Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
530 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 74 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 | #20291216 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20290878 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20290175 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20290136 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20289576 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20289565 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #20285703 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #16811646 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#13133282 | — | 2 | 1 | no | — |
| 10 | C2×#13133282 | — | 2 | 1 | no | — |
| 11 | C4×#11719936 | C22 | 1 | 1 | yes | characteristic |
| 12 | (C2×#6157)⋊Q8 | — | 2 | 1 | no | — |
| 13 | #16811573 | — | 2 | 1 | no | — |
| 14 | #16811573 | — | 2 | 1 | no | — |
| 15 | #16811571 | — | 2 | 1 | no | — |
| 16 | #16811570 | — | 2 | 1 | no | — |
| 17 | #16811568 | C22 | 1 | 1 | yes | characteristic |
| 18 | C4×C4⋊#6157 | C22 | 1 | 1 | yes | characteristic |
| 19 | C22⋊C4×#6157 | — | 2 | 1 | no | — |
| 20 | #16811479 | — | 2 | 1 | no | — |
| 21 | #16811478 | — | 2 | 1 | no | — |
| 22 | #16811475 | — | 2 | 1 | no | — |
| 23 | #16811475 | — | 2 | 1 | no | — |
| 24 | #16811174 | C22 | 1 | 1 | yes | characteristic |
| 25 | #124×D53 | C22 | 1 | 1 | yes | characteristic |
| 26 | #16811013 | C4 | 1 | 1 | yes | characteristic, complemented |
| 27 | #16811012 | C4 | 1 | 1 | yes | characteristic, complemented |
| 28 | #16810985 | C4 | 1 | 1 | yes | characteristic, complemented |
| 29 | #16810841 | — | 2 | 1 | no | — |
| 30 | #16810837 | — | 2 | 1 | no | — |
| 31 | #16810763 | — | 2 | 1 | no | — |
| 32 | #16810758 | — | 2 | 1 | no | — |
| 33 | #16810678 | C22 | 1 | 1 | yes | characteristic |
| 34 | C53×#489 | C4 | 1 | 1 | yes | characteristic, complemented |
| 35 | C23×#6157 | — | 2 | 1 | no | — |
| 36 | C2×#11719936 | — | 2 | 1 | no | — |
| 37 | C2×C4⋊#6157 | — | 2 | 1 | no | — |
| 38 | C2×C4⋊#6157 | — | 2 | 1 | no | — |
| 39 | C2×C22⋊#6157 | — | 2 | 1 | no | — |
| 40 | C2×C22⋊#6157 | — | 2 | 1 | no | — |
| 41 | C2×C22⋊#6157 | — | 2 | 1 | no | — |
| 42 | C2×C4×#6157 | — | 2 | 1 | no | — |
| 43 | C2×C4×#6157 | D4 | 1 | 1 | yes | characteristic |
| 44 | C2×C4×#6157 | D4 | 1 | 1 | yes | characteristic |
| 45 | #13133284 | — | 2 | 1 | no | — |
| 46 | #13133282 | — | 4 | 2 | no | — |
| 47 | #13133282 | — | 4 | 2 | no | — |
| 48 | #13133274 | — | 2 | 1 | no | — |
| 49 | #13133272 | — | 2 | 1 | no | — |
| 50 | #13133272 | — | 2 | 1 | no | — |
| 51 | C4×#88324 | — | 2 | 1 | no | — |
| 52 | (C2×#6157)⋊C4 | — | 2 | 1 | no | — |
| 53 | (C2×#6157)⋊C4 | — | 2 | 1 | no | — |
| 54 | (C2×#6157)⋊C4 | — | 2 | 1 | no | — |
| 55 | (C2×#6157)⋊C4 | — | 2 | 1 | no | — |
| 56 | (C2×#6157)⋊C4 | — | 2 | 1 | no | — |
| 57 | (C2×#6157)⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 58 | (C2×#6157)⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 59 | C2×#11719949 | — | 2 | 1 | no | — |
| 60 | C2×Q8×D53 | D4 | 1 | 1 | yes | characteristic |
| 61 | C2×D4×D53 | D4 | 1 | 1 | yes | characteristic |
| 62 | C2×#11719913 | — | 2 | 1 | no | — |
| 63 | C2×#11719924 | — | 2 | 1 | no | — |
| 64 | C2×D424 | — | 2 | 1 | no | — |
| 65 | C2×#11719922 | — | 2 | 1 | no | — |
| 66 | #13133214 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 67 | #13133206 | — | 2 | 1 | no | — |
| 68 | #13133206 | D4 | 1 | 1 | yes | characteristic |
| 69 | #13133205 | C2×C4 | 1 | 1 | yes | characteristic |
| 70 | #13133204 | D4 | 1 | 1 | yes | characteristic |
| 71 | #13133203 | — | 2 | 1 | no | — |
| 72 | #13133203 | — | 2 | 1 | no | — |
| 73 | #13133192 | — | 2 | 1 | no | — |
| 74 | #13133192 | — | 2 | 1 | no | — |
| 75 | #13133179 | — | 2 | 1 | no | — |
| 76 | #13133179 | — | 2 | 1 | no | — |
| 77 | C22⋊C4×D53 | — | 2 | 1 | no | — |
| 78 | C22⋊C4×D53 | — | 2 | 1 | no | — |
| 79 | C42×D53 | C23 | 1 | 1 | yes | characteristic |
| 80 | #13133146 | — | 2 | 1 | no | — |
| 81 | #13133140 | — | 2 | 1 | no | — |
| 82 | #13133137 | — | 2 | 1 | no | — |
| 83 | #13133129 | — | 2 | 1 | no | — |
| 84 | #13133128 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 85 | C4⋊Q8×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 86 | #124×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 87 | #103×C53 | — | 2 | 1 | no | — |
| 88 | #102×C53 | — | 2 | 1 | no | — |
| 89 | #97×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 90 | C23×D53 | — | 2 | 1 | no | — |
| 91 | C22×#6157 | — | 2 | 1 | no | — |
| 92 | C22×#6157 | — | 2 | 1 | no | — |
| 93 | C22×#6157 | — | 2 | 1 | no | — |
| 94 | C22×#6157 | — | 2 | 1 | no | — |
| 95 | C22×#6157 | — | 4 | 2 | no | — |
| 96 | C22×#6157 | — | 8 | 1 | no | — |
| 97 | C22×#6157 | — | 8 | 1 | no | — |
| 98 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 99 | C2×Q8×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 100 | C2×D4×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 101 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 102 | #11719949 | — | 4 | 1 | no | — |
| 103 | #11719949 | — | 4 | 1 | no | — |
| 104 | #11719949 | — | 4 | 1 | no | — |
| 105 | #11719949 | — | 4 | 1 | no | — |
| 106 | Q8×D53 | — | 8 | 1 | no | — |
| 107 | D4×D53 | — | 8 | 1 | no | — |
| 108 | C2×D212 | — | 2 | 1 | no | — |
| 109 | C2×D212 | — | 2 | 1 | no | — |
| 110 | C2×D212 | — | 2 | 1 | no | — |
| 111 | C2×D212 | — | 4 | 1 | no | — |
| 112 | C2×D212 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 113 | C2×C4×D53 | — | 2 | 1 | no | — |
| 114 | C2×C4×D53 | — | 4 | 1 | no | — |
| 115 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 117 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | C2×Dic106 | — | 2 | 1 | no | — |
| 119 | C2×Dic106 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 120 | C22⋊#6157 | — | 4 | 2 | no | — |
| 121 | C22⋊#6157 | — | 8 | 1 | no | — |
| 122 | C22⋊#6157 | — | 8 | 1 | no | — |
| 123 | C2×#88324 | — | 4 | 1 | no | — |
| 124 | C2×#88324 | — | 4 | 1 | no | — |
| 125 | C4⋊#6157 | — | 4 | 2 | no | — |
| 126 | C4⋊#6157 | — | 8 | 1 | no | — |
| 127 | C4×#6157 | — | 4 | 1 | no | — |
| 128 | C4×#6157 | — | 4 | 1 | no | — |
| 129 | C4×#6157 | — | 8 | 1 | no | — |
| 130 | #11719936 | — | 2 | 2 | no | — |
| 131 | #11719936 | — | 4 | 1 | no | — |
| 132 | C2×C8×C53 | — | 2 | 1 | no | — |
| 133 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 134 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 135 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 136 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 137 | C42×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 138 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 139 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 140 | #11719924 | — | 8 | 1 | no | — |
| 141 | #11719922 | — | 8 | 1 | no | — |
| 142 | #11719921 | — | 2 | 1 | no | — |
| 143 | #11719921 | — | 2 | 1 | no | — |
| 144 | #11719921 | — | 2 | 1 | no | — |
| 145 | #11719921 | — | 2 | 1 | no | — |
| 146 | #11719921 | — | 4 | 1 | no | — |
| 147 | #11719921 | — | 4 | 1 | no | — |
| 148 | C4×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 149 | C4×Dic53 | #41 | 1 | 1 | yes | characteristic |
| 150 | C4×Dic53 | #41 | 1 | 1 | yes | characteristic |
| 151 | C2×#88322 | — | 2 | 1 | no | — |
| 152 | D424 | — | 8 | 1 | no | — |
| 153 | #11719913 | — | 8 | 1 | no | — |
| 154 | C23×C53 | — | 2 | 1 | no | — |
| 155 | C22×D53 | — | 2 | 1 | no | — |
| 156 | C22×D53 | — | 4 | 1 | no | — |
| 157 | C22×D53 | — | 4 | 1 | no | — |
| 158 | C22×D53 | — | 4 | 1 | no | — |
| 159 | C22×D53 | — | 4 | 1 | no | — |
| 160 | C22×D53 | — | 4 | 1 | no | — |
| 161 | C22×D53 | — | 4 | 1 | no | — |
| 162 | C22×D53 | — | 4 | 1 | no | — |
| 163 | C22×D53 | #120 | 1 | 1 | yes | characteristic |
| 164 | C2×#6157 | — | 2 | 2 | no | — |
| 165 | C2×#6157 | — | 4 | 1 | no | — |
| 166 | C2×#6157 | — | 4 | 1 | no | — |
| 167 | C2×#6157 | — | 4 | 1 | no | — |
| 168 | C2×#6157 | — | 4 | 1 | no | — |
| 169 | C2×#6157 | — | 4 | 1 | no | — |
| 170 | C2×#6157 | — | 4 | 1 | no | — |
| 171 | C2×#6157 | — | 4 | 1 | no | — |
| 172 | C2×#6157 | — | 4 | 1 | no | — |
| 173 | C2×#6157 | — | 4 | 1 | no | — |
| 174 | C2×#6157 | — | 4 | 1 | no | — |
| 175 | C2×#6157 | — | 4 | 1 | no | — |
| 176 | C2×#6157 | — | 8 | 4 | no | — |
| 177 | Q8×C53 | — | 4 | 1 | no | — |
| 178 | Q8×C53 | — | 4 | 1 | no | — |
| 179 | Q8×C53 | — | 4 | 1 | no | — |
| 180 | D4×C53 | — | 4 | 1 | no | — |
| 181 | C2×C4×C53 | — | 2 | 1 | no | — |
| 182 | C2×C4×C53 | — | 4 | 1 | no | — |
| 183 | C2×C4×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 184 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 185 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 186 | C22⋊D53 | — | 8 | 1 | no | — |
| 187 | C2×Dic53 | — | 2 | 1 | no | — |
| 188 | C2×Dic53 | #121 | 1 | 1 | yes | characteristic |
| 189 | C2×Dic53 | #121 | 1 | 1 | yes | characteristic |
| 190 | C2×Dic53 | #123 | 1 | 1 | yes | characteristic |
| 191 | D212 | — | 4 | 1 | no | — |
| 192 | D212 | — | 4 | 1 | no | — |
| 193 | D212 | — | 4 | 1 | no | — |
| 194 | D212 | — | 4 | 1 | no | — |
| 195 | D212 | — | 4 | 1 | no | — |
| 196 | D212 | — | 8 | 1 | no | — |
| 197 | D212 | — | 8 | 1 | no | — |
| 198 | D212 | — | 8 | 1 | no | — |
| 199 | C4×D53 | — | 2 | 1 | no | — |
| 200 | C4×D53 | — | 2 | 1 | no | — |
| 201 | C4×D53 | — | 4 | 1 | no | — |
| 202 | C4×D53 | — | 4 | 1 | no | — |
| 203 | C4×D53 | — | 4 | 1 | no | — |
| 204 | C4×D53 | — | 4 | 1 | no | — |
| 205 | C4×D53 | — | 8 | 1 | no | — |
| 206 | C4×D53 | — | 8 | 1 | no | — |
| 207 | Dic106 | — | 4 | 1 | no | — |
| 208 | Dic106 | — | 8 | 1 | no | — |
| 209 | #88324 | — | 4 | 2 | no | — |
| 210 | #88324 | — | 8 | 1 | no | — |
| 211 | C8×C53 | — | 4 | 1 | no | — |
| 212 | #88322 | — | 4 | 1 | no | — |
| 213 | #9381 | — | 53 | 1 | no | maximal, Sylow |
| 214 | C22×C53 | — | 4 | 1 | no | — |
| 215 | C22×C53 | — | 4 | 1 | no | — |
| 216 | C22×C53 | — | 4 | 1 | no | — |
| 217 | C22×C53 | #386 | 1 | 1 | yes | characteristic |
| 218 | C2×D53 | — | 2 | 1 | no | — |
| 219 | C2×D53 | — | 2 | 1 | no | — |
| 220 | C2×D53 | — | 4 | 1 | no | — |
| 221 | C2×D53 | — | 4 | 1 | no | — |
| 222 | C2×D53 | — | 4 | 1 | no | — |
| 223 | C2×D53 | — | 8 | 1 | no | — |
| 224 | C2×D53 | — | 8 | 1 | no | — |
| 225 | C2×D53 | — | 8 | 1 | no | — |
| 226 | C2×D53 | — | 8 | 1 | no | — |
| 227 | C2×D53 | — | 8 | 1 | no | — |
| 228 | C2×D53 | — | 8 | 1 | no | — |
| 229 | C2×D53 | — | 8 | 1 | no | — |
| 230 | C2×D53 | #453 | 1 | 1 | yes | characteristic |
| 231 | C2×D53 | #454 | 1 | 1 | yes | characteristic |
| 232 | #6157 | — | 4 | 2 | no | — |
| 233 | #6157 | — | 8 | 1 | no | — |
| 234 | #6157 | — | 8 | 1 | no | — |
| 235 | #6157 | — | 8 | 1 | no | — |
| 236 | C4×C53 | — | 2 | 1 | no | — |
| 237 | C4×C53 | — | 2 | 1 | no | — |
| 238 | C4×C53 | — | 2 | 1 | no | — |
| 239 | C4×C53 | — | 4 | 1 | no | — |
| 240 | C4×C53 | — | 8 | 1 | no | — |
| 241 | Dic53 | — | 2 | 1 | no | — |
| 242 | Dic53 | — | 2 | 1 | no | — |
| 243 | Dic53 | — | 2 | 1 | no | — |
| 244 | Dic53 | — | 4 | 1 | no | — |
| 245 | #3213 | — | 53 | 1 | no | — |
| 246 | #2337 | — | 53 | 1 | no | — |
| 247 | #1980 | — | 53 | 1 | no | — |
| 248 | #1527 | — | 53 | 1 | no | — |
| 249 | #1514 | — | 53 | 1 | no | — |
| 250 | #1288 | — | 53 | 1 | no | — |
| 251 | #1285 | — | 53 | 1 | no | — |
| 252 | C2×C53 | — | 8 | 1 | no | — |
| 253 | C2×C53 | #1883 | 1 | 1 | yes | characteristic |
| 254 | C2×C53 | #1906 | 1 | 1 | yes | characteristic |
| 255 | C2×C53 | #1911 | 1 | 1 | yes | characteristic |
| 256 | D53 | — | 2 | 1 | no | — |
| 257 | D53 | — | 2 | 1 | no | — |
| 258 | D53 | — | 8 | 1 | no | — |
| 259 | D53 | — | 16 | 1 | no | — |
| 260 | #532 | — | 53 | 1 | no | — |
| 261 | C2×#124 | — | 53 | 1 | no | — |
| 262 | #496 | — | 53 | 1 | no | — |
| 263 | #496 | — | 53 | 1 | no | — |
| 264 | #489 | — | 53 | 1 | no | — |
| 265 | #489 | #6157 | 1 | 1 | yes | characteristic, complemented |
| 266 | #463 | — | 106 | 1 | no | — |
| 267 | #463 | — | 106 | 1 | no | — |
| 268 | #448 | — | 106 | 1 | no | — |
| 269 | #447 | — | 106 | 1 | no | — |
| 270 | #432 | — | 53 | 1 | no | — |
| 271 | #432 | — | 53 | 1 | no | — |
| 272 | C2×#104 | — | 106 | 1 | no | — |
| 273 | C2×#104 | — | 106 | 1 | no | — |
| 274 | C4×M16 | — | 53 | 1 | no | — |
| 275 | #391 | — | 106 | 1 | no | — |
| 276 | #388 | — | 106 | 1 | no | — |
| 277 | #388 | — | 106 | 1 | no | — |
| 278 | #386 | — | 106 | 1 | no | — |
| 279 | #385 | — | 106 | 1 | no | — |
| 280 | #383 | — | 53 | 1 | no | — |
| 281 | C4×C4⋊C4 | — | 53 | 1 | no | — |
| 282 | C4×C22⋊C4 | — | 106 | 1 | no | — |
| 283 | #329 | — | 106 | 1 | no | — |
| 284 | #329 | — | 106 | 1 | no | — |
| 285 | #327 | — | 106 | 1 | no | — |
| 286 | #327 | — | 106 | 1 | no | — |
| 287 | C53 | #9381 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 288 | C2×#41 | — | 106 | 1 | no | — |
| 289 | C22×Q8 | — | 53 | 1 | no | — |
| 290 | C22×D4 | — | 53 | 1 | no | — |
| 291 | C23×C4 | — | 106 | 1 | no | — |
| 292 | C2×SD16 | — | 106 | 1 | no | — |
| 293 | C2×SD16 | — | 106 | 1 | no | — |
| 294 | C2×D8 | — | 106 | 1 | no | — |
| 295 | C2×D8 | — | 106 | 1 | no | — |
| 296 | C2×M16 | — | 106 | 1 | no | — |
| 297 | C4⋊Q8 | C2×#6157 | 1 | 1 | yes | characteristic, complemented |
| 298 | #127 | — | 53 | 1 | no | — |
| 299 | #124 | — | 53 | 1 | no | — |
| 300 | #124 | — | 53 | 1 | no | — |
| 301 | #124 | — | 53 | 1 | no | — |
| 302 | #124 | — | 106 | 1 | no | — |
| 303 | #124 | — | 106 | 1 | no | — |
| 304 | #124 | — | 106 | 1 | no | — |
| 305 | #124 | C2×#6157 | 1 | 1 | yes | characteristic |
| 306 | #121 | — | 106 | 1 | no | — |
| 307 | #121 | — | 106 | 1 | no | — |
| 308 | C4×D4 | — | 106 | 1 | no | — |
| 309 | C4×D4 | — | 106 | 1 | no | — |
| 310 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 311 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 312 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 313 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 314 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 315 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 316 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 317 | C2×C42 | — | 53 | 1 | no | — |
| 318 | C2×C42 | — | 53 | 1 | no | — |
| 319 | C2×C42 | — | 53 | 1 | no | — |
| 320 | C2×C42 | — | 106 | 1 | no | — |
| 321 | C4⋊C8 | — | 106 | 1 | no | — |
| 322 | C4⋊C8 | — | 106 | 1 | no | — |
| 323 | #104 | — | 212 | 2 | no | — |
| 324 | #104 | — | 212 | 2 | no | — |
| 325 | #103 | — | 2 | 1 | no | — |
| 326 | #103 | — | 106 | 1 | no | — |
| 327 | #102 | — | 2 | 1 | no | — |
| 328 | #102 | — | 106 | 1 | no | — |
| 329 | C22⋊C8 | — | 106 | 1 | no | — |
| 330 | C22⋊C8 | — | 106 | 1 | no | — |
| 331 | #97 | — | 53 | 1 | no | — |
| 332 | #97 | — | 106 | 1 | no | — |
| 333 | #97 | — | 106 | 1 | no | — |
| 334 | #97 | C2×#6157 | 1 | 1 | yes | characteristic, complemented |
| 335 | C4×C8 | — | 106 | 1 | no | — |
| 336 | #95 | — | 53 | 1 | no | — |
| 337 | #95 | — | 53 | 1 | no | — |
| 338 | #95 | — | 106 | 1 | no | — |
| 339 | #95 | — | 106 | 1 | no | — |
| 340 | #95 | — | 106 | 1 | no | — |
| 341 | #95 | — | 106 | 1 | no | — |
| 342 | #95 | — | 106 | 1 | no | — |
| 343 | C24 | — | 106 | 1 | no | — |
| 344 | #41 | — | 212 | 1 | no | — |
| 345 | #41 | — | 212 | 1 | no | — |
| 346 | #41 | — | 212 | 1 | no | — |
| 347 | #41 | — | 212 | 1 | no | — |
| 348 | C2×Q8 | — | 2 | 1 | no | — |
| 349 | C2×Q8 | — | 53 | 1 | no | — |
| 350 | C2×Q8 | — | 106 | 1 | no | — |
| 351 | C2×Q8 | — | 424 | 1 | no | — |
| 352 | C2×Q8 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 353 | C2×D4 | — | 53 | 1 | no | — |
| 354 | C2×D4 | — | 106 | 1 | no | — |
| 355 | C2×D4 | — | 106 | 1 | no | — |
| 356 | C2×D4 | — | 106 | 1 | no | — |
| 357 | C2×D4 | — | 106 | 1 | no | — |
| 358 | C2×D4 | — | 424 | 1 | no | — |
| 359 | C2×D4 | — | 212 | 1 | no | — |
| 360 | C2×D4 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 361 | C22×C4 | — | 53 | 1 | no | — |
| 362 | C22×C4 | — | 53 | 1 | no | — |
| 363 | C22×C4 | — | 53 | 1 | no | — |
| 364 | C22×C4 | — | 106 | 1 | no | — |
| 365 | C22×C4 | — | 106 | 1 | no | — |
| 366 | C22×C4 | — | 106 | 1 | no | — |
| 367 | C22×C4 | — | 106 | 1 | no | — |
| 368 | C22×C4 | — | 106 | 1 | no | — |
| 369 | C22×C4 | — | 424 | 1 | no | — |
| 370 | C22×C4 | — | 424 | 1 | no | — |
| 371 | C22×C4 | — | 212 | 1 | no | — |
| 372 | C22×C4 | — | 212 | 2 | no | — |
| 373 | SD16 | — | 424 | 1 | no | — |
| 374 | SD16 | — | 424 | 1 | no | — |
| 375 | D8 | — | 424 | 1 | no | — |
| 376 | D8 | — | 424 | 1 | no | — |
| 377 | M16 | — | 106 | 2 | no | — |
| 378 | M16 | — | 212 | 1 | no | — |
| 379 | C2×C8 | — | 2 | 1 | no | — |
| 380 | C2×C8 | — | 106 | 1 | no | — |
| 381 | C2×C8 | — | 212 | 1 | no | — |
| 382 | C2×C8 | — | 212 | 1 | no | — |
| 383 | C4⋊C4 | — | 2 | 1 | no | — |
| 384 | C4⋊C4 | — | 2 | 1 | no | — |
| 385 | C4⋊C4 | — | 424 | 1 | no | — |
| 386 | C4⋊C4 | — | 212 | 2 | no | — |
| 387 | C22⋊C4 | — | 2 | 1 | no | — |
| 388 | C22⋊C4 | — | 2 | 1 | no | — |
| 389 | C22⋊C4 | — | 106 | 1 | no | — |
| 390 | C22⋊C4 | — | 106 | 1 | no | — |
| 391 | C22⋊C4 | — | 106 | 1 | no | — |
| 392 | C22⋊C4 | — | 106 | 1 | no | — |
| 393 | C22⋊C4 | — | 106 | 1 | no | — |
| 394 | C22⋊C4 | — | 106 | 1 | no | — |
| 395 | C22⋊C4 | — | 424 | 1 | no | — |
| 396 | C22⋊C4 | — | 424 | 1 | no | — |
| 397 | C22⋊C4 | — | 212 | 1 | no | — |
| 398 | C22⋊C4 | — | 212 | 1 | no | — |
| 399 | C22⋊C4 | — | 212 | 2 | no | — |
| 400 | C42 | — | 53 | 1 | no | — |
| 401 | C42 | — | 53 | 1 | no | — |
| 402 | C42 | — | 53 | 1 | no | — |
| 403 | C42 | — | 424 | 1 | no | — |
| 404 | C42 | — | 212 | 1 | no | — |
| 405 | C42 | — | 212 | 1 | no | — |
| 406 | C42 | C22×#6157 | 1 | 1 | yes | characteristic |
| 407 | C23 | — | 2 | 1 | no | — |
| 408 | C23 | — | 53 | 1 | no | — |
| 409 | C23 | — | 106 | 1 | no | — |
| 410 | C23 | — | 212 | 1 | no | — |
| 411 | C23 | — | 212 | 1 | no | — |
| 412 | C23 | — | 212 | 1 | no | — |
| 413 | C23 | — | 212 | 1 | no | — |
| 414 | C23 | — | 212 | 1 | no | — |
| 415 | C23 | — | 212 | 1 | no | — |
| 416 | C23 | — | 212 | 1 | no | — |
| 417 | Q8 | — | 4 | 1 | no | — |
| 418 | Q8 | — | 4 | 1 | no | — |
| 419 | Q8 | — | 4 | 1 | no | — |
| 420 | Q8 | — | 424 | 1 | no | — |
| 421 | Q8 | — | 212 | 1 | no | — |
| 422 | D4 | — | 4 | 1 | no | — |
| 423 | D4 | — | 424 | 1 | no | — |
| 424 | D4 | — | 424 | 1 | no | — |
| 425 | D4 | — | 424 | 1 | no | — |
| 426 | D4 | — | 424 | 1 | no | — |
| 427 | D4 | — | 212 | 1 | no | — |
| 428 | D4 | — | 212 | 1 | no | — |
| 429 | D4 | — | 212 | 1 | no | — |
| 430 | D4 | — | 212 | 1 | no | — |
| 431 | D4 | — | 212 | 1 | no | — |
| 432 | C2×C4 | — | 2 | 1 | no | — |
| 433 | C2×C4 | — | 4 | 1 | no | — |
| 434 | C2×C4 | — | 53 | 1 | no | — |
| 435 | C2×C4 | — | 53 | 1 | no | — |
| 436 | C2×C4 | — | 53 | 1 | no | — |
| 437 | C2×C4 | — | 106 | 1 | no | — |
| 438 | C2×C4 | — | 106 | 1 | no | — |
| 439 | C2×C4 | — | 106 | 2 | no | — |
| 440 | C2×C4 | — | 106 | 1 | no | — |
| 441 | C2×C4 | — | 424 | 1 | no | — |
| 442 | C2×C4 | — | 424 | 1 | no | — |
| 443 | C2×C4 | — | 424 | 4 | no | — |
| 444 | C2×C4 | — | 212 | 1 | no | — |
| 445 | C2×C4 | — | 212 | 1 | no | — |
| 446 | C2×C4 | — | 212 | 1 | no | — |
| 447 | C2×C4 | — | 212 | 1 | no | — |
| 448 | C2×C4 | — | 212 | 1 | no | — |
| 449 | C2×C4 | — | 212 | 1 | no | — |
| 450 | C2×C4 | — | 212 | 1 | no | — |
| 451 | C2×C4 | — | 212 | 1 | no | — |
| 452 | C2×C4 | — | 212 | 1 | no | — |
| 453 | C2×C4 | — | 212 | 1 | no | — |
| 454 | C2×C4 | — | 212 | 1 | no | — |
| 455 | C2×C4 | — | 212 | 1 | no | — |
| 456 | C2×C4 | — | 212 | 1 | no | — |
| 457 | C2×C4 | — | 212 | 1 | no | — |
| 458 | C2×C4 | — | 212 | 1 | no | — |
| 459 | C2×C4 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 460 | C2×C4 | D4×#6157 | 1 | 1 | yes | characteristic |
| 461 | C2×C4 | D4×#6157 | 1 | 1 | yes | characteristic |
| 462 | C8 | — | 4 | 1 | no | — |
| 463 | C8 | — | 424 | 1 | no | — |
| 464 | C8 | — | 212 | 1 | no | — |
| 465 | C8 | — | 212 | 2 | no | — |
| 466 | C22 | — | 4 | 1 | no | — |
| 467 | C22 | — | 4 | 1 | no | — |
| 468 | C22 | — | 4 | 1 | no | — |
| 469 | C22 | — | 53 | 1 | no | — |
| 470 | C22 | — | 53 | 1 | no | — |
| 471 | C22 | — | 106 | 1 | no | — |
| 472 | C22 | — | 106 | 1 | no | — |
| 473 | C22 | — | 424 | 1 | no | — |
| 474 | C22 | — | 424 | 1 | no | — |
| 475 | C22 | — | 424 | 1 | no | — |
| 476 | C22 | — | 424 | 1 | no | — |
| 477 | C22 | — | 424 | 1 | no | — |
| 478 | C22 | — | 424 | 1 | no | — |
| 479 | C22 | — | 424 | 1 | no | — |
| 480 | C22 | — | 212 | 1 | no | — |
| 481 | C22 | — | 212 | 1 | no | — |
| 482 | C22 | — | 212 | 1 | no | — |
| 483 | C22 | #16811571 | 1 | 1 | yes | characteristic |
| 484 | C4 | — | 2 | 1 | no | — |
| 485 | C4 | — | 2 | 1 | no | — |
| 486 | C4 | — | 2 | 1 | no | — |
| 487 | C4 | — | 4 | 1 | no | — |
| 488 | C4 | — | 8 | 1 | no | — |
| 489 | C4 | — | 106 | 1 | no | — |
| 490 | C4 | — | 106 | 1 | no | — |
| 491 | C4 | — | 106 | 1 | no | — |
| 492 | C4 | — | 424 | 1 | no | — |
| 493 | C4 | — | 424 | 1 | no | — |
| 494 | C4 | — | 424 | 1 | no | — |
| 495 | C4 | — | 212 | 2 | no | — |
| 496 | C4 | — | 212 | 1 | no | — |
| 497 | C2 | — | 8 | 1 | no | — |
| 498 | C2 | — | 848 | 1 | no | — |
| 499 | C2 | — | 106 | 1 | no | — |
| 500 | C2 | — | 106 | 1 | no | — |
| 501 | C2 | — | 424 | 1 | no | — |
| 502 | C2 | #20290715 | 1 | 1 | yes | characteristic |
| 503 | C2 | #20290753 | 1 | 1 | yes | characteristic |
| 504 | C2 | #20290760 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20291216 | C2 | semidirect |
| 2. #20290878 | C2 | semidirect |
| 3. #20290175 | C2 | semidirect |
| 4. #20290136 | C2 | semidirect |
| 5. #20289576 | C2 | semidirect |
| 6. #20289565 | C2 | semidirect |
| 26. #16811013 | C4 | semidirect |
| 27. #16811012 | C4 | semidirect |
| 28. #16810985 | C4 | semidirect |
| 34. C53×#489 | C4 | semidirect |
| 66. #13133214 | C2×C4 | semidirect |
| 84. #13133128 | C2×C4 | semidirect |
| 85. C4⋊Q8×C53 | C2×C4 | semidirect |
| 89. #97×C53 | C2×C4 | semidirect |
| 265. #489 | #6157 | semidirect |
| 287. C53 | #9381 | semidirect |
| 297. C4⋊Q8 | C2×#6157 | semidirect |
| 334. #97 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291216 | 2 |
| #20290878 | 2 |
| #20290175 | 2 |
| #20290136 | 2 |
| #20289576 | 2 |
| #20289565 | 2 |
| #20285703 | 2 |
| #9381 | 53 |