← #28293097
Subgroups — #28293097
Order 13568.
6624 conjugacy classes of subgroups.
The subgroup lattice has 416 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #20289409 | C2 | 1 | 8 | yes | maximal, complemented |
| 2 | #20289129 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #20288981 | C2 | 1 | 12 | yes | maximal, complemented |
| 4 | #20288731 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | #20288667 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | #20288610 | C2 | 1 | 12 | yes | maximal, complemented |
| 7 | #20288010 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C53×#3549 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #16811373 | C22 | 1 | 12 | yes | complemented |
| 10 | #16811366 | C22 | 1 | 8 | yes | complemented |
| 11 | #16811360 | C22 | 1 | 8 | yes | complemented |
| 12 | #16811359 | C22 | 1 | 24 | yes | complemented |
| 13 | #16811359 | C22 | 1 | 6 | yes | complemented |
| 14 | #16811353 | C22 | 1 | 6 | yes | complemented |
| 15 | #16811343 | C22 | 1 | 12 | yes | complemented |
| 16 | #16811342 | C22 | 1 | 48 | yes | complemented |
| 17 | #16811341 | C22 | 1 | 24 | yes | complemented |
| 18 | #16811337 | C22 | 1 | 24 | yes | complemented |
| 19 | #16811304 | C22 | 1 | 24 | yes | complemented |
| 20 | #16811304 | C22 | 1 | 48 | yes | complemented |
| 21 | D4×Dic106 | C22 | 1 | 12 | yes | complemented |
| 22 | #16811279 | C22 | 1 | 24 | yes | complemented |
| 23 | #16811267 | C22 | 1 | 24 | yes | complemented |
| 24 | #16811240 | C22 | 1 | 24 | yes | complemented |
| 25 | #16811240 | C22 | 1 | 24 | yes | complemented |
| 26 | #16811237 | C22 | 1 | 48 | yes | complemented |
| 27 | #16811208 | C22 | 1 | 48 | yes | complemented |
| 28 | #16811194 | C22 | 1 | 12 | yes | complemented |
| 29 | #16811180 | C22 | 1 | 3 | yes | complemented |
| 30 | #16811178 | C22 | 1 | 6 | yes | complemented |
| 31 | #16811176 | C22 | 1 | 12 | yes | complemented |
| 32 | #16811171 | C22 | 1 | 6 | yes | — |
| 33 | #16811155 | C22 | 1 | 12 | yes | complemented |
| 34 | #16811154 | C22 | 1 | 12 | yes | complemented |
| 35 | #16811154 | C22 | 1 | 24 | yes | complemented |
| 36 | #16811152 | C22 | 1 | 12 | yes | complemented |
| 37 | C2×#13133204 | C22 | 1 | 12 | yes | complemented |
| 38 | #16811133 | C22 | 1 | 12 | yes | complemented |
| 39 | #16811130 | C22 | 1 | 6 | yes | complemented |
| 40 | #16811100 | C22 | 1 | 12 | yes | complemented |
| 41 | #16811098 | C22 | 1 | 12 | yes | complemented |
| 42 | #41×Dic53 | C22 | 1 | 6 | yes | complemented |
| 43 | C4×#11719947 | C22 | 1 | 12 | yes | complemented |
| 44 | C2×C42×D53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | C53×H(3,𝔽4) | C22 | 1 | 4 | yes | complemented |
| 46 | C53×#555 | C22 | 1 | 6 | yes | complemented |
| 47 | D42×C53 | C22 | 1 | 6 | yes | complemented |
| 48 | C53×#535 | C22 | 1 | 12 | yes | — |
| 49 | C53×#532 | C22 | 1 | 3 | yes | — |
| 50 | C2×#11719947 | C23 | 1 | 12 | yes | — |
| 51 | C22×Dic106 | C23 | 1 | 12 | yes | — |
| 52 | C22×C4×D53 | C23 | 1 | 3 | yes | — |
| 53 | #13133217 | C23 | 1 | 6 | yes | — |
| 54 | #13133216 | C23 | 1 | 24 | yes | — |
| 55 | #13133215 | C23 | 1 | 24 | yes | — |
| 56 | #13133211 | C23 | 1 | 16 | yes | — |
| 57 | #13133210 | C23 | 1 | 24 | yes | — |
| 58 | #13133210 | C23 | 1 | 48 | yes | — |
| 59 | #13133210 | C23 | 1 | 48 | yes | — |
| 60 | #13133209 | C23 | 1 | 6 | yes | — |
| 61 | #13133208 | C23 | 1 | 12 | yes | — |
| 62 | #13133204 | C23 | 1 | 24 | yes | — |
| 63 | #13133204 | C23 | 1 | 48 | yes | — |
| 64 | #13133204 | C23 | 1 | 24 | yes | — |
| 65 | #13133204 | C23 | 1 | 12 | yes | — |
| 66 | #13133203 | C23 | 1 | 48 | yes | — |
| 67 | #13133199 | C23 | 1 | 24 | yes | — |
| 68 | #13133198 | C23 | 1 | 48 | yes | — |
| 69 | #13133198 | C23 | 1 | 12 | yes | — |
| 70 | #13133198 | C23 | 1 | 24 | yes | — |
| 71 | #13133198 | C23 | 1 | 24 | yes | — |
| 72 | #13133197 | C23 | 1 | 12 | yes | — |
| 73 | #13133196 | C23 | 1 | 24 | yes | — |
| 74 | #13133196 | C23 | 1 | 12 | yes | — |
| 75 | #13133194 | C23 | 1 | 48 | yes | — |
| 76 | #13133194 | C23 | 1 | 48 | yes | — |
| 77 | #13133193 | C23 | 1 | 12 | yes | — |
| 78 | #13133189 | C23 | 1 | 48 | yes | — |
| 79 | #13133188 | C23 | 1 | 12 | yes | — |
| 80 | #13133188 | C23 | 1 | 12 | yes | — |
| 81 | #13133186 | C23 | 1 | 16 | yes | — |
| 82 | #13133185 | C23 | 1 | 12 | yes | — |
| 83 | Q8×Dic53 | C23 | 1 | 12 | yes | — |
| 84 | C4×Dic106 | C23 | 1 | 12 | yes | — |
| 85 | C4×Dic106 | C23 | 1 | 48 | yes | — |
| 86 | #13133182 | C23 | 1 | 24 | yes | — |
| 87 | #13133182 | C23 | 1 | 12 | yes | — |
| 88 | D4×Dic53 | C23 | 1 | 24 | yes | — |
| 89 | D4×Dic53 | C23 | 1 | 48 | yes | — |
| 90 | D4×Dic53 | C23 | 1 | 12 | yes | — |
| 91 | D4×Dic53 | C23 | 1 | 24 | yes | — |
| 92 | D4×Dic53 | C23 | 1 | 12 | yes | — |
| 93 | C4×C22⋊D53 | C23 | 1 | 24 | yes | — |
| 94 | #13133177 | C23 | 1 | 24 | yes | — |
| 95 | #13133176 | C23 | 1 | 12 | yes | — |
| 96 | #13133176 | C23 | 1 | 12 | yes | — |
| 97 | #13133176 | C23 | 1 | 6 | yes | — |
| 98 | #13133175 | C23 | 1 | 12 | yes | — |
| 99 | #13133173 | C23 | 1 | 48 | yes | — |
| 100 | #13133173 | C23 | 1 | 24 | yes | — |
| 101 | C2×C22⋊Dic53 | C23 | 1 | 48 | yes | — |
