← #10847357
Subgroups — #10847357
Order 768.
616 conjugacy classes of subgroups.
The subgroup lattice has 580 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #79245 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #79204 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×#4877 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #78544 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C3×#1952 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #70717 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #70695 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #70679 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #70671 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #70626 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #69891 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #68984 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #68982 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #68975 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | #68973 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | #25494 | — | 3 | 1 | no | maximal, Sylow |
| 17 | #5517 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#890 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#887 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×C3×#108 | C22 | 1 | 1 | yes | characteristic |
| 21 | C3×#428 | C22 | 1 | 1 | yes | characteristic |
| 22 | C3×#428 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×C3×#107 | C22 | 1 | 1 | yes | characteristic |
| 24 | C3×#405 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#824 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#824 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#822 | C22 | 1 | 1 | yes | characteristic |
| 28 | #5122 | C22 | 1 | 1 | yes | characteristic |
| 29 | #5121 | C22 | 1 | 1 | yes | characteristic |
| 30 | #5120 | C22 | 1 | 1 | yes | characteristic |
| 31 | #5118 | C22 | 1 | 1 | yes | characteristic |
| 32 | Dic3×M16 | C22 | 1 | 1 | yes | characteristic |
| 33 | Dic3×M16 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×#816 | C22 | 1 | 1 | yes | characteristic |
| 35 | #5102 | C22 | 1 | 1 | yes | characteristic |
| 36 | C2×Dic3⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 37 | #5004 | C22 | 1 | 1 | yes | characteristic |
| 38 | #4999 | C22 | 1 | 1 | yes | characteristic |
| 39 | #4995 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×#810 | C22 | 1 | 1 | yes | characteristic |
| 41 | #4964 | C22 | 1 | 1 | yes | characteristic |
| 42 | #4964 | C22 | 1 | 1 | yes | characteristic |
| 43 | C2×#808 | C22 | 1 | 1 | yes | characteristic |
| 44 | #4878 | — | 2 | 1 | no | — |
| 45 | #4877 | — | 2 | 1 | no | — |
| 46 | #4877 | — | 2 | 1 | no | — |
| 47 | #4877 | — | 2 | 1 | no | — |
| 48 | #4877 | — | 2 | 1 | no | — |
| 49 | #4877 | — | 2 | 1 | no | — |
| 50 | #4876 | — | 2 | 1 | no | — |
| 51 | #4875 | — | 2 | 1 | no | — |
| 52 | #4858 | — | 2 | 1 | no | — |
| 53 | #4857 | — | 2 | 1 | no | — |
| 54 | #4856 | — | 2 | 1 | no | — |
| 55 | #4854 | — | 2 | 1 | no | — |
| 56 | #4701 | — | 2 | 1 | no | — |
| 57 | #4701 | — | 2 | 1 | no | — |
| 58 | #4679 | — | 2 | 1 | no | — |
| 59 | C8×Dic6 | — | 2 | 1 | no | — |
| 60 | C3×#343 | C22 | 1 | 1 | yes | characteristic |
| 61 | C3×#343 | C22 | 1 | 1 | yes | characteristic |
| 62 | #4558 | C22 | 1 | 1 | yes | characteristic |
| 63 | #4554 | C22 | 1 | 1 | yes | characteristic |
| 64 | #4554 | C22 | 1 | 1 | yes | characteristic |
| 65 | #4552 | C22 | 1 | 1 | yes | characteristic |
| 66 | #4530 | C22 | 1 | 1 | yes | characteristic |
| 67 | #4530 | C22 | 1 | 1 | yes | characteristic |
| 68 | #3166 | — | 3 | 1 | no | — |
| 69 | #3078 | — | 3 | 1 | no | — |
| 70 | C2×#479 | — | 3 | 1 | no | — |
| 71 | #2962 | — | 3 | 1 | no | — |
| 72 | #2090 | — | 3 | 1 | no | — |
| 73 | #2089 | — | 3 | 1 | no | — |
| 74 | #2064 | — | 3 | 1 | no | — |
| 75 | #2064 | — | 3 | 1 | no | — |
| 76 | #1998 | — | 3 | 1 | no | — |
| 77 | #1952 | D3 | 1 | 1 | yes | characteristic |
| 78 | #1951 | — | 3 | 1 | no | — |
| 79 | #1950 | — | 3 | 1 | no | — |
| 80 | #1930 | — | 3 | 1 | no | — |
| 81 | #1930 | — | 3 | 1 | no | — |
| 82 | C4×#101 | — | 3 | 1 | no | — |
| 83 | C22×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 84 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 85 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 86 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 87 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 88 | C3×#117 | C23 | 1 | 1 | yes | characteristic |
| 89 | C2×C3×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 90 | C2×C3×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 91 | #926 | C23 | 1 | 1 | yes | characteristic |
| 92 | C2×C4⋊Dic3 | — | 2 | 1 | no | — |
| 93 | C2×C4⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×Dic3⋊C4 | — | 2 | 1 | no | — |
| 95 | C2×Dic3⋊C4 | — | 2 | 1 | no | — |
| 96 | C2×C4×Dic3 | — | 2 | 1 | no | — |
| 97 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 98 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 99 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 100 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 101 | C22×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 102 | #890 | — | 2 | 1 | no | — |
| 103 | #890 | — | 2 | 1 | no | — |
| 104 | #890 | — | 2 | 1 | no | — |
| 105 | #890 | — | 2 | 1 | no | — |
| 106 | #890 | D4 | 1 | 1 | yes | characteristic |
| 107 | #890 | D4 | 1 | 1 | yes | characteristic |
| 108 | #888 | D4 | 1 | 1 | yes | characteristic |
| 109 | #888 | D4 | 1 | 1 | yes | characteristic |
| 110 | #887 | — | 2 | 1 | no | — |
| 111 | #887 | — | 2 | 1 | no | — |
| 112 | #887 | — | 2 | 1 | no | — |
| 113 | #887 | — | 2 | 1 | no | — |
| 114 | #878 | — | 2 | 1 | no | — |
| 115 | #878 | — | 2 | 1 | no | — |
| 116 | C4×Dic6 | — | 2 | 1 | no | — |
| 117 | C4×Dic6 | — | 2 | 1 | no | — |
| 118 | C3×#108 | — | 2 | 2 | no | — |
| 119 | C3×#107 | — | 2 | 1 | no | — |
| 120 | C3×#107 | — | 2 | 1 | no | — |
| 121 | C3×#107 | — | 2 | 1 | no | — |
| 122 | C3×#107 | — | 2 | 1 | no | — |
| 123 | C3×#106 | — | 2 | 1 | no | — |
| 124 | C3×#106 | — | 2 | 1 | no | — |
| 125 | C3×#97 | — | 2 | 1 | no | — |
| 126 | C3×C4×C8 | — | 2 | 1 | no | — |
| 127 | #824 | — | 2 | 2 | no | — |
| 128 | #824 | Q8 | 1 | 4 | yes | complemented |
| 129 | #822 | — | 2 | 2 | no | — |
| 130 | #818 | — | 2 | 1 | no | — |
| 131 | #817 | — | 2 | 1 | no | — |
| 132 | #816 | — | 2 | 1 | no | — |
| 133 | #816 | — | 2 | 1 | no | — |
| 134 | #816 | — | 2 | 1 | no | — |
| 135 | #816 | — | 2 | 1 | no | — |
| 136 | #815 | — | 2 | 1 | no | — |
| 137 | #815 | — | 2 | 1 | no | — |
| 138 | #815 | — | 2 | 1 | no | — |
| 139 | Dic3⋊C8 | — | 2 | 1 | no | — |
| 140 | Dic3⋊C8 | — | 2 | 1 | no | — |
| 141 | Dic3⋊C8 | — | 2 | 1 | no | — |
| 142 | Dic3⋊C8 | — | 2 | 1 | no | — |
| 143 | Dic3⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 144 | Dic3⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 145 | Dic3⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 146 | Dic3⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 147 | C8×Dic3 | — | 2 | 1 | no | — |
| 148 | C8×Dic3 | — | 2 | 1 | no | — |
| 149 | C8×Dic3 | — | 2 | 1 | no | — |
| 150 | #810 | — | 2 | 1 | no | — |
| 151 | #810 | — | 2 | 1 | no | — |
| 152 | #810 | — | 2 | 1 | no | — |
| 153 | #810 | — | 2 | 1 | no | — |
| 154 | #808 | — | 2 | 1 | no | — |
| 155 | #808 | — | 2 | 1 | no | — |
| 156 | #808 | — | 2 | 1 | no | — |
| 157 | #808 | — | 2 | 1 | no | — |
| 158 | #808 | — | 2 | 1 | no | — |
| 159 | #807 | — | 2 | 1 | no | — |
| 160 | #807 | — | 2 | 1 | no | — |
| 161 | #807 | — | 2 | 1 | no | — |
| 162 | C4⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 163 | C4⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 164 | #533 | — | 3 | 1 | no | — |
| 165 | C2×#125 | — | 3 | 1 | no | — |
| 166 | C2×C4×Q8 | — | 3 | 1 | no | — |
| 167 | #501 | — | 6 | 1 | no | — |
| 168 | #501 | — | 6 | 1 | no | — |
| 169 | #499 | — | 6 | 1 | no | — |
| 170 | #499 | — | 6 | 1 | no | — |
| 171 | #479 | — | 6 | 1 | no | — |
| 172 | #479 | — | 6 | 1 | no | — |
| 173 | #479 | — | 6 | 1 | no | — |
| 174 | #479 | — | 6 | 1 | no | — |
| 175 | #479 | — | 6 | 1 | no | — |
| 176 | #479 | — | 6 | 1 | no | — |
| 177 | #477 | — | 6 | 1 | no | — |
| 178 | #475 | — | 6 | 1 | no | — |
| 179 | #446 | — | 6 | 1 | no | — |
| 180 | #446 | — | 6 | 1 | no | — |
| 181 | #446 | — | 6 | 1 | no | — |
| 182 | C8×Q8 | — | 6 | 1 | no | — |
| 183 | C2×#108 | — | 3 | 1 | no | — |
| 184 | C2×#108 | C2×D3 | 1 | 1 | yes | characteristic |
| 185 | #428 | — | 3 | 1 | no | — |
| 186 | #428 | — | 3 | 1 | no | — |
| 187 | #428 | — | 3 | 1 | no | — |
| 188 | #428 | — | 3 | 1 | no | — |
| 189 | #428 | C2×D3 | 1 | 1 | yes | characteristic |
| 190 | #428 | C2×D3 | 1 | 1 | yes | characteristic |
| 191 | C2×#107 | C2×D3 | 1 | 1 | yes | characteristic |
| 192 | C2×#106 | — | 3 | 1 | no | — |
| 193 | #424 | — | 3 | 1 | no | — |
| 194 | #424 | — | 3 | 1 | no | — |
| 195 | #423 | — | 3 | 1 | no | — |
| 196 | C2×C4⋊C8 | — | 3 | 1 | no | — |
| 197 | #419 | — | 3 | 1 | no | — |
| 198 | #419 | — | 3 | 1 | no | — |
| 199 | C2×#103 | — | 3 | 1 | no | — |
| 200 | C2×#103 | — | 3 | 1 | no | — |
| 201 | C2×#101 | — | 3 | 1 | no | — |
| 202 | C2×#101 | — | 3 | 1 | no | — |
| 203 | #405 | — | 3 | 1 | no | — |
| 204 | #405 | C2×D3 | 1 | 1 | yes | characteristic |
| 205 | C4×M16 | — | 3 | 1 | no | — |
| 206 | C4×M16 | — | 3 | 1 | no | — |
| 207 | #343 | — | 3 | 1 | no | — |
| 208 | #343 | — | 3 | 1 | no | — |
| 209 | #343 | — | 3 | 1 | no | — |
| 210 | #343 | — | 3 | 1 | no | — |
| 211 | #343 | C2×D3 | 1 | 1 | yes | characteristic |
| 212 | #343 | C2×D3 | 1 | 1 | yes | characteristic |
| 213 | #341 | — | 3 | 1 | no | — |
| 214 | #341 | — | 3 | 1 | no | — |
| 215 | C22×C3×C4 | — | 2 | 1 | no | — |
| 216 | C22×C3×C4 | — | 2 | 1 | no | — |
| 217 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 218 | C22×Dic3 | — | 2 | 1 | no | — |
| 219 | C22×Dic3 | — | 2 | 1 | no | — |
| 220 | C22×Dic3 | #41 | 1 | 1 | yes | characteristic |
| 221 | C22×Dic3 | #41 | 1 | 1 | yes | characteristic |
| 222 | C2×Dic6 | — | 2 | 1 | no | — |
| 223 | C2×Dic6 | — | 2 | 1 | no | — |
| 224 | C2×Dic6 | — | 2 | 1 | no | — |
| 225 | C2×Dic6 | — | 2 | 1 | no | — |
| 226 | C2×Dic6 | — | 2 | 1 | no | — |
| 227 | C2×Dic6 | — | 2 | 1 | no | — |
| 228 | C2×Dic6 | — | 2 | 1 | no | — |
| 229 | C2×Dic6 | C2×Q8 | 1 | 2 | yes | — |
| 230 | C3×M16 | — | 2 | 1 | no | — |
| 231 | C3×M16 | — | 2 | 1 | no | — |
| 232 | C3×M16 | — | 2 | 1 | no | — |
| 233 | C3×M16 | — | 2 | 1 | no | — |
| 234 | C3×M16 | C2×Q8 | 1 | 2 | yes | — |
| 235 | C3×M16 | #41 | 1 | 2 | yes | — |
| 236 | C2×C3×C8 | — | 2 | 1 | no | — |
| 237 | C2×C3×C8 | — | 2 | 1 | no | — |
| 238 | C2×C3×C8 | — | 2 | 1 | no | — |
| 239 | C2×C3×C8 | — | 2 | 1 | no | — |
| 240 | C2×C3×C8 | — | 2 | 1 | no | — |
| 241 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 242 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 243 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 244 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 245 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 246 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 247 | C3×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 248 | C3×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 249 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 250 | C3×C42 | — | 2 | 1 | no | — |
| 251 | #217 | — | 2 | 1 | no | — |
| 252 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 253 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 254 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 255 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 256 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 257 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 258 | C4⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 259 | C4⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 260 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 261 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 262 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 263 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 264 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 265 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 266 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 267 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 268 | C4×Dic3 | — | 2 | 1 | no | — |
| 269 | C4×Dic3 | — | 4 | 1 | no | — |
| 270 | C4×Dic3 | — | 4 | 1 | no | — |
| 271 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 272 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 273 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 274 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 275 | #208 | — | 2 | 1 | no | — |
| 276 | #208 | — | 2 | 1 | no | — |
| 277 | #208 | — | 2 | 1 | no | — |
| 278 | #208 | — | 2 | 1 | no | — |
| 279 | #208 | — | 2 | 1 | no | — |
| 280 | #208 | C2×Q8 | 1 | 2 | yes | — |
| 281 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 282 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 283 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 284 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 285 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 286 | C2×C3⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 287 | C2×C3⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 288 | C22×Q8 | — | 3 | 1 | no | — |
| 289 | C2×M16 | — | 3 | 1 | no | — |
| 290 | C2×M16 | — | 3 | 1 | no | — |
| 291 | C2×M16 | — | 3 | 1 | no | — |
| 292 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 293 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 294 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 295 | C22×C8 | — | 3 | 1 | no | — |
| 296 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 297 | C4⋊Q8 | — | 3 | 1 | no | — |
| 298 | C4⋊Q8 | — | 3 | 1 | no | — |
| 299 | #125 | — | 3 | 1 | no | — |
| 300 | #125 | — | 3 | 1 | no | — |
| 301 | #125 | — | 6 | 1 | no | — |
| 302 | #125 | — | 6 | 1 | no | — |
| 303 | #125 | — | 6 | 1 | no | — |
| 304 | #125 | — | 6 | 1 | no | — |
| 305 | C22⋊Q8 | — | 6 | 1 | no | — |
| 306 | C22⋊Q8 | — | 6 | 1 | no | — |
| 307 | C4×Q8 | — | 6 | 1 | no | — |
| 308 | C4×Q8 | — | 6 | 1 | no | — |
| 309 | C4×Q8 | — | 6 | 1 | no | — |
| 310 | C4×Q8 | — | 6 | 1 | no | — |
| 311 | C4×Q8 | — | 6 | 1 | no | — |
| 312 | C4×Q8 | — | 6 | 1 | no | — |
| 313 | #117 | — | 3 | 1 | no | — |
| 314 | #117 | C22×D3 | 1 | 1 | yes | characteristic |
| 315 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 316 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 317 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 318 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 319 | C2×C4⋊C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 320 | C2×C4⋊C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 321 | C2×C42 | — | 3 | 1 | no | — |
| 322 | C2×C42 | — | 6 | 1 | no | — |
| 323 | #108 | — | 2 | 2 | no | — |
| 324 | #108 | — | 6 | 2 | no | — |
| 325 | #107 | — | 2 | 1 | no | — |
| 326 | #107 | — | 2 | 1 | no | — |
| 327 | #107 | — | 2 | 1 | no | — |
| 328 | #107 | — | 2 | 1 | no | — |
| 329 | #107 | — | 6 | 1 | no | — |
| 330 | #107 | — | 6 | 1 | no | — |
| 331 | #107 | — | 6 | 1 | no | — |
| 332 | #107 | — | 6 | 1 | no | — |
| 333 | #106 | — | 2 | 1 | no | — |
| 334 | #106 | — | 2 | 1 | no | — |
| 335 | #106 | — | 6 | 1 | no | — |
| 336 | #106 | — | 6 | 1 | no | — |
| 337 | #106 | — | 6 | 1 | no | — |
| 338 | #106 | — | 6 | 1 | no | — |
| 339 | #106 | — | 6 | 1 | no | — |
| 340 | #106 | — | 6 | 1 | no | — |
| 341 | C4⋊C8 | — | 3 | 1 | no | — |
| 342 | C4⋊C8 | — | 3 | 1 | no | — |
| 343 | C4⋊C8 | — | 3 | 1 | no | — |
| 344 | C4⋊C8 | — | 3 | 1 | no | — |
| 345 | C4⋊C8 | — | 6 | 1 | no | — |
| 346 | C4⋊C8 | — | 6 | 1 | no | — |
| 347 | C4⋊C8 | — | 6 | 1 | no | — |
| 348 | C4⋊C8 | — | 6 | 1 | no | — |
| 349 | C4⋊C8 | — | 6 | 1 | no | — |
| 350 | C4⋊C8 | — | 6 | 1 | no | — |
| 351 | #103 | — | 6 | 1 | no | — |
| 352 | #103 | — | 6 | 1 | no | — |
| 353 | #103 | — | 6 | 1 | no | — |
| 354 | #103 | — | 6 | 1 | no | — |
| 355 | #103 | — | 6 | 1 | no | — |
| 356 | #103 | — | 6 | 1 | no | — |
| 357 | #103 | — | 6 | 1 | no | — |
| 358 | #103 | — | 6 | 1 | no | — |
| 359 | #101 | — | 3 | 4 | no | — |
| 360 | #101 | — | 6 | 2 | no | — |
| 361 | #97 | — | 2 | 1 | no | — |
| 362 | #97 | — | 6 | 1 | no | — |
| 363 | #97 | — | 6 | 1 | no | — |
| 364 | #97 | — | 6 | 1 | no | — |
| 365 | C4×C8 | — | 2 | 1 | no | — |
| 366 | C4×C8 | — | 6 | 1 | no | — |
| 367 | C4×C8 | — | 6 | 1 | no | — |
| 368 | C4×C8 | — | 6 | 1 | no | — |
| 369 | C23×C3 | C2×#41 | 1 | 1 | yes | characteristic |
| 370 | C2×C3×C4 | — | 2 | 1 | no | — |
| 371 | C2×C3×C4 | — | 2 | 1 | no | — |
| 372 | C2×C3×C4 | — | 4 | 1 | no | — |
| 373 | C2×C3×C4 | — | 4 | 1 | no | — |
| 374 | C2×C3×C4 | — | 8 | 1 | no | — |
| 375 | C2×C3×C4 | — | 8 | 1 | no | — |
| 376 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 377 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 378 | C2×C3×C4 | C22×Q8 | 1 | 1 | yes | characteristic |
| 379 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 380 | C2×C3×C4 | 2−1+4 | 1 | 1 | yes | characteristic |
| 381 | C2×C3×C4 | 2−1+4 | 1 | 1 | yes | characteristic |
| 382 | C2×Dic3 | — | 2 | 1 | no | — |
| 383 | C2×Dic3 | — | 2 | 1 | no | — |
| 384 | C2×Dic3 | — | 2 | 2 | no | — |
| 385 | C2×Dic3 | — | 4 | 1 | no | — |
| 386 | C2×Dic3 | — | 4 | 1 | no | — |
| 387 | C2×Dic3 | — | 4 | 1 | no | — |
| 388 | C2×Dic3 | — | 4 | 1 | no | — |
| 389 | C2×Dic3 | — | 4 | 1 | no | — |
| 390 | C2×Dic3 | — | 8 | 1 | no | — |
| 391 | C2×Dic3 | #121 | 1 | 1 | yes | characteristic |
| 392 | C2×Dic3 | #121 | 1 | 1 | yes | characteristic |
| 393 | C2×Dic3 | #121 | 1 | 1 | yes | characteristic |
| 394 | C2×Dic3 | #121 | 1 | 1 | yes | characteristic |
| 395 | Dic6 | — | 2 | 2 | no | — |
| 396 | Dic6 | — | 2 | 2 | no | — |
| 397 | Dic6 | — | 4 | 2 | no | — |
| 398 | Dic6 | — | 4 | 1 | no | — |
| 399 | Dic6 | — | 4 | 1 | no | — |
| 400 | Dic6 | — | 8 | 1 | no | — |
| 401 | C3×C8 | — | 2 | 1 | no | — |
| 402 | C3×C8 | — | 2 | 1 | no | — |
| 403 | C3×C8 | — | 2 | 2 | no | — |
| 404 | C3×C8 | — | 2 | 2 | no | — |
| 405 | C3×C8 | — | 4 | 1 | no | — |
| 406 | C3⋊C8 | — | 2 | 1 | no | — |
| 407 | C3⋊C8 | — | 2 | 1 | no | — |
| 408 | C3⋊C8 | — | 2 | 2 | no | — |
| 409 | C3⋊C8 | — | 4 | 1 | no | — |
| 410 | C3⋊C8 | — | 4 | 1 | no | — |
| 411 | C2×Q8 | — | 3 | 2 | no | — |
| 412 | C2×Q8 | — | 6 | 1 | no | — |
| 413 | C2×Q8 | — | 6 | 1 | no | — |
| 414 | C2×Q8 | — | 6 | 1 | no | — |
| 415 | C2×Q8 | — | 6 | 1 | no | — |
| 416 | C2×Q8 | — | 6 | 1 | no | — |
| 417 | C2×Q8 | — | 6 | 1 | no | — |
| 418 | C2×Q8 | — | 6 | 1 | no | — |
| 419 | C22×C4 | — | 2 | 1 | no | — |
| 420 | C22×C4 | — | 2 | 1 | no | — |
| 421 | C22×C4 | — | 3 | 1 | no | — |
| 422 | C22×C4 | — | 3 | 1 | no | — |
| 423 | C22×C4 | — | 6 | 1 | no | — |
| 424 | C22×C4 | — | 6 | 1 | no | — |
| 425 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 426 | M16 | — | 2 | 1 | no | — |
| 427 | M16 | — | 2 | 1 | no | — |
| 428 | M16 | — | 2 | 1 | no | — |
| 429 | M16 | — | 2 | 1 | no | — |
| 430 | M16 | — | 3 | 2 | no | — |
| 431 | M16 | — | 6 | 1 | no | — |
| 432 | M16 | — | 6 | 1 | no | — |
| 433 | M16 | — | 6 | 1 | no | — |
| 434 | M16 | — | 6 | 1 | no | — |
| 435 | M16 | — | 6 | 1 | no | — |
| 436 | M16 | #235 | 1 | 2 | yes | — |
| 437 | M16 | D3×Q8 | 1 | 2 | yes | — |
| 438 | C2×C8 | — | 2 | 1 | no | — |
| 439 | C2×C8 | — | 2 | 1 | no | — |
| 440 | C2×C8 | — | 2 | 1 | no | — |
| 441 | C2×C8 | — | 2 | 1 | no | — |
| 442 | C2×C8 | — | 2 | 1 | no | — |
| 443 | C2×C8 | — | 3 | 1 | no | — |
| 444 | C2×C8 | — | 3 | 1 | no | — |
| 445 | C2×C8 | — | 6 | 1 | no | — |
| 446 | C2×C8 | — | 6 | 1 | no | — |
| 447 | C2×C8 | — | 6 | 1 | no | — |
| 448 | C2×C8 | — | 6 | 1 | no | — |
| 449 | C2×C8 | — | 6 | 1 | no | — |
| 450 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 451 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 452 | C4⋊C4 | — | 2 | 1 | no | — |
| 453 | C4⋊C4 | — | 2 | 1 | no | — |
| 454 | C4⋊C4 | — | 2 | 1 | no | — |
| 455 | C4⋊C4 | — | 2 | 1 | no | — |
| 456 | C4⋊C4 | — | 3 | 1 | no | — |
| 457 | C4⋊C4 | — | 3 | 1 | no | — |
| 458 | C4⋊C4 | — | 6 | 1 | no | — |
| 459 | C4⋊C4 | — | 6 | 1 | no | — |
| 460 | C4⋊C4 | — | 6 | 1 | no | — |
| 461 | C4⋊C4 | — | 6 | 1 | no | — |
| 462 | C4⋊C4 | — | 6 | 1 | no | — |
| 463 | C4⋊C4 | — | 6 | 1 | no | — |
| 464 | C4⋊C4 | — | 6 | 1 | no | — |
| 465 | C4⋊C4 | — | 6 | 1 | no | — |
| 466 | C4⋊C4 | — | 12 | 1 | no | — |
| 467 | C4⋊C4 | — | 12 | 1 | no | — |
| 468 | C4⋊C4 | — | 12 | 1 | no | — |
| 469 | C4⋊C4 | — | 12 | 1 | no | — |
| 470 | C4⋊C4 | — | 12 | 1 | no | — |
| 471 | C4⋊C4 | — | 12 | 1 | no | — |
| 472 | C4⋊C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 473 | C4⋊C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 474 | C22⋊C4 | — | 2 | 1 | no | — |
| 475 | C22⋊C4 | — | 6 | 1 | no | — |
| 476 | C42 | — | 2 | 1 | no | — |
| 477 | C42 | — | 3 | 1 | no | — |
| 478 | C42 | — | 3 | 1 | no | — |
| 479 | C42 | — | 3 | 1 | no | — |
| 480 | C42 | — | 3 | 1 | no | — |
| 481 | C42 | — | 6 | 1 | no | — |
| 482 | C42 | — | 12 | 1 | no | — |
| 483 | C42 | — | 12 | 1 | no | — |
| 484 | C22×C3 | — | 2 | 1 | no | — |
| 485 | C22×C3 | — | 2 | 1 | no | — |
| 486 | C22×C3 | C2×#121 | 1 | 1 | yes | characteristic |
| 487 | C22×C3 | #533 | 1 | 1 | yes | characteristic |
| 488 | C22×C3 | #541 | 1 | 1 | yes | characteristic |
| 489 | C3×C4 | — | 4 | 1 | no | — |
| 490 | C3×C4 | — | 4 | 1 | no | — |
| 491 | C3×C4 | — | 8 | 1 | no | — |
| 492 | C3×C4 | — | 8 | 1 | no | — |
| 493 | C3×C4 | #547 | 1 | 1 | yes | characteristic |
| 494 | C3×C4 | #548 | 1 | 1 | yes | characteristic |
| 495 | C3×C4 | D4×Q8 | 1 | 1 | yes | characteristic |
| 496 | C3×C4 | D4×Q8 | 1 | 1 | yes | characteristic |
| 497 | Dic3 | — | 2 | 1 | no | — |
| 498 | Dic3 | — | 2 | 1 | no | — |
| 499 | Dic3 | — | 2 | 1 | no | — |
| 500 | Dic3 | — | 2 | 1 | no | — |
| 501 | Dic3 | — | 4 | 2 | no | — |
| 502 | Dic3 | — | 4 | 1 | no | — |
| 503 | Dic3 | — | 4 | 1 | no | — |
| 504 | Dic3 | — | 8 | 1 | no | — |
| 505 | C23 | D3×#41 | 1 | 1 | yes | characteristic |
| 506 | Q8 | — | 6 | 2 | no | — |
| 507 | Q8 | — | 6 | 2 | no | — |
| 508 | Q8 | — | 12 | 2 | no | — |
| 509 | Q8 | — | 12 | 1 | no | — |
| 510 | Q8 | — | 12 | 1 | no | — |
| 511 | Q8 | — | 24 | 1 | no | — |
| 512 | C2×C4 | — | 2 | 1 | no | — |
| 513 | C2×C4 | — | 2 | 1 | no | — |
| 514 | C2×C4 | — | 3 | 1 | no | — |
| 515 | C2×C4 | — | 3 | 1 | no | — |
| 516 | C2×C4 | — | 3 | 1 | no | — |
| 517 | C2×C4 | — | 3 | 1 | no | — |
| 518 | C2×C4 | — | 4 | 1 | no | — |
| 519 | C2×C4 | — | 4 | 1 | no | — |
| 520 | C2×C4 | — | 6 | 2 | no | — |
| 521 | C2×C4 | — | 6 | 1 | no | — |
| 522 | C2×C4 | — | 6 | 1 | no | — |
| 523 | C2×C4 | — | 8 | 1 | no | — |
| 524 | C2×C4 | — | 8 | 1 | no | — |
| 525 | C2×C4 | — | 12 | 1 | no | — |
| 526 | C2×C4 | — | 12 | 1 | no | — |
| 527 | C2×C4 | — | 12 | 1 | no | — |
| 528 | C2×C4 | — | 12 | 1 | no | — |
| 529 | C2×C4 | — | 12 | 1 | no | — |
| 530 | C2×C4 | — | 24 | 1 | no | — |
| 531 | C2×C4 | C2×#235 | 1 | 1 | yes | characteristic |
| 532 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 533 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 534 | C2×C4 | C2×D3×Q8 | 1 | 1 | yes | characteristic |
| 535 | C2×C4 | #1007 | 1 | 1 | yes | characteristic |
| 536 | C2×C4 | #1010 | 1 | 1 | yes | characteristic |
| 537 | C8 | — | 2 | 2 | no | — |
| 538 | C8 | — | 2 | 1 | no | — |
| 539 | C8 | — | 2 | 1 | no | — |
| 540 | C8 | — | 2 | 2 | no | — |
| 541 | C8 | — | 4 | 1 | no | — |
| 542 | C8 | — | 6 | 2 | no | — |
| 543 | C8 | — | 6 | 1 | no | — |
| 544 | C8 | — | 6 | 1 | no | — |
| 545 | C8 | — | 12 | 1 | no | — |
| 546 | C8 | — | 12 | 1 | no | — |
| 547 | C2×C3 | — | 2 | 1 | no | — |
| 548 | C2×C3 | — | 2 | 1 | no | — |
| 549 | C2×C3 | #2429 | 1 | 1 | yes | characteristic |
| 550 | C2×C3 | #3067 | 1 | 1 | yes | characteristic |
| 551 | C2×C3 | #3069 | 1 | 1 | yes | characteristic |
| 552 | C22 | — | 2 | 1 | no | — |
| 553 | C22 | — | 2 | 1 | no | — |
| 554 | C22 | #5578 | 1 | 1 | yes | characteristic |
| 555 | C22 | D3×#121 | 1 | 1 | yes | characteristic |
| 556 | C22 | #5696 | 1 | 1 | yes | characteristic |
| 557 | C4 | — | 4 | 1 | no | — |
| 558 | C4 | — | 4 | 1 | no | — |
| 559 | C4 | — | 6 | 1 | no | — |
| 560 | C4 | — | 6 | 1 | no | — |
| 561 | C4 | — | 6 | 1 | no | — |
| 562 | C4 | — | 6 | 1 | no | — |
| 563 | C4 | — | 8 | 1 | no | — |
| 564 | C4 | — | 8 | 1 | no | — |
| 565 | C4 | — | 12 | 1 | no | — |
| 566 | C4 | — | 12 | 1 | no | — |
| 567 | C4 | — | 12 | 2 | no | — |
| 568 | C4 | — | 24 | 1 | no | — |
| 569 | C4 | #5507 | 1 | 1 | yes | characteristic |
| 570 | C4 | #5552 | 1 | 1 | yes | characteristic |
| 571 | C4 | #5632 | 1 | 1 | yes | characteristic |
| 572 | C4 | #5727 | 1 | 1 | yes | characteristic |
| 573 | C3 | #25494 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 574 | C2 | — | 2 | 1 | no | — |
| 575 | C2 | — | 2 | 1 | no | — |
| 576 | C2 | #75996 | 1 | 1 | yes | characteristic |
| 577 | C2 | #80937 | 1 | 1 | yes | characteristic |
| 578 | C2 | #80944 | 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