← #11675878
Subgroups — #11675878
Order 768.
1778 conjugacy classes of subgroups.
The subgroup lattice has 628 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #85889 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C3×#2952 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #83899 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | Dic3×#135 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #82560 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #79855 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #79819 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #79633 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | SD16×Dic6 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #79110 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C2×#4855 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #78873 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #78870 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #78545 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #78542 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #61374 | — | 3 | 1 | no | maximal, Sylow |
| 17 | C2×C3×#135 | C22 | 1 | 1 | yes | characteristic |
| 18 | C3×#520 | C22 | 1 | 2 | yes | — |
| 19 | #5827 | C22 | 1 | 2 | yes | — |
| 20 | Dic3×#41 | C22 | 1 | 2 | yes | — |
| 21 | #5569 | C22 | 1 | 4 | yes | — |
| 22 | Q8×Dic6 | C22 | 1 | 4 | yes | — |
| 23 | #5539 | — | 2 | 4 | no | — |
| 24 | #5539 | C22 | 1 | 4 | yes | — |
| 25 | D4×Dic6 | — | 2 | 4 | no | — |
| 26 | D4×Dic6 | C22 | 1 | 4 | yes | — |
| 27 | #5519 | — | 2 | 2 | no | — |
| 28 | #5519 | C22 | 1 | 2 | yes | — |
| 29 | #5517 | — | 2 | 2 | no | — |
| 30 | #5517 | C22 | 1 | 1 | yes | characteristic |
| 31 | #5500 | — | 2 | 2 | no | — |
| 32 | #5500 | C22 | 1 | 2 | yes | — |
| 33 | C2×#888 | — | 2 | 2 | no | — |
| 34 | C2×#888 | C22 | 1 | 2 | yes | — |
| 35 | C3×#442 | C22 | 1 | 2 | yes | — |
| 36 | C3×#441 | C22 | 1 | 2 | yes | — |
| 37 | C3×C4×SD16 | C22 | 1 | 4 | yes | — |
| 38 | C2×C3×#106 | C22 | 1 | 1 | yes | characteristic |
| 39 | C3×#417 | C22 | 1 | 2 | yes | — |
| 40 | C3×#405 | C22 | 1 | 1 | yes | characteristic |
| 41 | #5233 | C22 | 1 | 2 | yes | — |
| 42 | #5232 | C22 | 1 | 2 | yes | — |
| 43 | #5184 | C22 | 1 | 2 | yes | — |
| 44 | Dic3×Q16 | C22 | 1 | 2 | yes | — |
| 45 | Dic3×SD16 | C22 | 1 | 2 | yes | — |
| 46 | Dic3×SD16 | C22 | 1 | 4 | yes | — |
| 47 | Dic3×SD16 | C22 | 1 | 2 | yes | — |
| 48 | #5152 | C22 | 1 | 2 | yes | — |
| 49 | Dic3×D8 | C22 | 1 | 2 | yes | — |
| 50 | #5121 | C22 | 1 | 2 | yes | — |
| 51 | #5119 | C22 | 1 | 1 | yes | characteristic |
| 52 | #5118 | C22 | 1 | 1 | yes | characteristic |
| 53 | #5106 | C22 | 1 | 1 | yes | characteristic |
| 54 | C2×#817 | C22 | 1 | 1 | yes | characteristic |
| 55 | #5101 | C22 | 1 | 1 | yes | characteristic |
| 56 | C2×C8×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 57 | #5022 | C22 | 1 | 4 | yes | — |
| 58 | #5020 | C22 | 1 | 4 | yes | — |
| 59 | #5009 | C22 | 1 | 4 | yes | — |
| 60 | #5008 | C22 | 1 | 4 | yes | — |
| 61 | #4999 | C22 | 1 | 1 | yes | characteristic |
| 62 | #4964 | C22 | 1 | 2 | yes | — |
| 63 | C2×#808 | C22 | 1 | 2 | yes | — |
| 64 | #4858 | C22 | 1 | 2 | yes | — |
| 65 | #4856 | C22 | 1 | 4 | yes | — |
| 66 | #4855 | C22 | 1 | 4 | yes | — |
| 67 | #4855 | C22 | 1 | 4 | yes | — |
| 68 | #4855 | C22 | 1 | 2 | yes | — |
| 69 | #4796 | C22 | 1 | 4 | yes | — |
| 70 | #4793 | C22 | 1 | 4 | yes | — |
| 71 | #4791 | C22 | 1 | 4 | yes | — |
| 72 | #4791 | C22 | 1 | 4 | yes | — |
| 73 | #4766 | C22 | 1 | 4 | yes | — |
| 74 | #4761 | C22 | 1 | 4 | yes | — |
| 75 | #4761 | C22 | 1 | 4 | yes | — |
| 76 | #4759 | C22 | 1 | 4 | yes | — |
| 77 | #4702 | C22 | 1 | 4 | yes | — |
| 78 | #4701 | C22 | 1 | 4 | yes | — |
| 79 | #4683 | C22 | 1 | 2 | yes | — |
| 80 | #4680 | C22 | 1 | 2 | yes | — |
| 81 | C8×Dic6 | C22 | 1 | 4 | yes | — |
| 82 | #3503 | — | 3 | 2 | no | — |
| 83 | #3387 | — | 3 | 4 | no | — |
| 84 | #3384 | — | 3 | 4 | no | — |
| 85 | #3381 | — | 3 | 4 | no | — |
| 86 | Q8×SD16 | — | 3 | 4 | no | — |
| 87 | #3163 | — | 3 | 1 | no | — |
| 88 | #3163 | — | 3 | 1 | no | — |
| 89 | C2×#498 | — | 3 | 1 | no | — |
| 90 | #3084 | — | 3 | 2 | no | — |
| 91 | #3084 | — | 3 | 2 | no | — |
| 92 | #3079 | — | 3 | 2 | no | — |
| 93 | #2960 | — | 3 | 1 | no | — |
| 94 | #2952 | — | 3 | 1 | no | — |
| 95 | #2952 | D3 | 1 | 1 | yes | characteristic |
| 96 | C4×#135 | — | 3 | 1 | no | — |
| 97 | C2×C3×#41 | C23 | 1 | 2 | yes | — |
| 98 | C22×Dic6 | — | 2 | 2 | no | — |
| 99 | C22×Dic6 | — | 2 | 4 | no | — |
| 100 | C3×#135 | Q8 | 1 | 8 | yes | complemented |
| 101 | C2×C3×Q16 | C23 | 1 | 1 | yes | characteristic |
| 102 | C2×C3×SD16 | C23 | 1 | 2 | yes | — |
| 103 | C2×C3×D8 | C23 | 1 | 1 | yes | characteristic |
| 104 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 105 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 106 | C3×C4×Q8 | C23 | 1 | 4 | yes | — |
| 107 | C3×C4×D4 | — | 2 | 4 | no | — |
| 108 | C3×C4×D4 | C23 | 1 | 4 | yes | — |
| 109 | C3×#117 | — | 2 | 2 | no | — |
| 110 | C3×#117 | C23 | 1 | 1 | yes | characteristic |
| 111 | C2×C3×C4⋊C4 | — | 2 | 2 | no | — |
| 112 | C2×C3×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 113 | Q8×Dic3 | C23 | 1 | 2 | yes | — |
| 114 | Q8×Dic3 | C23 | 1 | 2 | yes | — |
| 115 | Q8×Dic3 | C23 | 1 | 4 | yes | — |
| 116 | D4×Dic3 | — | 2 | 2 | no | — |
| 117 | D4×Dic3 | — | 2 | 2 | no | — |
| 118 | D4×Dic3 | — | 2 | 4 | no | — |
| 119 | D4×Dic3 | C23 | 1 | 2 | yes | — |
| 120 | D4×Dic3 | C23 | 1 | 2 | yes | — |
| 121 | D4×Dic3 | C23 | 1 | 4 | yes | — |
| 122 | #926 | — | 2 | 2 | no | — |
| 123 | #926 | — | 2 | 2 | no | — |
| 124 | #926 | C23 | 1 | 2 | yes | — |
| 125 | #926 | C23 | 1 | 1 | yes | characteristic |
| 126 | C2×C4⋊Dic3 | — | 2 | 2 | no | — |
| 127 | C2×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 128 | #924 | — | 2 | 4 | no | — |
| 129 | #924 | — | 2 | 4 | no | — |
| 130 | #924 | — | 2 | 4 | no | — |
| 131 | C2×Dic3⋊C4 | — | 2 | 2 | no | — |
| 132 | C2×Dic3⋊C4 | — | 2 | 4 | no | — |
| 133 | C2×C4×Dic3 | — | 2 | 2 | no | — |
| 134 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 135 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 136 | C22×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 137 | #890 | — | 2 | 2 | no | — |
| 138 | #890 | — | 2 | 2 | no | — |
| 139 | #890 | — | 2 | 4 | no | — |
| 140 | #890 | D4 | 1 | 2 | yes | — |
| 141 | #890 | C23 | 1 | 4 | yes | — |
| 142 | #888 | — | 2 | 4 | no | — |
| 143 | #888 | — | 2 | 2 | no | — |
| 144 | #888 | — | 2 | 2 | no | — |
| 145 | #888 | — | 2 | 4 | no | — |
