← #72319907
Subgroups — #72319907
Order 1024.
759 conjugacy classes of subgroups.
The subgroup lattice has 470 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #483608 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #483463 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #225782 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #225708 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #140506 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #140494 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #136464 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #136462 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #135801 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #135073 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #129184 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #33484 | C22 | 1 | 2 | yes | — |
| 13 | #22686 | — | 2 | 1 | no | — |
| 14 | #18055 | — | 2 | 1 | no | — |
| 15 | C8×#135 | C22 | 1 | 1 | yes | characteristic |
| 16 | #17834 | C22 | 1 | 2 | yes | — |
| 17 | #17826 | C22 | 1 | 2 | yes | — |
| 18 | C4×#365 | C22 | 1 | 1 | yes | characteristic |
| 19 | #12062 | C4 | 1 | 2 | yes | complemented |
| 20 | #12061 | C4 | 1 | 2 | yes | complemented |
| 21 | #12057 | C4 | 1 | 2 | yes | complemented |
| 22 | #12057 | C4 | 1 | 2 | yes | complemented |
| 23 | #12030 | — | 2 | 2 | no | — |
| 24 | #12030 | C22 | 1 | 2 | yes | — |
| 25 | #12029 | C22 | 1 | 2 | yes | — |
| 26 | #12028 | — | 2 | 2 | no | — |
| 27 | #12020 | C22 | 1 | 2 | yes | — |
| 28 | #12020 | C22 | 1 | 2 | yes | — |
| 29 | #12019 | — | 2 | 2 | no | — |
| 30 | #12013 | C22 | 1 | 1 | yes | characteristic |
| 31 | #12000 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×#1368 | — | 2 | 2 | no | — |
| 33 | #11615 | C22 | 1 | 2 | yes | — |
| 34 | #11402 | C22 | 1 | 1 | yes | characteristic |
| 35 | #9634 | — | 2 | 1 | no | — |
| 36 | #9631 | — | 2 | 1 | no | — |
| 37 | #8904 | — | 2 | 2 | no | — |
| 38 | #8900 | — | 2 | 2 | no | — |
| 39 | #8824 | C22 | 1 | 1 | yes | characteristic |
| 40 | #8822 | C22 | 1 | 1 | yes | characteristic |
| 41 | #8670 | C22 | 1 | 2 | yes | — |
| 42 | #8666 | C22 | 1 | 2 | yes | — |
| 43 | C8×#108 | C22 | 1 | 1 | yes | characteristic |
| 44 | #8283 | C22 | 1 | 1 | yes | characteristic |
| 45 | #7302 | C22 | 1 | 2 | yes | — |
| 46 | #7300 | C22 | 1 | 2 | yes | — |
| 47 | #7174 | C22 | 1 | 1 | yes | characteristic |
| 48 | #7173 | C22 | 1 | 1 | yes | characteristic |
| 49 | #2990 | — | 2 | 2 | no | — |
| 50 | C8×#41 | C23 | 1 | 2 | yes | — |
| 51 | C2×#444 | — | 4 | 1 | no | — |
| 52 | C4×#135 | D4 | 1 | 1 | yes | characteristic |
| 53 | #2906 | — | 2 | 2 | no | — |
| 54 | #2183 | C2×C4 | 1 | 2 | yes | — |
| 55 | #2183 | C2×C4 | 1 | 2 | yes | — |
| 56 | #2168 | — | 2 | 2 | no | — |
| 57 | #2168 | — | 2 | 2 | no | — |
| 58 | D4×C16 | C2×C4 | 1 | 2 | yes | — |
| 59 | D4×C16 | C2×C4 | 1 | 2 | yes | — |
| 60 | #2163 | — | 2 | 2 | no | — |
| 61 | #2163 | C23 | 1 | 2 | yes | — |
| 62 | C2×#365 | — | 2 | 1 | no | — |
| 63 | C4×M32 | C23 | 1 | 1 | yes | characteristic |
| 64 | C4×M32 | C23 | 1 | 1 | yes | characteristic |
| 65 | C2×#346 | — | 2 | 2 | no | — |
| 66 | #1946 | — | 4 | 1 | no | — |
| 67 | #1866 | — | 4 | 2 | no | — |
| 68 | #1848 | — | 2 | 1 | no | — |
| 69 | #1837 | — | 2 | 1 | no | — |
| 70 | #1806 | — | 2 | 2 | no | — |
| 71 | C4×#108 | C23 | 1 | 1 | yes | characteristic |
| 72 | C4×#106 | C23 | 1 | 1 | yes | characteristic |
| 73 | #1770 | — | 2 | 1 | no | — |
| 74 | #1591 | — | 4 | 1 | no | — |
| 75 | #1585 | — | 4 | 2 | no | — |
| 76 | C8×Q16 | C2×C4 | 1 | 1 | yes | characteristic |
| 77 | C8×Q16 | Q8 | 1 | 1 | yes | characteristic |
| 78 | C8×SD16 | C2×C4 | 1 | 2 | yes | — |
| 79 | C8×SD16 | Q8 | 1 | 2 | yes | — |
| 80 | C8×D8 | — | 4 | 1 | no | — |
| 81 | C8×D8 | C2×C4 | 1 | 1 | yes | characteristic |
| 82 | C8×D8 | Q8 | 1 | 1 | yes | characteristic |
| 83 | #1574 | — | 2 | 2 | no | — |
| 84 | #1573 | — | 4 | 2 | no | — |
| 85 | #1570 | — | 2 | 2 | no | — |
| 86 | #1570 | — | 4 | 2 | no | — |
| 87 | #1568 | — | 2 | 2 | no | — |
| 88 | #1567 | — | 2 | 1 | no | — |
| 89 | #1566 | — | 2 | 2 | no | — |
| 90 | #1566 | — | 2 | 1 | no | — |
| 91 | #1566 | C23 | 1 | 2 | yes | — |
| 92 | #1566 | C23 | 1 | 2 | yes | — |
| 93 | #1564 | D4 | 1 | 1 | yes | characteristic |
| 94 | #1564 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×#334 | — | 2 | 2 | no | — |
| 96 | C2×#334 | — | 2 | 2 | no | — |
| 97 | C2×#334 | C23 | 1 | 1 | yes | characteristic |
| 98 | #1489 | — | 2 | 2 | no | — |
| 99 | #1476 | D4 | 1 | 2 | yes | — |
| 100 | C8×M16 | — | 2 | 1 | no | — |
| 101 | C2×C82 | C23 | 1 | 1 | yes | characteristic |
| 102 | #1383 | — | 2 | 1 | no | — |
| 103 | #1370 | C2×C4 | 1 | 1 | yes | characteristic |
| 104 | #1370 | C2×C4 | 1 | 1 | yes | characteristic |
| 105 | #1368 | — | 2 | 2 | no | — |
| 106 | #1368 | — | 2 | 2 | no | — |
| 107 | #1368 | — | 2 | 2 | no | — |
| 108 | #1368 | — | 2 | 2 | no | — |
| 109 | #1368 | — | 2 | 2 | no | — |
| 110 | #1368 | — | 2 | 2 | no | — |
| 111 | #1368 | — | 4 | 2 | no | — |
| 112 | #1368 | D4 | 1 | 2 | yes | — |
| 113 | #1368 | D4 | 1 | 2 | yes | — |
| 114 | #1367 | C2×C4 | 1 | 2 | yes | — |
| 115 | Q8⋊C16 | C2×C4 | 1 | 2 | yes | — |
| 116 | Q8⋊C16 | C2×C4 | 1 | 2 | yes | — |
| 117 | D4⋊C16 | C2×C4 | 1 | 2 | yes | — |
| 118 | D4⋊C16 | C2×C4 | 1 | 2 | yes | — |
| 119 | #1312 | C2×C4 | 1 | 2 | yes | — |
| 120 | #1312 | C2×C4 | 1 | 2 | yes | — |
| 121 | #1303 | — | 2 | 2 | no | — |
| 122 | #1299 | — | 2 | 2 | no | — |
| 123 | #1279 | — | 2 | 1 | no | — |
| 124 | #1278 | — | 2 | 1 | no | — |
| 125 | C2×#135 | SD16 | 1 | 1 | yes | characteristic |
| 126 | C2×#131 | — | 4 | 2 | no | — |
| 127 | C4×#41 | C2×D4 | 1 | 2 | yes | — |
| 128 | C2×M32 | — | 2 | 1 | no | — |
| 129 | C2×M32 | #41 | 1 | 1 | yes | characteristic |
| 130 | C2×M32 | #41 | 1 | 1 | yes | characteristic |
| 131 | C22×C16 | — | 2 | 2 | no | — |
| 132 | C22×C16 | — | 2 | 2 | no | — |
| 133 | #446 | — | 4 | 2 | no | — |
| 134 | C8×Q8 | C22×C4 | 1 | 2 | yes | — |
| 135 | C8×Q8 | C2×Q8 | 1 | 2 | yes | — |
| 136 | #444 | — | 8 | 4 | no | — |
| 137 | C4×Q16 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 138 | C4×Q16 | SD16 | 1 | 1 | yes | characteristic |
| 139 | C4×SD16 | C4⋊C4 | 1 | 2 | yes | — |
| 140 | C4×SD16 | SD16 | 1 | 2 | yes | — |
| 141 | C4×D8 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 142 | C4×D8 | SD16 | 1 | 1 | yes | characteristic |
| 143 | #435 | — | 8 | 2 | no | — |
| 144 | C8×D4 | — | 2 | 2 | no | — |
| 145 | C8×D4 | — | 2 | 2 | no | — |
| 146 | C8×D4 | — | 4 | 2 | no | — |
| 147 | C8×D4 | C22×C4 | 1 | 2 | yes | — |
| 148 | C8×D4 | C2×Q8 | 1 | 2 | yes | — |
| 149 | #432 | — | 4 | 2 | no | — |
| 150 | #431 | — | 2 | 2 | no | — |
| 151 | #431 | — | 2 | 1 | no | — |
| 152 | #431 | C2×D4 | 1 | 2 | yes | — |
| 153 | C2×#108 | — | 2 | 1 | no | — |
| 154 | C2×#108 | — | 4 | 1 | no | — |
| 155 | C2×#108 | — | 4 | 1 | no | — |
| 156 | #427 | SD16 | 1 | 1 | yes | characteristic |
| 157 | C2×#106 | — | 2 | 1 | no | — |
| 158 | #424 | — | 4 | 2 | no | — |
| 159 | #424 | — | 8 | 2 | no | — |
| 160 | #423 | — | 2 | 2 | no | — |
| 161 | #423 | — | 2 | 2 | no | — |
| 162 | #423 | — | 4 | 2 | no | — |
| 163 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 164 | C2×C4⋊C8 | — | 4 | 2 | no | — |
| 165 | C2×C4⋊C8 | — | 4 | 2 | no | — |
| 166 | C2×#104 | — | 4 | 2 | no | — |
| 167 | #416 | SD16 | 1 | 2 | yes | — |
| 168 | C4×M16 | — | 2 | 1 | no | — |
| 169 | C2×#97 | — | 4 | 1 | no | — |
| 170 | C2×C4×C8 | — | 2 | 2 | no | — |
| 171 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 172 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | C2×C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 174 | C4×C4⋊C4 | — | 2 | 1 | no | — |
| 175 | #365 | — | 4 | 2 | no | — |
| 176 | C4⋊C16 | — | 2 | 2 | no | — |
| 177 | C4⋊C16 | — | 2 | 2 | no | — |
| 178 | C4⋊C16 | C22×C4 | 1 | 2 | yes | — |
| 179 | C4⋊C16 | C22×C4 | 1 | 2 | yes | — |
| 180 | C22⋊C16 | — | 2 | 2 | no | — |
| 181 | C22⋊C16 | — | 2 | 2 | no | — |
| 182 | C22⋊C16 | — | 2 | 2 | no | — |
| 183 | #346 | — | 2 | 2 | no | — |
| 184 | #346 | — | 2 | 2 | no | — |
| 185 | #346 | — | 2 | 2 | no | — |
| 186 | #346 | — | 2 | 1 | no | — |
| 187 | #346 | C2×D4 | 1 | 2 | yes | — |
| 188 | C4×C16 | C22×C4 | 1 | 2 | yes | — |
| 189 | C4×C16 | C22×C4 | 1 | 2 | yes | — |
| 190 | #341 | — | 2 | 1 | no | — |
| 191 | #341 | — | 8 | 1 | no | — |
| 192 | #340 | — | 2 | 1 | no | — |
| 193 | #339 | — | 4 | 2 | no | — |
| 194 | #336 | — | 4 | 1 | no | — |
| 195 | #335 | — | 2 | 1 | no | — |
| 196 | #335 | — | 4 | 2 | no | — |
| 197 | #335 | — | 4 | 1 | no | — |
| 198 | #335 | — | 4 | 1 | no | — |
| 199 | #335 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 200 | #335 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 201 | #334 | — | 2 | 2 | no | — |
| 202 | #334 | — | 2 | 2 | no | — |
| 203 | #334 | — | 2 | 1 | no | — |
| 204 | #334 | — | 2 | 2 | no | — |
| 205 | #334 | — | 2 | 2 | no | — |
| 206 | #334 | — | 4 | 2 | no | — |
| 207 | #334 | — | 4 | 2 | no | — |
| 208 | #334 | — | 4 | 2 | no | — |
| 209 | #334 | — | 8 | 1 | no | — |
| 210 | #334 | C4⋊C4 | 1 | 2 | yes | — |
| 211 | #334 | C2×D4 | 1 | 1 | yes | characteristic |
| 212 | #334 | C2×D4 | 1 | 2 | yes | — |
| 213 | #334 | C2×D4 | 1 | 1 | yes | characteristic |
| 214 | Q8⋊C8 | — | 4 | 2 | no | — |
| 215 | Q8⋊C8 | C4⋊C4 | 1 | 2 | yes | — |
| 216 | Q8⋊C8 | C4⋊C4 | 1 | 2 | yes | — |
| 217 | D4⋊C8 | — | 4 | 2 | no | — |
| 218 | D4⋊C8 | C4⋊C4 | 1 | 2 | yes | — |
| 219 | D4⋊C8 | C4⋊C4 | 1 | 2 | yes | — |
| 220 | #322 | — | 4 | 1 | no | — |
| 221 | C82 | — | 4 | 1 | no | — |
| 222 | C82 | C22×C4 | 1 | 1 | yes | characteristic |
| 223 | C82 | C22×C4 | 1 | 1 | yes | characteristic |
| 224 | C82 | C2×Q8 | 1 | 1 | yes | characteristic |
| 225 | C82 | C2×Q8 | 1 | 1 | yes | characteristic |
| 226 | C2×#41 | C2×SD16 | 1 | 2 | yes | — |
| 227 | #135 | — | 2 | 4 | no | — |
| 228 | C2×Q16 | #106 | 1 | 1 | yes | characteristic |
| 229 | C2×SD16 | #106 | 1 | 2 | yes | — |
| 230 | C2×D8 | #106 | 1 | 1 | yes | characteristic |
| 231 | #131 | — | 8 | 4 | no | — |
| 232 | #131 | — | 16 | 2 | no | — |
| 233 | C2×M16 | — | 4 | 1 | no | — |
| 234 | C2×M16 | — | 4 | 2 | no | — |
| 235 | C2×M16 | — | 4 | 2 | no | — |
| 236 | C2×M16 | — | 8 | 2 | no | — |
| 237 | C22×C8 | — | 2 | 1 | no | — |
| 238 | C22×C8 | — | 2 | 2 | no | — |
| 239 | C22×C8 | — | 2 | 2 | no | — |
| 240 | C22×C8 | — | 4 | 1 | no | — |
| 241 | C22×C8 | — | 8 | 2 | no | — |
| 242 | C22×C8 | — | 8 | 2 | no | — |
| 243 | C22×C8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 244 | C22×C8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 245 | C22×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 246 | C22×C8 | 2−1+4 | 1 | 1 | yes | characteristic |
| 247 | C4×Q8 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 248 | C4×Q8 | C2×SD16 | 1 | 2 | yes | — |
| 249 | C4×D4 | — | 2 | 2 | no | — |
| 250 | C4×D4 | — | 2 | 2 | no | — |
| 251 | C4×D4 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 252 | C4×D4 | C2×SD16 | 1 | 2 | yes | — |
| 253 | #117 | — | 2 | 2 | no | — |
| 254 | #117 | C2×SD16 | 1 | 2 | yes | — |
| 255 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 256 | C2×C42 | — | 2 | 2 | no | — |
| 257 | C2×C42 | — | 4 | 1 | no | — |
| 258 | C2×C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 259 | M32 | — | 4 | 1 | no | — |
| 260 | M32 | — | 4 | 1 | no | — |
| 261 | M32 | — | 8 | 1 | no | — |
| 262 | C2×C16 | — | 2 | 2 | no | — |
| 263 | C2×C16 | — | 2 | 2 | no | — |
| 264 | C2×C16 | — | 2 | 2 | no | — |
| 265 | C2×C16 | — | 4 | 4 | no | — |
| 266 | C2×C16 | — | 8 | 2 | no | — |
| 267 | C2×C16 | C4×D4 | 1 | 2 | yes | — |
| 268 | C2×C16 | C4×D4 | 1 | 2 | yes | — |
| 269 | #108 | — | 2 | 2 | no | — |
| 270 | #108 | — | 4 | 1 | no | — |
| 271 | #108 | — | 8 | 2 | no | — |
| 272 | #108 | — | 16 | 1 | no | — |
| 273 | #107 | #106 | 1 | 1 | yes | characteristic |
| 274 | #107 | #106 | 1 | 1 | yes | characteristic |
| 275 | #106 | — | 4 | 1 | no | — |
| 276 | #106 | — | 4 | 1 | no | — |
| 277 | #106 | #106 | 1 | 2 | yes | — |
| 278 | C4⋊C8 | — | 2 | 2 | no | — |
| 279 | C4⋊C8 | — | 2 | 2 | no | — |
| 280 | C4⋊C8 | — | 2 | 2 | no | — |
| 281 | C4⋊C8 | — | 2 | 1 | no | — |
| 282 | C4⋊C8 | — | 2 | 1 | no | — |
| 283 | C4⋊C8 | — | 4 | 2 | no | — |
| 284 | C4⋊C8 | — | 4 | 2 | no | — |
| 285 | C4⋊C8 | — | 4 | 2 | no | — |
| 286 | C4⋊C8 | — | 4 | 1 | no | — |
| 287 | C4⋊C8 | — | 4 | 2 | no | — |
| 288 | C4⋊C8 | — | 8 | 2 | no | — |
| 289 | C4⋊C8 | — | 8 | 2 | no | — |
| 290 | C4⋊C8 | — | 8 | 2 | no | — |
| 291 | C4⋊C8 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 292 | C4⋊C8 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 293 | #104 | — | 8 | 4 | no | — |
| 294 | #103 | #106 | 1 | 2 | yes | — |
| 295 | #103 | #106 | 1 | 2 | yes | — |
| 296 | #102 | #106 | 1 | 2 | yes | — |
| 297 | #102 | #106 | 1 | 2 | yes | — |
| 298 | C22⋊C8 | — | 2 | 2 | no | — |
| 299 | C22⋊C8 | — | 2 | 2 | no | — |
| 300 | C22⋊C8 | — | 2 | 2 | no | — |
| 301 | C22⋊C8 | — | 4 | 1 | no | — |
| 302 | C22⋊C8 | — | 8 | 2 | no | — |
| 303 | #97 | — | 4 | 1 | no | — |
| 304 | #97 | — | 8 | 2 | no | — |
| 305 | #97 | — | 8 | 2 | no | — |
| 306 | C4×C8 | — | 2 | 2 | no | — |
| 307 | C4×C8 | — | 2 | 2 | no | — |
| 308 | C4×C8 | — | 2 | 2 | no | — |
| 309 | C4×C8 | — | 2 | 1 | no | — |
| 310 | C4×C8 | — | 4 | 1 | no | — |
| 311 | C4×C8 | — | 4 | 1 | no | — |
| 312 | C4×C8 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 313 | C4×C8 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 314 | C4×C8 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 315 | C4×C8 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 316 | C4×C8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 317 | C4×C8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 318 | C4×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 319 | C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 320 | C4×C8 | C22×Q8 | 1 | 1 | yes | characteristic |
| 321 | C4×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 322 | #95 | — | 4 | 1 | no | — |
| 323 | #41 | — | 2 | 4 | no | — |
| 324 | #41 | — | 4 | 2 | no | — |
| 325 | C2×Q8 | C2×#106 | 1 | 2 | yes | — |
| 326 | C2×D4 | — | 2 | 2 | no | — |
| 327 | C2×D4 | C2×#106 | 1 | 2 | yes | — |
| 328 | C22×C4 | — | 2 | 2 | no | — |
| 329 | C22×C4 | — | 2 | 2 | no | — |
| 330 | C22×C4 | — | 2 | 2 | no | — |
| 331 | C22×C4 | — | 8 | 1 | no | — |
| 332 | C22×C4 | #547 | 1 | 1 | yes | characteristic |
| 333 | C22×C4 | C22×SD16 | 1 | 1 | yes | characteristic |
| 334 | C22×C4 | #577 | 1 | 1 | yes | characteristic |
| 335 | Q16 | — | 2 | 2 | no | — |
| 336 | SD16 | — | 2 | 4 | no | — |
| 337 | D8 | #365 | 1 | 4 | yes | complemented |
| 338 | M16 | — | 4 | 2 | no | — |
| 339 | M16 | — | 8 | 1 | no | — |
| 340 | M16 | — | 8 | 2 | no | — |
| 341 | M16 | — | 8 | 2 | no | — |
| 342 | M16 | — | 16 | 4 | no | — |
| 343 | M16 | — | 16 | 2 | no | — |
| 344 | C2×C8 | — | 2 | 2 | no | — |
| 345 | C2×C8 | — | 2 | 1 | no | — |
| 346 | C2×C8 | — | 2 | 1 | no | — |
| 347 | C2×C8 | — | 2 | 2 | no | — |
| 348 | C2×C8 | — | 2 | 2 | no | — |
| 349 | C2×C8 | — | 2 | 1 | no | — |
| 350 | C2×C8 | — | 2 | 1 | no | — |
| 351 | C2×C8 | — | 4 | 1 | no | — |
| 352 | C2×C8 | — | 4 | 1 | no | — |
| 353 | C2×C8 | — | 4 | 2 | no | — |
| 354 | C2×C8 | — | 4 | 2 | no | — |
| 355 | C2×C8 | — | 4 | 1 | no | — |
| 356 | C2×C8 | — | 4 | 1 | no | — |
| 357 | C2×C8 | — | 4 | 2 | no | — |
| 358 | C2×C8 | — | 8 | 2 | no | — |
| 359 | C2×C8 | — | 8 | 1 | no | — |
| 360 | C2×C8 | — | 8 | 1 | no | — |
| 361 | C2×C8 | — | 8 | 1 | no | — |
| 362 | C2×C8 | — | 8 | 1 | no | — |
| 363 | C2×C8 | — | 8 | 2 | no | — |
| 364 | C2×C8 | — | 8 | 2 | no | — |
| 365 | C2×C8 | — | 16 | 4 | no | — |
| 366 | C2×C8 | — | 32 | 2 | no | — |
| 367 | C2×C8 | C2×#106 | 1 | 1 | yes | characteristic |
| 368 | C2×C8 | C2×#106 | 1 | 1 | yes | characteristic |
| 369 | C2×C8 | C2×#106 | 1 | 1 | yes | characteristic |
| 370 | C2×C8 | C2×#106 | 1 | 1 | yes | characteristic |
| 371 | C2×C8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 372 | C2×C8 | #520 | 1 | 1 | yes | characteristic |
| 373 | C2×C8 | D4×Q8 | 1 | 1 | yes | characteristic |
| 374 | C2×C8 | #554 | 1 | 1 | yes | characteristic |
| 375 | C4⋊C4 | — | 2 | 2 | no | — |
| 376 | C4⋊C4 | — | 2 | 2 | no | — |
| 377 | C4⋊C4 | — | 8 | 1 | no | — |
| 378 | C4⋊C4 | — | 8 | 1 | no | — |
| 379 | C4⋊C4 | C2×#106 | 1 | 2 | yes | — |
| 380 | C4⋊C4 | C2×#106 | 1 | 2 | yes | — |
| 381 | C22⋊C4 | — | 2 | 2 | no | — |
| 382 | C22⋊C4 | — | 2 | 2 | no | — |
| 383 | C22⋊C4 | — | 2 | 2 | no | — |
| 384 | C42 | — | 2 | 2 | no | — |
| 385 | C42 | — | 2 | 2 | no | — |
| 386 | C42 | — | 2 | 2 | no | — |
| 387 | C42 | — | 8 | 1 | no | — |
| 388 | C42 | — | 8 | 1 | no | — |
| 389 | C42 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 390 | C42 | D42 | 1 | 1 | yes | characteristic |
| 391 | C42 | C22×SD16 | 1 | 1 | yes | characteristic |
| 392 | C42 | #577 | 1 | 1 | yes | characteristic |
| 393 | C16 | — | 2 | 2 | no | — |
| 394 | C16 | — | 2 | 2 | no | — |
| 395 | C16 | — | 4 | 2 | no | — |
| 396 | C16 | — | 4 | 2 | no | — |
| 397 | C16 | — | 4 | 2 | no | — |
| 398 | C23 | — | 2 | 2 | no | — |
| 399 | C23 | #3335 | 1 | 1 | yes | characteristic |
| 400 | Q8 | — | 2 | 2 | no | — |
| 401 | Q8 | — | 2 | 2 | no | — |
| 402 | D4 | — | 2 | 2 | no | — |
| 403 | D4 | — | 4 | 4 | no | — |
| 404 | D4 | C2×#365 | 1 | 4 | yes | — |
| 405 | C2×C4 | — | 2 | 1 | no | — |
| 406 | C2×C4 | — | 2 | 1 | no | — |
| 407 | C2×C4 | — | 2 | 1 | no | — |
| 408 | C2×C4 | — | 2 | 1 | no | — |
| 409 | C2×C4 | — | 2 | 2 | no | — |
| 410 | C2×C4 | — | 2 | 2 | no | — |
| 411 | C2×C4 | — | 2 | 2 | no | — |
| 412 | C2×C4 | — | 4 | 1 | no | — |
| 413 | C2×C4 | — | 4 | 4 | no | — |
| 414 | C2×C4 | — | 4 | 2 | no | — |
| 415 | C2×C4 | — | 4 | 2 | no | — |
| 416 | C2×C4 | — | 8 | 2 | no | — |
| 417 | C2×C4 | — | 16 | 1 | no | — |
| 418 | C2×C4 | — | 16 | 1 | no | — |
| 419 | C2×C4 | — | 16 | 1 | no | — |
| 420 | C2×C4 | D4×C4⋊C4 | 1 | 1 | yes | characteristic |
| 421 | C2×C4 | C22×#106 | 1 | 1 | yes | characteristic |
| 422 | C2×C4 | #2912 | 1 | 1 | yes | characteristic |
| 423 | C2×C4 | D4×SD16 | 1 | 1 | yes | characteristic |
| 424 | C2×C4 | D4×SD16 | 1 | 1 | yes | characteristic |
| 425 | C2×C4 | #3335 | 1 | 1 | yes | characteristic |
| 426 | C8 | — | 2 | 1 | no | — |
| 427 | C8 | — | 2 | 1 | no | — |
| 428 | C8 | — | 2 | 1 | no | — |
| 429 | C8 | — | 2 | 1 | no | — |
| 430 | C8 | — | 2 | 1 | no | — |
| 431 | C8 | — | 2 | 1 | no | — |
| 432 | C8 | — | 4 | 1 | no | — |
| 433 | C8 | — | 4 | 1 | no | — |
| 434 | C8 | — | 4 | 2 | no | — |
| 435 | C8 | — | 4 | 2 | no | — |
| 436 | C8 | — | 8 | 1 | no | — |
| 437 | C8 | — | 8 | 2 | no | — |
| 438 | C8 | — | 8 | 1 | no | — |
| 439 | C8 | — | 8 | 2 | no | — |
| 440 | C8 | — | 16 | 2 | no | — |
| 441 | C8 | — | 16 | 2 | no | — |
| 442 | C8 | C2×#365 | 1 | 2 | yes | — |
| 443 | C8 | #2955 | 1 | 1 | yes | characteristic |
| 444 | C8 | #2956 | 1 | 1 | yes | characteristic |
| 445 | C22 | — | 2 | 1 | no | — |
| 446 | C22 | — | 2 | 4 | no | — |
| 447 | C22 | — | 2 | 1 | no | — |
| 448 | C22 | — | 2 | 1 | no | — |
| 449 | C22 | — | 4 | 2 | no | — |
| 450 | C22 | — | 4 | 2 | no | — |
| 451 | C22 | D4×#106 | 1 | 1 | yes | characteristic |
| 452 | C4 | — | 2 | 1 | no | — |
| 453 | C4 | — | 2 | 1 | no | — |
| 454 | C4 | — | 2 | 1 | no | — |
| 455 | C4 | — | 2 | 1 | no | — |
| 456 | C4 | — | 4 | 2 | no | — |
| 457 | C4 | — | 4 | 2 | no | — |
| 458 | C4 | — | 4 | 2 | no | — |
| 459 | C4 | — | 32 | 1 | no | — |
| 460 | C4 | #22687 | 1 | 1 | yes | characteristic |
| 461 | C4 | #22695 | 1 | 1 | yes | characteristic |
| 462 | C4 | C22×#365 | 1 | 1 | yes | characteristic |
| 463 | C4 | #33404 | 1 | 1 | yes | characteristic |
| 464 | C2 | — | 4 | 1 | no | — |
| 465 | C2 | — | 4 | 4 | no | — |
| 466 | C2 | #225714 | 1 | 1 | yes | characteristic |
| 467 | C2 | D4×#365 | 1 | 1 | yes | characteristic |
| 468 | C2 | #497839 | 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