← #36300995
Subgroups — #36300995
Order 21248.
1996 conjugacy classes of subgroups.
The subgroup lattice has 512 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #24921089 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | Q8×#13050578 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #24920098 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #24920058 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #24919784 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #24918841 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #24918591 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #24917517 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #24917272 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #24916595 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C83×#3499 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | Q8×Dic166 | C22 | 1 | 1 | yes | characteristic |
| 13 | #19128416 | C22 | 1 | 3 | yes | — |
| 14 | #19128414 | — | 2 | 3 | no | — |
| 15 | #19128373 | C22 | 1 | 1 | yes | characteristic |
| 16 | #19128372 | C22 | 1 | 3 | yes | — |
| 17 | #19128370 | — | 2 | 1 | no | — |
| 18 | #19128251 | C22 | 1 | 3 | yes | — |
| 19 | #19128248 | — | 2 | 3 | no | — |
| 20 | C4×#13050591 | — | 2 | 1 | no | — |
| 21 | C4×#13050590 | C22 | 1 | 3 | yes | — |
| 22 | #19128097 | C22 | 1 | 6 | yes | — |
| 23 | #19128049 | C22 | 1 | 6 | yes | — |
| 24 | #19128022 | C22 | 1 | 6 | yes | — |
| 25 | #19128019 | C22 | 1 | 12 | yes | — |
| 26 | #19127993 | C22 | 1 | 3 | yes | — |
| 27 | #19127991 | C22 | 1 | 6 | yes | — |
| 28 | #19127988 | C22 | 1 | 3 | yes | — |
| 29 | #19127988 | C22 | 1 | 6 | yes | — |
| 30 | #19127983 | C22 | 1 | 6 | yes | — |
| 31 | #19127978 | C22 | 1 | 6 | yes | — |
| 32 | #19127952 | C22 | 1 | 12 | yes | — |
| 33 | #19127898 | C22 | 1 | 1 | yes | characteristic |
| 34 | #19127896 | C22 | 1 | 6 | yes | — |
| 35 | #19127893 | C22 | 1 | 3 | yes | — |
| 36 | #19127844 | C22 | 1 | 6 | yes | — |
| 37 | Q8×C83⋊C8 | C22 | 1 | 2 | yes | — |
| 38 | C4×#13050578 | C22 | 1 | 6 | yes | — |
| 39 | C4×#13050575 | C22 | 1 | 6 | yes | — |
| 40 | #19127779 | C22 | 1 | 6 | yes | — |
| 41 | #19127754 | C22 | 1 | 3 | yes | — |
| 42 | #19127741 | C22 | 1 | 6 | yes | — |
| 43 | #19127725 | C22 | 1 | 3 | yes | — |
| 44 | #19127700 | C22 | 1 | 6 | yes | — |
| 45 | C2×2−1+4×C83 | — | 2 | 1 | no | — |
| 46 | D4×Q8×C83 | — | 2 | 1 | no | — |
| 47 | D4×Q8×C83 | C22 | 1 | 2 | yes | — |
| 48 | #547×C83 | — | 2 | 3 | no | — |
| 49 | #547×C83 | C22 | 1 | 6 | yes | — |
| 50 | #536×C83 | — | 2 | 3 | no | — |
| 51 | #532×C83 | C22 | 1 | 3 | yes | — |
| 52 | C2×C4⋊Q8×C83 | C22 | 1 | 3 | yes | — |
| 53 | C4×#41×C83 | C22 | 1 | 1 | yes | characteristic |
| 54 | C2×#13050591 | — | 2 | 1 | no | — |
| 55 | C2×#13050590 | — | 2 | 3 | no | — |
| 56 | C2×#13050590 | C23 | 1 | 3 | yes | — |
| 57 | C2×#13050578 | C23 | 1 | 2 | yes | — |
| 58 | C2×#13050575 | C23 | 1 | 6 | yes | — |
| 59 | C2×#13050574 | C23 | 1 | 6 | yes | — |
| 60 | #14581792 | C23 | 1 | 3 | yes | — |
| 61 | #14581791 | — | 2 | 3 | no | — |
| 62 | #14581789 | C23 | 1 | 3 | yes | — |
| 63 | #14581788 | — | 2 | 3 | no | — |
| 64 | #14581780 | — | 2 | 3 | no | — |
| 65 | #14581778 | — | 2 | 6 | no | — |
| 66 | #14581767 | — | 2 | 3 | no | — |
| 67 | #14581766 | — | 2 | 3 | no | — |
| 68 | #14581766 | C23 | 1 | 6 | yes | — |
| 69 | #14581765 | — | 2 | 6 | no | — |
| 70 | #14581763 | — | 2 | 3 | no | — |
| 71 | Q8×Dic83 | — | 2 | 1 | no | — |
| 72 | C4×Dic166 | C23 | 1 | 3 | yes | — |
| 73 | C4×Dic166 | C23 | 1 | 1 | yes | characteristic |
| 74 | C4×D332 | — | 2 | 3 | no | — |
| 75 | C4×D332 | C23 | 1 | 3 | yes | — |
| 76 | C4×D332 | C23 | 1 | 3 | yes | — |
| 77 | #14581754 | — | 2 | 3 | no | — |
| 78 | C4×C22⋊D83 | — | 2 | 3 | no | — |
| 79 | C4×C22⋊D83 | — | 2 | 3 | no | — |
| 80 | #14581751 | C23 | 1 | 3 | yes | — |
| 81 | #14581750 | — | 2 | 3 | no | — |
| 82 | #14581749 | — | 2 | 3 | no | — |
| 83 | C42×D83 | — | 2 | 3 | no | — |
| 84 | #14581725 | C23 | 1 | 6 | yes | — |
| 85 | #14581723 | C23 | 1 | 6 | yes | — |
| 86 | #14581723 | C23 | 1 | 12 | yes | — |
| 87 | C4⋊(C83⋊C8) | C23 | 1 | 6 | yes | — |
| 88 | C4⋊(C83⋊C8) | C23 | 1 | 3 | yes | — |
| 89 | C4⋊(C83⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 90 | #14581715 | C23 | 1 | 6 | yes | — |
| 91 | #14581713 | C23 | 1 | 6 | yes | — |
| 92 | #14581713 | C23 | 1 | 2 | yes | — |
| 93 | #14581712 | C23 | 1 | 6 | yes | — |
| 94 | #14581712 | C23 | 1 | 12 | yes | — |
| 95 | C22⋊(C83⋊C8) | C23 | 1 | 6 | yes | — |
| 96 | C4×C83⋊C8 | C23 | 1 | 6 | yes | — |
| 97 | 2−1+4×C83 | — | 4 | 8 | no | — |
| 98 | C2×#41×C83 | — | 2 | 6 | no | — |
| 99 | C2×#41×C83 | — | 2 | 3 | no | — |
| 100 | C2×#41×C83 | D4 | 1 | 1 | yes | characteristic |
| 101 | C22×Q8×C83 | — | 2 | 2 | no | — |
| 102 | C22×Q8×C83 | — | 2 | 3 | no | — |
| 103 | C4⋊Q8×C83 | — | 2 | 3 | no | — |
| 104 | C4⋊Q8×C83 | — | 2 | 3 | no | — |
| 105 | C4⋊Q8×C83 | C23 | 1 | 6 | yes | — |
| 106 | C4⋊Q8×C83 | C23 | 1 | 3 | yes | — |
| 107 | #127×C83 | C23 | 1 | 1 | yes | characteristic |
| 108 | #124×C83 | — | 2 | 3 | no | — |
| 109 | #123×C83 | — | 2 | 12 | no | — |
| 110 | C22⋊Q8×C83 | — | 2 | 6 | no | — |
| 111 | C22⋊Q8×C83 | — | 2 | 6 | no | — |
| 112 | #121×C83 | — | 2 | 3 | no | — |
| 113 | #121×C83 | C23 | 1 | 6 | yes | — |
| 114 | C4×Q8×C83 | D4 | 1 | 1 | yes | characteristic |
| 115 | C4×Q8×C83 | C23 | 1 | 1 | yes | characteristic |
| 116 | C4×D4×C83 | — | 2 | 3 | no | — |
| 117 | C4×D4×C83 | D4 | 1 | 3 | yes | — |
| 118 | C4×D4×C83 | C23 | 1 | 6 | yes | — |
| 119 | C4×D4×C83 | C23 | 1 | 3 | yes | — |
| 120 | #117×C83 | D4 | 1 | 3 | yes | — |
| 121 | C2×C4⋊C4×C83 | — | 2 | 3 | no | — |
| 122 | C2×C4⋊C4×C83 | C23 | 1 | 6 | yes | — |
| 123 | C2×C42×C83 | C23 | 1 | 3 | yes | — |
| 124 | #13050591 | — | 4 | 4 | no | — |
| 125 | #13050590 | — | 2 | 6 | no | — |
| 126 | #13050590 | — | 4 | 3 | no | — |
| 127 | #13050590 | — | 8 | 6 | no | — |
| 128 | C2×Dic166 | — | 2 | 3 | no | — |
| 129 | C2×Dic166 | C24 | 1 | 1 | yes | characteristic |
| 130 | C2×D332 | — | 2 | 3 | no | — |
| 131 | C2×D332 | — | 2 | 3 | no | — |
| 132 | C2×D332 | C24 | 1 | 3 | yes | — |
| 133 | C2×C22⋊D83 | — | 2 | 3 | no | — |
| 134 | C2×C22⋊D83 | — | 2 | 6 | no | — |
| 135 | C2×C4×D83 | — | 2 | 3 | no | — |
| 136 | C2×C4×D83 | — | 2 | 3 | no | — |
| 137 | C2×C4×D83 | — | 2 | 3 | no | — |
| 138 | #13050578 | — | 2 | 4 | no | — |
| 139 | #13050575 | — | 4 | 6 | no | — |
| 140 | #13050574 | — | 4 | 6 | no | — |
| 141 | C2×C83⋊C8 | C24 | 1 | 6 | yes | — |
| 142 | C2×C83⋊C8 | C24 | 1 | 2 | yes | — |
| 143 | C4⋊Dic83 | — | 2 | 3 | no | — |
| 144 | C4⋊Dic83 | C24 | 1 | 3 | yes | — |
| 145 | C4⋊Dic83 | C24 | 1 | 1 | yes | characteristic |
| 146 | Dic83⋊C4 | — | 2 | 3 | no | — |
| 147 | Dic83⋊C4 | — | 2 | 1 | no | — |
| 148 | C22⋊Dic83 | — | 2 | 3 | no | — |
| 149 | (C2×D83)⋊C4 | — | 2 | 6 | no | — |
| 150 | (C2×D83)⋊C4 | — | 2 | 3 | no | — |
| 151 | (C2×D83)⋊C4 | — | 2 | 3 | no | — |
| 152 | C4×Dic83 | — | 2 | 3 | no | — |
| 153 | C4×Dic83 | — | 2 | 3 | no | — |
| 154 | C4×Dic83 | — | 2 | 1 | no | — |
| 155 | #41×C83 | — | 2 | 4 | no | — |
| 156 | #41×C83 | — | 4 | 12 | no | — |
| 157 | #41×C83 | — | 4 | 24 | no | — |
| 158 | C2×Q8×C83 | — | 2 | 6 | no | — |
| 159 | C2×Q8×C83 | — | 2 | 3 | no | — |
| 160 | C2×Q8×C83 | — | 4 | 12 | no | — |
| 161 | C2×Q8×C83 | — | 4 | 8 | no | — |
| 162 | C2×Q8×C83 | C2×D4 | 1 | 1 | yes | characteristic |
| 163 | C2×D4×C83 | — | 2 | 6 | no | — |
| 164 | C2×D4×C83 | — | 2 | 1 | no | — |
| 165 | C2×D4×C83 | — | 2 | 1 | no | — |
| 166 | C2×D4×C83 | C2×D4 | 1 | 3 | yes | — |
| 167 | C2×D4×C83 | C24 | 1 | 2 | yes | — |
| 168 | C22×C4×C83 | — | 2 | 6 | no | — |
| 169 | C22×C4×C83 | — | 2 | 6 | no | — |
| 170 | C22×C4×C83 | C2×D4 | 1 | 3 | yes | — |
| 171 | C22×C4×C83 | C2×D4 | 1 | 3 | yes | — |
| 172 | C22×C4×C83 | C24 | 1 | 3 | yes | — |
| 173 | C4⋊C4×C83 | — | 2 | 3 | no | — |
| 174 | C4⋊C4×C83 | — | 2 | 6 | no | — |
| 175 | C4⋊C4×C83 | — | 2 | 6 | no | — |
| 176 | C4⋊C4×C83 | C2×D4 | 1 | 3 | yes | — |
| 177 | C4⋊C4×C83 | C2×D4 | 1 | 3 | yes | — |
| 178 | C4⋊C4×C83 | C24 | 1 | 6 | yes | — |
| 179 | C22⋊C4×C83 | — | 2 | 6 | no | — |
| 180 | C22⋊C4×C83 | — | 2 | 6 | no | — |
| 181 | C22⋊C4×C83 | C2×D4 | 1 | 6 | yes | — |
| 182 | C42×C83 | C2×D4 | 1 | 3 | yes | — |
| 183 | C42×C83 | C2×D4 | 1 | 3 | yes | — |
| 184 | C42×C83 | C24 | 1 | 3 | yes | — |
| 185 | C42×C83 | C24 | 1 | 1 | yes | characteristic |
| 186 | C23×C83 | — | 2 | 2 | no | — |
| 187 | C23×C83 | C22×D4 | 1 | 3 | yes | — |
| 188 | C22×D83 | — | 2 | 3 | no | — |
| 189 | Q8×C83 | — | 4 | 6 | no | — |
| 190 | Q8×C83 | — | 4 | 12 | no | — |
| 191 | Q8×C83 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 192 | D4×C83 | — | 2 | 6 | no | — |
| 193 | D4×C83 | — | 2 | 2 | no | — |
| 194 | D4×C83 | — | 2 | 2 | no | — |
| 195 | D4×C83 | — | 4 | 2 | no | — |
| 196 | D4×C83 | — | 4 | 12 | no | — |
| 197 | D4×C83 | — | 4 | 2 | no | — |
| 198 | C2×C4×C83 | — | 2 | 6 | no | — |
| 199 | C2×C4×C83 | — | 2 | 6 | no | — |
| 200 | C2×C4×C83 | — | 2 | 3 | no | — |
| 201 | C2×C4×C83 | — | 2 | 3 | no | — |
| 202 | C2×C4×C83 | — | 2 | 6 | no | — |
| 203 | C2×C4×C83 | — | 4 | 12 | no | — |
| 204 | C2×C4×C83 | — | 4 | 12 | no | — |
| 205 | C2×C4×C83 | C22×D4 | 1 | 1 | yes | characteristic |
| 206 | C2×C4×C83 | C22×D4 | 1 | 3 | yes | — |
| 207 | C2×C4×C83 | C22×D4 | 1 | 3 | yes | — |
| 208 | C2×C4×C83 | C22×D4 | 1 | 3 | yes | — |
| 209 | C2×C4×C83 | C22×D4 | 1 | 1 | yes | characteristic |
| 210 | C2×C4×C83 | C25 | 1 | 1 | yes | characteristic |
| 211 | C22⋊D83 | — | 4 | 6 | no | — |
| 212 | C22⋊D83 | — | 8 | 6 | no | — |
| 213 | C2×Dic83 | — | 2 | 1 | no | — |
| 214 | C2×Dic83 | — | 2 | 1 | no | — |
| 215 | C2×Dic83 | — | 2 | 3 | no | — |
| 216 | D332 | — | 2 | 3 | no | — |
| 217 | D332 | — | 2 | 3 | no | — |
| 218 | D332 | — | 4 | 6 | no | — |
| 219 | D332 | — | 8 | 3 | no | — |
| 220 | C4×D83 | — | 4 | 6 | no | — |
| 221 | C4×D83 | — | 4 | 6 | no | — |
| 222 | C4×D83 | — | 4 | 6 | no | — |
| 223 | Dic166 | — | 2 | 1 | no | — |
| 224 | Dic166 | — | 8 | 3 | no | — |
| 225 | Dic166 | 2−1+4 | 1 | 2 | yes | complemented |
| 226 | C83⋊C8 | — | 2 | 2 | no | — |
| 227 | C83⋊C8 | — | 2 | 6 | no | — |
| 228 | C22×C83 | — | 2 | 3 | no | — |
| 229 | C22×C83 | — | 2 | 3 | no | — |
| 230 | C22×C83 | — | 2 | 3 | no | — |
| 231 | C22×C83 | — | 4 | 2 | no | — |
| 232 | C22×C83 | — | 4 | 2 | no | — |
| 233 | C22×C83 | — | 4 | 2 | no | — |
| 234 | C22×C83 | C23×D4 | 1 | 1 | yes | characteristic |
| 235 | C2×D83 | — | 4 | 3 | no | — |
| 236 | C2×D83 | — | 4 | 3 | no | — |
| 237 | C2×D83 | — | 4 | 3 | no | — |
| 238 | C4×C83 | — | 2 | 3 | no | — |
| 239 | C4×C83 | — | 2 | 1 | no | — |
| 240 | C4×C83 | — | 2 | 3 | no | — |
| 241 | C4×C83 | — | 4 | 6 | no | — |
| 242 | C4×C83 | C2×AGL(1,ℤ/8) | 1 | 6 | yes | — |
| 243 | C4×C83 | #577 | 1 | 2 | yes | — |
| 244 | C4×C83 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 245 | C4×C83 | #585 | 1 | 1 | yes | characteristic |
| 246 | Dic83 | — | 2 | 2 | no | — |
| 247 | Dic83 | — | 4 | 1 | no | — |
| 248 | Dic83 | — | 4 | 3 | no | — |
| 249 | #62150 | — | 83 | 1 | no | maximal, Sylow |
| 250 | C2×C83 | — | 4 | 3 | no | — |
| 251 | C2×C83 | — | 8 | 2 | no | — |
| 252 | C2×C83 | #3489 | 1 | 1 | yes | characteristic |
| 253 | C2×C83 | C22×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 254 | C2×C83 | C2×#577 | 1 | 1 | yes | characteristic |
| 255 | D83 | — | 8 | 3 | no | — |
| 256 | #3499 | D83 | 1 | 1 | yes | characteristic, complemented |
| 257 | #3483 | — | 83 | 1 | no | — |
| 258 | Q8×SD16 | — | 83 | 2 | no | — |
| 259 | #3358 | — | 83 | 2 | no | — |
| 260 | #3354 | — | 83 | 6 | no | — |
| 261 | #3332 | — | 83 | 6 | no | — |
| 262 | #3253 | — | 83 | 3 | no | — |
| 263 | #3227 | — | 83 | 3 | no | — |
| 264 | #3106 | — | 83 | 3 | no | — |
| 265 | #3079 | — | 83 | 3 | no | — |
| 266 | #2991 | — | 83 | 1 | no | — |
| 267 | C83 | #62150 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 268 | C2×2−1+4 | — | 2 | 1 | no | — |
| 269 | Q82 | — | 83 | 1 | no | — |
| 270 | #555 | — | 83 | 3 | no | — |
| 271 | #555 | — | 166 | 3 | no | — |
| 272 | #550 | — | 83 | 1 | no | — |
| 273 | #550 | — | 83 | 3 | no | — |
| 274 | #550 | — | 166 | 1 | no | — |
| 275 | D4×Q8 | — | 2 | 1 | no | — |
| 276 | D4×Q8 | C2×D83 | 1 | 2 | yes | — |
| 277 | #547 | — | 2 | 3 | no | — |
| 278 | #547 | C2×D83 | 1 | 6 | yes | — |
| 279 | #536 | — | 2 | 3 | no | — |
| 280 | #532 | — | 83 | 3 | no | — |
| 281 | #532 | — | 166 | 3 | no | — |
| 282 | #532 | C2×D83 | 1 | 3 | yes | — |
| 283 | C2×C4⋊Q8 | C2×D83 | 1 | 3 | yes | — |
| 284 | C4×#41 | — | 83 | 3 | no | — |
| 285 | C4×#41 | — | 166 | 1 | no | — |
| 286 | C4×#41 | C2×D83 | 1 | 1 | yes | characteristic |
| 287 | #498 | — | 83 | 6 | no | — |
| 288 | #486 | — | 83 | 6 | no | — |
| 289 | #482 | — | 83 | 6 | no | — |
| 290 | #481 | — | 83 | 12 | no | — |
| 291 | #477 | — | 83 | 3 | no | — |
| 292 | #476 | — | 83 | 6 | no | — |
| 293 | #476 | — | 83 | 3 | no | — |
| 294 | #476 | — | 83 | 6 | no | — |
| 295 | #475 | — | 83 | 6 | no | — |
| 296 | #474 | — | 83 | 6 | no | — |
| 297 | #469 | — | 83 | 12 | no | — |
| 298 | #460 | — | 83 | 1 | no | — |
| 299 | #459 | — | 83 | 3 | no | — |
| 300 | #459 | — | 83 | 6 | no | — |
| 301 | #449 | — | 83 | 6 | no | — |
| 302 | C8×Q8 | — | 83 | 2 | no | — |
| 303 | C4×SD16 | — | 83 | 6 | no | — |
| 304 | C4×D8 | — | 83 | 6 | no | — |
| 305 | #436 | — | 83 | 6 | no | — |
| 306 | #431 | — | 83 | 3 | no | — |
| 307 | #428 | — | 83 | 6 | no | — |
| 308 | #423 | — | 83 | 3 | no | — |
| 309 | #417 | — | 83 | 6 | no | — |
| 310 | 2−1+4 | — | 4 | 8 | no | — |
| 311 | C2×#41 | — | 2 | 6 | no | — |
| 312 | C2×#41 | — | 2 | 3 | no | — |
| 313 | C2×#41 | — | 83 | 3 | no | — |
| 314 | C2×#41 | — | 166 | 1 | no | — |
| 315 | C2×#41 | — | 166 | 3 | no | — |
| 316 | C2×#41 | C22⋊D83 | 1 | 1 | yes | characteristic |
| 317 | C22×Q8 | — | 2 | 2 | no | — |
| 318 | C22×Q8 | — | 2 | 3 | no | — |
| 319 | C2×SD16 | — | 83 | 2 | no | — |
| 320 | C2×D8 | — | 83 | 6 | no | — |
| 321 | C2×M16 | — | 83 | 6 | no | — |
| 322 | C4⋊Q8 | — | 2 | 3 | no | — |
| 323 | C4⋊Q8 | — | 2 | 3 | no | — |
| 324 | C4⋊Q8 | — | 83 | 3 | no | — |
| 325 | C4⋊Q8 | — | 166 | 3 | no | — |
| 326 | C4⋊Q8 | C22×D83 | 1 | 3 | yes | — |
| 327 | C4⋊Q8 | C22×D83 | 1 | 6 | yes | — |
| 328 | #127 | — | 83 | 3 | no | — |
| 329 | #127 | — | 166 | 3 | no | — |
| 330 | #127 | C22×D83 | 1 | 1 | yes | characteristic |
| 331 | #124 | — | 2 | 3 | no | — |
| 332 | #124 | — | 166 | 6 | no | — |
| 333 | #124 | — | 166 | 3 | no | — |
| 334 | #123 | — | 2 | 12 | no | — |
| 335 | C22⋊Q8 | — | 2 | 6 | no | — |
| 336 | C22⋊Q8 | — | 2 | 6 | no | — |
| 337 | #121 | — | 2 | 3 | no | — |
| 338 | #121 | — | 83 | 6 | no | — |
| 339 | #121 | — | 166 | 3 | no | — |
| 340 | #121 | — | 166 | 3 | no | — |
| 341 | #121 | — | 166 | 3 | no | — |
| 342 | #121 | — | 166 | 6 | no | — |
| 343 | #121 | C22×D83 | 1 | 6 | yes | — |
| 344 | C4×Q8 | — | 83 | 1 | no | — |
| 345 | C4×Q8 | — | 83 | 3 | no | — |
| 346 | C4×Q8 | — | 166 | 1 | no | — |
| 347 | C4×Q8 | C22⋊D83 | 1 | 1 | yes | characteristic |
| 348 | C4×Q8 | C22×D83 | 1 | 1 | yes | characteristic |
| 349 | C4×D4 | — | 2 | 3 | no | — |
| 350 | C4×D4 | — | 83 | 3 | no | — |
| 351 | C4×D4 | — | 83 | 3 | no | — |
| 352 | C4×D4 | — | 166 | 3 | no | — |
| 353 | C4×D4 | — | 166 | 3 | no | — |
| 354 | C4×D4 | — | 166 | 3 | no | — |
| 355 | C4×D4 | — | 166 | 3 | no | — |
| 356 | C4×D4 | C22⋊D83 | 1 | 3 | yes | — |
| 357 | C4×D4 | C22×D83 | 1 | 6 | yes | — |
| 358 | C4×D4 | C22×D83 | 1 | 3 | yes | — |
| 359 | #117 | — | 83 | 3 | no | — |
| 360 | #117 | — | 166 | 3 | no | — |
| 361 | #117 | — | 166 | 3 | no | — |
| 362 | #117 | C22⋊D83 | 1 | 3 | yes | — |
| 363 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 364 | C2×C4⋊C4 | C22×D83 | 1 | 6 | yes | — |
| 365 | C2×C42 | — | 166 | 3 | no | — |
| 366 | C2×C42 | C22×D83 | 1 | 3 | yes | — |
| 367 | #107 | — | 83 | 6 | no | — |
| 368 | #106 | — | 83 | 12 | no | — |
| 369 | #106 | — | 83 | 6 | no | — |
| 370 | C4⋊C8 | — | 83 | 3 | no | — |
| 371 | C4⋊C8 | — | 83 | 6 | no | — |
| 372 | C4⋊C8 | — | 83 | 1 | no | — |
| 373 | #103 | — | 83 | 6 | no | — |
| 374 | #102 | — | 83 | 2 | no | — |
| 375 | #102 | — | 83 | 6 | no | — |
| 376 | #102 | — | 83 | 12 | no | — |
| 377 | #102 | — | 83 | 6 | no | — |
| 378 | C22⋊C8 | — | 83 | 6 | no | — |
| 379 | C4×C8 | — | 83 | 6 | no | — |
| 380 | #41 | — | 2 | 4 | no | — |
| 381 | #41 | — | 4 | 12 | no | — |
| 382 | #41 | — | 4 | 24 | no | — |
| 383 | #41 | — | 332 | 3 | no | — |
| 384 | #41 | — | 332 | 4 | no | — |
| 385 | #41 | — | 664 | 6 | no | — |
| 386 | #41 | — | 166 | 6 | no | — |
| 387 | C2×Q8 | — | 2 | 6 | no | — |
| 388 | C2×Q8 | — | 2 | 3 | no | — |
| 389 | C2×Q8 | — | 4 | 12 | no | — |
| 390 | C2×Q8 | — | 4 | 8 | no | — |
| 391 | C2×Q8 | — | 83 | 1 | no | — |
| 392 | C2×Q8 | — | 166 | 3 | no | — |
| 393 | C2×Q8 | C2×C22⋊D83 | 1 | 1 | yes | characteristic |
| 394 | C2×D4 | — | 2 | 6 | no | — |
| 395 | C2×D4 | — | 2 | 1 | no | — |
| 396 | C2×D4 | — | 2 | 1 | no | — |
| 397 | C2×D4 | — | 83 | 3 | no | — |
| 398 | C2×D4 | — | 166 | 3 | no | — |
| 399 | C2×D4 | — | 166 | 6 | no | — |
| 400 | C2×D4 | — | 166 | 3 | no | — |
| 401 | C2×D4 | — | 166 | 3 | no | — |
| 402 | C2×D4 | C2×C22⋊D83 | 1 | 3 | yes | — |
| 403 | C2×D4 | C23×D83 | 1 | 2 | yes | — |
| 404 | C22×C4 | — | 2 | 6 | no | — |
| 405 | C22×C4 | — | 2 | 6 | no | — |
| 406 | C22×C4 | — | 166 | 3 | no | — |
| 407 | C22×C4 | — | 166 | 3 | no | — |
| 408 | C22×C4 | — | 166 | 3 | no | — |
| 409 | C22×C4 | C2×C22⋊D83 | 1 | 3 | yes | — |
| 410 | C22×C4 | C2×C22⋊D83 | 1 | 3 | yes | — |
| 411 | C22×C4 | C23×D83 | 1 | 3 | yes | — |
| 412 | SD16 | — | 166 | 4 | no | — |
| 413 | D8 | — | 332 | 6 | no | — |
| 414 | M16 | — | 332 | 6 | no | — |
| 415 | C2×C8 | — | 83 | 2 | no | — |
| 416 | C2×C8 | — | 83 | 6 | no | — |
| 417 | C4⋊C4 | — | 2 | 3 | no | — |
| 418 | C4⋊C4 | — | 2 | 6 | no | — |
| 419 | C4⋊C4 | — | 2 | 6 | no | — |
| 420 | C4⋊C4 | — | 83 | 3 | no | — |
| 421 | C4⋊C4 | — | 83 | 1 | no | — |
| 422 | C4⋊C4 | — | 166 | 1 | no | — |
| 423 | C4⋊C4 | — | 166 | 3 | no | — |
| 424 | C4⋊C4 | — | 166 | 3 | no | — |
| 425 | C4⋊C4 | C2×C22⋊D83 | 1 | 3 | yes | — |
| 426 | C4⋊C4 | C2×C22⋊D83 | 1 | 3 | yes | — |
| 427 | C4⋊C4 | C23×D83 | 1 | 6 | yes | — |
| 428 | C22⋊C4 | — | 2 | 6 | no | — |
| 429 | C22⋊C4 | — | 2 | 6 | no | — |
| 430 | C22⋊C4 | — | 166 | 3 | no | — |
| 431 | C22⋊C4 | — | 166 | 3 | no | — |
| 432 | C22⋊C4 | — | 166 | 3 | no | — |
| 433 | C22⋊C4 | — | 166 | 6 | no | — |
| 434 | C22⋊C4 | C2×C22⋊D83 | 1 | 6 | yes | — |
| 435 | C42 | — | 166 | 1 | no | — |
| 436 | C42 | — | 166 | 3 | no | — |
| 437 | C42 | — | 166 | 3 | no | — |
| 438 | C42 | C2×C22⋊D83 | 1 | 3 | yes | — |
| 439 | C42 | C2×C22⋊D83 | 1 | 3 | yes | — |
| 440 | C42 | C23×D83 | 1 | 3 | yes | — |
| 441 | C42 | C23×D83 | 1 | 1 | yes | characteristic |
| 442 | C23 | — | 2 | 2 | no | — |
| 443 | C23 | — | 166 | 3 | no | — |
| 444 | C23 | C22×C22⋊D83 | 1 | 3 | yes | — |
| 445 | Q8 | — | 4 | 6 | no | — |
| 446 | Q8 | — | 4 | 12 | no | — |
| 447 | Q8 | — | 83 | 2 | no | — |
| 448 | Q8 | — | 664 | 3 | no | — |
| 449 | Q8 | — | 166 | 1 | no | — |
| 450 | Q8 | #14581818 | 1 | 4 | yes | — |
| 451 | D4 | — | 2 | 6 | no | — |
| 452 | D4 | — | 2 | 2 | no | — |
| 453 | D4 | — | 2 | 2 | no | — |
| 454 | D4 | — | 4 | 2 | no | — |
| 455 | D4 | — | 4 | 12 | no | — |
| 456 | D4 | — | 4 | 2 | no | — |
| 457 | D4 | — | 332 | 6 | no | — |
| 458 | D4 | — | 332 | 6 | no | — |
| 459 | D4 | — | 664 | 3 | no | — |
| 460 | D4 | — | 664 | 6 | no | — |
| 461 | D4 | — | 166 | 3 | no | — |
| 462 | D4 | — | 166 | 3 | no | — |
| 463 | C2×C4 | — | 2 | 6 | no | — |
| 464 | C2×C4 | — | 2 | 6 | no | — |
| 465 | C2×C4 | — | 2 | 3 | no | — |
| 466 | C2×C4 | — | 2 | 3 | no | — |
| 467 | C2×C4 | — | 2 | 6 | no | — |
| 468 | C2×C4 | — | 4 | 12 | no | — |
| 469 | C2×C4 | — | 4 | 12 | no | — |
| 470 | C2×C4 | — | 332 | 6 | no | — |
| 471 | C2×C4 | — | 332 | 6 | no | — |
| 472 | C2×C4 | — | 332 | 6 | no | — |
| 473 | C2×C4 | — | 166 | 1 | no | — |
| 474 | C2×C4 | — | 166 | 3 | no | — |
| 475 | C2×C4 | — | 166 | 1 | no | — |
| 476 | C2×C4 | C22×C22⋊D83 | 1 | 3 | yes | — |
| 477 | C2×C4 | C22×C22⋊D83 | 1 | 1 | yes | characteristic |
| 478 | C2×C4 | C22×C22⋊D83 | 1 | 3 | yes | — |
| 479 | C2×C4 | C22×C22⋊D83 | 1 | 3 | yes | — |
| 480 | C2×C4 | C22×C22⋊D83 | 1 | 1 | yes | characteristic |
| 481 | C2×C4 | C24×D83 | 1 | 1 | yes | characteristic |
| 482 | C8 | — | 166 | 2 | no | — |
| 483 | C8 | — | 166 | 6 | no | — |
| 484 | C22 | — | 2 | 3 | no | — |
| 485 | C22 | — | 2 | 3 | no | — |
| 486 | C22 | — | 2 | 3 | no | — |
| 487 | C22 | — | 4 | 2 | no | — |
| 488 | C22 | — | 4 | 2 | no | — |
| 489 | C22 | — | 4 | 2 | no | — |
| 490 | C22 | — | 332 | 3 | no | — |
| 491 | C22 | — | 332 | 3 | no | — |
| 492 | C22 | — | 332 | 3 | no | — |
| 493 | C22 | C23×C22⋊D83 | 1 | 1 | yes | characteristic |
| 494 | C4 | — | 2 | 3 | no | — |
| 495 | C4 | — | 2 | 1 | no | — |
| 496 | C4 | — | 2 | 3 | no | — |
| 497 | C4 | — | 4 | 6 | no | — |
| 498 | C4 | — | 332 | 1 | no | — |
| 499 | C4 | — | 332 | 3 | no | — |
| 500 | C4 | — | 166 | 2 | no | — |
| 501 | C4 | C2×#14581818 | 1 | 6 | yes | — |
| 502 | C4 | #19128509 | 1 | 2 | yes | — |
| 503 | C4 | 2−1+4×D83 | 1 | 1 | yes | characteristic |
| 504 | C4 | #19128538 | 1 | 1 | yes | characteristic |
| 505 | C2 | — | 4 | 3 | no | — |
| 506 | C2 | — | 8 | 2 | no | — |
| 507 | C2 | — | 664 | 3 | no | — |
| 508 | C2 | #24921136 | 1 | 1 | yes | characteristic |
| 509 | C2 | C22×#14581818 | 1 | 1 | yes | characteristic |
| 510 | C2 | C2×#19128509 | 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