Order 3072.
2414 conjugacy classes of subgroups.
The subgroup lattice has 708 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72226119 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72226118 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72226117 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72226113 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #72226112 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #72226111 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72225940 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #72225930 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #72225829 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C3×#491500 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #72225817 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #72213956 | — | 3 | 1 | no | maximal, Sylow |
| 13 | #10950879 | — | 2 | 4 | no | — |
| 14 | #10950618 | — | 2 | 4 | no | — |
| 15 | #10950617 | — | 2 | 2 | no | — |
| 16 | #10782888 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#68062 | C22 | 1 | 1 | yes | characteristic |
| 18 | #10709929 | C22 | 1 | 2 | yes | complemented |
| 19 | #10709916 | — | 2 | 4 | no | — |
| 20 | #10709915 | — | 2 | 2 | no | — |
| 21 | #10709906 | C22 | 1 | 2 | yes | — |
| 22 | #10709906 | C22 | 1 | 2 | yes | — |
| 23 | #10709905 | C22 | 1 | 1 | yes | characteristic |
| 24 | #10709905 | C22 | 1 | 1 | yes | characteristic |
| 25 | #10709899 | C22 | 1 | 1 | yes | characteristic |
| 26 | #10709899 | C22 | 1 | 1 | yes | characteristic |
| 27 | #10709898 | C22 | 1 | 2 | yes | — |
| 28 | #10709898 | C22 | 1 | 2 | yes | — |
| 29 | #10709898 | C22 | 1 | 2 | yes | complemented |
| 30 | #10709874 | C22 | 1 | 2 | yes | complemented |
| 31 | #10709872 | C22 | 1 | 2 | yes | complemented |
| 32 | #10709855 | — | 2 | 4 | no | — |
| 33 | C8×#812 | C22 | 1 | 2 | yes | — |
| 34 | #10681802 | C22 | 1 | 2 | yes | complemented |
| 35 | #10681801 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | C16×C3⋊C16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | C3×#33748 | — | 2 | 2 | no | — |
| 38 | C3×#19603 | C22 | 1 | 2 | yes | — |
| 39 | C3×#12523 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | C3×#12515 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | C3×#12509 | C22 | 1 | 2 | yes | complemented |
| 42 | C3×#12506 | — | 2 | 2 | no | — |
| 43 | C3×C8×M32 | C22 | 1 | 1 | yes | characteristic |
| 44 | #491500 | — | 3 | 2 | no | — |
| 45 | #491500 | D3 | 1 | 1 | yes | characteristic, complemented |
| 46 | #491469 | — | 3 | 2 | no | — |
| 47 | #491469 | — | 3 | 1 | no | — |
| 48 | #123419 | — | 3 | 1 | no | — |
| 49 | #123419 | — | 3 | 2 | no | — |
| 50 | #123412 | — | 3 | 1 | no | — |
| 51 | #123412 | — | 3 | 2 | no | — |
| 52 | #123411 | — | 3 | 1 | no | — |
| 53 | #123403 | — | 3 | 1 | no | — |
| 54 | #122211 | — | 3 | 1 | no | — |
| 55 | C3×#3169 | — | 2 | 2 | no | — |
| 56 | C3×#3169 | — | 2 | 2 | no | — |
| 57 | C3×#3147 | — | 2 | 2 | no | — |
| 58 | C2×#5193 | — | 4 | 8 | no | — |
| 59 | C2×#4908 | — | 4 | 4 | no | — |
| 60 | #78470 | — | 2 | 2 | no | — |
| 61 | #78467 | — | 2 | 1 | no | — |
| 62 | C2×#4695 | — | 2 | 1 | no | — |
| 63 | C2×#4695 | — | 2 | 2 | no | — |
| 64 | C3×#2254 | — | 2 | 2 | no | — |
| 65 | C3×#2246 | — | 2 | 2 | no | — |
| 66 | C3×#2240 | — | 2 | 4 | no | — |
| 67 | C3×#2218 | — | 4 | 4 | no | — |
| 68 | C3×#2177 | — | 4 | 4 | no | — |
| 69 | C3×C4×M32 | D4 | 1 | 2 | yes | — |
| 70 | C3×#1713 | C23 | 1 | 2 | yes | — |
| 71 | C3×#1712 | C23 | 1 | 2 | yes | — |
| 72 | C3×#1709 | — | 2 | 2 | no | — |
| 73 | C3×#1706 | — | 2 | 2 | no | — |
| 74 | C3×#1706 | — | 2 | 2 | no | — |
| 75 | C2×C3×C82 | C23 | 1 | 1 | yes | characteristic |
| 76 | #71385 | — | 2 | 4 | no | — |
