| 1 | #90409 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #90260 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C7×#460 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #89936 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #89935 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #89935 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | SD16×Dic7 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #89843 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #89798 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #89619 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #89600 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #89536 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #89535 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #89532 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #89531 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#1159 | — | 2 | 1 | no | — |
| 17 | C2×C7×SD16 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C7×SD16 | C22 | 1 | 1 | yes | characteristic |
| 19 | C7×#127 | C22 | 1 | 1 | yes | characteristic |
| 20 | C4×C7×Q8 | C22 | 1 | 1 | yes | characteristic |
| 21 | Q8×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 22 | Q8×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#1143 | C22 | 1 | 1 | yes | characteristic |
| 24 | #6503 | C22 | 1 | 1 | yes | characteristic |
| 25 | #6503 | C22 | 1 | 1 | yes | characteristic |
| 26 | #6502 | — | 2 | 1 | no | — |
| 27 | #6502 | — | 2 | 1 | no | — |
| 28 | #6501 | — | 2 | 1 | no | — |
| 29 | D4×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 30 | D4×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 31 | #6453 | — | 2 | 1 | no | — |
| 32 | #6453 | C22 | 1 | 1 | yes | characteristic |
| 33 | #6451 | — | 2 | 1 | no | — |
| 34 | #6451 | C22 | 1 | 1 | yes | characteristic |
| 35 | C4×D28 | C22 | 1 | 1 | yes | characteristic |
| 36 | #6433 | — | 2 | 1 | no | — |
| 37 | #6433 | C22 | 1 | 1 | yes | characteristic |
| 38 | C4×Dic14 | — | 2 | 1 | no | — |
| 39 | C4×Dic14 | C22 | 1 | 1 | yes | characteristic |
| 40 | C7×C4⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 41 | C7×#102 | C22 | 1 | 1 | yes | characteristic |
| 42 | C7×#102 | C22 | 1 | 1 | yes | characteristic |
| 43 | #6409 | C22 | 1 | 1 | yes | characteristic |
| 44 | #6406 | C22 | 1 | 1 | yes | characteristic |
| 45 | #6406 | C22 | 1 | 1 | yes | characteristic |
| 46 | #6406 | C22 | 1 | 1 | yes | characteristic |
| 47 | #6406 | C22 | 1 | 1 | yes | characteristic |
| 48 | #6395 | C22 | 1 | 1 | yes | characteristic |
| 49 | #6395 | C22 | 1 | 1 | yes | characteristic |
| 50 | #6392 | C22 | 1 | 1 | yes | characteristic |
| 51 | #6391 | C22 | 1 | 1 | yes | characteristic |
| 52 | #6389 | C22 | 1 | 1 | yes | characteristic |
| 53 | Dic7⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 54 | Dic7⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 55 | C8×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 56 | #6383 | C22 | 1 | 1 | yes | characteristic |
| 57 | #6381 | C22 | 1 | 1 | yes | characteristic |
| 58 | #6377 | C22 | 1 | 1 | yes | characteristic |
| 59 | #3368 | — | 7 | 1 | no | maximal, Sylow |
| 60 | C2×C7×Q8 | C23 | 1 | 1 | yes | characteristic |
| 61 | C2×C7×D4 | — | 2 | 1 | no | — |
| 62 | C2×C7×D4 | — | 2 | 1 | no | — |
| 63 | C2×C7×D4 | C23 | 1 | 1 | yes | characteristic |
| 64 | C2×C7×D4 | C23 | 1 | 1 | yes | characteristic |
| 65 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 66 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 67 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 68 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 69 | C22×Dic7 | — | 2 | 1 | no | — |
| 70 | C22×Dic7 | — | 2 | 1 | no | — |
| 71 | #1159 | — | 4 | 4 | no | — |
| 72 | C2×D28 | C23 | 1 | 1 | yes | characteristic |
| 73 | C2×C4×D7 | — | 2 | 1 | no | — |
| 74 | C2×Dic14 | — | 2 | 1 | no | — |
| 75 | C2×Dic14 | D4 | 1 | 1 | yes | characteristic |
| 76 | C7×SD16 | — | 2 | 2 | no | — |
| 77 | C7×SD16 | — | 2 | 2 | no | — |
| 78 | C2×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 79 | C2×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 80 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 81 | C7×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 82 | C42×C7 | — | 2 | 1 | no | — |
| 83 | C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 84 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 85 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 86 | #1143 | — | 2 | 2 | no | — |
| 87 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 88 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 89 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 90 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 91 | C4⋊Dic7 | D4 | 1 | 1 | yes | characteristic |
| 92 | C4⋊Dic7 | C23 | 1 | 1 | yes | characteristic |
| 93 | C4⋊Dic7 | C23 | 1 | 1 | yes | characteristic |
| 94 | C4⋊Dic7 | C23 | 1 | 1 | yes | characteristic |
| 95 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 96 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 97 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 98 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 99 | Dic7⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 100 | Dic7⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 101 | C4×Dic7 | — | 2 | 1 | no | — |
| 102 | C4×Dic7 | — | 2 | 1 | no | — |
| 103 | C4×Dic7 | C23 | 1 | 1 | yes | characteristic |
| 104 | C4×Dic7 | C23 | 1 | 1 | yes | characteristic |
| 105 | C2×C7⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 106 | C2×C7⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 107 | #557 | — | 7 | 1 | no | — |
| 108 | #550 | — | 7 | 1 | no | — |
| 109 | #490 | — | 7 | 1 | no | — |
| 110 | #490 | — | 7 | 1 | no | — |
| 111 | #486 | — | 7 | 1 | no | — |
| 112 | #478 | — | 7 | 1 | no | — |
| 113 | #478 | — | 7 | 1 | no | — |
| 114 | #474 | — | 7 | 1 | no | — |
| 115 | #460 | — | 7 | 1 | no | — |
| 116 | #460 | — | 7 | 1 | no | — |
| 117 | #460 | D7 | 1 | 1 | yes | characteristic, complemented |
| 118 | #446 | — | 7 | 1 | no | — |
| 119 | #440 | — | 7 | 1 | no | — |
| 120 | #440 | — | 7 | 1 | no | — |
| 121 | C4×SD16 | — | 7 | 1 | no | — |
| 122 | C23×C7 | — | 2 | 1 | no | — |
| 123 | C23×C7 | — | 2 | 1 | no | — |
| 124 | C22×D7 | — | 2 | 1 | no | — |
| 125 | C7×Q8 | — | 2 | 1 | no | — |
| 126 | C7×Q8 | #41 | 1 | 2 | yes | complemented |
| 127 | C7×D4 | — | 2 | 1 | no | — |
| 128 | C7×D4 | — | 2 | 1 | no | — |
| 129 | C7×D4 | — | 2 | 1 | no | — |
| 130 | C7×D4 | — | 2 | 1 | no | — |
| 131 | C7×D4 | — | 4 | 2 | no | — |
| 132 | C7×D4 | — | 8 | 1 | no | — |
| 133 | C2×C4×C7 | — | 2 | 1 | no | — |
| 134 | C2×C4×C7 | — | 2 | 1 | no | — |
| 135 | C2×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 136 | C2×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C2×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 138 | C22⋊D7 | — | 4 | 2 | no | — |
| 139 | C22⋊D7 | — | 4 | 2 | no | — |
| 140 | C22⋊D7 | — | 8 | 1 | no | — |
| 141 | C22⋊D7 | — | 8 | 1 | no | — |
| 142 | C2×Dic7 | — | 2 | 1 | no | — |
| 143 | C2×Dic7 | — | 2 | 1 | no | — |
| 144 | C2×Dic7 | — | 2 | 1 | no | — |
| 145 | C2×Dic7 | — | 4 | 2 | no | — |
| 146 | C2×Dic7 | — | 4 | 2 | no | — |
| 147 | C2×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 148 | C2×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 149 | C2×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 150 | C2×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 151 | D28 | — | 2 | 1 | no | — |
| 152 | D28 | — | 2 | 1 | no | — |
| 153 | C4×D7 | — | 4 | 2 | no | — |
| 154 | Dic14 | — | 2 | 2 | no | — |
| 155 | Dic14 | — | 4 | 2 | no | — |
| 156 | C7×C8 | — | 2 | 1 | no | — |
| 157 | C7×C8 | — | 2 | 1 | no | — |
| 158 | C7⋊C8 | — | 2 | 1 | no | — |
| 159 | C7⋊C8 | — | 2 | 1 | no | — |
| 160 | C2×#41 | — | 14 | 1 | no | — |
| 161 | C2×SD16 | — | 7 | 1 | no | — |
| 162 | C2×SD16 | C2×D7 | 1 | 1 | yes | characteristic |
| 163 | C2×SD16 | C2×D7 | 1 | 1 | yes | characteristic |
| 164 | C4⋊Q8 | — | 7 | 1 | no | — |
| 165 | C4⋊Q8 | — | 14 | 1 | no | — |
| 166 | #127 | — | 7 | 1 | no | — |
| 167 | #127 | — | 7 | 1 | no | — |
| 168 | #127 | C2×D7 | 1 | 1 | yes | characteristic |
| 169 | #125 | — | 7 | 1 | no | — |
| 170 | #125 | — | 7 | 1 | no | — |
| 171 | #125 | — | 14 | 1 | no | — |
| 172 | #125 | — | 14 | 1 | no | — |
| 173 | #121 | — | 14 | 1 | no | — |
| 174 | #121 | — | 14 | 1 | no | — |
| 175 | #121 | — | 14 | 1 | no | — |
| 176 | C4×Q8 | — | 7 | 1 | no | — |
| 177 | C4×Q8 | — | 7 | 1 | no | — |
| 178 | C4×Q8 | — | 7 | 1 | no | — |
| 179 | C4×Q8 | — | 14 | 1 | no | — |
| 180 | C4×Q8 | C2×D7 | 1 | 1 | yes | characteristic |
| 181 | C4×D4 | — | 7 | 1 | no | — |
| 182 | C4×D4 | — | 7 | 1 | no | — |
| 183 | C4×D4 | — | 7 | 1 | no | — |
| 184 | #107 | — | 7 | 1 | no | — |
| 185 | #107 | — | 7 | 1 | no | — |
| 186 | #106 | — | 7 | 1 | no | — |
| 187 | C4⋊C8 | — | 7 | 1 | no | — |
| 188 | C4⋊C8 | — | 7 | 1 | no | — |
| 189 | C4⋊C8 | C2×D7 | 1 | 1 | yes | characteristic |
| 190 | #103 | — | 7 | 1 | no | — |
| 191 | #102 | — | 7 | 1 | no | — |
| 192 | #102 | — | 7 | 1 | no | — |
| 193 | #102 | — | 7 | 1 | no | — |
| 194 | #102 | — | 7 | 1 | no | — |
