Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
384 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #20286509 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20276792 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20276791 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20274381 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20272755 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20272692 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C53×#1336 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #16811435 | — | 2 | 1 | no | — |
| 9 | #16811430 | — | 2 | 1 | no | — |
| 10 | #16811061 | — | 2 | 1 | no | — |
| 11 | #16811058 | — | 2 | 1 | no | — |
| 12 | #16811000 | — | 2 | 1 | no | — |
| 13 | #16811000 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | #16810996 | C22 | 1 | 1 | yes | characteristic |
| 15 | #16810970 | — | 2 | 1 | no | — |
| 16 | #16810887 | — | 2 | 1 | no | — |
| 17 | #16810886 | — | 2 | 1 | no | — |
| 18 | #16810807 | — | 2 | 1 | no | — |
| 19 | #16810792 | — | 2 | 1 | no | — |
| 20 | #16810741 | C22 | 1 | 1 | yes | characteristic |
| 21 | #16810444 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #16810437 | — | 2 | 1 | no | — |
| 23 | #16810435 | — | 2 | 1 | no | — |
| 24 | C53×#443 | C22 | 1 | 1 | yes | characteristic |
| 25 | C53×#364 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C53×#322 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #13133264 | — | 2 | 1 | no | — |
| 28 | #13133263 | — | 2 | 1 | no | — |
| 29 | #13133250 | — | 2 | 1 | no | — |
| 30 | #13133250 | — | 4 | 1 | no | — |
| 31 | #13133249 | — | 4 | 1 | no | — |
| 32 | #13133247 | — | 2 | 1 | no | — |
| 33 | #13133245 | — | 2 | 1 | no | — |
| 34 | #13133245 | — | 4 | 1 | no | — |
| 35 | #13133242 | — | 2 | 1 | no | — |
| 36 | #13133241 | — | 4 | 1 | no | — |
| 37 | #13133239 | — | 4 | 1 | no | — |
| 38 | #13133239 | D4 | 1 | 1 | yes | characteristic |
| 39 | #13133238 | — | 4 | 1 | no | — |
| 40 | C2×#11719913 | — | 2 | 1 | no | — |
| 41 | C2×#11719913 | — | 2 | 1 | no | — |
| 42 | C2×#11719913 | — | 4 | 1 | no | — |
| 43 | SD16×D53 | — | 4 | 1 | no | — |
| 44 | C2×D424 | — | 2 | 1 | no | — |
| 45 | C2×D424 | — | 2 | 1 | no | — |
| 46 | C2×D424 | — | 4 | 2 | no | — |
| 47 | #13133223 | — | 2 | 1 | no | — |
| 48 | #13133217 | D4 | 1 | 1 | yes | characteristic |
| 49 | #13133214 | — | 2 | 1 | no | — |
| 50 | #13133214 | D4 | 1 | 1 | yes | characteristic |
| 51 | #13133162 | — | 4 | 1 | no | — |
| 52 | #13133160 | — | 4 | 1 | no | — |
| 53 | D848 | — | 4 | 1 | no | — |
| 54 | #13133158 | — | 4 | 1 | no | — |
| 55 | #13133157 | — | 2 | 1 | no | — |
| 56 | #13133153 | D4 | 1 | 1 | yes | characteristic |
