Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1016 conjugacy classes of subgroups.
The subgroup lattice has 952 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #22601770 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22599361 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22599356 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22593338 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22587281 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22587278 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #22587276 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #22587273 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #22587271 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #22587269 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #22587267 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #22586864 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #22586862 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #22586682 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C71×#1597 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #17986628 | C22 | 1 | 1 | yes | characteristic |
| 17 | #17986619 | — | 2 | 1 | no | — |
| 18 | #17986617 | — | 2 | 1 | no | — |
| 19 | #17986608 | — | 2 | 1 | no | — |
| 20 | #17986606 | — | 2 | 1 | no | — |
| 21 | #17986596 | C22 | 1 | 1 | yes | characteristic |
| 22 | #17986591 | — | 2 | 1 | no | — |
| 23 | #17986576 | C22 | 1 | 1 | yes | characteristic |
| 24 | #17986571 | — | 2 | 1 | no | — |
| 25 | #17986555 | — | 2 | 1 | no | — |
| 26 | #17986551 | — | 2 | 1 | no | — |
| 27 | C2×#14556124 | C22 | 1 | 1 | yes | characteristic |
| 28 | #17986535 | C22 | 1 | 1 | yes | characteristic |
| 29 | #17986532 | — | 2 | 1 | no | — |
| 30 | #17986530 | C22 | 1 | 1 | yes | characteristic |
| 31 | #17986526 | — | 2 | 1 | no | — |
| 32 | #17986526 | — | 2 | 1 | no | — |
| 33 | C2×#14556114 | — | 2 | 1 | no | — |
| 34 | C4×#11765864 | — | 2 | 1 | no | — |
| 35 | C2×#14556093 | C22 | 1 | 1 | yes | characteristic |
| 36 | #17986387 | — | 2 | 1 | no | — |
| 37 | #17986385 | — | 2 | 1 | no | — |
| 38 | #17986362 | — | 2 | 1 | no | — |
| 39 | #17986362 | — | 2 | 1 | no | — |
| 40 | #17986198 | — | 2 | 1 | no | — |
| 41 | #17986197 | — | 2 | 1 | no | — |
| 42 | #17986193 | — | 2 | 1 | no | — |
| 43 | #17986192 | — | 2 | 1 | no | — |
| 44 | #17986152 | C22 | 1 | 1 | yes | characteristic |
| 45 | #17986150 | C22 | 1 | 1 | yes | characteristic |
| 46 | #17986149 | C22 | 1 | 1 | yes | characteristic |
| 47 | #17986135 | C22 | 1 | 1 | yes | characteristic |
| 48 | #17986133 | C22 | 1 | 1 | yes | characteristic |
| 49 | #17986132 | C22 | 1 | 1 | yes | characteristic |
| 50 | #17986053 | C22 | 1 | 1 | yes | characteristic |
| 51 | #17986053 | C22 | 1 | 1 | yes | characteristic |
| 52 | #17985917 | C22 | 1 | 1 | yes | characteristic |
| 53 | #17985916 | C22 | 1 | 1 | yes | characteristic |
| 54 | #17985913 | C22 | 1 | 1 | yes | characteristic |
| 55 | #17985899 | — | 2 | 1 | no | — |
| 56 | #17985899 | — | 2 | 1 | no | — |
| 57 | #17985899 | — | 2 | 1 | no | — |
| 58 | #17985850 | C22 | 1 | 1 | yes | characteristic |
| 59 | #17985737 | C22 | 1 | 1 | yes | characteristic |
| 60 | #17985736 | C22 | 1 | 1 | yes | characteristic |
| 61 | #17985735 | C22 | 1 | 1 | yes | characteristic |
| 62 | #17985734 | C22 | 1 | 1 | yes | characteristic |
| 63 | #17985733 | C22 | 1 | 1 | yes | characteristic |
| 64 | #17985732 | C22 | 1 | 1 | yes | characteristic |
| 65 | #17985725 | C22 | 1 | 1 | yes | characteristic |
| 66 | #17985724 | C22 | 1 | 1 | yes | characteristic |
| 67 | #17985724 | C22 | 1 | 1 | yes | characteristic |
| 68 | #539×C71 | C22 | 1 | 1 | yes | characteristic |
| 69 | #450×C71 | C22 | 1 | 1 | yes | characteristic |
| 70 | #447×C71 | C22 | 1 | 1 | yes | characteristic |
| 71 | #394×C71 | C22 | 1 | 1 | yes | characteristic |
| 72 | #328×C71 | C22 | 1 | 1 | yes | characteristic |
| 73 | #327×C71 | C22 | 1 | 1 | yes | characteristic |
| 74 | #324×C71 | C22 | 1 | 1 | yes | characteristic |
| 75 | C2×#11765864 | — | 2 | 1 | no | — |
| 76 | C22×Dic142 | D4 | 1 | 1 | yes | characteristic |
| 77 | C22×D284 | C23 | 1 | 1 | yes | characteristic |
| 78 | C22×C22⋊D71 | — | 2 | 1 | no | — |
| 79 | C22×C22⋊D71 | — | 2 | 1 | no | — |
| 80 | C2×#11765854 | — | 2 | 1 | no | — |
| 81 | C2×#11765853 | — | 2 | 1 | no | — |
| 82 | C2×#11765852 | — | 2 | 1 | no | — |
| 83 | C2×D568 | — | 2 | 1 | no | — |
| 84 | C2×#11765850 | — | 2 | 1 | no | — |
| 85 | C2×#11765850 | — | 2 | 1 | no | — |
| 86 | #14556127 | — | 2 | 1 | no | — |
| 87 | #14556127 | — | 2 | 1 | no | — |
| 88 | #14556127 | — | 2 | 1 | no | — |
| 89 | #14556126 | — | 2 | 1 | no | — |
| 90 | #14556124 | — | 2 | 1 | no | — |
| 91 | #14556124 | — | 2 | 1 | no | — |
| 92 | #14556124 | — | 2 | 1 | no | — |
| 93 | #14556124 | — | 2 | 1 | no | — |
| 94 | #14556123 | — | 2 | 1 | no | — |
| 95 | #14556123 | — | 2 | 1 | no | — |
| 96 | #14556123 | — | 2 | 1 | no | — |
| 97 | #14556122 | — | 2 | 1 | no | — |
| 98 | #14556121 | — | 2 | 1 | no | — |
| 99 | #14556121 | — | 2 | 1 | no | — |
| 100 | #14556121 | — | 2 | 1 | no | — |
| 101 | #14556120 | — | 2 | 1 | no | — |
| 102 | #14556119 | D4 | 1 | 1 | yes | characteristic |
| 103 | #14556119 | D4 | 1 | 1 | yes | characteristic |
| 104 | #14556118 | — | 2 | 1 | no | — |
| 105 | #14556118 | — | 2 | 1 | no | — |
| 106 | #14556118 | — | 2 | 1 | no | — |
| 107 | #14556118 | — | 2 | 1 | no | — |
| 108 | #14556118 | — | 2 | 1 | no | — |
| 109 | #14556117 | D4 | 1 | 1 | yes | characteristic |
| 110 | #14556115 | D4 | 1 | 1 | yes | characteristic |
| 111 | #14556114 | — | 2 | 1 | no | — |
| 112 | #14556114 | — | 2 | 1 | no | — |
| 113 | #14556114 | — | 2 | 1 | no | — |
| 114 | #14556114 | — | 4 | 4 | no | — |
| 115 | #14556113 | — | 2 | 1 | no | — |
| 116 | #14556112 | — | 2 | 1 | no | — |
| 117 | #14556111 | — | 2 | 1 | no | — |
| 118 | #14556111 | — | 2 | 1 | no | — |
| 119 | #14556110 | — | 2 | 1 | no | — |
| 120 | #14556109 | — | 2 | 1 | no | — |
| 121 | #14556107 | — | 2 | 1 | no | — |
| 122 | #14556107 | C23 | 1 | 1 | yes | characteristic |
| 123 | #14556106 | — | 2 | 1 | no | — |
| 124 | #14556106 | — | 2 | 1 | no | — |
| 125 | #14556106 | — | 2 | 1 | no | — |
| 126 | #14556106 | — | 2 | 1 | no | — |
| 127 | #14556106 | — | 2 | 1 | no | — |
| 128 | #14556105 | — | 2 | 1 | no | — |
| 129 | #14556105 | — | 2 | 1 | no | — |
| 130 | #14556105 | — | 2 | 1 | no | — |
| 131 | #14556105 | — | 2 | 1 | no | — |
| 132 | #14556102 | C23 | 1 | 1 | yes | characteristic |
| 133 | #14556101 | — | 2 | 1 | no | — |
| 134 | #14556100 | — | 2 | 1 | no | — |
| 135 | #14556100 | — | 2 | 1 | no | — |
| 136 | Q8×Dic71 | D4 | 1 | 1 | yes | characteristic |
| 137 | C4×Dic142 | — | 2 | 1 | no | — |
| 138 | #14556093 | — | 2 | 1 | no | — |
| 139 | #14556093 | — | 2 | 1 | no | — |
| 140 | #14556093 | — | 2 | 1 | no | — |
| 141 | #14556093 | — | 2 | 1 | no | — |
| 142 | #14556093 | — | 2 | 1 | no | — |
| 143 | #14556093 | — | 2 | 1 | no | — |
| 144 | #14556093 | D4 | 1 | 1 | yes | characteristic |
| 145 | D4×Dic71 | — | 2 | 1 | no | — |
| 146 | D4×Dic71 | D4 | 1 | 1 | yes | characteristic |
| 147 | #14556090 | D4 | 1 | 1 | yes | characteristic |
| 148 | C4×C22⋊D71 | — | 2 | 1 | no | — |
| 149 | C4×C22⋊D71 | — | 2 | 1 | no | — |
| 150 | (C22⋊D71)⋊C4 | — | 2 | 1 | no | — |
| 151 | (C22⋊D71)⋊C4 | — | 2 | 1 | no | — |
| 152 | (C22⋊D71)⋊C4 | — | 2 | 1 | no | — |
| 153 | #14556086 | — | 2 | 1 | no | — |
| 154 | #14556086 | — | 2 | 1 | no | — |
| 155 | #14556086 | — | 2 | 1 | no | — |
| 156 | #14556084 | — | 2 | 1 | no | — |
| 157 | #14556084 | — | 2 | 1 | no | — |
| 158 | #14556084 | — | 2 | 1 | no | — |
| 159 | #14556084 | — | 2 | 1 | no | — |
| 160 | C2×Dic71⋊C4 | — | 2 | 1 | no | — |
| 161 | C2×Dic71⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 162 | C2×Dic71⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 163 | C2×C22⋊Dic71 | — | 2 | 1 | no | — |
| 164 | C2×C22⋊Dic71 | — | 2 | 1 | no | — |
| 165 | C2×(C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 166 | C2×(C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 167 | C2×(C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 168 | C2×(C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 169 | C2×C4×Dic71 | — | 2 | 1 | no | — |
| 170 | C2×C4×Dic71 | — | 2 | 1 | no | — |
| 171 | C2×C4×Dic71 | D4 | 1 | 1 | yes | characteristic |
| 172 | C2×C4×Dic71 | D4 | 1 | 1 | yes | characteristic |
| 173 | C2×C4×Dic71 | C23 | 1 | 1 | yes | characteristic |
| 174 | C42×D71 | — | 2 | 1 | no | — |
| 175 | Dic71⋊C8 | — | 2 | 1 | no | — |
| 176 | Dic71⋊C8 | — | 2 | 1 | no | — |
| 177 | #14556050 | — | 2 | 1 | no | — |
| 178 | #14556050 | — | 2 | 1 | no | — |
| 179 | #14556049 | — | 2 | 1 | no | — |
| 180 | #14556049 | — | 2 | 1 | no | — |
| 181 | #14556048 | — | 2 | 1 | no | — |
| 182 | #14556048 | — | 2 | 1 | no | — |
| 183 | C22⋊(C71⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 184 | C22⋊(C71⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 185 | #14556038 | — | 2 | 1 | no | — |
| 186 | #14556038 | — | 2 | 1 | no | — |
| 187 | C71⋊#95 | C23 | 1 | 1 | yes | characteristic |
| 188 | C22×D4×C71 | C23 | 1 | 1 | yes | characteristic |
| 189 | C2×SD16×C71 | — | 2 | 1 | no | — |
| 190 | C2×D8×C71 | — | 2 | 1 | no | — |
| 191 | #126×C71 | — | 2 | 1 | no | — |
| 192 | #125×C71 | — | 2 | 1 | no | — |
| 193 | #123×C71 | — | 2 | 1 | no | — |
| 194 | #123×C71 | — | 2 | 1 | no | — |
| 195 | C22⋊Q8×C71 | — | 2 | 1 | no | — |
| 196 | C22⋊Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 197 | #121×C71 | C23 | 1 | 1 | yes | characteristic |
| 198 | C4×D4×C71 | — | 2 | 1 | no | — |
| 199 | C2×C4⋊C4×C71 | C23 | 1 | 1 | yes | characteristic |
| 200 | C2×C22⋊C4×C71 | — | 2 | 1 | no | — |
| 201 | C2×C22⋊C4×C71 | — | 2 | 1 | no | — |
| 202 | #102×C71 | — | 2 | 1 | no | — |
| 203 | #102×C71 | — | 2 | 1 | no | — |
| 204 | C22⋊C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 205 | C22⋊C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 206 | #95×C71 | C23 | 1 | 1 | yes | characteristic |
| 207 | C23×D71 | — | 2 | 1 | no | — |
| 208 | #11765864 | — | 4 | 2 | no | — |
| 209 | #11765864 | — | 4 | 2 | no | — |
| 210 | C2×Dic142 | — | 2 | 1 | no | — |
| 211 | C2×Dic142 | — | 2 | 1 | no | — |
| 212 | C2×Dic142 | — | 2 | 1 | no | — |
| 213 | C2×Dic142 | — | 2 | 2 | no | — |
| 214 | C2×Dic142 | — | 2 | 1 | no | — |
| 215 | C2×Dic142 | — | 4 | 1 | no | — |
| 216 | C2×Dic142 | C2×D4 | 1 | 1 | yes | characteristic |
| 217 | C2×D284 | — | 2 | 1 | no | — |
| 218 | C2×D284 | — | 2 | 1 | no | — |
| 219 | C2×D284 | — | 8 | 1 | no | — |
| 220 | C2×D284 | C2×D4 | 1 | 1 | yes | characteristic |
| 221 | C2×C22⋊D71 | — | 2 | 1 | no | — |
| 222 | C2×C22⋊D71 | — | 2 | 1 | no | — |
| 223 | C2×C22⋊D71 | — | 2 | 1 | no | — |
| 224 | C2×C22⋊D71 | — | 4 | 2 | no | — |
| 225 | C2×C22⋊D71 | — | 4 | 2 | no | — |
| 226 | C2×C22⋊D71 | — | 4 | 2 | no | — |
| 227 | C2×C22⋊D71 | — | 4 | 2 | no | — |
| 228 | C2×C22⋊D71 | — | 4 | 1 | no | — |
| 229 | C2×C22⋊D71 | — | 4 | 1 | no | — |
| 230 | C2×C22⋊D71 | — | 4 | 1 | no | — |
| 231 | C2×C22⋊D71 | — | 4 | 1 | no | — |
| 232 | C22×Dic71 | — | 2 | 1 | no | — |
| 233 | C22×Dic71 | — | 2 | 1 | no | — |
| 234 | C22×Dic71 | — | 2 | 1 | no | — |
| 235 | C22×Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 236 | C22×Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 237 | C22×Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 238 | C22×Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 239 | C2×C4×D71 | — | 2 | 1 | no | — |
| 240 | C2×C4×D71 | — | 2 | 1 | no | — |
| 241 | C2×C4×D71 | — | 2 | 1 | no | — |
| 242 | #11765854 | — | 8 | 1 | no | — |
| 243 | #11765853 | — | 8 | 1 | no | — |
| 244 | #11765852 | — | 8 | 1 | no | — |
| 245 | D568 | — | 8 | 1 | no | — |
| 246 | #11765850 | — | 8 | 1 | no | — |
| 247 | #11765850 | — | 8 | 1 | no | — |
| 248 | C2×C71⋊C8 | — | 2 | 1 | no | — |
| 249 | C2×C71⋊C8 | — | 2 | 1 | no | — |
| 250 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 251 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 252 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 253 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 254 | C4⋊Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 255 | C4⋊Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 256 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 257 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 258 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 259 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 260 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 261 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 262 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 263 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 264 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 265 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 266 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 267 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 268 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 269 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 270 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 271 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 272 | Dic71⋊C4 | — | 4 | 2 | no | — |
| 273 | C22⋊Dic71 | — | 2 | 1 | no | — |
| 274 | C22⋊Dic71 | — | 2 | 1 | no | — |
| 275 | C22⋊Dic71 | — | 2 | 1 | no | — |
| 276 | C22⋊Dic71 | — | 2 | 1 | no | — |
| 277 | C22⋊Dic71 | — | 2 | 1 | no | — |
| 278 | C22⋊Dic71 | — | 4 | 2 | no | — |
| 279 | C22⋊Dic71 | — | 8 | 1 | no | — |
| 280 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 281 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 282 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 283 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 284 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 285 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 286 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 287 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 288 | (C2×D71)⋊C4 | — | 4 | 2 | no | — |
| 289 | (C2×D71)⋊C4 | — | 4 | 2 | no | — |
| 290 | (C2×D71)⋊C4 | — | 8 | 1 | no | — |
| 291 | (C2×D71)⋊C4 | — | 8 | 1 | no | — |
| 292 | C4×Dic71 | — | 2 | 1 | no | — |
| 293 | C4×Dic71 | — | 2 | 1 | no | — |
| 294 | C4×Dic71 | — | 2 | 1 | no | — |
| 295 | C4×Dic71 | — | 2 | 1 | no | — |
| 296 | C4×Dic71 | — | 2 | 1 | no | — |
| 297 | C4×Dic71 | — | 2 | 1 | no | — |
| 298 | C4×Dic71 | — | 2 | 1 | no | — |
| 299 | C4×Dic71 | — | 2 | 1 | no | — |
| 300 | C4×Dic71 | — | 2 | 1 | no | — |
| 301 | C4×Dic71 | — | 4 | 2 | no | — |
| 302 | C4×Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 303 | C4×Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 304 | C4×Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 305 | C4×Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 306 | C24×C71 | — | 2 | 1 | no | — |
| 307 | C2×Q8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 308 | C2×D4×C71 | — | 2 | 1 | no | — |
| 309 | C2×D4×C71 | — | 2 | 1 | no | — |
| 310 | C2×D4×C71 | — | 2 | 1 | no | — |
| 311 | C2×D4×C71 | — | 8 | 1 | no | — |
| 312 | C2×D4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 313 | C22×C4×C71 | — | 2 | 1 | no | — |
| 314 | C22×C4×C71 | — | 2 | 1 | no | — |
| 315 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 316 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 317 | C22×C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 318 | SD16×C71 | — | 8 | 1 | no | — |
| 319 | D8×C71 | — | 8 | 1 | no | — |
| 320 | C2×C8×C71 | — | 2 | 1 | no | — |
| 321 | C2×C8×C71 | — | 2 | 1 | no | — |
| 322 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 323 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 324 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 325 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 326 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 327 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 328 | C4⋊C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 329 | C4⋊C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 330 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 331 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 332 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 333 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 334 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 335 | C22⋊C4×C71 | — | 4 | 2 | no | — |
| 336 | C22⋊C4×C71 | — | 8 | 1 | no | — |
| 337 | C42×C71 | — | 2 | 1 | no | — |
| 338 | C23×C71 | — | 2 | 1 | no | — |
| 339 | C23×C71 | — | 4 | 1 | no | — |
| 340 | C23×C71 | — | 4 | 1 | no | — |
| 341 | C23×C71 | — | 4 | 1 | no | — |
| 342 | C23×C71 | — | 4 | 1 | no | — |
| 343 | C23×C71 | — | 4 | 1 | no | — |
| 344 | C23×C71 | — | 4 | 1 | no | — |
| 345 | C23×C71 | — | 4 | 1 | no | — |
| 346 | C23×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 347 | C22×D71 | — | 2 | 1 | no | — |
| 348 | C22×D71 | — | 4 | 1 | no | — |
| 349 | C22×D71 | — | 4 | 1 | no | — |
| 350 | C22×D71 | — | 4 | 1 | no | — |
| 351 | C22×D71 | — | 4 | 1 | no | — |
| 352 | C22×D71 | — | 4 | 1 | no | — |
| 353 | C22×D71 | — | 4 | 1 | no | — |
| 354 | C22×D71 | — | 4 | 1 | no | — |
| 355 | Q8×C71 | — | 4 | 1 | no | — |
| 356 | D4×C71 | — | 4 | 1 | no | — |
| 357 | D4×C71 | — | 4 | 1 | no | — |
| 358 | D4×C71 | — | 4 | 1 | no | — |
| 359 | D4×C71 | — | 4 | 1 | no | — |
| 360 | D4×C71 | — | 4 | 1 | no | — |
| 361 | D4×C71 | — | 4 | 1 | no | — |
| 362 | D4×C71 | — | 4 | 1 | no | — |
| 363 | C2×C4×C71 | — | 2 | 1 | no | — |
| 364 | C2×C4×C71 | — | 2 | 1 | no | — |
| 365 | C2×C4×C71 | — | 2 | 1 | no | — |
| 366 | C2×C4×C71 | — | 2 | 1 | no | — |
| 367 | C2×C4×C71 | — | 2 | 1 | no | — |
| 368 | C2×C4×C71 | — | 2 | 1 | no | — |
| 369 | C2×C4×C71 | — | 2 | 1 | no | — |
| 370 | C2×C4×C71 | — | 4 | 1 | no | — |
| 371 | C2×C4×C71 | — | 4 | 1 | no | — |
| 372 | C2×C4×C71 | — | 4 | 1 | no | — |
| 373 | C2×C4×C71 | — | 4 | 1 | no | — |
| 374 | C2×C4×C71 | — | 4 | 1 | no | — |
| 375 | C2×C4×C71 | — | 8 | 1 | no | — |
| 376 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 377 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 378 | C22⋊D71 | — | 4 | 2 | no | — |
| 379 | C22⋊D71 | — | 4 | 1 | no | — |
| 380 | C22⋊D71 | — | 4 | 1 | no | — |
| 381 | C22⋊D71 | — | 8 | 2 | no | — |
| 382 | C22⋊D71 | — | 8 | 2 | no | — |
| 383 | C22⋊D71 | — | 8 | 2 | no | — |
| 384 | C22⋊D71 | — | 8 | 1 | no | — |
| 385 | C22⋊D71 | — | 8 | 2 | no | — |
| 386 | C2×Dic71 | — | 2 | 1 | no | — |
| 387 | C2×Dic71 | — | 2 | 1 | no | — |
| 388 | C2×Dic71 | — | 2 | 1 | no | — |
| 389 | C2×Dic71 | — | 2 | 1 | no | — |
| 390 | C2×Dic71 | — | 2 | 2 | no | — |
| 391 | C2×Dic71 | — | 2 | 1 | no | — |
| 392 | C2×Dic71 | — | 2 | 1 | no | — |
| 393 | C2×Dic71 | — | 2 | 1 | no | — |
| 394 | C2×Dic71 | — | 2 | 1 | no | — |
| 395 | C2×Dic71 | — | 4 | 2 | no | — |
| 396 | C2×Dic71 | — | 4 | 2 | no | — |
| 397 | C2×Dic71 | — | 4 | 1 | no | — |
| 398 | C2×Dic71 | — | 4 | 1 | no | — |
| 399 | C2×Dic71 | — | 4 | 1 | no | — |
| 400 | C2×Dic71 | — | 4 | 1 | no | — |
| 401 | C2×Dic71 | #120 | 1 | 1 | yes | characteristic |
| 402 | C2×Dic71 | #120 | 1 | 1 | yes | characteristic |
| 403 | C2×Dic71 | #120 | 1 | 1 | yes | characteristic |
| 404 | C2×Dic71 | #120 | 1 | 1 | yes | characteristic |
| 405 | C2×Dic71 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 406 | D284 | — | 4 | 1 | no | — |
| 407 | D284 | — | 4 | 1 | no | — |
| 408 | D284 | — | 4 | 1 | no | — |
| 409 | D284 | — | 4 | 1 | no | — |
| 410 | D284 | — | 4 | 1 | no | — |
| 411 | C4×D71 | — | 4 | 2 | no | — |
| 412 | C4×D71 | — | 4 | 2 | no | — |
| 413 | C4×D71 | — | 8 | 1 | no | — |
| 414 | Dic142 | — | 4 | 2 | no | — |
| 415 | Dic142 | — | 4 | 2 | no | — |
| 416 | Dic142 | — | 4 | 2 | no | — |
| 417 | Dic142 | — | 4 | 1 | no | — |
| 418 | Dic142 | — | 8 | 1 | no | — |
| 419 | C8×C71 | — | 4 | 1 | no | — |
| 420 | C8×C71 | — | 4 | 1 | no | — |
| 421 | C71⋊C8 | — | 4 | 1 | no | — |
| 422 | C71⋊C8 | — | 4 | 1 | no | — |
| 423 | C22×C71 | — | 2 | 1 | no | — |
| 424 | C22×C71 | — | 2 | 1 | no | — |
| 425 | C22×C71 | — | 4 | 1 | no | — |
| 426 | C22×C71 | — | 4 | 1 | no | — |
| 427 | C22×C71 | — | 4 | 1 | no | — |
| 428 | C22×C71 | — | 8 | 1 | no | — |
| 429 | C22×C71 | — | 8 | 1 | no | — |
| 430 | C22×C71 | — | 8 | 1 | no | — |
| 431 | C22×C71 | — | 8 | 1 | no | — |
| 432 | C22×C71 | — | 8 | 1 | no | — |
| 433 | C22×C71 | — | 8 | 1 | no | — |
| 434 | C22×C71 | — | 8 | 1 | no | — |
| 435 | C22×C71 | C2×#120 | 1 | 1 | yes | characteristic |
| 436 | C22×C71 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 437 | C22×C71 | #575 | 1 | 1 | yes | characteristic |
| 438 | C2×D71 | — | 4 | 1 | no | — |
| 439 | C2×D71 | — | 4 | 1 | no | — |
| 440 | C2×D71 | — | 4 | 1 | no | — |
| 441 | C2×D71 | — | 8 | 1 | no | — |
| 442 | C2×D71 | — | 8 | 1 | no | — |
| 443 | C2×D71 | — | 8 | 1 | no | — |
| 444 | C2×D71 | — | 8 | 1 | no | — |
| 445 | C2×D71 | — | 8 | 1 | no | — |
| 446 | C2×D71 | — | 8 | 1 | no | — |
| 447 | C2×D71 | — | 8 | 1 | no | — |
| 448 | C4×C71 | — | 2 | 1 | no | — |
| 449 | C4×C71 | — | 2 | 1 | no | — |
| 450 | C4×C71 | — | 4 | 1 | no | — |
| 451 | C4×C71 | — | 4 | 1 | no | — |
| 452 | C4×C71 | — | 4 | 1 | no | — |
| 453 | C4×C71 | — | 4 | 1 | no | — |
| 454 | C4×C71 | — | 4 | 1 | no | — |
| 455 | C4×C71 | — | 8 | 1 | no | — |
| 456 | Dic71 | — | 2 | 2 | no | — |
| 457 | Dic71 | — | 2 | 1 | no | — |
| 458 | Dic71 | — | 2 | 1 | no | — |
| 459 | Dic71 | — | 2 | 1 | no | — |
| 460 | Dic71 | — | 4 | 1 | no | — |
| 461 | Dic71 | — | 4 | 1 | no | — |
| 462 | Dic71 | — | 4 | 1 | no | — |
| 463 | Dic71 | — | 4 | 1 | no | — |
| 464 | Dic71 | — | 8 | 1 | no | — |
| 465 | Dic71 | #454 | 1 | 2 | yes | — |
| 466 | #18337 | — | 71 | 1 | no | maximal, Sylow |
| 467 | C2×C71 | — | 2 | 1 | no | — |
| 468 | C2×C71 | — | 2 | 1 | no | — |
| 469 | C2×C71 | — | 8 | 1 | no | — |
| 470 | C2×C71 | — | 16 | 1 | no | — |
| 471 | C2×C71 | #3006 | 1 | 1 | yes | characteristic |
| 472 | C2×C71 | C2×#454 | 1 | 1 | yes | characteristic |
| 473 | C2×C71 | #3027 | 1 | 1 | yes | characteristic |
| 474 | D71 | — | 8 | 1 | no | — |
| 475 | D71 | — | 16 | 1 | no | — |
| 476 | #3461 | — | 71 | 1 | no | — |
| 477 | #3217 | — | 71 | 1 | no | — |
| 478 | #3217 | — | 71 | 1 | no | — |
| 479 | #2548 | — | 71 | 1 | no | — |
| 480 | #1599 | — | 71 | 1 | no | — |
| 481 | #1599 | — | 71 | 1 | no | — |
| 482 | #1598 | — | 71 | 1 | no | — |
| 483 | #1598 | — | 71 | 1 | no | — |
| 484 | #1597 | — | 71 | 1 | no | — |
| 485 | #1597 | — | 71 | 1 | no | — |
| 486 | #1597 | — | 71 | 1 | no | — |
| 487 | #1597 | D71 | 1 | 1 | yes | characteristic, complemented |
| 488 | #1509 | — | 71 | 1 | no | — |
| 489 | #1509 | — | 71 | 1 | no | — |
| 490 | #1467 | — | 71 | 1 | no | — |
| 491 | C71 | #18337 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 492 | #544 | — | 71 | 1 | no | — |
| 493 | #542 | — | 142 | 1 | no | — |
| 494 | #542 | — | 142 | 1 | no | — |
| 495 | #541 | — | 142 | 1 | no | — |
| 496 | #541 | — | 142 | 1 | no | — |
| 497 | #539 | — | 71 | 1 | no | — |
| 498 | #539 | — | 142 | 1 | no | — |
| 499 | #539 | C2×D71 | 1 | 1 | yes | characteristic |
| 500 | #537 | — | 71 | 1 | no | — |
| 501 | #536 | — | 142 | 1 | no | — |
| 502 | #533 | — | 142 | 1 | no | — |
| 503 | #533 | — | 142 | 1 | no | — |
| 504 | C2×#127 | — | 71 | 1 | no | — |
| 505 | #529 | — | 71 | 1 | no | — |
| 506 | #529 | — | 71 | 1 | no | — |
| 507 | #529 | — | 142 | 1 | no | — |
| 508 | #529 | — | 142 | 1 | no | — |
| 509 | #529 | — | 142 | 1 | no | — |
| 510 | C2×#124 | — | 142 | 1 | no | — |
| 511 | C4×#41 | — | 142 | 1 | no | — |
| 512 | C2×C4×Q8 | — | 71 | 1 | no | — |
| 513 | #496 | — | 142 | 1 | no | — |
| 514 | #496 | — | 142 | 1 | no | — |
| 515 | #490 | — | 142 | 1 | no | — |
| 516 | #490 | — | 142 | 1 | no | — |
| 517 | #460 | — | 142 | 1 | no | — |
| 518 | #460 | — | 142 | 1 | no | — |
| 519 | #459 | — | 142 | 1 | no | — |
| 520 | #459 | — | 142 | 1 | no | — |
| 521 | #450 | — | 71 | 1 | no | — |
| 522 | #450 | — | 71 | 1 | no | — |
| 523 | #450 | — | 71 | 1 | no | — |
| 524 | #450 | C2×D71 | 1 | 1 | yes | characteristic |
| 525 | #447 | — | 71 | 1 | no | — |
| 526 | #447 | — | 71 | 1 | no | — |
| 527 | #447 | — | 71 | 1 | no | — |
| 528 | #447 | C2×D71 | 1 | 1 | yes | characteristic |
| 529 | #432 | — | 71 | 1 | no | — |
| 530 | #432 | — | 71 | 1 | no | — |
| 531 | #394 | — | 71 | 1 | no | — |
| 532 | #394 | — | 71 | 1 | no | — |
| 533 | #394 | — | 71 | 1 | no | — |
| 534 | #394 | C2×D71 | 1 | 1 | yes | characteristic |
| 535 | #390 | — | 142 | 1 | no | — |
| 536 | #390 | — | 142 | 1 | no | — |
| 537 | #390 | — | 142 | 1 | no | — |
| 538 | C4×C4⋊C4 | — | 71 | 1 | no | — |
| 539 | #328 | — | 71 | 1 | no | — |
| 540 | #328 | — | 71 | 1 | no | — |
| 541 | #328 | — | 71 | 1 | no | — |
| 542 | #328 | C2×D71 | 1 | 1 | yes | characteristic |
| 543 | #327 | — | 71 | 1 | no | — |
| 544 | #327 | — | 71 | 1 | no | — |
| 545 | #327 | — | 71 | 1 | no | — |
| 546 | #327 | C2×D71 | 1 | 1 | yes | characteristic |
| 547 | #324 | — | 71 | 1 | no | — |
| 548 | #324 | — | 71 | 1 | no | — |
| 549 | #324 | — | 71 | 1 | no | — |
| 550 | #324 | C2×D71 | 1 | 1 | yes | characteristic |
| 551 | C2×#41 | — | 142 | 1 | no | — |
| 552 | C22×Q8 | — | 71 | 1 | no | — |
| 553 | C22×D4 | — | 71 | 1 | no | — |
| 554 | C22×D4 | — | 142 | 1 | no | — |
| 555 | C22×D4 | — | 142 | 1 | no | — |
| 556 | C22×D4 | C22×D71 | 1 | 1 | yes | characteristic |
| 557 | C2×SD16 | — | 2 | 1 | no | — |
| 558 | C2×SD16 | — | 142 | 1 | no | — |
| 559 | C2×SD16 | — | 142 | 1 | no | — |
| 560 | C2×SD16 | — | 142 | 1 | no | — |
| 561 | C2×D8 | — | 2 | 1 | no | — |
| 562 | C2×D8 | — | 142 | 1 | no | — |
| 563 | C2×D8 | — | 142 | 1 | no | — |
| 564 | C2×D8 | — | 142 | 1 | no | — |
| 565 | C4⋊Q8 | — | 142 | 1 | no | — |
| 566 | C4⋊Q8 | — | 142 | 1 | no | — |
| 567 | C4⋊Q8 | — | 142 | 1 | no | — |
| 568 | C4⋊Q8 | — | 142 | 1 | no | — |
| 569 | #127 | — | 142 | 1 | no | — |
| 570 | #127 | — | 142 | 1 | no | — |
| 571 | #127 | — | 142 | 1 | no | — |
| 572 | #127 | — | 142 | 1 | no | — |
| 573 | #126 | — | 2 | 1 | no | — |
| 574 | #126 | — | 142 | 1 | no | — |
| 575 | #126 | — | 142 | 1 | no | — |
| 576 | #126 | — | 142 | 1 | no | — |
| 577 | #126 | — | 142 | 1 | no | — |
| 578 | #126 | — | 142 | 1 | no | — |
| 579 | #126 | — | 142 | 1 | no | — |
| 580 | #126 | — | 142 | 1 | no | — |
| 581 | #125 | — | 2 | 1 | no | — |
| 582 | #125 | — | 71 | 1 | no | — |
| 583 | #125 | — | 71 | 1 | no | — |
| 584 | #125 | — | 142 | 1 | no | — |
| 585 | #125 | — | 142 | 1 | no | — |
| 586 | #125 | — | 142 | 1 | no | — |
| 587 | #125 | — | 142 | 1 | no | — |
| 588 | #125 | — | 142 | 1 | no | — |
| 589 | #125 | — | 142 | 1 | no | — |
| 590 | #124 | — | 284 | 4 | no | — |
| 591 | #124 | — | 71 | 1 | no | — |
| 592 | #124 | — | 71 | 1 | no | — |
| 593 | #124 | — | 142 | 1 | no | — |
| 594 | #124 | — | 142 | 1 | no | — |
| 595 | #124 | — | 142 | 1 | no | — |
| 596 | #123 | — | 2 | 1 | no | — |
| 597 | #123 | — | 2 | 1 | no | — |
| 598 | #123 | — | 142 | 1 | no | — |
| 599 | #123 | — | 142 | 1 | no | — |
| 600 | #123 | — | 142 | 1 | no | — |
| 601 | #123 | — | 142 | 1 | no | — |
| 602 | #123 | — | 142 | 1 | no | — |
| 603 | #123 | — | 142 | 1 | no | — |
| 604 | C22⋊Q8 | — | 2 | 1 | no | — |
| 605 | C22⋊Q8 | — | 71 | 1 | no | — |
| 606 | C22⋊Q8 | — | 142 | 1 | no | — |
| 607 | C22⋊Q8 | — | 142 | 1 | no | — |
| 608 | C22⋊Q8 | — | 142 | 1 | no | — |
| 609 | C22⋊Q8 | — | 142 | 1 | no | — |
| 610 | C22⋊Q8 | — | 142 | 1 | no | — |
| 611 | C22⋊Q8 | — | 142 | 1 | no | — |
| 612 | C22⋊Q8 | — | 142 | 1 | no | — |
| 613 | C22⋊Q8 | — | 142 | 1 | no | — |
| 614 | C22⋊Q8 | — | 142 | 1 | no | — |
| 615 | C22⋊Q8 | — | 142 | 1 | no | — |
| 616 | C22⋊Q8 | C22×D71 | 1 | 1 | yes | characteristic |
| 617 | #121 | — | 71 | 1 | no | — |
| 618 | #121 | — | 142 | 1 | no | — |
| 619 | #121 | — | 142 | 1 | no | — |
| 620 | #121 | — | 142 | 1 | no | — |
| 621 | #121 | C22×D71 | 1 | 1 | yes | characteristic |
| 622 | C4×Q8 | — | 71 | 1 | no | — |
| 623 | C4×Q8 | — | 71 | 1 | no | — |
| 624 | C4×Q8 | — | 142 | 1 | no | — |
| 625 | C4×Q8 | — | 142 | 1 | no | — |
| 626 | C4×Q8 | — | 142 | 1 | no | — |
| 627 | C4×Q8 | — | 142 | 1 | no | — |
| 628 | C4×Q8 | — | 142 | 1 | no | — |
| 629 | C4×Q8 | — | 142 | 1 | no | — |
| 630 | C4×Q8 | — | 142 | 1 | no | — |
| 631 | C4×D4 | — | 2 | 1 | no | — |
| 632 | C4×D4 | — | 71 | 1 | no | — |
| 633 | C4×D4 | — | 71 | 1 | no | — |
| 634 | C4×D4 | — | 142 | 1 | no | — |
| 635 | C4×D4 | — | 142 | 1 | no | — |
| 636 | C4×D4 | — | 142 | 1 | no | — |
| 637 | C4×D4 | — | 142 | 1 | no | — |
| 638 | C4×D4 | — | 142 | 1 | no | — |
| 639 | C4×D4 | — | 142 | 1 | no | — |
| 640 | #117 | — | 142 | 1 | no | — |
| 641 | #117 | — | 142 | 1 | no | — |
| 642 | #117 | — | 142 | 1 | no | — |
| 643 | #117 | — | 142 | 1 | no | — |
| 644 | #117 | — | 142 | 1 | no | — |
| 645 | #117 | — | 142 | 1 | no | — |
| 646 | #117 | — | 142 | 1 | no | — |
| 647 | C2×C4⋊C4 | — | 71 | 1 | no | — |
| 648 | C2×C4⋊C4 | — | 71 | 1 | no | — |
| 649 | C2×C4⋊C4 | — | 142 | 1 | no | — |
| 650 | C2×C4⋊C4 | C22×D71 | 1 | 1 | yes | characteristic |
| 651 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 652 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 653 | C2×C22⋊C4 | — | 142 | 1 | no | — |
| 654 | C2×C22⋊C4 | — | 142 | 1 | no | — |
| 655 | C2×C22⋊C4 | — | 142 | 1 | no | — |
| 656 | C2×C22⋊C4 | — | 142 | 1 | no | — |
| 657 | C2×C22⋊C4 | — | 142 | 1 | no | — |
| 658 | C2×C22⋊C4 | — | 142 | 1 | no | — |
| 659 | C2×C42 | — | 71 | 1 | no | — |
| 660 | C2×C42 | — | 71 | 1 | no | — |
| 661 | C2×C42 | — | 71 | 1 | no | — |
| 662 | C2×C42 | — | 142 | 1 | no | — |
| 663 | C2×C42 | — | 142 | 1 | no | — |
| 664 | C2×C42 | — | 142 | 1 | no | — |
| 665 | C4⋊C8 | — | 142 | 1 | no | — |
| 666 | C4⋊C8 | — | 142 | 1 | no | — |
| 667 | #102 | — | 2 | 1 | no | — |
| 668 | #102 | — | 2 | 1 | no | — |
| 669 | #102 | — | 142 | 1 | no | — |
| 670 | #102 | — | 142 | 1 | no | — |
| 671 | #102 | — | 142 | 1 | no | — |
| 672 | #102 | — | 142 | 1 | no | — |
| 673 | #102 | — | 142 | 1 | no | — |
| 674 | #102 | — | 142 | 1 | no | — |
| 675 | C22⋊C8 | — | 71 | 1 | no | — |
| 676 | C22⋊C8 | — | 71 | 1 | no | — |
| 677 | C22⋊C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 678 | C22⋊C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 679 | #97 | — | 142 | 1 | no | — |
| 680 | #97 | — | 142 | 1 | no | — |
| 681 | #95 | — | 71 | 1 | no | — |
| 682 | #95 | C22×D71 | 1 | 1 | yes | characteristic |
| 683 | C24 | — | 2 | 1 | no | — |
| 684 | C24 | — | 142 | 1 | no | — |
| 685 | #41 | — | 284 | 2 | no | — |
| 686 | #41 | — | 284 | 2 | no | — |
| 687 | C2×Q8 | — | 284 | 1 | no | — |
| 688 | C2×Q8 | — | 71 | 1 | no | — |
| 689 | C2×Q8 | — | 142 | 1 | no | — |
| 690 | C2×Q8 | — | 142 | 1 | no | — |
| 691 | C2×Q8 | — | 142 | 2 | no | — |
| 692 | C2×Q8 | — | 142 | 1 | no | — |
| 693 | C2×Q8 | — | 142 | 1 | no | — |
| 694 | C2×Q8 | D4×D71 | 1 | 1 | yes | characteristic |
| 695 | C2×D4 | — | 2 | 1 | no | — |
| 696 | C2×D4 | — | 2 | 1 | no | — |
| 697 | C2×D4 | — | 2 | 1 | no | — |
| 698 | C2×D4 | — | 8 | 1 | no | — |
| 699 | C2×D4 | — | 284 | 1 | no | — |
| 700 | C2×D4 | — | 284 | 1 | no | — |
| 701 | C2×D4 | — | 284 | 1 | no | — |
| 702 | C2×D4 | — | 284 | 1 | no | — |
| 703 | C2×D4 | — | 284 | 2 | no | — |
| 704 | C2×D4 | — | 284 | 2 | no | — |
| 705 | C2×D4 | — | 284 | 2 | no | — |
| 706 | C2×D4 | — | 284 | 2 | no | — |
| 707 | C2×D4 | — | 568 | 1 | no | — |
| 708 | C2×D4 | — | 71 | 1 | no | — |
| 709 | C2×D4 | — | 142 | 1 | no | — |
| 710 | C2×D4 | — | 142 | 1 | no | — |
| 711 | C2×D4 | — | 142 | 1 | no | — |
| 712 | C2×D4 | — | 142 | 1 | no | — |
| 713 | C2×D4 | — | 142 | 1 | no | — |
| 714 | C2×D4 | D4×D71 | 1 | 1 | yes | characteristic |
| 715 | C22×C4 | — | 2 | 1 | no | — |
| 716 | C22×C4 | — | 2 | 1 | no | — |
| 717 | C22×C4 | — | 71 | 1 | no | — |
| 718 | C22×C4 | — | 71 | 1 | no | — |
| 719 | C22×C4 | — | 71 | 1 | no | — |
| 720 | C22×C4 | — | 71 | 1 | no | — |
| 721 | C22×C4 | — | 142 | 1 | no | — |
| 722 | C22×C4 | — | 142 | 1 | no | — |
| 723 | C22×C4 | — | 142 | 1 | no | — |
| 724 | C22×C4 | — | 142 | 1 | no | — |
| 725 | C22×C4 | — | 142 | 1 | no | — |
| 726 | C22×C4 | — | 142 | 1 | no | — |
| 727 | C22×C4 | D4×D71 | 1 | 1 | yes | characteristic |
| 728 | C22×C4 | D4×D71 | 1 | 1 | yes | characteristic |
| 729 | C22×C4 | C23×D71 | 1 | 1 | yes | characteristic |
| 730 | SD16 | — | 8 | 1 | no | — |
| 731 | SD16 | — | 568 | 1 | no | — |
| 732 | SD16 | — | 568 | 1 | no | — |
| 733 | SD16 | — | 568 | 1 | no | — |
| 734 | D8 | — | 8 | 1 | no | — |
| 735 | D8 | — | 568 | 1 | no | — |
| 736 | D8 | — | 568 | 1 | no | — |
| 737 | D8 | — | 568 | 1 | no | — |
| 738 | C2×C8 | — | 2 | 1 | no | — |
| 739 | C2×C8 | — | 2 | 1 | no | — |
| 740 | C2×C8 | — | 142 | 1 | no | — |
| 741 | C2×C8 | — | 142 | 1 | no | — |
| 742 | C4⋊C4 | — | 2 | 1 | no | — |
| 743 | C4⋊C4 | — | 2 | 1 | no | — |
| 744 | C4⋊C4 | — | 2 | 1 | no | — |
| 745 | C4⋊C4 | — | 2 | 1 | no | — |
| 746 | C4⋊C4 | — | 2 | 1 | no | — |
| 747 | C4⋊C4 | — | 2 | 1 | no | — |
| 748 | C4⋊C4 | — | 284 | 2 | no | — |
| 749 | C4⋊C4 | — | 71 | 1 | no | — |
| 750 | C4⋊C4 | — | 71 | 1 | no | — |
| 751 | C4⋊C4 | — | 142 | 1 | no | — |
| 752 | C4⋊C4 | — | 142 | 1 | no | — |
| 753 | C4⋊C4 | — | 142 | 1 | no | — |
| 754 | C4⋊C4 | — | 142 | 1 | no | — |
| 755 | C4⋊C4 | — | 142 | 1 | no | — |
| 756 | C4⋊C4 | — | 142 | 1 | no | — |
| 757 | C4⋊C4 | — | 142 | 1 | no | — |
| 758 | C4⋊C4 | — | 142 | 1 | no | — |
| 759 | C4⋊C4 | — | 142 | 1 | no | — |
| 760 | C4⋊C4 | — | 142 | 1 | no | — |
| 761 | C4⋊C4 | — | 142 | 1 | no | — |
| 762 | C4⋊C4 | — | 142 | 1 | no | — |
| 763 | C4⋊C4 | — | 142 | 1 | no | — |
| 764 | C4⋊C4 | — | 142 | 1 | no | — |
| 765 | C4⋊C4 | — | 142 | 1 | no | — |
| 766 | C4⋊C4 | — | 142 | 1 | no | — |
| 767 | C4⋊C4 | — | 142 | 1 | no | — |
| 768 | C4⋊C4 | — | 142 | 1 | no | — |
| 769 | C4⋊C4 | — | 142 | 1 | no | — |
| 770 | C4⋊C4 | — | 142 | 1 | no | — |
| 771 | C4⋊C4 | D4×D71 | 1 | 1 | yes | characteristic |
| 772 | C4⋊C4 | D4×D71 | 1 | 1 | yes | characteristic |
| 773 | C22⋊C4 | — | 2 | 1 | no | — |
| 774 | C22⋊C4 | — | 2 | 1 | no | — |
| 775 | C22⋊C4 | — | 2 | 1 | no | — |
| 776 | C22⋊C4 | — | 2 | 1 | no | — |
| 777 | C22⋊C4 | — | 2 | 1 | no | — |
| 778 | C22⋊C4 | — | 4 | 2 | no | — |
| 779 | C22⋊C4 | — | 8 | 1 | no | — |
| 780 | C22⋊C4 | — | 284 | 2 | no | — |
| 781 | C22⋊C4 | — | 284 | 2 | no | — |
| 782 | C22⋊C4 | — | 284 | 2 | no | — |
| 783 | C22⋊C4 | — | 568 | 1 | no | — |
| 784 | C22⋊C4 | — | 568 | 1 | no | — |
| 785 | C22⋊C4 | — | 568 | 1 | no | — |
| 786 | C22⋊C4 | — | 142 | 1 | no | — |
| 787 | C22⋊C4 | — | 142 | 1 | no | — |
| 788 | C22⋊C4 | — | 142 | 1 | no | — |
| 789 | C22⋊C4 | — | 142 | 1 | no | — |
| 790 | C22⋊C4 | — | 142 | 1 | no | — |
| 791 | C22⋊C4 | — | 142 | 1 | no | — |
| 792 | C22⋊C4 | — | 142 | 1 | no | — |
| 793 | C22⋊C4 | — | 142 | 1 | no | — |
| 794 | C22⋊C4 | — | 142 | 1 | no | — |
| 795 | C22⋊C4 | — | 142 | 1 | no | — |
| 796 | C22⋊C4 | — | 142 | 1 | no | — |
| 797 | C22⋊C4 | — | 142 | 1 | no | — |
| 798 | C22⋊C4 | — | 142 | 1 | no | — |
| 799 | C42 | — | 2 | 1 | no | — |
| 800 | C42 | — | 284 | 2 | no | — |
| 801 | C42 | — | 71 | 1 | no | — |
| 802 | C42 | — | 71 | 1 | no | — |
| 803 | C42 | — | 71 | 1 | no | — |
| 804 | C42 | — | 71 | 1 | no | — |
| 805 | C42 | — | 142 | 1 | no | — |
| 806 | C42 | — | 142 | 1 | no | — |
| 807 | C42 | — | 142 | 1 | no | — |
| 808 | C42 | — | 142 | 1 | no | — |
| 809 | C42 | — | 142 | 1 | no | — |
| 810 | C42 | — | 142 | 1 | no | — |
| 811 | C42 | — | 142 | 1 | no | — |
| 812 | C42 | — | 142 | 1 | no | — |
| 813 | C42 | — | 142 | 1 | no | — |
| 814 | C23 | — | 2 | 1 | no | — |
| 815 | C23 | — | 4 | 1 | no | — |
| 816 | C23 | — | 4 | 1 | no | — |
| 817 | C23 | — | 4 | 1 | no | — |
| 818 | C23 | — | 4 | 1 | no | — |
| 819 | C23 | — | 4 | 1 | no | — |
| 820 | C23 | — | 4 | 1 | no | — |
| 821 | C23 | — | 4 | 1 | no | — |
| 822 | C23 | — | 284 | 1 | no | — |
| 823 | C23 | — | 284 | 1 | no | — |
| 824 | C23 | — | 284 | 1 | no | — |
| 825 | C23 | — | 284 | 1 | no | — |
| 826 | C23 | — | 284 | 1 | no | — |
| 827 | C23 | — | 284 | 1 | no | — |
| 828 | C23 | — | 284 | 1 | no | — |
| 829 | C23 | — | 142 | 1 | no | — |
| 830 | C23 | C2×D4×D71 | 1 | 1 | yes | characteristic |
| 831 | Q8 | — | 4 | 1 | no | — |
| 832 | Q8 | — | 284 | 1 | no | — |
| 833 | Q8 | — | 284 | 2 | no | — |
| 834 | Q8 | — | 284 | 2 | no | — |
| 835 | Q8 | — | 284 | 2 | no | — |
| 836 | Q8 | — | 568 | 1 | no | — |
| 837 | D4 | — | 4 | 1 | no | — |
| 838 | D4 | — | 4 | 1 | no | — |
| 839 | D4 | — | 4 | 1 | no | — |
| 840 | D4 | — | 4 | 1 | no | — |
| 841 | D4 | — | 4 | 1 | no | — |
| 842 | D4 | — | 4 | 1 | no | — |
| 843 | D4 | — | 4 | 1 | no | — |
| 844 | D4 | — | 284 | 1 | no | — |
| 845 | D4 | — | 284 | 1 | no | — |
| 846 | D4 | — | 284 | 1 | no | — |
| 847 | D4 | — | 284 | 1 | no | — |
| 848 | D4 | — | 284 | 1 | no | — |
| 849 | D4 | — | 284 | 1 | no | — |
| 850 | D4 | — | 284 | 1 | no | — |
| 851 | D4 | — | 284 | 2 | no | — |
| 852 | D4 | — | 568 | 1 | no | — |
| 853 | D4 | — | 568 | 2 | no | — |
| 854 | D4 | — | 568 | 2 | no | — |
| 855 | D4 | — | 568 | 2 | no | — |
| 856 | D4 | — | 568 | 2 | no | — |
| 857 | C2×C4 | — | 2 | 1 | no | — |
| 858 | C2×C4 | — | 2 | 1 | no | — |
| 859 | C2×C4 | — | 2 | 1 | no | — |
| 860 | C2×C4 | — | 2 | 1 | no | — |
| 861 | C2×C4 | — | 2 | 1 | no | — |
| 862 | C2×C4 | — | 2 | 1 | no | — |
| 863 | C2×C4 | — | 2 | 1 | no | — |
| 864 | C2×C4 | — | 4 | 1 | no | — |
| 865 | C2×C4 | — | 4 | 1 | no | — |
| 866 | C2×C4 | — | 4 | 1 | no | — |
| 867 | C2×C4 | — | 4 | 1 | no | — |
| 868 | C2×C4 | — | 4 | 1 | no | — |
| 869 | C2×C4 | — | 8 | 1 | no | — |
| 870 | C2×C4 | — | 284 | 2 | no | — |
| 871 | C2×C4 | — | 284 | 2 | no | — |
| 872 | C2×C4 | — | 284 | 2 | no | — |
| 873 | C2×C4 | — | 284 | 2 | no | — |
| 874 | C2×C4 | — | 284 | 1 | no | — |
| 875 | C2×C4 | — | 284 | 1 | no | — |
| 876 | C2×C4 | — | 284 | 1 | no | — |
| 877 | C2×C4 | — | 284 | 1 | no | — |
| 878 | C2×C4 | — | 568 | 1 | no | — |
| 879 | C2×C4 | — | 71 | 1 | no | — |
| 880 | C2×C4 | — | 71 | 1 | no | — |
| 881 | C2×C4 | — | 71 | 1 | no | — |
| 882 | C2×C4 | — | 71 | 1 | no | — |
| 883 | C2×C4 | — | 71 | 2 | no | — |
| 884 | C2×C4 | — | 142 | 1 | no | — |
| 885 | C2×C4 | — | 142 | 1 | no | — |
| 886 | C2×C4 | — | 142 | 1 | no | — |
| 887 | C2×C4 | — | 142 | 1 | no | — |
| 888 | C2×C4 | — | 142 | 2 | no | — |
| 889 | C2×C4 | — | 142 | 1 | no | — |
| 890 | C2×C4 | — | 142 | 1 | no | — |
| 891 | C2×C4 | — | 142 | 1 | no | — |
| 892 | C2×C4 | — | 142 | 1 | no | — |
| 893 | C2×C4 | C2×D4×D71 | 1 | 1 | yes | characteristic |
| 894 | C2×C4 | C2×D4×D71 | 1 | 1 | yes | characteristic |
| 895 | C8 | — | 4 | 1 | no | — |
| 896 | C8 | — | 4 | 1 | no | — |
| 897 | C8 | — | 284 | 1 | no | — |
| 898 | C8 | — | 284 | 1 | no | — |
| 899 | C22 | — | 2 | 1 | no | — |
| 900 | C22 | — | 2 | 1 | no | — |
| 901 | C22 | — | 4 | 1 | no | — |
| 902 | C22 | — | 4 | 1 | no | — |
| 903 | C22 | — | 4 | 1 | no | — |
| 904 | C22 | — | 8 | 1 | no | — |
| 905 | C22 | — | 8 | 1 | no | — |
| 906 | C22 | — | 8 | 1 | no | — |
| 907 | C22 | — | 8 | 1 | no | — |
| 908 | C22 | — | 8 | 1 | no | — |
| 909 | C22 | — | 8 | 1 | no | — |
| 910 | C22 | — | 8 | 1 | no | — |
| 911 | C22 | — | 284 | 1 | no | — |
| 912 | C22 | — | 284 | 1 | no | — |
| 913 | C22 | — | 284 | 1 | no | — |
| 914 | C22 | — | 568 | 1 | no | — |
| 915 | C22 | — | 568 | 1 | no | — |
| 916 | C22 | — | 568 | 1 | no | — |
| 917 | C22 | — | 568 | 1 | no | — |
| 918 | C22 | — | 568 | 1 | no | — |
| 919 | C22 | — | 568 | 1 | no | — |
| 920 | C22 | — | 568 | 1 | no | — |
| 921 | C22 | #120×D71 | 1 | 1 | yes | characteristic |
| 922 | C22 | AGL(1,ℤ/8)×D71 | 1 | 1 | yes | characteristic |
| 923 | C22 | #17986796 | 1 | 1 | yes | characteristic |
| 924 | C4 | — | 2 | 1 | no | — |
| 925 | C4 | — | 2 | 1 | no | — |
| 926 | C4 | — | 4 | 1 | no | — |
| 927 | C4 | — | 4 | 1 | no | — |
| 928 | C4 | — | 4 | 1 | no | — |
| 929 | C4 | — | 4 | 1 | no | — |
| 930 | C4 | — | 4 | 1 | no | — |
| 931 | C4 | — | 8 | 1 | no | — |
| 932 | C4 | — | 284 | 1 | no | — |
| 933 | C4 | — | 284 | 1 | no | — |
| 934 | C4 | — | 284 | 1 | no | — |
| 935 | C4 | — | 284 | 1 | no | — |
| 936 | C4 | — | 568 | 1 | no | — |
| 937 | C4 | — | 71 | 2 | no | — |
| 938 | C4 | — | 142 | 1 | no | — |
| 939 | C4 | — | 142 | 2 | no | — |
| 940 | C4 | — | 142 | 1 | no | — |
| 941 | C4 | — | 142 | 1 | no | — |
| 942 | C2 | — | 2 | 1 | no | — |
| 943 | C2 | — | 2 | 1 | no | — |
| 944 | C2 | — | 8 | 1 | no | — |
| 945 | C2 | — | 16 | 1 | no | — |
| 946 | C2 | — | 568 | 1 | no | — |
| 947 | C2 | — | 1136 | 1 | no | — |
| 948 | C2 | #22597589 | 1 | 1 | yes | characteristic |
| 949 | C2 | #454×D71 | 1 | 1 | yes | characteristic |
| 950 | C2 | #22597740 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22601770 | C2 | semidirect |
| 2. #22599361 | C2 | semidirect |
| 3. #22599356 | C2 | semidirect |
| 4. #22593338 | C2 | semidirect |
| 5. #22587281 | C2 | semidirect |
| 6. #22587278 | C2 | semidirect |
| 7. #22587276 | C2 | semidirect |
| 8. #22587273 | C2 | semidirect |
| 9. #22587271 | C2 | semidirect |
| 10. #22587269 | C2 | semidirect |
| 11. #22587267 | C2 | semidirect |
| 12. #22586864 | C2 | semidirect |
| 13. #22586862 | C2 | semidirect |
| 14. #22586682 | C2 | semidirect |
| 15. C71×#1597 | C2 | semidirect |
| 487. #1597 | D71 | semidirect |
| 491. C71 | #18337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601770 | 2 |
| #22599361 | 2 |
| #22599356 | 2 |
| #22593338 | 2 |
| #22587281 | 2 |
| #22587278 | 2 |
| #22587276 | 2 |
| #22587273 | 2 |
| #22587271 | 2 |
| #22587269 | 2 |
| #22587267 | 2 |
| #22586864 | 2 |
| #22586862 | 2 |
| #22586682 | 2 |
| C71×#1597 | 2 |
| #18337 | 71 |