| 1 | #22597241 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22590100 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#17985784 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#17985783 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22589960 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22589944 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C71×#2115 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #17986797 | C4 | 1 | 1 | yes | characteristic |
| 9 | C2×#14556134 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#14556068 | C22 | 1 | 1 | yes | characteristic |
| 11 | C22×C71⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 12 | #17986119 | — | 2 | 2 | no | — |
| 13 | #17986114 | — | 2 | 2 | no | — |
| 14 | #17986047 | C4 | 1 | 1 | yes | characteristic |
| 15 | #17986016 | C4 | 1 | 1 | yes | characteristic |
| 16 | #17986015 | C4 | 1 | 1 | yes | characteristic |
| 17 | #17985954 | C22 | 1 | 1 | yes | characteristic |
| 18 | Dic71⋊C16 | — | 2 | 2 | no | — |
| 19 | #17985784 | — | 2 | 2 | no | — |
| 20 | #17985783 | — | 2 | 2 | no | — |
| 21 | #17985780 | — | 2 | 2 | no | — |
| 22 | #17985776 | — | 2 | 2 | no | — |
| 23 | C2×#131×C71 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×M32×C71 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×M32×C71 | C22 | 1 | 1 | yes | characteristic |
| 26 | #349×C71 | — | 2 | 2 | no | — |
| 27 | C2×#11765865 | C2×C4 | 1 | 1 | yes | characteristic |
| 28 | #14556159 | — | 2 | 1 | no | — |
| 29 | #14556158 | — | 2 | 1 | no | — |
| 30 | #14556154 | — | 2 | 1 | no | — |
| 31 | #14556153 | — | 2 | 1 | no | — |
| 32 | #14556148 | — | 2 | 2 | no | — |
| 33 | #14556134 | — | 2 | 1 | no | — |
| 34 | #14556134 | — | 2 | 1 | no | — |
| 35 | #14556134 | — | 2 | 1 | no | — |
| 36 | #14556134 | — | 2 | 1 | no | — |
| 37 | C2×#11765849 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | C2×#11765849 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | C2×#11765848 | — | 2 | 1 | no | — |
| 40 | C2×C8×D71 | — | 2 | 1 | no | — |
| 41 | #14556087 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | #14556068 | — | 2 | 1 | no | — |
| 43 | #14556068 | D4 | 1 | 2 | yes | — |
| 44 | C2×C71⋊C16 | — | 2 | 1 | no | — |
| 45 | C2×C71⋊C16 | — | 2 | 1 | no | — |
| 46 | C2×C71⋊C16 | — | 2 | 1 | no | — |
| 47 | C2×C71⋊C16 | — | 2 | 1 | no | — |
| 48 | #14556063 | — | 2 | 2 | no | — |
| 49 | #14556055 | — | 2 | 2 | no | — |
| 50 | #14556054 | — | 2 | 2 | no | — |
| 51 | #14556038 | D4 | 1 | 2 | yes | — |
| 52 | C8×Dic71 | D4 | 1 | 2 | yes | — |
