← #72227267
Subgroups — #72227267
Order 4096.
840 conjugacy classes of subgroups.
The subgroup lattice has 724 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72227235 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72226929 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #72226852 | C4 | 1 | 1 | yes | characteristic |
| 4 | #72225599 | C4 | 1 | 1 | yes | characteristic |
| 5 | #72225599 | C4 | 1 | 1 | yes | characteristic |
| 6 | #72225579 | C4 | 1 | 1 | yes | characteristic |
| 7 | #72225529 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #72225527 | — | 2 | 1 | no | — |
| 9 | #72225526 | — | 2 | 1 | no | — |
| 10 | #72225358 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #72225357 | — | 2 | 1 | no | — |
| 12 | #72225354 | — | 2 | 1 | no | — |
| 13 | #72225160 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #72225158 | — | 2 | 1 | no | — |
| 15 | #72225158 | — | 2 | 1 | no | — |
| 16 | #72225138 | C22 | 1 | 1 | yes | characteristic |
| 17 | #72216558 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 18 | #72216309 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 19 | #72216304 | — | 2 | 1 | no | — |
| 20 | #72216302 | — | 2 | 1 | no | — |
| 21 | #72216249 | C22 | 1 | 1 | yes | characteristic |
| 22 | #72216247 | C22 | 1 | 1 | yes | characteristic |
| 23 | #72216243 | C22 | 1 | 1 | yes | characteristic |
| 24 | #72216243 | C22 | 1 | 1 | yes | characteristic |
| 25 | #72216215 | C22 | 1 | 1 | yes | characteristic |
| 26 | #72216168 | C22 | 1 | 1 | yes | characteristic |
| 27 | #496112 | — | 2 | 1 | no | — |
| 28 | #496112 | — | 2 | 1 | no | — |
| 29 | #491465 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | #213237 | — | 2 | 1 | no | — |
| 31 | #151981 | — | 2 | 1 | no | — |
| 32 | #151981 | — | 2 | 1 | no | — |
| 33 | #151981 | — | 2 | 1 | no | — |
| 34 | C4×#1398 | D4 | 1 | 1 | yes | characteristic |
| 35 | C4×#1398 | D4 | 1 | 1 | yes | characteristic |
| 36 | C2×#7459 | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | C2×#7459 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | C2×#7459 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | C2×#7459 | C2×C4 | 1 | 1 | yes | characteristic |
| 40 | C2×#7457 | — | 4 | 1 | no | — |
| 41 | C2×#7456 | — | 2 | 1 | no | — |
| 42 | #150071 | — | 4 | 1 | no | — |
| 43 | #150071 | — | 4 | 1 | no | — |
| 44 | C2×#7389 | — | 4 | 1 | no | — |
| 45 | C2×#7389 | — | 4 | 1 | no | — |
| 46 | C2×#7389 | — | 4 | 2 | no | — |
| 47 | #149504 | — | 4 | 1 | no | — |
| 48 | #149502 | — | 2 | 1 | no | — |
| 49 | #149499 | — | 2 | 1 | no | — |
| 50 | #141684 | — | 2 | 1 | no | — |
| 51 | #141684 | — | 2 | 1 | no | — |
| 52 | #141671 | — | 2 | 1 | no | — |
| 53 | #135781 | C2×C4 | 1 | 1 | yes | characteristic |
| 54 | #135715 | — | 2 | 1 | no | — |
| 55 | #135715 | — | 2 | 1 | no | — |
| 56 | #129090 | D4 | 1 | 1 | yes | characteristic |
| 57 | #129088 | D4 | 1 | 1 | yes | characteristic |
| 58 | #129051 | — | 2 | 1 | no | — |
| 59 | C8×#346 | C23 | 1 | 1 | yes | characteristic |
| 60 | #99295 | — | 2 | 1 | no | — |
| 61 | #94030 | — | 4 | 1 | no | — |
| 62 | #94019 | — | 2 | 1 | no | — |
| 63 | #94019 | — | 2 | 1 | no | — |
| 64 | #94018 | — | 2 | 1 | no | — |
| 65 | #93996 | — | 4 | 1 | no | — |
| 66 | #93926 | — | 4 | 2 | no | — |
| 67 | #93868 | — | 2 | 2 | no | — |
| 68 | #93867 | C8 | 1 | 2 | yes | complemented |
| 69 | #93866 | C8 | 1 | 2 | yes | complemented |
| 70 | #93264 | — | 2 | 1 | no | — |
| 71 | #33713 | — | 2 | 1 | no | — |
| 72 | #33713 | — | 2 | 1 | no | — |
| 73 | C2×#2179 | — | 4 | 1 | no | — |
| 74 | C2×#2179 | — | 4 | 1 | no | — |
| 75 | C2×#2179 | — | 4 | 1 | no | — |
| 76 | C2×#2179 | — | 4 | 1 | no | — |
| 77 | #21705 | — | 4 | 1 | no | — |
| 78 | #19603 | — | 2 | 1 | no | — |
| 79 | #17956 | — | 8 | 1 | no | — |
| 80 | C2×#1422 | — | 2 | 1 | no | — |
| 81 | C2×#1422 | — | 2 | 1 | no | — |
| 82 | C2×#1422 | — | 2 | 1 | no | — |
| 83 | C2×#1422 | — | 2 | 1 | no | — |
| 84 | C2×#1422 | — | 4 | 1 | no | — |
| 85 | C2×#1398 | — | 2 | 1 | no | — |
| 86 | C2×#1398 | — | 2 | 1 | no | — |
| 87 | C2×#1398 | — | 2 | 1 | no | — |
| 88 | C2×#1398 | — | 4 | 1 | no | — |
| 89 | C2×#1398 | — | 4 | 1 | no | — |
| 90 | C2×#1398 | — | 4 | 1 | no | — |
| 91 | C2×#1398 | SD16 | 1 | 2 | yes | — |
| 92 | C4×M64 | — | 2 | 1 | no | — |
| 93 | C4×M64 | — | 2 | 1 | no | — |
| 94 | #13242 | — | 4 | 1 | no | — |
| 95 | #13242 | — | 4 | 1 | no | — |
| 96 | #13242 | — | 4 | 1 | no | — |
| 97 | #13242 | — | 4 | 1 | no | — |
| 98 | #13208 | — | 4 | 1 | no | — |
| 99 | #13208 | — | 4 | 1 | no | — |
| 100 | #12909 | — | 2 | 1 | no | — |
| 101 | #12909 | — | 2 | 1 | no | — |
| 102 | C4×#364 | — | 2 | 1 | no | — |
| 103 | C4×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 104 | C4×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 105 | #12518 | — | 2 | 1 | no | — |
| 106 | #12518 | — | 2 | 1 | no | — |
| 107 | #12517 | — | 2 | 1 | no | — |
| 108 | #12516 | C2×C8 | 1 | 1 | yes | characteristic |
| 109 | #12515 | C2×C8 | 1 | 1 | yes | characteristic |
| 110 | C2×#1369 | — | 2 | 1 | no | — |
| 111 | #11999 | — | 2 | 1 | no | — |
| 112 | C2×#1368 | — | 4 | 1 | no | — |
| 113 | C2×#1368 | — | 4 | 1 | no | — |
| 114 | C2×#1368 | — | 4 | 1 | no | — |
| 115 | C2×#1368 | — | 4 | 1 | no | — |
| 116 | #11405 | — | 4 | 1 | no | — |
| 117 | C2×#1311 | #41 | 1 | 1 | yes | characteristic |
| 118 | C2×#1311 | #41 | 1 | 1 | yes | characteristic |
| 119 | C2×C8×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 120 | C2×C8×C16 | #41 | 1 | 1 | yes | characteristic |
| 121 | #9856 | — | 4 | 1 | no | — |
| 122 | #9844 | — | 8 | 1 | no | — |
| 123 | #8823 | — | 2 | 1 | no | — |
| 124 | #8805 | — | 4 | 1 | no | — |
| 125 | #8805 | — | 8 | 1 | no | — |
| 126 | #8266 | — | 2 | 1 | no | — |
| 127 | C4×C82 | #41 | 1 | 1 | yes | characteristic |
| 128 | #7468 | — | 4 | 1 | no | — |
| 129 | #7468 | — | 4 | 1 | no | — |
| 130 | #7468 | — | 4 | 1 | no | — |
| 131 | #7459 | — | 2 | 1 | no | — |
| 132 | #7459 | — | 2 | 1 | no | — |
| 133 | #7459 | — | 2 | 1 | no | — |
| 134 | #7459 | — | 2 | 1 | no | — |
| 135 | #7459 | — | 2 | 1 | no | — |
| 136 | #7459 | C2×C8 | 1 | 2 | yes | — |
| 137 | #7459 | C2×C8 | 1 | 2 | yes | — |
| 138 | #7459 | M16 | 1 | 2 | yes | — |
| 139 | #7457 | — | 8 | 2 | no | — |
| 140 | #7456 | — | 2 | 2 | no | — |
| 141 | #7456 | — | 4 | 1 | no | — |
| 142 | #7389 | — | 8 | 2 | no | — |
| 143 | #7389 | — | 8 | 2 | no | — |
| 144 | #7389 | — | 8 | 4 | no | — |
| 145 | #7389 | — | 8 | 2 | no | — |
| 146 | #7389 | — | 8 | 2 | no | — |
| 147 | #7333 | — | 8 | 2 | no | — |
| 148 | #7332 | — | 4 | 1 | no | — |
| 149 | #7332 | — | 4 | 1 | no | — |
| 150 | #7331 | — | 4 | 2 | no | — |
| 151 | #7161 | — | 2 | 1 | no | — |
| 152 | #7157 | — | 2 | 1 | no | — |
| 153 | #7140 | — | 4 | 1 | no | — |
| 154 | C2×#508 | — | 4 | 1 | no | — |
| 155 | C2×#508 | — | 4 | 1 | no | — |
| 156 | C2×#508 | — | 4 | 1 | no | — |
| 157 | C2×#508 | — | 4 | 1 | no | — |
| 158 | #3169 | — | 8 | 1 | no | — |
| 159 | #3147 | — | 4 | 1 | no | — |
| 160 | C2×#443 | — | 8 | 1 | no | — |
| 161 | C2×#443 | — | 8 | 1 | no | — |
| 162 | #2931 | — | 8 | 1 | no | — |
| 163 | C2×M64 | — | 2 | 2 | no | — |
| 164 | C2×M64 | — | 4 | 1 | no | — |
| 165 | C2×M64 | — | 4 | 1 | no | — |
| 166 | C2×M64 | — | 4 | 1 | no | — |
| 167 | C2×M64 | — | 4 | 1 | no | — |
| 168 | C2×M64 | — | 4 | 1 | no | — |
| 169 | C2×M64 | — | 8 | 1 | no | — |
| 170 | #2249 | — | 4 | 1 | no | — |
| 171 | #2249 | — | 4 | 1 | no | — |
| 172 | #2249 | — | 4 | 1 | no | — |
| 173 | #2249 | — | 4 | 1 | no | — |
| 174 | #2248 | — | 4 | 1 | no | — |
| 175 | #2248 | — | 4 | 1 | no | — |
| 176 | #2247 | — | 2 | 1 | no | — |
| 177 | #2247 | — | 2 | 1 | no | — |
| 178 | #2246 | — | 2 | 1 | no | — |
| 179 | #2246 | — | 2 | 1 | no | — |
| 180 | #2179 | — | 8 | 1 | no | — |
| 181 | #2179 | — | 8 | 1 | no | — |
| 182 | #2179 | — | 8 | 1 | no | — |
| 183 | #2179 | — | 8 | 1 | no | — |
| 184 | #2179 | — | 8 | 2 | no | — |
| 185 | #2179 | — | 8 | 1 | no | — |
| 186 | #2179 | — | 8 | 1 | no | — |
| 187 | #2179 | — | 8 | 1 | no | — |
| 188 | #2179 | — | 8 | 1 | no | — |
| 189 | #2179 | — | 8 | 2 | no | — |
| 190 | #2179 | — | 16 | 1 | no | — |
| 191 | #2179 | — | 16 | 1 | no | — |
| 192 | C2×#368 | — | 4 | 1 | no | — |
| 193 | C2×#368 | — | 4 | 1 | no | — |
| 194 | C2×#368 | — | 4 | 1 | no | — |
| 195 | C2×#368 | — | 4 | 1 | no | — |
| 196 | C2×#364 | — | 4 | 1 | no | — |
| 197 | C2×#359 | — | 8 | 1 | no | — |
| 198 | C2×#359 | — | 8 | 1 | no | — |
| 199 | C2×#359 | — | 8 | 1 | no | — |
| 200 | C2×#359 | — | 8 | 1 | no | — |
| 201 | C4×M32 | — | 4 | 1 | no | — |
| 202 | C2×#346 | C2×SD16 | 1 | 1 | yes | characteristic |
| 203 | C2×#346 | #135 | 1 | 1 | yes | characteristic |
| 204 | C2×#346 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 205 | C2×#346 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 206 | C2×#346 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 207 | C2×#346 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 208 | C2×#346 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 209 | C2×#346 | #137 | 1 | 1 | yes | characteristic |
| 210 | C2×C4×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 211 | C2×C4×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 212 | C2×C4×C16 | #123 | 1 | 1 | yes | characteristic |
| 213 | C2×C4×C16 | #124 | 1 | 1 | yes | characteristic |
| 214 | #1974 | — | 8 | 1 | no | — |
| 215 | #1974 | — | 8 | 1 | no | — |
| 216 | #1962 | — | 8 | 1 | no | — |
| 217 | #1848 | — | 4 | 1 | no | — |
| 218 | #1842 | — | 8 | 1 | no | — |
| 219 | C42×C8 | — | 2 | 1 | no | — |
| 220 | C42×C8 | #121 | 1 | 1 | yes | characteristic |
| 221 | #1713 | — | 2 | 1 | no | — |
| 222 | #1712 | — | 2 | 1 | no | — |
| 223 | #1709 | — | 4 | 1 | no | — |
| 224 | #1706 | — | 8 | 1 | no | — |
| 225 | #1589 | — | 16 | 2 | no | — |
| 226 | C8×D8 | — | 16 | 2 | no | — |
| 227 | #1567 | — | 8 | 1 | no | — |
| 228 | #1564 | — | 4 | 1 | no | — |
| 229 | C2×#334 | — | 8 | 1 | no | — |
| 230 | C2×#334 | — | 8 | 1 | no | — |
| 231 | C2×#334 | — | 16 | 2 | no | — |
| 232 | #1492 | — | 8 | 2 | no | — |
| 233 | #1450 | — | 4 | 1 | no | — |
| 234 | C2×C82 | — | 2 | 1 | no | — |
| 235 | C2×C82 | #117 | 1 | 1 | yes | characteristic |
| 236 | C2×C82 | #126 | 1 | 1 | yes | characteristic |
| 237 | #1422 | — | 2 | 2 | no | — |
| 238 | #1422 | — | 2 | 2 | no | — |
| 239 | #1422 | — | 2 | 2 | no | — |
| 240 | #1422 | — | 4 | 2 | no | — |
| 241 | #1422 | — | 4 | 1 | no | — |
| 242 | #1422 | — | 4 | 1 | no | — |
| 243 | #1422 | — | 4 | 1 | no | — |
| 244 | #1422 | — | 4 | 1 | no | — |
| 245 | #1422 | — | 4 | 1 | no | — |
| 246 | #1422 | — | 8 | 1 | no | — |
| 247 | #1398 | — | 4 | 2 | no | — |
| 248 | #1398 | — | 4 | 1 | no | — |
| 249 | #1398 | — | 4 | 1 | no | — |
| 250 | #1398 | — | 4 | 1 | no | — |
| 251 | #1398 | — | 4 | 1 | no | — |
| 252 | #1398 | — | 8 | 1 | no | — |
| 253 | #1398 | — | 8 | 1 | no | — |
| 254 | #1398 | — | 8 | 1 | no | — |
| 255 | #1398 | — | 8 | 1 | no | — |
| 256 | #1398 | — | 8 | 1 | no | — |
| 257 | #1398 | — | 8 | 1 | no | — |
| 258 | #1398 | — | 8 | 1 | no | — |
| 259 | #1397 | — | 4 | 1 | no | — |
| 260 | #1397 | — | 4 | 1 | no | — |
| 261 | C4×C32 | — | 2 | 2 | no | — |
| 262 | C4×C32 | — | 4 | 1 | no | — |
| 263 | #1376 | — | 4 | 1 | no | — |
| 264 | #1369 | — | 4 | 1 | no | — |
| 265 | #1369 | — | 4 | 1 | no | — |
| 266 | #1368 | — | 4 | 1 | no | — |
| 267 | #1368 | — | 4 | 1 | no | — |
| 268 | #1368 | — | 8 | 1 | no | — |
| 269 | #1368 | — | 8 | 1 | no | — |
| 270 | #1368 | — | 8 | 1 | no | — |
| 271 | #1368 | — | 8 | 2 | no | — |
| 272 | #1368 | — | 8 | 1 | no | — |
| 273 | #1368 | — | 16 | 1 | no | — |
| 274 | #1313 | — | 8 | 1 | no | — |
| 275 | #1313 | — | 8 | 1 | no | — |
| 276 | #1311 | — | 2 | 1 | no | — |
| 277 | #1311 | — | 2 | 1 | no | — |
| 278 | #1311 | — | 2 | 1 | no | — |
| 279 | #1311 | — | 2 | 1 | no | — |
| 280 | C8×C16 | — | 4 | 1 | no | — |
| 281 | C8×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 282 | C8×C16 | C2×M16 | 1 | 1 | yes | characteristic |
| 283 | C8×C16 | #131 | 1 | 1 | yes | characteristic |
| 284 | C8×C16 | #131 | 1 | 1 | yes | characteristic |
| 285 | #1276 | — | 4 | 1 | no | — |
| 286 | C2×#135 | — | 8 | 1 | no | — |
| 287 | C2×#135 | — | 8 | 1 | no | — |
| 288 | C2×#131 | — | 16 | 1 | no | — |
| 289 | #532 | — | 8 | 1 | no | — |
| 290 | #508 | — | 8 | 2 | no | — |
| 291 | #508 | — | 8 | 2 | no | — |
| 292 | #508 | — | 8 | 1 | no | — |
| 293 | #508 | — | 8 | 1 | no | — |
| 294 | #508 | — | 8 | 1 | no | — |
| 295 | #508 | — | 8 | 1 | no | — |
| 296 | #508 | — | 8 | 1 | no | — |
| 297 | #508 | — | 8 | 1 | no | — |
| 298 | #508 | — | 8 | 1 | no | — |
| 299 | #508 | — | 8 | 1 | no | — |
| 300 | #508 | — | 16 | 1 | no | — |
| 301 | #508 | — | 16 | 1 | no | — |
| 302 | C2×Q32 | — | 4 | 1 | no | — |
| 303 | C2×Q32 | — | 4 | 1 | no | — |
| 304 | C2×Q32 | — | 4 | 1 | no | — |
| 305 | C2×Q32 | — | 4 | 1 | no | — |
| 306 | C2×SD32 | — | 8 | 1 | no | — |
| 307 | C2×SD32 | — | 8 | 1 | no | — |
| 308 | C2×SD32 | — | 8 | 1 | no | — |
| 309 | C2×SD32 | — | 8 | 1 | no | — |
| 310 | C2×D16 | — | 4 | 1 | no | — |
| 311 | C2×D16 | — | 4 | 1 | no | — |
| 312 | C2×D16 | — | 4 | 1 | no | — |
| 313 | C2×D16 | — | 4 | 1 | no | — |
| 314 | C2×M32 | — | 8 | 1 | no | — |
| 315 | C22×C16 | C4×SD16 | 1 | 1 | yes | characteristic |
| 316 | C22×C16 | #440 | 1 | 1 | yes | characteristic |
| 317 | C22×C16 | #442 | 1 | 1 | yes | characteristic |
| 318 | C22×C16 | #442 | 1 | 1 | yes | characteristic |
| 319 | C22×C16 | #481 | 1 | 1 | yes | characteristic |
| 320 | C22×C16 | #482 | 1 | 1 | yes | characteristic |
| 321 | C22×C16 | #489 | 1 | 1 | yes | characteristic |
| 322 | C22×C16 | #490 | 1 | 1 | yes | characteristic |
| 323 | #500 | — | 8 | 1 | no | — |
| 324 | #495 | — | 8 | 1 | no | — |
| 325 | #495 | — | 8 | 1 | no | — |
| 326 | #494 | — | 4 | 1 | no | — |
| 327 | #493 | — | 4 | 1 | no | — |
| 328 | #493 | — | 8 | 1 | no | — |
| 329 | #492 | — | 8 | 1 | no | — |
| 330 | #486 | — | 8 | 2 | no | — |
| 331 | #466 | — | 16 | 2 | no | — |
| 332 | #443 | — | 16 | 1 | no | — |
| 333 | #443 | — | 16 | 1 | no | — |
| 334 | #443 | — | 16 | 1 | no | — |
| 335 | #443 | — | 16 | 1 | no | — |
| 336 | #443 | — | 16 | 1 | no | — |
| 337 | #443 | — | 16 | 1 | no | — |
| 338 | #443 | — | 16 | 1 | no | — |
| 339 | #443 | — | 16 | 1 | no | — |
| 340 | C4×D8 | — | 16 | 2 | no | — |
| 341 | #436 | — | 16 | 2 | no | — |
| 342 | C8×D4 | — | 16 | 2 | no | — |
| 343 | #431 | — | 8 | 1 | no | — |
| 344 | C2×#108 | — | 8 | 1 | no | — |
| 345 | C2×#108 | — | 8 | 1 | no | — |
| 346 | #423 | — | 8 | 1 | no | — |
| 347 | C2×C4⋊C8 | — | 16 | 2 | no | — |
| 348 | C2×C4⋊C8 | — | 16 | 1 | no | — |
| 349 | C2×#104 | — | 16 | 1 | no | — |
| 350 | C2×#104 | — | 16 | 1 | no | — |
| 351 | #408 | — | 16 | 1 | no | — |
| 352 | C2×C4×C8 | — | 2 | 1 | no | — |
| 353 | C2×C4×C8 | — | 2 | 1 | no | — |
| 354 | C2×C4×C8 | — | 4 | 2 | no | — |
| 355 | C2×C4×C8 | #388 | 1 | 1 | yes | characteristic |
| 356 | C2×C4×C8 | #460 | 1 | 1 | yes | characteristic |
| 357 | C2×C4×C8 | #463 | 1 | 1 | yes | characteristic |
| 358 | C2×C4×C8 | #468 | 1 | 1 | yes | characteristic |
| 359 | C2×C4×C8 | #469 | 1 | 1 | yes | characteristic |
| 360 | C2×C4×C8 | #471 | 1 | 1 | yes | characteristic |
| 361 | C43 | #472 | 1 | 1 | yes | characteristic |
| 362 | M64 | — | 4 | 2 | no | — |
| 363 | M64 | — | 4 | 2 | no | — |
| 364 | M64 | — | 4 | 2 | no | — |
| 365 | M64 | — | 4 | 2 | no | — |
| 366 | M64 | — | 4 | 2 | no | — |
| 367 | M64 | — | 8 | 1 | no | — |
| 368 | M64 | — | 8 | 1 | no | — |
| 369 | M64 | — | 8 | 1 | no | — |
| 370 | M64 | — | 8 | 1 | no | — |
| 371 | M64 | — | 8 | 1 | no | — |
| 372 | M64 | — | 8 | 2 | no | — |
| 373 | M64 | — | 8 | 1 | no | — |
| 374 | M64 | — | 8 | 1 | no | — |
| 375 | M64 | — | 16 | 1 | no | — |
| 376 | C2×C32 | — | 4 | 2 | no | — |
| 377 | C2×C32 | — | 4 | 2 | no | — |
| 378 | C2×C32 | — | 8 | 1 | no | — |
| 379 | C2×C32 | — | 8 | 1 | no | — |
| 380 | C2×C32 | — | 8 | 1 | no | — |
| 381 | C2×C32 | — | 8 | 1 | no | — |
| 382 | C2×C32 | — | 16 | 1 | no | — |
| 383 | #368 | — | 8 | 2 | no | — |
| 384 | #368 | — | 8 | 1 | no | — |
| 385 | #368 | — | 8 | 1 | no | — |
| 386 | #368 | — | 8 | 1 | no | — |
| 387 | #368 | — | 8 | 1 | no | — |
| 388 | #368 | — | 16 | 1 | no | — |
| 389 | #364 | — | 8 | 1 | no | — |
| 390 | #364 | — | 8 | 1 | no | — |
| 391 | #359 | — | 16 | 1 | no | — |
| 392 | #359 | — | 16 | 1 | no | — |
| 393 | #359 | — | 16 | 1 | no | — |
| 394 | #359 | — | 16 | 1 | no | — |
| 395 | #359 | — | 16 | 2 | no | — |
| 396 | #359 | — | 16 | 2 | no | — |
| 397 | #346 | — | 2 | 1 | no | — |
| 398 | #346 | — | 2 | 1 | no | — |
| 399 | #346 | — | 2 | 1 | no | — |
| 400 | #346 | — | 2 | 1 | no | — |
| 401 | #346 | — | 2 | 1 | no | — |
| 402 | #346 | — | 2 | 1 | no | — |
| 403 | #346 | — | 2 | 1 | no | — |
| 404 | #346 | — | 2 | 1 | no | — |
| 405 | #346 | — | 2 | 2 | no | — |
| 406 | #346 | — | 4 | 1 | no | — |
| 407 | #346 | — | 4 | 1 | no | — |
| 408 | #346 | — | 4 | 1 | no | — |
| 409 | #346 | — | 8 | 1 | no | — |
| 410 | C4×C16 | — | 2 | 1 | no | — |
| 411 | C4×C16 | — | 2 | 1 | no | — |
| 412 | C4×C16 | — | 2 | 1 | no | — |
| 413 | C4×C16 | — | 2 | 1 | no | — |
| 414 | C4×C16 | — | 8 | 1 | no | — |
| 415 | C4×C16 | C8×D4 | 1 | 1 | yes | characteristic |
| 416 | C4×C16 | C8×D4 | 1 | 1 | yes | characteristic |
| 417 | C4×C16 | #435 | 1 | 1 | yes | characteristic |
| 418 | C4×C16 | #436 | 1 | 1 | yes | characteristic |
| 419 | C4×C16 | #443 | 1 | 1 | yes | characteristic |
| 420 | C4×C16 | #444 | 1 | 1 | yes | characteristic |
| 421 | C4×C16 | #444 | 1 | 1 | yes | characteristic |
| 422 | C4×C16 | #444 | 1 | 1 | yes | characteristic |
| 423 | #335 | — | 8 | 1 | no | — |
| 424 | #335 | — | 16 | 2 | no | — |
| 425 | #334 | — | 8 | 1 | no | — |
| 426 | #334 | — | 16 | 1 | no | — |
| 427 | #334 | — | 16 | 1 | no | — |
| 428 | #334 | — | 16 | 1 | no | — |
| 429 | #334 | — | 16 | 1 | no | — |
| 430 | #334 | — | 32 | 4 | no | — |
| 431 | D4⋊C8 | — | 16 | 4 | no | — |
| 432 | #322 | — | 8 | 1 | no | — |
| 433 | C82 | — | 2 | 1 | no | — |
| 434 | C82 | — | 2 | 1 | no | — |
| 435 | C82 | — | 2 | 1 | no | — |
| 436 | C82 | — | 4 | 2 | no | — |
| 437 | C82 | — | 8 | 1 | no | — |
| 438 | C82 | #431 | 1 | 1 | yes | characteristic |
| 439 | C82 | #433 | 1 | 1 | yes | characteristic |
| 440 | C2×#41 | — | 16 | 1 | no | — |
| 441 | #135 | — | 16 | 1 | no | — |
| 442 | #135 | — | 16 | 1 | no | — |
| 443 | #135 | — | 16 | 1 | no | — |
| 444 | #135 | — | 16 | 1 | no | — |
| 445 | #135 | — | 16 | 1 | no | — |
| 446 | #135 | — | 16 | 1 | no | — |
| 447 | #135 | — | 16 | 1 | no | — |
| 448 | #135 | — | 16 | 1 | no | — |
| 449 | C2×Q16 | — | 8 | 1 | no | — |
| 450 | C2×Q16 | — | 8 | 1 | no | — |
| 451 | C2×SD16 | — | 16 | 1 | no | — |
| 452 | C2×SD16 | — | 16 | 1 | no | — |
| 453 | C2×D8 | — | 8 | 1 | no | — |
| 454 | C2×D8 | — | 8 | 1 | no | — |
| 455 | C2×D8 | — | 16 | 2 | no | — |
| 456 | #131 | — | 32 | 1 | no | — |
| 457 | #131 | — | 32 | 1 | no | — |
| 458 | #131 | — | 32 | 1 | no | — |
| 459 | #131 | — | 32 | 1 | no | — |
| 460 | C2×M16 | — | 16 | 1 | no | — |
| 461 | C2×M16 | — | 32 | 1 | no | — |
| 462 | C22×C8 | — | 2 | 2 | no | — |
| 463 | C22×C8 | — | 4 | 1 | no | — |
| 464 | C22×C8 | — | 32 | 1 | no | — |
| 465 | C22×C8 | — | 32 | 1 | no | — |
| 466 | C22×C8 | #1686 | 1 | 1 | yes | characteristic |
| 467 | C22×C8 | #1701 | 1 | 1 | yes | characteristic |
| 468 | C22×C8 | #1926 | 1 | 1 | yes | characteristic |
| 469 | C22×C8 | #1936 | 1 | 1 | yes | characteristic |
| 470 | C4⋊Q8 | — | 8 | 1 | no | — |
| 471 | #127 | — | 8 | 1 | no | — |
| 472 | #124 | — | 16 | 1 | no | — |
| 473 | #121 | — | 16 | 2 | no | — |
| 474 | C4×D4 | — | 16 | 2 | no | — |
| 475 | C2×C42 | — | 4 | 1 | no | — |
| 476 | C2×C42 | #1688 | 1 | 1 | yes | characteristic |
| 477 | C2×C42 | #1697 | 1 | 1 | yes | characteristic |
| 478 | C2×C42 | #1931 | 1 | 1 | yes | characteristic |
| 479 | Q32 | — | 8 | 2 | no | — |
| 480 | Q32 | — | 8 | 1 | no | — |
| 481 | Q32 | — | 8 | 1 | no | — |
| 482 | Q32 | — | 8 | 1 | no | — |
| 483 | Q32 | — | 8 | 1 | no | — |
| 484 | Q32 | — | 16 | 1 | no | — |
| 485 | SD32 | — | 16 | 2 | no | — |
| 486 | SD32 | — | 16 | 2 | no | — |
| 487 | SD32 | — | 16 | 1 | no | — |
| 488 | SD32 | — | 16 | 1 | no | — |
| 489 | SD32 | — | 16 | 1 | no | — |
| 490 | SD32 | — | 16 | 1 | no | — |
| 491 | D16 | — | 8 | 2 | no | — |
| 492 | D16 | — | 8 | 1 | no | — |
| 493 | D16 | — | 8 | 1 | no | — |
| 494 | D16 | — | 8 | 1 | no | — |
| 495 | D16 | — | 8 | 1 | no | — |
| 496 | D16 | — | 16 | 1 | no | — |
| 497 | M32 | — | 16 | 1 | no | — |
| 498 | M32 | — | 16 | 1 | no | — |
| 499 | C2×C16 | — | 2 | 1 | no | — |
| 500 | C2×C16 | — | 2 | 1 | no | — |
| 501 | C2×C16 | — | 2 | 1 | no | — |
| 502 | C2×C16 | — | 2 | 1 | no | — |
| 503 | C2×C16 | — | 2 | 1 | no | — |
| 504 | C2×C16 | — | 2 | 1 | no | — |
| 505 | C2×C16 | — | 2 | 1 | no | — |
| 506 | C2×C16 | — | 2 | 1 | no | — |
| 507 | C2×C16 | — | 2 | 1 | no | — |
| 508 | C2×C16 | — | 2 | 1 | no | — |
| 509 | C2×C16 | — | 2 | 1 | no | — |
| 510 | C2×C16 | — | 2 | 1 | no | — |
| 511 | C2×C16 | — | 2 | 1 | no | — |
| 512 | C2×C16 | — | 2 | 1 | no | — |
| 513 | C2×C16 | — | 2 | 1 | no | — |
| 514 | C2×C16 | — | 16 | 1 | no | — |
| 515 | C2×C16 | C8×SD16 | 1 | 1 | yes | characteristic |
| 516 | C2×C16 | SD16⋊C8 | 1 | 1 | yes | characteristic |
| 517 | C2×C16 | #1580 | 1 | 1 | yes | characteristic |
| 518 | C2×C16 | #1580 | 1 | 1 | yes | characteristic |
| 519 | C2×C16 | #1583 | 1 | 1 | yes | characteristic |
| 520 | C2×C16 | #1586 | 1 | 1 | yes | characteristic |
| 521 | C2×C16 | #1592 | 1 | 1 | yes | characteristic |
| 522 | C2×C16 | #1594 | 1 | 1 | yes | characteristic |
| 523 | C2×C16 | #2180 | 1 | 1 | yes | characteristic |
| 524 | C2×C16 | #2180 | 1 | 1 | yes | characteristic |
| 525 | C2×C16 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 526 | C2×C16 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 527 | C2×C16 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 528 | C2×C16 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 529 | C2×C16 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 530 | C2×C16 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 531 | C2×C16 | #2238 | 1 | 2 | yes | — |
| 532 | #108 | — | 16 | 1 | no | — |
| 533 | #108 | — | 16 | 1 | no | — |
| 534 | #108 | — | 16 | 1 | no | — |
| 535 | #108 | — | 16 | 1 | no | — |
| 536 | #107 | — | 16 | 2 | no | — |
| 537 | C4⋊C8 | — | 16 | 2 | no | — |
| 538 | C4⋊C8 | — | 16 | 1 | no | — |
| 539 | C4⋊C8 | — | 32 | 1 | no | — |
| 540 | C4⋊C8 | — | 32 | 1 | no | — |
| 541 | C4⋊C8 | — | 32 | 4 | no | — |
| 542 | #104 | — | 32 | 1 | no | — |
| 543 | #104 | — | 32 | 1 | no | — |
| 544 | #104 | — | 32 | 1 | no | — |
| 545 | #104 | — | 32 | 1 | no | — |
| 546 | #102 | — | 16 | 4 | no | — |
| 547 | C22⋊C8 | — | 16 | 1 | no | — |
| 548 | C22⋊C8 | — | 32 | 2 | no | — |
| 549 | C4×C8 | — | 2 | 2 | no | — |
| 550 | C4×C8 | — | 2 | 1 | no | — |
| 551 | C4×C8 | — | 2 | 1 | no | — |
| 552 | C4×C8 | — | 2 | 1 | no | — |
| 553 | C4×C8 | — | 2 | 1 | no | — |
| 554 | C4×C8 | — | 2 | 1 | no | — |
| 555 | C4×C8 | — | 2 | 1 | no | — |
| 556 | C4×C8 | — | 2 | 1 | no | — |
| 557 | C4×C8 | — | 2 | 1 | no | — |
| 558 | C4×C8 | — | 2 | 1 | no | — |
| 559 | C4×C8 | — | 2 | 1 | no | — |
| 560 | C4×C8 | — | 4 | 1 | no | — |
| 561 | C4×C8 | — | 4 | 1 | no | — |
| 562 | C4×C8 | — | 4 | 1 | no | — |
| 563 | C4×C8 | — | 8 | 4 | no | — |
| 564 | C4×C8 | — | 16 | 1 | no | — |
| 565 | C4×C8 | #1923 | 1 | 1 | yes | characteristic |
| 566 | C4×C8 | #1929 | 1 | 1 | yes | characteristic |
| 567 | C4×C8 | #1932 | 1 | 1 | yes | characteristic |
| 568 | C4×C8 | #1938 | 1 | 1 | yes | characteristic |
| 569 | C32 | — | 8 | 2 | no | — |
| 570 | C32 | — | 8 | 2 | no | — |
| 571 | C32 | — | 8 | 2 | no | — |
| 572 | C32 | — | 8 | 2 | no | — |
| 573 | C32 | — | 8 | 2 | no | — |
| 574 | C32 | — | 16 | 2 | no | — |
| 575 | C32 | — | 16 | 1 | no | — |
| 576 | #41 | — | 32 | 1 | no | — |
| 577 | #41 | — | 32 | 1 | no | — |
| 578 | #41 | — | 32 | 1 | no | — |
| 579 | #41 | — | 32 | 1 | no | — |
| 580 | C2×Q8 | — | 16 | 1 | no | — |
| 581 | C2×D4 | — | 16 | 2 | no | — |
| 582 | C2×D4 | — | 16 | 1 | no | — |
| 583 | C2×D4 | — | 32 | 1 | no | — |
| 584 | C22×C4 | — | 2 | 1 | no | — |
| 585 | C22×C4 | — | 2 | 1 | no | — |
| 586 | C22×C4 | — | 2 | 1 | no | — |
| 587 | C22×C4 | — | 32 | 1 | no | — |
| 588 | C22×C4 | #9572 | 1 | 1 | yes | characteristic |
| 589 | Q16 | — | 16 | 1 | no | — |
| 590 | Q16 | — | 16 | 1 | no | — |
| 591 | Q16 | — | 16 | 1 | no | — |
| 592 | Q16 | — | 16 | 1 | no | — |
| 593 | SD16 | — | 32 | 1 | no | — |
| 594 | SD16 | — | 32 | 1 | no | — |
| 595 | SD16 | — | 32 | 1 | no | — |
| 596 | SD16 | — | 32 | 1 | no | — |
| 597 | D8 | — | 16 | 1 | no | — |
| 598 | D8 | — | 16 | 1 | no | — |
| 599 | D8 | — | 16 | 1 | no | — |
| 600 | D8 | — | 16 | 1 | no | — |
| 601 | D8 | — | 32 | 4 | no | — |
| 602 | M16 | — | 32 | 1 | no | — |
| 603 | M16 | — | 32 | 1 | no | — |
| 604 | M16 | — | 64 | 1 | no | — |
| 605 | M16 | — | 64 | 1 | no | — |
| 606 | C2×C8 | — | 2 | 2 | no | — |
| 607 | C2×C8 | — | 2 | 2 | no | — |
| 608 | C2×C8 | — | 2 | 1 | no | — |
| 609 | C2×C8 | — | 2 | 1 | no | — |
| 610 | C2×C8 | — | 2 | 1 | no | — |
| 611 | C2×C8 | — | 2 | 1 | no | — |
| 612 | C2×C8 | — | 2 | 1 | no | — |
| 613 | C2×C8 | — | 2 | 1 | no | — |
| 614 | C2×C8 | — | 4 | 4 | no | — |
| 615 | C2×C8 | — | 8 | 1 | no | — |
| 616 | C2×C8 | — | 8 | 2 | no | — |
| 617 | C2×C8 | — | 32 | 1 | no | — |
| 618 | C2×C8 | — | 32 | 1 | no | — |
| 619 | C2×C8 | — | 64 | 1 | no | — |
| 620 | C2×C8 | — | 64 | 1 | no | — |
| 621 | C2×C8 | — | 64 | 1 | no | — |
| 622 | C2×C8 | — | 64 | 2 | no | — |
| 623 | C2×C8 | #9542 | 1 | 1 | yes | characteristic |
| 624 | C2×C8 | #9556 | 1 | 1 | yes | characteristic |
| 625 | C2×C8 | #9582 | 1 | 1 | yes | characteristic |
| 626 | C2×C8 | #9592 | 1 | 1 | yes | characteristic |
| 627 | C2×C8 | #13138 | 1 | 1 | yes | characteristic |
| 628 | C2×C8 | #13140 | 1 | 1 | yes | characteristic |
| 629 | C2×C8 | #13142 | 1 | 1 | yes | characteristic |
| 630 | C2×C8 | #13143 | 1 | 1 | yes | characteristic |
| 631 | C2×C8 | #13153 | 1 | 1 | yes | characteristic |
| 632 | C2×C8 | #13155 | 1 | 1 | yes | characteristic |
| 633 | C2×C8 | #13156 | 1 | 1 | yes | characteristic |
| 634 | C2×C8 | #13158 | 1 | 1 | yes | characteristic |
| 635 | C4⋊C4 | — | 16 | 2 | no | — |
| 636 | C22⋊C4 | — | 32 | 2 | no | — |
| 637 | C42 | — | 2 | 1 | no | — |
| 638 | C42 | — | 2 | 1 | no | — |
| 639 | C42 | — | 2 | 1 | no | — |
| 640 | C42 | — | 2 | 1 | no | — |
| 641 | C42 | — | 2 | 1 | no | — |
| 642 | C42 | — | 8 | 2 | no | — |
| 643 | C42 | #9550 | 1 | 1 | yes | characteristic |
| 644 | C42 | #9588 | 1 | 1 | yes | characteristic |
| 645 | C16 | — | 2 | 2 | no | — |
| 646 | C16 | — | 2 | 1 | no | — |
| 647 | C16 | — | 2 | 1 | no | — |
| 648 | C16 | — | 2 | 1 | no | — |
| 649 | C16 | — | 2 | 1 | no | — |
| 650 | C16 | — | 4 | 1 | no | — |
| 651 | C16 | — | 4 | 1 | no | — |
| 652 | C16 | — | 4 | 1 | no | — |
| 653 | C16 | — | 32 | 1 | no | — |
| 654 | C16 | #12065 | 1 | 1 | yes | characteristic |
| 655 | C16 | #12065 | 1 | 1 | yes | characteristic |
| 656 | C16 | #12067 | 1 | 1 | yes | characteristic |
| 657 | C16 | #12067 | 1 | 1 | yes | characteristic |
| 658 | C16 | #12078 | 1 | 1 | yes | characteristic |
| 659 | C16 | #12080 | 1 | 1 | yes | characteristic |
| 660 | C16 | #12087 | 1 | 1 | yes | characteristic |
| 661 | C16 | #12089 | 1 | 1 | yes | characteristic |
| 662 | C23 | — | 32 | 1 | no | — |
| 663 | C23 | #140287 | 1 | 1 | yes | characteristic |
| 664 | Q8 | — | 32 | 1 | no | — |
| 665 | Q8 | — | 32 | 1 | no | — |
| 666 | D4 | — | 32 | 4 | no | — |
| 667 | D4 | — | 32 | 1 | no | — |
| 668 | D4 | — | 32 | 1 | no | — |
| 669 | D4 | — | 64 | 1 | no | — |
| 670 | D4 | — | 64 | 1 | no | — |
| 671 | C2×C4 | — | 2 | 1 | no | — |
| 672 | C2×C4 | — | 2 | 1 | no | — |
| 673 | C2×C4 | — | 4 | 2 | no | — |
| 674 | C2×C4 | — | 4 | 1 | no | — |
| 675 | C2×C4 | — | 4 | 1 | no | — |
| 676 | C2×C4 | — | 8 | 1 | no | — |
| 677 | C2×C4 | — | 8 | 1 | no | — |
| 678 | C2×C4 | — | 32 | 1 | no | — |
| 679 | C2×C4 | — | 64 | 1 | no | — |
| 680 | C2×C4 | — | 64 | 1 | no | — |
| 681 | C2×C4 | #101906 | 1 | 1 | yes | characteristic |
| 682 | C2×C4 | #140284 | 1 | 1 | yes | characteristic |
| 683 | C2×C4 | #140286 | 1 | 1 | yes | characteristic |
| 684 | C2×C4 | #140289 | 1 | 1 | yes | characteristic |
| 685 | C2×C4 | #140290 | 1 | 1 | yes | characteristic |
| 686 | C2×C4 | #140292 | 1 | 1 | yes | characteristic |
| 687 | C8 | — | 2 | 4 | no | — |
| 688 | C8 | — | 4 | 2 | no | — |
| 689 | C8 | — | 4 | 1 | no | — |
| 690 | C8 | — | 4 | 1 | no | — |
| 691 | C8 | — | 16 | 1 | no | — |
| 692 | C8 | — | 64 | 1 | no | — |
| 693 | C8 | — | 64 | 1 | no | — |
| 694 | C8 | — | 128 | 1 | no | — |
| 695 | C8 | #140118 | 1 | 1 | yes | characteristic |
| 696 | C8 | #140121 | 1 | 1 | yes | characteristic |
| 697 | C8 | #140188 | 1 | 1 | yes | characteristic |
| 698 | C8 | #140190 | 1 | 1 | yes | characteristic |
| 699 | C8 | #140319 | 1 | 1 | yes | characteristic |
| 700 | C8 | #140322 | 1 | 1 | yes | characteristic |
| 701 | C8 | #140332 | 1 | 1 | yes | characteristic |
| 702 | C8 | #140334 | 1 | 1 | yes | characteristic |
| 703 | C22 | — | 4 | 1 | no | — |
| 704 | C22 | — | 64 | 2 | no | — |
| 705 | C22 | — | 64 | 1 | no | — |
| 706 | C22 | #72216476 | 1 | 1 | yes | characteristic |
| 707 | C22 | #72227261 | 1 | 1 | yes | characteristic |
| 708 | C22 | #72227264 | 1 | 1 | yes | characteristic |
| 709 | C4 | — | 2 | 2 | no | — |
| 710 | C4 | — | 4 | 1 | no | — |
| 711 | C4 | — | 8 | 1 | no | — |
| 712 | C4 | — | 8 | 1 | no | — |
| 713 | C4 | — | 64 | 1 | no | — |
| 714 | C4 | #72216338 | 1 | 1 | yes | characteristic |
| 715 | C4 | #72227054 | 1 | 1 | yes | characteristic |
| 716 | C4 | #72227263 | 1 | 1 | yes | characteristic |
| 717 | C4 | #72227265 | 1 | 1 | yes | characteristic |
| 718 | C2 | — | 2 | 1 | no | — |
| 719 | C2 | — | 2 | 1 | no | — |
| 720 | C2 | — | 2 | 1 | no | — |
| 721 | C2 | — | 128 | 1 | no | — |
| 722 | C2 | #72227266 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta