| 1 | #22550484 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22550480 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #22550184 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22550183 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22550178 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22550174 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #22550121 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #22550119 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #22550104 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #22550102 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #22550079 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #22550079 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #22550073 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #22549901 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #460×C127 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#14523236 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#14523236 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#14523231 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×C8×D127 | C22 | 1 | 1 | yes | characteristic |
| 20 | #16861207 | C22 | 1 | 1 | yes | characteristic |
| 21 | #16861204 | — | 2 | 1 | no | — |
| 22 | #16861203 | — | 2 | 1 | no | — |
| 23 | #16861201 | — | 2 | 1 | no | — |
| 24 | #16861201 | C22 | 1 | 1 | yes | characteristic |
| 25 | #16861200 | C22 | 1 | 1 | yes | characteristic |
| 26 | #16861199 | — | 2 | 1 | no | — |
| 27 | #16861190 | — | 2 | 1 | no | — |
| 28 | #16861190 | — | 2 | 1 | no | — |
| 29 | #16861189 | C22 | 1 | 1 | yes | characteristic |
| 30 | #16861185 | C22 | 1 | 1 | yes | characteristic |
| 31 | #16861181 | — | 2 | 1 | no | — |
| 32 | #16861181 | — | 2 | 1 | no | — |
| 33 | #16861180 | C22 | 1 | 1 | yes | characteristic |
| 34 | #16861180 | C22 | 1 | 1 | yes | characteristic |
| 35 | C4×Dic254 | C22 | 1 | 1 | yes | characteristic |
| 36 | D4×Dic127 | C22 | 1 | 1 | yes | characteristic |
| 37 | D4×Dic127 | C22 | 1 | 1 | yes | characteristic |
| 38 | #16861166 | C22 | 1 | 1 | yes | characteristic |
| 39 | #16861143 | C22 | 1 | 1 | yes | characteristic |
| 40 | #16861142 | C22 | 1 | 1 | yes | characteristic |
| 41 | #16861141 | C22 | 1 | 1 | yes | characteristic |
| 42 | #16861140 | C22 | 1 | 1 | yes | characteristic |
| 43 | C4⋊(C127⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 44 | Dic127⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 45 | Dic127⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 46 | #16861134 | C22 | 1 | 1 | yes | characteristic |
| 47 | #16861134 | C22 | 1 | 1 | yes | characteristic |
| 48 | #16861133 | C22 | 1 | 1 | yes | characteristic |
| 49 | #16861133 | C22 | 1 | 1 | yes | characteristic |
| 50 | #16861130 | C22 | 1 | 1 | yes | characteristic |
| 51 | #16861130 | C22 | 1 | 1 | yes | characteristic |
| 52 | C2×SD16×C127 | C22 | 1 | 1 | yes | characteristic |
| 53 | C2×SD16×C127 | C22 | 1 | 1 | yes | characteristic |
| 54 | #127×C127 | C22 | 1 | 1 | yes | characteristic |
| 55 | C4×Q8×C127 | C22 | 1 | 1 | yes | characteristic |
