Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
936 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 155 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 | C2×#16811373 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20285907 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #20285179 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #20274027 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #20274014 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #20273318 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C53×#1533 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#13133248 | — | 2 | 1 | no | — |
| 9 | C2×#13133243 | — | 2 | 1 | no | — |
| 10 | #16811373 | — | 2 | 4 | no | — |
| 11 | #16811373 | — | 2 | 2 | no | — |
| 12 | #16811373 | C22 | 1 | 4 | yes | — |
| 13 | #16811173 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#13133215 | — | 2 | 1 | no | — |
| 15 | C2×#13133210 | — | 2 | 2 | no | — |
| 16 | C2×#13133209 | C22 | 1 | 2 | yes | — |
| 17 | C2×#13133198 | — | 2 | 1 | no | — |
| 18 | C2×#13133194 | — | 2 | 2 | no | — |
| 19 | #16811032 | C22 | 1 | 4 | yes | complemented |
| 20 | #16811018 | C22 | 1 | 2 | yes | — |
| 21 | #16811013 | C22 | 1 | 2 | yes | — |
| 22 | #16811005 | — | 2 | 2 | no | — |
| 23 | #16810988 | C22 | 1 | 4 | yes | complemented |
| 24 | #16810942 | — | 2 | 2 | no | — |
| 25 | #16810937 | — | 2 | 2 | no | — |
| 26 | #16810924 | — | 2 | 4 | no | — |
| 27 | C4×#11719917 | C22 | 1 | 1 | yes | characteristic |
| 28 | #16810364 | C22 | 1 | 8 | yes | complemented |
| 29 | C2×#124×C53 | C22 | 1 | 1 | yes | characteristic |
| 30 | C53×#432 | C22 | 1 | 2 | yes | — |
| 31 | C53×#329 | C22 | 1 | 4 | yes | — |
| 32 | C2×#11719945 | — | 2 | 1 | no | — |
| 33 | C22×Dic106 | — | 2 | 1 | no | — |
| 34 | C23×Dic53 | — | 2 | 1 | no | — |
| 35 | #13133248 | — | 4 | 4 | no | — |
| 36 | #13133243 | — | 4 | 4 | no | — |
| 37 | C2×#11719925 | — | 2 | 2 | no | — |
| 38 | C2×#11719923 | — | 2 | 2 | no | — |
| 39 | C2×#11719924 | — | 2 | 2 | no | — |
| 40 | C2×#11719922 | — | 2 | 2 | no | — |
| 41 | C2×#11719917 | — | 2 | 1 | no | — |
| 42 | #13133217 | C23 | 1 | 1 | yes | characteristic |
| 43 | #13133215 | — | 2 | 4 | no | — |
| 44 | #13133215 | — | 2 | 4 | no | — |
| 45 | #13133214 | C23 | 1 | 1 | yes | characteristic |
| 46 | #13133210 | — | 2 | 8 | no | — |
| 47 | #13133210 | — | 2 | 8 | no | — |
| 48 | #13133209 | — | 2 | 2 | no | — |
| 49 | #13133209 | — | 2 | 2 | no | — |
| 50 | #13133209 | D4 | 1 | 4 | yes | — |
| 51 | #13133209 | C23 | 1 | 4 | yes | — |
| 52 | #13133205 | — | 2 | 1 | no | — |
| 53 | #13133198 | — | 2 | 4 | no | — |
| 54 | #13133198 | — | 2 | 4 | no | — |
| 55 | #13133194 | — | 2 | 8 | no | — |
| 56 | #13133194 | — | 2 | 8 | no | — |
| 57 | #13133191 | — | 2 | 2 | no | — |
| 58 | C4×D212 | — | 2 | 2 | no | — |
| 59 | C2×C4⋊Dic53 | D4 | 1 | 2 | yes | — |
| 60 | C2×C4⋊Dic53 | D4 | 1 | 2 | yes | — |
| 61 | C2×#11719919 | — | 2 | 2 | no | — |
| 62 | C2×#11719919 | — | 2 | 2 | no | — |
| 63 | C2×#11719919 | — | 2 | 2 | no | — |
| 64 | C2×C22⋊Dic53 | — | 2 | 2 | no | — |
| 65 | C2×C22⋊Dic53 | — | 2 | 1 | no | — |
| 66 | C2×C4×Dic53 | — | 2 | 1 | no | — |
| 67 | #13133151 | — | 2 | 4 | no | — |
| 68 | #13133149 | — | 2 | 4 | no | — |
| 69 | #13133139 | — | 2 | 4 | no | — |
| 70 | #13133139 | — | 2 | 4 | no | — |
| 71 | #13133128 | C23 | 1 | 2 | yes | — |
| 72 | C4×#88322 | — | 2 | 1 | no | — |
| 73 | C22×Q8×C53 | D4 | 1 | 1 | yes | characteristic |
| 74 | C22×D4×C53 | D4 | 1 | 1 | yes | characteristic |
| 75 | #124×C53 | — | 2 | 2 | no | — |
| 76 | #124×C53 | D4 | 1 | 2 | yes | — |
| 77 | #124×C53 | C23 | 1 | 2 | yes | — |
| 78 | C2×C22⋊C4×C53 | — | 2 | 2 | no | — |
| 79 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 80 | C4⋊C8×C53 | — | 2 | 2 | no | — |
| 81 | C22⋊C8×C53 | — | 2 | 2 | no | — |
| 82 | #97×C53 | C23 | 1 | 4 | yes | — |
| 83 | C24×C53 | — | 2 | 1 | no | — |
| 84 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 85 | C2×Q8×C53 | — | 4 | 2 | no | — |
| 86 | C2×Q8×C53 | C2×D4 | 1 | 2 | yes | — |
| 87 | C2×D4×C53 | — | 2 | 1 | no | — |
| 88 | C2×D4×C53 | — | 4 | 2 | no | — |
| 89 | C2×D4×C53 | C2×D4 | 1 | 2 | yes | — |
| 90 | C22×C4×C53 | — | 2 | 1 | no | — |
| 91 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 92 | C22×C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 93 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 94 | C22×Dic53 | — | 2 | 2 | no | — |
| 95 | C22×Dic53 | — | 2 | 2 | no | — |
| 96 | C22×Dic53 | — | 2 | 4 | no | — |
| 97 | C22×Dic53 | — | 8 | 2 | no | — |
| 98 | #11719945 | — | 4 | 2 | no | — |
| 99 | #11719945 | — | 4 | 2 | no | — |
| 100 | C2×D212 | — | 2 | 2 | no | — |
| 101 | C2×D212 | — | 2 | 1 | no | — |
| 102 | C2×C4×D53 | — | 4 | 1 | no | — |
| 103 | C2×Dic106 | — | 2 | 1 | no | — |
| 104 | C2×Dic106 | — | 2 | 4 | no | — |
| 105 | C2×Dic106 | — | 8 | 2 | no | — |
| 106 | C2×C8×C53 | — | 2 | 4 | no | — |
| 107 | C22⋊C4×C53 | — | 2 | 4 | no | — |
| 108 | C22⋊C4×C53 | — | 2 | 4 | no | — |
| 109 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 110 | C42×C53 | C2×D4 | 1 | 2 | yes | — |
| 111 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 112 | C22⋊Dic53 | — | 2 | 8 | no | — |
| 113 | C22⋊Dic53 | — | 2 | 4 | no | — |
| 114 | #11719925 | — | 4 | 4 | no | — |
| 115 | #11719924 | — | 4 | 4 | no | — |
| 116 | #11719923 | — | 4 | 4 | no | — |
| 117 | #11719922 | — | 4 | 4 | no | — |
| 118 | #11719921 | — | 4 | 2 | no | — |
| 119 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 120 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 121 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 122 | C4⋊Dic53 | C2×D4 | 1 | 4 | yes | — |
| 123 | C4⋊Dic53 | C2×D4 | 1 | 4 | yes | — |
| 124 | #11719919 | — | 2 | 8 | no | — |
| 125 | #11719919 | — | 2 | 4 | no | — |
| 126 | #11719919 | — | 2 | 4 | no | — |
| 127 | #11719919 | — | 2 | 4 | no | — |
| 128 | #11719919 | — | 2 | 4 | no | — |
| 129 | C4×Dic53 | — | 2 | 4 | no | — |
| 130 | #11719917 | — | 2 | 4 | no | — |
| 131 | C2×#88322 | — | 2 | 2 | no | — |
| 132 | C23×C53 | — | 2 | 2 | no | — |
| 133 | C23×C53 | — | 4 | 4 | no | — |
| 134 | C23×C53 | — | 4 | 2 | no | — |
| 135 | C23×C53 | #120 | 1 | 1 | yes | characteristic |
| 136 | C22×D53 | — | 4 | 1 | no | — |
| 137 | Q8×C53 | — | 4 | 2 | no | — |
| 138 | Q8×C53 | — | 8 | 1 | no | — |
| 139 | D4×C53 | — | 4 | 2 | no | — |
| 140 | D4×C53 | — | 8 | 1 | no | — |
| 141 | C2×C4×C53 | — | 2 | 2 | no | — |
| 142 | C2×C4×C53 | — | 2 | 2 | no | — |
| 143 | C2×C4×C53 | — | 4 | 2 | no | — |
| 144 | C2×C4×C53 | — | 4 | 2 | no | — |
| 145 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 146 | C2×C4×C53 | #120 | 1 | 2 | yes | — |
| 147 | C2×C4×C53 | C22×D4 | 1 | 2 | yes | — |
| 148 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 149 | C22⋊D53 | — | 8 | 2 | no | — |
| 150 | C2×Dic53 | — | 2 | 4 | no | — |
| 151 | C2×Dic53 | — | 2 | 4 | no | — |
| 152 | C2×Dic53 | — | 4 | 4 | no | — |
| 153 | C2×Dic53 | — | 4 | 4 | no | — |
| 154 | C2×Dic53 | — | 4 | 1 | no | — |
| 155 | C2×Dic53 | — | 8 | 4 | no | — |
| 156 | D212 | — | 4 | 4 | no | — |
| 157 | D212 | — | 4 | 1 | no | — |
| 158 | D212 | — | 4 | 1 | no | — |
| 159 | C4×D53 | — | 8 | 2 | no | — |
| 160 | Dic106 | — | 4 | 1 | no | — |
| 161 | Dic106 | — | 4 | 1 | no | — |
| 162 | Dic106 | — | 8 | 4 | no | — |
| 163 | C8×C53 | — | 4 | 4 | no | — |
| 164 | #88322 | — | 2 | 4 | no | — |
| 165 | #18994 | — | 53 | 1 | no | maximal, Sylow |
| 166 | C22×C53 | — | 2 | 2 | no | — |
| 167 | C22×C53 | — | 4 | 2 | no | — |
| 168 | C22×C53 | — | 4 | 4 | no | — |
| 169 | C22×C53 | — | 8 | 4 | no | — |
| 170 | C22×C53 | #453 | 1 | 2 | yes | — |
| 171 | C22×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 172 | C2×D53 | — | 8 | 1 | no | — |
| 173 | C2×D53 | — | 8 | 2 | no | — |
| 174 | C4×C53 | — | 2 | 1 | no | — |
| 175 | C4×C53 | — | 2 | 1 | no | — |
| 176 | C4×C53 | — | 2 | 2 | no | — |
| 177 | C4×C53 | — | 2 | 2 | no | — |
| 178 | C4×C53 | — | 4 | 2 | no | — |
| 179 | Dic53 | — | 4 | 4 | no | — |
| 180 | Dic53 | — | 4 | 4 | no | — |
| 181 | Dic53 | — | 8 | 1 | no | — |
| 182 | C2×#563 | — | 53 | 1 | no | — |
| 183 | #3234 | — | 53 | 2 | no | — |
| 184 | #3153 | — | 53 | 1 | no | — |
| 185 | #1660 | — | 53 | 4 | no | — |
| 186 | #1657 | — | 53 | 4 | no | — |
| 187 | #1533 | D53 | 1 | 1 | yes | characteristic, complemented |
| 188 | #1528 | — | 53 | 2 | no | — |
| 189 | C2×C53 | — | 2 | 2 | no | — |
| 190 | C2×C53 | — | 8 | 2 | no | — |
| 191 | C2×C53 | C2×#453 | 1 | 1 | yes | characteristic |
| 192 | C2×C53 | #3020 | 1 | 2 | yes | — |
| 193 | D53 | — | 16 | 1 | no | — |
| 194 | C2×#137 | — | 106 | 1 | no | — |
| 195 | C2×AGL(1,ℤ/8) | — | 106 | 1 | no | — |
| 196 | #563 | — | 53 | 4 | no | — |
| 197 | #563 | — | 106 | 4 | no | — |
| 198 | #563 | — | 106 | 2 | no | — |
| 199 | #532 | — | 53 | 1 | no | — |
| 200 | C2×C4⋊Q8 | — | 106 | 1 | no | — |
| 201 | C2×#126 | — | 106 | 2 | no | — |
| 202 | C2×#125 | — | 53 | 2 | no | — |
| 203 | C2×#124 | C2×D53 | 1 | 1 | yes | characteristic |
| 204 | C2×#123 | — | 106 | 1 | no | — |
| 205 | C2×C22⋊Q8 | — | 106 | 2 | no | — |
| 206 | #501 | — | 53 | 4 | no | — |
| 207 | #497 | — | 53 | 2 | no | — |
| 208 | #496 | — | 53 | 2 | no | — |
| 209 | #495 | — | 106 | 2 | no | — |
| 210 | #490 | — | 53 | 4 | no | — |
| 211 | #481 | — | 106 | 2 | no | — |
| 212 | #480 | — | 106 | 2 | no | — |
| 213 | #478 | — | 106 | 4 | no | — |
| 214 | #432 | C2×D53 | 1 | 2 | yes | — |
| 215 | C4×M16 | — | 53 | 1 | no | — |
| 216 | #330 | — | 53 | 8 | no | — |
| 217 | #329 | C2×D53 | 1 | 4 | yes | — |
| 218 | C53 | #18994 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 219 | C2×#41 | — | 106 | 1 | no | — |
| 220 | C22×Q8 | — | 106 | 1 | no | — |
| 221 | C22×Q8 | D212 | 1 | 1 | yes | characteristic |
| 222 | C22×D4 | D212 | 1 | 1 | yes | characteristic |
| 223 | C23×C4 | — | 106 | 1 | no | — |
| 224 | #137 | — | 212 | 4 | no | — |
| 225 | AGL(1,ℤ/8) | — | 212 | 4 | no | — |
| 226 | C2×Q16 | — | 106 | 2 | no | — |
| 227 | C2×SD16 | — | 106 | 2 | no | — |
| 228 | C2×SD16 | — | 106 | 2 | no | — |
| 229 | C2×D8 | — | 106 | 2 | no | — |
| 230 | C2×M16 | — | 106 | 1 | no | — |
| 231 | C4⋊Q8 | — | 53 | 1 | no | — |
| 232 | C4⋊Q8 | — | 106 | 4 | no | — |
| 233 | C4⋊Q8 | — | 106 | 4 | no | — |
| 234 | #127 | — | 53 | 1 | no | — |
| 235 | #126 | — | 106 | 8 | no | — |
| 236 | #126 | — | 106 | 8 | no | — |
| 237 | #125 | — | 53 | 4 | no | — |
| 238 | #125 | — | 53 | 4 | no | — |
| 239 | #125 | — | 106 | 2 | no | — |
| 240 | #125 | — | 106 | 2 | no | — |
| 241 | #124 | — | 2 | 2 | no | — |
| 242 | #124 | — | 106 | 1 | no | — |
| 243 | #124 | D212 | 1 | 2 | yes | — |
| 244 | #124 | C22×D53 | 1 | 2 | yes | — |
| 245 | #123 | — | 106 | 4 | no | — |
| 246 | #123 | — | 106 | 4 | no | — |
| 247 | C22⋊Q8 | — | 106 | 8 | no | — |
| 248 | C22⋊Q8 | — | 106 | 8 | no | — |
| 249 | #121 | — | 106 | 2 | no | — |
| 250 | C4×D4 | — | 106 | 2 | no | — |
