← #10847321
Subgroups — #10847321
Order 768.
632 conjugacy classes of subgroups.
The subgroup lattice has 448 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #82431 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#5021 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #78508 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #78506 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C3×C4×#101 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #70109 | C2 | 1 | 2 | yes | maximal |
| 7 | #70106 | C2 | 1 | 2 | yes | maximal |
| 8 | #69879 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #69875 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #68985 | C2 | 1 | 2 | yes | maximal |
| 11 | #68980 | C2 | 1 | 2 | yes | maximal |
| 12 | #25491 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C2×C3×C4×Q8 | C22 | 1 | 1 | yes | characteristic |
| 14 | #5470 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#869 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×C3×#101 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C3×#101 | C22 | 1 | 1 | yes | characteristic |
| 18 | C3×C4×M16 | C22 | 1 | 1 | yes | characteristic |
| 19 | C3×C4×M16 | C22 | 1 | 1 | yes | characteristic |
| 20 | #5225 | C22 | 1 | 2 | yes | — |
| 21 | C2×#835 | C22 | 1 | 2 | yes | — |
| 22 | C2×#822 | C22 | 1 | 2 | yes | — |
| 23 | #5122 | C22 | 1 | 2 | yes | — |
| 24 | #5121 | C22 | 1 | 2 | yes | — |
| 25 | #5121 | C22 | 1 | 2 | yes | — |
| 26 | #5119 | C22 | 1 | 2 | yes | — |
| 27 | #5022 | — | 2 | 2 | no | — |
| 28 | #5021 | — | 2 | 1 | no | — |
| 29 | #5021 | — | 2 | 1 | no | — |
| 30 | #5021 | — | 2 | 1 | no | — |
| 31 | #5021 | — | 2 | 2 | no | — |
| 32 | #5020 | — | 2 | 1 | no | — |
| 33 | #4964 | C22 | 1 | 2 | yes | — |
| 34 | C2×#807 | C22 | 1 | 2 | yes | — |
| 35 | #4924 | C22 | 1 | 1 | yes | characteristic |
| 36 | C2×C4⋊(C3⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 37 | #4702 | — | 2 | 2 | no | — |
| 38 | #4701 | — | 2 | 2 | no | — |
| 39 | #4682 | — | 2 | 1 | no | — |
| 40 | #4680 | — | 2 | 1 | no | — |
| 41 | #4679 | — | 2 | 1 | no | — |
| 42 | C8×Dic6 | — | 2 | 1 | no | — |
| 43 | C3×#343 | C22 | 1 | 1 | yes | characteristic |
| 44 | C3×#343 | C22 | 1 | 1 | yes | characteristic |
| 45 | #4558 | C22 | 1 | 2 | yes | — |
| 46 | #4554 | C22 | 1 | 2 | yes | — |
| 47 | #4554 | C22 | 1 | 2 | yes | — |
| 48 | #3165 | — | 3 | 1 | no | — |
| 49 | #3078 | — | 3 | 1 | no | — |
| 50 | C2×#477 | — | 3 | 1 | no | — |
| 51 | #2962 | — | 3 | 1 | no | — |
| 52 | #2089 | — | 3 | 2 | no | — |
| 53 | #2064 | — | 3 | 2 | no | — |
| 54 | #1997 | — | 3 | 1 | no | — |
| 55 | #1952 | — | 3 | 2 | no | — |
| 56 | #1950 | — | 3 | 1 | no | — |
| 57 | #1930 | — | 3 | 2 | no | — |
| 58 | C4×#101 | D3 | 1 | 1 | yes | characteristic |
