| 1 | #31774449 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #31774428 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #31774305 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #31774288 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #31774264 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #31774255 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #31774155 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #31774153 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #31774141 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #31773991 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #31773989 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #31773988 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | SD16×Dic271 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | M16×Dic271 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #468×C271 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | C2×Dic1084 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#16864644 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#16864642 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#16864638 | C22 | 1 | 1 | yes | characteristic |
| 20 | #22576159 | C22 | 1 | 1 | yes | characteristic |
| 21 | #22576158 | C22 | 1 | 1 | yes | characteristic |
| 22 | #22576153 | — | 2 | 1 | no | — |
| 23 | #22576151 | C22 | 1 | 1 | yes | characteristic |
| 24 | #22576150 | — | 2 | 1 | no | — |
| 25 | #22576147 | C22 | 1 | 1 | yes | characteristic |
| 26 | #22576141 | — | 2 | 1 | no | — |
| 27 | #22576139 | C22 | 1 | 1 | yes | characteristic |
| 28 | #22576139 | C22 | 1 | 1 | yes | characteristic |
| 29 | #22576137 | — | 2 | 1 | no | — |
| 30 | Q8×Dic271 | C22 | 1 | 1 | yes | characteristic |
| 31 | #22576125 | — | 2 | 1 | no | — |
| 32 | #22576125 | C22 | 1 | 1 | yes | characteristic |
| 33 | #22576125 | C22 | 1 | 1 | yes | characteristic |
| 34 | D4×Dic271 | — | 2 | 1 | no | — |
| 35 | D4×Dic271 | C22 | 1 | 1 | yes | characteristic |
| 36 | #22576116 | — | 2 | 1 | no | — |
| 37 | #22576116 | — | 2 | 1 | no | — |
| 38 | C2×C4×Dic271 | C22 | 1 | 1 | yes | characteristic |
| 39 | #22576093 | C22 | 1 | 1 | yes | characteristic |
| 40 | #22576092 | C22 | 1 | 1 | yes | characteristic |
| 41 | #22576091 | C22 | 1 | 1 | yes | characteristic |
| 42 | #22576085 | C22 | 1 | 1 | yes | characteristic |
| 43 | #22576085 | C22 | 1 | 1 | yes | characteristic |
| 44 | #22576084 | C22 | 1 | 1 | yes | characteristic |
| 45 | #22576083 | C22 | 1 | 1 | yes | characteristic |