| 56 | C4⋊C8×C127 | C22 | 1 | 1 | yes | characteristic |
| 57 | #102×C127 | C22 | 1 | 1 | yes | characteristic |
| 58 | #102×C127 | C22 | 1 | 1 | yes | characteristic |
| 59 | C2×Dic254 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×C22⋊D127 | — | 2 | 1 | no | — |
| 61 | C2×C22⋊D127 | — | 2 | 1 | no | — |
| 62 | C22×Dic127 | — | 2 | 1 | no | — |
| 63 | C22×Dic127 | — | 2 | 1 | no | — |
| 64 | C2×C4×D127 | C23 | 1 | 1 | yes | characteristic |
| 65 | #14523236 | — | 4 | 1 | no | — |
| 66 | #14523236 | — | 4 | 1 | no | — |
| 67 | #14523231 | — | 4 | 1 | no | — |
| 68 | C2×C127⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×C127⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 70 | C8×D127 | — | 4 | 1 | no | — |
| 71 | C4⋊Dic127 | — | 2 | 1 | no | — |
| 72 | C4⋊Dic127 | — | 2 | 1 | no | — |
| 73 | C4⋊Dic127 | C23 | 1 | 1 | yes | characteristic |
| 74 | C4⋊Dic127 | C23 | 1 | 1 | yes | characteristic |
| 75 | C4⋊Dic127 | C23 | 1 | 1 | yes | characteristic |
| 76 | Dic127⋊C4 | — | 2 | 1 | no | — |
| 77 | Dic127⋊C4 | — | 2 | 1 | no | — |
| 78 | Dic127⋊C4 | — | 2 | 1 | no | — |
| 79 | Dic127⋊C4 | — | 2 | 1 | no | — |
| 80 | Dic127⋊C4 | — | 2 | 1 | no | — |
| 81 | Dic127⋊C4 | — | 2 | 1 | no | — |
| 82 | Dic127⋊C4 | — | 2 | 1 | no | — |
| 83 | Dic127⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 84 | Dic127⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 85 | C22⋊Dic127 | — | 2 | 1 | no | — |
| 86 | C22⋊Dic127 | — | 2 | 1 | no | — |
| 87 | C22⋊Dic127 | — | 2 | 1 | no | — |
| 88 | C22⋊Dic127 | — | 2 | 1 | no | — |
| 89 | (C2×D127)⋊C4 | — | 2 | 1 | no | — |
| 90 | (C2×D127)⋊C4 | — | 2 | 1 | no | — |
| 91 | (C2×D127)⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 92 | (C2×D127)⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 93 | C4×Dic127 | — | 2 | 1 | no | — |
| 94 | C4×Dic127 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×Q8×C127 | C23 | 1 | 1 | yes | characteristic |
| 96 | C2×D4×C127 | — | 2 | 1 | no | — |
| 97 | C2×D4×C127 | — | 2 | 1 | no | — |
| 98 | C2×D4×C127 | C23 | 1 | 1 | yes | characteristic |
| 99 | C2×D4×C127 | C23 | 1 | 1 | yes | characteristic |
| 100 | SD16×C127 | — | 4 | 1 | no | — |
| 101 | SD16×C127 | — | 4 | 1 | no | — |
| 102 | C2×C8×C127 | C23 | 1 | 1 | yes | characteristic |
| 103 | C2×C8×C127 | C23 | 1 | 1 | yes | characteristic |
| 104 | C4⋊C4×C127 | — | 2 | 1 | no | — |
| 105 | C4⋊C4×C127 | C23 | 1 | 1 | yes | characteristic |
| 106 | C42×C127 | — | 2 | 1 | no | — |
| 107 | C42×C127 | C23 | 1 | 1 | yes | characteristic |
| 108 | C22×D127 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | Dic254 | — | 2 | 1 | no | — |
| 110 | Dic254 | — | 2 | 1 | no | — |
| 111 | C22⋊D127 | — | 8 | 1 | no | — |
| 112 | C22⋊D127 | — | 8 | 1 | no | — |
| 113 | C2×Dic127 | — | 2 | 1 | no | — |
| 114 | C2×Dic127 | — | 2 | 1 | no | — |
| 115 | C2×Dic127 | — | 2 | 1 | no | — |
| 116 | C2×Dic127 | — | 2 | 1 | no | — |
| 117 | C2×Dic127 | — | 8 | 1 | no | — |
| 118 | C2×Dic127 | — | 8 | 1 | no | — |
| 119 | C2×Dic127 | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | C2×Dic127 | C2×D4 | 1 | 1 | yes | characteristic |
| 121 | C2×Dic127 | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | C4×D127 | — | 2 | 1 | no | — |
| 123 | C4×D127 | — | 2 | 1 | no | — |
| 124 | C127⋊C8 | — | 2 | 1 | no | — |
| 125 | C127⋊C8 | — | 2 | 1 | no | — |
| 126 | C23×C127 | — | 2 | 1 | no | — |
| 127 | C23×C127 | — | 2 | 1 | no | — |
| 128 | Q8×C127 | — | 2 | 1 | no | — |
| 129 | Q8×C127 | — | 2 | 1 | no | — |
| 130 | D4×C127 | — | 2 | 1 | no | — |
| 131 | D4×C127 | — | 2 | 1 | no | — |
| 132 | D4×C127 | — | 2 | 1 | no | — |
| 133 | D4×C127 | — | 2 | 1 | no | — |
| 134 | D4×C127 | — | 8 | 1 | no | — |
| 135 | D4×C127 | — | 8 | 1 | no | — |
| 136 | C2×C4×C127 | — | 2 | 1 | no | — |
| 137 | C2×C4×C127 | — | 2 | 1 | no | — |
| 138 | C2×C4×C127 | C2×D4 | 1 | 1 | yes | characteristic |
| 139 | C2×C4×C127 | C2×D4 | 1 | 1 | yes | characteristic |
| 140 | C2×C4×C127 | C24 | 1 | 1 | yes | characteristic |
| 141 | C8×C127 | — | 2 | 1 | no | — |
| 142 | C8×C127 | — | 2 | 1 | no | — |
| 143 | C22×C127 | — | 4 | 1 | no | — |
| 144 | C22×C127 | — | 4 | 1 | no | — |
| 145 | C22×C127 | — | 4 | 1 | no | — |
| 146 | C22×C127 | — | 4 | 1 | no | — |
| 147 | C22×C127 | — | 4 | 1 | no | — |
| 148 | C22×C127 | — | 4 | 1 | no | — |
| 149 | C22×C127 | C22×D4 | 1 | 1 | yes | characteristic |
| 150 | C2×D127 | — | 2 | 1 | no | — |
| 151 | C2×D127 | — | 2 | 1 | no | — |
| 152 | C2×D127 | — | 2 | 1 | no | — |
| 153 | C4×C127 | — | 2 | 1 | no | — |
| 154 | C4×C127 | — | 2 | 1 | no | — |
| 155 | C4×C127 | — | 4 | 1 | no | — |
| 156 | C4×C127 | — | 4 | 1 | no | — |
| 157 | C4×C127 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 158 | C4×C127 | 2−1+4 | 1 | 1 | yes | characteristic |
| 159 | Dic127 | — | 2 | 1 | no | — |
| 160 | Dic127 | — | 2 | 1 | no | — |
| 161 | Dic127 | — | 2 | 1 | no | — |
| 162 | Dic127 | — | 4 | 1 | no | — |
| 163 | Dic127 | — | 4 | 1 | no | — |
| 164 | Dic127 | — | 4 | 1 | no | — |
| 165 | Dic127 | — | 4 | 1 | no | — |
| 166 | C2×C127 | — | 8 | 1 | no | — |
| 167 | C2×C127 | — | 8 | 1 | no | — |
| 168 | C2×C127 | #537 | 1 | 1 | yes | characteristic |
| 169 | C2×C127 | #577 | 1 | 1 | yes | characteristic |
| 170 | C2×C127 | #577 | 1 | 1 | yes | characteristic |
| 171 | D127 | — | 4 | 1 | no | — |
| 172 | #3260 | — | 127 | 1 | no | maximal, Sylow |
| 173 | C127 | #3260 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 174 | #541 | — | 127 | 1 | no | — |
| 175 | #540 | — | 127 | 1 | no | — |
| 176 | #479 | — | 127 | 1 | no | — |
| 177 | #479 | — | 127 | 1 | no | — |
| 178 | #478 | — | 127 | 1 | no | — |
| 179 | #478 | — | 127 | 1 | no | — |
| 180 | #468 | — | 127 | 1 | no | — |
| 181 | #468 | — | 127 | 1 | no | — |
| 182 | #465 | — | 127 | 1 | no | — |
| 183 | #465 | — | 127 | 1 | no | — |
| 184 | #461 | — | 127 | 1 | no | — |
| 185 | #461 | — | 127 | 1 | no | — |
| 186 | #460 | — | 127 | 1 | no | — |
| 187 | #460 | D127 | 1 | 1 | yes | characteristic, complemented |
| 188 | #424 | — | 127 | 1 | no | — |
| 189 | C2×SD16 | — | 127 | 1 | no | — |
| 190 | C2×SD16 | — | 127 | 1 | no | — |
| 191 | C2×SD16 | C2×D127 | 1 | 1 | yes | characteristic |