| 59 | C22×C3×Q8 | C23 | 1 | 1 | yes | characteristic |
| 60 | C22×Dic6 | — | 2 | 1 | no | — |
| 61 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 62 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 63 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 64 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 65 | C3×C4×Q8 | — | 2 | 1 | no | — |
| 66 | C3×C4×Q8 | — | 2 | 1 | no | — |
| 67 | C3×C4×Q8 | — | 2 | 1 | no | — |
| 68 | C3×C4×Q8 | — | 2 | 1 | no | — |
| 69 | C2×C3×C4⋊C4 | — | 2 | 1 | no | — |
| 70 | C2×C3×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 71 | C2×C3×C42 | — | 2 | 1 | no | — |
| 72 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 73 | #926 | C23 | 1 | 2 | yes | — |
| 74 | C2×C4⋊Dic3 | — | 2 | 1 | no | — |
| 75 | C2×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 76 | #924 | — | 2 | 1 | no | — |
| 77 | #924 | — | 2 | 1 | no | — |
| 78 | C2×#208 | C23 | 1 | 2 | yes | — |
| 79 | C22×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 80 | #870 | D4 | 1 | 2 | yes | — |
| 81 | #869 | — | 2 | 1 | no | — |
| 82 | #869 | — | 2 | 1 | no | — |
| 83 | #869 | — | 2 | 1 | no | — |
| 84 | #869 | — | 2 | 1 | no | — |
| 85 | #869 | D4 | 1 | 1 | yes | characteristic |
| 86 | #869 | D4 | 1 | 1 | yes | characteristic |
| 87 | C4×Dic6 | — | 2 | 1 | no | — |
| 88 | C4×Dic6 | — | 2 | 1 | no | — |
| 89 | C3×#101 | — | 2 | 2 | no | — |
| 90 | C3×#101 | Q8 | 1 | 4 | yes | complemented |
| 91 | C3×#97 | — | 2 | 1 | no | — |
| 92 | C3×#97 | — | 2 | 1 | no | — |
| 93 | C3×C4×C8 | — | 2 | 1 | no | — |
| 94 | C3×C4×C8 | — | 2 | 1 | no | — |
| 95 | #835 | — | 2 | 2 | no | — |
| 96 | #835 | — | 2 | 2 | no | — |
| 97 | #835 | — | 2 | 2 | no | — |
| 98 | #835 | — | 2 | 2 | no | — |
| 99 | #822 | — | 2 | 4 | no | — |
| 100 | #818 | — | 2 | 2 | no | — |
| 101 | #818 | — | 2 | 2 | no | — |
| 102 | #817 | — | 2 | 2 | no | — |
| 103 | #817 | — | 2 | 2 | no | — |
| 104 | #815 | — | 2 | 2 | no | — |
| 105 | Dic3⋊C8 | — | 2 | 2 | no | — |
| 106 | Dic3⋊C8 | — | 2 | 2 | no | — |
| 107 | C8×Dic3 | — | 2 | 2 | no | — |
| 108 | #808 | — | 2 | 2 | no | — |
| 109 | #807 | — | 2 | 2 | no | — |
| 110 | #807 | — | 2 | 2 | no | — |
| 111 | #807 | — | 2 | 2 | no | — |
| 112 | C4⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 113 | C4⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 114 | C4⋊(C3⋊C8) | D4 | 1 | 1 | yes | characteristic |
| 115 | C4⋊(C3⋊C8) | D4 | 1 | 1 | yes | characteristic |
| 116 | C4⋊(C3⋊C8) | D4 | 1 | 2 | yes | — |
| 117 | #533 | — | 3 | 1 | no | — |
| 118 | C2×C4⋊Q8 | — | 3 | 1 | no | — |
| 119 | C2×C4×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 120 | #501 | — | 6 | 2 | no | — |
| 121 | #500 | — | 6 | 1 | no | — |
| 122 | #498 | — | 6 | 1 | no | — |
| 123 | #479 | — | 6 | 2 | no | — |
| 124 | #477 | — | 6 | 1 | no | — |
| 125 | #477 | — | 6 | 2 | no | — |
| 126 | #477 | — | 6 | 1 | no | — |
| 127 | #477 | — | 6 | 1 | no | — |
| 128 | #475 | — | 6 | 1 | no | — |
| 129 | #446 | — | 6 | 1 | no | — |
| 130 | #446 | — | 6 | 2 | no | — |
| 131 | C8×Q8 | — | 6 | 1 | no | — |
| 132 | C2×#108 | — | 3 | 2 | no | — |
| 133 | #428 | — | 3 | 2 | no | — |
| 134 | #428 | — | 3 | 2 | no | — |
| 135 | #428 | — | 3 | 2 | no | — |
| 136 | C2×#107 | — | 3 | 2 | no | — |
| 137 | #424 | — | 3 | 2 | no | — |
| 138 | #423 | — | 3 | 1 | no | — |
| 139 | C2×C4⋊C8 | — | 3 | 1 | no | — |
| 140 | #419 | — | 3 | 2 | no | — |
| 141 | C2×#103 | — | 3 | 2 | no | — |
| 142 | C2×#101 | C2×D3 | 1 | 1 | yes | characteristic |
| 143 | C2×#101 | C2×D3 | 1 | 1 | yes | characteristic |
| 144 | #405 | — | 3 | 2 | no | — |
| 145 | C4×M16 | C2×D3 | 1 | 1 | yes | characteristic |
| 146 | C4×M16 | C2×D3 | 1 | 1 | yes | characteristic |
| 147 | #343 | — | 3 | 2 | no | — |
| 148 | #343 | — | 3 | 2 | no | — |
| 149 | #343 | C2×D3 | 1 | 1 | yes | characteristic |
| 150 | #343 | C2×D3 | 1 | 1 | yes | characteristic |
| 151 | #341 | — | 3 | 2 | no | — |
| 152 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 153 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 154 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 155 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 156 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 157 | C2×C3×Q8 | C2×Q8 | 1 | 2 | yes | — |
| 158 | C22×C3×C4 | — | 2 | 1 | no | — |
| 159 | C22×C3×C4 | — | 2 | 1 | no | — |
| 160 | C22×C3×C4 | #41 | 1 | 1 | yes | characteristic |
| 161 | C22×C3×C4 | #41 | 1 | 1 | yes | characteristic |
| 162 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 163 | C22×Dic3 | — | 2 | 2 | no | — |
| 164 | C2×Dic6 | — | 2 | 1 | no | — |
| 165 | C2×Dic6 | — | 2 | 1 | no | — |
| 166 | C2×Dic6 | — | 4 | 1 | no | — |
| 167 | C2×Dic6 | — | 4 | 1 | no | — |
| 168 | C2×Dic6 | — | 8 | 2 | no | — |
| 169 | C3×M16 | — | 2 | 1 | no | — |
| 170 | C3×M16 | — | 2 | 1 | no | — |
| 171 | C3×M16 | — | 2 | 1 | no | — |
| 172 | C3×M16 | — | 2 | 1 | no | — |
| 173 | C3×M16 | — | 2 | 1 | no | — |
| 174 | C3×M16 | C2×Q8 | 1 | 2 | yes | — |
| 175 | C3×M16 | C2×Q8 | 1 | 2 | yes | — |
| 176 | C3×M16 | #41 | 1 | 2 | yes | — |
| 177 | C2×C3×C8 | — | 2 | 1 | no | — |
| 178 | C2×C3×C8 | — | 2 | 1 | no | — |
| 179 | C2×C3×C8 | — | 2 | 1 | no | — |
| 180 | C2×C3×C8 | — | 2 | 1 | no | — |
| 181 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 182 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 183 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 184 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 185 | C3×C42 | — | 4 | 1 | no | — |
| 186 | C3×C42 | — | 4 | 1 | no | — |
| 187 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 188 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 189 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 190 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | #217 | — | 2 | 2 | no | — |
| 192 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 193 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 194 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 195 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 196 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 197 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 198 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 199 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 200 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 201 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 202 | C4×Dic3 | — | 2 | 2 | no | — |
| 203 | #208 | — | 2 | 2 | no | — |
| 204 | #208 | — | 2 | 2 | no | — |
| 205 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 206 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 207 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 208 | C2×C3⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 209 | C2×C3⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 210 | C22×Q8 | — | 6 | 1 | no | — |
| 211 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 212 | C2×M16 | — | 3 | 2 | no | — |
| 213 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 214 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 215 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 216 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 217 | C22×C8 | — | 3 | 2 | no | — |
| 218 | C4⋊Q8 | — | 3 | 1 | no | — |
| 219 | C4⋊Q8 | — | 3 | 1 | no | — |
| 220 | C4⋊Q8 | — | 6 | 1 | no | — |
| 221 | C4⋊Q8 | — | 6 | 1 | no | — |
| 222 | C4⋊Q8 | — | 6 | 1 | no | — |
| 223 | C4⋊Q8 | — | 6 | 1 | no | — |
| 224 | #125 | — | 3 | 2 | no | — |
| 225 | C22⋊Q8 | — | 6 | 1 | no | — |
| 226 | C22⋊Q8 | — | 6 | 1 | no | — |
| 227 | C4×Q8 | — | 2 | 1 | no | — |
| 228 | C4×Q8 | — | 2 | 1 | no | — |
| 229 | C4×Q8 | — | 2 | 1 | no | — |
| 230 | C4×Q8 | — | 2 | 1 | no | — |
| 231 | C4×Q8 | — | 6 | 1 | no | — |
| 232 | C4×Q8 | — | 6 | 1 | no | — |
| 233 | #117 | — | 3 | 2 | no | — |
| 234 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 235 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 236 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 237 | C2×C4⋊C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 238 | C2×C42 | — | 2 | 1 | no | — |
| 239 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 240 | #108 | — | 6 | 4 | no | — |
| 241 | #107 | — | 6 | 2 | no | — |
| 242 | #107 | — | 6 | 2 | no | — |
| 243 | #107 | — | 6 | 2 | no | — |
| 244 | #107 | — | 6 | 2 | no | — |
| 245 | #107 | — | 6 | 2 | no | — |
| 246 | #106 | — | 6 | 2 | no | — |
| 247 | #106 | — | 6 | 2 | no | — |
| 248 | #106 | — | 6 | 2 | no | — |
| 249 | C4⋊C8 | — | 3 | 1 | no | — |
| 250 | C4⋊C8 | — | 3 | 1 | no | — |
| 251 | C4⋊C8 | — | 3 | 2 | no | — |
| 252 | C4⋊C8 | — | 6 | 2 | no | — |
| 253 | C4⋊C8 | — | 6 | 2 | no | — |
| 254 | C4⋊C8 | — | 6 | 1 | no | — |
| 255 | C4⋊C8 | — | 6 | 1 | no | — |
| 256 | #103 | — | 6 | 2 | no | — |
| 257 | #103 | — | 6 | 2 | no | — |
| 258 | #103 | — | 6 | 2 | no | — |
| 259 | #103 | — | 6 | 2 | no | — |
| 260 | #101 | — | 2 | 2 | no | — |
| 261 | #101 | Dic6 | 1 | 4 | yes | complemented |
| 262 | #97 | — | 2 | 1 | no | — |
| 263 | #97 | — | 2 | 1 | no | — |
| 264 | #97 | — | 6 | 2 | no | — |
| 265 | C4×C8 | — | 2 | 1 | no | — |
| 266 | C4×C8 | — | 2 | 1 | no | — |
| 267 | C4×C8 | — | 6 | 2 | no | — |
| 268 | C23×C3 | C2×#41 | 1 | 1 | yes | characteristic |
| 269 | C3×Q8 | — | 2 | 2 | no | — |
| 270 | C3×Q8 | — | 2 | 2 | no | — |
| 271 | C3×Q8 | — | 4 | 1 | no | — |
| 272 | C3×Q8 | — | 4 | 1 | no | — |
| 273 | C2×C3×C4 | — | 2 | 2 | no | — |
| 274 | C2×C3×C4 | — | 2 | 2 | no | — |
| 275 | C2×C3×C4 | — | 4 | 1 | no | — |
| 276 | C2×C3×C4 | — | 4 | 1 | no | — |
| 277 | C2×C3×C4 | — | 4 | 1 | no | — |
| 278 | C2×C3×C4 | — | 4 | 1 | no | — |
| 279 | C2×C3×C4 | — | 8 | 1 | no | — |
| 280 | C2×C3×C4 | #121 | 1 | 1 | yes | characteristic |
| 281 | C2×C3×C4 | #121 | 1 | 1 | yes | characteristic |
| 282 | C2×C3×C4 | #121 | 1 | 1 | yes | characteristic |
| 283 | C2×C3×C4 | #121 | 1 | 1 | yes | characteristic |
| 284 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 285 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 286 | C2×C3×C4 | C22×Q8 | 1 | 1 | yes | characteristic |
| 287 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 288 | C2×C3×C4 | 2−1+4 | 1 | 1 | yes | characteristic |
| 289 | C2×C3×C4 | 2−1+4 | 1 | 1 | yes | characteristic |
| 290 | C2×Dic3 | — | 2 | 2 | no | — |
| 291 | C2×Dic3 | — | 2 | 2 | no | — |
| 292 | C2×Dic3 | — | 4 | 2 | no | — |
| 293 | C2×Dic3 | — | 8 | 2 | no | — |
| 294 | Dic6 | — | 4 | 2 | no | — |
| 295 | Dic6 | — | 8 | 1 | no | — |
| 296 | Dic6 | — | 8 | 2 | no | — |
| 297 | Dic6 | — | 8 | 2 | no | — |
| 298 | C3×C8 | — | 2 | 2 | no | — |
| 299 | C3×C8 | — | 2 | 2 | no | — |
| 300 | C3×C8 | — | 2 | 2 | no | — |
| 301 | C3×C8 | — | 4 | 1 | no | — |
| 302 | C3⋊C8 | — | 2 | 2 | no | — |
| 303 | C3⋊C8 | — | 2 | 2 | no | — |
| 304 | C3⋊C8 | — | 4 | 2 | no | — |
| 305 | C2×Q8 | — | 2 | 1 | no | — |
| 306 | C2×Q8 | — | 2 | 1 | no | — |
| 307 | C2×Q8 | — | 2 | 1 | no | — |
| 308 | C2×Q8 | — | 2 | 1 | no | — |
| 309 | C2×Q8 | — | 2 | 1 | no | — |
| 310 | C2×Q8 | — | 6 | 1 | no | — |
| 311 | C2×Q8 | — | 6 | 1 | no | — |
| 312 | C2×Q8 | — | 12 | 1 | no | — |
| 313 | C2×Q8 | — | 12 | 1 | no | — |
| 314 | C2×Q8 | — | 24 | 2 | no | — |
| 315 | C2×Q8 | C2×Dic6 | 1 | 2 | yes | — |
| 316 | C22×C4 | — | 2 | 1 | no | — |
| 317 | C22×C4 | — | 2 | 1 | no | — |
| 318 | C22×C4 | — | 6 | 2 | no | — |
| 319 | C22×C4 | #235 | 1 | 1 | yes | characteristic |
| 320 | C22×C4 | #235 | 1 | 1 | yes | characteristic |
| 321 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 322 | M16 | — | 2 | 1 | no | — |
| 323 | M16 | — | 2 | 1 | no | — |
| 324 | M16 | — | 2 | 1 | no | — |
| 325 | M16 | — | 2 | 1 | no | — |
| 326 | M16 | — | 2 | 1 | no | — |
| 327 | M16 | — | 6 | 2 | no | — |
| 328 | M16 | — | 6 | 2 | no | — |
| 329 | M16 | C2×Dic6 | 1 | 2 | yes | — |
| 330 | M16 | C2×Dic6 | 1 | 2 | yes | — |
| 331 | M16 | #235 | 1 | 2 | yes | — |
| 332 | C2×C8 | — | 2 | 1 | no | — |
| 333 | C2×C8 | — | 2 | 1 | no | — |
| 334 | C2×C8 | — | 2 | 1 | no | — |
| 335 | C2×C8 | — | 2 | 1 | no | — |
| 336 | C2×C8 | — | 3 | 2 | no | — |
| 337 | C2×C8 | — | 3 | 2 | no | — |
| 338 | C2×C8 | — | 6 | 2 | no | — |
| 339 | C2×C8 | — | 6 | 2 | no | — |
| 340 | C2×C8 | — | 6 | 2 | no | — |
| 341 | C4⋊C4 | — | 2 | 1 | no | — |
| 342 | C4⋊C4 | — | 2 | 1 | no | — |
| 343 | C4⋊C4 | — | 3 | 2 | no | — |
| 344 | C4⋊C4 | — | 3 | 2 | no | — |
| 345 | C4⋊C4 | — | 4 | 1 | no | — |
| 346 | C4⋊C4 | — | 4 | 1 | no | — |
| 347 | C4⋊C4 | — | 6 | 2 | no | — |
| 348 | C4⋊C4 | — | 6 | 2 | no | — |
| 349 | C4⋊C4 | — | 6 | 1 | no | — |
| 350 | C4⋊C4 | — | 6 | 1 | no | — |
| 351 | C4⋊C4 | — | 6 | 2 | no | — |
| 352 | C4⋊C4 | — | 6 | 2 | no | — |
| 353 | C4⋊C4 | — | 12 | 1 | no | — |
| 354 | C4⋊C4 | — | 12 | 1 | no | — |
| 355 | C22⋊C4 | — | 6 | 2 | no | — |
| 356 | C42 | — | 4 | 1 | no | — |
| 357 | C42 | — | 4 | 1 | no | — |
| 358 | C42 | — | 6 | 2 | no | — |
| 359 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 360 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 361 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 362 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 363 | C22×C3 | — | 2 | 1 | no | — |
| 364 | C22×C3 | — | 2 | 1 | no | — |
| 365 | C22×C3 | C2×#121 | 1 | 1 | yes | characteristic |
| 366 | C22×C3 | #533 | 1 | 1 | yes | characteristic |
| 367 | C22×C3 | #541 | 1 | 1 | yes | characteristic |
| 368 | C3×C4 | — | 2 | 1 | no | — |
| 369 | C3×C4 | — | 2 | 1 | no | — |
| 370 | C3×C4 | — | 2 | 1 | no | — |
| 371 | C3×C4 | — | 4 | 2 | no | — |
| 372 | C3×C4 | — | 8 | 1 | no | — |
| 373 | C3×C4 | #473 | 1 | 2 | yes | — |
| 374 | C3×C4 | #547 | 1 | 1 | yes | characteristic |
| 375 | C3×C4 | #548 | 1 | 1 | yes | characteristic |
| 376 | C3×C4 | D4×Q8 | 1 | 1 | yes | characteristic |
| 377 | C3×C4 | D4×Q8 | 1 | 1 | yes | characteristic |
| 378 | Dic3 | — | 4 | 2 | no | — |
| 379 | Dic3 | — | 4 | 2 | no | — |
| 380 | Dic3 | — | 8 | 2 | no | — |
| 381 | C23 | C2×#235 | 1 | 1 | yes | characteristic |
| 382 | Q8 | — | 2 | 2 | no | — |
| 383 | Q8 | — | 2 | 2 | no | — |
| 384 | Q8 | — | 4 | 1 | no | — |
| 385 | Q8 | — | 4 | 1 | no | — |
| 386 | Q8 | — | 12 | 2 | no | — |
| 387 | Q8 | — | 24 | 1 | no | — |
| 388 | Q8 | — | 24 | 2 | no | — |
| 389 | Q8 | — | 24 | 2 | no | — |
| 390 | C2×C4 | — | 2 | 2 | no | — |
| 391 | C2×C4 | — | 2 | 2 | no | — |
| 392 | C2×C4 | — | 4 | 1 | no | — |
| 393 | C2×C4 | — | 4 | 1 | no | — |
| 394 | C2×C4 | — | 4 | 1 | no | — |
| 395 | C2×C4 | — | 4 | 1 | no | — |
| 396 | C2×C4 | — | 6 | 2 | no | — |
| 397 | C2×C4 | — | 6 | 2 | no | — |
| 398 | C2×C4 | — | 8 | 1 | no | — |
| 399 | C2×C4 | — | 12 | 2 | no | — |
| 400 | C2×C4 | — | 24 | 2 | no | — |
| 401 | C2×C4 | #884 | 1 | 1 | yes | characteristic |
| 402 | C2×C4 | #884 | 1 | 1 | yes | characteristic |
| 403 | C2×C4 | #884 | 1 | 1 | yes | characteristic |
| 404 | C2×C4 | #884 | 1 | 1 | yes | characteristic |
| 405 | C2×C4 | C22×Dic6 | 1 | 1 | yes | characteristic |
| 406 | C2×C4 | C2×#235 | 1 | 1 | yes | characteristic |
| 407 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 408 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 409 | C2×C4 | #1010 | 1 | 1 | yes | characteristic |
| 410 | C2×C4 | #1010 | 1 | 1 | yes | characteristic |
| 411 | C8 | — | 2 | 2 | no | — |
| 412 | C8 | — | 2 | 2 | no | — |
| 413 | C8 | — | 2 | 2 | no | — |
| 414 | C8 | — | 4 | 1 | no | — |
| 415 | C8 | — | 6 | 2 | no | — |
| 416 | C8 | — | 6 | 2 | no | — |
| 417 | C8 | — | 12 | 2 | no | — |
| 418 | C2×C3 | — | 2 | 1 | no | — |
| 419 | C2×C3 | — | 2 | 1 | no | — |
| 420 | C2×C3 | #2429 | 1 | 1 | yes | characteristic |
| 421 | C2×C3 | C2×#473 | 1 | 1 | yes | characteristic |
| 422 | C2×C3 | #3068 | 1 | 1 | yes | characteristic |
| 423 | C22 | — | 2 | 1 | no | — |
| 424 | C22 | — | 2 | 1 | no | — |
| 425 | C22 | #5470 | 1 | 1 | yes | characteristic |
| 426 | C22 | C2×#884 | 1 | 1 | yes | characteristic |
| 427 | C22 | #5518 | 1 | 1 | yes | characteristic |
| 428 | C4 | — | 2 | 1 | no | — |
| 429 | C4 | — | 2 | 1 | no | — |
| 430 | C4 | — | 2 | 1 | no | — |
| 431 | C4 | — | 4 | 2 | no | — |
| 432 | C4 | — | 8 | 1 | no | — |
| 433 | C4 | — | 12 | 2 | no | — |
| 434 | C4 | — | 12 | 2 | no | — |
| 435 | C4 | — | 24 | 2 | no | — |
| 436 | C4 | #4755 | 1 | 2 | yes | — |
| 437 | C4 | D4×Dic6 | 1 | 1 | yes | characteristic |
| 438 | C4 | D4×Dic6 | 1 | 1 | yes | characteristic |
| 439 | C4 | #5551 | 1 | 1 | yes | characteristic |
| 440 | C4 | #5552 | 1 | 1 | yes | characteristic |
| 441 | C3 | #25491 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 442 | C2 | — | 2 | 1 | no | — |
| 443 | C2 | — | 2 | 1 | no | — |
| 444 | C2 | #73488 | 1 | 1 | yes | characteristic |
| 445 | C2 | C2×#4755 | 1 | 1 | yes | characteristic |
| 446 | C2 | #78720 | 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