← #11675863
Subgroups — #11675863
Order 768.
1778 conjugacy classes of subgroups.
The subgroup lattice has 550 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #85828 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C3×C4×#135 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #83898 | C2 | 1 | 2 | yes | maximal |
| 4 | #82508 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #79706 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | Q16×Dic6 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #79635 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #79634 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #79574 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | D8×Dic6 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #79173 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #78823 | C2 | 1 | 4 | yes | maximal, complemented |
| 13 | #78445 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C2×#4682 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #61373 | — | 3 | 1 | no | maximal, Sylow |
| 16 | C2×C3×#135 | C22 | 1 | 1 | yes | characteristic |
| 17 | C3×C4×#41 | C22 | 1 | 2 | yes | — |
| 18 | #5827 | C22 | 1 | 4 | yes | — |
| 19 | #5570 | C22 | 1 | 4 | yes | — |
| 20 | Q8×Dic6 | C22 | 1 | 4 | yes | — |
| 21 | #5543 | — | 2 | 4 | no | — |
| 22 | #5543 | C22 | 1 | 4 | yes | — |
| 23 | D4×Dic6 | — | 2 | 4 | no | — |
| 24 | D4×Dic6 | C22 | 1 | 4 | yes | — |
| 25 | #5519 | — | 2 | 4 | no | — |
| 26 | #5519 | C22 | 1 | 4 | yes | — |
| 27 | #5470 | — | 2 | 2 | no | — |
| 28 | #5470 | C22 | 1 | 1 | yes | characteristic |
| 29 | C2×#869 | — | 2 | 2 | no | — |
| 30 | C2×#869 | C22 | 1 | 2 | yes | — |
| 31 | C3×C4×Q16 | C22 | 1 | 1 | yes | characteristic |
| 32 | C3×C4×Q16 | C22 | 1 | 1 | yes | characteristic |
| 33 | C3×C4×SD16 | C22 | 1 | 2 | yes | — |
| 34 | C3×C4×SD16 | C22 | 1 | 2 | yes | — |
| 35 | C3×C4×D8 | C22 | 1 | 1 | yes | characteristic |
| 36 | C3×C4×D8 | C22 | 1 | 1 | yes | characteristic |
| 37 | C3×#427 | C22 | 1 | 1 | yes | characteristic |
| 38 | C3×#416 | C22 | 1 | 2 | yes | — |
| 39 | C2×C3×C4×C8 | C22 | 1 | 1 | yes | characteristic |
| 40 | #5232 | C22 | 1 | 4 | yes | — |
| 41 | Dic3×Q16 | C22 | 1 | 4 | yes | — |
| 42 | #5164 | C22 | 1 | 8 | yes | — |
| 43 | Dic3×D8 | C22 | 1 | 4 | yes | — |
| 44 | C2×#818 | C22 | 1 | 2 | yes | — |
| 45 | C2×#818 | C22 | 1 | 2 | yes | — |
| 46 | #5102 | C22 | 1 | 2 | yes | — |
| 47 | #5101 | C22 | 1 | 2 | yes | — |
| 48 | #5021 | C22 | 1 | 4 | yes | — |
| 49 | #5020 | C22 | 1 | 4 | yes | — |
| 50 | #5008 | C22 | 1 | 4 | yes | — |
| 51 | #5007 | C22 | 1 | 4 | yes | — |
| 52 | #4995 | C22 | 1 | 4 | yes | — |
| 53 | #4924 | C22 | 1 | 1 | yes | characteristic |
| 54 | #4878 | C22 | 1 | 4 | yes | — |
| 55 | #4874 | C22 | 1 | 4 | yes | — |
| 56 | #4856 | C22 | 1 | 8 | yes | — |
| 57 | #4796 | C22 | 1 | 8 | yes | — |
| 58 | #4793 | C22 | 1 | 8 | yes | — |
| 59 | #4766 | C22 | 1 | 8 | yes | — |
| 60 | #4759 | C22 | 1 | 8 | yes | — |
| 61 | #4682 | C22 | 1 | 2 | yes | — |
| 62 | #4682 | C22 | 1 | 2 | yes | — |
| 63 | #4682 | C22 | 1 | 2 | yes | — |
| 64 | #4682 | C22 | 1 | 2 | yes | — |
| 65 | #4679 | C22 | 1 | 2 | yes | — |
| 66 | #4679 | C22 | 1 | 2 | yes | — |
| 67 | C8×Dic6 | C22 | 1 | 2 | yes | — |
| 68 | C8×Dic6 | C22 | 1 | 2 | yes | — |
| 69 | #3503 | — | 3 | 2 | no | — |
| 70 | #3386 | — | 3 | 4 | no | — |
| 71 | #3385 | — | 3 | 4 | no | — |
| 72 | #3383 | — | 3 | 2 | no | — |
| 73 | Q8×Q16 | — | 3 | 2 | no | — |
| 74 | #3380 | — | 3 | 2 | no | — |
| 75 | Q8×D8 | — | 3 | 2 | no | — |
| 76 | #3164 | — | 3 | 2 | no | — |
| 77 | C2×#500 | — | 3 | 1 | no | — |
| 78 | #3083 | — | 3 | 4 | no | — |
| 79 | #3079 | — | 3 | 2 | no | — |
| 80 | #2960 | — | 3 | 1 | no | — |
| 81 | #2951 | — | 3 | 2 | no | — |
| 82 | C4×#135 | D3 | 1 | 1 | yes | characteristic |
| 83 | C2×C3×#41 | C23 | 1 | 2 | yes | — |
| 84 | C22×Dic6 | — | 2 | 2 | no | — |
| 85 | C22×Dic6 | — | 2 | 4 | no | — |
| 86 | C3×#135 | Q8 | 1 | 8 | yes | complemented |
| 87 | C2×C3×Q16 | C23 | 1 | 1 | yes | characteristic |
| 88 | C2×C3×SD16 | C23 | 1 | 2 | yes | — |
| 89 | C2×C3×D8 | C23 | 1 | 1 | yes | characteristic |
| 90 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 91 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 92 | C3×C4×Q8 | C23 | 1 | 2 | yes | — |
| 93 | C3×C4×Q8 | C23 | 1 | 2 | yes | — |
| 94 | C3×C4×D4 | — | 2 | 2 | no | — |
| 95 | C3×C4×D4 | — | 2 | 2 | no | — |
| 96 | C3×C4×D4 | C23 | 1 | 2 | yes | — |
| 97 | C3×C4×D4 | C23 | 1 | 2 | yes | — |
| 98 | C3×#117 | — | 2 | 2 | no | — |
| 99 | C3×#117 | C23 | 1 | 2 | yes | — |
| 100 | C2×C3×C42 | — | 2 | 2 | no | — |
| 101 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 102 | Q8×Dic3 | C23 | 1 | 8 | yes | — |
| 103 | D4×Dic3 | — | 2 | 8 | no | — |
| 104 | D4×Dic3 | C23 | 1 | 8 | yes | — |
| 105 | #926 | — | 2 | 4 | no | — |
| 106 | #926 | C23 | 1 | 2 | yes | — |
| 107 | C2×C4⋊Dic3 | — | 2 | 2 | no | — |
| 108 | C2×C4⋊Dic3 | — | 2 | 4 | no | — |
| 109 | C2×C4⋊Dic3 | — | 2 | 4 | no | — |
| 110 | C2×C4⋊Dic3 | C23 | 1 | 4 | yes | — |
| 111 | #924 | — | 2 | 4 | no | — |
| 112 | #924 | — | 2 | 4 | no | — |
| 113 | #924 | D4 | 1 | 2 | yes | — |
| 114 | #924 | D4 | 1 | 2 | yes | — |
| 115 | C2×#208 | C23 | 1 | 2 | yes | — |
| 116 | #890 | — | 2 | 8 | no | — |
| 117 | #890 | C23 | 1 | 8 | yes | — |
| 118 | #888 | — | 2 | 8 | no | — |
| 119 | #888 | C23 | 1 | 8 | yes | — |
| 120 | #878 | — | 2 | 8 | no | — |
| 121 | #878 | — | 2 | 8 | no | — |
| 122 | #878 | — | 2 | 8 | no | — |
| 123 | #870 | — | 2 | 4 | no | — |
| 124 | #870 | D4 | 1 | 2 | yes | — |
| 125 | #869 | — | 2 | 4 | no | — |
| 126 | #869 | — | 2 | 2 | no | — |
| 127 | #869 | — | 2 | 2 | no | — |
| 128 | #869 | — | 2 | 4 | no | — |
| 129 | #869 | — | 2 | 4 | no | — |
| 130 | #869 | D4 | 1 | 1 | yes | characteristic |
| 131 | #869 | D4 | 1 | 1 | yes | characteristic |
| 132 | #869 | C23 | 1 | 4 | yes | — |
| 133 | #869 | C23 | 1 | 4 | yes | — |
| 134 | C4×Dic6 | — | 2 | 4 | no | — |
| 135 | C4×Dic6 | — | 2 | 4 | no | — |
| 136 | C4×Dic6 | C23 | 1 | 2 | yes | — |
| 137 | C4×Dic6 | C23 | 1 | 2 | yes | — |
| 138 | C3×#107 | C23 | 1 | 1 | yes | characteristic |
| 139 | C3×#107 | C23 | 1 | 1 | yes | characteristic |
| 140 | C3×#106 | C23 | 1 | 2 | yes | — |
| 141 | C3×#103 | C23 | 1 | 2 | yes | — |
| 142 | C3×#103 | C23 | 1 | 2 | yes | — |
| 143 | C3×#102 | C23 | 1 | 2 | yes | — |
| 144 | C3×#102 | C23 | 1 | 2 | yes | — |
| 145 | C3×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 146 | C3×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 147 | C3×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 148 | C3×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 149 | #835 | C23 | 1 | 8 | yes | — |
| 150 | #832 | C23 | 1 | 8 | yes | — |
| 151 | #818 | C23 | 1 | 4 | yes | — |
| 152 | #818 | C23 | 1 | 4 | yes | — |
| 153 | #818 | C23 | 1 | 4 | yes | — |
| 154 | #818 | C23 | 1 | 4 | yes | — |
| 155 | #815 | C23 | 1 | 4 | yes | — |
| 156 | Dic3⋊C8 | C23 | 1 | 4 | yes | — |
| 157 | Dic3⋊C8 | C23 | 1 | 4 | yes | — |
| 158 | C8×Dic3 | C23 | 1 | 4 | yes | — |
| 159 | #808 | C23 | 1 | 8 | yes | — |
| 160 | #807 | C23 | 1 | 8 | yes | — |
| 161 | C4⋊(C3⋊C8) | C23 | 1 | 2 | yes | — |
| 162 | C4⋊(C3⋊C8) | C23 | 1 | 2 | yes | — |
| 163 | C2×#135 | C2×D3 | 1 | 1 | yes | characteristic |
| 164 | Q82 | — | 3 | 4 | no | — |
| 165 | #557 | — | 3 | 4 | no | — |
| 166 | #554 | — | 3 | 4 | no | — |
| 167 | #554 | — | 6 | 4 | no | — |
| 168 | D4×Q8 | — | 3 | 4 | no | — |
| 169 | D4×Q8 | — | 6 | 4 | no | — |
| 170 | #544 | — | 3 | 4 | no | — |
| 171 | #544 | — | 6 | 4 | no | — |
| 172 | #533 | — | 3 | 1 | no | — |
| 173 | #533 | — | 6 | 2 | no | — |
| 174 | C2×C4⋊Q8 | — | 3 | 2 | no | — |
| 175 | C2×C4⋊Q8 | — | 6 | 2 | no | — |
| 176 | #520 | — | 3 | 4 | no | — |
| 177 | C4×#41 | C2×D3 | 1 | 2 | yes | — |
| 178 | #501 | — | 3 | 8 | no | — |
| 179 | #500 | — | 3 | 4 | no | — |
| 180 | #500 | — | 3 | 2 | no | — |
| 181 | #500 | — | 3 | 2 | no | — |
| 182 | #500 | — | 3 | 2 | no | — |
| 183 | #500 | — | 3 | 2 | no | — |
| 184 | #499 | — | 3 | 4 | no | — |
| 185 | #479 | — | 3 | 8 | no | — |
| 186 | #478 | — | 3 | 8 | no | — |
| 187 | #477 | — | 3 | 4 | no | — |
| 188 | #477 | — | 3 | 8 | no | — |
| 189 | #476 | — | 3 | 4 | no | — |
| 190 | #475 | — | 3 | 4 | no | — |
| 191 | #474 | — | 3 | 4 | no | — |
| 192 | #474 | — | 3 | 8 | no | — |
| 193 | #446 | — | 3 | 2 | no | — |
| 194 | #446 | — | 3 | 2 | no | — |
| 195 | C8×Q8 | — | 3 | 2 | no | — |
| 196 | C8×Q8 | — | 3 | 2 | no | — |
| 197 | #440 | — | 3 | 8 | no | — |
| 198 | C4×Q16 | — | 3 | 4 | no | — |
| 199 | C4×Q16 | C2×D3 | 1 | 1 | yes | characteristic |
| 200 | C4×Q16 | C2×D3 | 1 | 1 | yes | characteristic |
| 201 | C4×SD16 | C2×D3 | 1 | 2 | yes | — |
| 202 | C4×SD16 | C2×D3 | 1 | 2 | yes | — |
| 203 | C4×D8 | — | 3 | 4 | no | — |
| 204 | C4×D8 | C2×D3 | 1 | 1 | yes | characteristic |
| 205 | C4×D8 | C2×D3 | 1 | 1 | yes | characteristic |
| 206 | #428 | — | 3 | 4 | no | — |
| 207 | #427 | C2×D3 | 1 | 1 | yes | characteristic |
| 208 | C2×#107 | — | 3 | 2 | no | — |
| 209 | C2×#107 | — | 3 | 2 | no | — |
| 210 | #424 | — | 3 | 2 | no | — |
| 211 | #423 | — | 3 | 1 | no | — |
| 212 | #417 | — | 3 | 4 | no | — |
| 213 | #416 | C2×D3 | 1 | 2 | yes | — |
| 214 | #405 | — | 3 | 2 | no | — |
| 215 | C2×C4×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 216 | C3×#41 | — | 2 | 4 | no | — |
| 217 | C3×#41 | C2×Q8 | 1 | 8 | yes | complemented |
| 218 | C2×C3×Q8 | C24 | 1 | 2 | yes | — |
| 219 | C2×C3×D4 | — | 2 | 2 | no | — |
| 220 | C2×C3×D4 | C24 | 1 | 2 | yes | — |
| 221 | C22×C3×C4 | — | 2 | 2 | no | — |
| 222 | C22×C3×C4 | — | 2 | 2 | no | — |
| 223 | C22×C3×C4 | — | 2 | 2 | no | — |
| 224 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 225 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 226 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 227 | C22×Dic3 | — | 2 | 4 | no | — |
| 228 | C22×Dic3 | — | 2 | 8 | no | — |
| 229 | C2×Dic6 | — | 2 | 4 | no | — |
| 230 | C2×Dic6 | — | 2 | 4 | no | — |
| 231 | C2×Dic6 | — | 2 | 8 | no | — |
| 232 | C2×Dic6 | — | 8 | 8 | no | — |
| 233 | C2×Dic6 | — | 8 | 4 | no | — |
| 234 | C2×Dic6 | C2×D4 | 1 | 2 | yes | — |
| 235 | C2×Dic6 | C2×D4 | 1 | 2 | yes | — |
| 236 | C3×Q16 | C2×Q8 | 1 | 4 | yes | complemented |
| 237 | C3×SD16 | C2×Q8 | 1 | 8 | yes | complemented |
| 238 | C3×D8 | C2×Q8 | 1 | 4 | yes | complemented |
| 239 | C2×C3×C8 | — | 2 | 2 | no | — |
| 240 | C2×C3×C8 | C2×Q8 | 1 | 4 | yes | complemented |
| 241 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 242 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 243 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 244 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 245 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 246 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 247 | C3×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 248 | C3×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 249 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 250 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 251 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 252 | C3×C42 | — | 2 | 2 | no | — |
| 253 | C3×C42 | — | 2 | 2 | no | — |
| 254 | C3×C42 | — | 2 | 2 | no | — |
| 255 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 256 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 257 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 258 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 259 | #217 | — | 2 | 8 | no | — |
| 260 | #217 | C2×D4 | 1 | 4 | yes | — |
| 261 | C4⋊Dic3 | — | 2 | 4 | no | — |
| 262 | C4⋊Dic3 | — | 2 | 4 | no | — |
| 263 | C4⋊Dic3 | — | 2 | 4 | no | — |
| 264 | C4⋊Dic3 | — | 2 | 8 | no | — |
| 265 | C4⋊Dic3 | — | 2 | 8 | no | — |
| 266 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 267 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 268 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 269 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 270 | C4⋊Dic3 | C24 | 1 | 8 | yes | — |
| 271 | Dic3⋊C4 | — | 2 | 8 | no | — |
| 272 | Dic3⋊C4 | — | 2 | 8 | no | — |
| 273 | Dic3⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 274 | Dic3⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 275 | C4×Dic3 | — | 2 | 8 | no | — |
| 276 | C4×Dic3 | C24 | 1 | 4 | yes | — |
| 277 | #208 | — | 2 | 4 | no | — |
| 278 | C2×C3⋊C8 | C24 | 1 | 4 | yes | — |
| 279 | C2×#41 | C22×D3 | 1 | 2 | yes | — |
| 280 | C22×Q8 | — | 6 | 4 | no | — |
| 281 | C22×Q8 | — | 6 | 2 | no | — |
| 282 | #135 | Dic6 | 1 | 8 | yes | complemented |
| 283 | C2×Q16 | C22×D3 | 1 | 1 | yes | characteristic |
| 284 | C2×SD16 | C22×D3 | 1 | 2 | yes | — |
| 285 | C2×D8 | C22×D3 | 1 | 1 | yes | characteristic |
| 286 | C2×M16 | — | 3 | 2 | no | — |
| 287 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 288 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 289 | C4⋊Q8 | — | 3 | 8 | no | — |
| 290 | C4⋊Q8 | — | 3 | 1 | no | — |
| 291 | C4⋊Q8 | — | 3 | 1 | no | — |
| 292 | C4⋊Q8 | — | 3 | 4 | no | — |
| 293 | C4⋊Q8 | — | 3 | 4 | no | — |
| 294 | C4⋊Q8 | — | 6 | 4 | no | — |
| 295 | C4⋊Q8 | — | 6 | 4 | no | — |
| 296 | C4⋊Q8 | — | 6 | 4 | no | — |
| 297 | C4⋊Q8 | — | 6 | 8 | no | — |
| 298 | C4⋊Q8 | — | 6 | 2 | no | — |
| 299 | C4⋊Q8 | — | 6 | 2 | no | — |
| 300 | #125 | — | 3 | 8 | no | — |
| 301 | #125 | — | 3 | 2 | no | — |
| 302 | #125 | — | 6 | 4 | no | — |
| 303 | #125 | — | 6 | 8 | no | — |
| 304 | C22⋊Q8 | — | 3 | 2 | no | — |
| 305 | C22⋊Q8 | — | 3 | 2 | no | — |
| 306 | C22⋊Q8 | — | 6 | 8 | no | — |
| 307 | C22⋊Q8 | — | 6 | 8 | no | — |
| 308 | C22⋊Q8 | — | 6 | 8 | no | — |
| 309 | C22⋊Q8 | — | 6 | 4 | no | — |
| 310 | C22⋊Q8 | — | 6 | 4 | no | — |
| 311 | C4×Q8 | — | 3 | 2 | no | — |
| 312 | C4×Q8 | — | 3 | 2 | no | — |
| 313 | C4×Q8 | — | 3 | 8 | no | — |
| 314 | C4×Q8 | — | 6 | 4 | no | — |
| 315 | C4×Q8 | — | 6 | 4 | no | — |
| 316 | C4×Q8 | C22×D3 | 1 | 2 | yes | — |
| 317 | C4×Q8 | C22×D3 | 1 | 2 | yes | — |
| 318 | C4×D4 | — | 2 | 2 | no | — |
| 319 | C4×D4 | — | 2 | 2 | no | — |
| 320 | C4×D4 | — | 3 | 8 | no | — |
| 321 | C4×D4 | — | 6 | 8 | no | — |
| 322 | C4×D4 | C22×D3 | 1 | 2 | yes | — |
| 323 | C4×D4 | C22×D3 | 1 | 2 | yes | — |
| 324 | #117 | — | 2 | 2 | no | — |
| 325 | #117 | — | 3 | 2 | no | — |
| 326 | #117 | — | 6 | 4 | no | — |
| 327 | #117 | C22×D3 | 1 | 2 | yes | — |
| 328 | C2×C4⋊C4 | — | 3 | 4 | no | — |
| 329 | C2×C4⋊C4 | — | 6 | 4 | no | — |
| 330 | C2×C4⋊C4 | — | 6 | 4 | no | — |
| 331 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 332 | C2×C42 | — | 2 | 2 | no | — |
| 333 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 334 | #107 | — | 3 | 4 | no | — |
| 335 | #107 | — | 3 | 4 | no | — |
| 336 | #107 | — | 3 | 4 | no | — |
| 337 | #107 | — | 3 | 4 | no | — |
| 338 | #107 | — | 3 | 8 | no | — |
| 339 | #107 | C22×D3 | 1 | 1 | yes | characteristic |
| 340 | #107 | C22×D3 | 1 | 1 | yes | characteristic |
| 341 | #106 | — | 3 | 8 | no | — |
| 342 | #106 | C22×D3 | 1 | 2 | yes | — |
| 343 | C4⋊C8 | — | 3 | 4 | no | — |
| 344 | C4⋊C8 | — | 3 | 4 | no | — |
| 345 | C4⋊C8 | — | 3 | 2 | no | — |
| 346 | C4⋊C8 | — | 3 | 2 | no | — |
| 347 | #103 | — | 3 | 8 | no | — |
| 348 | #103 | C22×D3 | 1 | 2 | yes | — |
| 349 | #103 | C22×D3 | 1 | 2 | yes | — |
| 350 | #102 | — | 3 | 8 | no | — |
| 351 | #102 | C22×D3 | 1 | 2 | yes | — |
| 352 | #102 | C22×D3 | 1 | 2 | yes | — |
| 353 | #97 | — | 3 | 4 | no | — |
| 354 | C4×C8 | — | 3 | 4 | no | — |
| 355 | C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 356 | C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 357 | C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 358 | C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 359 | C23×C3 | — | 2 | 2 | no | — |
| 360 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 361 | C3×Q8 | — | 2 | 2 | no | — |
| 362 | C3×Q8 | C22×Q8 | 1 | 4 | yes | — |
| 363 | C3×D4 | — | 2 | 8 | no | — |
| 364 | C3×D4 | — | 2 | 2 | no | — |
| 365 | C3×D4 | C22×Q8 | 1 | 4 | yes | — |
| 366 | C2×C3×C4 | — | 2 | 2 | no | — |
| 367 | C2×C3×C4 | — | 2 | 8 | no | — |
| 368 | C2×C3×C4 | — | 2 | 2 | no | — |
| 369 | C2×C3×C4 | — | 2 | 2 | no | — |
| 370 | C2×C3×C4 | — | 2 | 2 | no | — |
| 371 | C2×C3×C4 | — | 2 | 2 | no | — |
| 372 | C2×C3×C4 | — | 4 | 4 | no | — |
| 373 | C2×C3×C4 | — | 4 | 4 | no | — |
| 374 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 375 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 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×D4 | 1 | 1 | yes | characteristic |
| 379 | C2×C3×C4 | C22×Q8 | 1 | 2 | yes | — |
| 380 | C2×C3×C4 | 2−1+4 | 1 | 2 | yes | — |
| 381 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 382 | C2×Dic3 | — | 2 | 8 | no | — |
| 383 | C2×Dic3 | — | 8 | 8 | no | — |
| 384 | C2×Dic3 | — | 8 | 4 | no | — |
| 385 | C2×Dic3 | C22×D4 | 1 | 4 | yes | — |
| 386 | C2×Dic3 | C22×D4 | 1 | 4 | yes | — |
| 387 | Dic6 | — | 2 | 4 | no | — |
| 388 | Dic6 | — | 2 | 4 | no | — |
| 389 | Dic6 | — | 4 | 8 | no | — |
| 390 | Dic6 | — | 8 | 8 | no | — |
| 391 | Dic6 | — | 8 | 4 | no | — |
| 392 | C3×C8 | — | 2 | 1 | no | — |
| 393 | C3×C8 | — | 2 | 1 | no | — |
| 394 | C3×C8 | C22×Q8 | 1 | 2 | yes | — |
| 395 | C3×C8 | C22×Q8 | 1 | 2 | yes | — |
| 396 | C3⋊C8 | — | 2 | 4 | no | — |
| 397 | #41 | — | 2 | 4 | no | — |
| 398 | #41 | C2×Dic6 | 1 | 8 | yes | complemented |
| 399 | C2×Q8 | — | 3 | 2 | no | — |
| 400 | C2×Q8 | — | 3 | 2 | no | — |
| 401 | C2×Q8 | — | 6 | 8 | no | — |
| 402 | C2×Q8 | — | 6 | 4 | no | — |
| 403 | C2×Q8 | — | 6 | 4 | no | — |
| 404 | C2×Q8 | — | 24 | 4 | no | — |
| 405 | C2×Q8 | — | 24 | 8 | no | — |
| 406 | C2×Q8 | C23×D3 | 1 | 2 | yes | — |
| 407 | C2×D4 | — | 2 | 2 | no | — |
| 408 | C2×D4 | C23×D3 | 1 | 2 | yes | — |
| 409 | C22×C4 | — | 2 | 2 | no | — |
| 410 | C22×C4 | — | 2 | 2 | no | — |
| 411 | C22×C4 | — | 2 | 2 | no | — |
| 412 | C22×C4 | — | 6 | 8 | no | — |
| 413 | C22×C4 | — | 6 | 4 | no | — |
| 414 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 415 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 416 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 417 | Q16 | C2×Dic6 | 1 | 4 | yes | complemented |
| 418 | SD16 | C2×Dic6 | 1 | 8 | yes | complemented |
| 419 | D8 | C2×Dic6 | 1 | 4 | yes | complemented |
| 420 | M16 | — | 6 | 4 | no | — |
| 421 | C2×C8 | — | 2 | 2 | no | — |
| 422 | C2×C8 | — | 3 | 4 | no | — |
| 423 | C2×C8 | C2×Dic6 | 1 | 4 | yes | complemented |
| 424 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 425 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 426 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 427 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 428 | C4⋊C4 | — | 2 | 2 | no | — |
| 429 | C4⋊C4 | — | 2 | 2 | no | — |
| 430 | C4⋊C4 | — | 3 | 2 | no | — |
| 431 | C4⋊C4 | — | 3 | 2 | no | — |
| 432 | C4⋊C4 | — | 3 | 2 | no | — |
| 433 | C4⋊C4 | — | 3 | 2 | no | — |
| 434 | C4⋊C4 | — | 3 | 4 | no | — |
| 435 | C4⋊C4 | — | 3 | 4 | no | — |
| 436 | C4⋊C4 | — | 3 | 8 | no | — |
| 437 | C4⋊C4 | — | 6 | 8 | no | — |
| 438 | C4⋊C4 | — | 6 | 8 | no | — |
| 439 | C4⋊C4 | — | 6 | 8 | no | — |
| 440 | C4⋊C4 | — | 6 | 8 | no | — |
| 441 | C4⋊C4 | — | 6 | 4 | no | — |
| 442 | C4⋊C4 | — | 6 | 4 | no | — |
| 443 | C4⋊C4 | — | 6 | 4 | no | — |
| 444 | C4⋊C4 | C23×D3 | 1 | 2 | yes | — |
| 445 | C4⋊C4 | C23×D3 | 1 | 2 | yes | — |
| 446 | C22⋊C4 | — | 2 | 2 | no | — |
| 447 | C22⋊C4 | — | 2 | 2 | no | — |
| 448 | C22⋊C4 | — | 2 | 2 | no | — |
| 449 | C22⋊C4 | — | 3 | 4 | no | — |
| 450 | C22⋊C4 | — | 6 | 8 | no | — |
| 451 | C42 | — | 2 | 2 | no | — |
| 452 | C42 | — | 2 | 2 | no | — |
| 453 | C42 | — | 2 | 2 | no | — |
| 454 | C42 | — | 3 | 4 | no | — |
| 455 | C42 | — | 6 | 8 | no | — |
| 456 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 457 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 458 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 459 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 460 | C22×C3 | — | 2 | 1 | no | — |
| 461 | C22×C3 | — | 2 | 1 | no | — |
| 462 | C22×C3 | — | 2 | 4 | no | — |
| 463 | C22×C3 | — | 4 | 2 | no | — |
| 464 | C22×C3 | — | 4 | 2 | no | — |
| 465 | C22×C3 | D4×Q8 | 1 | 2 | yes | — |
| 466 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 467 | C3×C4 | — | 2 | 4 | no | — |
| 468 | C3×C4 | — | 2 | 1 | no | — |
| 469 | C3×C4 | — | 2 | 1 | no | — |
| 470 | C3×C4 | — | 4 | 2 | no | — |
| 471 | C3×C4 | — | 4 | 2 | no | — |
| 472 | C3×C4 | D4×Q8 | 1 | 2 | yes | — |
| 473 | C3×C4 | #576 | 1 | 2 | yes | — |
| 474 | C3×C4 | #578 | 1 | 2 | yes | — |
| 475 | C3×C4 | C23×Q8 | 1 | 1 | yes | characteristic |
| 476 | C3×C4 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 477 | Dic3 | — | 2 | 4 | no | — |
| 478 | Dic3 | — | 2 | 4 | no | — |
| 479 | Dic3 | — | 4 | 8 | no | — |
| 480 | C23 | — | 2 | 2 | no | — |
| 481 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 482 | Q8 | — | 2 | 2 | no | — |
| 483 | Q8 | — | 6 | 4 | no | — |
| 484 | Q8 | — | 6 | 4 | no | — |
| 485 | Q8 | — | 12 | 8 | no | — |
| 486 | Q8 | — | 24 | 4 | no | — |
| 487 | Q8 | — | 24 | 8 | no | — |
| 488 | Q8 | C22×Dic6 | 1 | 4 | yes | — |
| 489 | D4 | — | 2 | 8 | no | — |
| 490 | D4 | — | 2 | 2 | no | — |
| 491 | D4 | C22×Dic6 | 1 | 4 | yes | — |
| 492 | C2×C4 | — | 2 | 2 | no | — |
| 493 | C2×C4 | — | 2 | 2 | no | — |
| 494 | C2×C4 | — | 2 | 2 | no | — |
| 495 | C2×C4 | — | 2 | 8 | no | — |
| 496 | C2×C4 | — | 2 | 2 | no | — |
| 497 | C2×C4 | — | 2 | 2 | no | — |
| 498 | C2×C4 | — | 3 | 4 | no | — |
| 499 | C2×C4 | — | 3 | 4 | no | — |
| 500 | C2×C4 | — | 4 | 4 | no | — |
| 501 | C2×C4 | — | 4 | 4 | no | — |
| 502 | C2×C4 | — | 6 | 8 | no | — |
| 503 | C2×C4 | — | 24 | 8 | no | — |
| 504 | C2×C4 | — | 24 | 4 | no | — |
| 505 | C2×C4 | C22×Dic6 | 1 | 2 | yes | — |
| 506 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 507 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 508 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 509 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 510 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 511 | C2×C4 | #1010 | 1 | 2 | yes | — |
| 512 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 513 | C8 | — | 2 | 1 | no | — |
| 514 | C8 | — | 2 | 1 | no | — |
| 515 | C8 | — | 6 | 4 | no | — |
| 516 | C8 | C22×Dic6 | 1 | 2 | yes | — |
| 517 | C8 | C22×Dic6 | 1 | 2 | yes | — |
| 518 | C2×C3 | — | 2 | 2 | no | — |
| 519 | C2×C3 | — | 4 | 4 | no | — |
| 520 | C2×C3 | C2×D4×Q8 | 1 | 1 | yes | characteristic |
| 521 | C2×C3 | C2×#576 | 1 | 1 | yes | characteristic |
| 522 | C2×C3 | C2×#578 | 1 | 1 | yes | characteristic |
| 523 | C22 | — | 2 | 1 | no | — |
| 524 | C22 | — | 2 | 1 | no | — |
| 525 | C22 | — | 2 | 4 | no | — |
| 526 | C22 | — | 4 | 2 | no | — |
| 527 | C22 | — | 4 | 2 | no | — |
| 528 | C22 | D4×Dic6 | 1 | 2 | yes | — |
| 529 | C22 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 530 | C4 | — | 2 | 1 | no | — |
| 531 | C4 | — | 2 | 1 | no | — |
| 532 | C4 | — | 2 | 4 | no | — |
| 533 | C4 | — | 4 | 2 | no | — |
| 534 | C4 | — | 4 | 2 | no | — |
| 535 | C4 | — | 6 | 4 | no | — |
| 536 | C4 | — | 6 | 4 | no | — |
| 537 | C4 | — | 12 | 8 | no | — |
| 538 | C4 | D4×Dic6 | 1 | 2 | yes | — |
| 539 | C4 | #5769 | 1 | 2 | yes | — |
| 540 | C4 | #5771 | 1 | 2 | yes | — |
| 541 | C4 | C23×Dic6 | 1 | 1 | yes | characteristic |
| 542 | C4 | C2×#1010 | 1 | 1 | yes | characteristic |
| 543 | C3 | #61373 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 544 | C2 | — | 2 | 2 | no | — |
| 545 | C2 | — | 4 | 4 | no | — |
| 546 | C2 | C2×D4×Dic6 | 1 | 1 | yes | characteristic |
| 547 | C2 | C2×#5769 | 1 | 1 | yes | characteristic |
| 548 | C2 | C2×#5771 | 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