| 46 | #22576083 | C22 | 1 | 1 | yes | characteristic |
| 47 | #22576081 | C22 | 1 | 1 | yes | characteristic |
| 48 | #22576070 | C22 | 1 | 1 | yes | characteristic |
| 49 | #22576070 | C22 | 1 | 1 | yes | characteristic |
| 50 | C8×Dic271 | C22 | 1 | 1 | yes | characteristic |
| 51 | C8×Dic271 | C22 | 1 | 1 | yes | characteristic |
| 52 | C2×SD16×C271 | C22 | 1 | 1 | yes | characteristic |
| 53 | C2×M16×C271 | C22 | 1 | 1 | yes | characteristic |
| 54 | C22⋊Q8×C271 | C22 | 1 | 1 | yes | characteristic |
| 55 | #121×C271 | C22 | 1 | 1 | yes | characteristic |
| 56 | #107×C271 | C22 | 1 | 1 | yes | characteristic |
| 57 | #103×C271 | C22 | 1 | 1 | yes | characteristic |
| 58 | #102×C271 | C22 | 1 | 1 | yes | characteristic |
| 59 | C2×Dic542 | — | 2 | 1 | no | — |
| 60 | C2×Dic542 | C23 | 1 | 1 | yes | characteristic |
| 61 | C2×Dic542 | C23 | 1 | 1 | yes | characteristic |
| 62 | C22×Dic271 | — | 2 | 1 | no | — |
| 63 | C22×Dic271 | D4 | 1 | 1 | yes | characteristic |
| 64 | C22×Dic271 | D4 | 1 | 1 | yes | characteristic |
| 65 | Dic1084 | — | 2 | 2 | no | — |
| 66 | #16864644 | — | 2 | 2 | no | — |
| 67 | #16864642 | — | 2 | 2 | no | — |
| 68 | #16864638 | — | 2 | 2 | no | — |
| 69 | C2×C271⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 70 | C2×C271⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 71 | C4⋊Dic271 | — | 2 | 1 | no | — |
| 72 | C4⋊Dic271 | — | 2 | 1 | no | — |
| 73 | C4⋊Dic271 | C23 | 1 | 1 | yes | characteristic |
| 74 | C4⋊Dic271 | C23 | 1 | 1 | yes | characteristic |
| 75 | Dic271⋊C4 | — | 2 | 1 | no | — |
| 76 | Dic271⋊C4 | — | 2 | 1 | no | — |
| 77 | Dic271⋊C4 | — | 2 | 1 | no | — |
| 78 | Dic271⋊C4 | — | 2 | 1 | no | — |
| 79 | Dic271⋊C4 | — | 2 | 1 | no | — |
| 80 | Dic271⋊C4 | — | 2 | 1 | no | — |
| 81 | Dic271⋊C4 | — | 2 | 1 | no | — |
| 82 | Dic271⋊C4 | — | 2 | 1 | no | — |
| 83 | C22⋊Dic271 | — | 2 | 1 | no | — |
| 84 | C22⋊Dic271 | — | 2 | 1 | no | — |
| 85 | C22⋊Dic271 | — | 2 | 1 | no | — |
| 86 | C22⋊Dic271 | — | 2 | 1 | no | — |
| 87 | C22⋊Dic271 | — | 2 | 1 | no | — |
| 88 | C4×Dic271 | — | 2 | 1 | no | — |
| 89 | C4×Dic271 | — | 2 | 1 | no | — |
| 90 | C4×Dic271 | — | 2 | 1 | no | — |
| 91 | C4×Dic271 | D4 | 1 | 1 | yes | characteristic |
| 92 | C4×Dic271 | D4 | 1 | 1 | yes | characteristic |
| 93 | C4×Dic271 | C23 | 1 | 1 | yes | characteristic |
| 94 | C4×Dic271 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×Q8×C271 | C23 | 1 | 1 | yes | characteristic |
| 96 | C2×D4×C271 | — | 2 | 1 | no | — |
| 97 | C2×D4×C271 | C23 | 1 | 1 | yes | characteristic |
| 98 | C22×C4×C271 | C23 | 1 | 1 | yes | characteristic |
| 99 | SD16×C271 | — | 2 | 2 | no | — |
| 100 | M16×C271 | — | 2 | 2 | no | — |
| 101 | C2×C8×C271 | C23 | 1 | 1 | yes | characteristic |
| 102 | C2×C8×C271 | C23 | 1 | 1 | yes | characteristic |
| 103 | C4⋊C4×C271 | — | 2 | 1 | no | — |
| 104 | C4⋊C4×C271 | C23 | 1 | 1 | yes | characteristic |
| 105 | C4⋊C4×C271 | C23 | 1 | 1 | yes | characteristic |
| 106 | C22⋊C4×C271 | — | 2 | 1 | no | — |
| 107 | C22⋊C4×C271 | — | 2 | 1 | no | — |
| 108 | Dic542 | — | 2 | 1 | no | — |
| 109 | Dic542 | — | 2 | 1 | no | — |
| 110 | Dic542 | — | 2 | 1 | no | — |
| 111 | Dic542 | — | 2 | 1 | no | — |
| 112 | Dic542 | — | 4 | 2 | no | — |
| 113 | C2×Dic271 | — | 2 | 2 | no | — |
| 114 | C2×Dic271 | — | 2 | 1 | no | — |
| 115 | C2×Dic271 | — | 2 | 1 | no | — |
| 116 | C2×Dic271 | — | 2 | 1 | no | — |
| 117 | C2×Dic271 | — | 2 | 1 | no | — |
| 118 | C2×Dic271 | — | 4 | 1 | no | — |
| 119 | C2×Dic271 | — | 4 | 2 | no | — |
| 120 | C2×Dic271 | C2×D4 | 1 | 1 | yes | characteristic |
| 121 | C2×Dic271 | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | C2×Dic271 | C2×D4 | 1 | 1 | yes | characteristic |
| 123 | C2×Dic271 | C2×D4 | 1 | 1 | yes | characteristic |
| 124 | C271⋊C8 | — | 2 | 1 | no | — |
| 125 | C271⋊C8 | #41 | 1 | 2 | yes | — |
| 126 | C23×C271 | — | 2 | 1 | no | — |
| 127 | C23×C271 | C2×D4 | 1 | 1 | yes | characteristic |
| 128 | Q8×C271 | — | 2 | 1 | no | — |
| 129 | Q8×C271 | — | 2 | 1 | no | — |
| 130 | D4×C271 | — | 2 | 1 | no | — |
| 131 | D4×C271 | — | 2 | 1 | no | — |
| 132 | D4×C271 | — | 4 | 2 | no | — |
| 133 | C2×C4×C271 | — | 2 | 1 | no | — |
| 134 | C2×C4×C271 | — | 2 | 1 | no | — |
| 135 | C2×C4×C271 | — | 2 | 1 | no | — |
| 136 | C2×C4×C271 | — | 2 | 1 | no | — |
| 137 | C2×C4×C271 | — | 2 | 1 | no | — |
| 138 | C2×C4×C271 | C2×D4 | 1 | 1 | yes | characteristic |
| 139 | C2×C4×C271 | C24 | 1 | 1 | yes | characteristic |
| 140 | C8×C271 | — | 2 | 1 | no | — |
| 141 | C8×C271 | #41 | 1 | 2 | yes | — |
| 142 | C22×C271 | — | 2 | 1 | no | — |
| 143 | C22×C271 | — | 2 | 1 | no | — |
| 144 | C22×C271 | — | 2 | 1 | no | — |
| 145 | C22×C271 | — | 4 | 1 | no | — |
| 146 | C22×C271 | — | 4 | 1 | no | — |
| 147 | C22×C271 | — | 4 | 1 | no | — |
| 148 | C22×C271 | C22×D4 | 1 | 1 | yes | characteristic |
| 149 | C4×C271 | — | 2 | 1 | no | — |
| 150 | C4×C271 | — | 4 | 1 | no | — |
| 151 | C4×C271 | — | 4 | 1 | no | — |
| 152 | C4×C271 | — | 4 | 1 | no | — |