| 251 | C2×C4⋊C4 | — | 53 | 2 | no | — |
| 252 | C2×C4⋊C4 | — | 53 | 2 | no | — |
| 253 | C2×C4⋊C4 | — | 106 | 2 | no | — |
| 254 | C2×C4⋊C4 | — | 106 | 2 | no | — |
| 255 | C2×C4⋊C4 | — | 106 | 2 | no | — |
| 256 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 257 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 258 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 259 | C2×C42 | — | 106 | 1 | no | — |
| 260 | C2×C42 | C22×D53 | 1 | 1 | yes | characteristic |
| 261 | #107 | — | 106 | 4 | no | — |
| 262 | #106 | — | 106 | 4 | no | — |
| 263 | C4⋊C8 | — | 2 | 2 | no | — |
| 264 | #102 | — | 106 | 4 | no | — |
| 265 | #102 | — | 106 | 4 | no | — |
| 266 | C22⋊C8 | — | 2 | 2 | no | — |
| 267 | #97 | — | 53 | 2 | no | — |
| 268 | #97 | C22×D53 | 1 | 4 | yes | — |
| 269 | C4×C8 | — | 106 | 1 | no | — |
| 270 | C24 | — | 2 | 1 | no | — |
| 271 | #41 | — | 212 | 2 | no | — |
| 272 | #41 | — | 212 | 2 | no | — |
| 273 | C2×Q8 | — | 2 | 1 | no | — |
| 274 | C2×Q8 | — | 4 | 2 | no | — |
| 275 | C2×Q8 | — | 106 | 4 | no | — |
| 276 | C2×Q8 | — | 106 | 1 | no | — |
| 277 | C2×Q8 | — | 424 | 2 | no | — |
| 278 | C2×Q8 | C2×D212 | 1 | 2 | yes | — |
| 279 | C2×D4 | — | 2 | 1 | no | — |
| 280 | C2×D4 | — | 4 | 2 | no | — |
| 281 | C2×D4 | — | 106 | 2 | no | — |
| 282 | C2×D4 | — | 106 | 1 | no | — |
| 283 | C2×D4 | — | 212 | 1 | no | — |
| 284 | C2×D4 | C2×D212 | 1 | 2 | yes | — |
| 285 | C22×C4 | — | 2 | 1 | no | — |
| 286 | C22×C4 | — | 106 | 4 | no | — |
| 287 | C22×C4 | — | 106 | 2 | no | — |
| 288 | C22×C4 | — | 106 | 2 | no | — |
| 289 | C22×C4 | — | 424 | 2 | no | — |
| 290 | C22×C4 | — | 212 | 1 | no | — |
| 291 | C22×C4 | C2×D212 | 1 | 1 | yes | characteristic |
| 292 | C22×C4 | D4×D53 | 1 | 2 | yes | — |
| 293 | Q16 | — | 212 | 4 | no | — |
| 294 | SD16 | — | 212 | 4 | no | — |
| 295 | SD16 | — | 212 | 4 | no | — |
| 296 | D8 | — | 212 | 4 | no | — |
| 297 | M16 | — | 106 | 4 | no | — |
| 298 | C2×C8 | — | 2 | 4 | no | — |
| 299 | C2×C8 | — | 106 | 2 | no | — |
| 300 | C4⋊C4 | — | 53 | 4 | no | — |
| 301 | C4⋊C4 | — | 53 | 4 | no | — |
| 302 | C4⋊C4 | — | 106 | 8 | no | — |
| 303 | C4⋊C4 | — | 106 | 2 | no | — |
| 304 | C4⋊C4 | — | 106 | 2 | no | — |
| 305 | C4⋊C4 | — | 106 | 4 | no | — |
| 306 | C4⋊C4 | — | 106 | 4 | no | — |
| 307 | C4⋊C4 | — | 106 | 4 | no | — |
| 308 | C4⋊C4 | — | 106 | 4 | no | — |
| 309 | C4⋊C4 | — | 106 | 2 | no | — |
| 310 | C22⋊C4 | — | 2 | 4 | no | — |
| 311 | C22⋊C4 | — | 2 | 4 | no | — |
| 312 | C22⋊C4 | — | 106 | 8 | no | — |
| 313 | C22⋊C4 | — | 106 | 4 | no | — |
| 314 | C22⋊C4 | — | 212 | 2 | no | — |
| 315 | C42 | — | 106 | 4 | no | — |
| 316 | C42 | C2×D212 | 1 | 1 | yes | characteristic |
| 317 | C42 | D4×D53 | 1 | 2 | yes | — |