| 53 | C2×#41×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 54 | #131×C71 | — | 2 | 1 | no | — |
| 55 | #131×C71 | — | 2 | 1 | no | — |
| 56 | #131×C71 | — | 2 | 1 | no | — |
| 57 | #131×C71 | — | 2 | 1 | no | — |
| 58 | C2×M16×C71 | — | 2 | 1 | no | — |
| 59 | C2×M16×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 60 | C22×C8×C71 | — | 2 | 1 | no | — |
| 61 | C22×C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 62 | M32×C71 | — | 2 | 1 | no | — |
| 63 | M32×C71 | — | 2 | 1 | no | — |
| 64 | M32×C71 | — | 2 | 1 | no | — |
| 65 | M32×C71 | D4 | 1 | 2 | yes | — |
| 66 | C2×C16×C71 | — | 2 | 1 | no | — |
| 67 | C2×C16×C71 | — | 2 | 1 | no | — |
| 68 | #11765865 | — | 2 | 1 | no | — |
| 69 | #11765865 | — | 2 | 1 | no | — |
| 70 | #11765865 | — | 2 | 1 | no | — |
| 71 | #11765865 | — | 2 | 1 | no | — |
| 72 | C2×Dic142 | M16 | 1 | 1 | yes | characteristic |
| 73 | C2×D284 | M16 | 1 | 1 | yes | characteristic |
| 74 | C2×C22⋊D71 | — | 2 | 1 | no | — |
| 75 | C2×C4×D71 | — | 2 | 1 | no | — |
| 76 | #11765855 | — | 2 | 2 | no | — |
| 77 | #11765853 | — | 2 | 2 | no | — |
| 78 | #11765852 | — | 2 | 2 | no | — |
| 79 | #11765850 | — | 2 | 2 | no | — |
| 80 | #11765849 | — | 2 | 1 | no | — |
| 81 | #11765849 | — | 2 | 1 | no | — |
| 82 | #11765849 | — | 2 | 1 | no | — |
| 83 | #11765849 | — | 2 | 1 | no | — |
| 84 | #11765848 | — | 4 | 1 | no | — |
| 85 | #11765848 | — | 4 | 1 | no | — |
| 86 | C2×C71⋊C8 | — | 2 | 1 | no | — |
| 87 | C2×C71⋊C8 | C22⋊C4 | 1 | 2 | yes | — |
| 88 | C8×D71 | — | 4 | 1 | no | — |
| 89 | C8×D71 | — | 4 | 1 | no | — |
| 90 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 91 | C22⋊Dic71 | — | 2 | 1 | no | — |
| 92 | C4×Dic71 | C22⋊C4 | 1 | 2 | yes | — |
| 93 | C71⋊C16 | — | 2 | 2 | no | — |
| 94 | C71⋊C16 | — | 4 | 1 | no | — |
| 95 | #41×C71 | — | 2 | 1 | no | — |
| 96 | #41×C71 | — | 2 | 1 | no | — |
| 97 | #41×C71 | — | 2 | 1 | no | — |
| 98 | #41×C71 | — | 2 | 1 | no | — |
| 99 | C2×Q8×C71 | M16 | 1 | 1 | yes | characteristic |
| 100 | C2×D4×C71 | — | 2 | 1 | no | — |
| 101 | C2×D4×C71 | M16 | 1 | 1 | yes | characteristic |
| 102 | C22×C4×C71 | — | 2 | 1 | no | — |
| 103 | C22×C4×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 104 | M16×C71 | — | 2 | 1 | no | — |
| 105 | M16×C71 | — | 2 | 1 | no | — |
| 106 | M16×C71 | — | 4 | 1 | no | — |
| 107 | M16×C71 | — | 4 | 1 | no | — |
| 108 | C2×C8×C71 | — | 2 | 1 | no | — |
| 109 | C2×C8×C71 | — | 4 | 1 | no | — |
| 110 | C2×C8×C71 | — | 4 | 1 | no | — |
| 111 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 112 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 113 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | C2×C8×C71 | #41 | 1 | 1 | yes | characteristic |
| 116 | C2×C8×C71 | #41 | 1 | 1 | yes | characteristic |
| 117 | C16×C71 | — | 2 | 2 | no | — |
| 118 | C16×C71 | — | 4 | 1 | no | — |
| 119 | C23×C71 | — | 2 | 1 | no | — |
| 120 | C23×C71 | #131 | 1 | 1 | yes | characteristic |
| 121 | C22×D71 | — | 2 | 1 | no | — |
| 122 | Q8×C71 | — | 2 | 1 | no | — |
| 123 | Q8×C71 | — | 2 | 1 | no | — |
| 124 | D4×C71 | — | 2 | 1 | no | — |
| 125 | D4×C71 | — | 2 | 1 | no | — |
| 126 | D4×C71 | — | 4 | 1 | no | — |
| 127 | D4×C71 | — | 4 | 1 | no | — |
| 128 | C2×C4×C71 | — | 2 | 1 | no | — |
| 129 | C2×C4×C71 | — | 4 | 1 | no | — |
| 130 | C2×C4×C71 | — | 4 | 1 | no | — |
| 131 | C2×C4×C71 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 132 | C2×C4×C71 | C4×D4 | 1 | 1 | yes | characteristic |
| 133 | C2×C4×C71 | C4×D4 | 1 | 1 | yes | characteristic |
| 134 | C2×C4×C71 | C2×M16 | 1 | 1 | yes | characteristic |
| 135 | C2×C4×C71 | C2×M16 | 1 | 1 | yes | characteristic |
| 136 | C2×C4×C71 | #131 | 1 | 1 | yes | characteristic |
| 137 | C22⋊D71 | — | 4 | 1 | no | — |
| 138 | C22⋊D71 | — | 4 | 1 | no | — |
| 139 | C2×Dic71 | — | 2 | 2 | no | — |
| 140 | C2×Dic71 | — | 2 | 1 | no | — |
| 141 | D284 | — | 2 | 1 | no | — |
| 142 | D284 | — | 2 | 1 | no | — |
| 143 | C4×D71 | — | 4 | 1 | no | — |
| 144 | C4×D71 | — | 4 | 1 | no | — |
| 145 | Dic142 | — | 2 | 1 | no | — |
| 146 | Dic142 | — | 2 | 1 | no | — |
| 147 | C8×C71 | — | 4 | 1 | no | — |
| 148 | C8×C71 | #121 | 1 | 1 | yes | characteristic |
| 149 | C8×C71 | #121 | 1 | 1 | yes | characteristic |
| 150 | C8×C71 | #124 | 1 | 1 | yes | characteristic |
| 151 | C8×C71 | #127 | 1 | 1 | yes | characteristic |
| 152 | C71⋊C8 | — | 2 | 2 | no | — |
| 153 | C71⋊C8 | — | 4 | 1 | no | — |
| 154 | C22×C71 | — | 4 | 1 | no | — |
| 155 | C22×C71 | — | 4 | 1 | no | — |
| 156 | C22×C71 | — | 8 | 1 | no | — |
| 157 | C22×C71 | #408 | 1 | 1 | yes | characteristic |
| 158 | C22×C71 | #435 | 1 | 1 | yes | characteristic |
| 159 | C22×C71 | #435 | 1 | 1 | yes | characteristic |
| 160 | C2×D71 | — | 4 | 1 | no | — |
| 161 | C2×D71 | — | 8 | 1 | no | — |
| 162 | C4×C71 | — | 4 | 1 | no | — |
| 163 | C4×C71 | #390 | 1 | 1 | yes | characteristic |
| 164 | C4×C71 | #407 | 1 | 1 | yes | characteristic |
| 165 | C4×C71 | #435 | 1 | 1 | yes | characteristic |
| 166 | C4×C71 | #435 | 1 | 1 | yes | characteristic |
| 167 | Dic71 | — | 4 | 2 | no | — |
