← #10802093
Subgroups — #10802093
Order 768.
874 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 | C2×#5143 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #83782 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×#4853 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #78867 | C2 | 1 | 2 | yes | maximal |
| 5 | C3×#1815 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #70710 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #70692 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #70572 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #70304 | C2 | 1 | 2 | yes | maximal |
| 10 | #68982 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #68973 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #21556 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C2×C3×#131 | C22 | 1 | 1 | yes | characteristic |
| 14 | Dic3×#41 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#951 | C22 | 1 | 2 | yes | — |
| 16 | C2×#948 | C22 | 1 | 1 | yes | characteristic |
| 17 | C22×Dic12 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#887 | C22 | 1 | 2 | yes | — |
| 19 | C2×C3×#108 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×C3×#106 | C22 | 1 | 1 | yes | characteristic |
| 21 | C3×#417 | C22 | 1 | 2 | yes | — |
| 22 | #5143 | C4 | 1 | 8 | yes | complemented |
| 23 | C2×#824 | C22 | 1 | 2 | yes | — |
| 24 | C2×#824 | C22 | 1 | 2 | yes | — |
| 25 | #5122 | — | 2 | 1 | no | — |
| 26 | #5122 | C22 | 1 | 1 | yes | characteristic |
| 27 | #5120 | C22 | 1 | 2 | yes | — |
| 28 | Dic3×M16 | — | 2 | 1 | no | — |
| 29 | Dic3×M16 | C22 | 1 | 2 | yes | — |
| 30 | Dic3×M16 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#819 | C22 | 1 | 1 | yes | characteristic |
| 32 | #5101 | — | 2 | 1 | no | — |
| 33 | #5101 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×#815 | — | 2 | 1 | no | — |
| 35 | C2×#815 | C22 | 1 | 1 | yes | characteristic |
| 36 | C2×#810 | C22 | 1 | 2 | yes | — |
| 37 | #4964 | C22 | 1 | 2 | yes | — |
| 38 | #4853 | — | 2 | 1 | no | — |
| 39 | #4853 | — | 2 | 1 | no | — |
| 40 | #4853 | — | 2 | 1 | no | — |
| 41 | #4853 | — | 2 | 1 | no | — |
| 42 | #4790 | — | 2 | 2 | no | — |
| 43 | #4789 | — | 2 | 2 | no | — |
| 44 | #4758 | — | 2 | 2 | no | — |
| 45 | #4757 | — | 2 | 2 | no | — |
| 46 | C3×#343 | C22 | 1 | 2 | yes | — |
| 47 | #4558 | C22 | 1 | 2 | yes | — |
| 48 | #4530 | C22 | 1 | 2 | yes | — |
| 49 | C2×#473 | — | 3 | 1 | no | — |
| 50 | C4×#137 | — | 3 | 2 | no | — |
| 51 | C2×#441 | — | 3 | 1 | no | — |
| 52 | #2875 | — | 3 | 1 | no | — |
| 53 | #1979 | — | 3 | 1 | no | — |
| 54 | #1951 | — | 3 | 1 | no | — |
| 55 | #1930 | — | 3 | 2 | no | — |
| 56 | #1908 | — | 3 | 2 | no | — |
| 57 | #1815 | D3 | 1 | 1 | yes | characteristic |
| 58 | #1778 | — | 3 | 1 | no | — |
| 59 | C4×#101 | — | 3 | 2 | no | — |
| 60 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 61 | C22×Dic6 | C23 | 1 | 2 | yes | — |
| 62 | C3×#131 | — | 2 | 2 | no | — |
| 63 | C3×#131 | C2×C4 | 1 | 4 | yes | — |
| 64 | C2×C3×M16 | — | 2 | 1 | no | — |
| 65 | C2×C3×M16 | C23 | 1 | 2 | yes | — |
| 66 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 67 | C22×C3×C8 | — | 2 | 1 | no | — |
| 68 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×C3×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 70 | #951 | — | 2 | 4 | no | — |
| 71 | #951 | C2×C4 | 1 | 8 | yes | — |
| 72 | #948 | — | 2 | 2 | no | — |
| 73 | #948 | — | 2 | 2 | no | — |
| 74 | Q8×Dic3 | D4 | 1 | 2 | yes | — |
| 75 | C2×#216 | — | 2 | 2 | no | — |
| 76 | D4×Dic3 | — | 2 | 2 | no | — |
| 77 | D4×Dic3 | D4 | 1 | 2 | yes | — |
| 78 | C2×#214 | — | 2 | 2 | no | — |
| 79 | #926 | — | 2 | 1 | no | — |
| 80 | #926 | C23 | 1 | 1 | yes | characteristic |
| 81 | C2×Dic3⋊C4 | — | 2 | 2 | no | — |
| 82 | C2×C4×Dic3 | — | 2 | 1 | no | — |
| 83 | C2×C4×Dic3 | — | 2 | 2 | no | — |
| 84 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 85 | C2×#208 | — | 2 | 1 | no | — |
| 86 | C2×#208 | C23 | 1 | 2 | yes | — |
| 87 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 88 | C22×C3⋊C8 | — | 2 | 1 | no | — |
| 89 | C22×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 90 | C2×Dic12 | — | 2 | 1 | no | — |
| 91 | C2×Dic12 | — | 2 | 1 | no | — |
| 92 | C2×Dic12 | — | 2 | 2 | no | — |
| 93 | C2×Dic12 | C2×C4 | 1 | 4 | yes | complemented |
| 94 | #887 | — | 2 | 2 | no | — |
| 95 | #887 | — | 2 | 2 | no | — |
| 96 | #887 | — | 2 | 2 | no | — |
| 97 | #887 | — | 2 | 2 | no | — |
| 98 | C3×#108 | — | 2 | 2 | no | — |
| 99 | C3×#106 | — | 2 | 1 | no | — |
| 100 | C3×#106 | — | 2 | 1 | no | — |
| 101 | C3×#103 | — | 2 | 2 | no | — |
| 102 | C3×#102 | — | 2 | 2 | no | — |
| 103 | #824 | — | 2 | 4 | no | — |
| 104 | #824 | C2×C4 | 1 | 8 | yes | complemented |
| 105 | #819 | C2×C4 | 1 | 4 | yes | complemented |
| 106 | #816 | — | 2 | 2 | no | — |
| 107 | #816 | — | 2 | 2 | no | — |
| 108 | #815 | — | 2 | 1 | no | — |
| 109 | #815 | — | 2 | 2 | no | — |
| 110 | #815 | — | 2 | 1 | no | — |
| 111 | #815 | — | 2 | 1 | no | — |
| 112 | #815 | D4 | 1 | 1 | yes | characteristic |
| 113 | #815 | D4 | 1 | 1 | yes | characteristic |
| 114 | #815 | D4 | 1 | 1 | yes | characteristic |
| 115 | #815 | D4 | 1 | 1 | yes | characteristic |
| 116 | C8×Dic3 | — | 2 | 1 | no | — |
| 117 | C8×Dic3 | — | 2 | 1 | no | — |
| 118 | C8×Dic3 | — | 2 | 2 | no | — |
| 119 | C8×Dic3 | — | 2 | 1 | no | — |
| 120 | #810 | — | 2 | 2 | no | — |
| 121 | #810 | — | 2 | 2 | no | — |
| 122 | #808 | — | 2 | 2 | no | — |
| 123 | #807 | — | 2 | 2 | no | — |
| 124 | C2×#137 | — | 3 | 2 | no | — |
| 125 | C22×Q16 | — | 3 | 1 | no | — |
| 126 | C2×#131 | — | 3 | 1 | no | — |
| 127 | C2×#131 | C2×D3 | 1 | 1 | yes | characteristic |
| 128 | C4×#41 | — | 3 | 1 | no | — |
| 129 | C2×C4×Q8 | — | 3 | 2 | no | — |
| 130 | #473 | — | 3 | 8 | no | — |
| 131 | #441 | — | 6 | 1 | no | — |
| 132 | #441 | — | 6 | 1 | no | — |
| 133 | #441 | — | 6 | 1 | no | — |
| 134 | #441 | — | 6 | 1 | no | — |
| 135 | #441 | — | 6 | 2 | no | — |
| 136 | #440 | — | 6 | 2 | no | — |
| 137 | C4×Q16 | — | 6 | 2 | no | — |
| 138 | C4×SD16 | — | 6 | 2 | no | — |
| 139 | C2×#108 | — | 3 | 1 | no | — |
| 140 | C2×#108 | C2×D3 | 1 | 1 | yes | characteristic |
| 141 | #428 | — | 3 | 2 | no | — |
| 142 | C2×#106 | C2×D3 | 1 | 1 | yes | characteristic |
| 143 | #419 | — | 3 | 2 | no | — |
| 144 | #417 | C2×D3 | 1 | 2 | yes | — |
| 145 | C2×#103 | — | 3 | 2 | no | — |
| 146 | C2×#101 | — | 3 | 2 | no | — |
| 147 | C2×#101 | — | 3 | 2 | no | — |
| 148 | #405 | — | 3 | 1 | no | — |
| 149 | #405 | — | 3 | 1 | no | — |
| 150 | #405 | — | 6 | 1 | no | — |
| 151 | #405 | — | 6 | 1 | no | — |
| 152 | C4×M16 | — | 3 | 1 | no | — |
| 153 | C4×M16 | — | 3 | 2 | no | — |
| 154 | C4×M16 | — | 6 | 1 | no | — |
| 155 | C2×#97 | — | 3 | 1 | no | — |
| 156 | C2×#97 | — | 6 | 1 | no | — |
| 157 | #343 | — | 3 | 2 | no | — |
| 158 | #343 | C2×D3 | 1 | 2 | yes | — |
| 159 | #341 | — | 3 | 2 | no | — |
| 160 | C3×#41 | — | 2 | 1 | no | — |
| 161 | C3×#41 | — | 2 | 1 | no | — |
| 162 | C3×#41 | C22×C4 | 1 | 2 | yes | — |
| 163 | C3×#41 | #41 | 1 | 2 | yes | — |
| 164 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 165 | C2×C3×D4 | — | 2 | 1 | no | — |
| 166 | C2×C3×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C22×C3×C4 | — | 2 | 1 | no | — |
| 168 | C22×C3×C4 | — | 2 | 2 | no | — |
| 169 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 170 | C22×Dic3 | — | 2 | 2 | no | — |
| 171 | C22×Dic3 | — | 2 | 2 | no | — |
| 172 | C22×Dic3 | #41 | 1 | 2 | yes | — |
| 173 | C2×Dic6 | — | 2 | 2 | no | — |
| 174 | C2×Dic6 | — | 2 | 2 | no | — |
| 175 | C2×Dic6 | — | 2 | 2 | no | — |
| 176 | C2×Dic6 | — | 2 | 2 | no | — |
| 177 | C2×Dic6 | — | 2 | 2 | no | — |
| 178 | C2×Dic6 | C22×C4 | 1 | 4 | yes | — |
| 179 | C3×M16 | — | 2 | 1 | no | — |
| 180 | C3×M16 | — | 2 | 4 | no | — |
| 181 | C3×M16 | — | 2 | 2 | no | — |
| 182 | C3×M16 | — | 2 | 2 | no | — |
| 183 | C3×M16 | C22×C4 | 1 | 2 | yes | — |
| 184 | C2×C3×C8 | — | 2 | 1 | no | — |
| 185 | C2×C3×C8 | — | 2 | 4 | no | — |
| 186 | C2×C3×C8 | — | 2 | 2 | no | — |
| 187 | C2×C3×C8 | C22×C4 | 1 | 2 | yes | — |
| 188 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 189 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 190 | C2×C3×C8 | #41 | 1 | 2 | yes | — |
| 191 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 192 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 193 | #217 | — | 2 | 1 | no | — |
| 194 | #217 | — | 2 | 2 | no | — |
| 195 | #216 | — | 2 | 8 | no | — |
| 196 | #214 | — | 2 | 8 | no | — |
| 197 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 198 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 199 | Dic3⋊C4 | — | 4 | 2 | no | — |
| 200 | Dic3⋊C4 | — | 4 | 2 | no | — |
| 201 | C4×Dic3 | — | 2 | 1 | no | — |
| 202 | C4×Dic3 | — | 2 | 2 | no | — |
| 203 | C4×Dic3 | — | 4 | 2 | no | — |
| 204 | C4×Dic3 | — | 4 | 2 | no | — |
| 205 | C4×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 206 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 207 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 208 | #208 | — | 2 | 4 | no | — |
| 209 | #208 | — | 2 | 1 | no | — |
| 210 | #208 | — | 2 | 2 | no | — |
| 211 | #208 | C22×C4 | 1 | 4 | yes | — |
| 212 | #208 | #41 | 1 | 2 | yes | — |
| 213 | C2×C3⋊C8 | — | 2 | 4 | no | — |
| 214 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 215 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 216 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 217 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 218 | C2×C3⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 219 | C2×C3⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 220 | Dic12 | — | 2 | 4 | no | — |
| 221 | Dic12 | — | 2 | 4 | no | — |
| 222 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 223 | C22×Q8 | — | 3 | 2 | no | — |
| 224 | #137 | — | 3 | 8 | no | — |
| 225 | #137 | — | 6 | 4 | no | — |
| 226 | C2×Q16 | — | 3 | 4 | no | — |
| 227 | C2×Q16 | — | 6 | 2 | no | — |
| 228 | C2×Q16 | — | 6 | 1 | no | — |
| 229 | C2×Q16 | — | 6 | 1 | no | — |
| 230 | C2×Q16 | — | 6 | 2 | no | — |
| 231 | C2×SD16 | — | 6 | 2 | no | — |
| 232 | #131 | — | 2 | 2 | no | — |
| 233 | #131 | — | 6 | 2 | no | — |
| 234 | #131 | — | 6 | 2 | no | — |
| 235 | #131 | C4×D3 | 1 | 4 | yes | — |
| 236 | C2×M16 | — | 2 | 1 | no | — |
| 237 | C2×M16 | — | 3 | 1 | no | — |
| 238 | C2×M16 | — | 3 | 2 | no | — |
| 239 | C2×M16 | — | 6 | 1 | no | — |
| 240 | C2×M16 | C22×D3 | 1 | 2 | yes | — |
| 241 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 242 | C22×C8 | — | 2 | 1 | no | — |
| 243 | C22×C8 | — | 3 | 1 | no | — |
| 244 | C22×C8 | — | 6 | 1 | no | — |
| 245 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 246 | C4×Q8 | — | 3 | 2 | no | — |
| 247 | C4×Q8 | — | 6 | 2 | no | — |
| 248 | C4×Q8 | — | 6 | 2 | no | — |
| 249 | C4×Q8 | — | 6 | 2 | no | — |
| 250 | C4×Q8 | — | 6 | 2 | no | — |
| 251 | C4×D4 | — | 3 | 2 | no | — |
| 252 | C4×D4 | — | 6 | 2 | no | — |
| 253 | #117 | — | 3 | 1 | no | — |
| 254 | #117 | — | 6 | 1 | no | — |
| 255 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 256 | C2×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 257 | C2×C42 | — | 3 | 1 | no | — |
| 258 | C2×C42 | — | 6 | 1 | no | — |
| 259 | C2×C42 | — | 6 | 2 | no | — |
| 260 | #108 | — | 2 | 2 | no | — |
| 261 | #108 | — | 3 | 4 | no | — |
| 262 | #107 | — | 6 | 2 | no | — |
| 263 | #106 | — | 2 | 1 | no | — |
| 264 | #106 | — | 2 | 1 | no | — |
| 265 | #106 | — | 6 | 2 | no | — |
| 266 | #103 | — | 2 | 2 | no | — |
| 267 | #103 | — | 6 | 2 | no | — |
| 268 | #103 | — | 6 | 2 | no | — |
| 269 | #103 | — | 6 | 2 | no | — |
| 270 | #103 | — | 6 | 2 | no | — |
| 271 | #102 | — | 2 | 2 | no | — |
| 272 | #101 | — | 3 | 8 | no | — |
| 273 | #101 | — | 6 | 4 | no | — |
| 274 | #97 | — | 3 | 1 | no | — |
| 275 | #97 | — | 3 | 1 | no | — |
| 276 | #97 | — | 3 | 1 | no | — |
| 277 | #97 | — | 3 | 1 | no | — |
| 278 | #97 | — | 6 | 1 | no | — |
| 279 | #97 | — | 6 | 2 | no | — |
| 280 | #97 | — | 6 | 1 | no | — |
| 281 | #97 | — | 6 | 1 | no | — |
| 282 | C4×C8 | — | 6 | 1 | no | — |
| 283 | C4×C8 | — | 6 | 2 | no | — |
| 284 | C4×C8 | — | 6 | 1 | no | — |
| 285 | C4×C8 | — | 6 | 1 | no | — |
| 286 | C23×C3 | — | 2 | 1 | no | — |
| 287 | C23×C3 | C2×#41 | 1 | 1 | yes | characteristic |
| 288 | C3×Q8 | — | 2 | 1 | no | — |
| 289 | C3×Q8 | C4×D4 | 1 | 2 | yes | — |
| 290 | C3×D4 | — | 2 | 2 | no | — |
| 291 | C3×D4 | — | 2 | 2 | no | — |
| 292 | C3×D4 | — | 2 | 1 | no | — |
| 293 | C3×D4 | C4×D4 | 1 | 2 | yes | — |
| 294 | C2×C3×C4 | — | 2 | 1 | no | — |
| 295 | C2×C3×C4 | — | 2 | 2 | no | — |
| 296 | C2×C3×C4 | — | 2 | 2 | no | — |
| 297 | C2×C3×C4 | — | 4 | 2 | no | — |
| 298 | C2×C3×C4 | — | 8 | 2 | no | — |
| 299 | C2×C3×C4 | C23×C4 | 1 | 1 | yes | characteristic |
| 300 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 301 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 302 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 303 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 304 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 305 | C2×Dic3 | — | 2 | 4 | no | — |
| 306 | C2×Dic3 | — | 2 | 2 | no | — |
| 307 | C2×Dic3 | — | 4 | 2 | no | — |
| 308 | C2×Dic3 | — | 4 | 2 | no | — |
| 309 | C2×Dic3 | — | 4 | 2 | no | — |
| 310 | C2×Dic3 | — | 8 | 2 | no | — |
| 311 | C2×Dic3 | #121 | 1 | 2 | yes | — |
| 312 | C2×Dic3 | #121 | 1 | 2 | yes | — |
| 313 | Dic6 | — | 2 | 4 | no | — |
| 314 | Dic6 | — | 2 | 4 | no | — |
| 315 | Dic6 | — | 4 | 2 | no | — |
| 316 | Dic6 | — | 4 | 2 | no | — |
| 317 | C3×C8 | — | 2 | 2 | no | — |
| 318 | C3×C8 | — | 4 | 2 | no | — |
| 319 | C3×C8 | C4×D4 | 1 | 2 | yes | — |
| 320 | C3×C8 | C4×D4 | 1 | 2 | yes | — |
| 321 | C3⋊C8 | — | 2 | 4 | no | — |
| 322 | C3⋊C8 | — | 2 | 1 | no | — |
| 323 | C3⋊C8 | — | 2 | 2 | no | — |
| 324 | C3⋊C8 | — | 2 | 1 | no | — |
| 325 | #41 | — | 2 | 1 | no | — |
| 326 | #41 | — | 2 | 1 | no | — |
| 327 | #41 | C2×C4×D3 | 1 | 2 | yes | — |
| 328 | #41 | #239 | 1 | 2 | yes | — |
| 329 | C2×Q8 | — | 3 | 4 | no | — |
| 330 | C2×Q8 | — | 6 | 2 | no | — |
| 331 | C2×Q8 | — | 6 | 2 | no | — |
| 332 | C2×Q8 | — | 6 | 2 | no | — |
| 333 | C2×Q8 | — | 6 | 2 | no | — |
| 334 | C2×Q8 | — | 6 | 2 | no | — |
| 335 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 336 | C2×D4 | — | 2 | 1 | no | — |
| 337 | C2×D4 | D3×D4 | 1 | 1 | yes | characteristic |
| 338 | C22×C4 | — | 2 | 1 | no | — |
| 339 | C22×C4 | — | 2 | 2 | no | — |
| 340 | C22×C4 | — | 3 | 2 | no | — |
| 341 | C22×C4 | — | 6 | 2 | no | — |
| 342 | C22×C4 | — | 6 | 2 | no | — |
| 343 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 344 | Q16 | — | 6 | 8 | no | — |
| 345 | Q16 | — | 6 | 4 | no | — |
| 346 | Q16 | — | 6 | 4 | no | — |
| 347 | SD16 | — | 6 | 8 | no | — |
| 348 | M16 | — | 2 | 1 | no | — |
| 349 | M16 | — | 2 | 4 | no | — |
| 350 | M16 | — | 2 | 2 | no | — |
| 351 | M16 | — | 2 | 2 | no | — |
| 352 | M16 | — | 3 | 4 | no | — |
| 353 | M16 | — | 3 | 2 | no | — |
| 354 | M16 | — | 6 | 4 | no | — |
| 355 | M16 | — | 6 | 1 | no | — |
| 356 | M16 | — | 6 | 2 | no | — |
| 357 | M16 | C2×C4×D3 | 1 | 2 | yes | — |
| 358 | C2×C8 | — | 2 | 1 | no | — |
| 359 | C2×C8 | — | 2 | 4 | no | — |
| 360 | C2×C8 | — | 2 | 2 | no | — |
| 361 | C2×C8 | — | 3 | 1 | no | — |
| 362 | C2×C8 | — | 3 | 1 | no | — |
| 363 | C2×C8 | — | 6 | 4 | no | — |
| 364 | C2×C8 | — | 6 | 1 | no | — |
| 365 | C2×C8 | — | 6 | 2 | no | — |
| 366 | C2×C8 | — | 6 | 1 | no | — |
| 367 | C2×C8 | — | 6 | 1 | no | — |
| 368 | C2×C8 | C2×C4×D3 | 1 | 2 | yes | — |
| 369 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 370 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 371 | C2×C8 | #237 | 1 | 2 | yes | — |
| 372 | C4⋊C4 | — | 2 | 2 | no | — |
| 373 | C4⋊C4 | — | 2 | 2 | no | — |
| 374 | C4⋊C4 | — | 3 | 2 | no | — |
| 375 | C4⋊C4 | — | 6 | 2 | no | — |
| 376 | C4⋊C4 | — | 12 | 2 | no | — |
| 377 | C4⋊C4 | — | 12 | 2 | no | — |
| 378 | C22⋊C4 | — | 6 | 2 | no | — |
| 379 | C22⋊C4 | — | 6 | 1 | no | — |
| 380 | C42 | — | 3 | 1 | no | — |
| 381 | C42 | — | 3 | 2 | no | — |
| 382 | C42 | — | 3 | 1 | no | — |
| 383 | C42 | — | 6 | 2 | no | — |
| 384 | C42 | — | 6 | 1 | no | — |
| 385 | C42 | — | 12 | 2 | no | — |
| 386 | C42 | — | 12 | 2 | no | — |
| 387 | C22×C3 | — | 2 | 2 | no | — |
| 388 | C22×C3 | — | 2 | 2 | no | — |
| 389 | C22×C3 | — | 4 | 2 | no | — |
| 390 | C22×C3 | C4×#41 | 1 | 1 | yes | characteristic |
| 391 | C22×C3 | C2×#121 | 1 | 1 | yes | characteristic |
| 392 | C22×C3 | #529 | 1 | 1 | yes | characteristic |
| 393 | C3×C4 | — | 2 | 2 | no | — |
| 394 | C3×C4 | — | 8 | 2 | no | — |
| 395 | C3×C4 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 396 | C3×C4 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 397 | C3×C4 | #525 | 1 | 1 | yes | characteristic |
| 398 | C3×C4 | #532 | 1 | 1 | yes | characteristic |
| 399 | Dic3 | — | 2 | 2 | no | — |
| 400 | Dic3 | — | 2 | 2 | no | — |
| 401 | Dic3 | — | 4 | 4 | no | — |
| 402 | Dic3 | — | 4 | 2 | no | — |
| 403 | C23 | — | 2 | 1 | no | — |
| 404 | C23 | D3×#41 | 1 | 1 | yes | characteristic |
| 405 | Q8 | — | 2 | 1 | no | — |
| 406 | Q8 | — | 6 | 4 | no | — |
| 407 | Q8 | — | 6 | 4 | no | — |
| 408 | Q8 | — | 12 | 2 | no | — |
| 409 | Q8 | — | 12 | 2 | no | — |
| 410 | Q8 | #893 | 1 | 2 | yes | — |
| 411 | D4 | — | 2 | 2 | no | — |
| 412 | D4 | — | 2 | 2 | no | — |
| 413 | D4 | — | 2 | 1 | no | — |
| 414 | D4 | #893 | 1 | 2 | yes | — |
| 415 | C2×C4 | — | 2 | 1 | no | — |
| 416 | C2×C4 | — | 2 | 2 | no | — |
| 417 | C2×C4 | — | 2 | 2 | no | — |
| 418 | C2×C4 | — | 3 | 2 | no | — |
| 419 | C2×C4 | — | 3 | 2 | no | — |
| 420 | C2×C4 | — | 4 | 2 | no | — |
| 421 | C2×C4 | — | 6 | 4 | no | — |
| 422 | C2×C4 | — | 6 | 2 | no | — |
| 423 | C2×C4 | — | 8 | 2 | no | — |
| 424 | C2×C4 | — | 12 | 2 | no | — |
| 425 | C2×C4 | — | 12 | 2 | no | — |
| 426 | C2×C4 | — | 12 | 2 | no | — |
| 427 | C2×C4 | — | 24 | 2 | no | — |
| 428 | C2×C4 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 429 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 430 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 431 | C2×C4 | C2×#237 | 1 | 1 | yes | characteristic |
| 432 | C2×C4 | C2×#239 | 1 | 1 | yes | characteristic |
| 433 | C2×C4 | D3×#41 | 1 | 1 | yes | characteristic |
| 434 | C8 | — | 2 | 2 | no | — |
| 435 | C8 | — | 4 | 2 | no | — |
| 436 | C8 | — | 6 | 4 | no | — |
| 437 | C8 | — | 6 | 1 | no | — |
| 438 | C8 | — | 6 | 1 | no | — |
| 439 | C8 | — | 6 | 2 | no | — |
| 440 | C8 | #67⋊C4 | 1 | 2 | yes | — |
| 441 | C8 | #67⋊C4 | 1 | 2 | yes | — |
| 442 | C2×C3 | — | 2 | 1 | no | — |
| 443 | C2×C3 | — | 2 | 1 | no | — |
| 444 | C2×C3 | — | 4 | 2 | no | — |
| 445 | C2×C3 | C4×#121 | 1 | 1 | yes | characteristic |
| 446 | C2×C3 | #3069 | 1 | 2 | yes | — |
| 447 | C22 | — | 2 | 2 | no | — |
| 448 | C22 | — | 2 | 2 | no | — |
| 449 | C22 | — | 4 | 2 | no | — |
| 450 | C22 | #5522 | 1 | 1 | yes | characteristic |
| 451 | C22 | D3×#121 | 1 | 1 | yes | characteristic |
| 452 | C22 | #5624 | 1 | 1 | yes | characteristic |
| 453 | C4 | — | 2 | 2 | no | — |
| 454 | C4 | — | 6 | 2 | no | — |
| 455 | C4 | — | 6 | 2 | no | — |
| 456 | C4 | — | 8 | 2 | no | — |
| 457 | C4 | — | 12 | 2 | no | — |
| 458 | C4 | — | 12 | 4 | no | — |
| 459 | C4 | C2×#67⋊C4 | 1 | 1 | yes | characteristic |
| 460 | C4 | C2×#893 | 1 | 1 | yes | characteristic |
| 461 | C4 | #5596 | 1 | 1 | yes | characteristic |
| 462 | C4 | #5627 | 1 | 1 | yes | characteristic |
| 463 | C3 | #21556 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 464 | C2 | — | 2 | 1 | no | — |
| 465 | C2 | — | 2 | 1 | no | — |
| 466 | C2 | — | 4 | 2 | no | — |
| 467 | C2 | #73865 | 1 | 1 | yes | characteristic |
| 468 | C2 | #80931 | 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