Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1198 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1198 conjugacy classes of subgroups — too many to draw. Only its 167 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 | #20288486 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20284807 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #20277998 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20273754 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #20273652 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #20273224 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C53×#1467 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#13133265 | — | 2 | 1 | no | — |
| 9 | #16811295 | — | 2 | 2 | no | — |
| 10 | Q8×D212 | — | 2 | 2 | no | — |
| 11 | #16811285 | — | 2 | 4 | no | — |
| 12 | #16811204 | — | 2 | 1 | no | — |
| 13 | #16811204 | C22 | 1 | 4 | yes | — |
| 14 | #16811173 | — | 2 | 2 | no | — |
| 15 | #16811173 | C22 | 1 | 2 | yes | — |
| 16 | C2×C4×D212 | C22 | 1 | 1 | yes | characteristic |
| 17 | #16810942 | C22 | 1 | 4 | yes | — |
| 18 | #16810914 | — | 2 | 2 | no | — |
| 19 | #16810819 | — | 2 | 2 | no | — |
| 20 | #16810759 | C22 | 1 | 4 | yes | — |
| 21 | #16810736 | — | 2 | 4 | no | — |
| 22 | #16810562 | C22 | 1 | 2 | yes | — |
| 23 | #16810549 | — | 2 | 1 | no | — |
| 24 | #16810540 | C22 | 1 | 2 | yes | — |
| 25 | #16810534 | — | 2 | 1 | no | — |
| 26 | C4×#11719921 | — | 2 | 2 | no | — |
| 27 | #16810469 | C22 | 1 | 1 | yes | characteristic |
| 28 | #16810358 | C22 | 1 | 8 | yes | — |
| 29 | C2×C4×Q8×C53 | C22 | 1 | 1 | yes | characteristic |
| 30 | C53×#432 | C22 | 1 | 2 | yes | — |
| 31 | C53×#324 | C22 | 1 | 4 | yes | — |
| 32 | #13133265 | — | 4 | 8 | no | — |
| 33 | C2×#11719949 | — | 2 | 4 | no | — |
| 34 | C2×#11719945 | — | 2 | 4 | no | — |
| 35 | C2×#11719945 | — | 2 | 2 | no | — |
| 36 | C2×Q8×D53 | — | 2 | 4 | no | — |
| 37 | C22×D212 | C23 | 1 | 1 | yes | characteristic |
| 38 | C22×C4×D53 | — | 2 | 1 | no | — |
| 39 | C2×D424 | — | 2 | 4 | no | — |
| 40 | #13133217 | — | 2 | 2 | no | — |
| 41 | #13133217 | D4 | 1 | 2 | yes | — |
| 42 | #13133214 | — | 2 | 2 | no | — |
| 43 | #13133214 | D4 | 1 | 2 | yes | — |
| 44 | #13133205 | — | 2 | 4 | no | — |
| 45 | #13133205 | — | 2 | 2 | no | — |
| 46 | #13133197 | — | 2 | 4 | no | — |
| 47 | #13133197 | — | 2 | 8 | no | — |
| 48 | #13133192 | — | 2 | 4 | no | — |
| 49 | #13133192 | — | 2 | 8 | no | — |
| 50 | #13133191 | — | 2 | 2 | no | — |
| 51 | #13133191 | — | 2 | 4 | no | — |
| 52 | #13133191 | C23 | 1 | 4 | yes | — |
| 53 | C4×D212 | — | 2 | 4 | no | — |
| 54 | C4×D212 | — | 2 | 4 | no | — |
| 55 | C4×D212 | — | 2 | 2 | no | — |
| 56 | C4×D212 | — | 2 | 2 | no | — |
| 57 | C4×D212 | — | 2 | 2 | no | — |
| 58 | C4×D212 | D4 | 1 | 4 | yes | — |
| 59 | C2×C4⋊Dic53 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×#11719921 | — | 2 | 2 | no | — |
| 61 | C2×#11719921 | — | 2 | 1 | no | — |
| 62 | C2×#11719921 | — | 2 | 2 | no | — |
| 63 | C2×C4×Dic53 | — | 2 | 1 | no | — |
| 64 | #13133149 | — | 2 | 4 | no | — |
| 65 | #13133139 | — | 2 | 4 | no | — |
| 66 | #13133139 | — | 2 | 4 | no | — |
| 67 | #13133124 | — | 2 | 1 | no | — |
| 68 | #13133124 | — | 2 | 2 | no | — |
| 69 | #13133124 | — | 2 | 2 | no | — |
| 70 | #13133124 | C23 | 1 | 2 | yes | — |
| 71 | C22×Q8×C53 | D4 | 1 | 1 | yes | characteristic |
| 72 | C4×Q8×C53 | — | 2 | 2 | no | — |
| 73 | C4×Q8×C53 | — | 2 | 2 | no | — |
| 74 | C2×C4⋊C4×C53 | D4 | 1 | 1 | yes | characteristic |
| 75 | C2×C4⋊C4×C53 | C23 | 1 | 2 | yes | — |
| 76 | C2×C42×C53 | D4 | 1 | 2 | yes | — |
| 77 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 78 | C4⋊C8×C53 | — | 2 | 2 | no | — |
| 79 | C22⋊C8×C53 | C23 | 1 | 4 | yes | — |
| 80 | #97×C53 | — | 2 | 2 | no | — |
| 81 | C23×D53 | — | 2 | 1 | no | — |
| 82 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 83 | C2×Q8×C53 | — | 2 | 4 | no | — |
| 84 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 85 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 86 | C22×C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 87 | C22×C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 88 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 89 | C2×C22⋊D53 | — | 2 | 4 | no | — |
| 90 | C22×Dic53 | — | 2 | 1 | no | — |
| 91 | C22×Dic53 | — | 2 | 2 | no | — |
| 92 | #11719949 | — | 4 | 16 | no | — |
| 93 | Q8×D53 | — | 4 | 16 | no | — |
| 94 | #11719945 | — | 4 | 8 | no | — |
| 95 | #11719945 | — | 4 | 8 | no | — |
| 96 | #11719945 | — | 4 | 8 | no | — |
| 97 | C2×D212 | — | 2 | 2 | no | — |
| 98 | C2×D212 | — | 2 | 4 | no | — |
| 99 | C2×D212 | — | 2 | 2 | no | — |
| 100 | C2×D212 | — | 2 | 2 | no | — |
| 101 | C2×D212 | — | 2 | 4 | no | — |
| 102 | C2×D212 | — | 4 | 2 | no | — |
| 103 | C2×D212 | C2×D4 | 1 | 4 | yes | — |
| 104 | C2×C4×D53 | — | 2 | 8 | no | — |
| 105 | C2×C4×D53 | — | 2 | 4 | no | — |
| 106 | C2×C4×D53 | — | 4 | 4 | no | — |
| 107 | C2×C4×D53 | — | 4 | 1 | no | — |
| 108 | C2×C4×D53 | — | 4 | 1 | no | — |
| 109 | C2×Dic106 | — | 2 | 4 | no | — |
| 110 | C2×Dic106 | — | 2 | 2 | no | — |
| 111 | C2×C8×C53 | — | 2 | 4 | no | — |
| 112 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 113 | C4⋊C4×C53 | — | 2 | 4 | no | — |
| 114 | C42×C53 | — | 2 | 2 | no | — |
| 115 | C42×C53 | — | 2 | 2 | no | — |
| 116 | C42×C53 | C2×D4 | 1 | 2 | yes | — |
| 117 | C42×C53 | C2×D4 | 1 | 2 | yes | — |
| 118 | #11719921 | — | 2 | 8 | no | — |
| 119 | #11719921 | — | 2 | 4 | no | — |
| 120 | #11719921 | — | 2 | 4 | no | — |
| 121 | #11719921 | — | 4 | 4 | no | — |
| 122 | #11719921 | — | 4 | 2 | no | — |
| 123 | #11719921 | — | 4 | 4 | no | — |
| 124 | C4⋊Dic53 | — | 2 | 4 | no | — |
| 125 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 126 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 127 | C4⋊Dic53 | C2×D4 | 1 | 4 | yes | — |
| 128 | C4×Dic53 | — | 4 | 2 | no | — |
| 129 | D424 | — | 4 | 8 | no | — |
| 130 | C23×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 131 | C22×D53 | — | 2 | 2 | no | — |
| 132 | C22×D53 | — | 2 | 4 | no | — |
| 133 | C22×D53 | — | 4 | 2 | no | — |
| 134 | C22×D53 | — | 4 | 1 | no | — |
| 135 | C22×D53 | — | 4 | 1 | no | — |
| 136 | C22×D53 | — | 4 | 2 | no | — |
| 137 | Q8×C53 | — | 2 | 8 | no | — |
| 138 | C2×C4×C53 | — | 2 | 2 | no | — |
| 139 | C2×C4×C53 | — | 2 | 2 | no | — |
| 140 | C2×C4×C53 | — | 2 | 2 | no | — |
| 141 | C2×C4×C53 | — | 2 | 2 | no | — |
| 142 | C2×C4×C53 | — | 2 | 2 | no | — |
| 143 | C2×C4×C53 | — | 4 | 1 | no | — |
| 144 | C2×C4×C53 | — | 4 | 2 | no | — |
| 145 | C2×C4×C53 | #120 | 1 | 2 | yes | — |
| 146 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 147 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 148 | C2×C4×C53 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 149 | C2×C4×C53 | C22×D4 | 1 | 2 | yes | — |
| 150 | C22⋊D53 | — | 4 | 8 | no | — |
| 151 | C2×Dic53 | — | 2 | 4 | no | — |
| 152 | C2×Dic53 | — | 4 | 2 | no | — |
| 153 | C2×Dic53 | — | 4 | 2 | no | — |
| 154 | C2×Dic53 | — | 4 | 2 | no | — |
| 155 | C2×Dic53 | — | 4 | 1 | no | — |
| 156 | C2×Dic53 | — | 4 | 2 | no | — |
| 157 | D212 | — | 2 | 4 | no | — |
| 158 | D212 | — | 4 | 4 | no | — |
| 159 | D212 | — | 4 | 2 | no | — |
| 160 | D212 | — | 4 | 4 | no | — |
| 161 | D212 | — | 4 | 8 | no | — |
| 162 | D212 | — | 4 | 4 | no | — |
| 163 | D212 | — | 8 | 4 | no | — |
| 164 | C4×D53 | — | 4 | 8 | no | — |
| 165 | C4×D53 | — | 4 | 16 | no | — |
| 166 | C4×D53 | — | 8 | 2 | no | — |
| 167 | C4×D53 | — | 8 | 2 | no | — |
| 168 | Dic106 | — | 4 | 4 | no | — |
| 169 | Dic106 | — | 4 | 8 | no | — |
| 170 | C8×C53 | — | 4 | 4 | no | — |
| 171 | #18186 | — | 53 | 1 | no | maximal, Sylow |
| 172 | C22×C53 | — | 2 | 1 | no | — |
| 173 | C22×C53 | — | 2 | 1 | no | — |
| 174 | C22×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 175 | C22×C53 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 176 | C2×D53 | — | 4 | 4 | no | — |
| 177 | C2×D53 | — | 4 | 4 | no | — |
| 178 | C2×D53 | — | 4 | 4 | no | — |
| 179 | C2×D53 | — | 4 | 2 | no | — |
| 180 | C2×D53 | — | 4 | 4 | no | — |
| 181 | C2×D53 | — | 8 | 2 | no | — |
| 182 | C2×D53 | — | 8 | 1 | no | — |
| 183 | C2×D53 | — | 8 | 1 | no | — |
| 184 | C4×C53 | — | 2 | 2 | no | — |
| 185 | C4×C53 | — | 2 | 4 | no | — |
| 186 | C4×C53 | — | 2 | 1 | no | — |
| 187 | C4×C53 | — | 2 | 2 | no | — |
| 188 | C4×C53 | — | 4 | 2 | no | — |
| 189 | C4×C53 | #454 | 1 | 2 | yes | — |
| 190 | Dic53 | — | 4 | 4 | no | — |
| 191 | Dic53 | — | 8 | 2 | no | — |
| 192 | Dic53 | — | 8 | 1 | no | — |
| 193 | #3497 | — | 53 | 1 | no | — |
| 194 | #3109 | — | 53 | 2 | no | — |
| 195 | #2398 | — | 53 | 1 | no | — |
| 196 | #1616 | — | 53 | 4 | no | — |
| 197 | #1598 | — | 53 | 4 | no | — |
| 198 | #1505 | — | 53 | 2 | no | — |
| 199 | #1467 | D53 | 1 | 1 | yes | characteristic, complemented |
| 200 | C2×C53 | — | 2 | 2 | no | — |
| 201 | C2×C53 | #3003 | 1 | 1 | yes | characteristic |
| 202 | C2×C53 | C2×#454 | 1 | 1 | yes | characteristic |
| 203 | C2×C53 | #3025 | 1 | 1 | yes | characteristic |
| 204 | D53 | — | 8 | 4 | no | — |
| 205 | D53 | — | 8 | 2 | no | — |
| 206 | C2×2−1+4 | — | 106 | 1 | no | — |
| 207 | #550 | — | 106 | 2 | no | — |
| 208 | D4×Q8 | — | 106 | 2 | no | — |
| 209 | #548 | — | 106 | 4 | no | — |
| 210 | #537 | — | 53 | 4 | no | — |
| 211 | #537 | — | 106 | 1 | no | — |
| 212 | #532 | — | 53 | 2 | no | — |
| 213 | #532 | — | 106 | 2 | no | — |
| 214 | C2×C4×Q8 | C2×D53 | 1 | 1 | yes | characteristic |
| 215 | C2×C4×D4 | — | 53 | 1 | no | — |
| 216 | #481 | — | 53 | 4 | no | — |
| 217 | #476 | — | 106 | 2 | no | — |
| 218 | #459 | — | 106 | 2 | no | — |
| 219 | #447 | — | 53 | 4 | no | — |
| 220 | #442 | — | 106 | 4 | no | — |
| 221 | #432 | C2×D53 | 1 | 2 | yes | — |
| 222 | #400 | — | 53 | 2 | no | — |
| 223 | #397 | — | 106 | 1 | no | — |
| 224 | #394 | — | 53 | 2 | no | — |
| 225 | #393 | — | 106 | 1 | no | — |
| 226 | C4×C22⋊C4 | — | 106 | 2 | no | — |
| 227 | #376 | — | 53 | 1 | no | — |
| 228 | #327 | — | 53 | 8 | no | — |
| 229 | #324 | C2×D53 | 1 | 4 | yes | — |
| 230 | C53 | #18186 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 231 | 2−1+4 | — | 212 | 8 | no | — |
| 232 | C2×#41 | — | 106 | 4 | no | — |
| 233 | C2×#41 | — | 106 | 2 | no | — |
| 234 | C2×#41 | — | 106 | 4 | no | — |
| 235 | C22×Q8 | — | 106 | 4 | no | — |
| 236 | C22×Q8 | D212 | 1 | 1 | yes | characteristic |
| 237 | C22×D4 | — | 53 | 1 | no | — |
| 238 | C23×C4 | — | 106 | 1 | no | — |
| 239 | C2×D8 | — | 106 | 4 | no | — |
| 240 | C4⋊Q8 | — | 53 | 2 | no | — |
| 241 | C4⋊Q8 | — | 106 | 2 | no | — |
| 242 | #127 | — | 53 | 2 | no | — |
| 243 | #127 | — | 106 | 2 | no | — |
| 244 | #124 | — | 106 | 4 | no | — |
| 245 | #124 | — | 106 | 2 | no | — |
| 246 | C22⋊Q8 | — | 106 | 8 | no | — |
| 247 | C22⋊Q8 | — | 106 | 4 | no | — |
| 248 | #121 | — | 53 | 4 | no | — |
| 249 | #121 | — | 106 | 8 | no | — |
| 250 | #121 | — | 106 | 4 | no | — |
| 251 | #121 | — | 106 | 2 | no | — |
| 252 | #121 | — | 106 | 4 | no | — |
| 253 | C4×Q8 | — | 2 | 2 | no | — |
| 254 | C4×Q8 | — | 2 | 2 | no | — |
| 255 | C4×D4 | — | 53 | 4 | no | — |
| 256 | C4×D4 | — | 106 | 4 | no | — |
| 257 | C4×D4 | — | 106 | 4 | no | — |
| 258 | C4×D4 | — | 106 | 2 | no | — |
| 259 | C4×D4 | — | 106 | 2 | no | — |
| 260 | C4×D4 | — | 106 | 2 | no | — |
| 261 | C2×C4⋊C4 | — | 53 | 1 | no | — |
| 262 | C2×C4⋊C4 | D212 | 1 | 1 | yes | characteristic |
| 263 | C2×C4⋊C4 | C22×D53 | 1 | 2 | yes | — |
| 264 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 265 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 266 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 267 | C2×C42 | — | 106 | 1 | no | — |
| 268 | C2×C42 | D212 | 1 | 2 | yes | — |
| 269 | C2×C42 | C22×D53 | 1 | 1 | yes | characteristic |
| 270 | #106 | — | 106 | 4 | no | — |
| 271 | C4⋊C8 | — | 2 | 2 | no | — |
| 272 | #102 | — | 106 | 4 | no | — |
| 273 | #102 | — | 106 | 4 | no | — |
| 274 | C22⋊C8 | C22×D53 | 1 | 4 | yes | — |
| 275 | #97 | — | 2 | 2 | no | — |
| 276 | #95 | — | 53 | 2 | no | — |
| 277 | #95 | — | 106 | 1 | no | — |
| 278 | #95 | — | 106 | 2 | no | — |
| 279 | #95 | — | 106 | 2 | no | — |
| 280 | C24 | — | 106 | 1 | no | — |
| 281 | #41 | — | 212 | 8 | no | — |
| 282 | #41 | — | 212 | 8 | no | — |
| 283 | #41 | — | 212 | 16 | no | — |
| 284 | #41 | — | 212 | 8 | no | — |
| 285 | C2×Q8 | — | 2 | 2 | no | — |
| 286 | C2×Q8 | — | 2 | 4 | no | — |
| 287 | C2×Q8 | — | 106 | 4 | no | — |
| 288 | C2×Q8 | — | 106 | 2 | no | — |
| 289 | C2×Q8 | — | 212 | 16 | no | — |
| 290 | C2×D4 | — | 53 | 4 | no | — |
| 291 | C2×D4 | — | 106 | 4 | no | — |
| 292 | C2×D4 | — | 106 | 4 | no | — |
| 293 | C2×D4 | — | 106 | 4 | no | — |
| 294 | C2×D4 | — | 106 | 2 | no | — |
| 295 | C2×D4 | — | 106 | 2 | no | — |
| 296 | C2×D4 | — | 106 | 2 | no | — |
| 297 | C2×D4 | — | 212 | 2 | no | — |
| 298 | C22×C4 | — | 106 | 8 | no | — |
| 299 | C22×C4 | — | 106 | 4 | no | — |
| 300 | C22×C4 | — | 106 | 2 | no | — |
| 301 | C22×C4 | — | 106 | 1 | no | — |
| 302 | C22×C4 | — | 212 | 4 | no | — |
| 303 | C22×C4 | — | 212 | 1 | no | — |
| 304 | C22×C4 | — | 212 | 1 | no | — |
| 305 | C22×C4 | C2×D212 | 1 | 1 | yes | characteristic |
| 306 | C22×C4 | C2×D212 | 1 | 1 | yes | characteristic |
| 307 | C22×C4 | C2×D212 | 1 | 2 | yes | — |
| 308 | C22×C4 | C2×D212 | 1 | 2 | yes | — |
| 309 | C22×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 310 | D8 | — | 212 | 8 | no | — |
| 311 | C2×C8 | — | 2 | 4 | no | — |
| 312 | C4⋊C4 | — | 2 | 2 | no | — |
| 313 | C4⋊C4 | — | 2 | 4 | no | — |
| 314 | C4⋊C4 | — | 53 | 4 | no | — |
| 315 | C4⋊C4 | — | 106 | 4 | no | — |
| 316 | C4⋊C4 | — | 106 | 2 | no | — |
| 317 | C4⋊C4 | — | 106 | 2 | no | — |
| 318 | C22⋊C4 | — | 106 | 8 | no | — |
| 319 | C22⋊C4 | — | 106 | 4 | no | — |
| 320 | C22⋊C4 | — | 106 | 4 | no | — |
| 321 | C22⋊C4 | — | 212 | 4 | no | — |
| 322 | C22⋊C4 | — | 212 | 2 | no | — |
| 323 | C22⋊C4 | — | 212 | 4 | no | — |
| 324 | C42 | — | 2 | 2 | no | — |
| 325 | C42 | — | 2 | 2 | no | — |
| 326 | C42 | — | 212 | 2 | no | — |
| 327 | C42 | D4×D53 | 1 | 2 | yes | — |
| 328 | C42 | D4×D53 | 1 | 2 | yes | — |
| 329 | C23 | — | 106 | 2 | no | — |
| 330 | C23 | — | 106 | 4 | no | — |
| 331 | C23 | — | 212 | 2 | no | — |
| 332 | C23 | — | 212 | 1 | no | — |
| 333 | C23 | — | 212 | 1 | no | — |
| 334 | C23 | — | 212 | 2 | no | — |
| 335 | C23 | C22×D212 | 1 | 1 | yes | characteristic |
| 336 | Q8 | — | 2 | 8 | no | — |
| 337 | Q8 | — | 212 | 4 | no | — |
| 338 | Q8 | — | 212 | 8 | no | — |
| 339 | D4 | — | 106 | 4 | no | — |
| 340 | D4 | — | 424 | 4 | no | — |
| 341 | D4 | — | 212 | 4 | no | — |
| 342 | D4 | — | 212 | 2 | no | — |
| 343 | D4 | — | 212 | 4 | no | — |
| 344 | D4 | — | 212 | 8 | no | — |
| 345 | D4 | — | 212 | 8 | no | — |
| 346 | D4 | — | 212 | 4 | no | — |
| 347 | C2×C4 | — | 2 | 2 | no | — |
| 348 | C2×C4 | — | 2 | 2 | no | — |
| 349 | C2×C4 | — | 2 | 2 | no | — |
| 350 | C2×C4 | — | 2 | 2 | no | — |
| 351 | C2×C4 | — | 2 | 2 | no | — |
| 352 | C2×C4 | — | 4 | 1 | no | — |
| 353 | C2×C4 | — | 4 | 2 | no | — |
| 354 | C2×C4 | — | 106 | 4 | no | — |
| 355 | C2×C4 | — | 424 | 2 | no | — |
| 356 | C2×C4 | — | 424 | 2 | no | — |
| 357 | C2×C4 | — | 212 | 8 | no | — |
| 358 | C2×C4 | — | 212 | 16 | no | — |
| 359 | C2×C4 | — | 212 | 2 | no | — |
| 360 | C2×C4 | — | 212 | 2 | no | — |
| 361 | C2×C4 | — | 212 | 2 | no | — |
| 362 | C2×C4 | — | 212 | 1 | no | — |
| 363 | C2×C4 | — | 212 | 2 | no | — |
| 364 | C2×C4 | #13133187 | 1 | 1 | yes | characteristic |
| 365 | C2×C4 | #13133187 | 1 | 2 | yes | — |
| 366 | C2×C4 | #13133187 | 1 | 1 | yes | characteristic |
| 367 | C2×C4 | #13133245 | 1 | 4 | yes | — |
| 368 | C2×C4 | C2×D4×D53 | 1 | 2 | yes | — |
| 369 | C8 | — | 4 | 4 | no | — |
| 370 | C22 | — | 2 | 1 | no | — |
| 371 | C22 | — | 2 | 1 | no | — |
| 372 | C22 | — | 424 | 2 | no | — |
| 373 | C22 | — | 424 | 1 | no | — |
| 374 | C22 | — | 424 | 1 | no | — |
| 375 | C22 | — | 212 | 4 | no | — |
| 376 | C22 | — | 212 | 4 | no | — |
| 377 | C22 | — | 212 | 4 | no | — |
| 378 | C22 | — | 212 | 2 | no | — |
| 379 | C22 | — | 212 | 4 | no | — |
| 380 | C22 | C2×#13133187 | 1 | 1 | yes | characteristic |
| 381 | C22 | C2×#13133245 | 1 | 2 | yes | — |
| 382 | C4 | — | 2 | 2 | no | — |
| 383 | C4 | — | 2 | 4 | no | — |
| 384 | C4 | — | 2 | 1 | no | — |
| 385 | C4 | — | 2 | 2 | no | — |
| 386 | C4 | — | 4 | 2 | no | — |
| 387 | C4 | — | 424 | 2 | no | — |
| 388 | C4 | — | 424 | 1 | no | — |
| 389 | C4 | — | 212 | 4 | no | — |
| 390 | C4 | #16810798 | 1 | 2 | yes | — |
| 391 | C2 | — | 2 | 2 | no | — |
| 392 | C2 | — | 424 | 2 | no | — |
| 393 | C2 | — | 424 | 4 | no | — |
| 394 | C2 | #20283945 | 1 | 1 | yes | characteristic |
| 395 | C2 | C2×#16810798 | 1 | 1 | yes | characteristic |
| 396 | C2 | #20284109 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20288486 | C2 | semidirect |
| 2. #20284807 | C2 | semidirect |
| 3. #20277998 | C2 | semidirect |
| 4. #20273754 | C2 | semidirect |
| 5. #20273652 | C2 | semidirect |
| 6. #20273224 | C2 | semidirect |
| 7. C53×#1467 | C2 | semidirect |
| 199. #1467 | D53 | semidirect |
| 230. C53 | #18186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288486 | 2 |
| #20284807 | 2 |
| #20277998 | 2 |
| #20273754 | 2 |
| #20273652 | 2 |
| #20273224 | 2 |
| C53×#1467 | 2 |
| #18186 | 53 |