| 102 | C2×C4×Dic53 | C23 | 1 | 3 | yes | — |
| 103 | C2×C4×Dic53 | C23 | 1 | 12 | yes | — |
| 104 | C42×D53 | C23 | 1 | 6 | yes | — |
| 105 | C42×D53 | C23 | 1 | 2 | yes | — |
| 106 | C2×#41×C53 | C23 | 1 | 6 | yes | — |
| 107 | C22×D4×C53 | C23 | 1 | 12 | yes | — |
| 108 | C4⋊Q8×C53 | C23 | 1 | 3 | yes | — |
| 109 | #127×C53 | C23 | 1 | 3 | yes | — |
| 110 | #127×C53 | C23 | 1 | 8 | yes | — |
| 111 | #124×C53 | C23 | 1 | 6 | yes | — |
| 112 | #124×C53 | C23 | 1 | 24 | yes | — |
| 113 | #121×C53 | C23 | 1 | 24 | yes | — |
| 114 | #121×C53 | C23 | 1 | 12 | yes | — |
| 115 | #120×C53 | C23 | 1 | 8 | yes | — |
| 116 | #120×C53 | C23 | 1 | 24 | yes | — |
| 117 | C4×D4×C53 | C23 | 1 | 12 | yes | — |
| 118 | #117×C53 | C23 | 1 | 12 | yes | — |
| 119 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 120 | C24×C53 | C24 | 1 | 8 | yes | — |
| 121 | C23×D53 | C24 | 1 | 1 | yes | characteristic |
| 122 | #41×C53 | — | 4 | 12 | no | — |
| 123 | C2×Q8×C53 | C24 | 1 | 6 | yes | — |
| 124 | C2×D4×C53 | — | 4 | 24 | no | — |
| 125 | C2×D4×C53 | C24 | 1 | 12 | yes | — |
| 126 | C2×D4×C53 | C24 | 1 | 6 | yes | — |
| 127 | C2×D4×C53 | C24 | 1 | 24 | yes | — |
| 128 | C2×D4×C53 | C24 | 1 | 12 | yes | — |
| 129 | C22×C4×C53 | C24 | 1 | 3 | yes | — |
| 130 | C22×C4×C53 | C24 | 1 | 12 | yes | — |
| 131 | C2×C22⋊D53 | C24 | 1 | 24 | yes | — |
| 132 | C22×Dic53 | C24 | 1 | 3 | yes | — |
| 133 | C22×Dic53 | C24 | 1 | 24 | yes | — |
| 134 | C22×Dic53 | C24 | 1 | 24 | yes | — |
| 135 | #11719947 | — | 4 | 24 | no | — |
| 136 | C2×C4×D53 | — | 4 | 6 | no | — |
| 137 | C2×C4×D53 | C24 | 1 | 6 | yes | — |
| 138 | C2×C4×D53 | C24 | 1 | 6 | yes | — |
| 139 | C2×Dic106 | — | 4 | 24 | no | — |
| 140 | C2×Dic106 | C24 | 1 | 12 | yes | — |
| 141 | C2×Dic106 | C24 | 1 | 24 | yes | — |
| 142 | C4⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 143 | C22⋊C4×C53 | C24 | 1 | 24 | yes | — |
| 144 | C22⋊C4×C53 | C24 | 1 | 24 | yes | — |
| 145 | C42×C53 | C24 | 1 | 3 | yes | — |
| 146 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 147 | C42×C53 | C24 | 1 | 8 | yes | — |
| 148 | C22⋊Dic53 | C24 | 1 | 24 | yes | — |
| 149 | C22⋊Dic53 | C24 | 1 | 24 | yes | — |
| 150 | C22⋊Dic53 | C24 | 1 | 24 | yes | — |
| 151 | C22⋊Dic53 | C24 | 1 | 48 | yes | — |
| 152 | C22⋊Dic53 | C24 | 1 | 12 | yes | — |
| 153 | #11719921 | C24 | 1 | 24 | yes | — |
| 154 | C4⋊Dic53 | C24 | 1 | 12 | yes | — |
| 155 | C4⋊Dic53 | C24 | 1 | 24 | yes | — |
| 156 | C4⋊Dic53 | C24 | 1 | 12 | yes | — |
| 157 | #11719919 | C24 | 1 | 24 | yes | — |
| 158 | #11719919 | C24 | 1 | 24 | yes | — |
| 159 | #11719919 | C24 | 1 | 48 | yes | — |
| 160 | C4×Dic53 | C24 | 1 | 3 | yes | — |
| 161 | C4×Dic53 | C24 | 1 | 6 | yes | — |
| 162 | C4×Dic53 | C24 | 1 | 3 | yes | — |
| 163 | C4×Dic53 | C24 | 1 | 24 | yes | — |
| 164 | C4×Dic53 | C24 | 1 | 12 | yes | — |
| 165 | C4×Dic53 | C24 | 1 | 24 | yes | — |
| 166 | C23×C53 | — | 4 | 24 | no | — |
| 167 | C23×C53 | C25 | 1 | 12 | yes | — |
| 168 | C23×C53 | C25 | 1 | 1 | yes | characteristic |
| 169 | C22×D53 | — | 4 | 3 | no | — |
| 170 | C22×D53 | C25 | 1 | 2 | yes | — |
| 171 | Q8×C53 | — | 4 | 6 | no | — |
| 172 | D4×C53 | — | 2 | 24 | no | — |
| 173 | D4×C53 | — | 4 | 24 | no | — |
| 174 | D4×C53 | — | 4 | 12 | no | — |
| 175 | D4×C53 | — | 4 | 6 | no | — |
| 176 | C2×C4×C53 | — | 2 | 24 | no | — |
| 177 | C2×C4×C53 | — | 2 | 6 | no | — |
| 178 | C2×C4×C53 | C25 | 1 | 12 | yes | — |
| 179 | C2×C4×C53 | C25 | 1 | 3 | yes | — |
| 180 | C2×C4×C53 | C25 | 1 | 3 | yes | — |
| 181 | C22⋊D53 | — | 4 | 24 | no | — |
| 182 | C2×Dic53 | — | 4 | 24 | no | — |
| 183 | C2×Dic53 | — | 4 | 3 | no | — |
| 184 | C2×Dic53 | — | 4 | 24 | no | — |
| 185 | C2×Dic53 | C25 | 1 | 24 | yes | — |
| 186 | C2×Dic53 | C25 | 1 | 6 | yes | — |
| 187 | C4×D53 | — | 2 | 12 | no | — |
| 188 | C4×D53 | — | 4 | 6 | no | — |
| 189 | Dic106 | — | 2 | 24 | no | — |
| 190 | Dic106 | — | 4 | 24 | no | — |
| 191 | #62841 | — | 53 | 1 | no | maximal, Sylow |
| 192 | C22×C53 | — | 2 | 12 | no | — |
| 193 | C22×C53 | — | 2 | 24 | no | — |
| 194 | C22×C53 | — | 2 | 3 | no | — |
| 195 | C22×C53 | — | 16 | 8 | no | — |
| 196 | C22×C53 | C26 | 1 | 1 | yes | characteristic |
| 197 | C2×D53 | — | 2 | 6 | no | — |
| 198 | C2×D53 | — | 4 | 4 | no | — |
| 199 | C4×C53 | — | 2 | 12 | no | — |
| 200 | C4×C53 | — | 2 | 3 | no | — |
| 201 | C4×C53 | #585 | 1 | 6 | yes | — |
| 202 | Dic53 | — | 2 | 24 | no | — |
| 203 | Dic53 | — | 2 | 6 | no | — |
| 204 | #3568 | — | 53 | 8 | no | — |
| 205 | #3550 | — | 53 | 3 | no | — |
| 206 | #3549 | D53 | 1 | 1 | yes | characteristic, complemented |
| 207 | #3540 | — | 53 | 12 | no | — |
| 208 | #3518 | — | 53 | 12 | no | — |
| 209 | #3514 | — | 53 | 12 | no | — |
| 210 | #3510 | — | 53 | 12 | no | — |
| 211 | #3444 | — | 53 | 3 | no | — |
| 212 | C2×C53 | — | 4 | 1 | no | — |
| 213 | C2×C53 | — | 4 | 12 | no | — |
| 214 | C2×C53 | C2×#585 | 1 | 3 | yes | — |
| 215 | D53 | — | 4 | 2 | no | — |
| 216 | #563 | — | 53 | 12 | no | — |
| 217 | H(3,𝔽4) | — | 53 | 8 | no | — |
| 218 | H(3,𝔽4) | C2×D53 | 1 | 4 | yes | complemented |
| 219 | #560 | — | 53 | 8 | no | — |
| 220 | #559 | — | 53 | 24 | no | — |
| 221 | #559 | — | 53 | 6 | no | — |
| 222 | Q82 | — | 53 | 6 | no | — |
| 223 | #556 | — | 53 | 48 | no | — |
| 224 | #556 | — | 53 | 12 | no | — |
| 225 | #556 | — | 53 | 24 | no | — |
| 226 | #555 | — | 53 | 24 | no | — |
| 227 | #555 | C2×D53 | 1 | 6 | yes | complemented |
| 228 | #551 | — | 53 | 24 | no | — |
| 229 | #551 | — | 53 | 48 | no | — |
| 230 | D4×Q8 | — | 53 | 12 | no | — |
| 231 | #548 | — | 53 | 24 | no | — |
| 232 | #546 | — | 53 | 24 | no | — |
| 233 | D42 | C2×D53 | 1 | 6 | yes | complemented |
| 234 | #542 | — | 53 | 48 | no | — |
| 235 | #542 | — | 53 | 24 | no | — |
| 236 | #542 | — | 53 | 24 | no | — |
| 237 | #538 | — | 53 | 48 | no | — |
| 238 | #536 | — | 53 | 12 | no | — |
| 239 | #535 | C2×D53 | 1 | 12 | yes | — |
| 240 | #533 | — | 53 | 6 | no | — |
| 241 | #533 | — | 53 | 12 | no | — |
| 242 | #533 | — | 53 | 3 | no | — |
| 243 | #532 | — | 53 | 6 | no | — |
| 244 | #532 | C2×D53 | 1 | 3 | yes | — |
| 245 | #529 | — | 53 | 12 | no | — |
| 246 | #529 | — | 53 | 12 | no | — |
| 247 | #529 | — | 53 | 24 | no | — |
| 248 | #529 | — | 53 | 12 | no | — |
| 249 | C2×#124 | — | 53 | 12 | no | — |
| 250 | #525 | — | 53 | 6 | no | — |
| 251 | #525 | — | 53 | 12 | no | — |
| 252 | #519 | — | 53 | 12 | no | — |
| 253 | #518 | — | 53 | 12 | no | — |
| 254 | C4×#41 | — | 53 | 6 | no | — |
| 255 | C4×#41 | — | 53 | 12 | no | — |
| 256 | C22×C42 | — | 53 | 1 | no | — |
| 257 | C53 | #62841 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 258 | C2×#41 | — | 53 | 12 | no | — |
| 259 | C2×#41 | C22×D53 | 1 | 6 | yes | — |
| 260 | C22×Q8 | — | 53 | 12 | no | — |
| 261 | C22×D4 | C22×D53 | 1 | 12 | yes | — |
| 262 | C23×C4 | — | 53 | 3 | no | — |
| 263 | C4⋊Q8 | — | 53 | 24 | no | — |
| 264 | C4⋊Q8 | — | 53 | 24 | no | — |
| 265 | C4⋊Q8 | — | 53 | 6 | no | — |
| 266 | C4⋊Q8 | C22×D53 | 1 | 3 | yes | — |
| 267 | #127 | C22×D53 | 1 | 3 | yes | — |
| 268 | #127 | C22×D53 | 1 | 8 | yes | — |
| 269 | #126 | — | 53 | 24 | no | — |
| 270 | #126 | — | 53 | 48 | no | — |
| 271 | #126 | — | 53 | 48 | no | — |
| 272 | #126 | — | 53 | 16 | no | — |
| 273 | #125 | — | 53 | 12 | no | — |
| 274 | #125 | — | 53 | 6 | no | — |
| 275 | #124 | — | 53 | 12 | no | — |
| 276 | #124 | — | 53 | 48 | no | — |
| 277 | #124 | — | 53 | 24 | no | — |
| 278 | #124 | — | 53 | 24 | no | — |
| 279 | #124 | — | 53 | 48 | no | — |
| 280 | #124 | C22×D53 | 1 | 6 | yes | — |
| 281 | #124 | C22×D53 | 1 | 24 | yes | — |
| 282 | #123 | — | 53 | 12 | no | — |
| 283 | #123 | — | 53 | 48 | no | — |
| 284 | #123 | — | 53 | 24 | no | — |
| 285 | #123 | — | 53 | 24 | no | — |
| 286 | #123 | — | 53 | 24 | no | — |
| 287 | C22⋊Q8 | — | 53 | 12 | no | — |
| 288 | C22⋊Q8 | — | 53 | 12 | no | — |
| 289 | C22⋊Q8 | — | 53 | 24 | no | — |
| 290 | C22⋊Q8 | — | 53 | 12 | no | — |
| 291 | C22⋊Q8 | — | 53 | 48 | no | — |
| 292 | C22⋊Q8 | — | 53 | 48 | no | — |
| 293 | #121 | — | 53 | 12 | no | — |
| 294 | #121 | — | 53 | 12 | no | — |
| 295 | #121 | — | 53 | 48 | no | — |
| 296 | #121 | C22×D53 | 1 | 12 | yes | — |
| 297 | #121 | C22×D53 | 1 | 24 | yes | — |
| 298 | #120 | — | 53 | 16 | no | — |
| 299 | #120 | — | 53 | 12 | no | — |
| 300 | #120 | C22×D53 | 1 | 8 | yes | — |
| 301 | #120 | C22×D53 | 1 | 24 | yes | — |
| 302 | C4×Q8 | — | 53 | 12 | no | — |
| 303 | C4×Q8 | — | 53 | 12 | no | — |
| 304 | C4×Q8 | — | 53 | 24 | no | — |
| 305 | C4×Q8 | — | 53 | 12 | no | — |
| 306 | C4×Q8 | — | 53 | 48 | no | — |
| 307 | C4×D4 | — | 53 | 12 | no | — |
| 308 | C4×D4 | — | 53 | 24 | no | — |
| 309 | C4×D4 | — | 53 | 12 | no | — |
| 310 | C4×D4 | — | 53 | 48 | no | — |
| 311 | C4×D4 | — | 53 | 24 | no | — |
| 312 | C4×D4 | — | 53 | 24 | no | — |
| 313 | C4×D4 | — | 53 | 24 | no | — |
| 314 | C4×D4 | C22×D53 | 1 | 12 | yes | — |
| 315 | #117 | — | 53 | 12 | no | — |
| 316 | #117 | — | 53 | 6 | no | — |
| 317 | #117 | — | 53 | 12 | no | — |
| 318 | #117 | — | 53 | 12 | no | — |
| 319 | #117 | — | 53 | 24 | no | — |
| 320 | #117 | — | 53 | 48 | no | — |
| 321 | #117 | C22×D53 | 1 | 12 | yes | — |
| 322 | C2×C22⋊C4 | — | 53 | 48 | no | — |
| 323 | C2×C42 | — | 53 | 12 | no | — |
| 324 | C2×C42 | — | 53 | 3 | no | — |
| 325 | C2×C42 | — | 53 | 6 | no | — |
| 326 | C2×C42 | — | 53 | 2 | no | — |
| 327 | C2×C42 | C22×D53 | 1 | 1 | yes | characteristic |
| 328 | C24 | — | 53 | 1 | no | — |
| 329 | C24 | C23×D53 | 1 | 8 | yes | — |
| 330 | #41 | — | 4 | 12 | no | — |
| 331 | #41 | — | 212 | 24 | no | — |
| 332 | C2×Q8 | — | 53 | 12 | no | — |
| 333 | C2×Q8 | — | 53 | 24 | no | — |
| 334 | C2×Q8 | — | 212 | 24 | no | — |
| 335 | C2×Q8 | C23×D53 | 1 | 6 | yes | — |
| 336 | C2×D4 | — | 4 | 24 | no | — |
| 337 | C2×D4 | — | 53 | 24 | no | — |
| 338 | C2×D4 | C23×D53 | 1 | 12 | yes | — |
| 339 | C2×D4 | C23×D53 | 1 | 12 | yes | — |
| 340 | C2×D4 | C23×D53 | 1 | 6 | yes | — |
| 341 | C2×D4 | C23×D53 | 1 | 24 | yes | — |
| 342 | C22×C4 | — | 53 | 3 | no | — |
| 343 | C22×C4 | — | 53 | 24 | no | — |
| 344 | C22×C4 | — | 53 | 24 | no | — |
| 345 | C22×C4 | — | 53 | 6 | no | — |
| 346 | C22×C4 | — | 53 | 6 | no | — |
| 347 | C22×C4 | — | 212 | 6 | no | — |
| 348 | C22×C4 | C23×D53 | 1 | 3 | yes | — |
| 349 | C22×C4 | C23×D53 | 1 | 12 | yes | — |
| 350 | C4⋊C4 | — | 53 | 12 | no | — |
| 351 | C4⋊C4 | — | 53 | 24 | no | — |
| 352 | C4⋊C4 | — | 53 | 24 | no | — |
| 353 | C4⋊C4 | — | 53 | 12 | no | — |
| 354 | C4⋊C4 | — | 53 | 24 | no | — |
| 355 | C4⋊C4 | — | 53 | 48 | no | — |
| 356 | C4⋊C4 | C23×D53 | 1 | 12 | yes | — |
| 357 | C22⋊C4 | — | 53 | 24 | no | — |
| 358 | C22⋊C4 | — | 53 | 24 | no | — |
| 359 | C22⋊C4 | — | 53 | 24 | no | — |
| 360 | C22⋊C4 | — | 53 | 48 | no | — |
| 361 | C22⋊C4 | — | 53 | 12 | no | — |
| 362 | C22⋊C4 | — | 53 | 24 | no | — |
| 363 | C22⋊C4 | C23×D53 | 1 | 24 | yes | — |
| 364 | C22⋊C4 | C23×D53 | 1 | 24 | yes | — |
| 365 | C42 | — | 53 | 3 | no | — |
| 366 | C42 | — | 53 | 3 | no | — |
| 367 | C42 | — | 53 | 6 | no | — |
| 368 | C42 | — | 53 | 24 | no | — |
| 369 | C42 | — | 53 | 12 | no | — |
| 370 | C42 | — | 53 | 24 | no | — |
| 371 | C42 | C23×D53 | 1 | 3 | yes | — |
| 372 | C42 | C23×D53 | 1 | 1 | yes | characteristic |
| 373 | C42 | C23×D53 | 1 | 8 | yes | — |
| 374 | C23 | — | 4 | 24 | no | — |
| 375 | C23 | — | 53 | 2 | no | — |
| 376 | C23 | — | 212 | 3 | no | — |
| 377 | C23 | C24×D53 | 1 | 1 | yes | characteristic |
| 378 | C23 | C24×D53 | 1 | 12 | yes | — |
| 379 | Q8 | — | 4 | 6 | no | — |
| 380 | Q8 | — | 106 | 24 | no | — |
| 381 | Q8 | — | 212 | 24 | no | — |
| 382 | D4 | — | 2 | 24 | no | — |
| 383 | D4 | — | 4 | 24 | no | — |
| 384 | D4 | — | 4 | 6 | no | — |
| 385 | D4 | — | 4 | 12 | no | — |
| 386 | D4 | — | 212 | 24 | no | — |
| 387 | C2×C4 | — | 2 | 6 | no | — |
| 388 | C2×C4 | — | 2 | 24 | no | — |
| 389 | C2×C4 | — | 53 | 6 | no | — |
| 390 | C2×C4 | — | 53 | 24 | no | — |
| 391 | C2×C4 | — | 106 | 12 | no | — |
| 392 | C2×C4 | — | 212 | 6 | no | — |
| 393 | C2×C4 | — | 212 | 3 | no | — |
| 394 | C2×C4 | — | 212 | 24 | no | — |
| 395 | C2×C4 | — | 212 | 24 | no | — |
| 396 | C2×C4 | C24×D53 | 1 | 12 | yes | — |
| 397 | C2×C4 | C24×D53 | 1 | 3 | yes | — |
| 398 | C2×C4 | C24×D53 | 1 | 3 | yes | — |
| 399 | C22 | — | 2 | 12 | no | — |
| 400 | C22 | — | 2 | 3 | no | — |
| 401 | C22 | — | 2 | 24 | no | — |
| 402 | C22 | — | 16 | 8 | no | — |
| 403 | C22 | — | 106 | 6 | no | — |
| 404 | C22 | — | 212 | 4 | no | — |
| 405 | C22 | C25×D53 | 1 | 1 | yes | characteristic |
| 406 | C4 | — | 2 | 3 | no | — |
| 407 | C4 | — | 2 | 12 | no | — |
| 408 | C4 | — | 106 | 6 | no | — |
| 409 | C4 | — | 106 | 24 | no | — |
| 410 | C4 | #16811458 | 1 | 6 | yes | — |
| 411 | C2 | — | 4 | 12 | no | — |
| 412 | C2 | — | 4 | 1 | no | — |
| 413 | C2 | — | 212 | 2 | no | — |
| 414 | C2 | C2×#16811458 | 1 | 3 | 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