| 57 | #13133145 | — | 2 | 1 | no | — |
| 58 | #13133139 | — | 4 | 2 | no | — |
| 59 | #13133135 | — | 2 | 1 | no | — |
| 60 | #13133133 | — | 2 | 1 | no | — |
| 61 | #135×C53 | D4 | 1 | 1 | yes | characteristic |
| 62 | #131×C53 | — | 2 | 1 | no | — |
| 63 | M32×C53 | — | 2 | 1 | no | — |
| 64 | #108×C53 | D4 | 1 | 1 | yes | characteristic |
| 65 | #104×C53 | — | 2 | 1 | no | — |
| 66 | C4×C8×C53 | — | 2 | 1 | no | — |
| 67 | C4×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 68 | #41×C53 | — | 2 | 1 | no | — |
| 69 | #11719949 | — | 4 | 1 | no | — |
| 70 | Q8×D53 | — | 4 | 1 | no | — |
| 71 | #11719947 | — | 4 | 1 | no | — |
| 72 | #11719947 | — | 8 | 1 | no | — |
| 73 | D4×D53 | — | 4 | 1 | no | — |
| 74 | D4×D53 | — | 8 | 1 | no | — |
| 75 | #11719945 | — | 2 | 1 | no | — |
| 76 | #11719945 | — | 4 | 1 | no | — |
| 77 | #11719945 | — | 4 | 1 | no | — |
| 78 | C2×D212 | — | 2 | 1 | no | — |
| 79 | C2×D212 | — | 4 | 1 | no | — |
| 80 | C2×D212 | — | 4 | 1 | no | — |
| 81 | C2×D212 | — | 4 | 1 | no | — |
| 82 | C2×D212 | — | 4 | 1 | no | — |
| 83 | C2×D212 | — | 4 | 1 | no | — |
| 84 | C2×Dic106 | — | 2 | 1 | no | — |
| 85 | C2×Dic106 | — | 4 | 1 | no | — |
| 86 | Q16×C53 | D8 | 1 | 1 | yes | characteristic, complemented |
| 87 | SD16×C53 | — | 2 | 1 | no | — |
| 88 | D8×C53 | D8 | 1 | 1 | yes | characteristic, complemented |
| 89 | M16×C53 | — | 2 | 1 | no | — |
| 90 | M16×C53 | — | 4 | 1 | no | — |
| 91 | C2×C8×C53 | — | 2 | 2 | no | — |
| 92 | C2×C8×C53 | — | 4 | 1 | no | — |
| 93 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 94 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 95 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 96 | #11719925 | — | 4 | 1 | no | — |
| 97 | #11719924 | — | 4 | 1 | no | — |
| 98 | #11719923 | — | 4 | 1 | no | — |
| 99 | #11719922 | — | 4 | 1 | no | — |
| 100 | C4⋊Dic53 | — | 4 | 1 | no | — |
| 101 | #11719917 | — | 2 | 1 | no | — |
| 102 | Dic212 | — | 4 | 1 | no | — |
| 103 | Dic212 | D8 | 1 | 1 | yes | characteristic, complemented |
| 104 | D424 | — | 4 | 1 | no | — |
| 105 | D424 | — | 4 | 1 | no | — |
| 106 | D424 | — | 4 | 1 | no | — |
| 107 | D424 | — | 4 | 1 | no | — |
| 108 | D424 | — | 4 | 1 | no | — |
| 109 | D424 | — | 8 | 4 | no | — |
| 110 | D424 | D8 | 1 | 1 | yes | characteristic, complemented |
| 111 | #11719913 | — | 2 | 1 | no | — |
| 112 | #11719913 | — | 4 | 1 | no | — |
| 113 | #11719913 | — | 4 | 1 | no | — |
| 114 | #11719913 | — | 4 | 1 | no | — |
| 115 | #11719913 | — | 4 | 1 | no | — |
| 116 | #11719913 | — | 4 | 1 | no | — |
| 117 | #11719913 | — | 4 | 1 | no | — |
| 118 | #11719912 | — | 4 | 1 | no | — |
| 119 | C8×D53 | — | 4 | 1 | no | — |
| 120 | C16×C53 | — | 4 | 1 | no | — |
| 121 | #11719908 | — | 4 | 1 | no | — |
| 122 | C22×D53 | — | 4 | 1 | no | — |
| 123 | C22×D53 | — | 8 | 1 | no | — |
| 124 | C22×D53 | — | 8 | 1 | no | — |
| 125 | Q8×C53 | — | 2 | 1 | no | — |
| 126 | D4×C53 | — | 2 | 1 | no | — |
| 127 | D4×C53 | — | 4 | 1 | no | — |
| 128 | C2×C4×C53 | — | 2 | 1 | no | — |
| 129 | C2×C4×C53 | — | 4 | 1 | no | — |
| 130 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 131 | C22⋊D53 | — | 4 | 1 | no | — |
| 132 | C22⋊D53 | — | 8 | 1 | no | — |
| 133 | C22⋊D53 | — | 8 | 1 | no | — |
| 134 | C2×Dic53 | — | 4 | 1 | no | — |
| 135 | C2×Dic53 | — | 8 | 1 | no | — |
| 136 | D212 | — | 2 | 1 | no | — |
| 137 | D212 | — | 4 | 1 | no | — |
| 138 | D212 | — | 4 | 1 | no | — |
| 139 | D212 | — | 8 | 2 | no | — |
| 140 | D212 | — | 8 | 2 | no | — |
| 141 | D212 | — | 8 | 2 | no | — |
| 142 | D212 | — | 8 | 1 | no | — |
| 143 | D212 | — | 8 | 1 | no | — |
| 144 | D212 | — | 8 | 1 | no | — |
| 145 | C4×D53 | — | 4 | 1 | no | — |
| 146 | C4×D53 | — | 8 | 1 | no | — |
| 147 | C4×D53 | — | 8 | 1 | no | — |
| 148 | Dic106 | — | 2 | 1 | no | — |
| 149 | Dic106 | — | 4 | 1 | no | — |
| 150 | Dic106 | — | 4 | 1 | no | — |
| 151 | Dic106 | — | 8 | 1 | no | — |
| 152 | C8×C53 | — | 4 | 2 | no | — |
| 153 | C8×C53 | — | 4 | 1 | no | — |
| 154 | C8×C53 | C2×D8 | 1 | 1 | yes | characteristic |
| 155 | C8×C53 | C2×D8 | 1 | 1 | yes | characteristic |
| 156 | C8×C53 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 157 | C8×C53 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 158 | #88322 | — | 4 | 1 | no | — |
| 159 | #12314 | — | 53 | 1 | no | maximal, Sylow |
| 160 | C22×C53 | — | 4 | 1 | no | — |
| 161 | C22×C53 | #453 | 1 | 1 | yes | characteristic |
| 162 | C2×D53 | — | 4 | 1 | no | — |
| 163 | C2×D53 | — | 8 | 1 | no | — |
| 164 | C2×D53 | — | 16 | 1 | no | — |
| 165 | C2×D53 | — | 16 | 1 | no | — |
| 166 | C2×D53 | — | 16 | 1 | no | — |
| 167 | C2×D53 | — | 16 | 1 | no | — |
| 168 | C2×D53 | — | 32 | 1 | no | — |
| 169 | C4×C53 | — | 2 | 2 | no | — |
| 170 | C4×C53 | — | 4 | 1 | no | — |
| 171 | C4×C53 | #447 | 1 | 1 | yes | characteristic |
| 172 | C4×C53 | #447 | 1 | 1 | yes | characteristic |
| 173 | Dic53 | — | 4 | 1 | no | — |
| 174 | Dic53 | — | 8 | 1 | no | — |
| 175 | #3291 | — | 53 | 1 | no | — |
| 176 | #2213 | — | 53 | 1 | no | — |
| 177 | #2213 | — | 53 | 1 | no | — |
| 178 | #1721 | — | 53 | 1 | no | — |
| 179 | #1359 | — | 53 | 1 | no | — |
| 180 | #1336 | — | 53 | 1 | no | — |
| 181 | #1336 | D53 | 1 | 1 | yes | characteristic, complemented |
| 182 | C2×C53 | — | 2 | 1 | no | — |
| 183 | C2×C53 | — | 8 | 1 | no | — |
| 184 | C2×C53 | #1619 | 1 | 1 | yes | characteristic |
| 185 | D53 | — | 8 | 1 | no | — |
| 186 | D53 | — | 16 | 1 | no | — |
| 187 | D53 | — | 32 | 1 | no | — |
| 188 | #577 | — | 106 | 1 | no | — |
| 189 | #577 | — | 106 | 1 | no | — |
| 190 | #509 | — | 106 | 1 | no | — |
| 191 | #509 | — | 106 | 1 | no | — |
| 192 | #493 | — | 53 | 1 | no | — |
| 193 | #493 | — | 106 | 1 | no | — |
| 194 | #492 | — | 53 | 1 | no | — |
| 195 | #486 | — | 106 | 1 | no | — |
| 196 | #471 | — | 106 | 1 | no | — |
| 197 | #471 | — | 106 | 1 | no | — |
| 198 | #456 | — | 106 | 1 | no | — |
| 199 | #453 | — | 106 | 1 | no | — |
| 200 | #443 | — | 53 | 1 | no | — |
| 201 | #443 | C2×D53 | 1 | 1 | yes | characteristic |
| 202 | #364 | — | 53 | 1 | no | — |
| 203 | #364 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 204 | #361 | — | 106 | 1 | no | — |
| 205 | #361 | — | 106 | 1 | no | — |
| 206 | #322 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 207 | C53 | #12314 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 208 | 2−1+4 | — | 106 | 1 | no | — |
| 209 | H(5,𝔽2) | — | 106 | 1 | no | — |
| 210 | #137 | — | 106 | 1 | no | — |
| 211 | #137 | — | 106 | 1 | no | — |
| 212 | #137 | — | 212 | 1 | no | — |
| 213 | #137 | — | 212 | 1 | no | — |
| 214 | AGL(1,ℤ/8) | — | 106 | 1 | no | — |
| 215 | AGL(1,ℤ/8) | — | 106 | 1 | no | — |
| 216 | AGL(1,ℤ/8) | — | 212 | 1 | no | — |
| 217 | AGL(1,ℤ/8) | — | 212 | 1 | no | — |
| 218 | #135 | — | 53 | 1 | no | — |
| 219 | #135 | — | 212 | 1 | no | — |
| 220 | #135 | — | 212 | 1 | no | — |
| 221 | #135 | D212 | 1 | 1 | yes | characteristic |
| 222 | C2×SD16 | — | 106 | 1 | no | — |
| 223 | C2×SD16 | — | 106 | 1 | no | — |
| 224 | C2×SD16 | — | 212 | 1 | no | — |
| 225 | C2×SD16 | — | 212 | 1 | no | — |
| 226 | C2×D8 | — | 106 | 1 | no | — |
| 227 | C2×D8 | — | 106 | 1 | no | — |
| 228 | C2×D8 | — | 212 | 2 | no | — |
| 229 | #131 | — | 2 | 1 | no | — |
| 230 | #131 | — | 106 | 1 | no | — |
| 231 | C4⋊Q8 | — | 53 | 1 | no | — |
| 232 | #127 | — | 53 | 1 | no | — |
| 233 | #127 | — | 106 | 1 | no | — |
| 234 | SD32 | — | 212 | 1 | no | — |
| 235 | SD32 | — | 212 | 1 | no | — |
| 236 | D16 | — | 212 | 1 | no | — |
| 237 | D16 | — | 212 | 1 | no | — |
| 238 | M32 | — | 2 | 1 | no | — |
| 239 | M32 | — | 106 | 1 | no | — |
| 240 | #108 | — | 53 | 1 | no | — |
| 241 | #108 | D212 | 1 | 1 | yes | characteristic |
| 242 | #104 | — | 2 | 1 | no | — |
| 243 | #104 | — | 106 | 1 | no | — |
| 244 | #102 | — | 212 | 2 | no | — |
| 245 | #101 | — | 106 | 1 | no | — |
| 246 | #100 | — | 106 | 1 | no | — |
| 247 | C4×C8 | — | 2 | 1 | no | — |
| 248 | C4×C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 249 | #41 | — | 2 | 1 | no | — |
| 250 | #41 | — | 106 | 1 | no | — |
| 251 | #41 | — | 424 | 1 | no | — |
| 252 | #41 | — | 212 | 1 | no | — |
| 253 | #41 | — | 212 | 1 | no | — |
| 254 | #41 | — | 212 | 1 | no | — |
| 255 | #41 | — | 212 | 1 | no | — |
| 256 | C2×Q8 | — | 106 | 1 | no | — |
| 257 | C2×Q8 | — | 212 | 1 | no | — |
| 258 | C2×Q8 | — | 212 | 1 | no | — |
| 259 | C2×D4 | — | 106 | 1 | no | — |
| 260 | C2×D4 | — | 424 | 1 | no | — |
| 261 | C2×D4 | — | 212 | 1 | no | — |
| 262 | C2×D4 | — | 212 | 1 | no | — |
| 263 | C2×D4 | — | 212 | 1 | no | — |
| 264 | C2×D4 | — | 212 | 1 | no | — |
| 265 | C2×D4 | — | 212 | 1 | no | — |
| 266 | C2×D4 | — | 212 | 1 | no | — |
| 267 | Q16 | — | 53 | 1 | no | — |
| 268 | Q16 | — | 212 | 1 | no | — |
| 269 | Q16 | — | 212 | 1 | no | — |
| 270 | Q16 | D424 | 1 | 1 | yes | characteristic, complemented |
| 271 | SD16 | — | 2 | 1 | no | — |
| 272 | SD16 | — | 106 | 1 | no | — |
| 273 | SD16 | — | 212 | 1 | no | — |
| 274 | SD16 | — | 212 | 1 | no | — |
| 275 | SD16 | — | 212 | 1 | no | — |
| 276 | SD16 | — | 212 | 1 | no | — |
| 277 | SD16 | — | 212 | 1 | no | — |
| 278 | SD16 | — | 212 | 1 | no | — |
| 279 | SD16 | — | 212 | 1 | no | — |
| 280 | SD16 | — | 212 | 1 | no | — |
| 281 | D8 | — | 53 | 1 | no | — |
| 282 | D8 | — | 424 | 4 | no | — |
| 283 | D8 | — | 212 | 1 | no | — |
| 284 | D8 | — | 212 | 1 | no | — |
| 285 | D8 | — | 212 | 1 | no | — |
| 286 | D8 | — | 212 | 1 | no | — |
| 287 | D8 | — | 212 | 1 | no | — |
| 288 | D8 | — | 212 | 1 | no | — |
| 289 | D8 | D424 | 1 | 1 | yes | characteristic, complemented |
| 290 | M16 | — | 2 | 1 | no | — |
| 291 | M16 | — | 4 | 1 | no | — |
| 292 | M16 | — | 106 | 1 | no | — |
| 293 | M16 | — | 212 | 1 | no | — |
| 294 | C2×C8 | — | 2 | 2 | no | — |
| 295 | C2×C8 | — | 4 | 1 | no | — |
| 296 | C2×C8 | — | 212 | 1 | no | — |
| 297 | C2×C8 | C2×D212 | 1 | 1 | yes | characteristic |
| 298 | C2×C8 | D4×D53 | 1 | 1 | yes | characteristic |
| 299 | C4⋊C4 | — | 212 | 1 | no | — |
| 300 | C42 | D4×D53 | 1 | 1 | yes | characteristic |
| 301 | C16 | — | 4 | 1 | no | — |
| 302 | C16 | — | 212 | 1 | no | — |
| 303 | C23 | — | 424 | 1 | no | — |
| 304 | C23 | — | 424 | 1 | no | — |
| 305 | C23 | — | 212 | 1 | no | — |
| 306 | Q8 | — | 2 | 1 | no | — |
| 307 | Q8 | — | 106 | 1 | no | — |
| 308 | Q8 | — | 424 | 1 | no | — |
| 309 | Q8 | — | 212 | 1 | no | — |
| 310 | Q8 | — | 212 | 1 | no | — |
| 311 | D4 | — | 2 | 1 | no | — |
| 312 | D4 | — | 4 | 1 | no | — |
| 313 | D4 | — | 106 | 1 | no | — |
| 314 | D4 | — | 424 | 2 | no | — |
| 315 | D4 | — | 424 | 2 | no | — |
| 316 | D4 | — | 424 | 2 | no | — |
| 317 | D4 | — | 424 | 1 | no | — |
| 318 | D4 | — | 424 | 1 | no | — |
| 319 | D4 | — | 424 | 1 | no | — |
| 320 | D4 | — | 424 | 1 | no | — |
| 321 | D4 | — | 424 | 1 | no | — |
| 322 | D4 | — | 212 | 1 | no | — |
| 323 | D4 | — | 212 | 1 | no | — |
| 324 | D4 | — | 212 | 1 | no | — |
| 325 | C2×C4 | — | 2 | 1 | no | — |
| 326 | C2×C4 | — | 4 | 1 | no | — |
| 327 | C2×C4 | — | 424 | 1 | no | — |
| 328 | C2×C4 | — | 424 | 1 | no | — |
| 329 | C2×C4 | — | 424 | 1 | no | — |
| 330 | C2×C4 | — | 212 | 1 | no | — |
| 331 | C2×C4 | — | 212 | 1 | no | — |
| 332 | C2×C4 | #13133187 | 1 | 1 | yes | characteristic |
| 333 | C8 | — | 4 | 2 | no | — |
| 334 | C8 | — | 4 | 1 | no | — |
| 335 | C8 | — | 212 | 1 | no | — |
| 336 | C8 | D8×D53 | 1 | 1 | yes | characteristic |
| 337 | C8 | C2×D424 | 1 | 1 | yes | characteristic |
| 338 | C8 | #13133244 | 1 | 1 | yes | characteristic |
| 339 | C8 | #13133245 | 1 | 1 | yes | characteristic |
| 340 | C22 | — | 4 | 1 | no | — |
| 341 | C22 | — | 848 | 1 | no | — |
| 342 | C22 | — | 848 | 1 | no | — |
| 343 | C22 | — | 848 | 1 | no | — |
| 344 | C22 | — | 848 | 1 | no | — |
| 345 | C22 | — | 1696 | 1 | no | — |
| 346 | C22 | — | 424 | 1 | no | — |
| 347 | C22 | — | 212 | 1 | no | — |
| 348 | C22 | #16810792 | 1 | 1 | yes | characteristic |
| 349 | C4 | — | 2 | 2 | no | — |
| 350 | C4 | — | 4 | 1 | no | — |
| 351 | C4 | — | 424 | 1 | no | — |
| 352 | C4 | — | 212 | 1 | no | — |
| 353 | C4 | #16810758 | 1 | 1 | yes | characteristic |
| 354 | C4 | #16810759 | 1 | 1 | yes | characteristic |
| 355 | C2 | — | 2 | 1 | no | — |
| 356 | C2 | — | 8 | 1 | no | — |
| 357 | C2 | — | 848 | 1 | no | — |
| 358 | C2 | — | 1696 | 1 | no | — |
| 359 | C2 | — | 424 | 1 | no | — |
| 360 | C2 | #20273771 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20286509 | C2 | semidirect |
| 2. #20276792 | C2 | semidirect |
| 3. #20276791 | C2 | semidirect |
| 4. #20274381 | C2 | semidirect |
| 5. #20272755 | C2 | semidirect |
| 6. #20272692 | C2 | semidirect |
| 7. C53×#1336 | C2 | semidirect |
| 13. #16811000 | C22 | semidirect |
| 21. #16810444 | C22 | semidirect |
| 25. C53×#364 | C22 | semidirect |
| 26. C53×#322 | C22 | semidirect |
| 86. Q16×C53 | D8 | semidirect |
| 88. D8×C53 | D8 | semidirect |
| 103. Dic212 | D8 | semidirect |
| 110. D424 | D8 | semidirect |
| 181. #1336 | D53 | semidirect |
| 203. #364 | C2×D53 | semidirect |
| 206. #322 | C2×D53 | semidirect |
| 207. C53 | #12314 | semidirect |
| 270. Q16 | D424 | semidirect |
| 289. D8 | D424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286509 | 2 |
| #20276792 | 2 |
| #20276791 | 2 |
| #20274381 | 2 |
| #20272755 | 2 |
| #20272692 | 2 |
| C53×#1336 | 2 |
| #12314 | 53 |