| 168 | Dic71 | — | 4 | 1 | no | — |
| 169 | #13199 | — | 71 | 1 | no | maximal, Sylow |
| 170 | C2×C71 | — | 2 | 1 | no | — |
| 171 | C2×C71 | — | 2 | 1 | no | — |
| 172 | C2×C71 | — | 2 | 1 | no | — |
| 173 | C2×C71 | — | 8 | 1 | no | — |
| 174 | C2×C71 | #1955 | 1 | 1 | yes | characteristic |
| 175 | D71 | — | 8 | 1 | no | — |
| 176 | #2955 | — | 71 | 1 | no | — |
| 177 | #2151 | — | 71 | 1 | no | — |
| 178 | C2×#350 | — | 71 | 1 | no | — |
| 179 | C2×#350 | — | 71 | 1 | no | — |
| 180 | #2115 | — | 71 | 1 | no | — |
| 181 | #2115 | D71 | 1 | 1 | yes | characteristic, complemented |
| 182 | #2110 | — | 71 | 1 | no | — |
| 183 | C71 | #13199 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 184 | #575 | — | 71 | 1 | no | — |
| 185 | C2×#131 | — | 71 | 1 | no | — |
| 186 | C2×#131 | C2×D71 | 1 | 1 | yes | characteristic |
| 187 | C2×M32 | — | 71 | 1 | no | — |
| 188 | C2×M32 | C2×D71 | 1 | 1 | yes | characteristic |
| 189 | C2×M32 | C2×D71 | 1 | 1 | yes | characteristic |
| 190 | C22×C16 | — | 71 | 1 | no | — |
| 191 | #444 | — | 142 | 2 | no | — |
| 192 | #443 | — | 142 | 2 | no | — |
| 193 | #430 | — | 71 | 1 | no | — |
| 194 | #421 | — | 71 | 1 | no | — |
| 195 | #421 | — | 71 | 1 | no | — |
| 196 | #405 | — | 71 | 1 | no | — |
| 197 | C4⋊C16 | — | 142 | 2 | no | — |
| 198 | #350 | — | 142 | 2 | no | — |
| 199 | #350 | — | 142 | 2 | no | — |
| 200 | #349 | — | 2 | 2 | no | — |
| 201 | #349 | — | 142 | 2 | no | — |
| 202 | #347 | — | 142 | 2 | no | — |
| 203 | C2×#41 | — | 71 | 1 | no | — |
| 204 | C2×#41 | C4×D71 | 1 | 1 | yes | characteristic |
| 205 | #137 | — | 142 | 1 | no | — |
| 206 | #137 | — | 142 | 1 | no | — |
| 207 | AGL(1,ℤ/8) | — | 142 | 1 | no | — |
| 208 | AGL(1,ℤ/8) | — | 142 | 1 | no | — |
| 209 | #135 | — | 142 | 2 | no | — |
| 210 | #131 | — | 2 | 1 | no | — |
| 211 | #131 | — | 2 | 1 | no | — |
| 212 | #131 | — | 2 | 1 | no | — |
| 213 | #131 | — | 2 | 1 | no | — |
| 214 | #131 | — | 142 | 1 | no | — |
| 215 | #131 | — | 142 | 1 | no | — |
| 216 | #131 | — | 142 | 1 | no | — |
| 217 | #131 | — | 142 | 1 | no | — |
| 218 | C2×M16 | — | 2 | 1 | no | — |
| 219 | C2×M16 | — | 71 | 1 | no | — |
| 220 | C2×M16 | — | 71 | 1 | no | — |
| 221 | C2×M16 | — | 142 | 1 | no | — |
| 222 | C2×M16 | C4×D71 | 1 | 1 | yes | characteristic |
| 223 | C22×C8 | — | 2 | 1 | no | — |
| 224 | C22×C8 | — | 142 | 1 | no | — |
| 225 | C22×C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 226 | #117 | — | 71 | 1 | no | — |
| 227 | M32 | — | 2 | 1 | no | — |
| 228 | M32 | — | 2 | 1 | no | — |
