Finite Group DatabasebetaFinite Group DatabasebetaOrder 3072.
1350 conjugacy classes of subgroups.
The subgroup lattice has 504 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72226126 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #72225892 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C3×#122220 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72225823 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72225817 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #72214020 | — | 3 | 1 | no | maximal, Sylow |
| 7 | #10950617 | — | 2 | 2 | no | — |
| 8 | #10782888 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#68062 | C22 | 1 | 1 | yes | characteristic |
| 10 | #10713447 | — | 2 | 4 | no | — |
| 11 | #10709915 | — | 2 | 2 | no | — |
| 12 | #10709905 | C4 | 1 | 1 | yes | characteristic |
| 13 | #10709905 | C4 | 1 | 1 | yes | characteristic |
| 14 | #10709899 | C4 | 1 | 1 | yes | characteristic |
| 15 | #10709899 | C4 | 1 | 1 | yes | characteristic |
| 16 | #10706823 | — | 2 | 2 | no | — |
| 17 | #10705316 | — | 2 | 4 | no | — |
| 18 | #10688988 | C22 | 1 | 2 | yes | — |
| 19 | C3×#11402 | C22 | 1 | 2 | yes | — |
| 20 | C3×C8×M32 | C22 | 1 | 1 | yes | characteristic |
| 21 | C3×#7053 | — | 2 | 2 | no | — |
| 22 | #491469 | — | 3 | 1 | no | — |
| 23 | #141837 | — | 3 | 2 | no | — |
| 24 | #141754 | — | 3 | 2 | no | — |
| 25 | #135792 | — | 3 | 1 | no | — |
| 26 | #122220 | D3 | 1 | 1 | yes | characteristic, complemented |
| 27 | C2×#4908 | — | 4 | 4 | no | — |
| 28 | #78470 | — | 2 | 2 | no | — |
| 29 | #78467 | — | 2 | 1 | no | — |
| 30 | C2×#4695 | — | 2 | 2 | no | — |
| 31 | C2×#4695 | — | 2 | 1 | no | — |
| 32 | C3×C4×M32 | D4 | 1 | 4 | yes | — |
| 33 | C3×C4×M32 | D4 | 1 | 2 | yes | — |
| 34 | C2×C3×C82 | C23 | 1 | 1 | yes | characteristic |
| 35 | C2×#4516 | — | 4 | 8 | no | — |
| 36 | #69792 | — | 2 | 2 | no | — |
| 37 | #69730 | — | 2 | 2 | no | — |
| 38 | #69730 | — | 2 | 2 | no | — |
| 39 | #69081 | — | 4 | 4 | no | — |
| 40 | #69061 | — | 2 | 2 | no | — |
| 41 | #69061 | — | 2 | 2 | no | — |
| 42 | #69060 | — | 2 | 2 | no | — |
| 43 | #69060 | — | 2 | 2 | no | — |
| 44 | #68065 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | #68062 | — | 2 | 1 | no | — |
| 46 | #68062 | — | 2 | 2 | no | — |
| 47 | #68062 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | #68062 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | #68062 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | #68060 | — | 2 | 1 | no | — |
| 51 | #68058 | — | 2 | 2 | no | — |
| 52 | C3×#1312 | — | 2 | 2 | no | — |
| 53 | C3×#1312 | — | 2 | 2 | no | — |
| 54 | C3×#1311 | D4 | 1 | 2 | yes | — |
| 55 | C3×C8×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 56 | C3×C8×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 57 | #67516 | — | 4 | 8 | no | — |
| 58 | #67513 | — | 4 | 4 | no | — |
| 59 | #33717 | — | 6 | 2 | no | — |
| 60 | #19603 | — | 3 | 1 | no | — |
| 61 | C2×#1712 | — | 3 | 1 | no | — |
| 62 | #13213 | — | 6 | 4 | no | — |
| 63 | #12519 | — | 6 | 2 | no | — |
| 64 | #12517 | — | 3 | 1 | no | — |
| 65 | #12517 | — | 3 | 1 | no | — |
| 66 | #12515 | — | 3 | 1 | no | — |
| 67 | #12515 | — | 3 | 1 | no | — |
| 68 | #12020 | — | 6 | 2 | no | — |
| 69 | #11680 | — | 6 | 4 | no | — |
| 70 | #11402 | C2×D3 | 1 | 2 | yes | — |
| 71 | C8×M32 | C2×D3 | 1 | 1 | yes | characteristic |
| 72 | #8822 | — | 3 | 2 | no | — |
| 73 | #7053 | — | 2 | 2 | no | — |
| 74 | C2×#904 | — | 4 | 2 | no | — |
| 75 | C22×D24 | — | 4 | 2 | no | — |
| 76 | C22×D24 | — | 4 | 4 | no | — |
| 77 | #5477 | — | 4 | 1 | no | — |
| 78 | C2×#874 | — | 4 | 1 | no | — |
| 79 | C2×C3×M32 | — | 2 | 4 | no | — |
| 80 | C2×C3×M32 | SD16 | 1 | 4 | yes | — |
| 81 | C2×C3×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 82 | C2×C3×C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 83 | #5115 | — | 4 | 4 | no | — |
| 84 | C2×#819 | — | 4 | 4 | no | — |
| 85 | #4924 | — | 4 | 2 | no | — |
| 86 | #4908 | — | 8 | 8 | no | — |
| 87 | #4908 | — | 8 | 8 | no | — |
| 88 | C2×#800 | — | 4 | 4 | no | — |
| 89 | C2×#800 | — | 4 | 4 | no | — |
| 90 | C2×D48 | — | 4 | 4 | no | — |
| 91 | C2×D48 | — | 4 | 4 | no | — |
| 92 | #4699 | — | 2 | 1 | no | — |
| 93 | #4696 | — | 4 | 2 | no | — |
| 94 | #4695 | — | 2 | 1 | no | — |
| 95 | #4695 | — | 2 | 1 | no | — |
| 96 | #4695 | — | 2 | 1 | no | — |
| 97 | #4695 | — | 2 | 2 | no | — |
| 98 | #4695 | — | 2 | 2 | no | — |
| 99 | #4695 | — | 2 | 2 | no | — |
| 100 | #4695 | — | 4 | 2 | no | — |
| 101 | #4695 | — | 4 | 1 | no | — |
| 102 | #4695 | — | 4 | 2 | no | — |
| 103 | #4695 | — | 4 | 4 | no | — |
| 104 | #4694 | — | 4 | 2 | no | — |
| 105 | #4693 | — | 4 | 1 | no | — |
| 106 | C4×D24 | — | 4 | 4 | no | — |
| 107 | #4682 | — | 2 | 2 | no | — |
| 108 | C3×#346 | — | 2 | 4 | no | — |
| 109 | C3×#346 | D8 | 1 | 4 | yes | — |
| 110 | C3×C4×C16 | — | 2 | 4 | no | — |
| 111 | C3×C4×C16 | C22⋊C4 | 1 | 2 | yes | — |
| 112 | C3×C4×C16 | C22⋊C4 | 1 | 2 | yes | — |
| 113 | C3×C82 | C22×C4 | 1 | 1 | yes | characteristic |
| 114 | C3×C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | C3×C82 | #41 | 1 | 2 | yes | — |
| 116 | #4516 | — | 8 | 16 | no | — |
| 117 | #4457 | — | 4 | 4 | no | — |
| 118 | #4457 | — | 4 | 4 | no | — |
| 119 | C2×#509 | — | 12 | 4 | no | — |
| 120 | #3169 | — | 6 | 2 | no | — |
| 121 | #3147 | — | 6 | 1 | no | — |
| 122 | C2×#493 | — | 6 | 2 | no | — |
| 123 | C2×#493 | — | 6 | 1 | no | — |
| 124 | #2250 | — | 12 | 4 | no | — |
| 125 | #2248 | — | 6 | 2 | no | — |
| 126 | #2248 | — | 6 | 2 | no | — |
| 127 | #2246 | — | 6 | 2 | no | — |
| 128 | #2246 | — | 6 | 2 | no | — |
| 129 | C2×#361 | — | 12 | 8 | no | — |
| 130 | C4×M32 | D12 | 1 | 4 | yes | — |
| 131 | C4×M32 | D12 | 1 | 2 | yes | — |
| 132 | #1848 | — | 6 | 2 | no | — |
| 133 | #1713 | — | 3 | 1 | no | — |
| 134 | #1712 | — | 3 | 1 | no | — |
| 135 | #1712 | — | 3 | 1 | no | — |
| 136 | #1712 | — | 3 | 1 | no | — |
| 137 | #1712 | — | 6 | 2 | no | — |
| 138 | #1712 | — | 6 | 1 | no | — |
| 139 | #1709 | — | 6 | 1 | no | — |
| 140 | #1706 | — | 6 | 2 | no | — |
| 141 | #1566 | — | 6 | 2 | no | — |
| 142 | #1566 | — | 6 | 2 | no | — |
| 143 | C2×C82 | C22×D3 | 1 | 1 | yes | characteristic |
| 144 | #1368 | — | 12 | 4 | no | — |
| 145 | #1333 | — | 12 | 8 | no | — |
| 146 | #1312 | — | 2 | 2 | no | — |
| 147 | #1312 | — | 2 | 2 | no | — |
| 148 | #1311 | #67 | 1 | 2 | yes | — |
| 149 | C8×C16 | C4×D3 | 1 | 1 | yes | characteristic |
| 150 | C8×C16 | C4×D3 | 1 | 1 | yes | characteristic |
| 151 | C2×#235 | — | 8 | 1 | no | — |
| 152 | C22×D12 | — | 8 | 1 | no | — |
| 153 | C22×D12 | — | 8 | 2 | no | — |
| 154 | C22×C3×C8 | C2×SD16 | 1 | 2 | yes | — |
| 155 | C22×C3×C8 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 156 | C2×C3×C42 | #127 | 1 | 1 | yes | characteristic |
| 157 | #930 | — | 8 | 2 | no | — |
| 158 | C2×#208 | — | 8 | 2 | no | — |
| 159 | C2×Dic12 | — | 4 | 2 | no | — |
| 160 | #904 | — | 8 | 4 | no | — |
| 161 | #904 | — | 8 | 4 | no | — |
| 162 | C2×D24 | — | 4 | 2 | no | — |
| 163 | C2×D24 | — | 4 | 2 | no | — |
| 164 | C2×D24 | — | 4 | 2 | no | — |
| 165 | C2×D24 | — | 4 | 4 | no | — |
| 166 | C2×D24 | — | 4 | 4 | no | — |
| 167 | C2×D24 | — | 4 | 4 | no | — |
| 168 | C2×D24 | — | 8 | 4 | no | — |
| 169 | C2×D24 | — | 8 | 4 | no | — |
| 170 | C2×D24 | — | 8 | 8 | no | — |
| 171 | C2×D24 | — | 8 | 8 | no | — |
| 172 | C2×D24 | — | 8 | 4 | no | — |
| 173 | C2×D24 | — | 8 | 2 | no | — |
| 174 | C2×#204 | — | 8 | 2 | no | — |
| 175 | #875 | — | 8 | 1 | no | — |
| 176 | #874 | — | 4 | 1 | no | — |
| 177 | #874 | — | 4 | 1 | no | — |
| 178 | #874 | — | 4 | 1 | no | — |
| 179 | #874 | — | 8 | 1 | no | — |
| 180 | #874 | — | 8 | 2 | no | — |
| 181 | C4×D12 | — | 8 | 2 | no | — |
| 182 | #869 | — | 4 | 1 | no | — |
| 183 | C3×M32 | — | 2 | 8 | no | — |
| 184 | C3×M32 | — | 4 | 8 | no | — |
| 185 | C2×C3×C16 | — | 4 | 4 | no | — |
| 186 | C2×C3×C16 | #102 | 1 | 4 | yes | — |
| 187 | C2×C3×C16 | #102 | 1 | 4 | yes | — |
| 188 | C3×C4×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 189 | C3×C4×C8 | C4×D4 | 1 | 2 | yes | — |
| 190 | C3×C4×C8 | #121 | 1 | 2 | yes | — |
| 191 | C3×C4×C8 | #124 | 1 | 1 | yes | characteristic |
| 192 | C3×C4×C8 | C2×D8 | 1 | 2 | yes | — |
| 193 | C3×C4×C8 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 194 | #821 | — | 8 | 4 | no | — |
| 195 | #819 | — | 8 | 8 | no | — |
| 196 | #818 | — | 4 | 4 | no | — |
| 197 | C4⋊(C3⋊C8) | — | 8 | 2 | no | — |
| 198 | C4⋊(C3⋊C8) | — | 8 | 2 | no | — |
| 199 | #800 | — | 8 | 8 | no | — |
| 200 | #800 | — | 8 | 8 | no | — |
| 201 | D48 | — | 8 | 8 | no | — |
| 202 | D48 | — | 8 | 8 | no | — |
| 203 | C2×#135 | — | 12 | 2 | no | — |
| 204 | C22×D8 | — | 12 | 2 | no | — |
| 205 | C22×D8 | — | 12 | 4 | no | — |
| 206 | #532 | — | 12 | 1 | no | — |
| 207 | C2×#127 | — | 12 | 1 | no | — |
| 208 | #509 | — | 24 | 8 | no | — |
| 209 | #509 | — | 24 | 8 | no | — |
| 210 | C2×SD32 | — | 12 | 4 | no | — |
| 211 | C2×SD32 | — | 12 | 4 | no | — |
| 212 | C2×D16 | — | 12 | 4 | no | — |
| 213 | C2×D16 | — | 12 | 4 | no | — |
| 214 | C2×M32 | — | 2 | 4 | no | — |
| 215 | C2×M32 | #204 | 1 | 4 | yes | — |
| 216 | #500 | — | 6 | 2 | no | — |
| 217 | #495 | — | 12 | 2 | no | — |
| 218 | #494 | — | 6 | 1 | no | — |
| 219 | #493 | — | 6 | 2 | no | — |
| 220 | #493 | — | 6 | 2 | no | — |
| 221 | #493 | — | 6 | 2 | no | — |
| 222 | #493 | — | 6 | 1 | no | — |
| 223 | #493 | — | 6 | 1 | no | — |
| 224 | #493 | — | 6 | 1 | no | — |
| 225 | #493 | — | 12 | 1 | no | — |
| 226 | #493 | — | 12 | 2 | no | — |
| 227 | #493 | — | 12 | 4 | no | — |
| 228 | #493 | — | 12 | 2 | no | — |
| 229 | #492 | — | 12 | 1 | no | — |
| 230 | #486 | — | 12 | 2 | no | — |
| 231 | #466 | — | 12 | 4 | no | — |
| 232 | C4×D8 | — | 12 | 4 | no | — |
| 233 | C2×#108 | — | 12 | 4 | no | — |
| 234 | #423 | — | 12 | 2 | no | — |
| 235 | C2×C4×C8 | C2×D12 | 1 | 2 | yes | — |
| 236 | C2×C4×C8 | C2×D12 | 1 | 1 | yes | characteristic |
| 237 | #361 | — | 24 | 16 | no | — |
| 238 | #346 | — | 2 | 4 | no | — |
| 239 | #346 | D24 | 1 | 4 | yes | — |
| 240 | C4×C16 | — | 2 | 4 | no | — |
| 241 | C4×C16 | (C2×D3)⋊C4 | 1 | 2 | yes | — |
| 242 | C4×C16 | (C2×D3)⋊C4 | 1 | 2 | yes | — |
| 243 | #334 | — | 12 | 4 | no | — |
| 244 | #334 | — | 12 | 4 | no | — |
| 245 | C82 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 246 | C82 | #235 | 1 | 2 | yes | — |
| 247 | C82 | C2×#67 | 1 | 1 | yes | characteristic |
| 248 | C23×D3 | — | 16 | 1 | no | — |
| 249 | C22×C3×C4 | #492 | 1 | 1 | yes | characteristic |
| 250 | C22×C3×C4 | #496 | 1 | 2 | yes | — |
| 251 | C2×#67 | — | 16 | 1 | no | — |
| 252 | #235 | — | 16 | 2 | no | — |
| 253 | #235 | — | 16 | 2 | no | — |
| 254 | C2×D12 | — | 8 | 1 | no | — |
| 255 | C2×D12 | — | 8 | 1 | no | — |
| 256 | C2×D12 | — | 8 | 1 | no | — |
| 257 | C2×D12 | — | 8 | 2 | no | — |
| 258 | C2×D12 | — | 8 | 2 | no | — |
| 259 | C2×D12 | — | 8 | 2 | no | — |
| 260 | C2×D12 | — | 16 | 2 | no | — |
| 261 | C2×D12 | — | 16 | 2 | no | — |
| 262 | C2×D12 | — | 16 | 4 | no | — |
| 263 | C2×D12 | — | 16 | 4 | no | — |
| 264 | C2×D12 | — | 16 | 1 | no | — |
| 265 | C2×D12 | — | 16 | 2 | no | — |
| 266 | C2×C4×D3 | — | 16 | 1 | no | — |
| 267 | C2×Dic6 | — | 8 | 1 | no | — |
| 268 | C2×C3×C8 | — | 2 | 4 | no | — |
| 269 | C2×C3×C8 | — | 2 | 8 | no | — |
| 270 | C2×C3×C8 | C2×#102 | 1 | 2 | yes | — |
| 271 | C2×C3×C8 | #442 | 1 | 4 | yes | — |
| 272 | C2×C3×C8 | #469 | 1 | 4 | yes | — |
| 273 | C2×C3×C8 | #486 | 1 | 2 | yes | — |
| 274 | C3×C42 | #390 | 1 | 1 | yes | characteristic |
| 275 | C3×C42 | #493 | 1 | 1 | yes | characteristic |
| 276 | C3×C42 | #496 | 1 | 2 | yes | — |
| 277 | (C2×D3)⋊C4 | — | 16 | 2 | no | — |
| 278 | C4⋊Dic3 | — | 8 | 2 | no | — |
| 279 | #208 | — | 16 | 4 | no | — |
| 280 | C2×C3⋊C8 | — | 16 | 2 | no | — |
| 281 | Dic12 | — | 8 | 4 | no | — |
| 282 | D24 | — | 8 | 4 | no | — |
| 283 | D24 | — | 8 | 4 | no | — |
| 284 | D24 | — | 8 | 4 | no | — |
| 285 | D24 | — | 8 | 8 | no | — |
| 286 | D24 | — | 8 | 8 | no | — |
| 287 | D24 | — | 8 | 8 | no | — |
| 288 | D24 | — | 16 | 4 | no | — |
| 289 | D24 | — | 16 | 8 | no | — |
| 290 | #204 | — | 16 | 4 | no | — |
| 291 | C3×C16 | — | 2 | 4 | no | — |
| 292 | C3×C16 | — | 8 | 4 | no | — |
| 293 | C3×C16 | #361 | 1 | 8 | yes | complemented |
| 294 | C2×#41 | — | 24 | 1 | no | — |
| 295 | C22×D4 | — | 24 | 1 | no | — |
| 296 | C22×D4 | — | 24 | 2 | no | — |
| 297 | #135 | — | 24 | 4 | no | — |
| 298 | #135 | — | 24 | 4 | no | — |
| 299 | C2×Q16 | — | 12 | 2 | no | — |
| 300 | C2×SD16 | — | 24 | 2 | no | — |
| 301 | C2×D8 | — | 12 | 4 | no | — |
| 302 | C2×D8 | — | 12 | 4 | no | — |
| 303 | C2×D8 | — | 12 | 4 | no | — |
| 304 | C2×D8 | — | 12 | 2 | no | — |
| 305 | C2×D8 | — | 12 | 2 | no | — |
| 306 | C2×D8 | — | 12 | 2 | no | — |
| 307 | C2×D8 | — | 24 | 8 | no | — |
| 308 | C2×D8 | — | 24 | 8 | no | — |
| 309 | C2×D8 | — | 24 | 4 | no | — |
| 310 | C2×D8 | — | 24 | 4 | no | — |
| 311 | C2×D8 | — | 24 | 4 | no | — |
| 312 | C2×D8 | — | 24 | 2 | no | — |
| 313 | C2×M16 | — | 24 | 2 | no | — |
| 314 | C22×C8 | C2×#204 | 1 | 2 | yes | — |
| 315 | C22×C8 | #908 | 1 | 4 | yes | — |
| 316 | C4⋊Q8 | — | 12 | 1 | no | — |
| 317 | #127 | — | 12 | 1 | no | — |
| 318 | #127 | — | 12 | 1 | no | — |
| 319 | #127 | — | 12 | 1 | no | — |
| 320 | #127 | — | 24 | 1 | no | — |
| 321 | #127 | — | 24 | 2 | no | — |
| 322 | #124 | — | 24 | 1 | no | — |
| 323 | #121 | — | 24 | 2 | no | — |
| 324 | C4×D4 | — | 24 | 2 | no | — |
| 325 | C2×C42 | #874 | 1 | 1 | yes | characteristic |
| 326 | SD32 | — | 24 | 8 | no | — |
| 327 | SD32 | — | 24 | 8 | no | — |
| 328 | D16 | — | 24 | 8 | no | — |
| 329 | D16 | — | 24 | 8 | no | — |
| 330 | M32 | — | 2 | 8 | no | — |
| 331 | M32 | — | 4 | 8 | no | — |
| 332 | C2×C16 | — | 4 | 4 | no | — |
| 333 | C2×C16 | #821 | 1 | 4 | yes | — |
| 334 | C2×C16 | #821 | 1 | 4 | yes | — |
| 335 | #108 | — | 24 | 8 | no | — |
| 336 | #107 | — | 12 | 4 | no | — |
| 337 | C4⋊C8 | — | 24 | 2 | no | — |
| 338 | C4⋊C8 | — | 24 | 2 | no | — |
| 339 | #102 | — | 24 | 4 | no | — |
| 340 | C4×C8 | C4×D12 | 1 | 2 | yes | — |
| 341 | C4×C8 | #875 | 1 | 1 | yes | characteristic |
| 342 | C4×C8 | C2×D24 | 1 | 2 | yes | — |
| 343 | C4×C8 | #908 | 1 | 4 | yes | — |
| 344 | C4×C8 | C2×(C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 345 | C4×C8 | #930 | 1 | 2 | yes | — |
| 346 | C23×C3 | #1715 | 1 | 1 | yes | characteristic |
| 347 | C22×D3 | — | 16 | 1 | no | — |
| 348 | C22×D3 | — | 16 | 1 | no | — |
| 349 | C22×D3 | — | 16 | 1 | no | — |
| 350 | C22×D3 | — | 32 | 1 | no | — |
| 351 | C22×D3 | — | 32 | 1 | no | — |
| 352 | C22×D3 | — | 32 | 2 | no | — |
| 353 | C22×D3 | — | 32 | 2 | no | — |
| 354 | C2×C3×C4 | — | 2 | 2 | no | — |
| 355 | C2×C3×C4 | — | 2 | 4 | no | — |
| 356 | C2×C3×C4 | #1715 | 1 | 1 | yes | characteristic |
| 357 | C2×C3×C4 | #1721 | 1 | 2 | yes | — |
| 358 | C2×C3×C4 | #1957 | 1 | 1 | yes | characteristic |
| 359 | C2×C3×C4 | #1972 | 1 | 2 | yes | — |
| 360 | #67 | — | 32 | 2 | no | — |
| 361 | C2×Dic3 | — | 16 | 1 | no | — |
| 362 | D12 | — | 16 | 2 | no | — |
| 363 | D12 | — | 16 | 2 | no | — |
| 364 | D12 | — | 16 | 2 | no | — |
| 365 | D12 | — | 16 | 4 | no | — |
| 366 | D12 | — | 16 | 4 | no | — |
| 367 | D12 | — | 16 | 4 | no | — |
| 368 | D12 | — | 32 | 2 | no | — |
| 369 | D12 | — | 32 | 4 | no | — |
| 370 | C4×D3 | — | 32 | 1 | no | — |
| 371 | C4×D3 | — | 32 | 1 | no | — |
| 372 | Dic6 | — | 16 | 2 | no | — |
| 373 | C3×C8 | — | 2 | 2 | no | — |
| 374 | C3×C8 | — | 2 | 4 | no | — |
| 375 | C3×C8 | C2×#361 | 1 | 4 | yes | — |
| 376 | C3×C8 | AGL(1,ℤ/16) | 1 | 8 | yes | — |
| 377 | C3⋊C8 | — | 32 | 2 | no | — |
| 378 | C24 | — | 48 | 1 | no | — |
| 379 | #41 | — | 48 | 2 | no | — |
| 380 | #41 | — | 48 | 2 | no | — |
| 381 | C2×Q8 | — | 24 | 1 | no | — |
| 382 | C2×D4 | — | 24 | 1 | no | — |
| 383 | C2×D4 | — | 24 | 1 | no | — |
| 384 | C2×D4 | — | 24 | 1 | no | — |
| 385 | C2×D4 | — | 24 | 2 | no | — |
| 386 | C2×D4 | — | 24 | 2 | no | — |
| 387 | C2×D4 | — | 24 | 2 | no | — |
| 388 | C2×D4 | — | 48 | 4 | no | — |
| 389 | C2×D4 | — | 48 | 4 | no | — |
| 390 | C2×D4 | — | 48 | 2 | no | — |
| 391 | C2×D4 | — | 48 | 2 | no | — |
| 392 | C2×D4 | — | 48 | 1 | no | — |
| 393 | C2×D4 | — | 48 | 1 | no | — |
| 394 | C2×D4 | — | 48 | 2 | no | — |
| 395 | C22×C4 | — | 48 | 1 | no | — |
| 396 | C22×C4 | #4693 | 1 | 1 | yes | characteristic |
| 397 | C22×C4 | #4712 | 1 | 2 | yes | — |
| 398 | Q16 | — | 24 | 4 | no | — |
| 399 | SD16 | — | 48 | 4 | no | — |
| 400 | D8 | — | 24 | 4 | no | — |
| 401 | D8 | — | 24 | 4 | no | — |
| 402 | D8 | — | 24 | 4 | no | — |
| 403 | D8 | — | 24 | 8 | no | — |
| 404 | D8 | — | 24 | 8 | no | — |
| 405 | D8 | — | 24 | 8 | no | — |
| 406 | D8 | — | 48 | 8 | no | — |
| 407 | D8 | — | 48 | 4 | no | — |
| 408 | M16 | — | 48 | 4 | no | — |
| 409 | C2×C8 | — | 2 | 4 | no | — |
| 410 | C2×C8 | — | 2 | 8 | no | — |
| 411 | C2×C8 | — | 48 | 2 | no | — |
| 412 | C2×C8 | #4694 | 1 | 2 | yes | — |
| 413 | C2×C8 | #4711 | 1 | 4 | yes | — |
| 414 | C2×C8 | C2×#821 | 1 | 2 | yes | — |
| 415 | C2×C8 | #5135 | 1 | 4 | yes | — |
| 416 | C4⋊C4 | — | 24 | 2 | no | — |
| 417 | C22⋊C4 | — | 48 | 2 | no | — |
| 418 | C42 | #4695 | 1 | 1 | yes | characteristic |
| 419 | C42 | #4712 | 1 | 2 | yes | — |
| 420 | C42 | #4939 | 1 | 1 | yes | characteristic |
| 421 | C16 | — | 2 | 4 | no | — |
| 422 | C16 | — | 8 | 4 | no | — |
| 423 | C16 | #4516 | 1 | 8 | yes | complemented |
| 424 | C22×C3 | — | 2 | 1 | no | — |
| 425 | C22×C3 | — | 2 | 2 | no | — |
| 426 | C22×C3 | #9837 | 1 | 1 | yes | characteristic |
| 427 | C2×D3 | — | 32 | 1 | no | — |
| 428 | C2×D3 | — | 32 | 1 | no | — |
| 429 | C2×D3 | — | 32 | 1 | no | — |
| 430 | C2×D3 | — | 32 | 2 | no | — |
| 431 | C2×D3 | — | 32 | 2 | no | — |
| 432 | C2×D3 | — | 32 | 2 | no | — |
| 433 | C2×D3 | — | 64 | 1 | no | — |
| 434 | C2×D3 | — | 64 | 2 | no | — |
| 435 | C2×D3 | — | 64 | 1 | no | — |
| 436 | C3×C4 | — | 2 | 1 | no | — |
| 437 | C3×C4 | — | 2 | 2 | no | — |
| 438 | C3×C4 | #13213 | 1 | 2 | yes | — |
| 439 | C3×C4 | #13249 | 1 | 4 | yes | — |
| 440 | Dic3 | — | 32 | 1 | no | — |
| 441 | C23 | — | 48 | 1 | no | — |
| 442 | C23 | — | 48 | 1 | no | — |
| 443 | C23 | — | 48 | 1 | no | — |
| 444 | C23 | — | 96 | 2 | no | — |
| 445 | C23 | — | 96 | 2 | no | — |
| 446 | C23 | — | 96 | 1 | no | — |
| 447 | C23 | — | 96 | 1 | no | — |
| 448 | C23 | #68091 | 1 | 1 | yes | characteristic |
| 449 | Q8 | — | 48 | 2 | no | — |
| 450 | D4 | — | 48 | 4 | no | — |
| 451 | D4 | — | 48 | 4 | no | — |
| 452 | D4 | — | 48 | 4 | no | — |
| 453 | D4 | — | 48 | 2 | no | — |
| 454 | D4 | — | 48 | 2 | no | — |
| 455 | D4 | — | 48 | 2 | no | — |
| 456 | D4 | — | 96 | 4 | no | — |
| 457 | D4 | — | 96 | 2 | no | — |
| 458 | D4 | — | 96 | 2 | no | — |
| 459 | C2×C4 | — | 2 | 4 | no | — |
| 460 | C2×C4 | — | 2 | 2 | no | — |
| 461 | C2×C4 | — | 48 | 1 | no | — |
| 462 | C2×C4 | — | 96 | 1 | no | — |
| 463 | C2×C4 | — | 96 | 1 | no | — |
| 464 | C2×C4 | #68091 | 1 | 1 | yes | characteristic |
| 465 | C2×C4 | #68094 | 1 | 2 | yes | — |
| 466 | C2×C4 | #69772 | 1 | 1 | yes | characteristic |
| 467 | C2×C4 | #69825 | 1 | 2 | yes | — |
| 468 | C8 | — | 2 | 4 | no | — |
| 469 | C8 | — | 2 | 2 | no | — |
| 470 | C8 | — | 96 | 2 | no | — |
| 471 | C8 | #69091 | 1 | 8 | yes | — |
| 472 | C8 | C2×#4516 | 1 | 4 | yes | — |
| 473 | C2×C3 | — | 4 | 1 | no | — |
| 474 | C2×C3 | #141754 | 1 | 1 | yes | characteristic |
| 475 | C2×C3 | #141758 | 1 | 2 | yes | — |
| 476 | D3 | — | 64 | 1 | no | — |
| 477 | D3 | — | 64 | 1 | no | — |
| 478 | D3 | — | 64 | 1 | no | — |
| 479 | C22 | — | 2 | 2 | no | — |
| 480 | C22 | — | 2 | 1 | no | — |
| 481 | C22 | — | 96 | 2 | no | — |
| 482 | C22 | — | 96 | 2 | no | — |
| 483 | C22 | — | 96 | 2 | no | — |
| 484 | C22 | — | 96 | 1 | no | — |
| 485 | C22 | — | 96 | 1 | no | — |
| 486 | C22 | — | 96 | 1 | no | — |
| 487 | C22 | — | 192 | 1 | no | — |
| 488 | C22 | — | 192 | 2 | no | — |
| 489 | C22 | — | 192 | 1 | no | — |
| 490 | C22 | #10695025 | 1 | 1 | yes | characteristic |
| 491 | C4 | — | 2 | 2 | no | — |
| 492 | C4 | — | 2 | 1 | no | — |
| 493 | C4 | — | 96 | 1 | no | — |
| 494 | C4 | #10713447 | 1 | 2 | yes | — |
| 495 | C4 | #10713637 | 1 | 4 | yes | — |
| 496 | C3 | #72214020 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 497 | C2 | — | 4 | 1 | no | — |
| 498 | C2 | — | 192 | 1 | no | — |
| 499 | C2 | — | 192 | 1 | no | — |
| 500 | C2 | — | 192 | 1 | no | — |
| 501 | C2 | #72225887 | 1 | 2 | yes | — |
| 502 | C2 | #72225892 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72226126 | C2 | semidirect |
| 2. #72225892 | C2 | semidirect |
| 3. C3×#122220 | C2 | semidirect |
| 4. #72225823 | C2 | semidirect |
| 26. #122220 | D3 | semidirect |
| 293. C3×C16 | #361 | semidirect |
| 423. C16 | #4516 | semidirect |
| 496. C3 | #72214020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72226126 | 2 |
| #72225892 | 2 |
| C3×#122220 | 2 |
| #72225823 | 2 |
| #72225817 | 2 |
| #72214020 | 3 |