← #72225522
Subgroups — #72225522
Order 2048.
763 conjugacy classes of subgroups.
The subgroup lattice has 500 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72225489 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72225474 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #72225456 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72225435 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #72225407 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72225375 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72216241 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #491485 | C22 | 1 | 1 | yes | characteristic |
| 9 | #483943 | — | 2 | 1 | no | — |
| 10 | #483943 | C4 | 1 | 2 | yes | — |
| 11 | #213237 | — | 2 | 1 | no | — |
| 12 | #151042 | C22 | 1 | 1 | yes | characteristic |
| 13 | #151042 | C22 | 1 | 1 | yes | characteristic |
| 14 | #149513 | — | 2 | 1 | no | — |
| 15 | #141812 | — | 2 | 1 | no | — |
| 16 | #141786 | — | 2 | 1 | no | — |
| 17 | #141786 | C4 | 1 | 2 | yes | — |
| 18 | #135796 | C22 | 1 | 1 | yes | characteristic |
| 19 | #129093 | — | 2 | 1 | no | — |
| 20 | C8×#346 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#7101 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#7100 | C22 | 1 | 1 | yes | characteristic |
| 23 | #94011 | — | 2 | 1 | no | — |
| 24 | #93873 | C4 | 1 | 2 | yes | complemented |
| 25 | #93869 | C4 | 1 | 2 | yes | complemented |
| 26 | #93864 | C4 | 1 | 4 | yes | complemented |
| 27 | #92911 | — | 2 | 1 | no | — |
| 28 | #33733 | — | 2 | 1 | no | — |
| 29 | #33733 | C2×C4 | 1 | 2 | yes | — |
| 30 | #21705 | — | 4 | 1 | no | — |
| 31 | #19603 | — | 2 | 1 | no | — |
| 32 | #17956 | — | 2 | 2 | no | — |
| 33 | #17956 | — | 4 | 1 | no | — |
| 34 | #13640 | — | 2 | 1 | no | — |
| 35 | #13640 | — | 2 | 1 | no | — |
| 36 | #12653 | — | 4 | 1 | no | — |
| 37 | C4×#346 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | C4×#346 | D4 | 1 | 1 | yes | characteristic |
| 39 | #12521 | C2×C4 | 1 | 1 | yes | characteristic |
| 40 | #12515 | C2×C4 | 1 | 1 | yes | characteristic |
| 41 | #12509 | — | 2 | 1 | no | — |
| 42 | #12503 | — | 2 | 1 | no | — |
| 43 | #12503 | C2×C4 | 1 | 2 | yes | — |
| 44 | #12086 | — | 4 | 2 | no | — |
| 45 | #12086 | — | 4 | 1 | no | — |
| 46 | #12086 | — | 4 | 1 | no | — |
| 47 | #12045 | — | 4 | 2 | no | — |
| 48 | #12045 | — | 4 | 1 | no | — |
| 49 | #12045 | — | 4 | 1 | no | — |
| 50 | #12023 | — | 2 | 1 | no | — |
| 51 | #12023 | C2×C4 | 1 | 2 | yes | — |
| 52 | C2×#1370 | — | 2 | 1 | no | — |
| 53 | C2×#1370 | — | 2 | 1 | no | — |
| 54 | #11671 | — | 2 | 2 | no | — |
| 55 | #11671 | — | 2 | 2 | no | — |
| 56 | C2×#1311 | C2×C4 | 1 | 1 | yes | characteristic |
| 57 | C2×#1311 | D4 | 1 | 1 | yes | characteristic |
| 58 | C2×C8×C16 | D4 | 1 | 1 | yes | characteristic |
| 59 | C2×C8×C16 | C23 | 1 | 1 | yes | characteristic |
| 60 | #9856 | — | 4 | 1 | no | — |
| 61 | #9844 | — | 2 | 2 | no | — |
| 62 | #9844 | — | 4 | 1 | no | — |
| 63 | #8823 | — | 2 | 1 | no | — |
| 64 | C4×C82 | D4 | 1 | 1 | yes | characteristic |
| 65 | #7458 | — | 2 | 1 | no | — |
| 66 | #7458 | C2×C4 | 1 | 2 | yes | — |
| 67 | #7455 | — | 2 | 1 | no | — |
| 68 | #7455 | C2×C4 | 1 | 2 | yes | — |
| 69 | #7332 | — | 4 | 1 | no | — |
| 70 | #7330 | — | 4 | 1 | no | — |
| 71 | #7151 | — | 4 | 1 | no | — |
| 72 | #7101 | — | 2 | 1 | no | — |
| 73 | #7101 | C2×C4 | 1 | 2 | yes | — |
| 74 | #7100 | — | 2 | 1 | no | — |
| 75 | #7100 | C2×C4 | 1 | 2 | yes | — |
| 76 | #3169 | — | 2 | 2 | no | — |
| 77 | #3169 | — | 4 | 1 | no | — |
| 78 | #3147 | — | 4 | 1 | no | — |
| 79 | C2×#443 | — | 8 | 2 | no | — |
| 80 | #2931 | — | 4 | 2 | no | — |
| 81 | #2252 | — | 2 | 1 | no | — |
| 82 | #2252 | C42 | 1 | 2 | yes | — |
| 83 | #2246 | — | 2 | 1 | no | — |
| 84 | #2246 | C42 | 1 | 2 | yes | — |
| 85 | #2240 | — | 2 | 2 | no | — |
| 86 | #2240 | — | 2 | 2 | no | — |
| 87 | #2215 | — | 4 | 1 | no | — |
| 88 | #2215 | — | 4 | 1 | no | — |
| 89 | #2215 | — | 4 | 2 | no | — |
| 90 | C4×D16 | — | 4 | 2 | no | — |
| 91 | C4×D16 | — | 4 | 1 | no | — |
| 92 | C4×D16 | — | 4 | 1 | no | — |
| 93 | C2×C4⋊C16 | — | 4 | 1 | no | — |
| 94 | C2×C4⋊C16 | — | 4 | 1 | no | — |
| 95 | C2×#346 | — | 2 | 1 | no | — |
| 96 | C2×#346 | — | 2 | 1 | no | — |
| 97 | C2×#346 | — | 4 | 1 | no | — |
| 98 | C2×#346 | — | 8 | 1 | no | — |
| 99 | C2×C4×C16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 100 | C2×C4×C16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 101 | C2×C4×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 102 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 103 | #1974 | — | 8 | 2 | no | — |
| 104 | #1962 | — | 4 | 2 | no | — |
| 105 | #1848 | — | 4 | 1 | no | — |
| 106 | C42×C8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 107 | C42×C8 | D8 | 1 | 1 | yes | characteristic |
| 108 | C42×C8 | SD16 | 1 | 1 | yes | characteristic |
| 109 | #1713 | — | 2 | 1 | no | — |
| 110 | #1712 | — | 2 | 1 | no | — |
| 111 | #1709 | — | 4 | 1 | no | — |
| 112 | #1706 | — | 2 | 2 | no | — |
| 113 | #1706 | — | 4 | 1 | no | — |
| 114 | #1589 | — | 4 | 2 | no | — |
| 115 | #1589 | — | 4 | 2 | no | — |
| 116 | #1589 | — | 8 | 1 | no | — |
| 117 | #1589 | — | 8 | 1 | no | — |
| 118 | C8×D8 | — | 4 | 2 | no | — |
| 119 | C8×D8 | — | 4 | 2 | no | — |
| 120 | C8×D8 | — | 8 | 1 | no | — |
| 121 | C8×D8 | — | 8 | 1 | no | — |
| 122 | #1567 | — | 2 | 2 | no | — |
| 123 | #1567 | — | 4 | 1 | no | — |
| 124 | #1492 | — | 4 | 2 | no | — |
| 125 | #1492 | — | 4 | 2 | no | — |
| 126 | C2×C82 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 127 | C2×C82 | D8 | 1 | 1 | yes | characteristic |
| 128 | C2×C82 | SD16 | 1 | 1 | yes | characteristic |
| 129 | C2×C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 130 | C4⋊C32 | — | 2 | 2 | no | — |
| 131 | C4⋊C32 | — | 2 | 2 | no | — |
| 132 | C22⋊C32 | — | 4 | 1 | no | — |
| 133 | C22⋊C32 | — | 4 | 1 | no | — |
| 134 | #1397 | — | 4 | 1 | no | — |
| 135 | #1397 | — | 4 | 1 | no | — |
| 136 | #1374 | — | 8 | 1 | no | — |
| 137 | #1372 | — | 4 | 1 | no | — |
| 138 | #1372 | — | 4 | 1 | no | — |
| 139 | #1372 | — | 4 | 2 | no | — |
| 140 | #1370 | — | 2 | 2 | no | — |
| 141 | #1370 | — | 2 | 2 | no | — |
| 142 | #1370 | — | 4 | 1 | no | — |
| 143 | #1370 | — | 4 | 1 | no | — |
| 144 | #1331 | — | 4 | 4 | no | — |
| 145 | #1331 | — | 4 | 2 | no | — |
| 146 | #1331 | — | 4 | 2 | no | — |
| 147 | #1311 | — | 2 | 1 | no | — |
| 148 | #1311 | — | 2 | 1 | no | — |
| 149 | #1311 | D8 | 1 | 1 | yes | characteristic |
| 150 | #1311 | D8 | 1 | 1 | yes | characteristic |
| 151 | #1311 | SD16 | 1 | 1 | yes | characteristic |
| 152 | #1311 | SD16 | 1 | 1 | yes | characteristic |
| 153 | C8×C16 | — | 2 | 1 | no | — |
| 154 | C8×C16 | — | 2 | 1 | no | — |
| 155 | C8×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 156 | C8×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 157 | C8×C16 | #41 | 1 | 1 | yes | characteristic |
| 158 | C8×C16 | #41 | 1 | 1 | yes | characteristic |
| 159 | C2×#135 | — | 8 | 2 | no | — |
| 160 | C2×#131 | — | 8 | 2 | no | — |
| 161 | #532 | — | 4 | 2 | no | — |
| 162 | C2×D16 | — | 4 | 2 | no | — |
| 163 | C2×D16 | — | 4 | 1 | no | — |
| 164 | C2×D16 | — | 4 | 1 | no | — |
| 165 | C22×C16 | — | 2 | 1 | no | — |
| 166 | C22×C16 | — | 2 | 1 | no | — |
| 167 | C22×C16 | — | 2 | 1 | no | — |
| 168 | C22×C16 | — | 8 | 1 | no | — |
| 169 | C22×C16 | — | 8 | 1 | no | — |
| 170 | C22×C16 | #135 | 1 | 1 | yes | characteristic |
| 171 | C22×C16 | #135 | 1 | 1 | yes | characteristic |
| 172 | #500 | — | 2 | 2 | no | — |
| 173 | #500 | — | 4 | 1 | no | — |
| 174 | #495 | — | 8 | 2 | no | — |
| 175 | #494 | — | 4 | 1 | no | — |
| 176 | #493 | — | 2 | 2 | no | — |
| 177 | #493 | — | 4 | 1 | no | — |
| 178 | #493 | — | 4 | 1 | no | — |
| 179 | #492 | — | 4 | 2 | no | — |
| 180 | #486 | — | 4 | 2 | no | — |
| 181 | #486 | — | 4 | 2 | no | — |
| 182 | #466 | — | 4 | 2 | no | — |
| 183 | #466 | — | 4 | 2 | no | — |
| 184 | #466 | — | 8 | 1 | no | — |
| 185 | #466 | — | 8 | 1 | no | — |
| 186 | #443 | — | 16 | 8 | no | — |
| 187 | C4×D8 | — | 4 | 2 | no | — |
| 188 | C4×D8 | — | 4 | 2 | no | — |
| 189 | C4×D8 | — | 8 | 1 | no | — |
| 190 | C4×D8 | — | 8 | 1 | no | — |
| 191 | #436 | — | 8 | 2 | no | — |
| 192 | #436 | — | 8 | 2 | no | — |
| 193 | C8×D4 | — | 8 | 2 | no | — |
| 194 | C8×D4 | — | 8 | 2 | no | — |
| 195 | C2×#108 | — | 8 | 2 | no | — |
| 196 | #423 | — | 4 | 2 | no | — |
| 197 | C2×#104 | — | 8 | 4 | no | — |
| 198 | #408 | — | 8 | 2 | no | — |
| 199 | C2×C4×C8 | — | 2 | 1 | no | — |
| 200 | C2×C4×C8 | — | 2 | 1 | no | — |
| 201 | C2×C4×C8 | — | 2 | 1 | no | — |
| 202 | C2×C4×C8 | — | 2 | 2 | no | — |
| 203 | C2×C4×C8 | — | 2 | 1 | no | — |
| 204 | C2×C4×C8 | #102 | 1 | 1 | yes | characteristic |
| 205 | C2×C4×C8 | #102 | 1 | 1 | yes | characteristic |
| 206 | C2×C4×C8 | #102 | 1 | 1 | yes | characteristic |
| 207 | C2×C4×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 208 | C2×C4×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 209 | C2×C4×C8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 210 | C43 | #102 | 1 | 1 | yes | characteristic |
| 211 | C2×C32 | — | 4 | 2 | no | — |
| 212 | C2×C32 | — | 4 | 2 | no | — |
| 213 | #366 | — | 4 | 1 | no | — |
| 214 | #366 | — | 4 | 1 | no | — |
| 215 | #366 | — | 4 | 2 | no | — |
| 216 | C4⋊C16 | — | 4 | 2 | no | — |
| 217 | C4⋊C16 | — | 4 | 2 | no | — |
| 218 | C4⋊C16 | — | 8 | 1 | no | — |
| 219 | C4⋊C16 | — | 8 | 1 | no | — |
| 220 | #357 | — | 4 | 4 | no | — |
| 221 | #357 | — | 4 | 2 | no | — |
| 222 | #357 | — | 4 | 2 | no | — |
| 223 | #346 | — | 4 | 2 | no | — |
| 224 | #346 | — | 4 | 2 | no | — |
| 225 | #346 | — | 4 | 4 | no | — |
| 226 | #346 | — | 16 | 2 | no | — |
| 227 | C4×C16 | — | 2 | 1 | no | — |
| 228 | C4×C16 | — | 2 | 1 | no | — |
| 229 | C4×C16 | — | 2 | 1 | no | — |
| 230 | C4×C16 | — | 2 | 1 | no | — |
| 231 | C4×C16 | #102 | 1 | 1 | yes | characteristic |
| 232 | C4×C16 | #102 | 1 | 1 | yes | characteristic |
| 233 | C4×C16 | C2×C42 | 1 | 1 | yes | characteristic |
| 234 | C4×C16 | #117 | 1 | 1 | yes | characteristic |
| 235 | C4×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 236 | C4×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 237 | C4×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 238 | C4×C16 | C2×SD16 | 1 | 1 | yes | characteristic |
| 239 | #335 | — | 4 | 2 | no | — |
| 240 | #335 | — | 4 | 2 | no | — |
| 241 | #335 | — | 8 | 1 | no | — |
| 242 | #335 | — | 8 | 1 | no | — |
| 243 | D4⋊C8 | — | 8 | 2 | no | — |
| 244 | D4⋊C8 | — | 8 | 2 | no | — |
| 245 | D4⋊C8 | — | 8 | 2 | no | — |
| 246 | D4⋊C8 | — | 8 | 2 | no | — |
| 247 | C82 | — | 2 | 1 | no | — |
| 248 | C82 | — | 2 | 1 | no | — |
| 249 | C82 | — | 4 | 1 | no | — |
| 250 | C82 | #100 | 1 | 1 | yes | characteristic |
| 251 | C82 | #100 | 1 | 1 | yes | characteristic |
| 252 | C82 | #102 | 1 | 1 | yes | characteristic |
| 253 | C82 | #102 | 1 | 1 | yes | characteristic |
| 254 | C82 | C4×D4 | 1 | 1 | yes | characteristic |
| 255 | C82 | C4×D4 | 1 | 1 | yes | characteristic |
| 256 | C82 | #135 | 1 | 1 | yes | characteristic |
| 257 | C82 | #135 | 1 | 1 | yes | characteristic |
| 258 | C2×#41 | — | 8 | 2 | no | — |
| 259 | #135 | — | 16 | 4 | no | — |
| 260 | #135 | — | 16 | 4 | no | — |
| 261 | C2×Q16 | — | 8 | 2 | no | — |
| 262 | C2×SD16 | — | 8 | 4 | no | — |
| 263 | C2×D8 | — | 4 | 2 | no | — |
| 264 | C2×D8 | — | 4 | 2 | no | — |
| 265 | C2×D8 | — | 8 | 2 | no | — |
| 266 | C2×D8 | — | 8 | 1 | no | — |
| 267 | C2×D8 | — | 8 | 1 | no | — |
| 268 | #131 | — | 16 | 8 | no | — |
| 269 | C2×M16 | — | 8 | 2 | no | — |
| 270 | C2×M16 | — | 16 | 2 | no | — |
| 271 | C22×C8 | — | 2 | 1 | no | — |
| 272 | C22×C8 | — | 2 | 1 | no | — |
| 273 | C22×C8 | — | 2 | 1 | no | — |
| 274 | C22×C8 | — | 2 | 1 | no | — |
| 275 | C22×C8 | — | 16 | 2 | no | — |
| 276 | C22×C8 | #413 | 1 | 1 | yes | characteristic |
| 277 | C22×C8 | #416 | 1 | 1 | yes | characteristic |
| 278 | C22×C8 | #509 | 1 | 1 | yes | characteristic |
| 279 | C22×C8 | #510 | 1 | 1 | yes | characteristic |
| 280 | C4⋊Q8 | — | 4 | 2 | no | — |
| 281 | #127 | — | 4 | 2 | no | — |
| 282 | #124 | — | 8 | 2 | no | — |
| 283 | #121 | — | 8 | 2 | no | — |
| 284 | #121 | — | 8 | 2 | no | — |
| 285 | C4×D4 | — | 8 | 2 | no | — |
| 286 | C4×D4 | — | 8 | 2 | no | — |
| 287 | C2×C42 | — | 2 | 1 | no | — |
| 288 | C2×C42 | — | 2 | 1 | no | — |
| 289 | C2×C42 | #361 | 1 | 2 | yes | — |
| 290 | C2×C42 | C2×#102 | 1 | 1 | yes | characteristic |
| 291 | D16 | — | 8 | 4 | no | — |
| 292 | D16 | — | 8 | 2 | no | — |
| 293 | D16 | — | 8 | 2 | no | — |
| 294 | C2×C16 | — | 2 | 1 | no | — |
| 295 | C2×C16 | — | 2 | 1 | no | — |
| 296 | C2×C16 | — | 2 | 2 | no | — |
| 297 | C2×C16 | — | 2 | 2 | no | — |
| 298 | C2×C16 | — | 2 | 1 | no | — |
| 299 | C2×C16 | — | 2 | 1 | no | — |
| 300 | C2×C16 | — | 4 | 1 | no | — |
| 301 | C2×C16 | — | 4 | 2 | no | — |
| 302 | C2×C16 | — | 4 | 2 | no | — |
| 303 | C2×C16 | — | 4 | 1 | no | — |
| 304 | C2×C16 | — | 4 | 1 | no | — |
| 305 | C2×C16 | — | 8 | 2 | no | — |
| 306 | C2×C16 | — | 8 | 2 | no | — |
| 307 | C2×C16 | — | 16 | 1 | no | — |
| 308 | C2×C16 | — | 16 | 1 | no | — |
| 309 | C2×C16 | — | 16 | 1 | no | — |
| 310 | C2×C16 | — | 16 | 1 | no | — |
| 311 | C2×C16 | C4×D8 | 1 | 1 | yes | characteristic |
| 312 | C2×C16 | C4×D8 | 1 | 1 | yes | characteristic |
| 313 | C2×C16 | C4×SD16 | 1 | 1 | yes | characteristic |
| 314 | C2×C16 | C4×SD16 | 1 | 1 | yes | characteristic |
| 315 | #108 | — | 16 | 4 | no | — |
| 316 | #107 | — | 4 | 2 | no | — |
| 317 | #107 | — | 4 | 2 | no | — |
| 318 | #107 | — | 8 | 1 | no | — |
| 319 | #107 | — | 8 | 1 | no | — |
| 320 | C4⋊C8 | — | 8 | 2 | no | — |
| 321 | C4⋊C8 | — | 8 | 2 | no | — |
| 322 | #104 | — | 16 | 8 | no | — |
| 323 | #102 | — | 8 | 2 | no | — |
| 324 | #102 | — | 8 | 2 | no | — |
| 325 | #102 | — | 8 | 2 | no | — |
| 326 | #102 | — | 8 | 2 | no | — |
| 327 | C22⋊C8 | — | 16 | 2 | no | — |
| 328 | C22⋊C8 | — | 16 | 2 | no | — |
| 329 | C4×C8 | — | 2 | 1 | no | — |
| 330 | C4×C8 | — | 2 | 1 | no | — |
| 331 | C4×C8 | — | 2 | 1 | no | — |
| 332 | C4×C8 | — | 2 | 1 | no | — |
| 333 | C4×C8 | — | 2 | 1 | no | — |
| 334 | C4×C8 | — | 4 | 1 | no | — |
| 335 | C4×C8 | — | 4 | 1 | no | — |
| 336 | C4×C8 | — | 4 | 2 | no | — |
| 337 | C4×C8 | — | 4 | 1 | no | — |
| 338 | C4×C8 | — | 4 | 1 | no | — |
| 339 | C4×C8 | — | 4 | 4 | no | — |
| 340 | C4×C8 | — | 8 | 1 | no | — |
| 341 | C4×C8 | #331 | 1 | 1 | yes | characteristic |
| 342 | C4×C8 | #331 | 1 | 1 | yes | characteristic |
| 343 | C4×C8 | #331 | 1 | 1 | yes | characteristic |
| 344 | C4×C8 | #331 | 1 | 1 | yes | characteristic |
| 345 | C4×C8 | C4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 346 | C4×C8 | C2×#100 | 1 | 1 | yes | characteristic |
| 347 | C4×C8 | C2×#102 | 1 | 1 | yes | characteristic |
| 348 | C4×C8 | #416 | 1 | 1 | yes | characteristic |
| 349 | C4×C8 | C4×D8 | 1 | 1 | yes | characteristic |
| 350 | C4×C8 | C4×D8 | 1 | 1 | yes | characteristic |
| 351 | C4×C8 | C4×SD16 | 1 | 1 | yes | characteristic |
| 352 | C4×C8 | C4×SD16 | 1 | 1 | yes | characteristic |
| 353 | C4×C8 | #509 | 1 | 1 | yes | characteristic |
| 354 | C4×C8 | #509 | 1 | 1 | yes | characteristic |
| 355 | C32 | — | 8 | 2 | no | — |
| 356 | C32 | — | 8 | 2 | no | — |
| 357 | #41 | — | 16 | 4 | no | — |
| 358 | #41 | — | 16 | 4 | no | — |
| 359 | C2×Q8 | — | 8 | 2 | no | — |
| 360 | C2×D4 | — | 8 | 2 | no | — |
| 361 | C2×D4 | — | 8 | 2 | no | — |
| 362 | C2×D4 | — | 8 | 2 | no | — |
| 363 | C2×D4 | — | 16 | 2 | no | — |
| 364 | C22×C4 | — | 2 | 2 | no | — |
| 365 | C22×C4 | — | 16 | 2 | no | — |
| 366 | C22×C4 | #1540 | 1 | 1 | yes | characteristic |
| 367 | C22×C4 | #2139 | 1 | 1 | yes | characteristic |
| 368 | C22×C4 | C2×#361 | 1 | 1 | yes | characteristic |
| 369 | Q16 | — | 16 | 4 | no | — |
| 370 | SD16 | — | 16 | 8 | no | — |
| 371 | D8 | — | 8 | 4 | no | — |
| 372 | D8 | — | 8 | 2 | no | — |
| 373 | D8 | — | 8 | 2 | no | — |
| 374 | D8 | — | 16 | 2 | no | — |
| 375 | D8 | — | 16 | 4 | no | — |
| 376 | D8 | — | 16 | 1 | no | — |
| 377 | D8 | — | 16 | 1 | no | — |
| 378 | M16 | — | 16 | 4 | no | — |
| 379 | M16 | — | 32 | 4 | no | — |
| 380 | C2×C8 | — | 2 | 4 | no | — |
| 381 | C2×C8 | — | 2 | 1 | no | — |
| 382 | C2×C8 | — | 2 | 1 | no | — |
| 383 | C2×C8 | — | 2 | 1 | no | — |
| 384 | C2×C8 | — | 2 | 1 | no | — |
| 385 | C2×C8 | — | 2 | 1 | no | — |
| 386 | C2×C8 | — | 2 | 1 | no | — |
| 387 | C2×C8 | — | 2 | 2 | no | — |
| 388 | C2×C8 | — | 2 | 1 | no | — |
| 389 | C2×C8 | — | 2 | 1 | no | — |
| 390 | C2×C8 | — | 2 | 1 | no | — |
| 391 | C2×C8 | — | 2 | 1 | no | — |
| 392 | C2×C8 | — | 4 | 1 | no | — |
| 393 | C2×C8 | — | 4 | 1 | no | — |
| 394 | C2×C8 | — | 4 | 1 | no | — |
| 395 | C2×C8 | — | 4 | 1 | no | — |
| 396 | C2×C8 | — | 4 | 2 | no | — |
| 397 | C2×C8 | — | 4 | 1 | no | — |
| 398 | C2×C8 | — | 4 | 1 | no | — |
| 399 | C2×C8 | — | 16 | 2 | no | — |
| 400 | C2×C8 | — | 32 | 4 | no | — |
| 401 | C2×C8 | #1540 | 1 | 1 | yes | characteristic |
| 402 | C2×C8 | #1543 | 1 | 1 | yes | characteristic |
| 403 | C2×C8 | C4×#100 | 1 | 1 | yes | characteristic |
| 404 | C2×C8 | C4×#102 | 1 | 1 | yes | characteristic |
| 405 | C2×C8 | #2175 | 1 | 1 | yes | characteristic |
| 406 | C2×C8 | #2175 | 1 | 1 | yes | characteristic |
| 407 | C2×C8 | #2177 | 1 | 1 | yes | characteristic |
| 408 | C2×C8 | #2177 | 1 | 1 | yes | characteristic |
| 409 | C4⋊C4 | — | 8 | 2 | no | — |
| 410 | C4⋊C4 | — | 8 | 2 | no | — |
| 411 | C22⋊C4 | — | 16 | 2 | no | — |
| 412 | C22⋊C4 | — | 16 | 2 | no | — |
| 413 | C42 | — | 4 | 2 | no | — |
| 414 | C42 | — | 4 | 1 | no | — |
| 415 | C42 | — | 4 | 1 | no | — |
| 416 | C42 | — | 4 | 1 | no | — |
| 417 | C42 | — | 4 | 1 | no | — |
| 418 | C42 | C2×#331 | 1 | 1 | yes | characteristic |
| 419 | C42 | C4×#102 | 1 | 1 | yes | characteristic |
| 420 | C42 | #2140 | 1 | 1 | yes | characteristic |
| 421 | C42 | #2148 | 1 | 1 | yes | characteristic |
| 422 | C16 | — | 2 | 2 | no | — |
| 423 | C16 | — | 2 | 2 | no | — |
| 424 | C16 | — | 2 | 1 | no | — |
| 425 | C16 | — | 2 | 1 | no | — |
| 426 | C16 | — | 2 | 1 | no | — |
| 427 | C16 | — | 4 | 1 | no | — |
| 428 | C16 | — | 4 | 1 | no | — |
| 429 | C16 | — | 4 | 2 | no | — |
| 430 | C16 | — | 16 | 2 | no | — |
| 431 | C16 | — | 16 | 2 | no | — |
| 432 | C16 | #2179 | 1 | 2 | yes | — |
| 433 | C23 | — | 16 | 2 | no | — |
| 434 | C23 | #11952 | 1 | 1 | yes | characteristic |
| 435 | Q8 | — | 16 | 4 | no | — |
| 436 | D4 | — | 16 | 4 | no | — |
| 437 | D4 | — | 16 | 2 | no | — |
| 438 | D4 | — | 16 | 2 | no | — |
| 439 | D4 | — | 16 | 2 | no | — |
| 440 | D4 | — | 16 | 2 | no | — |
| 441 | D4 | — | 32 | 4 | no | — |
| 442 | C2×C4 | — | 2 | 2 | no | — |
| 443 | C2×C4 | — | 2 | 1 | no | — |
| 444 | C2×C4 | — | 2 | 1 | no | — |
| 445 | C2×C4 | — | 2 | 1 | no | — |
| 446 | C2×C4 | — | 2 | 1 | no | — |
| 447 | C2×C4 | — | 4 | 2 | no | — |
| 448 | C2×C4 | — | 4 | 2 | no | — |
| 449 | C2×C4 | — | 4 | 2 | no | — |
| 450 | C2×C4 | — | 16 | 2 | no | — |
| 451 | C2×C4 | — | 32 | 2 | no | — |
| 452 | C2×C4 | — | 32 | 2 | no | — |
| 453 | C2×C4 | C4×#331 | 1 | 1 | yes | characteristic |
| 454 | C2×C4 | #11930 | 1 | 1 | yes | characteristic |
| 455 | C2×C4 | #11931 | 1 | 1 | yes | characteristic |
| 456 | C2×C4 | #11951 | 1 | 1 | yes | characteristic |
| 457 | C2×C4 | #12637 | 1 | 1 | yes | characteristic |
| 458 | C2×C4 | C4×#361 | 1 | 1 | yes | characteristic |
| 459 | C8 | — | 2 | 2 | no | — |
| 460 | C8 | — | 2 | 2 | no | — |
| 461 | C8 | — | 2 | 1 | no | — |
| 462 | C8 | — | 2 | 1 | no | — |
| 463 | C8 | — | 2 | 1 | no | — |
| 464 | C8 | — | 2 | 1 | no | — |
| 465 | C8 | — | 2 | 1 | no | — |
| 466 | C8 | — | 2 | 1 | no | — |
| 467 | C8 | — | 4 | 2 | no | — |
| 468 | C8 | — | 4 | 1 | no | — |
| 469 | C8 | — | 4 | 1 | no | — |
| 470 | C8 | — | 4 | 1 | no | — |
| 471 | C8 | — | 4 | 1 | no | — |
| 472 | C8 | — | 32 | 2 | no | — |
| 473 | C8 | #12642 | 1 | 1 | yes | characteristic |
| 474 | C8 | #12646 | 1 | 1 | yes | characteristic |
| 475 | C8 | #13657 | 1 | 1 | yes | characteristic |
| 476 | C8 | #13658 | 1 | 1 | yes | characteristic |
| 477 | C22 | — | 2 | 1 | no | — |
| 478 | C22 | — | 2 | 1 | no | — |
| 479 | C22 | — | 32 | 2 | no | — |
| 480 | C22 | — | 32 | 2 | no | — |
| 481 | C22 | — | 32 | 2 | no | — |
| 482 | C22 | #128900 | 1 | 1 | yes | characteristic |
| 483 | C22 | #150977 | 1 | 2 | yes | — |
| 484 | C4 | — | 2 | 1 | no | — |
| 485 | C4 | — | 2 | 1 | no | — |
| 486 | C4 | — | 2 | 1 | no | — |
| 487 | C4 | — | 2 | 1 | no | — |
| 488 | C4 | — | 8 | 2 | no | — |
| 489 | C4 | — | 32 | 2 | no | — |
| 490 | C4 | #128897 | 1 | 1 | yes | characteristic |
| 491 | C4 | #128905 | 1 | 1 | yes | characteristic |
| 492 | C4 | #151972 | 1 | 1 | yes | characteristic |
| 493 | C4 | #151973 | 1 | 1 | yes | characteristic |
| 494 | C2 | — | 2 | 2 | no | — |
| 495 | C2 | — | 64 | 2 | no | — |
| 496 | C2 | #72216259 | 1 | 1 | yes | characteristic |
| 497 | C2 | #72225520 | 1 | 1 | yes | characteristic |
| 498 | C2 | #72225521 | 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