| 229 | M32 | — | 2 | 1 | no | — |
| 230 | M32 | — | 71 | 2 | no | — |
| 231 | M32 | — | 142 | 1 | no | — |
| 232 | M32 | C22⋊D71 | 1 | 2 | yes | — |
| 233 | C2×C16 | — | 2 | 1 | no | — |
| 234 | C2×C16 | — | 2 | 1 | no | — |
| 235 | C2×C16 | — | 142 | 1 | no | — |
| 236 | C2×C16 | — | 142 | 1 | no | — |
| 237 | C2×C16 | — | 142 | 1 | no | — |
| 238 | C2×C16 | — | 142 | 1 | no | — |
| 239 | #108 | — | 142 | 2 | no | — |
| 240 | #104 | — | 142 | 2 | no | — |
| 241 | #104 | — | 142 | 2 | no | — |
| 242 | #97 | — | 71 | 2 | no | — |
| 243 | C4×C8 | — | 71 | 2 | no | — |
| 244 | #41 | — | 2 | 1 | no | — |
| 245 | #41 | — | 2 | 1 | no | — |
| 246 | #41 | — | 2 | 1 | no | — |
| 247 | #41 | — | 2 | 1 | no | — |
| 248 | #41 | — | 142 | 1 | no | — |
| 249 | #41 | — | 142 | 1 | no | — |
| 250 | #41 | — | 142 | 1 | no | — |
| 251 | #41 | — | 142 | 1 | no | — |
| 252 | C2×Q8 | — | 71 | 1 | no | — |
| 253 | C2×Q8 | #11765848 | 1 | 1 | yes | characteristic |
| 254 | C2×D4 | — | 2 | 1 | no | — |
| 255 | C2×D4 | — | 71 | 1 | no | — |
| 256 | C2×D4 | — | 142 | 1 | no | — |
| 257 | C2×D4 | #11765848 | 1 | 1 | yes | characteristic |
| 258 | C22×C4 | — | 2 | 1 | no | — |
| 259 | C22×C4 | — | 142 | 1 | no | — |
| 260 | C22×C4 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 261 | Q16 | — | 142 | 2 | no | — |
| 262 | SD16 | — | 142 | 2 | no | — |
| 263 | SD16 | — | 142 | 2 | no | — |
| 264 | D8 | — | 142 | 2 | no | — |
| 265 | M16 | — | 2 | 1 | no | — |
| 266 | M16 | — | 2 | 1 | no | — |
| 267 | M16 | — | 4 | 1 | no | — |
| 268 | M16 | — | 4 | 1 | no | — |
| 269 | M16 | — | 284 | 1 | no | — |
| 270 | M16 | — | 284 | 1 | no | — |
| 271 | M16 | — | 142 | 1 | no | — |
| 272 | M16 | — | 142 | 1 | no | — |
| 273 | M16 | — | 142 | 1 | no | — |
| 274 | M16 | — | 142 | 1 | no | — |
| 275 | C2×C8 | — | 2 | 1 | no | — |
| 276 | C2×C8 | — | 4 | 1 | no | — |
| 277 | C2×C8 | — | 4 | 1 | no | — |
| 278 | C2×C8 | — | 284 | 1 | no | — |
| 279 | C2×C8 | — | 284 | 1 | no | — |
| 280 | C2×C8 | — | 71 | 2 | no | — |
| 281 | C2×C8 | — | 142 | 1 | no | — |
| 282 | C2×C8 | D4×D71 | 1 | 1 | yes | characteristic |
| 283 | C2×C8 | D4×D71 | 1 | 1 | yes | characteristic |
| 284 | C2×C8 | D4×D71 | 1 | 1 | yes | characteristic |
| 285 | C2×C8 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 286 | C2×C8 | #11765864 | 1 | 1 | yes | characteristic |
| 287 | C2×C8 | #11765865 | 1 | 1 | yes | characteristic |
| 288 | C4⋊C4 | — | 142 | 1 | no | — |
| 289 | C22⋊C4 | — | 142 | 1 | no | — |
| 290 | C42 | — | 71 | 2 | no | — |
| 291 | C16 | — | 2 | 2 | no | — |
| 292 | C16 | — | 4 | 1 | no | — |
| 293 | C16 | — | 284 | 1 | no | — |
| 294 | C16 | — | 142 | 2 | no | — |
| 295 | C23 | — | 2 | 1 | no | — |
| 296 | C23 | — | 142 | 1 | no | — |
| 297 | C23 | #14556134 | 1 | 1 | yes | characteristic |
| 298 | Q8 | — | 2 | 1 | no | — |
| 299 | Q8 | — | 2 | 1 | no | — |
| 300 | Q8 | — | 142 | 1 | no | — |
| 301 | Q8 | — | 142 | 1 | no | — |
| 302 | D4 | — | 2 | 1 | no | — |
| 303 | D4 | — | 2 | 1 | no | — |
| 304 | D4 | — | 4 | 1 | no | — |
| 305 | D4 | — | 4 | 1 | no | — |
| 306 | D4 | — | 284 | 1 | no | — |
| 307 | D4 | — | 284 | 1 | no | — |
| 308 | D4 | — | 142 | 1 | no | — |
| 309 | D4 | — | 142 | 1 | no | — |
| 310 | C2×C4 | — | 2 | 1 | no | — |
| 311 | C2×C4 | — | 4 | 1 | no | — |
| 312 | C2×C4 | — | 4 | 1 | no | — |
| 313 | C2×C4 | — | 284 | 1 | no | — |
| 314 | C2×C4 | — | 284 | 1 | no | — |
| 315 | C2×C4 | — | 142 | 1 | no | — |
| 316 | C2×C4 | — | 142 | 2 | no | — |
| 317 | C2×C4 | C22⋊C4×D71 | 1 | 1 | yes | characteristic |
| 318 | C2×C4 | (C22⋊D71)⋊C4 | 1 | 1 | yes | characteristic |
| 319 | C2×C4 | C4×C22⋊D71 | 1 | 1 | yes | characteristic |
| 320 | C2×C4 | M16×D71 | 1 | 1 | yes | characteristic |
| 321 | C2×C4 | C2×#11765848 | 1 | 1 | yes | characteristic |
| 322 | C2×C4 | #14556136 | 1 | 1 | yes | characteristic |
| 323 | C8 | — | 4 | 1 | no | — |
| 324 | C8 | — | 284 | 1 | no | — |
| 325 | C8 | — | 142 | 2 | no | — |
| 326 | C8 | #14556100 | 1 | 1 | yes | characteristic |
| 327 | C8 | #14556101 | 1 | 1 | yes | characteristic |
| 328 | C8 | #14556114 | 1 | 1 | yes | characteristic |
| 329 | C8 | #14556124 | 1 | 1 | yes | characteristic |
| 330 | C22 | — | 4 | 1 | no | — |
| 331 | C22 | — | 4 | 1 | no | — |
| 332 | C22 | — | 8 | 1 | no | — |
| 333 | C22 | — | 284 | 1 | no | — |
| 334 | C22 | — | 568 | 1 | no | — |
| 335 | C22 | #17985964 | 1 | 1 | yes | characteristic |
| 336 | C22 | #17986070 | 1 | 1 | yes | characteristic |
| 337 | C22 | #17986073 | 1 | 1 | yes | characteristic |
| 338 | C4 | — | 4 | 1 | no | — |
| 339 | C4 | — | 284 | 2 | no | — |
| 340 | C4 | — | 284 | 1 | no | — |
| 341 | C4 | #17985899 | 1 | 1 | yes | characteristic |
| 342 | C4 | #17985961 | 1 | 1 | yes | characteristic |
| 343 | C4 | #17986067 | 1 | 1 | yes | characteristic |
| 344 | C4 | #17986068 | 1 | 1 | yes | characteristic |
| 345 | C2 | — | 2 | 1 | no | — |
| 346 | C2 | — | 2 | 1 | no | — |
| 347 | C2 | — | 2 | 1 | no | — |
| 348 | C2 | — | 8 | 1 | no | — |
| 349 | C2 | — | 568 | 1 | no | — |
| 350 | C2 | #22589136 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta