← #28292324
Subgroups — #28292324
Order 13568.
7094 conjugacy classes of subgroups.
The subgroup lattice has 682 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #20288806 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #20288795 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #20288701 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | #20288577 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #20288525 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20288422 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #20288363 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #20288331 | C2 | 1 | 8 | yes | maximal, complemented |
| 9 | #20288314 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | Q8×#11719947 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #20288143 | C2 | 1 | 6 | yes | maximal, complemented |
| 12 | #20288010 | C2 | 1 | 6 | yes | maximal, complemented |
| 13 | 2−1+4×Dic53 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | C2×C4×Q8×D53 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C53×#3497 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C22×Q8×D53 | C22 | 1 | 1 | yes | characteristic |
| 17 | #16811359 | C22 | 1 | 12 | yes | complemented |
| 18 | Q8×Dic106 | C22 | 1 | 4 | yes | complemented |
| 19 | #16811352 | C22 | 1 | 4 | yes | complemented |
| 20 | #16811349 | C22 | 1 | 8 | yes | complemented |
| 21 | #16811348 | C22 | 1 | 12 | yes | complemented |
| 22 | #16811343 | C22 | 1 | 12 | yes | complemented |
| 23 | #16811342 | C22 | 1 | 24 | yes | complemented |
| 24 | #16811331 | C22 | 1 | 24 | yes | — |
| 25 | #16811330 | C22 | 1 | 12 | yes | complemented |
| 26 | #16811320 | C22 | 1 | 24 | yes | — |
| 27 | #16811313 | C22 | 1 | 24 | yes | complemented |
| 28 | #16811307 | C22 | 1 | 24 | yes | — |
| 29 | Q8×C22⋊D53 | C22 | 1 | 8 | yes | — |
| 30 | Q8×C22⋊D53 | C22 | 1 | 8 | yes | — |
| 31 | #16811280 | C22 | 1 | 8 | yes | — |
| 32 | #16811280 | C22 | 1 | 8 | yes | — |
| 33 | #16811273 | C22 | 1 | 24 | yes | — |
| 34 | #16811254 | C22 | 1 | 6 | yes | — |
| 35 | #16811240 | C22 | 1 | 24 | yes | complemented |
| 36 | #16811233 | C22 | 1 | 24 | yes | complemented |
| 37 | #16811218 | C22 | 1 | 24 | yes | — |
| 38 | #16811194 | C22 | 1 | 12 | yes | — |
| 39 | #16811180 | C22 | 1 | 6 | yes | — |
| 40 | #16811178 | C22 | 1 | 6 | yes | — |
| 41 | #16811178 | C22 | 1 | 6 | yes | — |
| 42 | #16811175 | C22 | 1 | 24 | yes | complemented |
| 43 | #16811171 | C22 | 1 | 6 | yes | — |
| 44 | #16811171 | C22 | 1 | 6 | yes | — |
| 45 | #16811155 | C22 | 1 | 12 | yes | — |
| 46 | #16811155 | C22 | 1 | 12 | yes | — |
| 47 | #16811154 | C22 | 1 | 12 | yes | — |
| 48 | #16811154 | C22 | 1 | 12 | yes | — |
| 49 | #16811154 | C22 | 1 | 24 | yes | complemented |
| 50 | #16811152 | C22 | 1 | 12 | yes | — |
| 51 | #16811152 | C22 | 1 | 12 | yes | — |
| 52 | #16811133 | C22 | 1 | 4 | yes | — |
| 53 | #16811133 | C22 | 1 | 12 | yes | — |
| 54 | #16811130 | C22 | 1 | 12 | yes | — |
| 55 | #16811106 | C22 | 1 | 12 | yes | — |
| 56 | #16811106 | C22 | 1 | 8 | yes | complemented |
| 57 | #16811101 | C22 | 1 | 2 | yes | — |
| 58 | #16811101 | C22 | 1 | 8 | yes | complemented |
| 59 | #41×Dic53 | C22 | 1 | 12 | yes | — |
| 60 | #41×Dic53 | C22 | 1 | 8 | yes | complemented |
| 61 | C4×#11719947 | C22 | 1 | 12 | yes | — |
| 62 | C4×#11719947 | C22 | 1 | 12 | yes | — |
| 63 | C2×Q8×Dic53 | C22 | 1 | 1 | yes | characteristic |
| 64 | C2×Q8×Dic53 | C22 | 1 | 8 | yes | complemented |
| 65 | C2×C4×Dic106 | C22 | 1 | 3 | yes | — |
| 66 | C2×#13133182 | C22 | 1 | 3 | yes | — |
| 67 | C4×Q8×D53 | C22 | 1 | 4 | yes | — |
| 68 | C4×Q8×D53 | C22 | 1 | 4 | yes | — |