| 195 | #102 | — | 7 | 1 | no | — |
| 196 | #102 | — | 7 | 1 | no | — |
| 197 | #102 | — | 7 | 1 | no | — |
| 198 | #102 | C2×D7 | 1 | 1 | yes | characteristic |
| 199 | #102 | C2×D7 | 1 | 1 | yes | characteristic |
| 200 | #97 | — | 7 | 1 | no | — |
| 201 | #97 | — | 7 | 1 | no | — |
| 202 | C4×C8 | — | 7 | 1 | no | — |
| 203 | C22×C7 | — | 4 | 1 | no | — |
| 204 | C22×C7 | — | 4 | 1 | no | — |
| 205 | C22×C7 | — | 4 | 1 | no | — |
| 206 | C22×C7 | — | 4 | 1 | no | — |
| 207 | C22×C7 | — | 4 | 1 | no | — |
| 208 | C22×C7 | — | 4 | 1 | no | — |
| 209 | C22×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 210 | C2×D7 | — | 4 | 1 | no | — |
| 211 | C2×D7 | — | 4 | 1 | no | — |
| 212 | C2×D7 | — | 4 | 1 | no | — |
| 213 | C4×C7 | — | 2 | 2 | no | — |
| 214 | C4×C7 | — | 2 | 1 | no | — |
| 215 | C4×C7 | — | 2 | 1 | no | — |
| 216 | C4×C7 | — | 4 | 1 | no | — |
| 217 | C4×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 218 | C4×C7 | 2−1+4 | 1 | 1 | yes | characteristic |
| 219 | Dic7 | — | 2 | 1 | no | — |
| 220 | Dic7 | — | 2 | 1 | no | — |
| 221 | Dic7 | — | 2 | 1 | no | — |
| 222 | Dic7 | — | 4 | 1 | no | — |
| 223 | Dic7 | — | 4 | 1 | no | — |
| 224 | Dic7 | — | 4 | 1 | no | — |
| 225 | Dic7 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 226 | #41 | — | 28 | 4 | no | — |
| 227 | C2×Q8 | — | 7 | 1 | no | — |
| 228 | C2×Q8 | — | 14 | 1 | no | — |
| 229 | C2×Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 230 | C2×D4 | — | 2 | 1 | no | — |
| 231 | C2×D4 | — | 2 | 1 | no | — |
| 232 | C2×D4 | — | 7 | 1 | no | — |
| 233 | C2×D4 | — | 14 | 1 | no | — |
| 234 | C2×D4 | — | 14 | 1 | no | — |
| 235 | C2×D4 | — | 14 | 1 | no | — |
| 236 | C2×D4 | — | 14 | 1 | no | — |
| 237 | C2×D4 | C22×D7 | 1 | 1 | yes | characteristic |
| 238 | C2×D4 | C22×D7 | 1 | 1 | yes | characteristic |
| 239 | C22×C4 | — | 14 | 1 | no | — |
| 240 | C22×C4 | — | 14 | 1 | no | — |
| 241 | C22×C4 | — | 14 | 1 | no | — |
| 242 | SD16 | — | 2 | 2 | no | — |
| 243 | SD16 | — | 2 | 2 | no | — |
| 244 | SD16 | — | 14 | 2 | no | — |
| 245 | C2×C8 | — | 7 | 1 | no | — |
| 246 | C2×C8 | — | 7 | 1 | no | — |
| 247 | C2×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 248 | C2×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 249 | C4⋊C4 | — | 2 | 1 | no | — |
| 250 | C4⋊C4 | — | 7 | 1 | no | — |
| 251 | C4⋊C4 | — | 7 | 1 | no | — |
| 252 | C4⋊C4 | — | 7 | 1 | no | — |
| 253 | C4⋊C4 | — | 7 | 1 | no | — |
| 254 | C4⋊C4 | — | 7 | 1 | no | — |
| 255 | C4⋊C4 | — | 7 | 1 | no | — |
| 256 | C4⋊C4 | — | 14 | 1 | no | — |
| 257 | C4⋊C4 | — | 14 | 1 | no | — |
| 258 | C4⋊C4 | — | 14 | 1 | no | — |
| 259 | C4⋊C4 | — | 14 | 1 | no | — |
| 260 | C4⋊C4 | — | 14 | 1 | no | — |
| 261 | C4⋊C4 | — | 14 | 1 | no | — |
| 262 | C4⋊C4 | — | 14 | 1 | no | — |
| 263 | C4⋊C4 | C22×D7 | 1 | 1 | yes | characteristic |
| 264 | C22⋊C4 | — | 14 | 1 | no | — |
| 265 | C22⋊C4 | — | 14 | 1 | no | — |
| 266 | C22⋊C4 | — | 14 | 1 | no | — |
| 267 | C42 | — | 2 | 1 | no | — |
| 268 | C42 | — | 7 | 1 | no | — |
| 269 | C42 | — | 7 | 1 | no | — |
| 270 | C42 | — | 14 | 1 | no | — |
| 271 | C42 | — | 14 | 1 | no | — |
| 272 | C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 273 | C2×C7 | — | 8 | 1 | no | — |
| 274 | C2×C7 | — | 8 | 1 | no | — |
| 275 | C2×C7 | #548 | 1 | 1 | yes | characteristic |
| 276 | C2×C7 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 277 | C2×C7 | #577 | 1 | 1 | yes | characteristic |
| 278 | D7 | — | 8 | 1 | no | — |
| 279 | C23 | — | 2 | 1 | no | — |
| 280 | C23 | — | 2 | 1 | no | — |
| 281 | C23 | — | 14 | 1 | no | — |
| 282 | Q8 | — | 2 | 1 | no | — |
| 283 | Q8 | — | 14 | 2 | no | — |
| 284 | Q8 | — | 28 | 2 | no | — |
| 285 | Q8 | #1159 | 1 | 2 | yes | complemented |
| 286 | D4 | — | 2 | 1 | no | — |
| 287 | D4 | — | 2 | 1 | no | — |
| 288 | D4 | — | 2 | 1 | no | — |
| 289 | D4 | — | 2 | 1 | no | — |
| 290 | D4 | — | 4 | 2 | no | — |
| 291 | D4 | — | 8 | 1 | no | — |
| 292 | D4 | — | 14 | 1 | no | — |
| 293 | D4 | — | 14 | 1 | no | — |
| 294 | D4 | — | 28 | 2 | no | — |
| 295 | D4 | — | 28 | 2 | no | — |
| 296 | D4 | — | 56 | 1 | no | — |
| 297 | D4 | — | 56 | 1 | no | — |
| 298 | C2×C4 | — | 2 | 1 | no | — |
| 299 | C2×C4 | — | 2 | 1 | no | — |
| 300 | C2×C4 | — | 7 | 1 | no | — |
| 301 | C2×C4 | — | 7 | 1 | no | — |
| 302 | C2×C4 | — | 7 | 1 | no | — |
| 303 | C2×C4 | — | 7 | 1 | no | — |
| 304 | C2×C4 | — | 14 | 1 | no | — |
| 305 | C2×C4 | — | 14 | 1 | no | — |
| 306 | C2×C4 | — | 14 | 1 | no | — |
| 307 | C2×C4 | — | 28 | 2 | no | — |
| 308 | C2×C4 | — | 28 | 2 | no | — |
| 309 | C2×C4 | — | 28 | 2 | no | — |
| 310 | C2×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 311 | C2×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 312 | C2×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 313 | C8 | — | 2 | 1 | no | — |
| 314 | C8 | — | 2 | 1 | no | — |
| 315 | C8 | — | 14 | 1 | no | — |
| 316 | C8 | — | 14 | 1 | no | — |
| 317 | C7 | #3368 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 318 | C22 | — | 4 | 1 | no | — |
| 319 | C22 | — | 4 | 1 | no | — |
| 320 | C22 | — | 4 | 1 | no | — |
| 321 | C22 | — | 4 | 1 | no | — |
| 322 | C22 | — | 4 | 1 | no | — |
| 323 | C22 | — | 4 | 1 | no | — |
| 324 | C22 | — | 28 | 1 | no | — |
| 325 | C22 | — | 28 | 1 | no | — |
| 326 | C22 | — | 28 | 1 | no | — |
| 327 | C22 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 328 | C4 | — | 2 | 1 | no | — |
| 329 | C4 | — | 2 | 1 | no | — |
| 330 | C4 | — | 2 | 2 | no | — |
| 331 | C4 | — | 4 | 1 | no | — |
| 332 | C4 | — | 7 | 2 | no | — |
| 333 | C4 | — | 14 | 1 | no | — |
| 334 | C4 | — | 14 | 1 | no | — |
| 335 | C4 | — | 14 | 1 | no | — |
| 336 | C4 | — | 28 | 1 | no | — |
| 337 | C4 | — | 28 | 1 | no | — |
| 338 | C4 | — | 28 | 1 | no | — |
| 339 | C4 | C2×#1159 | 1 | 1 | yes | characteristic |
| 340 | C4 | #6554 | 1 | 1 | yes | characteristic |
| 341 | C2 | — | 8 | 1 | no | — |
| 342 | C2 | — | 8 | 1 | no | — |
| 343 | C2 | — | 56 | 1 | no | — |
| 344 | C2 | #90289 | 1 | 1 | yes | characteristic |
| 345 | C2 | #90453 | 1 | 1 | yes | characteristic |
| 346 | C2 | D7×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
Finite Group Databasebeta