← #72227227
Subgroups — #72227227
Order 2048.
1224 conjugacy classes of subgroups.
The subgroup lattice has 574 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72227182 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72225535 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72216566 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #72216299 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #72216165 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #496104 | — | 2 | 1 | no | — |
| 7 | #496104 | — | 2 | 1 | no | — |
| 8 | C2×#12515 | C4 | 1 | 1 | yes | characteristic |
| 9 | C4×#1712 | C22 | 1 | 2 | yes | — |
| 10 | #141681 | — | 2 | 1 | no | — |
| 11 | #141681 | — | 2 | 1 | no | — |
| 12 | #141665 | C4 | 1 | 2 | yes | — |
| 13 | #140846 | — | 2 | 2 | no | — |
| 14 | #135778 | C4 | 1 | 1 | yes | characteristic |
| 15 | #129086 | C22 | 1 | 2 | yes | — |
| 16 | #129086 | C22 | 1 | 1 | yes | characteristic |
| 17 | #129049 | — | 2 | 1 | no | — |
| 18 | C8×#346 | C22 | 1 | 1 | yes | characteristic |
| 19 | #124220 | — | 2 | 2 | no | — |
| 20 | C2×#7099 | — | 2 | 1 | no | — |
| 21 | #96889 | C22 | 1 | 1 | yes | characteristic |
| 22 | #93261 | — | 2 | 1 | no | — |
| 23 | #92913 | — | 2 | 1 | no | — |
| 24 | #92866 | — | 2 | 4 | no | — |
| 25 | C2×#2246 | — | 2 | 1 | no | — |
| 26 | C2×#2246 | — | 2 | 1 | no | — |
| 27 | C2×#2177 | — | 4 | 2 | no | — |
| 28 | C2×#2177 | — | 4 | 1 | no | — |
| 29 | C2×#2177 | — | 4 | 1 | no | — |
| 30 | C4×#493 | — | 2 | 2 | no | — |
| 31 | C4×#493 | — | 2 | 2 | no | — |
| 32 | C4×#493 | — | 2 | 2 | no | — |
| 33 | C2×#1712 | C2×C4 | 1 | 2 | yes | — |
| 34 | #13239 | — | 4 | 2 | no | — |
| 35 | #13239 | — | 4 | 1 | no | — |
| 36 | #13239 | — | 4 | 1 | no | — |
| 37 | #13202 | — | 2 | 2 | no | — |
| 38 | #13202 | — | 2 | 2 | no | — |
| 39 | #12906 | — | 2 | 1 | no | — |
| 40 | #12906 | — | 2 | 1 | no | — |
| 41 | #12653 | — | 2 | 1 | no | — |
| 42 | #12653 | — | 2 | 2 | no | — |
| 43 | C4×#346 | D4 | 1 | 1 | yes | characteristic |
| 44 | C4×#346 | D4 | 1 | 1 | yes | characteristic |
| 45 | #12515 | — | 2 | 2 | no | — |
| 46 | #12515 | C8 | 1 | 4 | yes | complemented |
| 47 | C2×#1367 | — | 2 | 2 | no | — |
| 48 | C2×#1367 | — | 2 | 1 | no | — |
| 49 | C2×#1333 | — | 4 | 4 | no | — |
| 50 | C2×#1313 | — | 4 | 1 | no | — |
| 51 | C2×#1311 | D4 | 1 | 1 | yes | characteristic |
| 52 | C2×#1311 | D4 | 1 | 1 | yes | characteristic |
| 53 | C2×C8×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 54 | C2×C8×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 55 | #9824 | — | 2 | 2 | no | — |
| 56 | #9824 | — | 2 | 2 | no | — |
| 57 | #9824 | — | 2 | 2 | no | — |
| 58 | #8818 | C2×C4 | 1 | 2 | yes | — |
| 59 | C4×#334 | D4 | 1 | 2 | yes | — |
| 60 | #8260 | — | 2 | 1 | no | — |
| 61 | C4×C82 | C23 | 1 | 1 | yes | characteristic |
| 62 | #7151 | — | 2 | 2 | no | — |
| 63 | #7151 | D4 | 1 | 2 | yes | — |
| 64 | #7137 | — | 4 | 1 | no | — |
| 65 | #7112 | — | 4 | 4 | no | — |
| 66 | #7099 | — | 2 | 4 | no | — |
| 67 | #7015 | — | 2 | 1 | no | — |
| 68 | C22×D16 | — | 4 | 2 | no | — |
| 69 | C22×D16 | — | 4 | 1 | no | — |
| 70 | C22×D16 | — | 4 | 1 | no | — |
| 71 | C2×#493 | — | 2 | 2 | no | — |
| 72 | C2×#493 | — | 2 | 2 | no | — |
| 73 | C2×#493 | — | 2 | 2 | no | — |
| 74 | C2×C4×D8 | — | 4 | 2 | no | — |
| 75 | C2×C4×D8 | — | 4 | 2 | no | — |
| 76 | C2×C4×D8 | — | 4 | 2 | no | — |
| 77 | C2×C4×D8 | — | 4 | 2 | no | — |
| 78 | C2×C4×D8 | — | 8 | 2 | no | — |
| 79 | C4×#127 | — | 4 | 2 | no | — |
| 80 | #2246 | — | 2 | 4 | no | — |
| 81 | #2246 | — | 2 | 4 | no | — |
| 82 | #2246 | — | 4 | 2 | no | — |
| 83 | #2246 | — | 4 | 2 | no | — |
| 84 | #2177 | — | 8 | 8 | no | — |
| 85 | #2177 | — | 8 | 4 | no | — |
| 86 | #2177 | — | 8 | 4 | no | — |
| 87 | C2×#367 | — | 4 | 2 | no | — |
| 88 | C2×#367 | — | 4 | 1 | no | — |
| 89 | C2×#367 | — | 4 | 1 | no | — |
| 90 | C2×C4⋊C16 | — | 2 | 2 | no | — |
| 91 | C2×C4⋊C16 | — | 4 | 2 | no | — |
| 92 | C2×#357 | — | 4 | 4 | no | — |
| 93 | C2×#357 | — | 4 | 2 | no | — |
| 94 | C2×#357 | — | 4 | 2 | no | — |
| 95 | C2×#346 | — | 2 | 1 | no | — |
| 96 | C2×#346 | — | 2 | 1 | no | — |
| 97 | C2×#346 | — | 4 | 1 | no | — |
| 98 | C2×#346 | — | 4 | 2 | no | — |
| 99 | C2×#346 | D8 | 1 | 1 | yes | characteristic |
| 100 | C2×#346 | D8 | 1 | 1 | yes | characteristic |
| 101 | C2×#346 | SD16 | 1 | 1 | yes | characteristic |
| 102 | C2×#346 | SD16 | 1 | 1 | yes | characteristic |
| 103 | C2×C4×C16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 104 | C2×C4×C16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 105 | C2×C4×C16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 106 | C2×C4×C16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 107 | #1970 | — | 4 | 2 | no | — |
| 108 | #1970 | — | 4 | 2 | no | — |
| 109 | #1970 | — | 4 | 2 | no | — |
| 110 | #1970 | — | 4 | 2 | no | — |
| 111 | #1970 | — | 8 | 2 | no | — |
| 112 | #1957 | — | 4 | 2 | no | — |
| 113 | #1957 | — | 4 | 2 | no | — |
| 114 | #1957 | — | 4 | 2 | no | — |
| 115 | #1845 | — | 2 | 2 | no | — |
| 116 | #1845 | — | 2 | 2 | no | — |
| 117 | #1845 | — | 2 | 2 | no | — |
| 118 | C4×C4⋊C8 | — | 2 | 2 | no | — |
| 119 | C42×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | C42×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 121 | C42×C8 | #41 | 1 | 1 | yes | characteristic |
| 122 | #1712 | — | 2 | 2 | no | — |
| 123 | #1712 | — | 2 | 2 | no | — |
| 124 | #1712 | — | 2 | 2 | no | — |
| 125 | #1712 | C2×C8 | 1 | 4 | yes | — |
| 126 | C2×#334 | — | 2 | 2 | no | — |
| 127 | C2×#322 | — | 4 | 1 | no | — |
| 128 | C2×C82 | C22×C4 | 1 | 1 | yes | characteristic |
| 129 | C2×C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 130 | C2×C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 131 | C2×C82 | #41 | 1 | 1 | yes | characteristic |
| 132 | #1374 | — | 4 | 1 | no | — |
| 133 | #1374 | — | 4 | 2 | no | — |
| 134 | #1367 | — | 2 | 4 | no | — |
| 135 | #1367 | — | 4 | 2 | no | — |
| 136 | #1367 | — | 4 | 1 | no | — |
| 137 | #1367 | — | 4 | 1 | no | — |
| 138 | #1333 | — | 8 | 8 | no | — |
| 139 | #1313 | — | 8 | 2 | no | — |
| 140 | #1311 | — | 2 | 2 | no | — |
| 141 | #1311 | — | 4 | 1 | no | — |
| 142 | C8×C16 | — | 2 | 1 | no | — |
| 143 | C8×C16 | — | 2 | 1 | no | — |
| 144 | C8×C16 | C2×C8 | 1 | 2 | yes | — |
| 145 | C8×C16 | M16 | 1 | 2 | yes | — |
| 146 | #1277 | — | 2 | 2 | no | — |
| 147 | #1273 | — | 4 | 1 | no | — |
| 148 | C22×D8 | — | 4 | 2 | no | — |
| 149 | C22×D8 | — | 4 | 2 | no | — |
| 150 | C22×D8 | — | 4 | 2 | no | — |
| 151 | C22×D8 | — | 4 | 2 | no | — |
| 152 | C22×D8 | — | 8 | 2 | no | — |
| 153 | C2×#127 | — | 4 | 2 | no | — |
| 154 | C2×C4×D4 | — | 8 | 2 | no | — |
| 155 | C2×C4×D4 | — | 8 | 2 | no | — |
| 156 | C2×C4×D4 | — | 8 | 2 | no | — |
| 157 | C2×D16 | — | 4 | 8 | no | — |
| 158 | C2×D16 | — | 4 | 4 | no | — |
| 159 | C2×D16 | — | 4 | 4 | no | — |
| 160 | C2×D16 | — | 8 | 4 | no | — |
| 161 | C2×D16 | — | 8 | 2 | no | — |
| 162 | C2×D16 | — | 8 | 4 | no | — |
| 163 | C2×D16 | — | 8 | 2 | no | — |
| 164 | C2×D16 | — | 8 | 2 | no | — |
| 165 | C2×D16 | — | 8 | 2 | no | — |
| 166 | C22×C16 | — | 2 | 1 | no | — |
| 167 | C22×C16 | — | 2 | 1 | no | — |
| 168 | C22×C16 | — | 4 | 2 | no | — |
| 169 | C22×C16 | — | 8 | 2 | no | — |
| 170 | C22×C16 | #102 | 1 | 1 | yes | characteristic |
| 171 | C22×C16 | #102 | 1 | 1 | yes | characteristic |
| 172 | C22×C16 | #102 | 1 | 1 | yes | characteristic |
| 173 | C22×C16 | #102 | 1 | 1 | yes | characteristic |
| 174 | #493 | — | 2 | 4 | no | — |
| 175 | #493 | — | 2 | 4 | no | — |
| 176 | #493 | — | 2 | 4 | no | — |
| 177 | #493 | — | 4 | 2 | no | — |
| 178 | #493 | — | 4 | 2 | no | — |
| 179 | #493 | — | 4 | 2 | no | — |
| 180 | #493 | — | 4 | 2 | no | — |
| 181 | #493 | — | 4 | 2 | no | — |
| 182 | #493 | — | 4 | 2 | no | — |
| 183 | #493 | — | 4 | 2 | no | — |
| 184 | #493 | — | 8 | 2 | no | — |
| 185 | C4×D8 | — | 8 | 4 | no | — |
| 186 | C4×D8 | — | 8 | 4 | no | — |
| 187 | C4×D8 | — | 8 | 4 | no | — |
| 188 | C4×D8 | — | 8 | 4 | no | — |
| 189 | C4×D8 | — | 8 | 8 | no | — |
| 190 | C4×D8 | — | 16 | 8 | no | — |
| 191 | C4×D8 | — | 16 | 4 | no | — |
| 192 | C2×#107 | — | 4 | 2 | no | — |
| 193 | C2×#107 | — | 4 | 2 | no | — |
| 194 | C2×#107 | — | 4 | 2 | no | — |
| 195 | C2×#107 | — | 4 | 2 | no | — |
| 196 | C2×#107 | — | 8 | 2 | no | — |
| 197 | C2×C4⋊C8 | — | 4 | 2 | no | — |
| 198 | C2×#102 | — | 8 | 4 | no | — |
| 199 | C2×#102 | — | 8 | 2 | no | — |
| 200 | C2×#102 | — | 8 | 2 | no | — |
| 201 | C2×#102 | — | 8 | 2 | no | — |
| 202 | C2×#102 | — | 8 | 2 | no | — |
| 203 | C2×C4×C8 | — | 2 | 2 | no | — |
| 204 | C2×C4×C8 | — | 4 | 2 | no | — |
| 205 | C2×C4×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 206 | C2×C4×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 207 | C2×C4×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 208 | C2×C4×C8 | #121 | 1 | 1 | yes | characteristic |
| 209 | C2×C4×C8 | #124 | 1 | 1 | yes | characteristic |
| 210 | C2×C4×C8 | #127 | 1 | 1 | yes | characteristic |
| 211 | C2×C4×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 212 | C2×C4×C8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 213 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 214 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 215 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 216 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 217 | #390 | — | 8 | 2 | no | — |
| 218 | #390 | — | 8 | 2 | no | — |
| 219 | #390 | — | 8 | 2 | no | — |
| 220 | #384 | — | 4 | 2 | no | — |
| 221 | C43 | #121 | 1 | 1 | yes | characteristic |
| 222 | #367 | — | 8 | 4 | no | — |
| 223 | #367 | — | 8 | 2 | no | — |
| 224 | #367 | — | 8 | 2 | no | — |
| 225 | C4⋊C16 | — | 4 | 4 | no | — |
| 226 | C4⋊C16 | — | 4 | 2 | no | — |
| 227 | C4⋊C16 | — | 4 | 2 | no | — |
| 228 | C4⋊C16 | — | 8 | 2 | no | — |
| 229 | #357 | — | 8 | 8 | no | — |
| 230 | #357 | — | 8 | 4 | no | — |
| 231 | #357 | — | 8 | 4 | no | — |
| 232 | #346 | — | 2 | 4 | no | — |
| 233 | #346 | — | 2 | 2 | no | — |
| 234 | #346 | — | 2 | 2 | no | — |
| 235 | #346 | — | 2 | 2 | no | — |
| 236 | #346 | — | 4 | 1 | no | — |
| 237 | #346 | — | 4 | 2 | no | — |
| 238 | #346 | — | 8 | 1 | no | — |
| 239 | #346 | — | 8 | 1 | no | — |
| 240 | #346 | — | 8 | 4 | no | — |
| 241 | C4×C16 | — | 2 | 1 | no | — |
| 242 | C4×C16 | — | 2 | 1 | no | — |
| 243 | C4×C16 | — | 2 | 1 | no | — |
| 244 | C4×C16 | — | 2 | 1 | no | — |
| 245 | C4×C16 | — | 2 | 1 | no | — |
| 246 | C4×C16 | C22⋊C8 | 1 | 2 | yes | — |
| 247 | C4×C16 | C22⋊C8 | 1 | 2 | yes | — |
| 248 | C4×C16 | #104 | 1 | 2 | yes | — |
| 249 | #336 | — | 4 | 2 | no | — |
| 250 | #334 | — | 4 | 4 | no | — |
| 251 | #322 | — | 8 | 1 | no | — |
| 252 | #322 | — | 8 | 1 | no | — |
| 253 | C82 | — | 2 | 1 | no | — |
| 254 | C82 | — | 2 | 1 | no | — |
| 255 | C82 | — | 2 | 1 | no | — |
| 256 | C82 | — | 2 | 1 | no | — |
| 257 | C82 | — | 4 | 1 | no | — |
| 258 | C82 | C22×C8 | 1 | 1 | yes | characteristic |
| 259 | C82 | C2×M16 | 1 | 1 | yes | characteristic |
| 260 | C82 | #131 | 1 | 1 | yes | characteristic |
| 261 | C82 | #131 | 1 | 1 | yes | characteristic |
| 262 | C22×D4 | — | 8 | 2 | no | — |
| 263 | C22×D4 | — | 8 | 2 | no | — |
| 264 | C22×D4 | — | 8 | 2 | no | — |
| 265 | C23×C4 | — | 16 | 2 | no | — |
| 266 | C2×D8 | — | 4 | 4 | no | — |
| 267 | C2×D8 | — | 4 | 4 | no | — |
| 268 | C2×D8 | — | 4 | 4 | no | — |
| 269 | C2×D8 | — | 4 | 4 | no | — |
| 270 | C2×D8 | — | 8 | 4 | no | — |
| 271 | C2×D8 | — | 8 | 4 | no | — |
| 272 | C2×D8 | — | 8 | 4 | no | — |
| 273 | C2×D8 | — | 8 | 4 | no | — |
| 274 | C2×D8 | — | 8 | 2 | no | — |
| 275 | C2×D8 | — | 8 | 2 | no | — |
| 276 | C2×D8 | — | 8 | 2 | no | — |
| 277 | C2×D8 | — | 8 | 2 | no | — |
| 278 | C2×D8 | — | 8 | 2 | no | — |
| 279 | C2×D8 | — | 8 | 2 | no | — |
| 280 | C2×D8 | — | 8 | 4 | no | — |
| 281 | C2×D8 | — | 8 | 4 | no | — |
| 282 | C2×D8 | — | 8 | 2 | no | — |
| 283 | C2×D8 | — | 8 | 2 | no | — |
| 284 | C2×D8 | — | 16 | 2 | no | — |
| 285 | C2×D8 | — | 16 | 2 | no | — |
| 286 | C2×D8 | — | 16 | 4 | no | — |
| 287 | C2×D8 | — | 16 | 4 | no | — |
| 288 | C22×C8 | — | 2 | 1 | no | — |
| 289 | C22×C8 | — | 2 | 1 | no | — |
| 290 | C22×C8 | — | 8 | 2 | no | — |
| 291 | C22×C8 | C2×#102 | 1 | 1 | yes | characteristic |
| 292 | C22×C8 | #418 | 1 | 1 | yes | characteristic |
| 293 | C22×C8 | #442 | 1 | 1 | yes | characteristic |
| 294 | C22×C8 | #442 | 1 | 1 | yes | characteristic |
| 295 | C22×C8 | #459 | 1 | 1 | yes | characteristic |
| 296 | C22×C8 | #460 | 1 | 1 | yes | characteristic |
| 297 | C22×C8 | #496 | 1 | 2 | yes | — |
| 298 | #127 | — | 4 | 4 | no | — |
| 299 | #127 | — | 8 | 2 | no | — |
| 300 | #127 | — | 8 | 2 | no | — |
| 301 | #127 | — | 8 | 2 | no | — |
| 302 | C4×D4 | — | 16 | 4 | no | — |
| 303 | C4×D4 | — | 16 | 4 | no | — |
| 304 | C4×D4 | — | 16 | 4 | no | — |
| 305 | C4×D4 | — | 16 | 4 | no | — |
| 306 | C4×D4 | — | 16 | 8 | no | — |
| 307 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 308 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 309 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 310 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 311 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 312 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 313 | C2×C42 | #390 | 1 | 1 | yes | characteristic |
| 314 | C2×C42 | #459 | 1 | 1 | yes | characteristic |
| 315 | C2×C42 | #460 | 1 | 1 | yes | characteristic |
| 316 | C2×C42 | #469 | 1 | 2 | yes | — |
| 317 | C2×C42 | #472 | 1 | 2 | yes | — |
| 318 | D16 | — | 8 | 16 | no | — |
| 319 | D16 | — | 8 | 8 | no | — |
| 320 | D16 | — | 8 | 8 | no | — |
| 321 | C2×C16 | — | 2 | 2 | no | — |
| 322 | C2×C16 | — | 2 | 2 | no | — |
| 323 | C2×C16 | — | 2 | 1 | no | — |
| 324 | C2×C16 | — | 2 | 1 | no | — |
| 325 | C2×C16 | — | 2 | 1 | no | — |
| 326 | C2×C16 | — | 2 | 2 | no | — |
| 327 | C2×C16 | — | 2 | 1 | no | — |
| 328 | C2×C16 | — | 2 | 2 | no | — |
| 329 | C2×C16 | — | 2 | 1 | no | — |
| 330 | C2×C16 | — | 2 | 1 | no | — |
| 331 | C2×C16 | — | 2 | 1 | no | — |
| 332 | C2×C16 | — | 4 | 1 | no | — |
| 333 | C2×C16 | — | 4 | 1 | no | — |
| 334 | C2×C16 | — | 8 | 2 | no | — |
| 335 | C2×C16 | — | 8 | 2 | no | — |
| 336 | C2×C16 | — | 8 | 4 | no | — |
| 337 | C2×C16 | — | 8 | 2 | no | — |
| 338 | C2×C16 | — | 16 | 2 | no | — |
| 339 | C2×C16 | — | 16 | 2 | no | — |
| 340 | C2×C16 | D4⋊C8 | 1 | 2 | yes | — |
| 341 | C2×C16 | D4⋊C8 | 1 | 2 | yes | — |
| 342 | C2×C16 | #360 | 1 | 2 | yes | — |
| 343 | C2×C16 | #361 | 1 | 2 | yes | — |
| 344 | C2×C16 | #361 | 1 | 2 | yes | — |
| 345 | #107 | — | 8 | 4 | no | — |
| 346 | #107 | — | 8 | 2 | no | — |
| 347 | #107 | — | 8 | 2 | no | — |
| 348 | #107 | — | 8 | 4 | no | — |
| 349 | #107 | — | 16 | 4 | no | — |
| 350 | #107 | — | 16 | 2 | no | — |
| 351 | C4⋊C8 | — | 8 | 2 | no | — |
| 352 | C4⋊C8 | — | 8 | 2 | no | — |
| 353 | #102 | — | 16 | 2 | no | — |
| 354 | #102 | — | 16 | 2 | no | — |
| 355 | #102 | — | 16 | 4 | no | — |
| 356 | #102 | — | 16 | 4 | no | — |
| 357 | #102 | — | 16 | 8 | no | — |
| 358 | #102 | — | 16 | 4 | no | — |
| 359 | C4×C8 | — | 2 | 1 | no | — |
| 360 | C4×C8 | — | 2 | 1 | no | — |
| 361 | C4×C8 | — | 2 | 1 | no | — |
| 362 | C4×C8 | — | 2 | 1 | no | — |
| 363 | C4×C8 | — | 2 | 4 | no | — |
| 364 | C4×C8 | — | 2 | 2 | no | — |
| 365 | C4×C8 | — | 2 | 1 | no | — |
| 366 | C4×C8 | — | 2 | 1 | no | — |
| 367 | C4×C8 | — | 2 | 1 | no | — |
| 368 | C4×C8 | — | 2 | 1 | no | — |
| 369 | C4×C8 | — | 2 | 1 | no | — |
| 370 | C4×C8 | — | 2 | 1 | no | — |
| 371 | C4×C8 | — | 2 | 1 | no | — |
| 372 | C4×C8 | — | 4 | 1 | no | — |
| 373 | C4×C8 | — | 4 | 2 | no | — |
| 374 | C4×C8 | — | 4 | 4 | no | — |
| 375 | C4×C8 | — | 8 | 2 | no | — |
| 376 | C4×C8 | — | 8 | 2 | no | — |
| 377 | C4×C8 | C2×C22⋊C8 | 1 | 1 | yes | characteristic |
| 378 | C4×C8 | #408 | 1 | 1 | yes | characteristic |
| 379 | C4×C8 | C2×#104 | 1 | 1 | yes | characteristic |
| 380 | C4×C8 | #421 | 1 | 1 | yes | characteristic |
| 381 | C4×C8 | C8×D4 | 1 | 1 | yes | characteristic |
| 382 | C4×C8 | C8×D4 | 1 | 1 | yes | characteristic |
| 383 | C4×C8 | #436 | 1 | 1 | yes | characteristic |
| 384 | C4×C8 | #436 | 1 | 1 | yes | characteristic |
| 385 | C4×C8 | #444 | 1 | 1 | yes | characteristic |
| 386 | C4×C8 | #444 | 1 | 1 | yes | characteristic |
| 387 | C24 | — | 16 | 2 | no | — |
| 388 | C2×D4 | — | 8 | 4 | no | — |
| 389 | C2×D4 | — | 8 | 4 | no | — |
| 390 | C2×D4 | — | 8 | 4 | no | — |
| 391 | C2×D4 | — | 16 | 4 | no | — |
| 392 | C2×D4 | — | 16 | 4 | no | — |
| 393 | C2×D4 | — | 16 | 2 | no | — |
| 394 | C2×D4 | — | 16 | 2 | no | — |
| 395 | C2×D4 | — | 16 | 2 | no | — |
| 396 | C2×D4 | — | 16 | 2 | no | — |
| 397 | C2×D4 | — | 16 | 2 | no | — |
| 398 | C2×D4 | — | 16 | 2 | no | — |
| 399 | C2×D4 | — | 16 | 2 | no | — |
| 400 | C2×D4 | — | 16 | 2 | no | — |
| 401 | C2×D4 | — | 16 | 2 | no | — |
| 402 | C2×D4 | — | 16 | 2 | no | — |
| 403 | C2×D4 | — | 16 | 2 | no | — |
| 404 | C22×C4 | — | 16 | 2 | no | — |
| 405 | C22×C4 | — | 32 | 4 | no | — |
| 406 | C22×C4 | — | 32 | 4 | no | — |
| 407 | C22×C4 | — | 32 | 4 | no | — |
| 408 | C22×C4 | #1687 | 1 | 2 | yes | — |
| 409 | C22×C4 | #1688 | 1 | 2 | yes | — |
| 410 | C22×C4 | #1972 | 1 | 1 | yes | characteristic |
| 411 | C22×C4 | #1978 | 1 | 1 | yes | characteristic |
| 412 | C22×C4 | #1982 | 1 | 1 | yes | characteristic |
| 413 | D8 | — | 8 | 8 | no | — |
| 414 | D8 | — | 8 | 8 | no | — |
| 415 | D8 | — | 8 | 4 | no | — |
| 416 | D8 | — | 8 | 4 | no | — |
| 417 | D8 | — | 16 | 4 | no | — |
| 418 | D8 | — | 16 | 4 | no | — |
| 419 | D8 | — | 16 | 8 | no | — |
| 420 | D8 | — | 16 | 8 | no | — |
| 421 | D8 | — | 16 | 4 | no | — |
| 422 | D8 | — | 16 | 4 | no | — |
| 423 | D8 | — | 16 | 2 | no | — |
| 424 | D8 | — | 16 | 2 | no | — |
| 425 | C2×C8 | — | 2 | 4 | no | — |
| 426 | C2×C8 | — | 2 | 1 | no | — |
| 427 | C2×C8 | — | 2 | 2 | no | — |
| 428 | C2×C8 | — | 2 | 1 | no | — |
| 429 | C2×C8 | — | 2 | 1 | no | — |
| 430 | C2×C8 | — | 2 | 1 | no | — |
| 431 | C2×C8 | — | 2 | 1 | no | — |
| 432 | C2×C8 | — | 2 | 1 | no | — |
| 433 | C2×C8 | — | 2 | 1 | no | — |
| 434 | C2×C8 | — | 2 | 2 | no | — |
| 435 | C2×C8 | — | 2 | 2 | no | — |
| 436 | C2×C8 | — | 2 | 1 | no | — |
| 437 | C2×C8 | — | 2 | 1 | no | — |
| 438 | C2×C8 | — | 2 | 2 | no | — |
| 439 | C2×C8 | — | 4 | 2 | no | — |
| 440 | C2×C8 | — | 4 | 1 | no | — |
| 441 | C2×C8 | — | 16 | 2 | no | — |
| 442 | C2×C8 | — | 16 | 2 | no | — |
| 443 | C2×C8 | — | 16 | 2 | no | — |
| 444 | C2×C8 | C2×D4⋊C8 | 1 | 1 | yes | characteristic |
| 445 | C2×C8 | #1478 | 1 | 1 | yes | characteristic |
| 446 | C2×C8 | #1480 | 1 | 1 | yes | characteristic |
| 447 | C2×C8 | #1484 | 1 | 1 | yes | characteristic |
| 448 | C2×C8 | #1580 | 1 | 1 | yes | characteristic |
| 449 | C2×C8 | #1580 | 1 | 1 | yes | characteristic |
| 450 | C2×C8 | #1594 | 1 | 1 | yes | characteristic |
| 451 | C2×C8 | #1594 | 1 | 1 | yes | characteristic |
| 452 | C2×C8 | C2×#360 | 1 | 1 | yes | characteristic |
| 453 | C2×C8 | #2145 | 1 | 1 | yes | characteristic |
| 454 | C2×C8 | C2×#361 | 1 | 1 | yes | characteristic |
| 455 | C2×C8 | C2×#361 | 1 | 1 | yes | characteristic |
| 456 | C2×C8 | AGL(1,ℤ/16) | 1 | 4 | yes | — |
| 457 | C2×C8 | #2213 | 1 | 2 | yes | — |
| 458 | C4⋊C4 | — | 16 | 4 | no | — |
| 459 | C4⋊C4 | — | 16 | 2 | no | — |
| 460 | C4⋊C4 | — | 16 | 2 | no | — |
| 461 | C4⋊C4 | — | 16 | 2 | no | — |
| 462 | C4⋊C4 | — | 16 | 2 | no | — |
| 463 | C22⋊C4 | — | 32 | 4 | no | — |
| 464 | C22⋊C4 | — | 32 | 4 | no | — |
| 465 | C22⋊C4 | — | 32 | 4 | no | — |
| 466 | C42 | — | 2 | 2 | no | — |
| 467 | C42 | — | 2 | 2 | no | — |
| 468 | C42 | — | 2 | 1 | no | — |
| 469 | C42 | — | 2 | 1 | no | — |
| 470 | C42 | — | 2 | 1 | no | — |
| 471 | C42 | — | 2 | 1 | no | — |
| 472 | C42 | — | 4 | 2 | no | — |
| 473 | C42 | #1954 | 1 | 1 | yes | characteristic |
| 474 | C42 | #1975 | 1 | 1 | yes | characteristic |
| 475 | C42 | #1976 | 1 | 1 | yes | characteristic |
| 476 | C42 | #1980 | 1 | 1 | yes | characteristic |
| 477 | C16 | — | 2 | 4 | no | — |
| 478 | C16 | — | 2 | 2 | no | — |
| 479 | C16 | — | 2 | 2 | no | — |
| 480 | C16 | — | 4 | 2 | no | — |
| 481 | C16 | — | 4 | 1 | no | — |
| 482 | C16 | — | 16 | 2 | no | — |
| 483 | C16 | — | 16 | 4 | no | — |
| 484 | C16 | #1333 | 1 | 4 | yes | complemented |
| 485 | C23 | — | 16 | 4 | no | — |
| 486 | C23 | — | 32 | 2 | no | — |
| 487 | C23 | — | 32 | 2 | no | — |
| 488 | C23 | — | 32 | 2 | no | — |
| 489 | C23 | — | 32 | 2 | no | — |
| 490 | C23 | — | 32 | 2 | no | — |
| 491 | C23 | — | 32 | 2 | no | — |
| 492 | C23 | #9743 | 1 | 1 | yes | characteristic |
| 493 | D4 | — | 16 | 8 | no | — |
| 494 | D4 | — | 16 | 4 | no | — |
| 495 | D4 | — | 16 | 4 | no | — |
| 496 | D4 | — | 16 | 4 | no | — |
| 497 | D4 | — | 16 | 4 | no | — |
| 498 | D4 | — | 32 | 4 | no | — |
| 499 | D4 | — | 32 | 2 | no | — |
| 500 | D4 | — | 32 | 2 | no | — |
| 501 | D4 | — | 32 | 2 | no | — |
| 502 | D4 | — | 32 | 2 | no | — |
| 503 | C2×C4 | — | 2 | 2 | no | — |
| 504 | C2×C4 | — | 2 | 2 | no | — |
| 505 | C2×C4 | — | 2 | 2 | no | — |
| 506 | C2×C4 | — | 2 | 2 | no | — |
| 507 | C2×C4 | — | 2 | 2 | no | — |
| 508 | C2×C4 | — | 2 | 2 | no | — |
| 509 | C2×C4 | — | 2 | 2 | no | — |
| 510 | C2×C4 | — | 32 | 2 | no | — |
| 511 | C2×C4 | — | 32 | 2 | no | — |
| 512 | C2×C4 | — | 32 | 2 | no | — |
| 513 | C2×C4 | — | 64 | 8 | no | — |
| 514 | C2×C4 | #9659 | 1 | 1 | yes | characteristic |
| 515 | C2×C4 | #9668 | 1 | 1 | yes | characteristic |
| 516 | C2×C4 | #9674 | 1 | 1 | yes | characteristic |
| 517 | C2×C4 | #9721 | 1 | 1 | yes | characteristic |
| 518 | C2×C4 | #9726 | 1 | 1 | yes | characteristic |
| 519 | C2×C4 | #9753 | 1 | 1 | yes | characteristic |
| 520 | C2×C4 | #13247 | 1 | 2 | yes | — |
| 521 | C2×C4 | #13249 | 1 | 2 | yes | — |
| 522 | C2×C4 | #13255 | 1 | 1 | yes | characteristic |
| 523 | C2×C4 | #13257 | 1 | 1 | yes | characteristic |
| 524 | C2×C4 | #13259 | 1 | 1 | yes | characteristic |
| 525 | C2×C4 | #13261 | 1 | 1 | yes | characteristic |
| 526 | C8 | — | 2 | 2 | no | — |
| 527 | C8 | — | 2 | 2 | no | — |
| 528 | C8 | — | 2 | 2 | no | — |
| 529 | C8 | — | 2 | 1 | no | — |
| 530 | C8 | — | 2 | 1 | no | — |
| 531 | C8 | — | 2 | 1 | no | — |
| 532 | C8 | — | 2 | 1 | no | — |
| 533 | C8 | — | 4 | 1 | no | — |
| 534 | C8 | — | 4 | 2 | no | — |
| 535 | C8 | — | 8 | 1 | no | — |
| 536 | C8 | — | 32 | 2 | no | — |
| 537 | C8 | C2×#1333 | 1 | 1 | yes | characteristic |
| 538 | C8 | #11599 | 1 | 1 | yes | characteristic |
| 539 | C8 | #11652 | 1 | 1 | yes | characteristic |
| 540 | C8 | #11654 | 1 | 1 | yes | characteristic |
| 541 | C8 | #12067 | 1 | 2 | yes | — |
| 542 | C8 | #12089 | 1 | 2 | yes | — |
| 543 | C22 | — | 32 | 4 | no | — |
| 544 | C22 | — | 32 | 4 | no | — |
| 545 | C22 | — | 32 | 4 | no | — |
| 546 | C22 | — | 64 | 2 | no | — |
| 547 | C22 | — | 64 | 2 | no | — |
| 548 | C22 | — | 64 | 2 | no | — |
| 549 | C22 | — | 64 | 2 | no | — |
| 550 | C22 | #102005 | 1 | 1 | yes | characteristic |
| 551 | C22 | #141294 | 1 | 1 | yes | characteristic |
| 552 | C22 | #141296 | 1 | 1 | yes | characteristic |
| 553 | C22 | #141298 | 1 | 2 | yes | — |
| 554 | C22 | #141301 | 1 | 2 | yes | — |
| 555 | C4 | — | 2 | 1 | no | — |
| 556 | C4 | — | 2 | 1 | no | — |
| 557 | C4 | — | 4 | 2 | no | — |
| 558 | C4 | — | 4 | 2 | no | — |
| 559 | C4 | — | 64 | 2 | no | — |
| 560 | C4 | #140747 | 1 | 1 | yes | characteristic |
| 561 | C4 | #140751 | 1 | 1 | yes | characteristic |
| 562 | C4 | #140846 | 1 | 1 | yes | characteristic |
| 563 | C4 | #140849 | 1 | 1 | yes | characteristic |
| 564 | C4 | #141213 | 1 | 2 | yes | — |
| 565 | C4 | #141339 | 1 | 1 | yes | characteristic |
| 566 | C4 | #141341 | 1 | 1 | yes | characteristic |
| 567 | C2 | — | 64 | 4 | no | — |
| 568 | C2 | #72216299 | 1 | 1 | yes | characteristic |
| 569 | C2 | #72216424 | 1 | 1 | yes | characteristic |
| 570 | C2 | #72227094 | 1 | 1 | yes | characteristic |
| 571 | C2 | #72227225 | 1 | 2 | yes | — |
| 572 | C2 | #72227226 | 1 | 2 | yes | — |
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