| 69 | C4×Q8×D53 | C22 | 1 | 4 | yes | — |
| 70 | C4×Q8×D53 | C22 | 1 | 4 | yes | — |
| 71 | C2×C4⋊C4×D53 | C22 | 1 | 3 | yes | — |
| 72 | C2×C42×D53 | C22 | 1 | 3 | yes | — |
| 73 | C2×2−1+4×C53 | C22 | 1 | 2 | yes | — |
| 74 | C53×#550 | C22 | 1 | 4 | yes | complemented |
| 75 | D4×Q8×C53 | C22 | 1 | 4 | yes | complemented |
| 76 | C53×#548 | C22 | 1 | 8 | yes | complemented |
| 77 | C53×#537 | C22 | 1 | 6 | yes | — |
| 78 | C53×#532 | C22 | 1 | 6 | yes | — |
| 79 | C2×C4×Q8×C53 | C22 | 1 | 1 | yes | characteristic |
| 80 | C2×#11719947 | C23 | 1 | 4 | yes | — |
| 81 | C2×#11719947 | C23 | 1 | 12 | yes | — |
| 82 | C22×Dic106 | C23 | 1 | 3 | yes | — |
| 83 | C2×Q8×D53 | — | 2 | 8 | no | — |
| 84 | C2×Q8×D53 | C23 | 1 | 4 | yes | — |
| 85 | C2×Q8×D53 | C23 | 1 | 4 | yes | — |
| 86 | C22×C4×D53 | C23 | 1 | 1 | yes | characteristic |
| 87 | C22×C4×D53 | C23 | 1 | 3 | yes | — |
| 88 | C22×C4×D53 | C23 | 1 | 3 | yes | — |
| 89 | #13133217 | C23 | 1 | 6 | yes | — |
| 90 | #13133217 | C23 | 1 | 6 | yes | — |
| 91 | #13133216 | C23 | 1 | 24 | yes | — |
| 92 | #13133215 | C23 | 1 | 24 | yes | — |
| 93 | #13133210 | C23 | 1 | 48 | yes | — |
| 94 | #13133210 | C23 | 1 | 24 | yes | — |
| 95 | #13133210 | C23 | 1 | 24 | yes | — |
| 96 | #13133209 | C23 | 1 | 12 | yes | — |
| 97 | #13133208 | C23 | 1 | 24 | yes | — |
| 98 | #13133208 | C23 | 1 | 12 | yes | — |
| 99 | #13133208 | C23 | 1 | 12 | yes | — |
| 100 | #13133207 | C23 | 1 | 48 | yes | — |
| 101 | #13133204 | C23 | 1 | 24 | yes | — |
| 102 | #13133204 | C23 | 1 | 12 | yes | — |
| 103 | #13133204 | C23 | 1 | 12 | yes | — |
| 104 | #13133199 | C23 | 1 | 24 | yes | — |
| 105 | #13133199 | C23 | 1 | 8 | yes | — |
| 106 | #13133198 | C23 | 1 | 48 | yes | — |
| 107 | #13133198 | C23 | 1 | 24 | yes | — |
| 108 | #13133197 | C23 | 1 | 12 | yes | — |
| 109 | #13133197 | C23 | 1 | 4 | yes | — |
| 110 | #13133196 | C23 | 1 | 24 | yes | — |
| 111 | #13133196 | C23 | 1 | 24 | yes | — |
| 112 | #13133196 | C23 | 1 | 4 | yes | — |
| 113 | #13133196 | C23 | 1 | 12 | yes | — |
| 114 | #13133194 | C23 | 1 | 48 | yes | — |
| 115 | #13133193 | C23 | 1 | 12 | yes | — |
| 116 | #13133193 | C23 | 1 | 12 | yes | — |
| 117 | #13133188 | C23 | 1 | 12 | yes | — |
| 118 | #13133188 | C23 | 1 | 12 | yes | — |
| 119 | #13133188 | C23 | 1 | 12 | yes | — |
| 120 | #13133188 | C23 | 1 | 4 | yes | — |
| 121 | #13133185 | C23 | 1 | 8 | yes | — |
| 122 | Q8×Dic53 | C23 | 1 | 8 | yes | — |
| 123 | Q8×Dic53 | C23 | 1 | 8 | yes | — |
| 124 | Q8×Dic53 | C23 | 1 | 24 | yes | — |
| 125 | Q8×Dic53 | C23 | 1 | 4 | yes | — |
| 126 | Q8×Dic53 | C23 | 1 | 4 | yes | — |
| 127 | Q8×Dic53 | C23 | 1 | 12 | yes | — |
| 128 | Q8×Dic53 | C23 | 1 | 12 | yes | — |
| 129 | C4×Dic106 | C23 | 1 | 12 | yes | — |
| 130 | C4×Dic106 | C23 | 1 | 12 | yes | — |
| 131 | C4×Dic106 | C23 | 1 | 12 | yes | — |
| 132 | C4×Dic106 | C23 | 1 | 12 | yes | — |
| 133 | #13133182 | C23 | 1 | 12 | yes | — |
| 134 | #13133182 | C23 | 1 | 12 | yes | — |
| 135 | #13133182 | C23 | 1 | 12 | yes | — |
| 136 | #13133182 | C23 | 1 | 12 | yes | — |
| 137 | D4×Dic53 | C23 | 1 | 24 | yes | — |
| 138 | D4×Dic53 | C23 | 1 | 12 | yes | — |
| 139 | D4×Dic53 | C23 | 1 | 12 | yes | — |
| 140 | D4×Dic53 | C23 | 1 | 8 | yes | — |
| 141 | D4×Dic53 | C23 | 1 | 12 | yes | — |
| 142 | D4×Dic53 | C23 | 1 | 24 | yes | — |
| 143 | D4×Dic53 | C23 | 1 | 12 | yes | — |
| 144 | C4×C22⋊D53 | C23 | 1 | 24 | yes | — |
| 145 | C4×C22⋊D53 | C23 | 1 | 24 | yes | — |
| 146 | #13133177 | C23 | 1 | 24 | yes | — |
| 147 | #13133177 | C23 | 1 | 8 | yes | — |
| 148 | #13133176 | C23 | 1 | 24 | yes | — |
| 149 | #13133176 | C23 | 1 | 12 | yes | — |
| 150 | #13133176 | C23 | 1 | 24 | yes | — |
