← #27539184
Subgroups — #27539184
Order 13568.
548 conjugacy classes of subgroups.
The subgroup lattice has 390 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #20285280 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#16810717 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20276917 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20276882 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #20276776 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #20276651 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #20276631 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #20276585 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #20276576 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #20276515 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C53×#2233 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C22×Dic212 | C22 | 1 | 1 | yes | characteristic |
| 13 | #16811154 | — | 2 | 1 | no | — |
| 14 | C2×#13133182 | — | 2 | 1 | no | — |
| 15 | C2×Dic424 | C22 | 1 | 2 | yes | — |
| 16 | C2×#13133161 | C22 | 1 | 2 | yes | — |
| 17 | #16811024 | C22 | 1 | 1 | yes | characteristic |
| 18 | #16811006 | C22 | 1 | 1 | yes | characteristic |
| 19 | #16810976 | — | 2 | 1 | no | — |
| 20 | #16810864 | C22 | 1 | 1 | yes | characteristic |
| 21 | #16810850 | — | 2 | 1 | no | — |
| 22 | #16810717 | — | 2 | 1 | no | — |
| 23 | #16810717 | — | 2 | 1 | no | — |
| 24 | #16810717 | C22 | 1 | 2 | yes | — |
| 25 | #16810717 | C22 | 1 | 2 | yes | — |
| 26 | #16810717 | C22 | 1 | 1 | yes | characteristic |
| 27 | #16810714 | — | 2 | 1 | no | — |
| 28 | D8×Dic53 | C22 | 1 | 1 | yes | characteristic |
| 29 | C2×#13133140 | — | 2 | 1 | no | — |
| 30 | C2×C8×Dic53 | C22 | 1 | 1 | yes | characteristic |
| 31 | #16810448 | C22 | 1 | 2 | yes | — |
| 32 | #16810441 | C22 | 1 | 2 | yes | — |
| 33 | #16810428 | C22 | 1 | 2 | yes | — |
| 34 | #16810426 | C22 | 1 | 2 | yes | — |
| 35 | #16810426 | C22 | 1 | 2 | yes | — |
| 36 | C22⋊#11719908 | C22 | 1 | 1 | yes | characteristic |
| 37 | #16810398 | C22 | 1 | 2 | yes | — |
| 38 | C53×#466 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×#107×C53 | C22 | 1 | 1 | yes | characteristic |
| 40 | C53×#367 | C22 | 1 | 2 | yes | — |
| 41 | C53×#357 | C22 | 1 | 2 | yes | — |
| 42 | C53×C22⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 43 | C22×Dic106 | — | 2 | 1 | no | — |
| 44 | C2×Dic212 | — | 2 | 1 | no | — |
| 45 | C2×Dic212 | — | 2 | 4 | no | — |
| 46 | C2×Dic212 | C23 | 1 | 1 | yes | characteristic |
| 47 | C2×Dic212 | C23 | 1 | 2 | yes | — |
| 48 | C2×#11719923 | — | 2 | 1 | no | — |
| 49 | C22×#88322 | D4 | 1 | 1 | yes | characteristic |
| 50 | #13133210 | — | 4 | 1 | no | — |
| 51 | #13133208 | — | 2 | 1 | no | — |
| 52 | #13133204 | — | 2 | 1 | no | — |
| 53 | #13133198 | — | 4 | 1 | no | — |