| 153 | C4×C271 | C2×#41 | 1 | 1 | yes | characteristic |
| 154 | C4×C271 | C2×#41 | 1 | 1 | yes | characteristic |
| 155 | Dic271 | — | 2 | 1 | no | — |
| 156 | Dic271 | — | 2 | 1 | no | — |
| 157 | Dic271 | — | 2 | 1 | no | — |
| 158 | Dic271 | — | 4 | 1 | no | — |
| 159 | Dic271 | — | 4 | 1 | no | — |
| 160 | Dic271 | — | 4 | 1 | no | — |
| 161 | Dic271 | — | 4 | 1 | no | — |
| 162 | Dic271 | #137 | 1 | 2 | yes | — |
| 163 | C2×C271 | — | 4 | 1 | no | — |
| 164 | C2×C271 | — | 8 | 1 | no | — |
| 165 | C2×C271 | #532 | 1 | 1 | yes | characteristic |
| 166 | C2×C271 | C2×#137 | 1 | 1 | yes | characteristic |
| 167 | C2×C271 | #575 | 1 | 1 | yes | characteristic |
| 168 | C271 | #3172 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 169 | #3172 | — | 271 | 1 | no | maximal, Sylow |
| 170 | #533 | — | 271 | 1 | no | — |
| 171 | #529 | — | 271 | 1 | no | — |
| 172 | #501 | — | 271 | 1 | no | — |
| 173 | #497 | — | 271 | 1 | no | — |
| 174 | #491 | — | 271 | 1 | no | — |
| 175 | #489 | — | 271 | 1 | no | — |
| 176 | #470 | — | 271 | 1 | no | — |
| 177 | #470 | — | 271 | 1 | no | — |
| 178 | #468 | — | 271 | 1 | no | — |
| 179 | #468 | D271 | 1 | 1 | yes | characteristic |
| 180 | C4×Q16 | — | 271 | 1 | no | — |
| 181 | C4×Q16 | — | 271 | 1 | no | — |
| 182 | C4×SD16 | — | 271 | 1 | no | — |
| 183 | C4×SD16 | — | 271 | 1 | no | — |
| 184 | C4×M16 | — | 271 | 1 | no | — |
| 185 | C2×Q16 | — | 271 | 1 | no | — |
| 186 | C2×Q16 | — | 271 | 1 | no | — |
| 187 | C2×SD16 | — | 271 | 1 | no | — |
| 188 | C2×SD16 | C2×D271 | 1 | 1 | yes | characteristic |
| 189 | C2×M16 | — | 271 | 1 | no | — |
| 190 | C2×M16 | C2×D271 | 1 | 1 | yes | characteristic |
| 191 | C4⋊Q8 | — | 271 | 1 | no | — |
| 192 | C4⋊Q8 | — | 271 | 1 | no | — |
| 193 | #126 | — | 542 | 1 | no | — |
| 194 | #125 | — | 271 | 1 | no | — |
| 195 | #125 | — | 542 | 1 | no | — |
| 196 | #124 | — | 271 | 1 | no | — |
| 197 | #123 | — | 542 | 1 | no | — |
| 198 | C22⋊Q8 | — | 271 | 1 | no | — |
| 199 | C22⋊Q8 | — | 271 | 1 | no | — |
| 200 | C22⋊Q8 | — | 542 | 1 | no | — |
| 201 | C22⋊Q8 | C2×D271 | 1 | 1 | yes | characteristic |
| 202 | #121 | C2×D271 | 1 | 1 | yes | characteristic |
| 203 | C4×Q8 | — | 271 | 1 | no | — |
| 204 | C4×Q8 | — | 271 | 1 | no | — |
| 205 | C4×Q8 | — | 271 | 1 | no | — |
| 206 | C4×Q8 | — | 542 | 1 | no | — |
| 207 | C4×D4 | — | 271 | 1 | no | — |
| 208 | C4×D4 | — | 542 | 1 | no | — |
| 209 | #117 | — | 542 | 1 | no | — |
| 210 | #117 | — | 542 | 1 | no | — |
| 211 | C2×C42 | — | 271 | 1 | no | — |
| 212 | #107 | — | 271 | 1 | no | — |
| 213 | #107 | C2×D271 | 1 | 1 | yes | characteristic |
| 214 | #106 | — | 271 | 1 | no | — |
| 215 | #106 | — | 271 | 1 | no | — |
| 216 | #103 | — | 271 | 1 | no | — |
| 217 | #103 | — | 271 | 1 | no | — |
| 218 | #103 | — | 271 | 1 | no | — |
| 219 | #103 | — | 271 | 1 | no | — |
| 220 | #103 | — | 271 | 1 | no | — |
| 221 | #103 | C2×D271 | 1 | 1 | yes | characteristic |
| 222 | #102 | — | 271 | 1 | no | — |
| 223 | #102 | C2×D271 | 1 | 1 | yes | characteristic |
| 224 | #97 | — | 271 | 1 | no | — |
| 225 | #97 | — | 271 | 1 | no | — |
| 226 | C4×C8 | — | 271 | 1 | no | — |
| 227 | C4×C8 | — | 271 | 1 | no | — |
| 228 | C2×Q8 | — | 271 | 1 | no | — |
| 229 | C2×Q8 | — | 271 | 1 | no | — |
| 230 | C2×Q8 | — | 542 | 1 | no | — |
| 231 | C2×Q8 | C22×D271 | 1 | 1 | yes | characteristic |
| 232 | C2×D4 | — | 2 | 1 | no | — |
| 233 | C2×D4 | C22×D271 | 1 | 1 | yes | characteristic |
| 234 | C22×C4 | — | 271 | 1 | no | — |
| 235 | C22×C4 | — | 271 | 1 | no | — |
| 236 | C22×C4 | — | 542 | 1 | no | — |
| 237 | C22×C4 | C22×D271 | 1 | 1 | yes | characteristic |
| 238 | Q16 | — | 542 | 2 | no | — |
| 239 | Q16 | — | 542 | 2 | no | — |
| 240 | SD16 | — | 2 | 2 | no | — |
| 241 | SD16 | — | 542 | 2 | no | — |
| 242 | M16 | — | 2 | 2 | no | — |
| 243 | M16 | — | 542 | 2 | no | — |
| 244 | C2×C8 | — | 271 | 1 | no | — |
| 245 | C2×C8 | — | 271 | 1 | no | — |
| 246 | C2×C8 | C22×D271 | 1 | 1 | yes | characteristic |
| 247 | C2×C8 | C22×D271 | 1 | 1 | yes | characteristic |
| 248 | C4⋊C4 | — | 2 | 1 | no | — |
| 249 | C4⋊C4 | — | 271 | 1 | no | — |
| 250 | C4⋊C4 | — | 271 | 1 | no | — |
| 251 | C4⋊C4 | — | 542 | 1 | no | — |
| 252 | C4⋊C4 | — | 542 | 1 | no | — |
| 253 | C4⋊C4 | — | 542 | 1 | no | — |
| 254 | C4⋊C4 | — | 542 | 1 | no | — |
| 255 | C4⋊C4 | — | 542 | 1 | no | — |
| 256 | C4⋊C4 | — | 542 | 1 | no | — |
| 257 | C4⋊C4 | — | 542 | 1 | no | — |
| 258 | C4⋊C4 | — | 542 | 1 | no | — |
| 259 | C4⋊C4 | — | 542 | 1 | no | — |
| 260 | C4⋊C4 | — | 542 | 1 | no | — |
| 261 | C4⋊C4 | C22×D271 | 1 | 1 | yes | characteristic |
| 262 | C4⋊C4 | C22×D271 | 1 | 1 | yes | characteristic |
| 263 | C22⋊C4 | — | 2 | 1 | no | — |
| 264 | C22⋊C4 | — | 2 | 1 | no | — |
| 265 | C22⋊C4 | — | 542 | 1 | no | — |
| 266 | C22⋊C4 | — | 542 | 1 | no | — |
| 267 | C22⋊C4 | — | 542 | 1 | no | — |
| 268 | C22⋊C4 | — | 542 | 1 | no | — |
| 269 | C22⋊C4 | — | 542 | 1 | no | — |
| 270 | C42 | — | 271 | 1 | no | — |
| 271 | C42 | — | 271 | 1 | no | — |
| 272 | C42 | — | 271 | 1 | no | — |
| 273 | C42 | — | 271 | 1 | no | — |
| 274 | C42 | — | 542 | 1 | no | — |
| 275 | C42 | — | 542 | 1 | no | — |
| 276 | C42 | — | 542 | 1 | no | — |
| 277 | C23 | — | 2 | 1 | no | — |
| 278 | C23 | D4×D271 | 1 | 1 | yes | characteristic |
| 279 | Q8 | — | 2 | 1 | no | — |
| 280 | Q8 | — | 2 | 1 | no | — |
| 281 | Q8 | — | 542 | 1 | no | — |
| 282 | Q8 | — | 542 | 1 | no | — |
| 283 | Q8 | — | 542 | 1 | no | — |
| 284 | Q8 | — | 542 | 1 | no | — |
| 285 | Q8 | — | 1084 | 2 | no | — |
| 286 | D4 | — | 2 | 1 | no | — |
| 287 | D4 | — | 2 | 1 | no | — |
| 288 | D4 | — | 4 | 2 | no | — |
| 289 | C2×C4 | — | 2 | 1 | no | — |
| 290 | C2×C4 | — | 2 | 1 | no | — |
| 291 | C2×C4 | — | 2 | 1 | no | — |
| 292 | C2×C4 | — | 2 | 1 | no | — |
| 293 | C2×C4 | — | 2 | 1 | no | — |
| 294 | C2×C4 | — | 271 | 1 | no | — |
| 295 | C2×C4 | — | 271 | 1 | no | — |
| 296 | C2×C4 | — | 271 | 1 | no | — |
| 297 | C2×C4 | — | 271 | 1 | no | — |
| 298 | C2×C4 | — | 542 | 2 | no | — |
| 299 | C2×C4 | — | 542 | 1 | no | — |
| 300 | C2×C4 | — | 542 | 1 | no | — |
| 301 | C2×C4 | — | 542 | 1 | no | — |
| 302 | C2×C4 | — | 542 | 1 | no | — |
| 303 | C2×C4 | — | 1084 | 2 | no | — |
| 304 | C2×C4 | — | 1084 | 1 | no | — |
| 305 | C2×C4 | D4×D271 | 1 | 1 | yes | characteristic |
| 306 | C2×C4 | C23×D271 | 1 | 1 | yes | characteristic |
| 307 | C8 | — | 2 | 1 | no | — |
| 308 | C8 | — | 271 | 2 | no | — |
| 309 | C8 | — | 542 | 1 | no | — |
| 310 | C8 | #16864653 | 1 | 2 | yes | — |
| 311 | C22 | — | 2 | 1 | no | — |
| 312 | C22 | — | 2 | 1 | no | — |
| 313 | C22 | — | 2 | 1 | no | — |
| 314 | C22 | — | 4 | 1 | no | — |
| 315 | C22 | — | 4 | 1 | no | — |
| 316 | C22 | — | 4 | 1 | no | — |
| 317 | C22 | C2×D4×D271 | 1 | 1 | yes | characteristic |
| 318 | C4 | — | 2 | 1 | no | — |
| 319 | C4 | — | 4 | 1 | no | — |
| 320 | C4 | — | 4 | 1 | no | — |
| 321 | C4 | — | 4 | 1 | no | — |
| 322 | C4 | — | 271 | 2 | no | — |
| 323 | C4 | — | 542 | 1 | no | — |
| 324 | C4 | — | 542 | 1 | no | — |
| 325 | C4 | — | 542 | 1 | no | — |
| 326 | C4 | — | 1084 | 1 | no | — |
| 327 | C4 | — | 1084 | 1 | no | — |
| 328 | C4 | — | 1084 | 1 | no | — |
| 329 | C4 | — | 1084 | 1 | no | — |
| 330 | C4 | #41×D271 | 1 | 1 | yes | characteristic |
| 331 | C4 | C2×#16864653 | 1 | 1 | yes | characteristic |
| 332 | C2 | — | 4 | 1 | no | — |
| 333 | C2 | — | 8 | 1 | no | — |
| 334 | C2 | #31774442 | 1 | 1 | yes | characteristic |
| 335 | C2 | #137×D271 | 1 | 1 | yes | characteristic |
| 336 | C2 | #31774693 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta