| 1 | #22550604 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22550240 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #22550235 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22550230 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22550183 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22550176 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #22550166 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #22550095 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #22550095 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #22550073 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #22550007 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #22549981 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #22549976 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C4×#14523236 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #559×C127 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | C2×#14523238 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#14523236 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#14523236 | C22 | 1 | 1 | yes | characteristic |
| 19 | #16861209 | C22 | 1 | 1 | yes | characteristic |
| 20 | #16861207 | — | 2 | 1 | no | — |
| 21 | #16861201 | C22 | 1 | 1 | yes | characteristic |
| 22 | #16861201 | C22 | 1 | 1 | yes | characteristic |
| 23 | #16861199 | — | 2 | 1 | no | — |
| 24 | #16861199 | — | 2 | 1 | no | — |
| 25 | C4×Dic254 | C22 | 1 | 1 | yes | characteristic |
| 26 | C4×Dic254 | C22 | 1 | 1 | yes | characteristic |
| 27 | C4×Dic254 | C22 | 1 | 1 | yes | characteristic |
| 28 | #16861174 | — | 2 | 1 | no | — |
| 29 | #16861142 | C22 | 1 | 1 | yes | characteristic |
| 30 | #16861140 | C22 | 1 | 1 | yes | characteristic |
| 31 | #16861140 | C22 | 1 | 1 | yes | characteristic |
| 32 | C4⋊(C127⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 33 | C4⋊(C127⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 34 | C4⋊(C127⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 35 | #16861133 | C22 | 1 | 1 | yes | characteristic |
| 36 | #16861133 | C22 | 1 | 1 | yes | characteristic |
| 37 | #16861133 | C22 | 1 | 1 | yes | characteristic |
| 38 | #16861132 | C22 | 1 | 1 | yes | characteristic |
| 39 | #16861130 | C22 | 1 | 1 | yes | characteristic |
| 40 | #16861130 | C22 | 1 | 1 | yes | characteristic |
| 41 | #16861130 | C22 | 1 | 1 | yes | characteristic |
| 42 | #16861130 | C22 | 1 | 1 | yes | characteristic |
| 43 | #16861130 | C22 | 1 | 1 | yes | characteristic |
| 44 | #16861130 | C22 | 1 | 1 | yes | characteristic |
| 45 | #16861120 | C22 | 1 | 1 | yes | characteristic |
| 46 | #16861120 | C22 | 1 | 1 | yes | characteristic |
| 47 | C4×C127⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 48 | #127×C127 | C22 | 1 | 1 | yes | characteristic |
| 49 | #124×C127 | — | 2 | 1 | no | — |
| 50 | #124×C127 | C22 | 1 | 1 | yes | characteristic |
| 51 | #124×C127 | C22 | 1 | 1 | yes | characteristic |
| 52 | #123×C127 | — | 2 | 1 | no | — |
| 53 | #123×C127 | — | 2 | 1 | no | — |
| 54 | C4×Q8×C127 | C22 | 1 | 1 | yes | characteristic |
| 55 | C4×Q8×C127 | C22 | 1 | 1 | yes | characteristic |
| 56 | C4×D4×C127 | — | 2 | 1 | no | — |
| 57 | C4×D4×C127 | C22 | 1 | 1 | yes | characteristic |
| 58 | C4×D4×C127 | C22 | 1 | 1 | yes | characteristic |
| 59 | C2×Dic254 | — | 2 | 1 | no | — |
| 60 | C2×Dic254 | C23 | 1 | 1 | yes | characteristic |
| 61 | #14523238 | — | 2 | 2 | no | — |
| 62 | #14523236 | — | 2 | 2 | no | — |
| 63 | #14523236 | — | 2 | 2 | no | — |
| 64 | C2×C127⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 65 | C2×C127⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 66 | C2×C127⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 67 | C2×C127⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 68 | C4⋊Dic127 | — | 2 | 1 | no | — |
| 69 | C4⋊Dic127 | C23 | 1 | 1 | yes | characteristic |
| 70 | C4⋊Dic127 | C23 | 1 | 1 | yes | characteristic |
| 71 | C4⋊Dic127 | C23 | 1 | 1 | yes | characteristic |
| 72 | Dic127⋊C4 | — | 2 | 1 | no | — |
| 73 | Dic127⋊C4 | — | 2 | 1 | no | — |
| 74 | Dic127⋊C4 | — | 2 | 1 | no | — |
| 75 | Dic127⋊C4 | — | 2 | 1 | no | — |
| 76 | Dic127⋊C4 | — | 2 | 1 | no | — |
| 77 | Dic127⋊C4 | — | 2 | 1 | no | — |
| 78 | Dic127⋊C4 | — | 2 | 1 | no | — |
| 79 | C4×Dic127 | — | 2 | 1 | no | — |
| 80 | C4×Dic127 | — | 2 | 1 | no | — |
| 81 | C4×Dic127 | — | 2 | 1 | no | — |
| 82 | C2×Q8×C127 | D4 | 1 | 1 | yes | characteristic |
| 83 | C2×Q8×C127 | C23 | 1 | 1 | yes | characteristic |
| 84 | C2×D4×C127 | — | 2 | 1 | no | — |
| 85 | C2×D4×C127 | — | 2 | 1 | no | — |
| 86 | C2×D4×C127 | C23 | 1 | 1 | yes | characteristic |
| 87 | C2×D4×C127 | C23 | 1 | 1 | yes | characteristic |
| 88 | C22×C4×C127 | — | 2 | 1 | no | — |
| 89 | C22×C4×C127 | — | 2 | 1 | no | — |
| 90 | C4⋊C4×C127 | — | 2 | 1 | no | — |
| 91 | C4⋊C4×C127 | D4 | 1 | 1 | yes | characteristic |
| 92 | C4⋊C4×C127 | D4 | 1 | 1 | yes | characteristic |
| 93 | C4⋊C4×C127 | D4 | 1 | 1 | yes | characteristic |
| 94 | C4⋊C4×C127 | C23 | 1 | 1 | yes | characteristic |
| 95 | C22⋊C4×C127 | — | 2 | 1 | no | — |
| 96 | C22⋊C4×C127 | — | 2 | 1 | no | — |
| 97 | C22⋊C4×C127 | — | 2 | 1 | no | — |
| 98 | C22⋊C4×C127 | — | 2 | 1 | no | — |
| 99 | C22⋊C4×C127 | — | 2 | 1 | no | — |
| 100 | C22⋊C4×C127 | — | 2 | 1 | no | — |
| 101 | C42×C127 | — | 2 | 1 | no | — |
| 102 | C42×C127 | C23 | 1 | 1 | yes | characteristic |
| 103 | C42×C127 | C23 | 1 | 1 | yes | characteristic |
| 104 | C42×C127 | C23 | 1 | 1 | yes | characteristic |
| 105 | Dic254 | — | 2 | 1 | no | — |
| 106 | Dic254 | — | 4 | 2 | no | — |
| 107 | Dic254 | #41 | 1 | 2 | yes | — |
| 108 | C2×Dic127 | — | 2 | 1 | no | — |
| 109 | C2×Dic127 | — | 2 | 1 | no | — |
| 110 | C2×Dic127 | — | 2 | 1 | no | — |
| 111 | C2×Dic127 | — | 2 | 1 | no | — |
| 112 | C127⋊C8 | — | 2 | 1 | no | — |
| 113 | C127⋊C8 | — | 2 | 1 | no | — |
| 114 | C127⋊C8 | — | 2 | 1 | no | — |
| 115 | C127⋊C8 | — | 2 | 1 | no | — |
| 116 | C23×C127 | — | 2 | 1 | no | — |