| 54 | #13133196 | — | 2 | 1 | no | — |
| 55 | #13133182 | — | 2 | 2 | no | — |
| 56 | #13133182 | — | 2 | 2 | no | — |
| 57 | #13133182 | — | 2 | 1 | no | — |
| 58 | #13133182 | — | 4 | 1 | no | — |
| 59 | #13133182 | — | 4 | 1 | no | — |
| 60 | D4×Dic53 | — | 2 | 1 | no | — |
| 61 | D4×Dic53 | — | 4 | 1 | no | — |
| 62 | #13133173 | — | 4 | 1 | no | — |
| 63 | C2×#11719919 | — | 4 | 1 | no | — |
| 64 | C2×C4×Dic53 | — | 4 | 1 | no | — |
| 65 | C2×C4×Dic53 | D4 | 1 | 1 | yes | characteristic |
| 66 | Dic424 | — | 2 | 4 | no | — |
| 67 | #13133161 | — | 2 | 4 | no | — |
| 68 | C2×#11719908 | C23 | 1 | 2 | yes | — |
| 69 | #13133151 | C23 | 1 | 1 | yes | characteristic |
| 70 | #13133148 | — | 2 | 1 | no | — |
| 71 | #13133142 | — | 2 | 1 | no | — |
| 72 | #13133140 | — | 2 | 1 | no | — |
| 73 | #13133140 | — | 2 | 2 | no | — |
| 74 | #13133140 | — | 2 | 2 | no | — |
| 75 | #13133138 | — | 2 | 1 | no | — |
| 76 | C8×Dic53 | D4 | 1 | 1 | yes | characteristic |
| 77 | C8×Dic53 | D4 | 1 | 1 | yes | characteristic |
| 78 | C8×Dic53 | C23 | 1 | 1 | yes | characteristic |
| 79 | C8×Dic53 | C23 | 1 | 1 | yes | characteristic |
| 80 | C2×D8×C53 | C23 | 1 | 1 | yes | characteristic |
| 81 | C22×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 82 | #121×C53 | — | 2 | 1 | no | — |
| 83 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 84 | C2×C16×C53 | C23 | 1 | 2 | yes | — |
| 85 | #107×C53 | — | 2 | 1 | no | — |
| 86 | #107×C53 | C23 | 1 | 1 | yes | characteristic |
| 87 | #107×C53 | C23 | 1 | 2 | yes | — |
| 88 | #102×C53 | — | 2 | 1 | no | — |
| 89 | C2×D4×C53 | — | 2 | 1 | no | — |
| 90 | C2×D4×C53 | — | 4 | 1 | no | — |
| 91 | C22×C4×C53 | — | 4 | 1 | no | — |
| 92 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 93 | C22×Dic53 | — | 4 | 1 | no | — |
| 94 | C22×Dic53 | — | 4 | 1 | no | — |
| 95 | C22×Dic53 | D8 | 1 | 1 | yes | characteristic |
| 96 | C22×Dic53 | D8 | 1 | 1 | yes | characteristic |
| 97 | C2×Dic106 | — | 2 | 4 | no | — |
| 98 | C2×Dic106 | — | 2 | 2 | no | — |
| 99 | C2×Dic106 | — | 2 | 1 | no | — |
| 100 | C2×Dic106 | — | 4 | 2 | no | — |
| 101 | C2×Dic106 | — | 4 | 1 | no | — |
| 102 | D8×C53 | — | 2 | 2 | no | — |
| 103 | C2×C8×C53 | — | 2 | 2 | no | — |
| 104 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 105 | C2×C8×C53 | C24 | 1 | 1 | yes | characteristic |
| 106 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 107 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 108 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 109 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 110 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 111 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 112 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 113 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 114 | #11719923 | — | 4 | 2 | no | — |
| 115 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 116 | C4⋊Dic53 | — | 4 | 1 | no | — |
| 117 | #11719919 | — | 4 | 1 | no | — |
| 118 | #11719919 | — | 4 | 2 | no | — |
| 119 | #11719919 | — | 4 | 2 | no | — |
| 120 | #11719919 | — | 4 | 1 | no | — |
| 121 | #11719919 | — | 4 | 1 | no | — |
| 122 | C4×Dic53 | — | 4 | 2 | no | — |
| 123 | C4×Dic53 | — | 4 | 2 | no | — |
| 124 | C4×Dic53 | — | 4 | 1 | no | — |
| 125 | C4×Dic53 | D8 | 1 | 1 | yes | characteristic |
| 126 | C4×Dic53 | D8 | 1 | 1 | yes | characteristic |
| 127 | C4×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 128 | C4×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | C2×#88322 | — | 4 | 1 | no | — |
| 130 | C2×#88322 | C2×D4 | 1 | 1 | yes | characteristic |
| 131 | C2×#88322 | C2×D4 | 1 | 1 | yes | characteristic |
| 132 | Dic212 | — | 2 | 4 | no | — |
| 133 | Dic212 | — | 2 | 2 | no | — |
| 134 | Dic212 | — | 2 | 2 | no | — |
| 135 | Dic212 | #41 | 1 | 4 | yes | — |
| 136 | C16×C53 | — | 2 | 2 | no | — |
| 137 | #11719908 | — | 2 | 2 | no | — |
| 138 | C23×C53 | — | 4 | 1 | no | — |
| 139 | C23×C53 | C2×D8 | 1 | 1 | yes | characteristic |
| 140 | D4×C53 | — | 4 | 1 | no | — |
| 141 | D4×C53 | — | 4 | 1 | no | — |
| 142 | D4×C53 | — | 8 | 2 | no | — |
| 143 | C2×C4×C53 | — | 2 | 1 | no | — |
| 144 | C2×C4×C53 | — | 2 | 1 | no | — |
| 145 | C2×C4×C53 | — | 4 | 2 | no | — |
| 146 | C2×C4×C53 | — | 4 | 1 | no | — |
| 147 | C2×C4×C53 | — | 8 | 2 | no | — |
| 148 | C2×C4×C53 | C2×D8 | 1 | 1 | yes | characteristic |
| 149 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 150 | C2×Dic53 | — | 2 | 2 | no | — |
| 151 | C2×Dic53 | — | 4 | 1 | no | — |
| 152 | C2×Dic53 | — | 4 | 4 | no | — |
| 153 | C2×Dic53 | — | 4 | 2 | no | — |
| 154 | C2×Dic53 | — | 4 | 1 | no | — |
| 155 | C2×Dic53 | — | 4 | 1 | no | — |
| 156 | C2×Dic53 | — | 8 | 2 | no | — |
| 157 | C2×Dic53 | C2×D8 | 1 | 1 | yes | characteristic |
| 158 | C2×Dic53 | C2×D8 | 1 | 1 | yes | characteristic |
| 159 | C2×Dic53 | C2×D8 | 1 | 1 | yes | characteristic |
| 160 | C2×Dic53 | C2×D8 | 1 | 1 | yes | characteristic |
| 161 | Dic106 | — | 2 | 4 | no | — |
| 162 | Dic106 | — | 4 | 4 | no | — |
| 163 | Dic106 | — | 4 | 2 | no | — |
| 164 | Dic106 | — | 4 | 1 | no | — |
| 165 | Dic106 | — | 4 | 1 | no | — |
| 166 | C8×C53 | — | 2 | 1 | no | — |
| 167 | C8×C53 | C2×#41 | 1 | 2 | yes | — |
| 168 | #88322 | — | 2 | 1 | no | — |
| 169 | #88322 | — | 2 | 1 | no | — |
| 170 | #33677 | — | 53 | 1 | no | maximal, Sylow |
| 171 | C22×C53 | — | 2 | 1 | no | — |
| 172 | C22×C53 | — | 2 | 1 | no | — |
| 173 | C22×C53 | — | 8 | 1 | no | — |
| 174 | C22×C53 | — | 8 | 1 | no | — |
| 175 | C22×C53 | — | 8 | 1 | no | — |
| 176 | C22×C53 | #510 | 1 | 2 | yes | — |
| 177 | C22×C53 | C22×D8 | 1 | 1 | yes | characteristic |
| 178 | C4×C53 | — | 2 | 1 | no | — |
| 179 | C4×C53 | — | 8 | 1 | no | — |
| 180 | C4×C53 | — | 8 | 2 | no | — |
| 181 | C4×C53 | #525 | 1 | 1 | yes | characteristic |
| 182 | C4×C53 | #575 | 1 | 1 | yes | characteristic |
| 183 | Dic53 | — | 2 | 1 | no | — |
| 184 | Dic53 | — | 2 | 1 | no | — |
| 185 | Dic53 | — | 2 | 1 | no | — |
| 186 | Dic53 | — | 2 | 1 | no | — |
| 187 | Dic53 | — | 4 | 4 | no | — |
| 188 | Dic53 | — | 8 | 1 | no | — |
| 189 | Dic53 | — | 8 | 1 | no | — |
| 190 | #3168 | — | 53 | 1 | no | — |
| 191 | C2×C4×Q16 | — | 53 | 1 | no | — |
| 192 | #2236 | — | 53 | 1 | no | — |
| 193 | #2233 | D53 | 1 | 1 | yes | characteristic |
| 194 | #2229 | — | 53 | 2 | no | — |
| 195 | #2211 | — | 53 | 2 | no | — |
| 196 | #2188 | — | 53 | 1 | no | — |
| 197 | #2185 | — | 53 | 1 | no | — |
| 198 | #2176 | — | 53 | 2 | no | — |
| 199 | #2175 | — | 53 | 2 | no | — |
| 200 | #2163 | — | 53 | 1 | no | — |
| 201 | C2×C53 | — | 2 | 2 | no | — |
| 202 | C2×C53 | — | 16 | 1 | no | — |
| 203 | C2×C53 | #3100 | 1 | 1 | yes | characteristic |
| 204 | C2×C53 | C2×#510 | 1 | 1 | yes | characteristic |
| 205 | C2×C53 | #3414 | 1 | 1 | yes | characteristic |
| 206 | C22×Q16 | — | 53 | 1 | no | — |
| 207 | #529 | — | 106 | 1 | no | — |
| 208 | C2×C4×Q8 | — | 106 | 1 | no | — |
| 209 | C2×Q32 | — | 53 | 2 | no | — |
| 210 | C2×SD32 | — | 53 | 2 | no | — |
| 211 | #499 | — | 53 | 1 | no | — |
| 212 | #495 | — | 53 | 1 | no | — |
| 213 | #488 | — | 106 | 1 | no | — |
| 214 | #467 | — | 53 | 1 | no | — |
| 215 | #466 | C2×D53 | 1 | 1 | yes | characteristic |
| 216 | #465 | — | 106 | 1 | no | — |
| 217 | C4×Q16 | — | 53 | 1 | no | — |
| 218 | C4×Q16 | — | 53 | 2 | no | — |
| 219 | C4×Q16 | — | 53 | 2 | no | — |
| 220 | C4×Q16 | — | 106 | 1 | no | — |
| 221 | C4×Q16 | — | 106 | 1 | no | — |
| 222 | C4×SD16 | — | 106 | 1 | no | — |
| 223 | C4×D8 | — | 53 | 1 | no | — |
| 224 | C2×#107 | C2×D53 | 1 | 1 | yes | characteristic |
| 225 | C2×#103 | — | 106 | 1 | no | — |
| 226 | C2×C4×C8 | — | 53 | 1 | no | — |
| 227 | #367 | C2×D53 | 1 | 2 | yes | — |
| 228 | #366 | — | 53 | 2 | no | — |
| 229 | C4⋊C16 | — | 53 | 2 | no | — |
| 230 | #358 | — | 53 | 2 | no | — |
| 231 | #358 | — | 53 | 2 | no | — |
| 232 | #358 | — | 53 | 2 | no | — |
| 233 | #357 | C2×D53 | 1 | 2 | yes | — |
| 234 | C22⋊C16 | — | 53 | 1 | no | — |
| 235 | C22⋊C16 | C2×D53 | 1 | 1 | yes | characteristic |
| 236 | #346 | — | 53 | 2 | no | — |
| 237 | C53 | #33677 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 238 | C22×Q8 | — | 106 | 1 | no | — |
| 239 | C2×Q16 | — | 53 | 2 | no | — |
| 240 | C2×Q16 | — | 53 | 1 | no | — |
| 241 | C2×Q16 | — | 106 | 4 | no | — |
| 242 | C2×Q16 | — | 106 | 1 | no | — |
| 243 | C2×SD16 | — | 106 | 1 | no | — |
| 244 | C2×D8 | C22×D53 | 1 | 1 | yes | characteristic |
| 245 | C22×C8 | — | 53 | 1 | no | — |
| 246 | C22×C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 247 | #126 | — | 212 | 1 | no | — |
| 248 | #125 | — | 106 | 1 | no | — |
| 249 | #124 | — | 106 | 1 | no | — |
| 250 | #123 | — | 212 | 1 | no | — |
| 251 | C22⋊Q8 | — | 106 | 1 | no | — |
| 252 | #121 | — | 2 | 1 | no | — |
| 253 | C4×Q8 | — | 106 | 2 | no | — |
| 254 | C4×Q8 | — | 106 | 2 | no | — |
| 255 | C4×Q8 | — | 106 | 1 | no | — |
| 256 | C4×Q8 | — | 212 | 1 | no | — |
| 257 | C4×Q8 | — | 212 | 1 | no | — |
| 258 | C4×D4 | — | 106 | 1 | no | — |
| 259 | C4×D4 | — | 212 | 1 | no | — |
| 260 | #117 | — | 212 | 1 | no | — |
| 261 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 262 | C2×C4⋊C4 | — | 212 | 1 | no | — |
| 263 | C2×C42 | — | 53 | 1 | no | — |
| 264 | C2×C42 | — | 212 | 1 | no | — |
| 265 | Q32 | — | 106 | 4 | no | — |
| 266 | SD32 | — | 106 | 4 | no | — |
| 267 | C2×C16 | — | 53 | 2 | no | — |
| 268 | C2×C16 | C22×D53 | 1 | 2 | yes | — |
| 269 | #107 | — | 2 | 1 | no | — |
| 270 | #107 | — | 53 | 1 | no | — |
| 271 | #107 | C22×D53 | 1 | 2 | yes | — |
| 272 | #107 | C22×D53 | 1 | 1 | yes | characteristic |
| 273 | #106 | — | 106 | 1 | no | — |
| 274 | #103 | — | 106 | 2 | no | — |
| 275 | #103 | — | 106 | 2 | no | — |
| 276 | #103 | — | 106 | 1 | no | — |
| 277 | #103 | — | 106 | 1 | no | — |
| 278 | #102 | — | 2 | 1 | no | — |
| 279 | #102 | — | 106 | 1 | no | — |
| 280 | C4×C8 | — | 53 | 1 | no | — |
| 281 | C4×C8 | — | 53 | 1 | no | — |
| 282 | C4×C8 | — | 53 | 1 | no | — |
| 283 | C4×C8 | — | 53 | 1 | no | — |
| 284 | C2×Q8 | — | 106 | 4 | no | — |
| 285 | C2×Q8 | — | 106 | 2 | no | — |
| 286 | C2×Q8 | — | 106 | 1 | no | — |
| 287 | C2×Q8 | — | 212 | 2 | no | — |
| 288 | C2×Q8 | — | 212 | 1 | no | — |
| 289 | C2×D4 | — | 2 | 1 | no | — |
| 290 | C2×D4 | — | 4 | 1 | no | — |
| 291 | C22×C4 | — | 4 | 1 | no | — |
| 292 | C22×C4 | — | 53 | 1 | no | — |
| 293 | C22×C4 | — | 53 | 1 | no | — |
| 294 | C22×C4 | — | 212 | 1 | no | — |
| 295 | C22×C4 | — | 212 | 1 | no | — |
| 296 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 297 | Q16 | — | 53 | 4 | no | — |
| 298 | Q16 | — | 106 | 4 | no | — |
| 299 | Q16 | — | 106 | 2 | no | — |
| 300 | Q16 | — | 106 | 2 | no | — |
| 301 | SD16 | — | 212 | 2 | no | — |
| 302 | D8 | — | 2 | 2 | no | — |
| 303 | C2×C8 | — | 2 | 2 | no | — |
| 304 | C2×C8 | — | 53 | 1 | no | — |
| 305 | C2×C8 | — | 53 | 1 | no | — |
| 306 | C2×C8 | — | 212 | 1 | no | — |
| 307 | C2×C8 | D4×D53 | 1 | 1 | yes | characteristic |
| 308 | C2×C8 | C23×D53 | 1 | 1 | yes | characteristic |
| 309 | C4⋊C4 | — | 2 | 1 | no | — |
| 310 | C4⋊C4 | — | 2 | 2 | no | — |
| 311 | C4⋊C4 | — | 4 | 1 | no | — |
| 312 | C4⋊C4 | — | 106 | 1 | no | — |
| 313 | C4⋊C4 | — | 212 | 2 | no | — |
| 314 | C4⋊C4 | — | 212 | 2 | no | — |
| 315 | C4⋊C4 | — | 212 | 1 | no | — |
| 316 | C4⋊C4 | — | 212 | 1 | no | — |
| 317 | C4⋊C4 | — | 212 | 1 | no | — |