| 192 | C2×SD16 | C2×D127 | 1 | 1 | yes | characteristic |
| 193 | C2×M16 | — | 127 | 1 | no | — |
| 194 | C22×C8 | — | 127 | 1 | no | — |
| 195 | C4⋊Q8 | — | 127 | 1 | no | — |
| 196 | #127 | C2×D127 | 1 | 1 | yes | characteristic |
| 197 | #126 | — | 254 | 1 | no | — |
| 198 | #126 | — | 254 | 1 | no | — |
| 199 | #125 | — | 127 | 1 | no | — |
| 200 | #125 | — | 127 | 1 | no | — |
| 201 | #125 | — | 254 | 1 | no | — |
| 202 | #125 | — | 254 | 1 | no | — |
| 203 | #123 | — | 254 | 1 | no | — |
| 204 | #123 | — | 254 | 1 | no | — |
| 205 | C22⋊Q8 | — | 127 | 1 | no | — |
| 206 | C22⋊Q8 | — | 127 | 1 | no | — |
| 207 | #121 | — | 127 | 1 | no | — |
| 208 | #121 | — | 127 | 1 | no | — |
| 209 | #121 | — | 254 | 1 | no | — |
| 210 | #121 | — | 254 | 1 | no | — |
| 211 | C4×Q8 | — | 127 | 1 | no | — |
| 212 | C4×Q8 | C2×D127 | 1 | 1 | yes | characteristic |
| 213 | C4×D4 | — | 127 | 1 | no | — |
| 214 | C4×D4 | — | 127 | 1 | no | — |
| 215 | #117 | — | 127 | 1 | no | — |
| 216 | #107 | — | 127 | 1 | no | — |
| 217 | #107 | — | 127 | 1 | no | — |
| 218 | #106 | — | 127 | 1 | no | — |
| 219 | #106 | — | 127 | 1 | no | — |
| 220 | C4⋊C8 | — | 127 | 1 | no | — |
| 221 | C4⋊C8 | — | 127 | 1 | no | — |
| 222 | C4⋊C8 | — | 127 | 1 | no | — |
| 223 | C4⋊C8 | C2×D127 | 1 | 1 | yes | characteristic |
| 224 | #103 | — | 127 | 1 | no | — |
| 225 | #103 | — | 127 | 1 | no | — |
| 226 | #103 | — | 127 | 1 | no | — |
| 227 | #103 | — | 127 | 1 | no | — |
| 228 | #102 | — | 127 | 1 | no | — |
| 229 | #102 | — | 127 | 1 | no | — |
| 230 | #102 | C2×D127 | 1 | 1 | yes | characteristic |
| 231 | #102 | C2×D127 | 1 | 1 | yes | characteristic |
| 232 | C2×Q8 | — | 127 | 1 | no | — |
| 233 | C2×Q8 | C22×D127 | 1 | 1 | yes | characteristic |
| 234 | C2×D4 | — | 2 | 1 | no | — |
| 235 | C2×D4 | — | 2 | 1 | no | — |
| 236 | C2×D4 | — | 254 | 1 | no | — |
| 237 | C2×D4 | — | 254 | 1 | no | — |
| 238 | C2×D4 | C22×D127 | 1 | 1 | yes | characteristic |
| 239 | C2×D4 | C22×D127 | 1 | 1 | yes | characteristic |
| 240 | C22×C4 | — | 127 | 1 | no | — |
| 241 | C22×C4 | — | 254 | 1 | no | — |
| 242 | C22×C4 | — | 254 | 1 | no | — |
| 243 | SD16 | — | 4 | 1 | no | — |
| 244 | SD16 | — | 4 | 1 | no | — |
| 245 | SD16 | — | 508 | 1 | no | — |
| 246 | SD16 | — | 508 | 1 | no | — |
| 247 | M16 | — | 508 | 1 | no | — |
| 248 | C2×C8 | — | 127 | 1 | no | — |
| 249 | C2×C8 | — | 127 | 1 | no | — |
| 250 | C2×C8 | — | 508 | 1 | no | — |
| 251 | C2×C8 | C22×D127 | 1 | 1 | yes | characteristic |
| 252 | C2×C8 | C22×D127 | 1 | 1 | yes | characteristic |
| 253 | C4⋊C4 | — | 2 | 1 | no | — |
| 254 | C4⋊C4 | — | 127 | 1 | no | — |
| 255 | C4⋊C4 | — | 127 | 1 | no | — |
| 256 | C4⋊C4 | — | 127 | 1 | no | — |
| 257 | C4⋊C4 | — | 127 | 1 | no | — |
| 258 | C4⋊C4 | — | 127 | 1 | no | — |
| 259 | C4⋊C4 | — | 254 | 1 | no | — |
| 260 | C4⋊C4 | — | 254 | 1 | no | — |
| 261 | C4⋊C4 | — | 254 | 1 | no | — |
| 262 | C4⋊C4 | — | 254 | 1 | no | — |
| 263 | C4⋊C4 | — | 254 | 1 | no | — |
| 264 | C4⋊C4 | — | 254 | 1 | no | — |
| 265 | C4⋊C4 | — | 254 | 1 | no | — |
| 266 | C4⋊C4 | — | 254 | 1 | no | — |
| 267 | C4⋊C4 | — | 254 | 1 | no | — |
| 268 | C4⋊C4 | C22×D127 | 1 | 1 | yes | characteristic |
| 269 | C22⋊C4 | — | 127 | 1 | no | — |
| 270 | C22⋊C4 | — | 127 | 1 | no | — |
| 271 | C22⋊C4 | — | 254 | 1 | no | — |
| 272 | C22⋊C4 | — | 254 | 1 | no | — |
| 273 | C22⋊C4 | — | 254 | 1 | no | — |
| 274 | C22⋊C4 | — | 254 | 1 | no | — |
| 275 | C22⋊C4 | — | 254 | 1 | no | — |
| 276 | C22⋊C4 | — | 254 | 1 | no | — |
| 277 | C42 | — | 2 | 1 | no | — |
| 278 | C42 | — | 127 | 1 | no | — |
| 279 | C42 | — | 254 | 1 | no | — |
| 280 | C42 | C22×D127 | 1 | 1 | yes | characteristic |
| 281 | C23 | — | 2 | 1 | no | — |
| 282 | C23 | — | 2 | 1 | no | — |
| 283 | C23 | — | 127 | 1 | no | — |
| 284 | Q8 | — | 2 | 1 | no | — |
| 285 | Q8 | — | 2 | 1 | no | — |
| 286 | Q8 | — | 254 | 1 | no | — |
| 287 | Q8 | — | 254 | 1 | no | — |
| 288 | D4 | — | 2 | 1 | no | — |
| 289 | D4 | — | 2 | 1 | no | — |
| 290 | D4 | — | 2 | 1 | no | — |
| 291 | D4 | — | 2 | 1 | no | — |
| 292 | D4 | — | 8 | 1 | no | — |
| 293 | D4 | — | 8 | 1 | no | — |
| 294 | D4 | — | 1016 | 1 | no | — |
| 295 | D4 | — | 1016 | 1 | no | — |
| 296 | C2×C4 | — | 2 | 1 | no | — |
| 297 | C2×C4 | — | 2 | 1 | no | — |
| 298 | C2×C4 | — | 127 | 1 | no | — |
| 299 | C2×C4 | — | 127 | 1 | no | — |
| 300 | C2×C4 | — | 127 | 1 | no | — |
| 301 | C2×C4 | — | 1016 | 1 | no | — |
| 302 | C2×C4 | — | 1016 | 1 | no | — |
| 303 | C2×C4 | — | 254 | 1 | no | — |
| 304 | C2×C4 | — | 254 | 1 | no | — |
| 305 | C2×C4 | — | 254 | 1 | no | — |
| 306 | C2×C4 | — | 254 | 1 | no | — |
| 307 | C2×C4 | — | 254 | 1 | no | — |
| 308 | C2×C4 | — | 254 | 1 | no | — |
| 309 | C2×C4 | D4×D127 | 1 | 1 | yes | characteristic |
| 310 | C2×C4 | D4×D127 | 1 | 1 | yes | characteristic |
| 311 | C2×C4 | C23×D127 | 1 | 1 | yes | characteristic |
| 312 | C8 | — | 2 | 1 | no | — |
| 313 | C8 | — | 2 | 1 | no | — |
| 314 | C8 | — | 254 | 1 | no | — |
| 315 | C8 | — | 254 | 1 | no | — |
| 316 | C22 | — | 4 | 1 | no | — |
| 317 | C22 | — | 4 | 1 | no | — |
| 318 | C22 | — | 4 | 1 | no | — |
| 319 | C22 | — | 4 | 1 | no | — |
| 320 | C22 | — | 4 | 1 | no | — |
| 321 | C22 | — | 4 | 1 | no | — |
| 322 | C22 | — | 254 | 1 | no | — |
| 323 | C22 | — | 254 | 1 | no | — |
| 324 | C22 | — | 254 | 1 | no | — |
| 325 | C22 | C2×D4×D127 | 1 | 1 | yes | characteristic |
| 326 | C4 | — | 2 | 1 | no | — |
| 327 | C4 | — | 2 | 1 | no | — |
| 328 | C4 | — | 4 | 1 | no | — |
| 329 | C4 | — | 4 | 1 | no | — |
| 330 | C4 | — | 508 | 1 | no | — |
| 331 | C4 | — | 508 | 1 | no | — |
| 332 | C4 | — | 508 | 1 | no | — |
| 333 | C4 | — | 508 | 1 | no | — |
| 334 | C4 | — | 254 | 1 | no | — |
| 335 | C4 | — | 254 | 1 | no | — |
| 336 | C4 | — | 254 | 1 | no | — |
| 337 | C4 | #16861254 | 1 | 1 | yes | characteristic |
| 338 | C4 | #16861256 | 1 | 1 | yes | characteristic |
| 339 | C2 | — | 8 | 1 | no | — |
| 340 | C2 | — | 8 | 1 | no | — |
| 341 | C2 | — | 508 | 1 | no | — |
| 342 | C2 | #22550455 | 1 | 1 | yes | characteristic |
| 343 | C2 | #22550682 | 1 | 1 | yes | characteristic |
| 344 | C2 | #22550686 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta