| 1 | #3392 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #3364 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #3324 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #3274 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #1717 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #1699 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #1685 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #1682 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #1668 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #1641 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #1639 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #1628 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #1626 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #1588 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #1588 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 17 | #557 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | #556 | C22 | 1 | 1 | yes | characteristic |
| 19 | #550 | C22 | 1 | 1 | yes | characteristic |
| 20 | D42 | C22 | 1 | 1 | yes | characteristic |
| 21 | #493 | C22 | 1 | 1 | yes | characteristic |
| 22 | #492 | — | 2 | 1 | no | — |
| 23 | #492 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #488 | — | 2 | 1 | no | — |
| 25 | #487 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #486 | C22 | 1 | 1 | yes | characteristic |
| 27 | #486 | C22 | 1 | 1 | yes | characteristic |
| 28 | #486 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #482 | — | 2 | 1 | no | — |
| 30 | #479 | — | 2 | 1 | no | — |
| 31 | #474 | C22 | 1 | 1 | yes | characteristic |
| 32 | #474 | C22 | 1 | 1 | yes | characteristic |
| 33 | #469 | — | 2 | 1 | no | — |
| 34 | #468 | — | 2 | 1 | no | — |
| 35 | #464 | — | 2 | 1 | no | — |
| 36 | #462 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #461 | — | 2 | 1 | no | — |
| 38 | #461 | C22 | 1 | 1 | yes | characteristic |
| 39 | #460 | — | 2 | 1 | no | — |
| 40 | #460 | C22 | 1 | 1 | yes | characteristic |
| 41 | #460 | C22 | 1 | 1 | yes | characteristic |
| 42 | #460 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | #459 | C22 | 1 | 1 | yes | characteristic |
| 44 | #450 | — | 2 | 1 | no | — |
| 45 | #449 | — | 2 | 1 | no | — |
| 46 | #447 | — | 2 | 1 | no | — |
| 47 | C8×Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | C8×Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | C4×Q16 | — | 2 | 1 | no | — |
| 50 | C4×SD16 | — | 2 | 1 | no | — |
| 51 | C4×SD16 | C22 | 1 | 1 | yes | characteristic |
| 52 | C4×SD16 | C22 | 1 | 1 | yes | characteristic |
| 53 | #436 | C22 | 1 | 1 | yes | characteristic |
| 54 | #436 | C22 | 1 | 1 | yes | characteristic |
| 55 | #418 | — | 2 | 1 | no | — |
| 56 | #335 | C22 | 1 | 1 | yes | characteristic, complemented |
| 57 | #335 | C22 | 1 | 1 | yes | characteristic, complemented |
| 58 | #332 | C22 | 1 | 1 | yes | characteristic, complemented |
| 59 | #332 | C22 | 1 | 1 | yes | characteristic, complemented |
| 60 | #331 | C22 | 1 | 1 | yes | characteristic |
| 61 | #331 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | Q8⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | Q8⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 64 | D4⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 65 | D4⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 66 | #322 | C22 | 1 | 1 | yes | characteristic, complemented |
| 67 | C2×#41 | — | 2 | 1 | no | — |
| 68 | C22×D4 | — | 2 | 1 | no | — |
| 69 | C22×D4 | — | 2 | 1 | no | — |
| 70 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 71 | C2×Q16 | — | 2 | 1 | no | — |
| 72 | C2×SD16 | — | 2 | 1 | no | — |
| 73 | C2×SD16 | — | 2 | 1 | no | — |
| 74 | C2×SD16 | — | 2 | 1 | no | — |
| 75 | C2×SD16 | — | 2 | 1 | no | — |
| 76 | C2×SD16 | — | 2 | 1 | no | — |
| 77 | C2×SD16 | — | 2 | 1 | no | — |
| 78 | C2×SD16 | D4 | 1 | 1 | yes | characteristic |
| 79 | C2×SD16 | D4 | 1 | 1 | yes | characteristic |
| 80 | C2×D8 | — | 2 | 1 | no | — |
| 81 | C2×D8 | — | 2 | 1 | no | — |
| 82 | C2×D8 | — | 2 | 1 | no | — |
| 83 | C2×M16 | — | 2 | 1 | no | — |
| 84 | C2×M16 | — | 2 | 1 | no | — |
| 85 | C4⋊Q8 | — | 2 | 1 | no | — |
| 86 | C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 87 | C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 88 | #127 | — | 2 | 1 | no | — |
| 89 | #127 | C23 | 1 | 1 | yes | characteristic |
| 90 | #127 | C23 | 1 | 1 | yes | characteristic |
| 91 | #126 | — | 4 | 1 | no | — |
| 92 | #125 | — | 2 | 1 | no | — |
| 93 | #125 | — | 4 | 1 | no | — |
| 94 | #124 | — | 2 | 1 | no | — |
| 95 | C22⋊Q8 | — | 2 | 1 | no | — |
| 96 | #121 | — | 2 | 1 | no | — |
| 97 | #121 | — | 2 | 1 | no | — |
| 98 | #121 | — | 2 | 1 | no | — |
| 99 | #121 | — | 4 | 1 | no | — |
| 100 | #120 | — | 4 | 1 | no | — |
| 101 | C4×Q8 | — | 2 | 1 | no | — |
| 102 | C4×Q8 | — | 2 | 1 | no | — |
| 103 | C4×Q8 | — | 2 | 1 | no | — |
| 104 | C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 105 | C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 106 | C4×D4 | — | 2 | 1 | no | — |
| 107 | C4×D4 | C23 | 1 | 1 | yes | characteristic |
| 108 | C4×D4 | C23 | 1 | 1 | yes | characteristic |
| 109 | #117 | — | 2 | 1 | no | — |
| 110 | #107 | — | 2 | 1 | no | — |
| 111 | #107 | — | 2 | 1 | no | — |
| 112 | #106 | D4 | 1 | 1 | yes | characteristic |
| 113 | #106 | D4 | 1 | 1 | yes | characteristic |
| 114 | C4⋊C8 | — | 2 | 1 | no | — |
| 115 | C4⋊C8 | — | 2 | 1 | no | — |
| 116 | C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 117 | C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 118 | C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 119 | C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 120 | #103 | — | 2 | 1 | no | — |
| 121 | #103 | — | 2 | 1 | no | — |
| 122 | #103 | — | 2 | 1 | no | — |
| 123 | #103 | — | 2 | 1 | no | — |
| 124 | #103 | D4 | 1 | 1 | yes | characteristic |
| 125 | #103 | D4 | 1 | 1 | yes | characteristic |
| 126 | #102 | — | 2 | 1 | no | — |
| 127 | #102 | — | 2 | 1 | no | — |
| 128 | #102 | — | 2 | 1 | no | — |
| 129 | #102 | — | 2 | 1 | no | — |
| 130 | #102 | — | 2 | 1 | no | — |
| 131 | #102 | — | 2 | 1 | no | — |
| 132 | #102 | — | 2 | 1 | no | — |
| 133 | #102 | — | 2 | 1 | no | — |
| 134 | #102 | — | 4 | 1 | no | — |
| 135 | #102 | — | 4 | 1 | no | — |
| 136 | #102 | D4 | 1 | 1 | yes | characteristic |
| 137 | #102 | D4 | 1 | 1 | yes | characteristic |
| 138 | C22⋊C8 | — | 2 | 1 | no | — |
| 139 | C22⋊C8 | — | 2 | 1 | no | — |
| 140 | C4×C8 | — | 2 | 1 | no | — |
| 141 | C4×C8 | — | 2 | 1 | no | — |
| 142 | C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 143 | C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 144 | C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 145 | C24 | — | 4 | 1 | no | — |
| 146 | #41 | — | 4 | 2 | no | — |
| 147 | #41 | — | 8 | 1 | no | — |
| 148 | C2×Q8 | — | 2 | 1 | no | — |
| 149 | C2×Q8 | — | 2 | 1 | no | — |
| 150 | C2×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 151 | C2×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 152 | C2×D4 | — | 2 | 1 | no | — |
| 153 | C2×D4 | — | 2 | 1 | no | — |
| 154 | C2×D4 | — | 2 | 1 | no | — |
| 155 | C2×D4 | — | 2 | 1 | no | — |
| 156 | C2×D4 | — | 2 | 1 | no | — |
| 157 | C2×D4 | — | 2 | 1 | no | — |
| 158 | C2×D4 | — | 4 | 1 | no | — |
| 159 | C2×D4 | — | 4 | 1 | no | — |
| 160 | C2×D4 | — | 4 | 1 | no | — |
| 161 | C2×D4 | — | 4 | 1 | no | — |
| 162 | C2×D4 | — | 4 | 2 | no | — |
| 163 | C2×D4 | — | 4 | 2 | no | — |
| 164 | C2×D4 | — | 8 | 1 | no | — |
| 165 | C2×D4 | — | 8 | 1 | no | — |
| 166 | C2×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C2×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 168 | C22×C4 | — | 2 | 1 | no | — |
| 169 | C22×C4 | — | 2 | 1 | no | — |
| 170 | C22×C4 | — | 4 | 1 | no | — |
| 171 | Q16 | — | 4 | 2 | no | — |
| 172 | SD16 | — | 2 | 2 | no | — |
| 173 | SD16 | — | 4 | 1 | no | — |
| 174 | SD16 | — | 4 | 2 | no | — |
| 175 | SD16 | — | 4 | 2 | no | — |
| 176 | SD16 | — | 8 | 1 | no | — |
| 177 | SD16 | — | 8 | 1 | no | — |
| 178 | SD16 | — | 8 | 1 | no | — |
| 179 | SD16 | — | 8 | 1 | no | — |
| 180 | D8 | — | 4 | 2 | no | — |
| 181 | D8 | — | 4 | 2 | no | — |
| 182 | D8 | — | 8 | 1 | no | — |
| 183 | M16 | — | 4 | 2 | no | — |
| 184 | M16 | — | 8 | 1 | no | — |
| 185 | C2×C8 | — | 2 | 1 | no | — |
| 186 | C2×C8 | — | 2 | 1 | no | — |
| 187 | C2×C8 | — | 2 | 1 | no | — |
| 188 | C2×C8 | — | 2 | 1 | no | — |
| 189 | C2×C8 | — | 2 | 1 | no | — |
| 190 | C2×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | C2×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C2×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C2×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 194 | C4⋊C4 | — | 2 | 1 | no | — |
| 195 | C4⋊C4 | — | 2 | 1 | no | — |
| 196 | C4⋊C4 | — | 2 | 1 | no | — |
| 197 | C4⋊C4 | — | 2 | 1 | no | — |
| 198 | C4⋊C4 | — | 2 | 1 | no | — |
| 199 | C4⋊C4 | — | 2 | 1 | no | — |
| 200 | C4⋊C4 | — | 4 | 1 | no | — |
| 201 | C4⋊C4 | — | 4 | 1 | no | — |
| 202 | C4⋊C4 | — | 4 | 1 | no | — |
| 203 | C4⋊C4 | — | 4 | 1 | no | — |
| 204 | C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 205 | C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 206 | C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 207 | C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 208 | C22⋊C4 | — | 2 | 1 | no | — |
| 209 | C22⋊C4 | — | 2 | 1 | no | — |
| 210 | C22⋊C4 | — | 4 | 1 | no | — |
| 211 | C22⋊C4 | — | 4 | 1 | no | — |
| 212 | C22⋊C4 | — | 4 | 1 | no | — |
| 213 | C22⋊C4 | — | 4 | 1 | no | — |
| 214 | C42 | — | 2 | 1 | no | — |
| 215 | C42 | — | 2 | 1 | no | — |
| 216 | C42 | — | 4 | 1 | no | — |
| 217 | C42 | — | 4 | 1 | no | — |
| 218 | C42 | C24 | 1 | 1 | yes | characteristic |
| 219 | C23 | — | 2 | 1 | no | — |
| 220 | C23 | — | 2 | 1 | no | — |
| 221 | C23 | — | 4 | 1 | no | — |
| 222 | C23 | — | 4 | 1 | no | — |
| 223 | C23 | — | 8 | 2 | no | — |
| 224 | C23 | — | 8 | 2 | no | — |
| 225 | C23 | — | 16 | 1 | no | — |
| 226 | Q8 | — | 2 | 1 | no | — |
| 227 | Q8 | — | 2 | 1 | no | — |
| 228 | Q8 | — | 2 | 1 | no | — |
| 229 | Q8 | — | 4 | 1 | no | — |
| 230 | Q8 | — | 4 | 1 | no | — |
| 231 | Q8 | — | 4 | 1 | no | — |
| 232 | Q8 | — | 4 | 1 | no | — |
| 233 | Q8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 234 | D4 | — | 2 | 1 | no | — |
| 235 | D4 | — | 2 | 1 | no | — |
| 236 | D4 | — | 2 | 1 | no | — |
| 237 | D4 | — | 2 | 1 | no | — |
| 238 | D4 | — | 4 | 1 | no | — |
| 239 | D4 | — | 4 | 1 | no | — |
| 240 | D4 | — | 4 | 1 | no | — |
| 241 | D4 | — | 4 | 1 | no | — |
| 242 | D4 | — | 4 | 1 | no | — |
| 243 | D4 | — | 4 | 1 | no | — |
| 244 | D4 | — | 4 | 1 | no | — |
| 245 | D4 | — | 4 | 1 | no | — |
| 246 | D4 | — | 8 | 2 | no | — |
| 247 | D4 | — | 8 | 1 | no | — |
| 248 | D4 | — | 8 | 1 | no | — |
| 249 | D4 | — | 8 | 2 | no | — |
| 250 | D4 | — | 8 | 2 | no | — |
| 251 | D4 | — | 16 | 1 | no | — |
| 252 | C2×C4 | — | 2 | 1 | no | — |
| 253 | C2×C4 | — | 2 | 1 | no | — |
| 254 | C2×C4 | — | 2 | 1 | no | — |
| 255 | C2×C4 | — | 2 | 1 | no | — |
| 256 | C2×C4 | — | 2 | 1 | no | — |
| 257 | C2×C4 | — | 2 | 1 | no | — |
| 258 | C2×C4 | — | 4 | 1 | no | — |
| 259 | C2×C4 | — | 4 | 1 | no | — |
| 260 | C2×C4 | — | 4 | 1 | no | — |
| 261 | C2×C4 | — | 4 | 1 | no | — |
| 262 | C2×C4 | — | 4 | 1 | no | — |
| 263 | C2×C4 | — | 4 | 1 | no | — |
| 264 | C2×C4 | — | 8 | 2 | no | — |
| 265 | C2×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 266 | C2×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 267 | C2×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 268 | C8 | — | 2 | 1 | no | — |
| 269 | C8 | — | 2 | 1 | no | — |
| 270 | C8 | — | 2 | 1 | no | — |
| 271 | C8 | — | 2 | 1 | no | — |
| 272 | C8 | — | 4 | 1 | no | — |
| 273 | C8 | — | 4 | 1 | no | — |
| 274 | C8 | — | 4 | 1 | no | — |
| 275 | C8 | — | 4 | 1 | no | — |
| 276 | C8 | — | 4 | 1 | no | — |
| 277 | C22 | — | 4 | 1 | no | — |
| 278 | C22 | — | 4 | 1 | no | — |
| 279 | C22 | — | 4 | 1 | no | — |
| 280 | C22 | — | 4 | 1 | no | — |
| 281 | C22 | — | 4 | 1 | no | — |
| 282 | C22 | — | 4 | 1 | no | — |
| 283 | C22 | — | 8 | 1 | no | — |
| 284 | C22 | — | 8 | 1 | no | — |
| 285 | C22 | — | 8 | 1 | no | — |
| 286 | C22 | — | 8 | 1 | no | — |
| 287 | C22 | — | 8 | 1 | no | — |
| 288 | C22 | — | 8 | 1 | no | — |
| 289 | C22 | — | 16 | 4 | no | — |
| 290 | C22 | D42 | 1 | 1 | yes | characteristic |
| 291 | C4 | — | 2 | 2 | no | — |
| 292 | C4 | — | 2 | 1 | no | — |
| 293 | C4 | — | 4 | 1 | no | — |
| 294 | C4 | — | 4 | 1 | no | — |
| 295 | C4 | — | 4 | 1 | no | — |
| 296 | C4 | — | 4 | 1 | no | — |
| 297 | C4 | — | 4 | 1 | no | — |
| 298 | C4 | — | 8 | 1 | no | — |
| 299 | C4 | — | 8 | 1 | no | — |
| 300 | C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 301 | C4 | #575 | 1 | 1 | yes | characteristic |
| 302 | C4 | #576 | 1 | 1 | yes | characteristic |
| 303 | C4 | #577 | 1 | 1 | yes | characteristic |
| 304 | C2 | — | 8 | 1 | no | — |
| 305 | C2 | — | 8 | 1 | no | — |
| 306 | C2 | — | 16 | 1 | no | — |
| 307 | C2 | — | 16 | 1 | no | — |
| 308 | C2 | #3265 | 1 | 1 | yes | characteristic |
| 309 | C2 | #3268 | 1 | 1 | yes | characteristic |
| 310 | C2 | #3290 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta