Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
902 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 902 conjugacy classes of subgroups — too many to draw. Only its 143 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 | #20284219 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #20284088 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #20276166 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #20275990 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #20275824 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20275246 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #20275199 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #20274678 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C53×#2098 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #16811459 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#13133245 | C22 | 1 | 2 | yes | — |
| 12 | C2×#13133242 | C22 | 1 | 2 | yes | — |
| 13 | C22×D424 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | #16811192 | C22 | 1 | 2 | yes | — |
| 15 | #16811097 | C22 | 1 | 2 | yes | complemented |
| 16 | #16810839 | — | 2 | 4 | no | — |
| 17 | #16810819 | — | 2 | 4 | no | — |
| 18 | #16810797 | — | 2 | 4 | no | — |
| 19 | #16810792 | — | 2 | 4 | no | — |
| 20 | #16810641 | C22 | 1 | 2 | yes | — |
| 21 | #16810639 | C22 | 1 | 2 | yes | — |
| 22 | #16810629 | C22 | 1 | 2 | yes | complemented |
| 23 | #16810620 | C22 | 1 | 2 | yes | — |
| 24 | #16810605 | C22 | 1 | 2 | yes | — |
| 25 | C2×#13133133 | C22 | 1 | 2 | yes | complemented |
| 26 | #16810597 | C22 | 1 | 1 | yes | characteristic |
| 27 | #16810395 | C22 | 1 | 2 | yes | complemented |
| 28 | #16810388 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #16810379 | C22 | 1 | 2 | yes | complemented |
| 30 | C53×#430 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | C53×#424 | C22 | 1 | 2 | yes | complemented |
| 32 | C53×#421 | C22 | 1 | 2 | yes | — |
| 33 | C53×#408 | C22 | 1 | 1 | yes | characteristic |
| 34 | C53×H(3,ℤ/4) | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | #13133265 | — | 2 | 1 | no | — |
| 36 | #13133264 | — | 2 | 2 | no | — |
| 37 | #13133263 | — | 2 | 2 | no | — |
| 38 | #13133262 | — | 2 | 1 | no | — |
| 39 | #13133262 | — | 4 | 1 | no | — |
| 40 | C2×#11719945 | — | 4 | 1 | no | — |
| 41 | C2×#11719945 | C23 | 1 | 2 | yes | — |
| 42 | #41×D53 | — | 4 | 2 | no | — |
| 43 | C22×D212 | C23 | 1 | 2 | yes | — |
| 44 | #13133245 | — | 2 | 4 | no | — |
| 45 | #13133245 | — | 4 | 2 | no | — |
| 46 | #13133242 | — | 2 | 4 | no | — |
| 47 | #13133242 | — | 4 | 2 | no | — |
| 48 | C2×#11719913 | — | 2 | 2 | no | — |
| 49 | C2×#11719924 | — | 2 | 2 | no | — |
| 50 | C2×D424 | — | 2 | 2 | no | — |
| 51 | C2×D424 | — | 2 | 4 | no | — |
| 52 | C2×D424 | — | 4 | 1 | no | — |
| 53 | C2×#11719922 | — | 2 | 2 | no | — |
| 54 | C2×#11719917 | C23 | 1 | 2 | yes | — |
| 55 | #13133214 | D4 | 1 | 4 | yes | complemented |
| 56 | #13133205 | D4 | 1 | 4 | yes | complemented |
| 57 | #13133192 | — | 4 | 2 | no | — |
| 58 | #13133187 | — | 4 | 2 | no | — |
| 59 | C4×D212 | — | 2 | 4 | no | — |
| 60 | #13133179 | — | 4 | 2 | no | — |
| 61 | #13133176 | C23 | 1 | 2 | yes | — |
| 62 | C22⋊C4×D53 | — | 4 | 2 | no | — |
| 63 | #13133145 | — | 2 | 4 | no | — |
| 64 | #13133143 | — | 4 | 2 | no | — |
| 65 | #13133142 | — | 2 | 2 | no | — |
| 66 | #13133139 | — | 2 | 2 | no | — |
| 67 | #13133139 | — | 2 | 4 | no | — |
| 68 | #13133135 | — | 2 | 2 | no | — |
| 69 | #13133133 | — | 2 | 2 | no | — |
| 70 | #13133133 | — | 4 | 2 | no | — |
| 71 | #13133132 | — | 4 | 1 | no | — |
| 72 | C2×#41×C53 | C23 | 1 | 1 | yes | characteristic |
| 73 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×M16×C53 | C23 | 1 | 2 | yes | — |
| 75 | C22×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 76 | #117×C53 | C23 | 1 | 2 | yes | — |
| 77 | #108×C53 | — | 4 | 1 | no | — |
| 78 | C4⋊C8×C53 | — | 2 | 4 | no | — |
| 79 | #104×C53 | — | 2 | 4 | no | — |
| 80 | C22⋊C8×C53 | — | 4 | 1 | no | — |
| 81 | C23×D53 | — | 2 | 2 | no | — |
| 82 | #41×C53 | — | 2 | 2 | no | — |
| 83 | #41×C53 | — | 2 | 2 | no | — |
| 84 | C2×Q8×C53 | #41 | 1 | 1 | yes | characteristic |
| 85 | C2×D4×C53 | — | 2 | 1 | no | — |
| 86 | C2×D4×C53 | #41 | 1 | 1 | yes | characteristic |
| 87 | C22×C4×C53 | — | 2 | 1 | no | — |
| 88 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 89 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 90 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 91 | #11719949 | — | 4 | 2 | no | — |
| 92 | Q8×D53 | — | 4 | 2 | no | — |
| 93 | #11719947 | — | 4 | 2 | no | — |
| 94 | #11719947 | — | 4 | 4 | no | — |
| 95 | D4×D53 | — | 4 | 2 | no | — |
| 96 | D4×D53 | — | 4 | 4 | no | — |
| 97 | #11719945 | — | 2 | 2 | no | — |
| 98 | #11719945 | — | 2 | 2 | no | — |
| 99 | #11719945 | — | 2 | 2 | no | — |
| 100 | #11719945 | — | 2 | 2 | no | — |
| 101 | #11719945 | — | 4 | 2 | no | — |
| 102 | #11719945 | — | 4 | 2 | no | — |
| 103 | #11719945 | — | 4 | 2 | no | — |
| 104 | C2×D212 | — | 2 | 2 | no | — |
| 105 | C2×D212 | — | 2 | 2 | no | — |
| 106 | C2×D212 | — | 2 | 2 | no | — |
| 107 | C2×D212 | — | 2 | 2 | no | — |
| 108 | C2×D212 | — | 2 | 2 | no | — |
| 109 | C2×D212 | — | 4 | 1 | no | — |
| 110 | C2×D212 | — | 4 | 4 | no | — |
| 111 | C2×D212 | C2×D4 | 1 | 2 | yes | — |
| 112 | C2×D212 | C2×D4 | 1 | 4 | yes | — |
| 113 | C2×C4×D53 | — | 2 | 2 | no | — |
| 114 | C2×C4×D53 | — | 4 | 2 | no | — |
| 115 | C2×C4×D53 | — | 4 | 4 | no | — |
| 116 | C2×Dic106 | — | 4 | 1 | no | — |
| 117 | C2×Dic106 | C2×D4 | 1 | 2 | yes | — |
| 118 | M16×C53 | — | 2 | 2 | no | — |
| 119 | M16×C53 | — | 2 | 2 | no | — |
| 120 | M16×C53 | — | 2 | 2 | no | — |
| 121 | C2×C8×C53 | — | 2 | 2 | no | — |
| 122 | C2×C8×C53 | — | 2 | 2 | no | — |
| 123 | C2×C8×C53 | — | 2 | 1 | no | — |
| 124 | C2×C8×C53 | — | 2 | 1 | no | — |
| 125 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 126 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 127 | C42×C53 | C2×D4 | 1 | 4 | yes | — |
| 128 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 129 | #11719924 | — | 4 | 4 | no | — |
| 130 | #11719922 | — | 4 | 4 | no | — |
| 131 | #11719921 | — | 4 | 4 | no | — |
| 132 | #11719921 | — | 4 | 4 | no | — |
| 133 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 134 | C4×Dic53 | — | 2 | 2 | no | — |
| 135 | #11719917 | — | 2 | 2 | no | — |
| 136 | #11719917 | — | 2 | 2 | no | — |
| 137 | C2×#88322 | — | 2 | 2 | no | — |
| 138 | D424 | — | 4 | 4 | no | — |
| 139 | D424 | — | 4 | 4 | no | — |
| 140 | #11719913 | — | 4 | 4 | no | — |
| 141 | C23×C53 | — | 2 | 1 | no | — |
| 142 | C23×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 143 | C22×D53 | — | 2 | 2 | no | — |
| 144 | C22×D53 | — | 2 | 4 | no | — |
| 145 | C22×D53 | — | 4 | 2 | no | — |
| 146 | C22×D53 | — | 4 | 2 | no | — |
| 147 | C22×D53 | — | 4 | 2 | no | — |
| 148 | C22×D53 | — | 16 | 2 | no | — |
| 149 | Q8×C53 | — | 2 | 2 | no | — |
| 150 | D4×C53 | — | 2 | 2 | no | — |
| 151 | D4×C53 | — | 4 | 2 | no | — |
| 152 | C2×C4×C53 | — | 2 | 4 | no | — |
| 153 | C2×C4×C53 | — | 2 | 1 | no | — |
| 154 | C2×C4×C53 | — | 4 | 1 | no | — |
| 155 | C2×C4×C53 | — | 4 | 1 | no | — |
| 156 | C2×C4×C53 | C22×D4 | 1 | 2 | yes | — |
| 157 | C2×C4×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 158 | C2×C4×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 159 | C2×C4×C53 | H(5,𝔽2) | 1 | 2 | yes | — |
| 160 | C22⋊D53 | — | 4 | 4 | no | — |
| 161 | C22⋊D53 | — | 4 | 2 | no | — |
| 162 | C22⋊D53 | — | 4 | 2 | no | — |
| 163 | C2×Dic53 | — | 2 | 2 | no | — |
| 164 | C2×Dic53 | — | 4 | 2 | no | — |
| 165 | C2×Dic53 | — | 4 | 2 | no | — |
| 166 | D212 | — | 2 | 4 | no | — |
| 167 | D212 | — | 2 | 2 | no | — |
| 168 | D212 | — | 2 | 4 | no | — |
| 169 | D212 | — | 2 | 2 | no | — |
| 170 | D212 | — | 4 | 2 | no | — |
| 171 | D212 | — | 4 | 2 | no | — |
| 172 | D212 | — | 4 | 2 | no | — |
| 173 | D212 | — | 16 | 4 | no | — |
| 174 | C4×D53 | — | 4 | 4 | no | — |
| 175 | C4×D53 | — | 4 | 2 | no | — |
| 176 | C4×D53 | — | 4 | 2 | no | — |
| 177 | C4×D53 | — | 16 | 4 | no | — |
| 178 | Dic106 | — | 2 | 2 | no | — |
| 179 | Dic106 | — | 2 | 2 | no | — |
| 180 | Dic106 | — | 4 | 2 | no | — |
| 181 | C8×C53 | — | 4 | 2 | no | — |
| 182 | C8×C53 | — | 4 | 1 | no | — |
| 183 | C8×C53 | — | 4 | 1 | no | — |
| 184 | #88322 | — | 4 | 2 | no | — |
| 185 | #30441 | — | 53 | 1 | no | maximal, Sylow |
| 186 | C22×C53 | — | 4 | 1 | no | — |
| 187 | C22×C53 | — | 4 | 1 | no | — |
| 188 | C22×C53 | — | 8 | 1 | no | — |
| 189 | C22×C53 | #534 | 1 | 2 | yes | — |
| 190 | C22×C53 | #538 | 1 | 1 | yes | characteristic |
| 191 | C2×D53 | — | 4 | 2 | no | — |
| 192 | C2×D53 | — | 4 | 4 | no | — |
| 193 | C2×D53 | — | 8 | 4 | no | — |
| 194 | C2×D53 | — | 8 | 2 | no | — |
| 195 | C2×D53 | — | 8 | 4 | no | — |
| 196 | C2×D53 | — | 16 | 2 | no | — |
| 197 | C2×D53 | — | 16 | 2 | no | — |
| 198 | C4×C53 | — | 4 | 4 | no | — |
| 199 | C4×C53 | — | 4 | 1 | no | — |
| 200 | C4×C53 | D42 | 1 | 1 | yes | characteristic |
| 201 | C4×C53 | #546 | 1 | 2 | yes | — |
| 202 | C4×C53 | #560 | 1 | 1 | yes | characteristic |
| 203 | Dic53 | — | 4 | 2 | no | — |
| 204 | Dic53 | — | 8 | 2 | no | — |
| 205 | #3041 | — | 53 | 2 | no | — |
| 206 | #3021 | — | 53 | 2 | no | — |
| 207 | #2098 | D53 | 1 | 1 | yes | characteristic, complemented |
| 208 | #2080 | — | 53 | 2 | no | — |
| 209 | #2048 | — | 53 | 2 | no | — |
| 210 | #2018 | — | 53 | 1 | no | — |
| 211 | #1911 | — | 53 | 2 | no | — |
| 212 | #1904 | — | 53 | 2 | no | — |
| 213 | #1794 | — | 53 | 1 | no | — |
| 214 | C2×C53 | — | 2 | 2 | no | — |
| 215 | C2×C53 | — | 2 | 1 | no | — |
| 216 | C2×C53 | — | 8 | 1 | no | — |
| 217 | C2×C53 | #2668 | 1 | 1 | yes | characteristic |
| 218 | D53 | — | 8 | 4 | no | — |
| 219 | D53 | — | 8 | 2 | no | — |
| 220 | #585 | — | 53 | 1 | no | — |
| 221 | C2×AGL(1,ℤ/8) | — | 53 | 2 | no | — |
| 222 | C2×AGL(1,ℤ/8) | — | 53 | 2 | no | — |
| 223 | C22×D8 | — | 53 | 1 | no | — |
| 224 | #535 | — | 53 | 2 | no | — |
| 225 | #518 | — | 53 | 2 | no | — |
| 226 | #463 | — | 106 | 4 | no | — |
| 227 | #459 | — | 106 | 4 | no | — |
| 228 | #454 | — | 106 | 4 | no | — |
| 229 | #453 | — | 106 | 4 | no | — |
| 230 | #430 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 231 | #424 | C2×D53 | 1 | 2 | yes | complemented |
| 232 | #421 | — | 53 | 2 | no | — |
| 233 | #421 | — | 53 | 2 | no | — |
| 234 | #421 | C2×D53 | 1 | 2 | yes | — |
| 235 | #418 | — | 53 | 2 | no | — |
| 236 | #416 | — | 53 | 2 | no | — |
| 237 | #413 | — | 53 | 2 | no | — |
| 238 | C2×#100 | — | 53 | 2 | no | — |
| 239 | #410 | — | 53 | 1 | no | — |
| 240 | #408 | C2×D53 | 1 | 1 | yes | characteristic |
| 241 | #344 | — | 53 | 2 | no | — |
| 242 | #341 | — | 53 | 1 | no | — |
| 243 | H(3,ℤ/4) | — | 53 | 2 | no | — |
| 244 | H(3,ℤ/4) | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 245 | C53 | #30441 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 246 | 2−1+4 | — | 106 | 2 | no | — |
| 247 | 2−1+4 | — | 106 | 1 | no | — |
| 248 | H(5,𝔽2) | — | 106 | 2 | no | — |
| 249 | H(5,𝔽2) | — | 106 | 1 | no | — |
| 250 | H(5,𝔽2) | — | 212 | 1 | no | — |
| 251 | C2×#41 | — | 53 | 2 | no | — |
| 252 | C2×#41 | — | 212 | 1 | no | — |
| 253 | C2×#41 | — | 212 | 2 | no | — |
| 254 | C2×#41 | C22×D53 | 1 | 1 | yes | characteristic |
| 255 | C22×D4 | — | 53 | 2 | no | — |
| 256 | AGL(1,ℤ/8) | — | 106 | 4 | no | — |
| 257 | AGL(1,ℤ/8) | — | 106 | 4 | no | — |
| 258 | AGL(1,ℤ/8) | — | 212 | 2 | no | — |
| 259 | AGL(1,ℤ/8) | — | 212 | 2 | no | — |
| 260 | C2×SD16 | — | 106 | 2 | no | — |
| 261 | C2×SD16 | — | 106 | 2 | no | — |
| 262 | C2×D8 | — | 106 | 4 | no | — |
| 263 | C2×D8 | — | 106 | 2 | no | — |
| 264 | C2×D8 | — | 106 | 2 | no | — |
| 265 | C2×D8 | — | 212 | 1 | no | — |
| 266 | C2×M16 | — | 53 | 2 | no | — |
| 267 | C2×M16 | C22×D53 | 1 | 2 | yes | — |
| 268 | C2×M16 | C22×D53 | 1 | 1 | yes | characteristic |
| 269 | C22×C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 270 | #127 | — | 53 | 4 | no | — |
| 271 | #124 | — | 53 | 4 | no | — |
| 272 | #121 | — | 212 | 2 | no | — |
| 273 | #120 | — | 212 | 2 | no | — |
| 274 | C4×D4 | — | 106 | 4 | no | — |
| 275 | C4×D4 | — | 212 | 2 | no | — |
| 276 | #117 | — | 53 | 2 | no | — |
| 277 | #117 | C22×D53 | 1 | 2 | yes | — |
| 278 | C2×C22⋊C4 | — | 212 | 2 | no | — |
| 279 | #108 | — | 4 | 1 | no | — |
| 280 | C4⋊C8 | — | 2 | 4 | no | — |
| 281 | #104 | — | 2 | 4 | no | — |
| 282 | #104 | — | 106 | 4 | no | — |
| 283 | #104 | — | 212 | 2 | no | — |
| 284 | #103 | — | 106 | 2 | no | — |
| 285 | #102 | — | 106 | 2 | no | — |
| 286 | #102 | — | 106 | 4 | no | — |
| 287 | #101 | — | 106 | 2 | no | — |
| 288 | #100 | — | 106 | 2 | no | — |
| 289 | #100 | — | 212 | 2 | no | — |
| 290 | #99 | — | 212 | 1 | no | — |
| 291 | C22⋊C8 | — | 4 | 1 | no | — |
| 292 | C24 | — | 106 | 2 | no | — |
| 293 | #41 | — | 2 | 2 | no | — |
| 294 | #41 | — | 2 | 2 | no | — |
| 295 | #41 | — | 106 | 2 | no | — |
| 296 | #41 | — | 106 | 2 | no | — |
| 297 | #41 | — | 106 | 2 | no | — |
| 298 | #41 | — | 106 | 2 | no | — |
| 299 | #41 | — | 212 | 2 | no | — |
| 300 | #41 | — | 212 | 2 | no | — |
| 301 | #41 | — | 212 | 2 | no | — |
| 302 | #41 | — | 212 | 4 | no | — |
| 303 | #41 | — | 212 | 2 | no | — |
| 304 | #41 | — | 212 | 2 | no | — |
| 305 | C2×Q8 | — | 53 | 2 | no | — |
| 306 | C2×Q8 | — | 212 | 1 | no | — |
| 307 | C2×Q8 | — | 212 | 2 | no | — |
| 308 | C2×Q8 | #11719949 | 1 | 1 | yes | characteristic |
| 309 | C2×D4 | — | 2 | 1 | no | — |
| 310 | C2×D4 | — | 53 | 2 | no | — |
| 311 | C2×D4 | — | 53 | 4 | no | — |
| 312 | C2×D4 | — | 106 | 2 | no | — |
| 313 | C2×D4 | — | 106 | 2 | no | — |
| 314 | C2×D4 | — | 106 | 2 | no | — |
| 315 | C2×D4 | — | 106 | 2 | no | — |
| 316 | C2×D4 | — | 106 | 2 | no | — |
| 317 | C2×D4 | — | 106 | 2 | no | — |
| 318 | C2×D4 | — | 212 | 4 | no | — |
| 319 | C2×D4 | — | 212 | 1 | no | — |
| 320 | C2×D4 | — | 212 | 2 | no | — |
| 321 | C2×D4 | — | 212 | 4 | no | — |
| 322 | C2×D4 | — | 212 | 2 | no | — |
| 323 | C2×D4 | #11719949 | 1 | 1 | yes | characteristic |
| 324 | C22×C4 | — | 2 | 1 | no | — |
| 325 | C22×C4 | — | 106 | 2 | no | — |
| 326 | C22×C4 | — | 212 | 4 | no | — |
| 327 | C22×C4 | — | 212 | 2 | no | — |
| 328 | C22×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 329 | SD16 | — | 212 | 4 | no | — |
| 330 | SD16 | — | 212 | 4 | no | — |
| 331 | D8 | — | 212 | 4 | no | — |
| 332 | D8 | — | 212 | 4 | no | — |
| 333 | D8 | — | 212 | 4 | no | — |
| 334 | M16 | — | 2 | 2 | no | — |
| 335 | M16 | — | 2 | 2 | no | — |
| 336 | M16 | — | 2 | 2 | no | — |
| 337 | M16 | — | 106 | 2 | no | — |
| 338 | M16 | — | 106 | 2 | no | — |
| 339 | C2×C8 | — | 2 | 2 | no | — |
| 340 | C2×C8 | — | 2 | 2 | no | — |
| 341 | C2×C8 | — | 2 | 1 | no | — |
| 342 | C2×C8 | — | 2 | 1 | no | — |
| 343 | C2×C8 | — | 106 | 2 | no | — |
| 344 | C4⋊C4 | — | 2 | 2 | no | — |
| 345 | C4⋊C4 | — | 106 | 2 | no | — |
| 346 | C22⋊C4 | — | 2 | 2 | no | — |
| 347 | C22⋊C4 | — | 106 | 2 | no | — |
| 348 | C22⋊C4 | — | 212 | 4 | no | — |
| 349 | C22⋊C4 | — | 212 | 4 | no | — |
| 350 | C42 | — | 106 | 2 | no | — |
| 351 | C42 | D4×D53 | 1 | 4 | yes | — |
| 352 | C23 | — | 2 | 1 | no | — |
| 353 | C23 | — | 848 | 2 | no | — |
| 354 | C23 | — | 106 | 4 | no | — |
| 355 | C23 | — | 106 | 2 | no | — |
| 356 | C23 | — | 212 | 2 | no | — |
| 357 | C23 | — | 212 | 2 | no | — |
| 358 | C23 | — | 212 | 2 | no | — |
| 359 | C23 | #13133263 | 1 | 1 | yes | characteristic |
| 360 | Q8 | — | 2 | 2 | no | — |
| 361 | Q8 | — | 106 | 2 | no | — |
| 362 | Q8 | — | 106 | 2 | no | — |
| 363 | Q8 | — | 212 | 2 | no | — |
| 364 | D4 | — | 2 | 2 | no | — |
| 365 | D4 | — | 4 | 2 | no | — |
| 366 | D4 | — | 848 | 4 | no | — |
| 367 | D4 | — | 106 | 4 | no | — |
| 368 | D4 | — | 106 | 2 | no | — |
| 369 | D4 | — | 106 | 4 | no | — |
| 370 | D4 | — | 106 | 2 | no | — |
| 371 | D4 | — | 212 | 2 | no | — |
| 372 | D4 | — | 212 | 4 | no | — |
| 373 | D4 | — | 212 | 2 | no | — |
| 374 | D4 | — | 212 | 2 | no | — |
| 375 | D4 | — | 212 | 2 | no | — |
| 376 | D4 | — | 212 | 2 | no | — |
| 377 | C2×C4 | — | 2 | 4 | no | — |
| 378 | C2×C4 | — | 2 | 1 | no | — |
| 379 | C2×C4 | — | 4 | 1 | no | — |
| 380 | C2×C4 | — | 4 | 1 | no | — |
| 381 | C2×C4 | — | 848 | 4 | no | — |
| 382 | C2×C4 | — | 106 | 2 | no | — |
| 383 | C2×C4 | — | 212 | 4 | no | — |
| 384 | C2×C4 | — | 212 | 2 | no | — |
| 385 | C2×C4 | — | 212 | 2 | no | — |
| 386 | C2×C4 | — | 212 | 2 | no | — |
| 387 | C2×C4 | — | 212 | 2 | no | — |
| 388 | C2×C4 | C2×D4×D53 | 1 | 2 | yes | — |
| 389 | C2×C4 | C2×#11719949 | 1 | 1 | yes | characteristic |
| 390 | C2×C4 | #13133262 | 1 | 1 | yes | characteristic |
| 391 | C2×C4 | #13133263 | 1 | 2 | yes | — |
| 392 | C8 | — | 4 | 1 | no | — |
| 393 | C8 | — | 4 | 1 | no | — |
| 394 | C8 | — | 4 | 2 | no | — |
| 395 | C8 | — | 212 | 2 | no | — |
| 396 | C22 | — | 4 | 1 | no | — |
| 397 | C22 | — | 4 | 1 | no | — |
| 398 | C22 | — | 8 | 1 | no | — |
| 399 | C22 | — | 848 | 2 | no | — |
| 400 | C22 | — | 848 | 2 | no | — |
| 401 | C22 | — | 424 | 2 | no | — |
| 402 | C22 | — | 424 | 4 | no | — |
| 403 | C22 | — | 424 | 4 | no | — |
| 404 | C22 | — | 212 | 2 | no | — |
| 405 | C22 | — | 212 | 4 | no | — |
| 406 | C22 | #16811184 | 1 | 2 | yes | — |
| 407 | C22 | #16811213 | 1 | 1 | yes | characteristic |
| 408 | C4 | — | 4 | 4 | no | — |
| 409 | C4 | — | 4 | 1 | no | — |
| 410 | C4 | — | 424 | 2 | no | — |
| 411 | C4 | — | 212 | 2 | no | — |
| 412 | C4 | #16811258 | 1 | 1 | yes | characteristic |
| 413 | C4 | #16811264 | 1 | 2 | yes | — |
| 414 | C4 | #16811363 | 1 | 1 | yes | characteristic |
| 415 | C2 | — | 2 | 2 | no | — |
| 416 | C2 | — | 2 | 1 | no | — |
| 417 | C2 | — | 8 | 1 | no | — |
| 418 | C2 | — | 424 | 2 | no | — |
| 419 | C2 | — | 424 | 4 | no | — |
| 420 | C2 | #20280924 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20284219 | C2 | semidirect |
| 2. #20284088 | C2 | semidirect |
| 3. #20276166 | C2 | semidirect |
| 4. #20275990 | C2 | semidirect |
| 5. #20275824 | C2 | semidirect |
| 6. #20275246 | C2 | semidirect |
| 7. #20275199 | C2 | semidirect |
| 8. #20274678 | C2 | semidirect |
| 9. C53×#2098 | C2 | semidirect |
| 13. C22×D424 | C22 | semidirect |
| 15. #16811097 | C22 | semidirect |
| 22. #16810629 | C22 | semidirect |
| 25. C2×#13133133 | C22 | semidirect |
| 27. #16810395 | C22 | semidirect |
| 28. #16810388 | C22 | semidirect |
| 29. #16810379 | C22 | semidirect |
| 30. C53×#430 | C22 | semidirect |
| 31. C53×#424 | C22 | semidirect |
| 34. C53×H(3,ℤ/4) | C22 | semidirect |
| 55. #13133214 | D4 | semidirect |
| 56. #13133205 | D4 | semidirect |
| 207. #2098 | D53 | semidirect |
| 230. #430 | C2×D53 | semidirect |
| 231. #424 | C2×D53 | semidirect |
| 244. H(3,ℤ/4) | C2×D53 | semidirect |
| 245. C53 | #30441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284219 | 2 |
| #20284088 | 2 |
| #20276166 | 2 |
| #20275990 | 2 |
| #20275824 | 2 |
| #20275246 | 2 |
| #20275199 | 2 |
| #20274678 | 2 |
| C53×#2098 | 2 |
| #30441 | 53 |