| 151 | #13133175 | C23 | 1 | 12 | yes | — |
| 152 | #13133175 | C23 | 1 | 4 | yes | — |
| 153 | #13133173 | C23 | 1 | 24 | yes | — |
| 154 | #13133173 | C23 | 1 | 24 | yes | — |
| 155 | C2×C4⋊Dic53 | C23 | 1 | 24 | yes | — |
| 156 | C2×C4⋊Dic53 | C23 | 1 | 3 | yes | — |
| 157 | C2×#11719919 | C23 | 1 | 6 | yes | — |
| 158 | C4⋊C4×D53 | C23 | 1 | 12 | yes | — |
| 159 | C4⋊C4×D53 | C23 | 1 | 12 | yes | — |
| 160 | C2×C4×Dic53 | C23 | 1 | 3 | yes | — |
| 161 | C2×C4×Dic53 | C23 | 1 | 3 | yes | — |
| 162 | C2×C4×Dic53 | C23 | 1 | 3 | yes | — |
| 163 | C2×C4×Dic53 | C23 | 1 | 24 | yes | — |
| 164 | C42×D53 | C23 | 1 | 6 | yes | — |
| 165 | C42×D53 | C23 | 1 | 6 | yes | — |
| 166 | C42×D53 | C23 | 1 | 6 | yes | — |
| 167 | C42×D53 | C23 | 1 | 6 | yes | — |
| 168 | 2−1+4×C53 | — | 2 | 16 | no | — |
| 169 | C2×#41×C53 | C23 | 1 | 8 | yes | — |
| 170 | C2×#41×C53 | C23 | 1 | 12 | yes | — |
| 171 | C22×Q8×C53 | C23 | 1 | 8 | yes | — |
| 172 | C22×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 173 | C4⋊Q8×C53 | C23 | 1 | 6 | yes | — |
| 174 | #127×C53 | C23 | 1 | 6 | yes | — |
| 175 | #124×C53 | C23 | 1 | 12 | yes | — |
| 176 | C22⋊Q8×C53 | C23 | 1 | 24 | yes | — |
| 177 | #121×C53 | C23 | 1 | 24 | yes | — |
| 178 | #121×C53 | C23 | 1 | 4 | yes | — |
| 179 | #121×C53 | C23 | 1 | 12 | yes | — |
| 180 | C4×Q8×C53 | C23 | 1 | 4 | yes | — |
| 181 | C4×Q8×C53 | C23 | 1 | 4 | yes | — |
| 182 | C4×D4×C53 | C23 | 1 | 12 | yes | — |
| 183 | C4×D4×C53 | C23 | 1 | 12 | yes | — |
| 184 | C2×C4⋊C4×C53 | C23 | 1 | 3 | yes | — |
| 185 | C2×C42×C53 | C23 | 1 | 3 | yes | — |
| 186 | C23×D53 | C24 | 1 | 1 | yes | characteristic |
| 187 | #41×C53 | — | 2 | 32 | no | — |
| 188 | #41×C53 | — | 2 | 48 | no | — |
| 189 | C2×Q8×C53 | — | 2 | 32 | no | — |
| 190 | C2×Q8×C53 | #41 | 1 | 8 | yes | complemented |
| 191 | C2×Q8×C53 | C24 | 1 | 12 | yes | — |
| 192 | C2×Q8×C53 | C24 | 1 | 4 | yes | — |
| 193 | C2×D4×C53 | C24 | 1 | 4 | yes | — |
| 194 | C2×D4×C53 | C24 | 1 | 8 | yes | — |
| 195 | C2×D4×C53 | C24 | 1 | 12 | yes | — |
| 196 | C2×D4×C53 | C24 | 1 | 12 | yes | — |
| 197 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 198 | C22×C4×C53 | C24 | 1 | 24 | yes | — |
| 199 | C22×C4×C53 | C24 | 1 | 3 | yes | — |
| 200 | C22×C4×C53 | C24 | 1 | 3 | yes | — |
| 201 | C2×C22⋊D53 | C24 | 1 | 8 | yes | — |
| 202 | C2×C22⋊D53 | C24 | 1 | 8 | yes | — |
| 203 | C22×Dic53 | C24 | 1 | 1 | yes | characteristic |
| 204 | C22×Dic53 | C24 | 1 | 8 | yes | — |
| 205 | C22×Dic53 | C24 | 1 | 3 | yes | — |
| 206 | C22×Dic53 | C24 | 1 | 3 | yes | — |
| 207 | C22×Dic53 | C24 | 1 | 24 | yes | — |
| 208 | Q8×D53 | — | 2 | 16 | no | — |
| 209 | Q8×D53 | — | 2 | 16 | no | — |
| 210 | #11719947 | — | 2 | 16 | no | — |
| 211 | #11719947 | — | 4 | 24 | no | — |
| 212 | C2×C4×D53 | — | 2 | 12 | no | — |
| 213 | C2×C4×D53 | — | 2 | 4 | no | — |
| 214 | C2×C4×D53 | — | 4 | 6 | no | — |
| 215 | C2×C4×D53 | C24 | 1 | 1 | yes | characteristic |
| 216 | C2×C4×D53 | C24 | 1 | 1 | yes | characteristic |
| 217 | C2×C4×D53 | C24 | 1 | 1 | yes | characteristic |
| 218 | C2×C4×D53 | C24 | 1 | 6 | yes | — |
| 219 | C2×C4×D53 | C24 | 1 | 6 | yes | — |
| 220 | C2×C4×D53 | C24 | 1 | 6 | yes | — |
| 221 | C2×C4×D53 | C24 | 1 | 6 | yes | — |
| 222 | C2×C4×D53 | C24 | 1 | 1 | yes | characteristic |
| 223 | C2×Dic106 | — | 2 | 12 | no | — |
| 224 | C2×Dic106 | C24 | 1 | 4 | yes | — |
| 225 | C2×Dic106 | C24 | 1 | 12 | yes | — |
| 226 | C2×Dic106 | C24 | 1 | 12 | yes | — |
| 227 | C4⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 228 | C4⋊C4×C53 | C24 | 1 | 4 | yes | — |
| 229 | C4⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 230 | C22⋊C4×C53 | C24 | 1 | 8 | yes | — |
| 231 | C22⋊C4×C53 | C24 | 1 | 24 | yes | — |
| 232 | C42×C53 | C24 | 1 | 6 | yes | — |
| 233 | C42×C53 | C24 | 1 | 6 | yes | — |
| 234 | C22⋊Dic53 | C24 | 1 | 24 | yes | — |
| 235 | C22⋊Dic53 | C24 | 1 | 24 | yes | — |
| 236 | C22⋊Dic53 | C24 | 1 | 8 | yes | — |
| 237 | C22⋊Dic53 | C24 | 1 | 24 | yes | — |
| 238 | C22⋊Dic53 | C24 | 1 | 8 | yes | — |
| 239 | #11719921 | C24 | 1 | 8 | yes | — |
| 240 | #11719921 | C24 | 1 | 8 | yes | — |
| 241 | C4⋊Dic53 | C24 | 1 | 12 | yes | — |
| 242 | C4⋊Dic53 | C24 | 1 | 12 | yes | — |
| 243 | C4⋊Dic53 | C24 | 1 | 24 | yes | — |
| 244 | C4⋊Dic53 | C24 | 1 | 4 | yes | — |
| 245 | C4⋊Dic53 | C24 | 1 | 12 | yes | — |
| 246 | C4⋊Dic53 | C24 | 1 | 12 | yes | — |
| 247 | C4⋊Dic53 | C24 | 1 | 8 | yes | — |
| 248 | #11719919 | C24 | 1 | 24 | yes | — |
| 249 | #11719919 | C24 | 1 | 8 | yes | — |
| 250 | #11719919 | C24 | 1 | 24 | yes | — |
| 251 | #11719919 | C24 | 1 | 24 | yes | — |
| 252 | #11719919 | C24 | 1 | 24 | yes | — |
| 253 | C4×Dic53 | C24 | 1 | 6 | yes | — |
| 254 | C4×Dic53 | C24 | 1 | 6 | yes | — |
| 255 | C4×Dic53 | C24 | 1 | 6 | yes | — |
| 256 | C4×Dic53 | C24 | 1 | 6 | yes | — |
| 257 | C4×Dic53 | C24 | 1 | 6 | yes | — |
| 258 | C4×Dic53 | C24 | 1 | 6 | yes | — |
| 259 | C4×Dic53 | C24 | 1 | 8 | yes | — |
| 260 | C4×Dic53 | C24 | 1 | 24 | yes | — |
| 261 | C4×Dic53 | C24 | 1 | 24 | yes | — |
| 262 | C23×C53 | C25 | 1 | 8 | yes | — |
| 263 | C23×C53 | C25 | 1 | 1 | yes | characteristic |
| 264 | C22×D53 | — | 2 | 2 | no | — |
| 265 | C22×D53 | — | 2 | 2 | no | — |
| 266 | C22×D53 | — | 2 | 2 | no | — |
| 267 | C22×D53 | C25 | 1 | 1 | yes | characteristic |
| 268 | C22×D53 | C25 | 1 | 1 | yes | characteristic |
| 269 | Q8×C53 | — | 2 | 24 | no | — |
| 270 | Q8×C53 | C2×#41 | 1 | 16 | yes | — |
| 271 | D4×C53 | — | 2 | 16 | no | — |
| 272 | D4×C53 | — | 2 | 24 | no | — |
| 273 | D4×C53 | — | 2 | 8 | no | — |
| 274 | D4×C53 | — | 4 | 12 | no | — |
| 275 | C2×C4×C53 | — | 2 | 48 | no | — |
| 276 | C2×C4×C53 | — | 2 | 2 | no | — |
| 277 | C2×C4×C53 | — | 4 | 3 | no | — |
| 278 | C2×C4×C53 | C2×#41 | 1 | 12 | yes | — |
| 279 | C2×C4×C53 | C25 | 1 | 6 | yes | — |
| 280 | C2×C4×C53 | C25 | 1 | 1 | yes | characteristic |
| 281 | C2×C4×C53 | C25 | 1 | 8 | yes | — |
| 282 | C2×C4×C53 | C25 | 1 | 6 | yes | — |
| 283 | C2×C4×C53 | C25 | 1 | 1 | yes | characteristic |
| 284 | C22⋊D53 | — | 2 | 16 | no | — |
| 285 | C22⋊D53 | — | 2 | 16 | no | — |
| 286 | C2×Dic53 | — | 2 | 6 | no | — |
| 287 | C2×Dic53 | — | 2 | 2 | no | — |
| 288 | C2×Dic53 | — | 2 | 16 | no | — |
| 289 | C2×Dic53 | — | 4 | 3 | no | — |
| 290 | C2×Dic53 | — | 4 | 24 | no | — |
| 291 | C2×Dic53 | C25 | 1 | 6 | yes | — |
| 292 | C2×Dic53 | C25 | 1 | 8 | yes | — |
| 293 | C2×Dic53 | C25 | 1 | 8 | yes | — |
| 294 | C2×Dic53 | C25 | 1 | 6 | yes | — |
| 295 | C2×Dic53 | C25 | 1 | 1 | yes | characteristic |
| 296 | C2×Dic53 | C25 | 1 | 1 | yes | characteristic |
| 297 | C4×D53 | — | 2 | 2 | no | — |
| 298 | C4×D53 | — | 2 | 12 | no | — |
| 299 | C4×D53 | — | 2 | 12 | no | — |
| 300 | C4×D53 | — | 2 | 12 | no | — |
| 301 | C4×D53 | — | 2 | 2 | no | — |
| 302 | C4×D53 | — | 2 | 2 | no | — |
| 303 | C4×D53 | — | 4 | 6 | no | — |
| 304 | C4×D53 | 2−1+4 | 1 | 4 | yes | complemented |
| 305 | Dic106 | — | 2 | 24 | no | — |
| 306 | Dic106 | — | 2 | 8 | no | — |
| 307 | Dic106 | — | 4 | 12 | no | — |
| 308 | #62788 | — | 53 | 1 | no | maximal, Sylow |
| 309 | C22×C53 | — | 2 | 1 | no | — |
| 310 | C22×C53 | — | 2 | 1 | no | — |
| 311 | C22×C53 | — | 2 | 8 | no | — |
| 312 | C22×C53 | — | 2 | 8 | no | — |
| 313 | C22×C53 | — | 2 | 8 | no | — |
| 314 | C22×C53 | C22×#41 | 1 | 2 | yes | — |
| 315 | C22×C53 | C26 | 1 | 1 | yes | characteristic |
| 316 | C2×D53 | — | 2 | 8 | no | — |
| 317 | C2×D53 | — | 2 | 1 | no | — |
| 318 | C2×D53 | — | 2 | 1 | no | — |
| 319 | C2×D53 | — | 2 | 1 | no | — |
| 320 | C2×D53 | — | 2 | 1 | no | — |
| 321 | C2×D53 | C2×2−1+4 | 1 | 2 | yes | — |
| 322 | C2×D53 | #585 | 1 | 2 | yes | — |
| 323 | C4×C53 | — | 2 | 8 | no | — |
| 324 | C4×C53 | — | 2 | 1 | no | — |
| 325 | C4×C53 | — | 2 | 6 | no | — |
| 326 | C4×C53 | C22×#41 | 1 | 12 | yes | — |
| 327 | C4×C53 | C2×2−1+4 | 1 | 2 | yes | — |
| 328 | Dic53 | — | 2 | 6 | no | — |
| 329 | Dic53 | — | 2 | 8 | no | — |
| 330 | Dic53 | — | 2 | 1 | no | — |
| 331 | Dic53 | — | 2 | 8 | no | — |
| 332 | Dic53 | — | 2 | 6 | no | — |
| 333 | Dic53 | C2×2−1+4 | 1 | 2 | yes | — |
| 334 | #3523 | — | 53 | 4 | no | — |
| 335 | #3522 | — | 53 | 4 | no | — |
| 336 | #3516 | — | 53 | 8 | no | — |
| 337 | #3507 | — | 53 | 6 | no | — |
| 338 | #3502 | — | 53 | 1 | no | — |
| 339 | #3497 | D53 | 1 | 1 | yes | characteristic, complemented |
| 340 | #3492 | — | 53 | 6 | no | — |
| 341 | #3486 | — | 53 | 2 | no | — |
| 342 | #3482 | — | 53 | 8 | no | — |
| 343 | #3480 | — | 53 | 4 | no | — |
| 344 | Q8×#41 | — | 53 | 4 | no | — |
| 345 | #3461 | — | 53 | 6 | no | — |
| 346 | #3444 | — | 53 | 6 | no | — |
| 347 | C4×2−1+4 | — | 53 | 2 | no | — |
| 348 | C22×C4×Q8 | — | 53 | 1 | no | — |
| 349 | C2×C53 | — | 2 | 2 | no | — |
| 350 | C2×C53 | — | 4 | 8 | no | — |
| 351 | C2×C53 | C23×#41 | 1 | 1 | yes | characteristic |
| 352 | C2×C53 | C22×2−1+4 | 1 | 1 | yes | characteristic |
| 353 | C2×C53 | C2×#585 | 1 | 1 | yes | characteristic |
| 354 | D53 | — | 2 | 2 | no | — |
| 355 | D53 | — | 2 | 2 | no | — |
| 356 | C2×2−1+4 | C2×D53 | 1 | 2 | yes | — |
| 357 | C23×Q8 | — | 53 | 1 | no | — |
| 358 | #559 | — | 53 | 12 | no | — |
| 359 | Q82 | — | 53 | 4 | no | — |
| 360 | #557 | — | 53 | 12 | no | — |
| 361 | #557 | — | 53 | 8 | no | — |
| 362 | #557 | — | 53 | 4 | no | — |
| 363 | #556 | — | 53 | 24 | no | — |
| 364 | #556 | — | 53 | 12 | no | — |
| 365 | #554 | — | 53 | 24 | no | — |
| 366 | #554 | — | 53 | 12 | no | — |
| 367 | #553 | — | 53 | 24 | no | — |
| 368 | #552 | — | 53 | 24 | no | — |
| 369 | #552 | — | 53 | 24 | no | — |
| 370 | #550 | C2×D53 | 1 | 4 | yes | complemented |
| 371 | D4×Q8 | — | 53 | 8 | no | — |
| 372 | D4×Q8 | — | 53 | 8 | no | — |
| 373 | D4×Q8 | C2×D53 | 1 | 4 | yes | complemented |
| 374 | #548 | — | 53 | 8 | no | — |
| 375 | #548 | — | 53 | 8 | no | — |
| 376 | #548 | C2×D53 | 1 | 8 | yes | complemented |
| 377 | #547 | — | 53 | 24 | no | — |
| 378 | #544 | — | 53 | 6 | no | — |
| 379 | #542 | — | 53 | 24 | no | — |
| 380 | #541 | — | 53 | 24 | no | — |
| 381 | #539 | — | 53 | 24 | no | — |
| 382 | #537 | C2×D53 | 1 | 6 | yes | — |
| 383 | #536 | — | 53 | 12 | no | — |
| 384 | #533 | — | 53 | 6 | no | — |
| 385 | #533 | — | 53 | 6 | no | — |
| 386 | #533 | — | 53 | 24 | no | — |
| 387 | #533 | — | 53 | 6 | no | — |
| 388 | #532 | — | 53 | 6 | no | — |
| 389 | #532 | — | 53 | 6 | no | — |
| 390 | #532 | C2×D53 | 1 | 6 | yes | — |
| 391 | #529 | — | 53 | 12 | no | — |
| 392 | #529 | — | 53 | 12 | no | — |
| 393 | #529 | — | 53 | 12 | no | — |
| 394 | #529 | — | 53 | 12 | no | — |
| 395 | #529 | — | 53 | 24 | no | — |
| 396 | #529 | — | 53 | 12 | no | — |
| 397 | #529 | — | 53 | 12 | no | — |
| 398 | #525 | — | 53 | 12 | no | — |
| 399 | #525 | — | 53 | 4 | no | — |
| 400 | #525 | — | 53 | 12 | no | — |
| 401 | #520 | — | 53 | 12 | no | — |
| 402 | #520 | — | 53 | 8 | no | — |
| 403 | #519 | — | 53 | 2 | no | — |
| 404 | #519 | — | 53 | 8 | no | — |
| 405 | C4×#41 | — | 53 | 12 | no | — |
| 406 | C4×#41 | — | 53 | 8 | no | — |
| 407 | C4×#41 | — | 53 | 12 | no | — |
| 408 | C4×#41 | — | 53 | 12 | no | — |
| 409 | C2×C4×Q8 | — | 53 | 1 | no | — |
| 410 | C2×C4×Q8 | — | 53 | 8 | no | — |
| 411 | C2×C4×Q8 | — | 53 | 4 | no | — |
| 412 | C2×C4×Q8 | — | 53 | 4 | no | — |
| 413 | C2×C4×Q8 | — | 53 | 4 | no | — |
| 414 | C2×C4×Q8 | — | 53 | 4 | no | — |
| 415 | C2×C4×Q8 | — | 53 | 3 | no | — |
| 416 | C2×C4×Q8 | — | 53 | 3 | no | — |
| 417 | C2×C4×Q8 | C2×D53 | 1 | 1 | yes | characteristic |
| 418 | C22×C4⋊C4 | — | 53 | 3 | no | — |
| 419 | C22×C42 | — | 53 | 3 | no | — |
| 420 | C53 | #62788 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 421 | 2−1+4 | — | 2 | 16 | no | — |
| 422 | C2×#41 | — | 53 | 4 | no | — |
| 423 | C2×#41 | — | 53 | 12 | no | — |
| 424 | C2×#41 | C22×D53 | 1 | 12 | yes | — |
| 425 | C2×#41 | C22×D53 | 1 | 8 | yes | — |
| 426 | C22×Q8 | — | 53 | 4 | no | — |
| 427 | C22×Q8 | — | 53 | 4 | no | — |
| 428 | C22×Q8 | — | 53 | 3 | no | — |
| 429 | C22×Q8 | — | 106 | 8 | no | — |
| 430 | C22×Q8 | C22×D53 | 1 | 8 | yes | — |
| 431 | C22×Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 432 | C23×C4 | — | 53 | 3 | no | — |
| 433 | C23×C4 | — | 53 | 1 | no | — |
| 434 | C23×C4 | — | 53 | 3 | no | — |
| 435 | C4⋊Q8 | — | 53 | 24 | no | — |
| 436 | C4⋊Q8 | — | 53 | 24 | no | — |
| 437 | C4⋊Q8 | — | 53 | 6 | no | — |
| 438 | C4⋊Q8 | — | 53 | 6 | no | — |
| 439 | C4⋊Q8 | C22×D53 | 1 | 6 | yes | — |
| 440 | #127 | C22×D53 | 1 | 6 | yes | — |
| 441 | #126 | — | 53 | 24 | no | — |
| 442 | #126 | — | 53 | 24 | no | — |
| 443 | #126 | — | 53 | 48 | no | — |
| 444 | #125 | — | 53 | 12 | no | — |
| 445 | #125 | — | 53 | 12 | no | — |
| 446 | #125 | — | 53 | 24 | no | — |
| 447 | #125 | — | 53 | 48 | no | — |
| 448 | #125 | — | 53 | 12 | no | — |
| 449 | #124 | — | 53 | 12 | no | — |
| 450 | #124 | — | 53 | 12 | no | — |
| 451 | #124 | — | 53 | 24 | no | — |
| 452 | #124 | C22×D53 | 1 | 12 | yes | — |
| 453 | #123 | — | 53 | 24 | no | — |
| 454 | #123 | — | 53 | 48 | no | — |
| 455 | #123 | — | 53 | 8 | no | — |
| 456 | #123 | — | 53 | 24 | no | — |
| 457 | C22⋊Q8 | — | 53 | 12 | no | — |
| 458 | C22⋊Q8 | — | 53 | 12 | no | — |
| 459 | C22⋊Q8 | — | 53 | 4 | no | — |
| 460 | C22⋊Q8 | — | 53 | 12 | no | — |
| 461 | C22⋊Q8 | — | 53 | 24 | no | — |
| 462 | C22⋊Q8 | — | 53 | 24 | no | — |
| 463 | C22⋊Q8 | — | 53 | 4 | no | — |
| 464 | C22⋊Q8 | — | 53 | 12 | no | — |
| 465 | C22⋊Q8 | — | 53 | 48 | no | — |
| 466 | C22⋊Q8 | C22×D53 | 1 | 24 | yes | — |
| 467 | #121 | — | 53 | 4 | no | — |
| 468 | #121 | — | 53 | 12 | no | — |
| 469 | #121 | — | 53 | 12 | no | — |
| 470 | #121 | — | 53 | 12 | no | — |
| 471 | #121 | C22×D53 | 1 | 4 | yes | — |
| 472 | #121 | C22×D53 | 1 | 12 | yes | — |
| 473 | #121 | C22×D53 | 1 | 24 | yes | — |
| 474 | #120 | — | 53 | 8 | no | — |
| 475 | C4×Q8 | — | 53 | 4 | no | — |
| 476 | C4×Q8 | — | 53 | 4 | no | — |
| 477 | C4×Q8 | — | 53 | 12 | no | — |
| 478 | C4×Q8 | — | 53 | 8 | no | — |
| 479 | C4×Q8 | — | 53 | 24 | no | — |
| 480 | C4×Q8 | — | 53 | 12 | no | — |
| 481 | C4×Q8 | — | 53 | 8 | no | — |
| 482 | C4×Q8 | — | 53 | 12 | no | — |
| 483 | C4×Q8 | — | 53 | 12 | no | — |
| 484 | C4×Q8 | — | 53 | 12 | no | — |
| 485 | C4×Q8 | — | 53 | 12 | no | — |
| 486 | C4×Q8 | — | 53 | 12 | no | — |
| 487 | C4×Q8 | — | 53 | 12 | no | — |
| 488 | C4×Q8 | — | 53 | 12 | no | — |
| 489 | C4×Q8 | — | 53 | 12 | no | — |
| 490 | C4×Q8 | C22×D53 | 1 | 4 | yes | — |
| 491 | C4×Q8 | C22×D53 | 1 | 4 | yes | — |
| 492 | C4×D4 | — | 53 | 8 | no | — |
| 493 | C4×D4 | — | 53 | 12 | no | — |
| 494 | C4×D4 | — | 53 | 24 | no | — |
| 495 | C4×D4 | — | 53 | 12 | no | — |
| 496 | C4×D4 | — | 53 | 24 | no | — |
| 497 | C4×D4 | — | 53 | 12 | no | — |
| 498 | C4×D4 | — | 53 | 12 | no | — |
| 499 | C4×D4 | — | 53 | 24 | no | — |
| 500 | C4×D4 | — | 53 | 24 | no | — |
| 501 | C4×D4 | — | 53 | 8 | no | — |
| 502 | C4×D4 | — | 53 | 24 | no | — |
| 503 | C4×D4 | C22×D53 | 1 | 12 | yes | — |
| 504 | C4×D4 | C22×D53 | 1 | 12 | yes | — |
| 505 | #117 | — | 53 | 12 | no | — |
| 506 | #117 | — | 53 | 24 | no | — |
| 507 | #117 | — | 53 | 24 | no | — |
| 508 | #117 | — | 53 | 4 | no | — |
| 509 | #117 | — | 53 | 12 | no | — |
| 510 | #117 | — | 53 | 24 | no | — |
| 511 | #117 | — | 53 | 24 | no | — |
| 512 | C2×C4⋊C4 | — | 53 | 3 | no | — |
| 513 | C2×C4⋊C4 | — | 53 | 6 | no | — |
| 514 | C2×C4⋊C4 | — | 53 | 24 | no | — |
| 515 | C2×C4⋊C4 | — | 53 | 12 | no | — |
| 516 | C2×C4⋊C4 | — | 53 | 12 | no | — |
| 517 | C2×C4⋊C4 | C22×D53 | 1 | 3 | yes | — |
| 518 | C2×C42 | — | 53 | 3 | no | — |
| 519 | C2×C42 | — | 53 | 3 | no | — |
| 520 | C2×C42 | — | 53 | 3 | no | — |
| 521 | C2×C42 | — | 53 | 24 | no | — |
| 522 | C2×C42 | — | 53 | 6 | no | — |
| 523 | C2×C42 | — | 53 | 6 | no | — |
| 524 | C2×C42 | — | 53 | 6 | no | — |
| 525 | C2×C42 | — | 53 | 6 | no | — |
| 526 | C2×C42 | C22×D53 | 1 | 3 | yes | — |
| 527 | C24 | — | 53 | 1 | no | — |
| 528 | #41 | — | 2 | 32 | no | — |
| 529 | #41 | — | 2 | 48 | no | — |
| 530 | #41 | — | 106 | 16 | no | — |
| 531 | #41 | — | 212 | 24 | no | — |
| 532 | C2×Q8 | — | 2 | 32 | no | — |
| 533 | C2×Q8 | — | 53 | 4 | no | — |
| 534 | C2×Q8 | — | 53 | 12 | no | — |
| 535 | C2×Q8 | — | 53 | 12 | no | — |
| 536 | C2×Q8 | — | 106 | 16 | no | — |
| 537 | C2×Q8 | — | 106 | 16 | no | — |
| 538 | C2×Q8 | — | 106 | 12 | no | — |
| 539 | C2×Q8 | #11719947 | 1 | 8 | yes | complemented |
| 540 | C2×Q8 | C23×D53 | 1 | 12 | yes | — |
| 541 | C2×Q8 | C23×D53 | 1 | 4 | yes | — |
| 542 | C2×D4 | — | 53 | 8 | no | — |
| 543 | C2×D4 | — | 53 | 8 | no | — |
| 544 | C2×D4 | C23×D53 | 1 | 8 | yes | — |
| 545 | C2×D4 | C23×D53 | 1 | 12 | yes | — |
| 546 | C2×D4 | C23×D53 | 1 | 4 | yes | — |
| 547 | C2×D4 | C23×D53 | 1 | 12 | yes | — |
| 548 | C22×C4 | — | 53 | 1 | no | — |
| 549 | C22×C4 | — | 53 | 1 | no | — |
| 550 | C22×C4 | — | 53 | 8 | no | — |
| 551 | C22×C4 | — | 53 | 3 | no | — |
| 552 | C22×C4 | — | 53 | 3 | no | — |
| 553 | C22×C4 | — | 53 | 24 | no | — |
| 554 | C22×C4 | — | 53 | 1 | no | — |
| 555 | C22×C4 | — | 53 | 1 | no | — |
| 556 | C22×C4 | — | 53 | 1 | no | — |
| 557 | C22×C4 | — | 53 | 6 | no | — |
| 558 | C22×C4 | — | 53 | 6 | no | — |
| 559 | C22×C4 | — | 53 | 6 | no | — |
| 560 | C22×C4 | — | 53 | 6 | no | — |
| 561 | C22×C4 | — | 106 | 4 | no | — |
| 562 | C22×C4 | — | 106 | 12 | no | — |
| 563 | C22×C4 | — | 212 | 6 | no | — |
| 564 | C22×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 565 | C22×C4 | C23×D53 | 1 | 24 | yes | — |
| 566 | C22×C4 | C23×D53 | 1 | 3 | yes | — |
| 567 | C22×C4 | C23×D53 | 1 | 3 | yes | — |
| 568 | C4⋊C4 | — | 53 | 12 | no | — |
| 569 | C4⋊C4 | — | 53 | 24 | no | — |
| 570 | C4⋊C4 | — | 53 | 12 | no | — |
| 571 | C4⋊C4 | — | 53 | 24 | no | — |
| 572 | C4⋊C4 | — | 53 | 12 | no | — |
| 573 | C4⋊C4 | — | 53 | 8 | no | — |
| 574 | C4⋊C4 | — | 53 | 8 | no | — |
| 575 | C4⋊C4 | — | 53 | 4 | no | — |
| 576 | C4⋊C4 | — | 53 | 12 | no | — |
| 577 | C4⋊C4 | — | 53 | 24 | no | — |
| 578 | C4⋊C4 | — | 53 | 24 | no | — |
| 579 | C4⋊C4 | — | 53 | 24 | no | — |
| 580 | C4⋊C4 | C23×D53 | 1 | 12 | yes | — |
| 581 | C4⋊C4 | C23×D53 | 1 | 4 | yes | — |
| 582 | C4⋊C4 | C23×D53 | 1 | 12 | yes | — |
| 583 | C22⋊C4 | — | 53 | 8 | no | — |
| 584 | C22⋊C4 | — | 53 | 24 | no | — |
| 585 | C22⋊C4 | — | 53 | 8 | no | — |
| 586 | C22⋊C4 | — | 53 | 24 | no | — |
| 587 | C22⋊C4 | — | 53 | 24 | no | — |
| 588 | C22⋊C4 | — | 53 | 8 | no | — |
| 589 | C22⋊C4 | — | 53 | 8 | no | — |
| 590 | C22⋊C4 | C23×D53 | 1 | 8 | yes | — |
| 591 | C22⋊C4 | C23×D53 | 1 | 24 | yes | — |
| 592 | C42 | — | 53 | 6 | no | — |
| 593 | C42 | — | 53 | 6 | no | — |
| 594 | C42 | — | 53 | 8 | no | — |
| 595 | C42 | — | 53 | 6 | no | — |
| 596 | C42 | — | 53 | 6 | no | — |
| 597 | C42 | — | 53 | 6 | no | — |
| 598 | C42 | — | 53 | 6 | no | — |
| 599 | C42 | — | 53 | 24 | no | — |
| 600 | C42 | — | 53 | 24 | no | — |
| 601 | C42 | C23×D53 | 1 | 6 | yes | — |
| 602 | C42 | C23×D53 | 1 | 6 | yes | — |
| 603 | C23 | — | 53 | 1 | no | — |
| 604 | C23 | — | 53 | 1 | no | — |
| 605 | C23 | — | 106 | 2 | no | — |
| 606 | C23 | — | 106 | 2 | no | — |
| 607 | C23 | — | 106 | 2 | no | — |
| 608 | C23 | C24×D53 | 1 | 8 | yes | — |
| 609 | C23 | C24×D53 | 1 | 1 | yes | characteristic |
| 610 | Q8 | — | 2 | 24 | no | — |
| 611 | Q8 | — | 106 | 24 | no | — |
| 612 | Q8 | — | 106 | 8 | no | — |
| 613 | Q8 | — | 212 | 12 | no | — |
| 614 | Q8 | C2×#11719947 | 1 | 16 | yes | — |
| 615 | D4 | — | 2 | 16 | no | — |
| 616 | D4 | — | 2 | 24 | no | — |
| 617 | D4 | — | 2 | 8 | no | — |
| 618 | D4 | — | 4 | 12 | no | — |
| 619 | D4 | — | 106 | 16 | no | — |
| 620 | D4 | — | 106 | 16 | no | — |
| 621 | C2×C4 | — | 2 | 48 | no | — |
| 622 | C2×C4 | — | 2 | 2 | no | — |
| 623 | C2×C4 | — | 4 | 3 | no | — |
| 624 | C2×C4 | — | 53 | 1 | no | — |
| 625 | C2×C4 | — | 53 | 4 | no | — |
| 626 | C2×C4 | — | 53 | 1 | no | — |
| 627 | C2×C4 | — | 53 | 6 | no | — |
| 628 | C2×C4 | — | 53 | 8 | no | — |
| 629 | C2×C4 | — | 53 | 6 | no | — |
| 630 | C2×C4 | — | 53 | 8 | no | — |
| 631 | C2×C4 | — | 106 | 2 | no | — |
| 632 | C2×C4 | — | 106 | 2 | no | — |
| 633 | C2×C4 | — | 106 | 12 | no | — |
| 634 | C2×C4 | — | 106 | 2 | no | — |
| 635 | C2×C4 | — | 106 | 16 | no | — |
| 636 | C2×C4 | — | 106 | 6 | no | — |
| 637 | C2×C4 | — | 106 | 12 | no | — |
| 638 | C2×C4 | — | 106 | 12 | no | — |
| 639 | C2×C4 | — | 106 | 2 | no | — |
| 640 | C2×C4 | — | 212 | 6 | no | — |
| 641 | C2×C4 | — | 212 | 3 | no | — |
| 642 | C2×C4 | — | 212 | 24 | no | — |
| 643 | C2×C4 | C2×#11719947 | 1 | 12 | yes | — |
| 644 | C2×C4 | C24×D53 | 1 | 1 | yes | characteristic |
| 645 | C2×C4 | C24×D53 | 1 | 8 | yes | — |
| 646 | C2×C4 | C24×D53 | 1 | 6 | yes | — |
| 647 | C2×C4 | C24×D53 | 1 | 6 | yes | — |
| 648 | C2×C4 | C24×D53 | 1 | 1 | yes | characteristic |
| 649 | C22 | — | 2 | 1 | no | — |
| 650 | C22 | — | 2 | 1 | no | — |
| 651 | C22 | — | 2 | 8 | no | — |
| 652 | C22 | — | 2 | 8 | no | — |
| 653 | C22 | — | 2 | 8 | no | — |
| 654 | C22 | — | 53 | 2 | no | — |
| 655 | C22 | — | 53 | 2 | no | — |
| 656 | C22 | — | 106 | 8 | no | — |
| 657 | C22 | — | 106 | 1 | no | — |
| 658 | C22 | — | 106 | 1 | no | — |
| 659 | C22 | — | 106 | 1 | no | — |
| 660 | C22 | — | 106 | 1 | no | — |
| 661 | C22 | C22×#11719947 | 1 | 2 | yes | — |
| 662 | C22 | C25×D53 | 1 | 1 | yes | characteristic |
| 663 | C4 | — | 2 | 8 | no | — |
| 664 | C4 | — | 2 | 1 | no | — |
| 665 | C4 | — | 2 | 6 | no | — |
| 666 | C4 | — | 53 | 2 | no | — |
| 667 | C4 | — | 106 | 6 | no | — |
| 668 | C4 | — | 106 | 1 | no | — |
| 669 | C4 | — | 106 | 8 | no | — |
| 670 | C4 | — | 106 | 6 | no | — |
| 671 | C4 | — | 106 | 8 | no | — |
| 672 | C4 | C22×#11719947 | 1 | 12 | yes | — |
| 673 | C4 | 2−1+4×D53 | 1 | 2 | yes | — |
| 674 | C2 | — | 2 | 2 | no | — |
| 675 | C2 | — | 4 | 8 | no | — |
| 676 | C2 | — | 106 | 2 | no | — |
| 677 | C2 | — | 106 | 2 | no | — |
| 678 | C2 | C23×#11719947 | 1 | 1 | yes | characteristic |
| 679 | C2 | C2×2−1+4×D53 | 1 | 1 | yes | characteristic |
| 680 | C2 | #585×D53 | 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