| 117 | C23×C127 | — | 2 | 1 | no | — |
| 118 | Q8×C127 | — | 2 | 1 | no | — |
| 119 | Q8×C127 | — | 2 | 1 | no | — |
| 120 | Q8×C127 | — | 4 | 1 | no | — |
| 121 | D4×C127 | — | 2 | 1 | no | — |
| 122 | D4×C127 | — | 2 | 1 | no | — |
| 123 | D4×C127 | — | 2 | 1 | no | — |
| 124 | D4×C127 | — | 2 | 1 | no | — |
| 125 | D4×C127 | — | 4 | 2 | no | — |
| 126 | D4×C127 | — | 8 | 1 | no | — |
| 127 | C2×C4×C127 | — | 2 | 1 | no | — |
| 128 | C2×C4×C127 | — | 2 | 1 | no | — |
| 129 | C2×C4×C127 | — | 8 | 1 | no | — |
| 130 | C2×C4×C127 | — | 8 | 1 | no | — |
| 131 | C2×C4×C127 | C2×D4 | 1 | 1 | yes | characteristic |
| 132 | C2×C4×C127 | C2×D4 | 1 | 1 | yes | characteristic |
| 133 | C2×C4×C127 | C2×D4 | 1 | 1 | yes | characteristic |
| 134 | C2×C4×C127 | C2×D4 | 1 | 1 | yes | characteristic |
| 135 | C2×C4×C127 | C2×D4 | 1 | 1 | yes | characteristic |
| 136 | C2×C4×C127 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C2×C4×C127 | C24 | 1 | 1 | yes | characteristic |
| 138 | C22×C127 | — | 4 | 1 | no | — |
| 139 | C22×C127 | — | 4 | 1 | no | — |
| 140 | C22×C127 | — | 4 | 1 | no | — |
| 141 | C22×C127 | — | 4 | 1 | no | — |
| 142 | C22×C127 | — | 4 | 1 | no | — |
| 143 | C22×C127 | — | 4 | 1 | no | — |
| 144 | C22×C127 | C22×D4 | 1 | 1 | yes | characteristic |
| 145 | C4×C127 | — | 2 | 1 | no | — |
| 146 | C4×C127 | — | 2 | 1 | no | — |
| 147 | C4×C127 | — | 2 | 1 | no | — |
| 148 | C4×C127 | — | 2 | 1 | no | — |
| 149 | C4×C127 | — | 2 | 1 | no | — |
| 150 | C4×C127 | — | 2 | 1 | no | — |
| 151 | C4×C127 | — | 4 | 1 | no | — |
| 152 | C4×C127 | — | 4 | 1 | no | — |
| 153 | C4×C127 | C2×#41 | 1 | 1 | yes | characteristic |
| 154 | C4×C127 | 2−1+4 | 1 | 1 | yes | characteristic |
| 155 | Dic127 | — | 2 | 2 | no | — |
| 156 | Dic127 | — | 4 | 1 | no | — |
| 157 | Dic127 | — | 4 | 1 | no | — |
| 158 | Dic127 | — | 4 | 1 | no | — |
| 159 | C2×C127 | — | 8 | 1 | no | — |
| 160 | C2×C127 | — | 8 | 1 | no | — |
| 161 | C2×C127 | #548 | 1 | 1 | yes | characteristic |
| 162 | C2×C127 | #575 | 1 | 1 | yes | characteristic |
| 163 | C2×C127 | #577 | 1 | 1 | yes | characteristic |
| 164 | #3371 | — | 127 | 1 | no | maximal, Sylow |
| 165 | C127 | #3371 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 166 | #559 | D127 | 1 | 1 | yes | characteristic |
| 167 | #557 | — | 127 | 1 | no | — |
| 168 | #490 | — | 127 | 1 | no | — |
| 169 | #489 | — | 127 | 1 | no | — |
| 170 | #488 | — | 127 | 1 | no | — |
| 171 | #479 | — | 127 | 1 | no | — |
| 172 | #478 | — | 127 | 1 | no | — |
| 173 | #476 | — | 127 | 1 | no | — |
| 174 | #464 | — | 127 | 1 | no | — |
| 175 | #464 | — | 127 | 1 | no | — |
| 176 | #460 | — | 127 | 1 | no | — |
| 177 | #446 | — | 127 | 1 | no | — |
| 178 | #441 | — | 127 | 1 | no | — |
| 179 | #440 | — | 127 | 1 | no | — |
| 180 | C4×SD16 | — | 127 | 1 | no | — |
| 181 | C2×Q16 | — | 127 | 1 | no | — |
| 182 | C2×SD16 | — | 127 | 1 | no | — |
| 183 | C2×SD16 | — | 127 | 1 | no | — |
| 184 | C4⋊Q8 | — | 127 | 1 | no | — |
| 185 | C4⋊Q8 | — | 254 | 1 | no | — |
| 186 | #127 | C2×D127 | 1 | 1 | yes | characteristic |
| 187 | #125 | — | 127 | 1 | no | — |
| 188 | #125 | — | 127 | 1 | no | — |
| 189 | #125 | — | 254 | 1 | no | — |
| 190 | #125 | — | 254 | 1 | no | — |
| 191 | #124 | — | 2 | 1 | no | — |
| 192 | #124 | C2×D127 | 1 | 1 | yes | characteristic |
| 193 | #124 | C2×D127 | 1 | 1 | yes | characteristic |
| 194 | #123 | — | 2 | 1 | no | — |
| 195 | #123 | — | 2 | 1 | no | — |
| 196 | C4×Q8 | — | 127 | 1 | no | — |
| 197 | C4×Q8 | — | 127 | 1 | no | — |
| 198 | C4×Q8 | — | 127 | 1 | no | — |
| 199 | C4×Q8 | — | 254 | 1 | no | — |
| 200 | C4×Q8 | C2×D127 | 1 | 1 | yes | characteristic |
| 201 | C4×Q8 | C2×D127 | 1 | 1 | yes | characteristic |
| 202 | C4×D4 | — | 2 | 1 | no | — |
| 203 | C4×D4 | C2×D127 | 1 | 1 | yes | characteristic |
| 204 | C4×D4 | C2×D127 | 1 | 1 | yes | characteristic |
| 205 | #107 | — | 127 | 1 | no | — |
| 206 | #106 | — | 127 | 1 | no | — |
| 207 | #106 | — | 127 | 1 | no | — |
| 208 | C4⋊C8 | — | 127 | 1 | no | — |
| 209 | C4⋊C8 | — | 127 | 1 | no | — |
| 210 | C4⋊C8 | — | 127 | 1 | no | — |
| 211 | #103 | — | 127 | 1 | no | — |
| 212 | #103 | — | 127 | 1 | no | — |
| 213 | #103 | — | 127 | 1 | no | — |
| 214 | #103 | — | 127 | 1 | no | — |
| 215 | #102 | — | 127 | 1 | no | — |
| 216 | #102 | — | 127 | 1 | no | — |
| 217 | #102 | — | 127 | 1 | no | — |
| 218 | #102 | — | 127 | 1 | no | — |
| 219 | #102 | — | 127 | 1 | no | — |
| 220 | #102 | — | 127 | 1 | no | — |
| 221 | #97 | — | 127 | 1 | no | — |
| 222 | #97 | — | 127 | 1 | no | — |
| 223 | C4×C8 | — | 127 | 1 | no | — |
| 224 | C2×Q8 | — | 127 | 1 | no | — |
| 225 | C2×Q8 | — | 254 | 1 | no | — |
| 226 | C2×Q8 | C22⋊D127 | 1 | 1 | yes | characteristic |
| 227 | C2×Q8 | C22×D127 | 1 | 1 | yes | characteristic |
| 228 | C2×D4 | — | 2 | 1 | no | — |
| 229 | C2×D4 | — | 2 | 1 | no | — |
| 230 | C2×D4 | C22×D127 | 1 | 1 | yes | characteristic |
| 231 | C2×D4 | C22×D127 | 1 | 1 | yes | characteristic |
| 232 | C22×C4 | — | 2 | 1 | no | — |
| 233 | C22×C4 | — | 2 | 1 | no | — |
| 234 | Q16 | — | 254 | 2 | no | — |
| 235 | SD16 | — | 254 | 2 | no | — |
| 236 | SD16 | — | 254 | 2 | no | — |
| 237 | C2×C8 | — | 127 | 1 | no | — |
| 238 | C2×C8 | — | 127 | 1 | no | — |
| 239 | C2×C8 | — | 127 | 1 | no | — |
| 240 | C2×C8 | — | 127 | 1 | no | — |
| 241 | C4⋊C4 | — | 2 | 1 | no | — |
| 242 | C4⋊C4 | — | 127 | 1 | no | — |
| 243 | C4⋊C4 | — | 127 | 1 | no | — |
| 244 | C4⋊C4 | — | 127 | 1 | no | — |
| 245 | C4⋊C4 | — | 254 | 1 | no | — |
| 246 | C4⋊C4 | — | 254 | 1 | no | — |
| 247 | C4⋊C4 | — | 254 | 1 | no | — |
| 248 | C4⋊C4 | — | 254 | 1 | no | — |
| 249 | C4⋊C4 | — | 254 | 1 | no | — |
| 250 | C4⋊C4 | — | 254 | 1 | no | — |
| 251 | C4⋊C4 | — | 254 | 1 | no | — |
| 252 | C4⋊C4 | — | 254 | 1 | no | — |
| 253 | C4⋊C4 | C22⋊D127 | 1 | 1 | yes | characteristic |
| 254 | C4⋊C4 | C22⋊D127 | 1 | 1 | yes | characteristic |
| 255 | C4⋊C4 | C22⋊D127 | 1 | 1 | yes | characteristic |
| 256 | C4⋊C4 | C22×D127 | 1 | 1 | yes | characteristic |
| 257 | C22⋊C4 | — | 2 | 1 | no | — |
| 258 | C22⋊C4 | — | 2 | 1 | no | — |
| 259 | C22⋊C4 | — | 2 | 1 | no | — |
| 260 | C22⋊C4 | — | 2 | 1 | no | — |
| 261 | C22⋊C4 | — | 2 | 1 | no | — |
| 262 | C22⋊C4 | — | 2 | 1 | no | — |
| 263 | C42 | — | 2 | 1 | no | — |
| 264 | C42 | — | 254 | 1 | no | — |
| 265 | C42 | — | 254 | 1 | no | — |
| 266 | C42 | — | 254 | 1 | no | — |
| 267 | C42 | C22×D127 | 1 | 1 | yes | characteristic |
| 268 | C42 | C22×D127 | 1 | 1 | yes | characteristic |
| 269 | C42 | C22×D127 | 1 | 1 | yes | characteristic |
| 270 | C23 | — | 2 | 1 | no | — |
| 271 | C23 | — | 2 | 1 | no | — |
| 272 | Q8 | — | 2 | 1 | no | — |
| 273 | Q8 | — | 2 | 1 | no | — |
| 274 | Q8 | — | 4 | 1 | no | — |
| 275 | Q8 | — | 127 | 2 | no | — |
| 276 | Q8 | — | 508 | 2 | no | — |
| 277 | Q8 | — | 254 | 1 | no | — |
| 278 | D4 | — | 2 | 1 | no | — |
| 279 | D4 | — | 2 | 1 | no | — |
| 280 | D4 | — | 2 | 1 | no | — |
| 281 | D4 | — | 2 | 1 | no | — |
| 282 | D4 | — | 4 | 2 | no | — |
| 283 | D4 | — | 8 | 1 | no | — |
| 284 | C2×C4 | — | 2 | 1 | no | — |
| 285 | C2×C4 | — | 2 | 1 | no | — |
| 286 | C2×C4 | — | 8 | 1 | no | — |
| 287 | C2×C4 | — | 8 | 1 | no | — |
| 288 | C2×C4 | — | 254 | 1 | no | — |
| 289 | C2×C4 | — | 254 | 1 | no | — |
| 290 | C2×C4 | — | 254 | 1 | no | — |
| 291 | C2×C4 | — | 254 | 1 | no | — |
| 292 | C2×C4 | C2×C22⋊D127 | 1 | 1 | yes | characteristic |
| 293 | C2×C4 | C2×C22⋊D127 | 1 | 1 | yes | characteristic |
| 294 | C2×C4 | C2×C22⋊D127 | 1 | 1 | yes | characteristic |
| 295 | C2×C4 | C2×C22⋊D127 | 1 | 1 | yes | characteristic |
| 296 | C2×C4 | C2×C22⋊D127 | 1 | 1 | yes | characteristic |
| 297 | C2×C4 | C2×C22⋊D127 | 1 | 1 | yes | characteristic |
| 298 | C2×C4 | C23×D127 | 1 | 1 | yes | characteristic |
| 299 | C8 | — | 254 | 1 | no | — |
| 300 | C8 | — | 254 | 1 | no | — |
| 301 | C8 | — | 254 | 1 | no | — |
| 302 | C8 | — | 254 | 1 | no | — |
| 303 | C22 | — | 4 | 1 | no | — |
| 304 | C22 | — | 4 | 1 | no | — |
| 305 | C22 | — | 4 | 1 | no | — |
| 306 | C22 | — | 4 | 1 | no | — |
| 307 | C22 | — | 4 | 1 | no | — |
| 308 | C22 | — | 4 | 1 | no | — |
| 309 | C22 | C22×C22⋊D127 | 1 | 1 | yes | characteristic |
| 310 | C4 | — | 2 | 1 | no | — |
| 311 | C4 | — | 2 | 1 | no | — |
| 312 | C4 | — | 2 | 1 | no | — |
| 313 | C4 | — | 2 | 1 | no | — |
| 314 | C4 | — | 2 | 1 | no | — |
| 315 | C4 | — | 2 | 1 | no | — |
| 316 | C4 | — | 4 | 1 | no | — |
| 317 | C4 | — | 4 | 1 | no | — |
| 318 | C4 | — | 508 | 1 | no | — |
| 319 | C4 | — | 508 | 1 | no | — |
| 320 | C4 | — | 508 | 1 | no | — |
| 321 | C4 | — | 254 | 2 | no | — |
| 322 | C4 | #41×D127 | 1 | 1 | yes | characteristic |
| 323 | C4 | #16861256 | 1 | 1 | yes | characteristic |
| 324 | C2 | — | 8 | 1 | no | — |
| 325 | C2 | — | 8 | 1 | no | — |
| 326 | C2 | #22550533 | 1 | 1 | yes | characteristic |
| 327 | C2 | #22550674 | 1 | 1 | yes | characteristic |
| 328 | C2 | #22550687 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta