D12 | — | 12 | 2 | no | — |
| 409 | D12 | — | 12 | 2 | no | — |
| 410 | D12 | — | 24 | 2 | no | — |
| 411 | D12 | — | 24 | 1 | no | — |
| 412 | D12 | — | 24 | 1 | no | — |
| 413 | D12 | — | 24 | 2 | no | — |
| 414 | D12 | — | 24 | 2 | no | — |
| 415 | D12 | — | 24 | 2 | no | — |
| 416 | C4×D3 | — | 4 | 2 | no | — |
| 417 | C4×D3 | — | 12 | 4 | no | — |
| 418 | C4×D3 | — | 12 | 4 | no | — |
| 419 | C4×D3 | — | 12 | 2 | no | — |
| 420 | C4×D3 | — | 12 | 2 | no | — |
| 421 | C4×D3 | — | 12 | 4 | no | — |
| 422 | C4×D3 | — | 24 | 2 | no | — |
| 423 | Dic6 | D24 | 1 | 4 | yes | complemented |
| 424 | C3×C8 | — | 2 | 2 | no | — |
| 425 | C3×C8 | — | 2 | 2 | no | — |
| 426 | C3×C8 | — | 3 | 2 | no | — |
| 427 | C3×C8 | — | 4 | 2 | no | — |
| 428 | C3×C8 | — | 6 | 1 | no | — |
| 429 | C3⋊C8 | — | 2 | 1 | no | — |
| 430 | C3⋊C8 | #239 | 1 | 2 | yes | complemented |
| 431 | C2×C32 | #550 | 1 | 1 | yes | characteristic |
| 432 | C2×C32 | C22×D8 | 1 | 1 | yes | characteristic |
| 433 | C2×C32 | #576 | 1 | 1 | yes | characteristic |
| 434 | C3⋊D3 | — | 8 | 1 | no | — |
| 435 | C3⋊D3 | — | 8 | 2 | no | — |
| 436 | C3×D3 | — | 8 | 2 | no | — |
| 437 | C3×D3 | — | 8 | 1 | no | — |
| 438 | #41 | — | 36 | 4 | no | — |
| 439 | #41 | — | 36 | 4 | no | — |
| 440 | C2×Q8 | — | 3 | 1 | no | — |
| 441 | C2×D4 | — | 3 | 2 | no | — |
| 442 | C2×D4 | — | 3 | 1 | no | — |
| 443 | C2×D4 | — | 6 | 1 | no | — |
| 444 | C2×D4 | — | 6 | 1 | no | — |
| 445 | C2×D4 | — | 9 | 1 | no | — |
| 446 | C2×D4 | — | 9 | 2 | no | — |
| 447 | C2×D4 | — | 18 | 2 | no | — |
| 448 | C2×D4 | — | 18 | 2 | no | — |
| 449 | C2×D4 | — | 18 | 2 | no | — |
| 450 | C2×D4 | — | 18 | 2 | no | — |
| 451 | C2×D4 | — | 18 | 1 | no | — |
| 452 | C2×D4 | — | 18 | 1 | no | — |
| 453 | C22×C4 | — | 6 | 1 | no | — |
| 454 | C22×C4 | — | 18 | 2 | no | — |
| 455 | C22×C4 | — | 18 | 2 | no | — |
| 456 | C22×C4 | — | 18 | 1 | no | — |
| 457 | D8 | — | 12 | 2 | no | — |
| 458 | D8 | — | 18 | 4 | no | — |
| 459 | D8 | — | 18 | 2 | no | — |
| 460 | D8 | — | 36 | 2 | no | — |
| 461 | D8 | — | 36 | 2 | no | — |
| 462 | C2×C8 | — | 3 | 1 | no | — |
| 463 | C2×C8 | — | 3 | 1 | no | — |
| 464 | C2×C8 | C2×D32 | 1 | 2 | yes | — |
| 465 | C4⋊C4 | — | 3 | 2 | no | — |
| 466 | C4⋊C4 | — | 3 | 1 | no | — |
| 467 | C4⋊C4 | — | 3 | 1 | no | — |
| 468 | C4⋊C4 | — | 9 | 1 | no | — |
| 469 | C22⋊C4 | — | 6 | 1 | no | — |
| 470 | C22⋊C4 | — | 18 | 2 | no | — |
| 471 | C22⋊C4 | — | 18 | 2 | no | — |
| 472 | C22⋊C4 | — | 18 | 1 | no | — |
| 473 | C42 | — | 3 | 2 | no | — |
| 474 | C42 | C2×D32 | 1 | 1 | yes | characteristic |
| 475 | C22×C3 | — | 2 | 1 | no | — |
| 476 | C22×C3 | — | 12 | 2 | no | — |
| 477 | C22×C3 | — | 12 | 1 | no | — |
| 478 | C22×C3 | — | 12 | 1 | no | — |
| 479 | C22×C3 | — | 12 | 2 | no | — |
| 480 | C22×C3 | — | 12 | 2 | no | — |
| 481 | C22×C3 | — | 12 | 1 | no | — |
| 482 | C22×C3 | C22×D12 | 1 | 1 | yes | characteristic |
| 483 | C22×C3 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 484 | C2×D3 | — | 4 | 1 | no | — |
| 485 | C2×D3 | — | 4 | 2 | no | — |
| 486 | C2×D3 | — | 4 | 2 | no | — |
| 487 | C2×D3 | — | 4 | 1 | no | — |
| 488 | C2×D3 | — | 4 | 1 | no | — |
| 489 | C2×D3 | — | 4 | 2 | no | — |
| 490 | C2×D3 | — | 12 | 2 | no | — |
| 491 | C2×D3 | — | 12 | 2 | no | — |
| 492 | C2×D3 | — | 12 | 1 | no | — |
| 493 | C2×D3 | — | 12 | 2 | no | — |
| 494 | C2×D3 | — | 12 | 1 | no | — |
| 495 | C2×D3 | — | 12 | 2 | no | — |
| 496 | C2×D3 | — | 12 | 1 | no | — |
| 497 | C2×D3 | — | 12 | 2 | no | — |
| 498 | C2×D3 | — | 12 | 1 | no | — |
| 499 | C2×D3 | — | 12 | 1 | no | — |
| 500 | C2×D3 | — | 12 | 2 | no | — |
| 501 | C2×D3 | — | 12 | 1 | no | — |
| 502 | C2×D3 | — | 12 | 2 | no | — |
| 503 | C2×D3 | — | 24 | 1 | no | — |
| 504 | C2×D3 | — | 24 | 1 | no | — |
| 505 | C2×D3 | — | 24 | 2 | no | — |
| 506 | C2×D3 | — | 24 | 2 | no | — |
| 507 | C2×D3 | — | 24 | 2 | no | — |
| 508 | C3×C4 | — | 2 | 1 | no | — |
| 509 | C3×C4 | — | 2 | 1 | no | — |
| 510 | C3×C4 | — | 2 | 2 | no | — |
| 511 | C3×C4 | — | 2 | 1 | no | — |
| 512 | C3×C4 | — | 2 | 1 | no | — |
| 513 | C3×C4 | — | 3 | 4 | no | — |
| 514 | C3×C4 | — | 4 | 1 | no | — |
| 515 | C3×C4 | — | 6 | 2 | no | — |
| 516 | C3×C4 | — | 12 | 1 | no | — |
| 517 | C3×C4 | C2×D24 | 1 | 2 | yes | — |
| 518 | C3×C4 | D3×D8 | 1 | 2 | yes | — |
| 519 | C3×C4 | #1004 | 1 | 1 | yes | characteristic |
| 520 | C3×C4 | C2×#239 | 1 | 1 | yes | characteristic |
| 521 | C3×C4 | D3×#41 | 1 | 1 | yes | characteristic |
| 522 | C3×C4 | #1009 | 1 | 1 | yes | characteristic |
| 523 | Dic3 | — | 2 | 2 | no | — |
| 524 | Dic3 | — | 4 | 1 | no | — |
| 525 | Dic3 | — | 12 | 1 | no | — |
| 526 | Dic3 | — | 12 | 1 | no | — |
| 527 | Dic3 | — | 24 | 1 | no | — |
| 528 | Dic3 | C2×D24 | 1 | 4 | yes | — |
| 529 | C32 | #3391 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 530 | C23 | — | 6 | 1 | no | — |
| 531 | C23 | — | 6 | 2 | no | — |
| 532 | C23 | — | 18 | 1 | no | — |
| 533 | C23 | — | 18 | 2 | no | — |
| 534 | Q8 | — | 3 | 4 | no | — |
| 535 | D4 | — | 6 | 1 | no | — |
| 536 | D4 | — | 6 | 2 | no | — |
| 537 | D4 | — | 6 | 2 | no | — |
| 538 | D4 | — | 6 | 1 | no | — |
| 539 | D4 | — | 12 | 2 | no | — |
| 540 | D4 | — | 18 | 1 | no | — |
| 541 | D4 | — | 18 | 2 | no | — |
| 542 | D4 | — | 18 | 1 | no | — |
| 543 | D4 | — | 18 | 2 | no | — |
| 544 | D4 | — | 24 | 1 | no | — |
| 545 | D4 | — | 36 | 4 | no | — |
| 546 | D4 | — | 36 | 4 | no | — |
| 547 | D4 | — | 36 | 2 | no | — |
| 548 | D4 | — | 72 | 1 | no | — |
| 549 | D4 | — | 72 | 2 | no | — |
| 550 | D4 | — | 72 | 2 | no | — |
| 551 | C2×C4 | — | 3 | 2 | no | — |
| 552 | C2×C4 | — | 3 | 2 | no | — |
| 553 | C2×C4 | — | 6 | 1 | no | — |
| 554 | C2×C4 | — | 12 | 2 | no | — |
| 555 | C2×C4 | — | 18 | 1 | no | — |
| 556 | C2×C4 | — | 36 | 4 | no | — |
| 557 | C2×C4 | — | 36 | 4 | no | — |
| 558 | C2×C4 | — | 36 | 2 | no | — |
| 559 | C2×C4 | D3×D12 | 1 | 1 | yes | characteristic |
| 560 | C2×C4 | D3×D12 | 1 | 1 | yes | characteristic |
| 561 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 562 | C8 | — | 2 | 2 | no | — |
| 563 | C8 | — | 3 | 2 | no | — |
| 564 | C8 | — | 6 | 1 | no | — |
| 565 | C2×C3 | — | 2 | 1 | no | — |
| 566 | C2×C3 | — | 2 | 1 | no | — |
| 567 | C2×C3 | — | 2 | 1 | no | — |
| 568 | C2×C3 | — | 24 | 2 | no | — |
| 569 | C2×C3 | — | 24 | 1 | no | — |
| 570 | C2×C3 | #5577 | 1 | 1 | yes | characteristic |
| 571 | C2×C3 | #5599 | 1 | 1 | yes | characteristic |
| 572 | C2×C3 | C22×D24 | 1 | 1 | yes | characteristic |
| 573 | C2×C3 | #5752 | 1 | 1 | yes | characteristic |
| 574 | C2×C3 | C2×D3×D8 | 1 | 1 | yes | characteristic |
| 575 | C2×C3 | #5774 | 1 | 1 | yes | characteristic |
| 576 | D3 | — | 8 | 1 | no | — |
| 577 | D3 | — | 8 | 2 | no | — |
| 578 | D3 | — | 24 | 2 | no | — |
| 579 | D3 | — | 24 | 1 | no | — |
| 580 | D3 | — | 24 | 2 | no | — |
| 581 | D3 | — | 24 | 1 | no | — |
| 582 | D3 | — | 24 | 2 | no | — |
| 583 | D3 | — | 48 | 2 | no | — |
| 584 | C22 | — | 12 | 1 | no | — |
| 585 | C22 | — | 12 | 2 | no | — |
| 586 | C22 | — | 12 | 2 | no | — |
| 587 | C22 | — | 12 | 1 | no | — |
| 588 | C22 | — | 12 | 1 | no | — |
| 589 | C22 | — | 12 | 2 | no | — |
| 590 | C22 | — | 36 | 1 | no | — |
| 591 | C22 | — | 36 | 2 | no | — |
| 592 | C22 | — | 36 | 1 | no | — |
| 593 | C22 | — | 36 | 2 | no | — |
| 594 | C22 | — | 36 | 1 | no | — |
| 595 | C22 | — | 36 | 2 | no | — |
| 596 | C22 | C2×D3×D12 | 1 | 1 | yes | characteristic |
| 597 | C4 | — | 2 | 1 | no | — |
| 598 | C4 | — | 3 | 4 | no | — |
| 599 | C4 | — | 6 | 2 | no | — |
| 600 | C4 | — | 12 | 1 | no | — |
| 601 | C4 | — | 36 | 1 | no | — |
| 602 | C4 | D3×D24 | 1 | 2 | yes | — |
| 603 | C4 | #64314 | 1 | 1 | yes | characteristic |
| 604 | C4 | D3×#239 | 1 | 1 | yes | characteristic |
| 605 | C3 | — | 2 | 1 | no | — |
| 606 | C3 | #79910 | 1 | 1 | yes | characteristic, complemented |
| 607 | C3 | #80324 | 1 | 1 | yes | characteristic, complemented |
| 608 | C2 | — | 24 | 1 | no | — |
| 609 | C2 | — | 24 | 2 | no | — |
| 610 | C2 | — | 72 | 1 | no | — |
| 611 | C2 | — | 72 | 2 | no | — |
| 612 | C2 | #10594524 | 1 | 1 | yes | characteristic |
| 613 | C2 | C2×D3×D24 | 1 | 1 | yes | characteristic |
| 614 | C2 | #10594714 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10593902 | C2 | semidirect |
| 2. #10593900 | C2 | semidirect |
| 3. #10592542 | C2 | semidirect |
| 4. C3×#4843 | C2 | semidirect |
| 5. C3×#4830 | C2 | semidirect |
| 6. #10590880 | C2 | semidirect |
| 7. #10590765 | C2 | semidirect |
| 8. #10590753 | C2 | semidirect |
| 9. #10590745 | C2 | semidirect |
| 10. #10590350 | C2 | semidirect |
| 11. C4×#3714 | C2 | semidirect |
| 58. #4843 | D3 | semidirect |
| 59. #4830 | D3 | semidirect |
| 192. C3×Dic6 | D8 | semidirect |
| 201. C3×C3⋊C8 | #41 | semidirect |
| 423. Dic6 | D24 | semidirect |
| 430. C3⋊C8 | #239 | semidirect |
| 529. C32 | #3391 | semidirect |
| 606. C3 | #79910 | semidirect |
| 607. C3 | #80324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593902 | 2 |
| #10593900 | 2 |
| #10592542 | 2 |
| C3×#4843 | 2 |
| C3×#4830 | 2 |
| #10590880 | 2 |
| #10590765 | 2 |
| #10590753 | 2 |
| #10590745 | 2 |
| #10590350 | 2 |
| C4×#3714 | 2 |
| #80324 | 3 |
| #79910 | 3 |