| 146 | #888 | — | 2 | 4 | no | — |
| 147 | #888 | — | 2 | 2 | no | — |
| 148 | #888 | — | 2 | 2 | no | — |
| 149 | #888 | D4 | 1 | 2 | yes | — |
| 150 | #888 | C23 | 1 | 4 | yes | — |
| 151 | #888 | C23 | 1 | 4 | yes | — |
| 152 | #888 | C23 | 1 | 4 | yes | — |
| 153 | #878 | — | 2 | 4 | no | — |
| 154 | #878 | — | 2 | 4 | no | — |
| 155 | #878 | — | 2 | 4 | no | — |
| 156 | #878 | — | 2 | 4 | no | — |
| 157 | #878 | — | 2 | 4 | no | — |
| 158 | #878 | D4 | 1 | 4 | yes | — |
| 159 | #870 | — | 2 | 4 | no | — |
| 160 | #870 | C23 | 1 | 4 | yes | — |
| 161 | #869 | — | 2 | 4 | no | — |
| 162 | #869 | C23 | 1 | 4 | yes | — |
| 163 | C4×Dic6 | — | 2 | 4 | no | — |
| 164 | C4×Dic6 | — | 2 | 4 | no | — |
| 165 | C4×Dic6 | C23 | 1 | 4 | yes | — |
| 166 | C3×#106 | C23 | 1 | 2 | yes | — |
| 167 | C3×#106 | C23 | 1 | 2 | yes | — |
| 168 | C3×#103 | C23 | 1 | 4 | yes | — |
| 169 | C3×#102 | C23 | 1 | 4 | yes | — |
| 170 | C3×#97 | C23 | 1 | 2 | yes | — |
| 171 | C3×C4×C8 | C23 | 1 | 2 | yes | — |
| 172 | #835 | C23 | 1 | 2 | yes | — |
| 173 | #835 | C23 | 1 | 2 | yes | — |
| 174 | #835 | C23 | 1 | 4 | yes | — |
| 175 | #832 | C23 | 1 | 2 | yes | — |
| 176 | #832 | C23 | 1 | 2 | yes | — |
| 177 | #832 | C23 | 1 | 4 | yes | — |
| 178 | #818 | C23 | 1 | 4 | yes | — |
| 179 | #818 | C23 | 1 | 2 | yes | — |
| 180 | #817 | C23 | 1 | 4 | yes | — |
| 181 | #817 | C23 | 1 | 2 | yes | — |
| 182 | #817 | C23 | 1 | 1 | yes | characteristic |
| 183 | #817 | C23 | 1 | 2 | yes | — |
| 184 | #817 | C23 | 1 | 1 | yes | characteristic |
| 185 | #815 | C23 | 1 | 2 | yes | — |
| 186 | Dic3⋊C8 | C23 | 1 | 4 | yes | — |
| 187 | Dic3⋊C8 | C23 | 1 | 4 | yes | — |
| 188 | C8×Dic3 | C23 | 1 | 2 | yes | — |
| 189 | C8×Dic3 | C23 | 1 | 2 | yes | — |
| 190 | C8×Dic3 | C23 | 1 | 2 | yes | — |
| 191 | #808 | C23 | 1 | 4 | yes | — |
| 192 | #808 | C23 | 1 | 4 | yes | — |
| 193 | #808 | C23 | 1 | 4 | yes | — |
| 194 | #807 | C23 | 1 | 4 | yes | — |
| 195 | C4⋊(C3⋊C8) | C23 | 1 | 4 | yes | — |
| 196 | C2×#135 | C2×D3 | 1 | 1 | yes | characteristic |
| 197 | Q82 | — | 3 | 4 | no | — |
| 198 | #557 | — | 3 | 4 | no | — |
| 199 | #554 | — | 3 | 4 | no | — |
| 200 | #554 | — | 6 | 4 | no | — |
| 201 | D4×Q8 | — | 3 | 4 | no | — |
| 202 | D4×Q8 | — | 6 | 4 | no | — |
| 203 | #544 | — | 3 | 2 | no | — |
| 204 | #544 | — | 3 | 2 | no | — |
| 205 | #544 | — | 6 | 2 | no | — |
| 206 | #544 | — | 6 | 2 | no | — |
| 207 | #533 | — | 3 | 1 | no | — |
| 208 | #533 | — | 6 | 2 | no | — |
| 209 | C2×C4⋊Q8 | — | 3 | 2 | no | — |
| 210 | C2×C4⋊Q8 | — | 6 | 2 | no | — |
| 211 | #520 | — | 3 | 2 | no | — |
| 212 | #520 | C2×D3 | 1 | 2 | yes | — |
| 213 | C4×#41 | — | 3 | 2 | no | — |
| 214 | #501 | — | 3 | 4 | no | — |
| 215 | #501 | — | 3 | 4 | no | — |
| 216 | #499 | — | 3 | 2 | no | — |
| 217 | #499 | — | 3 | 2 | no | — |
| 218 | #498 | — | 3 | 2 | no | — |
| 219 | #498 | — | 3 | 4 | no | — |
| 220 | #498 | — | 3 | 4 | no | — |
| 221 | #498 | — | 3 | 2 | no | — |
| 222 | #479 | — | 3 | 4 | no | — |
| 223 | #479 | — | 3 | 4 | no | — |
| 224 | #478 | — | 3 | 4 | no | — |
| 225 | #478 | — | 3 | 4 | no | — |
| 226 | #477 | — | 3 | 4 | no | — |
| 227 | #476 | — | 3 | 4 | no | — |
| 228 | #476 | — | 3 | 4 | no | — |
| 229 | #476 | — | 3 | 4 | no | — |
| 230 | #475 | — | 3 | 4 | no | — |
| 231 | #475 | — | 3 | 4 | no | — |
| 232 | #475 | — | 3 | 4 | no | — |
| 233 | #474 | — | 3 | 4 | no | — |
| 234 | #446 | — | 3 | 4 | no | — |
| 235 | C8×Q8 | — | 3 | 4 | no | — |
| 236 | #442 | — | 3 | 2 | no | — |
| 237 | #442 | C2×D3 | 1 | 2 | yes | — |
| 238 | #441 | — | 3 | 2 | no | — |
| 239 | #441 | C2×D3 | 1 | 2 | yes | — |
| 240 | C4×Q16 | — | 3 | 2 | no | — |
| 241 | C4×SD16 | — | 3 | 2 | no | — |
| 242 | C4×SD16 | — | 3 | 4 | no | — |
| 243 | C4×SD16 | — | 3 | 2 | no | — |
| 244 | C4×SD16 | C2×D3 | 1 | 4 | yes | — |
| 245 | C4×D8 | — | 3 | 2 | no | — |
| 246 | #428 | — | 3 | 2 | no | — |
| 247 | #428 | — | 3 | 2 | no | — |
| 248 | #427 | — | 3 | 1 | no | — |
| 249 | C2×#106 | — | 3 | 1 | no | — |
| 250 | C2×#106 | — | 3 | 2 | no | — |
| 251 | C2×#106 | C2×D3 | 1 | 1 | yes | characteristic |
| 252 | #424 | — | 3 | 1 | no | — |
| 253 | #424 | — | 3 | 1 | no | — |
| 254 | #423 | — | 3 | 1 | no | — |
| 255 | #417 | — | 3 | 2 | no | — |
| 256 | #417 | C2×D3 | 1 | 2 | yes | — |
| 257 | #416 | — | 3 | 2 | no | — |
| 258 | #405 | — | 3 | 1 | no | — |
| 259 | #405 | C2×D3 | 1 | 1 | yes | characteristic |
| 260 | C2×C4×C8 | — | 3 | 1 | no | — |
| 261 | C3×#41 | — | 2 | 4 | no | — |
| 262 | C3×#41 | C2×Q8 | 1 | 8 | yes | complemented |
| 263 | C2×C3×Q8 | C24 | 1 | 2 | yes | — |
| 264 | C2×C3×D4 | — | 2 | 2 | no | — |
| 265 | C2×C3×D4 | C24 | 1 | 2 | yes | — |
| 266 | C22×C3×C4 | — | 2 | 2 | no | — |
| 267 | C22×C3×C4 | — | 2 | 2 | no | — |
| 268 | C22×C3×C4 | — | 2 | 4 | no | — |
| 269 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 270 | C22×Dic3 | — | 2 | 2 | no | — |
| 271 | C22×Dic3 | — | 2 | 2 | no | — |
| 272 | C22×Dic3 | — | 2 | 2 | no | — |
| 273 | C22×Dic3 | — | 2 | 4 | no | — |
| 274 | C22×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 275 | C2×Dic6 | — | 2 | 4 | no | — |
| 276 | C2×Dic6 | — | 2 | 4 | no | — |
| 277 | C2×Dic6 | — | 2 | 4 | no | — |
| 278 | C2×Dic6 | — | 2 | 4 | no | — |
| 279 | C2×Dic6 | — | 8 | 8 | no | — |
| 280 | C2×Dic6 | — | 8 | 4 | no | — |
| 281 | C2×Dic6 | C2×D4 | 1 | 4 | yes | — |
| 282 | C3×Q16 | C2×Q8 | 1 | 4 | yes | complemented |
| 283 | C3×SD16 | C2×Q8 | 1 | 8 | yes | complemented |
| 284 | C3×D8 | C2×Q8 | 1 | 4 | yes | complemented |
| 285 | C3×M16 | — | 2 | 2 | no | — |
| 286 | C2×C3×C8 | C2×Q8 | 1 | 4 | yes | complemented |
| 287 | C2×C3×C8 | C24 | 1 | 2 | yes | — |
| 288 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 289 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 290 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 291 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 292 | C3×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 293 | C3×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 294 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 295 | C3×C22⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 296 | C3×C42 | — | 2 | 4 | no | — |
| 297 | C3×C42 | C24 | 1 | 2 | yes | — |
| 298 | #217 | — | 2 | 2 | no | — |
| 299 | #217 | — | 2 | 2 | no | — |
| 300 | #217 | — | 2 | 2 | no | — |
| 301 | #217 | — | 2 | 4 | no | — |
| 302 | #217 | C2×D4 | 1 | 2 | yes | — |
| 303 | C4⋊Dic3 | — | 2 | 4 | no | — |
| 304 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 305 | C4⋊Dic3 | — | 2 | 4 | no | — |
| 306 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 307 | C4⋊Dic3 | — | 2 | 4 | no | — |
| 308 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 309 | C4⋊Dic3 | C2×D4 | 1 | 4 | yes | — |
| 310 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 311 | C4⋊Dic3 | C24 | 1 | 2 | yes | — |
| 312 | C4⋊Dic3 | C24 | 1 | 2 | yes | — |
| 313 | C4⋊Dic3 | C24 | 1 | 4 | yes | — |
| 314 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 315 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 316 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 317 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 318 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 319 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 320 | Dic3⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 321 | Dic3⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 322 | C4×Dic3 | — | 2 | 2 | no | — |
| 323 | C4×Dic3 | — | 2 | 2 | no | — |
| 324 | C4×Dic3 | — | 2 | 2 | no | — |
| 325 | C4×Dic3 | — | 2 | 4 | no | — |
| 326 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 327 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 328 | C4×Dic3 | C24 | 1 | 2 | yes | — |
| 329 | C4×Dic3 | C24 | 1 | 2 | yes | — |
| 330 | #208 | — | 2 | 2 | no | — |
| 331 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 332 | C2×C3⋊C8 | C24 | 1 | 2 | yes | — |
| 333 | C2×C3⋊C8 | C24 | 1 | 2 | yes | — |
| 334 | C2×#41 | C22×D3 | 1 | 2 | yes | — |
| 335 | C22×Q8 | — | 6 | 2 | no | — |
| 336 | C22×Q8 | — | 6 | 4 | no | — |
| 337 | #135 | Dic6 | 1 | 8 | yes | complemented |
| 338 | C2×Q16 | C22×D3 | 1 | 1 | yes | characteristic |
| 339 | C2×SD16 | C22×D3 | 1 | 2 | yes | — |
| 340 | C2×D8 | C22×D3 | 1 | 1 | yes | characteristic |
| 341 | C2×M16 | — | 3 | 1 | no | — |
| 342 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 343 | C22×C8 | — | 3 | 1 | no | — |
| 344 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 345 | C4⋊Q8 | — | 3 | 2 | no | — |
| 346 | C4⋊Q8 | — | 3 | 4 | no | — |
| 347 | C4⋊Q8 | — | 3 | 4 | no | — |
| 348 | C4⋊Q8 | — | 3 | 4 | no | — |
| 349 | C4⋊Q8 | — | 3 | 4 | no | — |
| 350 | C4⋊Q8 | — | 6 | 4 | no | — |
| 351 | C4⋊Q8 | — | 6 | 2 | no | — |
| 352 | C4⋊Q8 | — | 6 | 2 | no | — |
| 353 | C4⋊Q8 | — | 6 | 2 | no | — |
| 354 | C4⋊Q8 | — | 6 | 4 | no | — |
| 355 | C4⋊Q8 | — | 6 | 4 | no | — |
| 356 | C4⋊Q8 | — | 6 | 4 | no | — |
| 357 | C4⋊Q8 | — | 6 | 2 | no | — |
| 358 | #125 | — | 3 | 2 | no | — |
| 359 | #125 | — | 3 | 4 | no | — |
| 360 | #125 | — | 3 | 4 | no | — |
| 361 | #125 | — | 6 | 4 | no | — |
| 362 | #125 | — | 6 | 2 | no | — |
| 363 | #125 | — | 6 | 4 | no | — |
| 364 | #125 | — | 6 | 2 | no | — |
| 365 | C22⋊Q8 | — | 3 | 4 | no | — |
| 366 | C22⋊Q8 | — | 6 | 4 | no | — |
| 367 | C22⋊Q8 | — | 6 | 4 | no | — |
| 368 | C22⋊Q8 | — | 6 | 4 | no | — |
| 369 | C22⋊Q8 | — | 6 | 4 | no | — |
| 370 | C22⋊Q8 | — | 6 | 4 | no | — |
| 371 | C22⋊Q8 | — | 6 | 4 | no | — |
| 372 | C22⋊Q8 | — | 6 | 4 | no | — |
| 373 | C22⋊Q8 | — | 6 | 4 | no | — |
| 374 | C4×Q8 | — | 3 | 4 | no | — |
| 375 | C4×Q8 | — | 3 | 2 | no | — |
| 376 | C4×Q8 | — | 3 | 2 | no | — |
| 377 | C4×Q8 | — | 3 | 4 | no | — |
| 378 | C4×Q8 | — | 6 | 4 | no | — |
| 379 | C4×Q8 | — | 6 | 4 | no | — |
| 380 | C4×Q8 | C22×D3 | 1 | 4 | yes | — |
| 381 | C4×D4 | — | 2 | 4 | no | — |
| 382 | C4×D4 | — | 3 | 2 | no | — |
| 383 | C4×D4 | — | 3 | 2 | no | — |
| 384 | C4×D4 | — | 3 | 4 | no | — |
| 385 | C4×D4 | — | 6 | 4 | no | — |
| 386 | C4×D4 | — | 6 | 2 | no | — |
| 387 | C4×D4 | — | 6 | 2 | no | — |
| 388 | C4×D4 | C22×D3 | 1 | 4 | yes | — |
| 389 | #117 | — | 2 | 2 | no | — |
| 390 | #117 | — | 3 | 1 | no | — |
| 391 | #117 | — | 3 | 2 | no | — |
| 392 | #117 | — | 6 | 2 | no | — |
| 393 | #117 | — | 6 | 2 | no | — |
| 394 | #117 | C22×D3 | 1 | 1 | yes | characteristic |
| 395 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 396 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 397 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 398 | C2×C4⋊C4 | — | 6 | 4 | no | — |
| 399 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 400 | C2×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 401 | C2×C42 | — | 3 | 1 | no | — |
| 402 | C2×C42 | — | 6 | 2 | no | — |
| 403 | #107 | — | 3 | 2 | no | — |
| 404 | #107 | — | 3 | 4 | no | — |
| 405 | #107 | — | 3 | 4 | no | — |
| 406 | #106 | — | 3 | 2 | no | — |
| 407 | #106 | — | 3 | 2 | no | — |
| 408 | #106 | — | 3 | 1 | no | — |
| 409 | #106 | — | 3 | 1 | no | — |
| 410 | #106 | — | 3 | 4 | no | — |
| 411 | #106 | — | 3 | 4 | no | — |
| 412 | #106 | — | 3 | 4 | no | — |
| 413 | #106 | — | 3 | 4 | no | — |
| 414 | #106 | C22×D3 | 1 | 2 | yes | — |
| 415 | #106 | C22×D3 | 1 | 2 | yes | — |
| 416 | C4⋊C8 | — | 3 | 4 | no | — |
| 417 | C4⋊C8 | — | 3 | 4 | no | — |
| 418 | C4⋊C8 | — | 3 | 4 | no | — |
| 419 | #103 | — | 3 | 2 | no | — |
| 420 | #103 | — | 3 | 2 | no | — |
| 421 | #103 | — | 3 | 4 | no | — |
| 422 | #103 | C22×D3 | 1 | 4 | yes | — |
| 423 | #102 | — | 3 | 2 | no | — |
| 424 | #102 | — | 3 | 2 | no | — |
| 425 | #102 | — | 3 | 4 | no | — |
| 426 | #102 | C22×D3 | 1 | 4 | yes | — |
| 427 | #97 | — | 3 | 2 | no | — |
| 428 | #97 | C22×D3 | 1 | 2 | yes | — |
| 429 | C4×C8 | — | 3 | 2 | no | — |
| 430 | C4×C8 | — | 3 | 2 | no | — |
| 431 | C4×C8 | — | 3 | 2 | no | — |
| 432 | C4×C8 | C22×D3 | 1 | 2 | yes | — |
| 433 | C23×C3 | — | 2 | 2 | no | — |
| 434 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 435 | C3×Q8 | — | 2 | 2 | no | — |
| 436 | C3×Q8 | C22×Q8 | 1 | 4 | yes | — |
| 437 | C3×D4 | — | 2 | 8 | no | — |
| 438 | C3×D4 | — | 2 | 2 | no | — |
| 439 | C3×D4 | C22×Q8 | 1 | 4 | yes | — |
| 440 | C2×C3×C4 | — | 2 | 2 | no | — |
| 441 | C2×C3×C4 | — | 2 | 8 | no | — |
| 442 | C2×C3×C4 | — | 2 | 4 | no | — |
| 443 | C2×C3×C4 | — | 8 | 4 | no | — |
| 444 | C2×C3×C4 | — | 8 | 2 | no | — |
| 445 | C2×C3×C4 | C22×D4 | 1 | 4 | yes | — |
| 446 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 447 | C2×C3×C4 | C22×Q8 | 1 | 2 | yes | — |
| 448 | C2×C3×C4 | 2−1+4 | 1 | 2 | yes | — |
| 449 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 450 | C2×Dic3 | — | 2 | 4 | no | — |
| 451 | C2×Dic3 | — | 2 | 2 | no | — |
| 452 | C2×Dic3 | — | 2 | 2 | no | — |
| 453 | C2×Dic3 | — | 2 | 4 | no | — |
| 454 | C2×Dic3 | — | 4 | 4 | no | — |
| 455 | C2×Dic3 | — | 4 | 4 | no | — |
| 456 | C2×Dic3 | — | 8 | 4 | no | — |
| 457 | C2×Dic3 | — | 8 | 2 | no | — |
| 458 | C2×Dic3 | C22×D4 | 1 | 4 | yes | — |
| 459 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 460 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 461 | Dic6 | — | 2 | 8 | no | — |
| 462 | Dic6 | — | 4 | 8 | no | — |
| 463 | Dic6 | — | 8 | 4 | no | — |
| 464 | Dic6 | — | 8 | 4 | no | — |
| 465 | Dic6 | — | 8 | 4 | no | — |
| 466 | C3×C8 | — | 2 | 2 | no | — |
| 467 | C3×C8 | C22×Q8 | 1 | 2 | yes | — |
| 468 | C3×C8 | C22×Q8 | 1 | 2 | yes | — |
| 469 | C3⋊C8 | — | 2 | 2 | no | — |
| 470 | C3⋊C8 | — | 2 | 2 | no | — |
| 471 | #41 | — | 2 | 4 | no | — |
| 472 | #41 | C2×Dic6 | 1 | 8 | yes | complemented |
| 473 | C2×Q8 | — | 3 | 4 | no | — |
| 474 | C2×Q8 | — | 6 | 4 | no | — |
| 475 | C2×Q8 | — | 6 | 4 | no | — |
| 476 | C2×Q8 | — | 6 | 4 | no | — |
| 477 | C2×Q8 | — | 6 | 4 | no | — |
| 478 | C2×Q8 | — | 24 | 4 | no | — |
| 479 | C2×Q8 | — | 24 | 8 | no | — |
| 480 | C2×Q8 | C23×D3 | 1 | 2 | yes | — |
| 481 | C2×D4 | — | 2 | 2 | no | — |
| 482 | C2×D4 | C23×D3 | 1 | 2 | yes | — |
| 483 | C22×C4 | — | 2 | 2 | no | — |
| 484 | C22×C4 | — | 2 | 2 | no | — |
| 485 | C22×C4 | — | 2 | 4 | no | — |
| 486 | C22×C4 | — | 3 | 2 | no | — |
| 487 | C22×C4 | — | 6 | 2 | no | — |
| 488 | C22×C4 | — | 6 | 2 | no | — |
| 489 | C22×C4 | — | 6 | 4 | no | — |
| 490 | C22×C4 | — | 6 | 2 | no | — |
| 491 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 492 | Q16 | C2×Dic6 | 1 | 4 | yes | complemented |
| 493 | SD16 | C2×Dic6 | 1 | 8 | yes | complemented |
| 494 | D8 | C2×Dic6 | 1 | 4 | yes | complemented |
| 495 | M16 | — | 2 | 2 | no | — |
| 496 | M16 | — | 6 | 2 | no | — |
| 497 | C2×C8 | — | 3 | 2 | no | — |
| 498 | C2×C8 | — | 3 | 2 | no | — |
| 499 | C2×C8 | — | 6 | 2 | no | — |
| 500 | C2×C8 | C2×Dic6 | 1 | 4 | yes | complemented |
| 501 | C2×C8 | C23×D3 | 1 | 2 | yes | — |
| 502 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 503 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 504 | C4⋊C4 | — | 2 | 2 | no | — |
| 505 | C4⋊C4 | — | 2 | 4 | no | — |
| 506 | C4⋊C4 | — | 3 | 2 | no | — |
| 507 | C4⋊C4 | — | 3 | 4 | no | — |
| 508 | C4⋊C4 | — | 3 | 4 | no | — |
| 509 | C4⋊C4 | — | 3 | 4 | no | — |
| 510 | C4⋊C4 | — | 3 | 4 | no | — |
| 511 | C4⋊C4 | — | 3 | 2 | no | — |
| 512 | C4⋊C4 | — | 3 | 2 | no | — |
| 513 | C4⋊C4 | — | 6 | 4 | no | — |
| 514 | C4⋊C4 | — | 6 | 4 | no | — |
| 515 | C4⋊C4 | — | 6 | 4 | no | — |
| 516 | C4⋊C4 | — | 6 | 4 | no | — |
| 517 | C4⋊C4 | — | 6 | 2 | no | — |
| 518 | C4⋊C4 | — | 6 | 2 | no | — |
| 519 | C4⋊C4 | — | 6 | 4 | no | — |
| 520 | C4⋊C4 | — | 6 | 4 | no | — |
| 521 | C4⋊C4 | — | 6 | 2 | no | — |
| 522 | C4⋊C4 | — | 6 | 4 | no | — |
| 523 | C4⋊C4 | — | 6 | 4 | no | — |
| 524 | C4⋊C4 | — | 6 | 4 | no | — |
| 525 | C4⋊C4 | D3×D4 | 1 | 2 | yes | — |
| 526 | C4⋊C4 | C23×D3 | 1 | 4 | yes | — |
| 527 | C22⋊C4 | — | 2 | 4 | no | — |
| 528 | C22⋊C4 | — | 3 | 2 | no | — |
| 529 | C22⋊C4 | — | 6 | 2 | no | — |
| 530 | C22⋊C4 | — | 6 | 2 | no | — |
| 531 | C22⋊C4 | — | 6 | 4 | no | — |
| 532 | C22⋊C4 | — | 6 | 2 | no | — |
| 533 | C22⋊C4 | D3×D4 | 1 | 2 | yes | — |
| 534 | C42 | — | 2 | 4 | no | — |
| 535 | C42 | — | 3 | 1 | no | — |
| 536 | C42 | — | 3 | 1 | no | — |
| 537 | C42 | — | 3 | 2 | no | — |
| 538 | C42 | — | 3 | 2 | no | — |
| 539 | C42 | — | 6 | 2 | no | — |
| 540 | C42 | — | 6 | 2 | no | — |
| 541 | C42 | — | 6 | 4 | no | — |
| 542 | C42 | — | 6 | 2 | no | — |
| 543 | C42 | C23×D3 | 1 | 2 | yes | — |
| 544 | C22×C3 | — | 2 | 2 | no | — |
| 545 | C22×C3 | — | 2 | 4 | no | — |
| 546 | C22×C3 | — | 4 | 2 | no | — |
| 547 | C22×C3 | — | 4 | 2 | no | — |
| 548 | C22×C3 | D4×Q8 | 1 | 2 | yes | — |
| 549 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 550 | C3×C4 | — | 2 | 4 | no | — |
| 551 | C3×C4 | — | 2 | 4 | no | — |
| 552 | C3×C4 | — | 4 | 4 | no | — |
| 553 | C3×C4 | D4×Q8 | 1 | 2 | yes | — |
| 554 | C3×C4 | C23×Q8 | 1 | 1 | yes | characteristic |
| 555 | C3×C4 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 556 | Dic3 | — | 2 | 4 | no | — |
| 557 | Dic3 | — | 2 | 2 | no | — |
| 558 | Dic3 | — | 4 | 4 | no | — |
| 559 | Dic3 | — | 4 | 2 | no | — |
| 560 | Dic3 | — | 4 | 2 | no | — |
| 561 | Dic3 | #577 | 1 | 4 | yes | — |
| 562 | C23 | — | 2 | 2 | no | — |
| 563 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 564 | Q8 | — | 2 | 2 | no | — |
| 565 | Q8 | — | 6 | 8 | no | — |
| 566 | Q8 | — | 12 | 8 | no | — |
| 567 | Q8 | — | 24 | 4 | no | — |
| 568 | Q8 | — | 24 | 4 | no | — |
| 569 | Q8 | — | 24 | 4 | no | — |
| 570 | Q8 | C22×Dic6 | 1 | 4 | yes | — |
| 571 | D4 | — | 2 | 8 | no | — |
| 572 | D4 | — | 2 | 2 | no | — |
| 573 | D4 | C22×Dic6 | 1 | 4 | yes | — |
| 574 | C2×C4 | — | 2 | 2 | no | — |
| 575 | C2×C4 | — | 2 | 8 | no | — |
| 576 | C2×C4 | — | 2 | 4 | no | — |
| 577 | C2×C4 | — | 3 | 2 | no | — |
| 578 | C2×C4 | — | 3 | 2 | no | — |
| 579 | C2×C4 | — | 3 | 4 | no | — |
| 580 | C2×C4 | — | 6 | 4 | no | — |
| 581 | C2×C4 | — | 6 | 2 | no | — |
| 582 | C2×C4 | — | 6 | 2 | no | — |
| 583 | C2×C4 | — | 6 | 4 | no | — |
| 584 | C2×C4 | — | 8 | 4 | no | — |
| 585 | C2×C4 | — | 8 | 2 | no | — |
| 586 | C2×C4 | — | 12 | 4 | no | — |
| 587 | C2×C4 | — | 12 | 4 | no | — |
| 588 | C2×C4 | — | 24 | 4 | no | — |
| 589 | C2×C4 | — | 24 | 2 | no | — |
| 590 | C2×C4 | C22×Dic6 | 1 | 2 | yes | — |
| 591 | C2×C4 | C2×D3×D4 | 1 | 4 | yes | — |
| 592 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 593 | C2×C4 | #1010 | 1 | 2 | yes | — |
| 594 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 595 | C8 | — | 2 | 2 | no | — |
| 596 | C8 | — | 6 | 2 | no | — |
| 597 | C8 | — | 6 | 2 | no | — |
| 598 | C8 | C22×Dic6 | 1 | 2 | yes | — |
| 599 | C8 | C22×Dic6 | 1 | 2 | yes | — |
| 600 | C2×C3 | — | 2 | 2 | no | — |
| 601 | C2×C3 | — | 4 | 4 | no | — |
| 602 | C2×C3 | C2×D4×Q8 | 1 | 1 | yes | characteristic |
| 603 | C2×C3 | C2×#577 | 1 | 2 | yes | — |
| 604 | C22 | — | 2 | 2 | no | — |
| 605 | C22 | — | 2 | 4 | no | — |
| 606 | C22 | — | 4 | 2 | no | — |
| 607 | C22 | — | 4 | 2 | no | — |
| 608 | C22 | D4×Dic6 | 1 | 2 | yes | — |
| 609 | C22 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 610 | C4 | — | 2 | 4 | no | — |
| 611 | C4 | — | 2 | 4 | no | — |
| 612 | C4 | — | 3 | 4 | no | — |
| 613 | C4 | — | 4 | 4 | no | — |
| 614 | C4 | — | 6 | 2 | no | — |
| 615 | C4 | — | 6 | 4 | no | — |
| 616 | C4 | — | 12 | 2 | no | — |
| 617 | C4 | — | 12 | 2 | no | — |
| 618 | C4 | — | 12 | 4 | no | — |
| 619 | C4 | D4×Dic6 | 1 | 2 | yes | — |
| 620 | C4 | C23×Dic6 | 1 | 1 | yes | characteristic |
| 621 | C4 | C2×#1010 | 1 | 1 | yes | characteristic |
| 622 | C3 | #61374 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 623 | C2 | — | 2 | 2 | no | — |
| 624 | C2 | — | 4 | 4 | no | — |
| 625 | C2 | C2×D4×Dic6 | 1 | 1 | yes | characteristic |
| 626 | C2 | D3×#577 | 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