| 318 | C42 | C23×D53 | 1 | 1 | yes | characteristic |
| 319 | C23 | — | 2 | 2 | no | — |
| 320 | C23 | — | 4 | 4 | no | — |
| 321 | C23 | — | 4 | 2 | no | — |
| 322 | C23 | — | 212 | 1 | no | — |
| 323 | C23 | #13133187 | 1 | 1 | yes | characteristic |
| 324 | Q8 | — | 4 | 2 | no | — |
| 325 | Q8 | — | 8 | 1 | no | — |
| 326 | Q8 | — | 424 | 4 | no | — |
| 327 | Q8 | — | 212 | 1 | no | — |
| 328 | Q8 | — | 212 | 1 | no | — |
| 329 | D4 | — | 4 | 2 | no | — |
| 330 | D4 | — | 8 | 1 | no | — |
| 331 | D4 | — | 424 | 2 | no | — |
| 332 | D4 | — | 212 | 1 | no | — |
| 333 | D4 | — | 212 | 1 | no | — |
| 334 | D4 | — | 212 | 4 | no | — |
| 335 | C2×C4 | — | 2 | 2 | no | — |
| 336 | C2×C4 | — | 2 | 2 | no | — |
| 337 | C2×C4 | — | 4 | 2 | no | — |
| 338 | C2×C4 | — | 4 | 2 | no | — |
| 339 | C2×C4 | — | 106 | 4 | no | — |
| 340 | C2×C4 | — | 106 | 4 | no | — |
| 341 | C2×C4 | — | 424 | 2 | no | — |
| 342 | C2×C4 | — | 424 | 4 | no | — |
| 343 | C2×C4 | — | 212 | 1 | no | — |
| 344 | C2×C4 | — | 212 | 4 | no | — |
| 345 | C2×C4 | — | 212 | 4 | no | — |
| 346 | C2×C4 | #13133187 | 1 | 2 | yes | — |
| 347 | C2×C4 | #13133187 | 1 | 1 | yes | characteristic |
| 348 | C2×C4 | C2×D4×D53 | 1 | 2 | yes | — |
| 349 | C2×C4 | C22×D212 | 1 | 1 | yes | characteristic |
| 350 | C8 | — | 4 | 4 | no | — |
| 351 | C8 | — | 106 | 4 | no | — |
| 352 | C22 | — | 2 | 2 | no | — |
| 353 | C22 | — | 4 | 2 | no | — |
| 354 | C22 | — | 4 | 4 | no | — |
| 355 | C22 | — | 8 | 4 | no | — |
| 356 | C22 | — | 424 | 1 | no | — |
| 357 | C22 | — | 424 | 2 | no | — |
| 358 | C22 | #16810793 | 1 | 2 | yes | — |
| 359 | C22 | C2×#13133187 | 1 | 1 | yes | characteristic |
| 360 | C4 | — | 2 | 1 | no | — |
| 361 | C4 | — | 2 | 1 | no | — |
| 362 | C4 | — | 2 | 2 | no | — |
| 363 | C4 | — | 2 | 2 | no | — |
| 364 | C4 | — | 4 | 2 | no | — |
| 365 | C4 | — | 424 | 1 | no | — |
| 366 | C4 | — | 212 | 4 | no | — |
| 367 | C4 | — | 212 | 4 | no | — |
| 368 | C2 | — | 2 | 2 | no | — |
| 369 | C2 | — | 8 | 2 | no | — |
| 370 | C2 | — | 848 | 1 | no | — |
| 371 | C2 | C2×#16810793 | 1 | 1 | yes | characteristic |
| 372 | C2 | #20284081 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16811373 | C2 | semidirect |
| 2. #20285907 | C2 | semidirect |
| 4. #20274027 | C2 | semidirect |
| 5. #20274014 | C2 | semidirect |
| 6. #20273318 | C2 | semidirect |
| 7. C53×#1533 | C2 | semidirect |
| 19. #16811032 | C22 | semidirect |
| 23. #16810988 | C22 | semidirect |
| 28. #16810364 | C22 | semidirect |
| 187. #1533 | D53 | semidirect |
| 218. C53 | #18994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811373 | 2 |
| #20285907 | 2 |
| #20285179 | 2 |
| #20274027 | 2 |
| #20274014 | 2 |
| #20273318 | 2 |
| C53×#1533 | 2 |
| #18994 | 53 |