| 318 | C4⋊C4 | — | 212 | 1 | no | — |
| 319 | C22⋊C4 | — | 4 | 1 | no | — |
| 320 | C22⋊C4 | — | 212 | 1 | no | — |
| 321 | C22⋊C4 | — | 212 | 1 | no | — |
| 322 | C22⋊C4 | — | 212 | 1 | no | — |
| 323 | C22⋊C4 | — | 212 | 1 | no | — |
| 324 | C42 | — | 53 | 1 | no | — |
| 325 | C42 | — | 53 | 1 | no | — |
| 326 | C42 | — | 53 | 1 | no | — |
| 327 | C42 | — | 53 | 1 | no | — |
| 328 | C42 | — | 212 | 2 | no | — |
| 329 | C42 | — | 212 | 2 | no | — |
| 330 | C42 | — | 212 | 1 | no | — |
| 331 | C16 | — | 2 | 2 | no | — |
| 332 | C16 | — | 106 | 2 | no | — |
| 333 | C23 | — | 4 | 1 | no | — |
| 334 | C23 | D8×D53 | 1 | 1 | yes | characteristic |
| 335 | Q8 | — | 106 | 4 | no | — |
| 336 | Q8 | — | 212 | 4 | no | — |
| 337 | Q8 | — | 212 | 1 | no | — |
| 338 | Q8 | — | 212 | 1 | no | — |
| 339 | Q8 | — | 212 | 2 | no | — |
| 340 | D4 | — | 4 | 1 | no | — |
| 341 | D4 | — | 4 | 1 | no | — |
| 342 | D4 | — | 8 | 2 | no | — |
| 343 | C2×C4 | — | 2 | 1 | no | — |
| 344 | C2×C4 | — | 2 | 1 | no | — |
| 345 | C2×C4 | — | 4 | 2 | no | — |
| 346 | C2×C4 | — | 4 | 1 | no | — |
| 347 | C2×C4 | — | 8 | 2 | no | — |
| 348 | C2×C4 | — | 53 | 1 | no | — |
| 349 | C2×C4 | — | 53 | 1 | no | — |
| 350 | C2×C4 | — | 53 | 1 | no | — |
| 351 | C2×C4 | — | 53 | 1 | no | — |
| 352 | C2×C4 | — | 106 | 2 | no | — |
| 353 | C2×C4 | — | 424 | 2 | no | — |
| 354 | C2×C4 | — | 212 | 1 | no | — |
| 355 | C2×C4 | — | 212 | 1 | no | — |
| 356 | C2×C4 | — | 212 | 1 | no | — |
| 357 | C2×C4 | — | 212 | 4 | no | — |
| 358 | C2×C4 | — | 212 | 2 | no | — |
| 359 | C2×C4 | D8×D53 | 1 | 1 | yes | characteristic |
| 360 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 361 | C8 | — | 2 | 1 | no | — |
| 362 | C8 | — | 106 | 1 | no | — |
| 363 | C8 | — | 106 | 1 | no | — |
| 364 | C8 | #41×D53 | 1 | 2 | yes | — |
| 365 | C22 | — | 2 | 1 | no | — |
| 366 | C22 | — | 2 | 1 | no | — |
| 367 | C22 | — | 8 | 1 | no | — |
| 368 | C22 | — | 8 | 1 | no | — |
| 369 | C22 | — | 8 | 1 | no | — |
| 370 | C22 | #16811062 | 1 | 2 | yes | — |
| 371 | C22 | C2×D8×D53 | 1 | 1 | yes | characteristic |
| 372 | C4 | — | 2 | 1 | no | — |
| 373 | C4 | — | 8 | 1 | no | — |
| 374 | C4 | — | 8 | 2 | no | — |
| 375 | C4 | — | 106 | 1 | no | — |
| 376 | C4 | — | 106 | 1 | no | — |
| 377 | C4 | — | 106 | 1 | no | — |
| 378 | C4 | — | 106 | 1 | no | — |
| 379 | C4 | — | 424 | 1 | no | — |
| 380 | C4 | — | 424 | 1 | no | — |
| 381 | C4 | — | 212 | 4 | no | — |
| 382 | C4 | #16811131 | 1 | 1 | yes | characteristic |
| 383 | C4 | #16811422 | 1 | 1 | yes | characteristic |
| 384 | C2 | — | 2 | 2 | no | — |
| 385 | C2 | — | 16 | 1 | no | — |
| 386 | C2 | #20284712 | 1 | 1 | yes | characteristic |
| 387 | C2 | C2×#16811062 | 1 | 1 | yes | characteristic |
| 388 | C2 | #20287847 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta