← #72227074
Subgroups — #72227074
Order 2048.
769 conjugacy classes of subgroups.
The subgroup lattice has 529 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72225526 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72225420 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72225350 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72225316 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72225172 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #72216421 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #72216259 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #496104 | C22 | 1 | 1 | yes | characteristic |
| 9 | #483596 | — | 2 | 1 | no | — |
| 10 | #231469 | — | 2 | 1 | no | — |
| 11 | #151981 | C22 | 1 | 1 | yes | characteristic |
| 12 | C4×#1398 | C22 | 1 | 1 | yes | characteristic |
| 13 | #151024 | — | 2 | 1 | no | — |
| 14 | C2×#7448 | C4 | 1 | 1 | yes | characteristic |
| 15 | C2×#7448 | C4 | 1 | 1 | yes | characteristic |
| 16 | C2×#7390 | — | 2 | 2 | no | — |
| 17 | #140849 | — | 2 | 1 | no | — |
| 18 | #140747 | — | 2 | 1 | no | — |
| 19 | #140393 | — | 2 | 1 | no | — |
| 20 | #136703 | — | 2 | 2 | no | — |
| 21 | #135718 | C22 | 1 | 1 | yes | characteristic |
| 22 | #129101 | C22 | 1 | 1 | yes | characteristic |
| 23 | #129088 | C22 | 1 | 1 | yes | characteristic |
| 24 | #129051 | C22 | 1 | 1 | yes | characteristic |
| 25 | #94364 | C4 | 1 | 1 | yes | characteristic |
| 26 | #94364 | C4 | 1 | 1 | yes | characteristic |
| 27 | #94031 | — | 2 | 1 | no | — |
| 28 | #93448 | — | 2 | 1 | no | — |
| 29 | C2×#2246 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | C2×#2177 | — | 2 | 1 | no | — |
| 31 | C2×#2177 | D4 | 1 | 2 | yes | — |
| 32 | C4×#493 | — | 2 | 1 | no | — |
| 33 | #17854 | — | 2 | 2 | no | — |
| 34 | #17854 | — | 4 | 1 | no | — |
| 35 | C2×#1422 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | C2×#1422 | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | C2×#1398 | — | 2 | 1 | no | — |
| 38 | C2×#1398 | — | 2 | 1 | no | — |
| 39 | C2×#1398 | — | 2 | 1 | no | — |
| 40 | C4×M64 | — | 2 | 1 | no | — |
| 41 | #13239 | — | 2 | 1 | no | — |
| 42 | #13239 | Q8 | 1 | 2 | yes | — |
| 43 | #13202 | — | 2 | 1 | no | — |
| 44 | #12906 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | #12900 | — | 2 | 1 | no | — |
| 46 | C4×#364 | — | 2 | 1 | no | — |
| 47 | C4×#364 | D4 | 1 | 1 | yes | characteristic |
| 48 | C4×#346 | C23 | 1 | 1 | yes | characteristic |
| 49 | #12067 | — | 4 | 2 | no | — |
| 50 | #12067 | — | 4 | 2 | no | — |
| 51 | C2×#1373 | C2×C4 | 1 | 1 | yes | characteristic |
| 52 | C2×#1373 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | #12002 | — | 4 | 1 | no | — |
| 54 | C2×#1369 | — | 2 | 1 | no | — |
| 55 | C2×#1369 | — | 2 | 1 | no | — |
| 56 | #11999 | D4 | 1 | 1 | yes | characteristic |
| 57 | #11999 | D4 | 1 | 1 | yes | characteristic |
| 58 | #11599 | — | 2 | 2 | no | — |
| 59 | #11593 | — | 2 | 2 | no | — |
| 60 | #11405 | — | 2 | 1 | no | — |
| 61 | #9668 | — | 2 | 2 | no | — |
| 62 | #9668 | — | 4 | 1 | no | — |
| 63 | #8959 | — | 4 | 2 | no | — |
| 64 | #8266 | — | 2 | 1 | no | — |
| 65 | #8266 | D4 | 1 | 1 | yes | characteristic |
| 66 | #7468 | — | 2 | 1 | no | — |
| 67 | #7457 | — | 4 | 2 | no | — |
| 68 | #7448 | — | 2 | 2 | no | — |
| 69 | #7448 | C8 | 1 | 4 | yes | complemented |
| 70 | #7390 | — | 4 | 4 | no | — |
| 71 | #7162 | — | 4 | 1 | no | — |
| 72 | #7160 | — | 2 | 1 | no | — |
| 73 | #7157 | — | 2 | 1 | no | — |
| 74 | #7140 | — | 2 | 1 | no | — |
| 75 | C22×D16 | — | 2 | 1 | no | — |
| 76 | C22×D16 | C4⋊C4 | 1 | 2 | yes | — |
| 77 | C2×#493 | — | 2 | 1 | no | — |
| 78 | #2972 | — | 4 | 2 | no | — |
| 79 | C2×C4×D8 | — | 2 | 2 | no | — |
| 80 | C2×C4×D8 | — | 4 | 1 | no | — |
| 81 | C4×#127 | — | 4 | 1 | no | — |
| 82 | C2×M64 | — | 2 | 1 | no | — |
| 83 | C2×M64 | — | 2 | 1 | no | — |
| 84 | C2×M64 | — | 4 | 1 | no | — |
| 85 | #2246 | — | 2 | 1 | no | — |
| 86 | #2246 | — | 2 | 1 | no | — |
| 87 | #2246 | C2×C8 | 1 | 2 | yes | — |
| 88 | #2246 | M16 | 1 | 2 | yes | — |
| 89 | #2177 | — | 4 | 2 | no | — |
| 90 | #2177 | — | 4 | 2 | no | — |
| 91 | #2177 | — | 4 | 1 | no | — |
| 92 | #2177 | — | 4 | 1 | no | — |
| 93 | #2177 | — | 4 | 1 | no | — |
| 94 | #2177 | — | 4 | 1 | no | — |
| 95 | C2×#367 | — | 2 | 1 | no | — |
| 96 | C2×#367 | C4⋊C4 | 1 | 2 | yes | — |
| 97 | C2×#364 | — | 2 | 1 | no | — |
| 98 | C2×#364 | — | 2 | 1 | no | — |
| 99 | C2×#364 | — | 2 | 1 | no | — |
| 100 | C2×#364 | — | 4 | 1 | no | — |
| 101 | C2×#364 | — | 4 | 1 | no | — |
| 102 | #2150 | — | 4 | 1 | no | — |
| 103 | C2×#357 | — | 2 | 2 | no | — |
| 104 | C2×#357 | — | 2 | 2 | no | — |
| 105 | C4×M32 | — | 2 | 1 | no | — |
| 106 | C4×M32 | — | 4 | 1 | no | — |
| 107 | C2×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 108 | C2×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | C2×#346 | C2×Q8 | 1 | 1 | yes | characteristic |
| 110 | C2×#346 | #41 | 1 | 1 | yes | characteristic |
| 111 | C2×C4×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 112 | C2×C4×C16 | #41 | 1 | 1 | yes | characteristic |
| 113 | #1970 | — | 2 | 2 | no | — |
| 114 | #1970 | — | 4 | 1 | no | — |
| 115 | #1957 | — | 4 | 1 | no | — |
| 116 | #1845 | — | 2 | 1 | no | — |
| 117 | C42×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | #1580 | — | 4 | 4 | no | — |
| 119 | #1580 | — | 8 | 2 | no | — |
| 120 | C8×D8 | — | 8 | 2 | no | — |
| 121 | C8×D8 | — | 8 | 2 | no | — |
| 122 | #1564 | — | 2 | 1 | no | — |
| 123 | #1564 | — | 2 | 1 | no | — |
| 124 | #1564 | — | 2 | 1 | no | — |
| 125 | #1478 | — | 4 | 2 | no | — |
| 126 | #1478 | — | 4 | 2 | no | — |
| 127 | #1460 | — | 4 | 2 | no | — |
| 128 | #1450 | — | 2 | 1 | no | — |
| 129 | #1450 | — | 4 | 1 | no | — |
| 130 | #1422 | — | 2 | 1 | no | — |
| 131 | #1422 | — | 2 | 1 | no | — |
| 132 | #1422 | — | 2 | 1 | no | — |
| 133 | #1422 | C2×C8 | 1 | 2 | yes | complemented |
| 134 | #1398 | — | 2 | 2 | no | — |
| 135 | #1398 | — | 2 | 2 | no | — |
| 136 | #1398 | — | 4 | 1 | no | — |
| 137 | #1398 | — | 4 | 1 | no | — |
| 138 | #1398 | — | 4 | 1 | no | — |
| 139 | #1398 | — | 4 | 1 | no | — |
| 140 | #1397 | — | 4 | 1 | no | — |
| 141 | C4×C32 | — | 2 | 2 | no | — |
| 142 | #1376 | — | 2 | 1 | no | — |
| 143 | #1376 | — | 4 | 1 | no | — |
| 144 | #1373 | — | 2 | 1 | no | — |
| 145 | #1373 | — | 2 | 1 | no | — |
| 146 | #1373 | — | 2 | 1 | no | — |
| 147 | #1373 | C2×C8 | 1 | 2 | yes | complemented |
| 148 | #1369 | — | 4 | 2 | no | — |
| 149 | #1369 | — | 4 | 1 | no | — |
| 150 | #1369 | — | 4 | 1 | no | — |
| 151 | #1369 | — | 8 | 2 | no | — |
| 152 | #1368 | — | 2 | 1 | no | — |
| 153 | #1368 | — | 2 | 1 | no | — |
| 154 | #1368 | — | 2 | 1 | no | — |
| 155 | #1368 | SD16 | 1 | 2 | yes | — |
| 156 | #1333 | — | 4 | 4 | no | — |
| 157 | #1331 | — | 8 | 2 | no | — |
| 158 | #1313 | — | 4 | 1 | no | — |
| 159 | #1313 | — | 4 | 1 | no | — |
| 160 | #1276 | — | 4 | 1 | no | — |
| 161 | #1276 | SD16 | 1 | 2 | yes | — |
| 162 | C22×D8 | — | 2 | 2 | no | — |
| 163 | C22×D8 | — | 4 | 1 | no | — |
| 164 | C2×#127 | — | 4 | 1 | no | — |
| 165 | C2×C4×D4 | — | 4 | 2 | no | — |
| 166 | C2×C4×D4 | — | 16 | 1 | no | — |
| 167 | C2×D16 | — | 2 | 2 | no | — |
| 168 | C2×D16 | — | 2 | 2 | no | — |
| 169 | C2×D16 | — | 2 | 2 | no | — |
| 170 | C2×D16 | — | 4 | 2 | no | — |
| 171 | C2×D16 | — | 4 | 2 | no | — |
| 172 | C2×D16 | — | 4 | 1 | no | — |
| 173 | C2×D16 | — | 4 | 1 | no | — |
| 174 | C2×D16 | — | 4 | 1 | no | — |
| 175 | C2×D16 | — | 4 | 1 | no | — |
| 176 | C2×D16 | C4⋊C8 | 1 | 4 | yes | — |
| 177 | C2×M32 | — | 4 | 1 | no | — |
| 178 | C2×M32 | — | 4 | 1 | no | — |
| 179 | C2×M32 | — | 4 | 1 | no | — |
| 180 | C2×M32 | — | 8 | 1 | no | — |
| 181 | C22×C16 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 182 | C22×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 183 | C22×C16 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 184 | C22×C16 | #123 | 1 | 1 | yes | characteristic |
| 185 | #493 | — | 2 | 2 | no | — |
| 186 | #493 | — | 2 | 2 | no | — |
| 187 | #493 | — | 4 | 1 | no | — |
| 188 | #493 | — | 4 | 1 | no | — |
| 189 | C4×D8 | — | 4 | 2 | no | — |
| 190 | C4×D8 | — | 4 | 2 | no | — |
| 191 | C4×D8 | — | 4 | 2 | no | — |
| 192 | C4×D8 | — | 4 | 2 | no | — |
| 193 | C4×D8 | — | 8 | 1 | no | — |
| 194 | C4×D8 | — | 8 | 1 | no | — |
| 195 | C4×D8 | — | 8 | 1 | no | — |
| 196 | C4×D8 | — | 8 | 1 | no | — |
| 197 | C8×D4 | — | 8 | 4 | no | — |
| 198 | C8×D4 | — | 8 | 4 | no | — |
| 199 | #431 | — | 2 | 2 | no | — |
| 200 | #431 | — | 4 | 1 | no | — |
| 201 | #431 | — | 4 | 1 | no | — |
| 202 | C2×#107 | — | 2 | 2 | no | — |
| 203 | C2×#107 | — | 4 | 1 | no | — |
| 204 | C2×#102 | — | 4 | 2 | no | — |
| 205 | C2×#102 | — | 4 | 2 | no | — |
| 206 | C2×C22⋊C8 | — | 16 | 2 | no | — |
| 207 | C2×C4×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 208 | C2×C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 209 | C2×C4×C8 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 210 | C2×C4×C8 | #135 | 1 | 1 | yes | characteristic |
| 211 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 212 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 213 | #390 | — | 4 | 2 | no | — |
| 214 | #390 | — | 16 | 1 | no | — |
| 215 | #384 | — | 4 | 1 | no | — |
| 216 | C43 | C2×SD16 | 1 | 1 | yes | characteristic |
| 217 | M64 | — | 2 | 2 | no | — |
| 218 | M64 | — | 4 | 2 | no | — |
| 219 | M64 | — | 4 | 2 | no | — |
| 220 | M64 | — | 4 | 1 | no | — |
| 221 | M64 | — | 4 | 1 | no | — |
| 222 | M64 | — | 4 | 1 | no | — |
| 223 | C2×C32 | — | 4 | 2 | no | — |
| 224 | C2×C32 | — | 4 | 1 | no | — |
| 225 | C2×C32 | — | 4 | 1 | no | — |
| 226 | #367 | — | 4 | 1 | no | — |
| 227 | #367 | — | 4 | 1 | no | — |
| 228 | #367 | — | 4 | 2 | no | — |
| 229 | #364 | — | 2 | 2 | no | — |
| 230 | #364 | — | 4 | 1 | no | — |
| 231 | #364 | — | 4 | 1 | no | — |
| 232 | #364 | — | 4 | 1 | no | — |
| 233 | #364 | — | 4 | 1 | no | — |
| 234 | #364 | — | 4 | 1 | no | — |
| 235 | #364 | — | 8 | 1 | no | — |
| 236 | #364 | — | 8 | 1 | no | — |
| 237 | #364 | — | 8 | 1 | no | — |
| 238 | #364 | — | 8 | 1 | no | — |
| 239 | C4⋊C16 | — | 16 | 1 | no | — |
| 240 | #357 | — | 4 | 2 | no | — |
| 241 | #357 | — | 4 | 2 | no | — |
| 242 | #357 | — | 8 | 2 | no | — |
| 243 | #346 | — | 2 | 1 | no | — |
| 244 | #346 | — | 2 | 1 | no | — |
| 245 | #346 | — | 2 | 1 | no | — |
| 246 | #346 | — | 2 | 1 | no | — |
| 247 | #346 | — | 4 | 1 | no | — |
| 248 | #346 | — | 4 | 1 | no | — |
| 249 | #346 | — | 8 | 1 | no | — |
| 250 | #346 | C2×SD16 | 1 | 1 | yes | characteristic |
| 251 | #346 | #135 | 1 | 1 | yes | characteristic |
| 252 | #346 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 253 | #346 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 254 | C4×C16 | — | 2 | 1 | no | — |
| 255 | C4×C16 | — | 2 | 1 | no | — |
| 256 | C4×C16 | — | 4 | 1 | no | — |
| 257 | C4×C16 | — | 8 | 1 | no | — |
| 258 | C4×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 259 | C4×C16 | C2×M16 | 1 | 1 | yes | characteristic |
| 260 | C4×C16 | #131 | 1 | 1 | yes | characteristic |
| 261 | C4×C16 | #131 | 1 | 1 | yes | characteristic |
| 262 | #335 | — | 4 | 1 | no | — |
| 263 | #335 | — | 4 | 1 | no | — |
| 264 | #335 | — | 4 | 1 | no | — |
| 265 | #334 | — | 2 | 2 | no | — |
| 266 | #334 | — | 4 | 1 | no | — |
| 267 | #334 | — | 4 | 1 | no | — |
| 268 | D4⋊C8 | — | 8 | 4 | no | — |
| 269 | D4⋊C8 | — | 8 | 4 | no | — |
| 270 | #323 | — | 16 | 2 | no | — |
| 271 | #322 | — | 4 | 1 | no | — |
| 272 | #322 | — | 8 | 1 | no | — |
| 273 | C82 | — | 4 | 1 | no | — |
| 274 | C82 | — | 8 | 1 | no | — |
| 275 | C22×D4 | — | 4 | 2 | no | — |
| 276 | C22×D4 | — | 16 | 1 | no | — |
| 277 | C23×C4 | — | 8 | 2 | no | — |
| 278 | C2×D8 | — | 2 | 4 | no | — |
| 279 | C2×D8 | — | 4 | 2 | no | — |
| 280 | C2×D8 | — | 4 | 2 | no | — |
| 281 | C2×D8 | — | 4 | 2 | no | — |
| 282 | C2×D8 | — | 4 | 2 | no | — |
| 283 | C2×D8 | — | 4 | 2 | no | — |
| 284 | C2×D8 | — | 4 | 2 | no | — |
| 285 | C2×D8 | — | 4 | 2 | no | — |
| 286 | C2×D8 | — | 8 | 1 | no | — |
| 287 | C2×D8 | — | 8 | 1 | no | — |
| 288 | C2×D8 | — | 8 | 1 | no | — |
| 289 | C2×D8 | — | 8 | 1 | no | — |
| 290 | C22×C8 | — | 16 | 4 | no | — |
| 291 | C22×C8 | #385 | 1 | 1 | yes | characteristic |
| 292 | C22×C8 | #442 | 1 | 1 | yes | characteristic |
| 293 | C22×C8 | #449 | 1 | 1 | yes | characteristic |
| 294 | C22×C8 | #478 | 1 | 1 | yes | characteristic |
| 295 | #127 | — | 4 | 2 | no | — |
| 296 | #127 | — | 4 | 2 | no | — |
| 297 | #127 | — | 16 | 1 | no | — |
| 298 | C4×D4 | — | 8 | 2 | no | — |
| 299 | C4×D4 | — | 8 | 2 | no | — |
| 300 | C4×D4 | — | 8 | 2 | no | — |
| 301 | C4×D4 | — | 8 | 2 | no | — |
| 302 | C4×D4 | — | 32 | 4 | no | — |
| 303 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 304 | C2×C4⋊C4 | — | 16 | 1 | no | — |
| 305 | C2×C22⋊C4 | — | 8 | 2 | no | — |
| 306 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 307 | C2×C42 | — | 4 | 1 | no | — |
| 308 | C2×C42 | C4×SD16 | 1 | 1 | yes | characteristic |
| 309 | C2×C42 | #450 | 1 | 1 | yes | characteristic |
| 310 | C2×C42 | #476 | 1 | 1 | yes | characteristic |
| 311 | D16 | — | 4 | 4 | no | — |
| 312 | D16 | — | 4 | 2 | no | — |
| 313 | D16 | — | 4 | 2 | no | — |
| 314 | D16 | — | 4 | 2 | no | — |
| 315 | D16 | — | 4 | 2 | no | — |
| 316 | D16 | — | 8 | 2 | no | — |
| 317 | M32 | — | 4 | 2 | no | — |
| 318 | M32 | — | 8 | 1 | no | — |
| 319 | M32 | — | 8 | 1 | no | — |
| 320 | M32 | — | 8 | 1 | no | — |
| 321 | M32 | — | 8 | 1 | no | — |
| 322 | M32 | — | 8 | 1 | no | — |
| 323 | M32 | — | 16 | 1 | no | — |
| 324 | M32 | — | 16 | 1 | no | — |
| 325 | C2×C16 | — | 2 | 1 | no | — |
| 326 | C2×C16 | — | 2 | 1 | no | — |
| 327 | C2×C16 | — | 2 | 1 | no | — |
| 328 | C2×C16 | — | 2 | 1 | no | — |
| 329 | C2×C16 | — | 2 | 1 | no | — |
| 330 | C2×C16 | — | 2 | 1 | no | — |
| 331 | C2×C16 | — | 2 | 1 | no | — |
| 332 | C2×C16 | — | 8 | 1 | no | — |
| 333 | C2×C16 | — | 8 | 1 | no | — |
| 334 | C2×C16 | — | 8 | 1 | no | — |
| 335 | C2×C16 | — | 16 | 1 | no | — |
| 336 | C2×C16 | C2×C4⋊C8 | 1 | 1 | yes | characteristic |
| 337 | C2×C16 | #424 | 1 | 1 | yes | characteristic |
| 338 | C2×C16 | C8×D4 | 1 | 1 | yes | characteristic |
| 339 | C2×C16 | #435 | 1 | 1 | yes | characteristic |
| 340 | C2×C16 | C4×SD16 | 1 | 1 | yes | characteristic |
| 341 | C2×C16 | #442 | 1 | 1 | yes | characteristic |
| 342 | C2×C16 | #443 | 1 | 1 | yes | characteristic |
| 343 | C2×C16 | #444 | 1 | 1 | yes | characteristic |
| 344 | C2×C16 | #476 | 1 | 1 | yes | characteristic |
| 345 | C2×C16 | #478 | 1 | 1 | yes | characteristic |
| 346 | #107 | — | 4 | 2 | no | — |
| 347 | #107 | — | 4 | 2 | no | — |
| 348 | #107 | — | 8 | 1 | no | — |
| 349 | #107 | — | 8 | 1 | no | — |
| 350 | C4⋊C8 | — | 4 | 2 | no | — |
| 351 | C4⋊C8 | — | 4 | 2 | no | — |
| 352 | C4⋊C8 | — | 8 | 1 | no | — |
| 353 | #102 | — | 8 | 2 | no | — |
| 354 | #102 | — | 8 | 2 | no | — |
| 355 | #102 | — | 8 | 2 | no | — |
| 356 | #102 | — | 8 | 2 | no | — |
| 357 | C22⋊C8 | — | 4 | 2 | no | — |
| 358 | C22⋊C8 | — | 8 | 1 | no | — |
| 359 | C22⋊C8 | — | 8 | 1 | no | — |
| 360 | C22⋊C8 | — | 16 | 4 | no | — |
| 361 | C4×C8 | — | 2 | 1 | no | — |
| 362 | C4×C8 | — | 2 | 1 | no | — |
| 363 | C4×C8 | — | 2 | 1 | no | — |
| 364 | C4×C8 | — | 2 | 1 | no | — |
| 365 | C4×C8 | — | 2 | 1 | no | — |
| 366 | C4×C8 | — | 2 | 1 | no | — |
| 367 | C4×C8 | — | 4 | 1 | no | — |
| 368 | C4×C8 | — | 4 | 2 | no | — |
| 369 | C4×C8 | — | 8 | 1 | no | — |
| 370 | C4×C8 | — | 8 | 1 | no | — |
| 371 | C4×C8 | C8×D4 | 1 | 1 | yes | characteristic |
| 372 | C4×C8 | #435 | 1 | 1 | yes | characteristic |
| 373 | C4×C8 | #443 | 1 | 1 | yes | characteristic |
| 374 | C4×C8 | #444 | 1 | 1 | yes | characteristic |
| 375 | C4×C8 | #449 | 1 | 1 | yes | characteristic |
| 376 | C4×C8 | #450 | 1 | 1 | yes | characteristic |
| 377 | C4×C8 | #453 | 1 | 1 | yes | characteristic |
| 378 | C4×C8 | #455 | 1 | 1 | yes | characteristic |
| 379 | C32 | — | 4 | 4 | no | — |
| 380 | C32 | — | 4 | 2 | no | — |
| 381 | C32 | — | 8 | 1 | no | — |
| 382 | C24 | — | 8 | 2 | no | — |
| 383 | C2×D4 | — | 4 | 4 | no | — |
| 384 | C2×D4 | — | 8 | 2 | no | — |
| 385 | C2×D4 | — | 8 | 2 | no | — |
| 386 | C2×D4 | — | 8 | 2 | no | — |
| 387 | C2×D4 | — | 8 | 2 | no | — |
| 388 | C2×D4 | — | 8 | 2 | no | — |
| 389 | C2×D4 | — | 16 | 2 | no | — |
| 390 | C2×D4 | — | 16 | 2 | no | — |
| 391 | C2×D4 | — | 32 | 2 | no | — |
| 392 | C2×D4 | — | 32 | 2 | no | — |
| 393 | C22×C4 | — | 2 | 1 | no | — |
| 394 | C22×C4 | — | 2 | 1 | no | — |
| 395 | C22×C4 | — | 2 | 1 | no | — |
| 396 | C22×C4 | — | 8 | 2 | no | — |
| 397 | C22×C4 | — | 16 | 2 | no | — |
| 398 | C22×C4 | — | 16 | 2 | no | — |
| 399 | C22×C4 | — | 32 | 4 | no | — |
| 400 | C22×C4 | #1864 | 1 | 1 | yes | characteristic |
| 401 | D8 | — | 4 | 4 | no | — |
| 402 | D8 | — | 4 | 4 | no | — |
| 403 | D8 | — | 8 | 2 | no | — |
| 404 | D8 | — | 8 | 2 | no | — |
| 405 | D8 | — | 8 | 2 | no | — |
| 406 | D8 | — | 8 | 2 | no | — |
| 407 | D8 | — | 8 | 2 | no | — |
| 408 | D8 | — | 8 | 2 | no | — |
| 409 | C2×C8 | — | 2 | 1 | no | — |
| 410 | C2×C8 | — | 2 | 1 | no | — |
| 411 | C2×C8 | — | 2 | 1 | no | — |
| 412 | C2×C8 | — | 2 | 1 | no | — |
| 413 | C2×C8 | — | 2 | 1 | no | — |
| 414 | C2×C8 | — | 8 | 2 | no | — |
| 415 | C2×C8 | — | 8 | 2 | no | — |
| 416 | C2×C8 | — | 16 | 1 | no | — |
| 417 | C2×C8 | — | 64 | 4 | no | — |
| 418 | C2×C8 | #1580 | 1 | 1 | yes | characteristic |
| 419 | C2×C8 | #1586 | 1 | 1 | yes | characteristic |
| 420 | C2×C8 | #1620 | 1 | 1 | yes | characteristic |
| 421 | C2×C8 | #1642 | 1 | 1 | yes | characteristic |
| 422 | C2×C8 | #1850 | 1 | 1 | yes | characteristic |
| 423 | C2×C8 | #1856 | 1 | 1 | yes | characteristic |
| 424 | C2×C8 | #1858 | 1 | 1 | yes | characteristic |
| 425 | C2×C8 | #1864 | 1 | 1 | yes | characteristic |
| 426 | C2×C8 | #1866 | 1 | 1 | yes | characteristic |
| 427 | C2×C8 | #1866 | 1 | 1 | yes | characteristic |
| 428 | C2×C8 | #2180 | 1 | 1 | yes | characteristic |
| 429 | C2×C8 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 430 | C2×C8 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 431 | C2×C8 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 432 | C4⋊C4 | — | 8 | 2 | no | — |
| 433 | C4⋊C4 | — | 8 | 2 | no | — |
| 434 | C4⋊C4 | — | 32 | 2 | no | — |
| 435 | C22⋊C4 | — | 16 | 2 | no | — |
| 436 | C22⋊C4 | — | 16 | 2 | no | — |
| 437 | C22⋊C4 | — | 32 | 4 | no | — |
| 438 | C42 | — | 2 | 1 | no | — |
| 439 | C42 | — | 2 | 1 | no | — |
| 440 | C42 | — | 2 | 1 | no | — |
| 441 | C42 | — | 2 | 1 | no | — |
| 442 | C42 | — | 8 | 2 | no | — |
| 443 | C42 | C8×SD16 | 1 | 1 | yes | characteristic |
| 444 | C42 | #1582 | 1 | 1 | yes | characteristic |
| 445 | C42 | #1629 | 1 | 1 | yes | characteristic |
| 446 | C42 | #1642 | 1 | 1 | yes | characteristic |
| 447 | C16 | — | 2 | 1 | no | — |
| 448 | C16 | — | 2 | 1 | no | — |
| 449 | C16 | — | 2 | 1 | no | — |
| 450 | C16 | — | 2 | 1 | no | — |
| 451 | C16 | — | 4 | 1 | no | — |
| 452 | C16 | — | 8 | 2 | no | — |
| 453 | C16 | — | 16 | 1 | no | — |
| 454 | C16 | — | 16 | 1 | no | — |
| 455 | C16 | — | 32 | 1 | no | — |
| 456 | C16 | C8×SD16 | 1 | 1 | yes | characteristic |
| 457 | C16 | #1580 | 1 | 1 | yes | characteristic |
| 458 | C16 | #1582 | 1 | 1 | yes | characteristic |
| 459 | C16 | #1586 | 1 | 1 | yes | characteristic |
| 460 | C23 | — | 8 | 4 | no | — |
| 461 | C23 | — | 16 | 2 | no | — |
| 462 | C23 | — | 16 | 2 | no | — |
| 463 | C23 | — | 32 | 2 | no | — |
| 464 | C23 | — | 32 | 2 | no | — |
| 465 | C23 | #12953 | 1 | 1 | yes | characteristic |
| 466 | D4 | — | 8 | 4 | no | — |
| 467 | D4 | — | 8 | 4 | no | — |
| 468 | D4 | — | 16 | 2 | no | — |
| 469 | D4 | — | 16 | 2 | no | — |
| 470 | D4 | — | 32 | 4 | no | — |
| 471 | D4 | — | 32 | 4 | no | — |
| 472 | C2×C4 | — | 2 | 1 | no | — |
| 473 | C2×C4 | — | 2 | 1 | no | — |
| 474 | C2×C4 | — | 2 | 1 | no | — |
| 475 | C2×C4 | — | 2 | 1 | no | — |
| 476 | C2×C4 | — | 4 | 2 | no | — |
| 477 | C2×C4 | — | 4 | 1 | no | — |
| 478 | C2×C4 | — | 8 | 1 | no | — |
| 479 | C2×C4 | — | 8 | 1 | no | — |
| 480 | C2×C4 | — | 16 | 2 | no | — |
| 481 | C2×C4 | — | 32 | 4 | no | — |
| 482 | C2×C4 | — | 32 | 2 | no | — |
| 483 | C2×C4 | — | 64 | 2 | no | — |
| 484 | C2×C4 | #8845 | 1 | 1 | yes | characteristic |
| 485 | C2×C4 | #8924 | 1 | 1 | yes | characteristic |
| 486 | C2×C4 | #8932 | 1 | 1 | yes | characteristic |
| 487 | C2×C4 | #12952 | 1 | 1 | yes | characteristic |
| 488 | C2×C4 | #12955 | 1 | 1 | yes | characteristic |
| 489 | C2×C4 | #12956 | 1 | 1 | yes | characteristic |
| 490 | C8 | — | 2 | 1 | no | — |
| 491 | C8 | — | 2 | 1 | no | — |
| 492 | C8 | — | 4 | 1 | no | — |
| 493 | C8 | — | 16 | 2 | no | — |
| 494 | C8 | — | 16 | 2 | no | — |
| 495 | C8 | — | 32 | 1 | no | — |
| 496 | C8 | #8835 | 1 | 1 | yes | characteristic |
| 497 | C8 | #8845 | 1 | 1 | yes | characteristic |
| 498 | C8 | #8932 | 1 | 1 | yes | characteristic |
| 499 | C8 | #8934 | 1 | 1 | yes | characteristic |
| 500 | C8 | #12065 | 1 | 1 | yes | characteristic |
| 501 | C8 | #12067 | 1 | 1 | yes | characteristic |
| 502 | C8 | #12077 | 1 | 1 | yes | characteristic |
| 503 | C8 | #12078 | 1 | 1 | yes | characteristic |
| 504 | C22 | — | 4 | 1 | no | — |
| 505 | C22 | — | 16 | 4 | no | — |
| 506 | C22 | — | 32 | 4 | no | — |
| 507 | C22 | — | 32 | 2 | no | — |
| 508 | C22 | — | 32 | 2 | no | — |
| 509 | C22 | — | 64 | 2 | no | — |
| 510 | C22 | #135906 | 1 | 1 | yes | characteristic |
| 511 | C22 | #136543 | 1 | 1 | yes | characteristic |
| 512 | C22 | #136569 | 1 | 1 | yes | characteristic |
| 513 | C4 | — | 2 | 2 | no | — |
| 514 | C4 | — | 4 | 1 | no | — |
| 515 | C4 | — | 4 | 1 | no | — |
| 516 | C4 | — | 4 | 1 | no | — |
| 517 | C4 | — | 8 | 1 | no | — |
| 518 | C4 | — | 32 | 2 | no | — |
| 519 | C4 | #99341 | 1 | 1 | yes | characteristic |
| 520 | C4 | #135908 | 1 | 1 | yes | characteristic |
| 521 | C4 | #136542 | 1 | 1 | yes | characteristic |
| 522 | C4 | #136567 | 1 | 1 | yes | characteristic |
| 523 | C2 | — | 2 | 1 | no | — |
| 524 | C2 | — | 2 | 1 | no | — |
| 525 | C2 | — | 2 | 1 | no | — |
| 526 | C2 | — | 32 | 4 | no | — |
| 527 | C2 | #72225256 | 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