| 77 | #71381 | — | 2 | 4 | no | — |
| 78 | #71321 | — | 4 | 8 | no | — |
| 79 | #71313 | — | 2 | 4 | no | — |
| 80 | #71313 | — | 2 | 4 | no | — |
| 81 | #71290 | — | 2 | 4 | no | — |
| 82 | #71290 | — | 2 | 4 | no | — |
| 83 | #71290 | — | 2 | 4 | no | — |
| 84 | #71288 | — | 2 | 4 | no | — |
| 85 | #71073 | — | 4 | 8 | no | — |
| 86 | #70885 | — | 4 | 8 | no | — |
| 87 | C4×#812 | D4 | 1 | 4 | yes | — |
| 88 | #69081 | — | 4 | 4 | no | — |
| 89 | #69061 | — | 2 | 2 | no | — |
| 90 | #69061 | — | 2 | 2 | no | — |
| 91 | #69060 | — | 2 | 2 | no | — |
| 92 | #69060 | — | 2 | 2 | no | — |
| 93 | #68065 | C23 | 1 | 1 | yes | characteristic |
| 94 | #68062 | — | 2 | 1 | no | — |
| 95 | #68062 | — | 2 | 2 | no | — |
| 96 | #68062 | C23 | 1 | 1 | yes | characteristic |
| 97 | #68062 | C23 | 1 | 1 | yes | characteristic |
| 98 | #68062 | C23 | 1 | 1 | yes | characteristic |
| 99 | #68060 | — | 2 | 1 | no | — |
| 100 | #68058 | — | 2 | 2 | no | — |
| 101 | C3×#1311 | D4 | 1 | 2 | yes | — |
| 102 | C3×C8×C16 | C23 | 1 | 1 | yes | characteristic |
| 103 | C3×C8×C16 | C23 | 1 | 1 | yes | characteristic |
| 104 | #67437 | D4 | 1 | 4 | yes | — |
| 105 | C8×C3⋊C16 | C23 | 1 | 2 | yes | — |
| 106 | C8×C3⋊C16 | C23 | 1 | 2 | yes | — |
| 107 | #33748 | — | 2 | 2 | no | — |
| 108 | #33748 | — | 6 | 4 | no | — |
| 109 | #33717 | — | 6 | 4 | no | — |
| 110 | #33717 | — | 6 | 2 | no | — |
| 111 | #19603 | — | 3 | 1 | no | — |
| 112 | #19603 | C2×D3 | 1 | 2 | yes | — |
| 113 | C2×#1712 | — | 3 | 1 | no | — |
| 114 | #12523 | — | 3 | 2 | no | — |
| 115 | #12523 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 116 | #12519 | — | 6 | 4 | no | — |
| 117 | #12519 | — | 6 | 2 | no | — |
| 118 | #12517 | — | 3 | 2 | no | — |
| 119 | #12517 | — | 3 | 2 | no | — |
| 120 | #12517 | — | 3 | 1 | no | — |
| 121 | #12517 | — | 3 | 1 | no | — |
| 122 | #12515 | — | 3 | 2 | no | — |
| 123 | #12515 | — | 3 | 2 | no | — |
| 124 | #12515 | — | 3 | 2 | no | — |
| 125 | #12515 | — | 3 | 1 | no | — |
| 126 | #12515 | — | 3 | 1 | no | — |
| 127 | #12515 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 128 | #12509 | — | 3 | 2 | no | — |
| 129 | #12509 | — | 3 | 2 | no | — |
| 130 | #12509 | C2×D3 | 1 | 2 | yes | complemented |
| 131 | #12506 | — | 2 | 2 | no | — |
| 132 | #12506 | — | 6 | 4 | no | — |
| 133 | C8×M32 | — | 3 | 2 | no | — |
| 134 | C8×M32 | C2×D3 | 1 | 1 | yes | characteristic |
| 135 | #7052 | — | 3 | 1 | no | — |
| 136 | #7052 | — | 3 | 2 | no | — |
| 137 | C162 | — | 3 | 1 | no | — |
| 138 | C2×C3×#135 | — | 4 | 4 | no | — |
| 139 | C3×#532 | — | 4 | 2 | no | — |
| 140 | C2×#904 | — | 4 | 2 | no | — |
| 141 | C22×D24 | — | 4 | 2 | no | — |
| 142 | C22×D24 | — | 4 | 4 | no | — |
| 143 | #5477 | — | 4 | 1 | no | — |
| 144 | C2×#874 | — | 4 | 1 | no | — |
| 145 | C2×C3×D16 | — | 4 | 4 | no | — |
| 146 | C2×C3×M32 | D8 | 1 | 4 | yes | — |
| 147 | C3×#500 | — | 2 | 2 | no | — |
| 148 | C3×#500 | — | 2 | 2 | no | — |
| 149 | C3×#495 | — | 4 | 4 | no | — |
| 150 | C3×#494 | — | 2 | 2 | no | — |
| 151 | C3×#493 | — | 2 | 2 | no | — |
| 152 | C3×#493 | — | 2 | 2 | no | — |
| 153 | C3×#493 | — | 2 | 2 | no | — |
| 154 | C3×#492 | — | 4 | 2 | no | — |
| 155 | C3×#486 | — | 4 | 2 | no | — |
| 156 | C3×#486 | — | 4 | 2 | no | — |
| 157 | C3×#466 | — | 4 | 4 | no | — |
| 158 | C3×#466 | — | 4 | 4 | no | — |
| 159 | C3×C4×D8 | — | 4 | 4 | no | — |
| 160 | C3×C4×D8 | — | 4 | 4 | no | — |
| 161 | C2×C3×C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 162 | C2×C3×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 163 | #5193 | — | 8 | 32 | no | — |
| 164 | C2×#828 | — | 4 | 8 | no | — |
| 165 | C2×#828 | — | 4 | 8 | no | — |
| 166 | C2×#826 | — | 4 | 8 | no | — |
| 167 | C2×#826 | — | 4 | 8 | no | — |
| 168 | C2×#826 | — | 4 | 8 | no | — |
| 169 | #5115 | — | 4 | 4 | no | — |
| 170 | C2×#812 | D8 | 1 | 8 | yes | — |
| 171 | #4908 | — | 8 | 16 | no | — |
| 172 | C2×#800 | — | 4 | 4 | no | — |
| 173 | C2×#800 | — | 4 | 4 | no | — |
| 174 | C2×D48 | — | 4 | 4 | no | — |
| 175 | C2×D48 | — | 4 | 4 | no | — |
| 176 | #4699 | — | 2 | 1 | no | — |
| 177 | #4696 | — | 4 | 2 | no | — |
| 178 | #4695 | — | 2 | 2 | no | — |
| 179 | #4695 | — | 2 | 2 | no | — |
| 180 | #4695 | — | 2 | 2 | no | — |
| 181 | #4695 | — | 2 | 1 | no | — |
| 182 | #4695 | — | 2 | 1 | no | — |
| 183 | #4695 | — | 2 | 1 | no | — |
| 184 | #4695 | — | 4 | 1 | no | — |
| 185 | #4695 | — | 4 | 2 | no | — |
| 186 | #4695 | — | 4 | 4 | no | — |
| 187 | #4695 | — | 4 | 2 | no | — |
| 188 | #4694 | — | 4 | 2 | no | — |
| 189 | #4693 | — | 4 | 1 | no | — |
| 190 | C4×D24 | — | 4 | 4 | no | — |
| 191 | #4682 | — | 2 | 2 | no | — |
| 192 | C3×#367 | — | 4 | 4 | no | — |
| 193 | C3×#357 | — | 4 | 8 | no | — |
| 194 | C3×#346 | D8 | 1 | 4 | yes | — |
| 195 | C3×C4×C16 | C2×D4 | 1 | 2 | yes | — |
| 196 | C3×C4×C16 | C2×D4 | 1 | 2 | yes | — |
| 197 | C3×C82 | C2×D4 | 1 | 2 | yes | — |
| 198 | C3×C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 199 | C3×C82 | C24 | 1 | 1 | yes | characteristic |
| 200 | #4562 | — | 4 | 8 | no | — |
| 201 | #4491 | — | 4 | 8 | no | — |
| 202 | #4490 | — | 4 | 8 | no | — |
| 203 | #4461 | D8 | 1 | 8 | yes | — |
| 204 | C4×C3⋊C16 | C2×D4 | 1 | 4 | yes | — |
| 205 | C4×C3⋊C16 | C2×D4 | 1 | 4 | yes | — |
| 206 | C2×#509 | — | 12 | 8 | no | — |
| 207 | C2×#509 | — | 12 | 4 | no | — |
| 208 | #3169 | — | 2 | 2 | no | — |
| 209 | #3169 | — | 2 | 2 | no | — |
| 210 | #3169 | — | 6 | 2 | no | — |
| 211 | #3147 | — | 2 | 2 | no | — |
| 212 | #3147 | — | 6 | 1 | no | — |
| 213 | C2×#493 | — | 6 | 2 | no | — |
| 214 | C2×#493 | — | 6 | 1 | no | — |
| 215 | #2254 | — | 2 | 2 | no | — |
| 216 | #2254 | — | 6 | 4 | no | — |
| 217 | #2250 | — | 12 | 8 | no | — |
| 218 | #2250 | — | 12 | 4 | no | — |
| 219 | #2248 | — | 6 | 4 | no | — |
| 220 | #2248 | — | 6 | 4 | no | — |
| 221 | #2248 | — | 6 | 2 | no | — |
| 222 | #2248 | — | 6 | 2 | no | — |
| 223 | #2246 | — | 2 | 2 | no | — |
| 224 | #2246 | — | 6 | 4 | no | — |
| 225 | #2246 | — | 6 | 4 | no | — |
| 226 | #2246 | — | 6 | 4 | no | — |
| 227 | #2246 | — | 6 | 2 | no | — |
| 228 | #2246 | — | 6 | 2 | no | — |
| 229 | #2240 | — | 2 | 4 | no | — |
| 230 | #2240 | — | 6 | 4 | no | — |
| 231 | #2240 | — | 6 | 4 | no | — |
| 232 | #2218 | — | 4 | 4 | no | — |
| 233 | #2218 | — | 12 | 8 | no | — |
| 234 | #2177 | — | 4 | 4 | no | — |
| 235 | #2177 | — | 12 | 8 | no | — |
| 236 | C4×M32 | — | 3 | 4 | no | — |
| 237 | C4×M32 | #67 | 1 | 2 | yes | — |
| 238 | #1713 | — | 3 | 1 | no | — |
| 239 | #1713 | C22×D3 | 1 | 2 | yes | — |
| 240 | #1712 | — | 3 | 1 | no | — |
| 241 | #1712 | — | 3 | 1 | no | — |
| 242 | #1712 | — | 3 | 1 | no | — |
| 243 | #1712 | — | 6 | 2 | no | — |
| 244 | #1712 | — | 6 | 1 | no | — |
| 245 | #1712 | C22×D3 | 1 | 2 | yes | — |
| 246 | #1709 | — | 2 | 2 | no | — |
| 247 | #1709 | — | 6 | 1 | no | — |
| 248 | #1706 | — | 2 | 2 | no | — |
| 249 | #1706 | — | 2 | 2 | no | — |
| 250 | #1706 | — | 6 | 2 | no | — |
| 251 | C2×C82 | C22×D3 | 1 | 1 | yes | characteristic |
| 252 | #1311 | — | 3 | 4 | no | — |
| 253 | #1311 | #67 | 1 | 2 | yes | — |
| 254 | C8×C16 | — | 3 | 2 | no | — |
| 255 | C8×C16 | — | 3 | 2 | no | — |
| 256 | C8×C16 | C22×D3 | 1 | 1 | yes | characteristic |
| 257 | C8×C16 | C22×D3 | 1 | 1 | yes | characteristic |
| 258 | C2×C3×#41 | — | 8 | 2 | no | — |
| 259 | C2×#235 | — | 8 | 1 | no | — |
| 260 | C22×D12 | — | 8 | 2 | no | — |
| 261 | C22×D12 | — | 8 | 1 | no | — |
| 262 | C3×#135 | — | 8 | 16 | no | — |
| 263 | C2×C3×Q16 | — | 4 | 4 | no | — |
| 264 | C2×C3×SD16 | — | 8 | 4 | no | — |
| 265 | C2×C3×D8 | — | 4 | 4 | no | — |
| 266 | C2×C3×D8 | — | 4 | 4 | no | — |
| 267 | C2×C3×D8 | — | 4 | 4 | no | — |
| 268 | C22×C3×C8 | C2×D8 | 1 | 4 | yes | — |
| 269 | C22×C3×C8 | C2×D8 | 1 | 2 | yes | — |
| 270 | C3×C4⋊Q8 | — | 4 | 2 | no | — |
| 271 | C3×#127 | — | 4 | 2 | no | — |
| 272 | C3×#124 | — | 8 | 2 | no | — |
| 273 | C3×#121 | — | 8 | 2 | no | — |
| 274 | C3×#121 | — | 8 | 2 | no | — |
| 275 | C3×C4×D4 | — | 8 | 2 | no | — |
| 276 | C3×C4×D4 | — | 8 | 2 | no | — |
| 277 | C2×C3×C42 | #127 | 1 | 1 | yes | characteristic |
| 278 | #930 | — | 8 | 2 | no | — |
| 279 | C2×Dic12 | — | 4 | 2 | no | — |
| 280 | #904 | — | 8 | 8 | no | — |
| 281 | C2×D24 | — | 4 | 4 | no | — |
| 282 | C2×D24 | — | 4 | 4 | no | — |
| 283 | C2×D24 | — | 4 | 4 | no | — |
| 284 | C2×D24 | — | 4 | 2 | no | — |
| 285 | C2×D24 | — | 4 | 2 | no | — |
| 286 | C2×D24 | — | 4 | 2 | no | — |
| 287 | C2×D24 | — | 8 | 8 | no | — |
| 288 | C2×D24 | — | 8 | 16 | no | — |
| 289 | C2×D24 | — | 8 | 4 | no | — |
| 290 | C2×D24 | — | 8 | 2 | no | — |
| 291 | C2×#204 | — | 8 | 2 | no | — |
| 292 | #875 | — | 8 | 1 | no | — |
| 293 | #874 | — | 4 | 1 | no | — |
| 294 | #874 | — | 4 | 1 | no | — |
| 295 | #874 | — | 4 | 1 | no | — |
| 296 | #874 | — | 8 | 2 | no | — |
| 297 | #874 | — | 8 | 1 | no | — |
| 298 | C4×D12 | — | 8 | 2 | no | — |
| 299 | #869 | — | 4 | 1 | no | — |
| 300 | C3×D16 | — | 8 | 8 | no | — |
| 301 | C3×M32 | — | 2 | 8 | no | — |
| 302 | C2×C3×C16 | C2×D8 | 1 | 4 | yes | — |
| 303 | C2×C3×C16 | C2×D8 | 1 | 4 | yes | — |
| 304 | C3×#107 | — | 4 | 4 | no | — |
| 305 | C3×#107 | — | 4 | 4 | no | — |
| 306 | C3×#102 | — | 8 | 4 | no | — |
| 307 | C3×#102 | — | 8 | 4 | no | — |
| 308 | C3×C4×C8 | #127 | 1 | 1 | yes | characteristic |
| 309 | C3×C4×C8 | #127 | 1 | 2 | yes | — |
| 310 | C3×C4×C8 | C2×D8 | 1 | 4 | yes | — |
| 311 | C3×C4×C8 | C2×D8 | 1 | 2 | yes | — |
| 312 | C3×C4×C8 | C22×D4 | 1 | 2 | yes | — |
| 313 | C3×C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 314 | #828 | — | 8 | 16 | no | — |
| 315 | #828 | — | 8 | 16 | no | — |
| 316 | #826 | — | 8 | 16 | no | — |
| 317 | #826 | — | 8 | 16 | no | — |
| 318 | #826 | — | 8 | 16 | no | — |
| 319 | #821 | — | 8 | 4 | no | — |
| 320 | #818 | — | 4 | 4 | no | — |
| 321 | #812 | — | 2 | 16 | no | — |
| 322 | C2×C3⋊C16 | C2×D8 | 1 | 8 | yes | — |
| 323 | C2×C3⋊C16 | C2×D8 | 1 | 8 | yes | — |
| 324 | #800 | — | 8 | 8 | no | — |
| 325 | #800 | — | 8 | 8 | no | — |
| 326 | D48 | — | 8 | 8 | no | — |
| 327 | D48 | — | 8 | 8 | no | — |
| 328 | C2×#135 | — | 4 | 4 | no | — |
| 329 | C2×#135 | — | 12 | 2 | no | — |
| 330 | C22×D8 | — | 12 | 4 | no | — |
| 331 | C22×D8 | — | 12 | 2 | no | — |
| 332 | #532 | — | 4 | 2 | no | — |
| 333 | #532 | — | 12 | 1 | no | — |
| 334 | C2×#127 | — | 12 | 1 | no | — |
| 335 | #509 | — | 24 | 16 | no | — |
| 336 | #509 | — | 24 | 32 | no | — |
| 337 | C2×SD32 | — | 12 | 8 | no | — |
| 338 | C2×SD32 | — | 12 | 8 | no | — |
| 339 | C2×SD32 | — | 12 | 4 | no | — |
| 340 | C2×SD32 | — | 12 | 4 | no | — |
| 341 | C2×D16 | — | 4 | 4 | no | — |
| 342 | C2×D16 | — | 12 | 8 | no | — |
| 343 | C2×D16 | — | 12 | 8 | no | — |
| 344 | C2×D16 | — | 12 | 8 | no | — |
| 345 | C2×D16 | — | 12 | 4 | no | — |
| 346 | C2×D16 | — | 12 | 4 | no | — |
| 347 | C2×M32 | — | 3 | 8 | no | — |
| 348 | C2×M32 | #213 | 1 | 4 | yes | — |
| 349 | #500 | — | 2 | 2 | no | — |
| 350 | #500 | — | 2 | 2 | no | — |
| 351 | #500 | — | 6 | 2 | no | — |
| 352 | #495 | — | 4 | 4 | no | — |
| 353 | #495 | — | 12 | 2 | no | — |
| 354 | #494 | — | 2 | 2 | no | — |
| 355 | #494 | — | 6 | 1 | no | — |
| 356 | #493 | — | 2 | 2 | no | — |
| 357 | #493 | — | 2 | 2 | no | — |
| 358 | #493 | — | 2 | 2 | no | — |
| 359 | #493 | — | 6 | 2 | no | — |
| 360 | #493 | — | 6 | 2 | no | — |
| 361 | #493 | — | 6 | 2 | no | — |
| 362 | #493 | — | 6 | 1 | no | — |
| 363 | #493 | — | 6 | 1 | no | — |
| 364 | #493 | — | 6 | 1 | no | — |
| 365 | #493 | — | 12 | 4 | no | — |
| 366 | #493 | — | 12 | 2 | no | — |
| 367 | #493 | — | 12 | 2 | no | — |
| 368 | #493 | — | 12 | 1 | no | — |
| 369 | #492 | — | 4 | 2 | no | — |
| 370 | #492 | — | 12 | 1 | no | — |
| 371 | #486 | — | 4 | 2 | no | — |
| 372 | #486 | — | 4 | 2 | no | — |
| 373 | #486 | — | 12 | 2 | no | — |
| 374 | #466 | — | 4 | 4 | no | — |
| 375 | #466 | — | 4 | 4 | no | — |
| 376 | #466 | — | 12 | 4 | no | — |
| 377 | C4×D8 | — | 4 | 4 | no | — |
| 378 | C4×D8 | — | 4 | 4 | no | — |
| 379 | C4×D8 | — | 12 | 4 | no | — |
| 380 | C2×C4×C8 | D3×D4 | 1 | 2 | yes | — |
| 381 | C2×C4×C8 | C2×#67 | 1 | 1 | yes | characteristic |
| 382 | #367 | — | 4 | 4 | no | — |
| 383 | #367 | — | 12 | 8 | no | — |
| 384 | #357 | — | 4 | 8 | no | — |
| 385 | #357 | — | 12 | 8 | no | — |
| 386 | #357 | — | 12 | 8 | no | — |
| 387 | #346 | — | 3 | 8 | no | — |
| 388 | #346 | #213 | 1 | 4 | yes | — |
| 389 | C4×C16 | — | 3 | 4 | no | — |
| 390 | C4×C16 | — | 3 | 4 | no | — |
| 391 | C4×C16 | C2×#67 | 1 | 2 | yes | — |
| 392 | C4×C16 | C2×#67 | 1 | 2 | yes | — |
| 393 | C82 | D3×D4 | 1 | 2 | yes | — |
| 394 | C82 | C2×#67 | 1 | 1 | yes | characteristic |
| 395 | C82 | C23×D3 | 1 | 1 | yes | characteristic |
| 396 | C23×D3 | — | 16 | 1 | no | — |
| 397 | C3×#41 | — | 16 | 8 | no | — |
| 398 | C2×C3×Q8 | — | 8 | 2 | no | — |
| 399 | C2×C3×D4 | — | 8 | 2 | no | — |
| 400 | C2×C3×D4 | — | 8 | 2 | no | — |
| 401 | C2×C3×D4 | — | 8 | 2 | no | — |
| 402 | C2×C3×D4 | — | 16 | 2 | no | — |
| 403 | C22×C3×C4 | — | 16 | 2 | no | — |
| 404 | C22×C3×C4 | #493 | 1 | 2 | yes | — |
| 405 | C22×C3×C4 | #493 | 1 | 1 | yes | characteristic |
| 406 | C2×#67 | — | 16 | 1 | no | — |
| 407 | #235 | — | 16 | 4 | no | — |
| 408 | C2×D12 | — | 8 | 2 | no | — |
| 409 | C2×D12 | — | 8 | 2 | no | — |
| 410 | C2×D12 | — | 8 | 2 | no | — |
| 411 | C2×D12 | — | 8 | 1 | no | — |
| 412 | C2×D12 | — | 8 | 1 | no | — |
| 413 | C2×D12 | — | 8 | 1 | no | — |
| 414 | C2×D12 | — | 16 | 4 | no | — |
| 415 | C2×D12 | — | 16 | 8 | no | — |
| 416 | C2×D12 | — | 16 | 2 | no | — |
| 417 | C2×D12 | — | 16 | 1 | no | — |
| 418 | C2×C4×D3 | — | 16 | 1 | no | — |
| 419 | C2×Dic6 | — | 8 | 1 | no | — |
| 420 | C3×Q16 | — | 8 | 8 | no | — |
| 421 | C3×SD16 | — | 16 | 8 | no | — |
| 422 | C3×D8 | — | 8 | 8 | no | — |
| 423 | C3×D8 | — | 8 | 8 | no | — |
| 424 | C3×D8 | — | 8 | 8 | no | — |
| 425 | C2×C3×C8 | — | 2 | 8 | no | — |
| 426 | C2×C3×C8 | — | 2 | 4 | no | — |
| 427 | C2×C3×C8 | #493 | 1 | 4 | yes | — |
| 428 | C2×C3×C8 | #493 | 1 | 2 | yes | — |
| 429 | C2×C3×C8 | C22×D8 | 1 | 4 | yes | — |
| 430 | C2×C3×C8 | C22×D8 | 1 | 2 | yes | — |
| 431 | C3×C4⋊C4 | — | 8 | 2 | no | — |
| 432 | C3×C4⋊C4 | — | 8 | 2 | no | — |
| 433 | C3×C22⋊C4 | — | 16 | 2 | no | — |
| 434 | C3×C22⋊C4 | — | 16 | 2 | no | — |
| 435 | C3×C42 | #493 | 1 | 2 | yes | — |
| 436 | C3×C42 | #493 | 1 | 1 | yes | characteristic |
| 437 | C3×C42 | C2×#127 | 1 | 1 | yes | characteristic |
| 438 | (C2×D3)⋊C4 | — | 16 | 2 | no | — |
| 439 | C4⋊Dic3 | — | 8 | 2 | no | — |
| 440 | Dic12 | — | 8 | 4 | no | — |
| 441 | D24 | — | 8 | 4 | no | — |
| 442 | D24 | — | 8 | 4 | no | — |
| 443 | D24 | — | 8 | 4 | no | — |
| 444 | D24 | — | 8 | 8 | no | — |
| 445 | D24 | — | 8 | 8 | no | — |
| 446 | D24 | — | 8 | 8 | no | — |
| 447 | D24 | — | 16 | 4 | no | — |
| 448 | D24 | — | 16 | 8 | no | — |
| 449 | #204 | — | 16 | 4 | no | — |
| 450 | C3×C16 | — | 2 | 4 | no | — |
| 451 | C3×C16 | #509 | 1 | 8 | yes | complemented |
| 452 | C3⋊C16 | — | 2 | 8 | no | — |
| 453 | C3⋊C16 | #509 | 1 | 16 | yes | complemented |
| 454 | C2×#41 | — | 8 | 2 | no | — |
| 455 | C2×#41 | — | 24 | 1 | no | — |
| 456 | C22×D4 | — | 24 | 2 | no | — |
| 457 | C22×D4 | — | 24 | 1 | no | — |
| 458 | #135 | — | 8 | 16 | no | — |
| 459 | #135 | — | 24 | 8 | no | — |
| 460 | C2×Q16 | — | 4 | 4 | no | — |
| 461 | C2×Q16 | — | 12 | 2 | no | — |
| 462 | C2×SD16 | — | 8 | 4 | no | — |
| 463 | C2×SD16 | — | 24 | 2 | no | — |
| 464 | C2×D8 | — | 4 | 4 | no | — |
| 465 | C2×D8 | — | 4 | 4 | no | — |
| 466 | C2×D8 | — | 4 | 4 | no | — |
| 467 | C2×D8 | — | 12 | 4 | no | — |
| 468 | C2×D8 | — | 12 | 4 | no | — |
| 469 | C2×D8 | — | 12 | 4 | no | — |
| 470 | C2×D8 | — | 12 | 2 | no | — |
| 471 | C2×D8 | — | 12 | 2 | no | — |
| 472 | C2×D8 | — | 12 | 2 | no | — |
| 473 | C2×D8 | — | 24 | 16 | no | — |
| 474 | C2×D8 | — | 24 | 8 | no | — |
| 475 | C2×D8 | — | 24 | 4 | no | — |
| 476 | C2×D8 | — | 24 | 2 | no | — |
| 477 | C22×C8 | D3×D8 | 1 | 4 | yes | — |
| 478 | C22×C8 | C2×#213 | 1 | 2 | yes | — |
| 479 | C4⋊Q8 | — | 4 | 2 | no | — |
| 480 | C4⋊Q8 | — | 12 | 1 | no | — |
| 481 | #127 | — | 4 | 2 | no | — |
| 482 | #127 | — | 12 | 1 | no | — |
| 483 | #127 | — | 12 | 1 | no | — |
| 484 | #127 | — | 12 | 1 | no | — |
| 485 | #127 | — | 24 | 2 | no | — |
| 486 | #127 | — | 24 | 1 | no | — |
| 487 | #124 | — | 8 | 2 | no | — |
| 488 | #124 | — | 24 | 1 | no | — |
| 489 | #121 | — | 8 | 2 | no | — |
| 490 | #121 | — | 8 | 2 | no | — |
| 491 | #121 | — | 24 | 2 | no | — |
| 492 | C4×D4 | — | 8 | 2 | no | — |
| 493 | C4×D4 | — | 8 | 2 | no | — |
| 494 | C4×D4 | — | 24 | 2 | no | — |
| 495 | C2×C42 | #940 | 1 | 1 | yes | characteristic |
| 496 | SD32 | — | 24 | 8 | no | — |
| 497 | SD32 | — | 24 | 16 | no | — |
| 498 | SD32 | — | 24 | 16 | no | — |
| 499 | SD32 | — | 24 | 8 | no | — |
| 500 | D16 | — | 8 | 8 | no | — |
| 501 | D16 | — | 24 | 8 | no | — |
| 502 | D16 | — | 24 | 16 | no | — |
| 503 | D16 | — | 24 | 16 | no | — |
| 504 | D16 | — | 24 | 16 | no | — |
| 505 | D16 | — | 24 | 8 | no | — |
| 506 | M32 | — | 2 | 8 | no | — |
| 507 | M32 | — | 6 | 16 | no | — |
| 508 | C2×C16 | — | 3 | 8 | no | — |
| 509 | C2×C16 | — | 3 | 8 | no | — |
| 510 | C2×C16 | C2×#213 | 1 | 4 | yes | — |
| 511 | C2×C16 | C2×#213 | 1 | 4 | yes | — |
| 512 | #107 | — | 4 | 4 | no | — |
| 513 | #107 | — | 4 | 4 | no | — |
| 514 | #107 | — | 12 | 4 | no | — |
| 515 | #102 | — | 8 | 4 | no | — |
| 516 | #102 | — | 8 | 4 | no | — |
| 517 | #102 | — | 24 | 4 | no | — |
| 518 | C4×C8 | D3×D8 | 1 | 4 | yes | — |
| 519 | C4×C8 | C2×#213 | 1 | 2 | yes | — |
| 520 | C4×C8 | #940 | 1 | 2 | yes | — |
| 521 | C4×C8 | #940 | 1 | 1 | yes | characteristic |
| 522 | C4×C8 | C2×D3×D4 | 1 | 2 | yes | — |
| 523 | C4×C8 | C22×#67 | 1 | 1 | yes | characteristic |
| 524 | C23×C3 | — | 16 | 2 | no | — |
| 525 | C23×C3 | #1712 | 1 | 1 | yes | characteristic |
| 526 | C22×D3 | — | 16 | 1 | no | — |
| 527 | C22×D3 | — | 16 | 1 | no | — |
| 528 | C22×D3 | — | 16 | 1 | no | — |
| 529 | C22×D3 | — | 32 | 2 | no | — |
| 530 | C22×D3 | — | 32 | 4 | no | — |
| 531 | C3×Q8 | — | 16 | 4 | no | — |
| 532 | C3×D4 | — | 16 | 4 | no | — |
| 533 | C3×D4 | — | 16 | 4 | no | — |
| 534 | C3×D4 | — | 16 | 4 | no | — |
| 535 | C3×D4 | — | 32 | 4 | no | — |
| 536 | C2×C3×C4 | — | 2 | 2 | no | — |
| 537 | C2×C3×C4 | — | 2 | 4 | no | — |
| 538 | C2×C3×C4 | — | 16 | 2 | no | — |
| 539 | C2×C3×C4 | — | 32 | 4 | no | — |
| 540 | C2×C3×C4 | #1712 | 1 | 2 | yes | — |
| 541 | C2×C3×C4 | #1712 | 1 | 1 | yes | characteristic |
| 542 | C2×C3×C4 | C2×#493 | 1 | 2 | yes | — |
| 543 | C2×C3×C4 | C2×#493 | 1 | 1 | yes | characteristic |
| 544 | #67 | — | 32 | 2 | no | — |
| 545 | C2×Dic3 | — | 16 | 1 | no | — |
| 546 | D12 | — | 16 | 2 | no | — |
| 547 | D12 | — | 16 | 4 | no | — |
| 548 | D12 | — | 16 | 4 | no | — |
| 549 | D12 | — | 16 | 2 | no | — |
| 550 | D12 | — | 16 | 2 | no | — |
| 551 | D12 | — | 16 | 4 | no | — |
| 552 | D12 | — | 32 | 2 | no | — |
| 553 | D12 | — | 32 | 4 | no | — |
| 554 | C4×D3 | — | 32 | 2 | no | — |
| 555 | Dic6 | — | 16 | 2 | no | — |
| 556 | C3×C8 | — | 2 | 2 | no | — |
| 557 | C3×C8 | — | 2 | 4 | no | — |
| 558 | C3×C8 | C2×#509 | 1 | 8 | yes | — |
| 559 | C3×C8 | C2×#509 | 1 | 4 | yes | — |
| 560 | C24 | — | 48 | 1 | no | — |
| 561 | #41 | — | 16 | 8 | no | — |
| 562 | #41 | — | 48 | 4 | no | — |
| 563 | C2×Q8 | — | 8 | 2 | no | — |
| 564 | C2×Q8 | — | 24 | 1 | no | — |
| 565 | C2×D4 | — | 8 | 2 | no | — |
| 566 | C2×D4 | — | 8 | 2 | no | — |
| 567 | C2×D4 | — | 8 | 2 | no | — |
| 568 | C2×D4 | — | 16 | 2 | no | — |
| 569 | C2×D4 | — | 24 | 2 | no | — |
| 570 | C2×D4 | — | 24 | 2 | no | — |
| 571 | C2×D4 | — | 24 | 2 | no | — |
| 572 | C2×D4 | — | 24 | 1 | no | — |
| 573 | C2×D4 | — | 24 | 1 | no | — |
| 574 | C2×D4 | — | 24 | 1 | no | — |
| 575 | C2×D4 | — | 48 | 8 | no | — |
| 576 | C2×D4 | — | 48 | 4 | no | — |
| 577 | C2×D4 | — | 48 | 1 | no | — |
| 578 | C2×D4 | — | 48 | 1 | no | — |
| 579 | C2×D4 | — | 48 | 2 | no | — |
| 580 | C22×C4 | — | 16 | 2 | no | — |
| 581 | C22×C4 | — | 48 | 1 | no | — |
| 582 | C22×C4 | #5073 | 1 | 1 | yes | characteristic |
| 583 | C22×C4 | #5151 | 1 | 2 | yes | — |
| 584 | Q16 | — | 8 | 8 | no | — |
| 585 | Q16 | — | 24 | 4 | no | — |
| 586 | SD16 | — | 16 | 8 | no | — |
| 587 | SD16 | — | 48 | 4 | no | — |
| 588 | D8 | — | 8 | 8 | no | — |
| 589 | D8 | — | 8 | 8 | no | — |
| 590 | D8 | — | 8 | 8 | no | — |
| 591 | D8 | — | 24 | 8 | no | — |
| 592 | D8 | — | 24 | 8 | no | — |
| 593 | D8 | — | 24 | 8 | no | — |
| 594 | D8 | — | 24 | 4 | no | — |
| 595 | D8 | — | 24 | 4 | no | — |
| 596 | D8 | — | 24 | 4 | no | — |
| 597 | D8 | — | 48 | 8 | no | — |
| 598 | D8 | — | 48 | 4 | no | — |
| 599 | C2×C8 | — | 2 | 8 | no | — |
| 600 | C2×C8 | — | 2 | 4 | no | — |
| 601 | C2×C8 | #5073 | 1 | 2 | yes | — |
| 602 | C2×C8 | #5151 | 1 | 4 | yes | — |
| 603 | C2×C8 | C2×D3×D8 | 1 | 4 | yes | — |
| 604 | C2×C8 | C22×#213 | 1 | 2 | yes | — |
| 605 | C4⋊C4 | — | 8 | 2 | no | — |
| 606 | C4⋊C4 | — | 8 | 2 | no | — |
| 607 | C4⋊C4 | — | 24 | 2 | no | — |
| 608 | C22⋊C4 | — | 16 | 2 | no | — |
| 609 | C22⋊C4 | — | 16 | 2 | no | — |
| 610 | C22⋊C4 | — | 48 | 2 | no | — |
| 611 | C42 | #5073 | 1 | 1 | yes | characteristic |
| 612 | C42 | #5151 | 1 | 2 | yes | — |
| 613 | C42 | C2×#940 | 1 | 1 | yes | characteristic |
| 614 | C16 | — | 2 | 4 | no | — |
| 615 | C16 | — | 3 | 16 | no | — |
| 616 | C16 | — | 6 | 8 | no | — |
| 617 | C16 | #5193 | 1 | 8 | yes | complemented |
| 618 | C22×C3 | — | 2 | 1 | no | — |
| 619 | C22×C3 | — | 2 | 2 | no | — |
| 620 | C22×C3 | — | 32 | 2 | no | — |
| 621 | C22×C3 | — | 32 | 2 | no | — |
| 622 | C22×C3 | — | 32 | 2 | no | — |
| 623 | C22×C3 | C2×#1712 | 1 | 1 | yes | characteristic |
| 624 | C2×D3 | — | 32 | 1 | no | — |
| 625 | C2×D3 | — | 32 | 2 | no | — |
| 626 | C2×D3 | — | 32 | 2 | no | — |
| 627 | C2×D3 | — | 32 | 1 | no | — |
| 628 | C2×D3 | — | 32 | 1 | no | — |
| 629 | C2×D3 | — | 32 | 2 | no | — |
| 630 | C2×D3 | — | 64 | 4 | no | — |
| 631 | C3×C4 | — | 2 | 1 | no | — |
| 632 | C3×C4 | — | 2 | 2 | no | — |
| 633 | C3×C4 | — | 32 | 2 | no | — |
| 634 | C3×C4 | #33717 | 1 | 4 | yes | — |
| 635 | C3×C4 | #33717 | 1 | 2 | yes | — |
| 636 | Dic3 | — | 32 | 1 | no | — |
| 637 | C23 | — | 16 | 2 | no | — |
| 638 | C23 | — | 48 | 1 | no | — |
| 639 | C23 | — | 48 | 1 | no | — |
| 640 | C23 | — | 48 | 1 | no | — |
| 641 | C23 | — | 96 | 4 | no | — |
| 642 | C23 | — | 96 | 2 | no | — |
| 643 | C23 | #71276 | 1 | 1 | yes | characteristic |
| 644 | Q8 | — | 16 | 4 | no | — |
| 645 | Q8 | — | 48 | 2 | no | — |
| 646 | D4 | — | 16 | 4 | no | — |
| 647 | D4 | — | 16 | 4 | no | — |
| 648 | D4 | — | 16 | 4 | no | — |
| 649 | D4 | — | 32 | 4 | no | — |
| 650 | D4 | — | 48 | 4 | no | — |
| 651 | D4 | — | 48 | 4 | no | — |
| 652 | D4 | — | 48 | 4 | no | — |
| 653 | D4 | — | 48 | 2 | no | — |
| 654 | D4 | — | 48 | 2 | no | — |
| 655 | D4 | — | 48 | 2 | no | — |
| 656 | D4 | — | 96 | 4 | no | — |
| 657 | D4 | — | 96 | 2 | no | — |
| 658 | D4 | — | 96 | 2 | no | — |
| 659 | C2×C4 | — | 2 | 4 | no | — |
| 660 | C2×C4 | — | 2 | 2 | no | — |
| 661 | C2×C4 | — | 16 | 2 | no | — |
| 662 | C2×C4 | — | 32 | 4 | no | — |
| 663 | C2×C4 | — | 48 | 1 | no | — |
| 664 | C2×C4 | — | 96 | 2 | no | — |
| 665 | C2×C4 | #71276 | 1 | 1 | yes | characteristic |
| 666 | C2×C4 | #71276 | 1 | 2 | yes | — |
| 667 | C2×C4 | C2×#5073 | 1 | 1 | yes | characteristic |
| 668 | C2×C4 | C2×#5151 | 1 | 2 | yes | — |
| 669 | C8 | — | 2 | 4 | no | — |
| 670 | C8 | — | 2 | 2 | no | — |
| 671 | C8 | D3×#509 | 1 | 8 | yes | — |
| 672 | C8 | C2×#5193 | 1 | 4 | yes | — |
| 673 | C2×C3 | — | 4 | 1 | no | — |
| 674 | C2×C3 | — | 64 | 2 | no | — |
| 675 | C2×C3 | #491469 | 1 | 2 | yes | — |
| 676 | C2×C3 | #491469 | 1 | 1 | yes | characteristic |
| 677 | D3 | — | 64 | 1 | no | — |
| 678 | D3 | — | 64 | 1 | no | — |
| 679 | D3 | — | 64 | 1 | no | — |
| 680 | C22 | — | 2 | 2 | no | — |
| 681 | C22 | — | 2 | 1 | no | — |
| 682 | C22 | — | 32 | 2 | no | — |
| 683 | C22 | — | 32 | 2 | no | — |
| 684 | C22 | — | 32 | 2 | no | — |
| 685 | C22 | — | 96 | 2 | no | — |
| 686 | C22 | — | 96 | 2 | no | — |
| 687 | C22 | — | 96 | 2 | no | — |
| 688 | C22 | — | 96 | 1 | no | — |
| 689 | C22 | — | 96 | 1 | no | — |
| 690 | C22 | — | 96 | 1 | no | — |
| 691 | C22 | — | 192 | 4 | no | — |
| 692 | C22 | C2×#71276 | 1 | 1 | yes | characteristic |
| 693 | C4 | — | 2 | 2 | no | — |
| 694 | C4 | — | 2 | 1 | no | — |
| 695 | C4 | — | 32 | 2 | no | — |
| 696 | C4 | — | 96 | 1 | no | — |
| 697 | C4 | #10950613 | 1 | 4 | yes | — |
| 698 | C4 | #10950618 | 1 | 2 | yes | — |
| 699 | C3 | #72213956 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 700 | C2 | — | 4 | 1 | no | — |
| 701 | C2 | — | 64 | 2 | no | — |
| 702 | C2 | — | 192 | 1 | no | — |
| 703 | C2 | — | 192 | 1 | no | — |
| 704 | C2 | — | 192 | 1 | no | — |
| 705 | C2 | #72225919 | 1 | 2 | yes | — |
| 706 | C2 | #72225930 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72226119 | C2 | semidirect |
| 2. #72226118 | C2 | semidirect |
| 3. #72226117 | C2 | semidirect |
| 4. #72226113 | C2 | semidirect |
| 5. #72226112 | C2 | semidirect |
| 6. #72226111 | C2 | semidirect |
| 7. #72225940 | C2 | semidirect |
| 8. #72225930 | C2 | semidirect |
| 9. #72225829 | C2 | semidirect |
| 10. C3×#491500 | C2 | semidirect |
| 11. #72225817 | C2 | semidirect |
| 18. #10709929 | C22 | semidirect |
| 29. #10709898 | C22 | semidirect |
| 30. #10709874 | C22 | semidirect |
| 31. #10709872 | C22 | semidirect |
| 34. #10681802 | C22 | semidirect |
| 35. #10681801 | C22 | semidirect |
| 36. C16×C3⋊C16 | C22 | semidirect |
| 39. C3×#12523 | C22 | semidirect |
| 40. C3×#12515 | C22 | semidirect |
| 41. C3×#12509 | C22 | semidirect |
| 45. #491500 | D3 | semidirect |
| 115. #12523 | C2×D3 | semidirect |
| 127. #12515 | C2×D3 | semidirect |
| 130. #12509 | C2×D3 | semidirect |
| 451. C3×C16 | #509 | semidirect |
| 453. C3⋊C16 | #509 | semidirect |
| 617. C16 | #5193 | semidirect |
| 699. C3 | #72213956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72226119 | 2 |
| #72226118 | 2 |
| #72226117 | 2 |
| #72226113 | 2 |
| #72226112 | 2 |
| #72226111 | 2 |
| #72225940 | 2 |
| #72225930 | 2 |
| #72225829 | 2 |
| C3×#491500 | 2 |
| #72225817 | 2 |
| #72213956 | 3 |