← #27429228
Subgroups — #27429228
Order 13568.
620 conjugacy classes of subgroups.
The subgroup lattice has 406 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#16810898 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #20283584 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20276185 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #20275995 | C2 | 1 | 2 | yes | maximal |
| 5 | #20275630 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20275505 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #20275212 | C2 | 1 | 2 | yes | maximal |
| 8 | #20274839 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #20274828 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #20274769 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | C53×#1757 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C2×#13133247 | C22 | 1 | 2 | yes | — |
| 13 | C22×Dic212 | C22 | 1 | 1 | yes | characteristic |
| 14 | #16811100 | C22 | 1 | 2 | yes | — |
| 15 | #16810898 | — | 2 | 2 | no | — |
| 16 | #16810898 | — | 2 | 2 | no | — |
| 17 | #16810731 | — | 2 | 2 | no | — |
| 18 | C4×Dic212 | — | 2 | 2 | no | — |
| 19 | #16810671 | C22 | 1 | 2 | yes | — |
| 20 | C2×#13133153 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#13133153 | C22 | 1 | 1 | yes | characteristic |
| 22 | #16810661 | C22 | 1 | 1 | yes | characteristic |
| 23 | #16810640 | C22 | 1 | 2 | yes | — |
| 24 | #16810633 | C22 | 1 | 2 | yes | — |
| 25 | #16810631 | C22 | 1 | 2 | yes | — |
| 26 | C2×#13133135 | C22 | 1 | 2 | yes | — |
| 27 | C2×#13133135 | C22 | 1 | 2 | yes | — |
| 28 | #16810395 | C22 | 1 | 2 | yes | — |
| 29 | #16810394 | C22 | 1 | 2 | yes | — |
| 30 | #16810393 | C22 | 1 | 2 | yes | — |
| 31 | #16810379 | C22 | 1 | 2 | yes | — |
| 32 | C2×#131×C53 | C22 | 1 | 1 | yes | characteristic |
| 33 | C53×#413 | C22 | 1 | 1 | yes | characteristic |
| 34 | C53×#410 | C22 | 1 | 1 | yes | characteristic |
| 35 | C53×#405 | C22 | 1 | 1 | yes | characteristic |
| 36 | C53×#405 | C22 | 1 | 1 | yes | characteristic |
| 37 | C53×#344 | C22 | 1 | 1 | yes | characteristic |
| 38 | C53×#344 | C22 | 1 | 1 | yes | characteristic |
| 39 | C22×Dic106 | C23 | 1 | 2 | yes | — |
| 40 | #13133247 | — | 2 | 4 | no | — |
| 41 | #13133247 | — | 4 | 2 | no | — |
| 42 | C2×Dic212 | — | 2 | 1 | no | — |
| 43 | C2×Dic212 | — | 2 | 1 | no | — |
| 44 | C2×Dic212 | — | 2 | 1 | no | — |
| 45 | C2×Dic212 | — | 2 | 1 | no | — |
| 46 | C2×Dic212 | D4 | 1 | 2 | yes | — |
| 47 | C2×Dic212 | D4 | 1 | 2 | yes | — |
| 48 | C2×#11719925 | — | 2 | 2 | no | — |
| 49 | C2×#11719923 | — | 2 | 2 | no | — |
| 50 | C2×#11719917 | C23 | 1 | 2 | yes | — |
| 51 | C2×#11719917 | C23 | 1 | 2 | yes | — |
| 52 | C4×Dic106 | — | 2 | 4 | no | — |
| 53 | #13133182 | — | 4 | 2 | no | — |
| 54 | #13133176 | C23 | 1 | 2 | yes | — |
| 55 | #13133173 | — | 2 | 4 | no | — |
| 56 | #13133153 | — | 2 | 1 | no | — |
| 57 | #13133153 | — | 2 | 1 | no | — |
| 58 | #13133153 | — | 2 | 1 | no | — |
| 59 | #13133153 | — | 2 | 1 | no | — |
| 60 | #13133152 | — | 4 | 2 | no | — |
| 61 | #13133151 | — | 2 | 1 | no | — |
| 62 | #13133149 | — | 2 | 1 | no | — |
| 63 | #13133144 | — | 4 | 2 | no | — |
| 64 | #13133142 | — | 2 | 4 | no | — |
| 65 | #13133140 | — | 4 | 2 | no | — |
| 66 | #13133135 | — | 2 | 4 | no | — |
| 67 | #13133135 | — | 4 | 2 | no | — |
| 68 | C2×#41×C53 | C23 | 1 | 1 | yes | characteristic |
| 69 | #131×C53 | — | 2 | 1 | no | — |
| 70 | #131×C53 | — | 2 | 1 | no | — |
| 71 | #131×C53 | — | 2 | 1 | no | — |
| 72 | #131×C53 | — | 2 | 1 | no | — |
| 73 | C2×M16×C53 | — | 2 | 1 | no | — |
| 74 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 75 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 76 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 77 | C22×C8×C53 | — | 2 | 1 | no | — |
| 78 | C22×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 79 | #117×C53 | C23 | 1 | 1 | yes | characteristic |
| 80 | #117×C53 | C23 | 1 | 1 | yes | characteristic |
| 81 | #101×C53 | — | 2 | 1 | no | — |
| 82 | #100×C53 | — | 2 | 1 | no | — |
| 83 | #99×C53 | — | 2 | 2 | no | — |
| 84 | #97×C53 | — | 2 | 1 | no | — |
| 85 | #97×C53 | — | 2 | 1 | no | — |
| 86 | C4×C8×C53 | — | 2 | 1 | no | — |
| 87 | C4×C8×C53 | — | 2 | 1 | no | — |
| 88 | #41×C53 | — | 2 | 1 | no | — |
| 89 | #41×C53 | — | 2 | 1 | no | — |
| 90 | #41×C53 | — | 2 | 1 | no | — |
| 91 | #41×C53 | — | 2 | 1 | no | — |
| 92 | C2×Q8×C53 | #41 | 1 | 1 | yes | characteristic |
| 93 | C2×D4×C53 | — | 2 | 1 | no | — |
| 94 | C2×D4×C53 | #41 | 1 | 1 | yes | characteristic |
| 95 | C22×C4×C53 | — | 2 | 1 | no | — |
| 96 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 97 | C22×Dic53 | — | 2 | 2 | no | — |
| 98 | C2×Dic106 | — | 2 | 2 | no | — |
| 99 | C2×Dic106 | — | 2 | 2 | no | — |
| 100 | C2×Dic106 | — | 2 | 2 | no | — |
| 101 | C2×Dic106 | — | 2 | 2 | no | — |
| 102 | C2×Dic106 | — | 2 | 2 | no | — |
| 103 | C2×Dic106 | C2×D4 | 1 | 4 | yes | — |
| 104 | M16×C53 | — | 2 | 1 | no | — |
| 105 | M16×C53 | — | 2 | 1 | no | — |
| 106 | M16×C53 | — | 2 | 1 | no | — |
| 107 | M16×C53 | — | 2 | 1 | no | — |
| 108 | M16×C53 | — | 2 | 1 | no | — |
| 109 | M16×C53 | — | 2 | 1 | no | — |
| 110 | M16×C53 | — | 4 | 1 | no | — |
| 111 | M16×C53 | — | 4 | 1 | no | — |
| 112 | C2×C8×C53 | — | 2 | 1 | no | — |
| 113 | C2×C8×C53 | — | 2 | 1 | no | — |
| 114 | C2×C8×C53 | — | 2 | 1 | no | — |
| 115 | C2×C8×C53 | — | 4 | 1 | no | — |
| 116 | C2×C8×C53 | — | 4 | 1 | no | — |
| 117 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | C2×C8×C53 | #41 | 1 | 1 | yes | characteristic |
| 120 | C2×C8×C53 | #41 | 1 | 1 | yes | characteristic |
| 121 | C2×C8×C53 | #41 | 1 | 1 | yes | characteristic |
| 122 | C2×C8×C53 | #41 | 1 | 1 | yes | characteristic |
| 123 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 124 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 125 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 126 | C22⋊C4×C53 | #41 | 1 | 2 | yes | — |
| 127 | C42×C53 | — | 2 | 1 | no | — |
| 128 | C42×C53 | — | 2 | 1 | no | — |
| 129 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 130 | #11719925 | — | 4 | 4 | no | — |
| 131 | #11719923 | — | 4 | 4 | no | — |
| 132 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 133 | #11719919 | — | 4 | 4 | no | — |
| 134 | C4×Dic53 | — | 2 | 2 | no | — |
| 135 | C4×Dic53 | — | 4 | 4 | no | — |
| 136 | #11719917 | — | 2 | 2 | no | — |
| 137 | #11719917 | — | 2 | 2 | no | — |
| 138 | #11719917 | — | 2 | 2 | no | — |
| 139 | #11719917 | — | 2 | 2 | no | — |
| 140 | C2×#88322 | — | 2 | 2 | no | — |
| 141 | C2×#88322 | — | 2 | 2 | no | — |
| 142 | Dic212 | — | 2 | 2 | no | — |
| 143 | Dic212 | — | 2 | 2 | no | — |
| 144 | Dic212 | — | 2 | 2 | no | — |
| 145 | Dic212 | — | 2 | 2 | no | — |
| 146 | C23×C53 | — | 2 | 1 | no | — |
| 147 | C23×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 148 | Q8×C53 | — | 2 | 1 | no | — |
| 149 | Q8×C53 | — | 2 | 1 | no | — |
| 150 | D4×C53 | — | 2 | 1 | no | — |
| 151 | D4×C53 | — | 2 | 1 | no | — |
| 152 | D4×C53 | — | 4 | 1 | no | — |
| 153 | D4×C53 | — | 4 | 1 | no | — |
| 154 | C2×C4×C53 | — | 2 | 1 | no | — |
| 155 | C2×C4×C53 | — | 2 | 2 | no | — |
| 156 | C2×C4×C53 | — | 4 | 1 | no | — |
| 157 | C2×C4×C53 | — | 4 | 1 | no | — |
| 158 | C2×C4×C53 | — | 4 | 1 | no | — |
| 159 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 160 | C2×C4×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 161 | C2×C4×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 162 | C2×C4×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 163 | C2×C4×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 164 | C2×C4×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 165 | C2×Dic53 | — | 2 | 4 | no | — |
| 166 | C2×Dic53 | — | 4 | 2 | no | — |
| 167 | C2×Dic53 | — | 4 | 2 | no | — |
| 168 | C2×Dic53 | — | 4 | 2 | no | — |
| 169 | Dic106 | — | 2 | 4 | no | — |
| 170 | Dic106 | — | 2 | 4 | no | — |
| 171 | Dic106 | — | 4 | 2 | no | — |
| 172 | Dic106 | — | 4 | 2 | no | — |
| 173 | C8×C53 | — | 4 | 1 | no | — |
| 174 | C8×C53 | — | 4 | 1 | no | — |
| 175 | C8×C53 | — | 4 | 1 | no | — |
| 176 | C8×C53 | #123 | 1 | 1 | yes | characteristic |
| 177 | C8×C53 | #123 | 1 | 1 | yes | characteristic |
| 178 | C8×C53 | #123 | 1 | 1 | yes | characteristic |
| 179 | C8×C53 | #123 | 1 | 1 | yes | characteristic |
| 180 | #88322 | — | 4 | 2 | no | — |
| 181 | #88322 | — | 4 | 2 | no | — |
| 182 | #24989 | — | 53 | 1 | no | maximal, Sylow |
| 183 | C22×C53 | — | 4 | 1 | no | — |
| 184 | C22×C53 | — | 4 | 1 | no | — |
| 185 | C22×C53 | — | 8 | 1 | no | — |
| 186 | C22×C53 | #529 | 1 | 1 | yes | characteristic |
| 187 | C22×C53 | #546 | 1 | 1 | yes | characteristic |
| 188 | C22×C53 | #555 | 1 | 1 | yes | characteristic |
| 189 | C4×C53 | — | 4 | 2 | no | — |
| 190 | C4×C53 | — | 4 | 1 | no | — |
| 191 | C4×C53 | — | 8 | 1 | no | — |
| 192 | C4×C53 | C2×#123 | 1 | 1 | yes | characteristic |
| 193 | C4×C53 | #540 | 1 | 1 | yes | characteristic |
| 194 | C4×C53 | #546 | 1 | 1 | yes | characteristic |
| 195 | C4×C53 | #553 | 1 | 1 | yes | characteristic |
| 196 | Dic53 | — | 4 | 4 | no | — |
| 197 | Dic53 | — | 8 | 2 | no | — |
| 198 | C2×#473 | — | 53 | 1 | no | — |
| 199 | #2950 | — | 53 | 1 | no | — |
| 200 | #2082 | — | 53 | 2 | no | — |
| 201 | #2049 | — | 53 | 2 | no | — |
| 202 | #1979 | — | 53 | 1 | no | — |
| 203 | #1953 | — | 53 | 1 | no | — |
| 204 | #1905 | — | 53 | 2 | no | — |
| 205 | #1833 | — | 53 | 1 | no | — |
| 206 | #1830 | — | 53 | 2 | no | — |
| 207 | #1814 | — | 53 | 1 | no | — |
| 208 | #1757 | D53 | 1 | 1 | yes | characteristic |
| 209 | C2×C53 | — | 2 | 1 | no | — |
| 210 | C2×C53 | — | 2 | 1 | no | — |
| 211 | C2×C53 | — | 2 | 1 | no | — |
| 212 | C2×C53 | — | 8 | 1 | no | — |
| 213 | C2×C53 | #2420 | 1 | 1 | yes | characteristic |
| 214 | C2×#137 | — | 53 | 2 | no | — |
| 215 | C22×Q16 | — | 53 | 1 | no | — |
| 216 | C2×#131 | C2×D53 | 1 | 1 | yes | characteristic |
| 217 | #519 | — | 53 | 2 | no | — |
| 218 | #473 | — | 106 | 2 | no | — |
| 219 | #473 | — | 106 | 2 | no | — |
| 220 | #441 | — | 106 | 2 | no | — |
| 221 | C4×Q16 | — | 106 | 2 | no | — |
| 222 | #430 | — | 53 | 2 | no | — |
| 223 | C2×#108 | — | 53 | 1 | no | — |
| 224 | C2×#108 | — | 53 | 1 | no | — |
| 225 | #427 | — | 53 | 1 | no | — |
| 226 | #421 | — | 53 | 2 | no | — |
| 227 | #419 | — | 53 | 2 | no | — |
| 228 | #419 | — | 53 | 2 | no | — |
| 229 | #413 | C2×D53 | 1 | 1 | yes | characteristic |
| 230 | C2×#101 | — | 53 | 2 | no | — |
| 231 | C2×#101 | — | 53 | 2 | no | — |
| 232 | #410 | C2×D53 | 1 | 1 | yes | characteristic |
| 233 | #405 | C2×D53 | 1 | 1 | yes | characteristic |
| 234 | #405 | C2×D53 | 1 | 1 | yes | characteristic |
| 235 | #344 | — | 53 | 2 | no | — |
| 236 | #344 | — | 53 | 2 | no | — |
| 237 | #344 | — | 53 | 2 | no | — |
| 238 | #344 | C2×D53 | 1 | 1 | yes | characteristic |
| 239 | #344 | C2×D53 | 1 | 1 | yes | characteristic |
| 240 | H(3,ℤ/4) | — | 53 | 2 | no | — |
| 241 | C53 | #24989 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 242 | C2×#41 | C22×D53 | 1 | 1 | yes | characteristic |
| 243 | C22×Q8 | — | 53 | 2 | no | — |
| 244 | #137 | — | 106 | 4 | no | — |
| 245 | #137 | — | 212 | 2 | no | — |
| 246 | C2×Q16 | — | 53 | 2 | no | — |
| 247 | C2×Q16 | — | 53 | 2 | no | — |
| 248 | C2×Q16 | — | 106 | 2 | no | — |
| 249 | C2×Q16 | — | 106 | 1 | no | — |
| 250 | C2×Q16 | — | 106 | 1 | no | — |
| 251 | C2×Q16 | — | 106 | 1 | no | — |
| 252 | C2×Q16 | — | 106 | 1 | no | — |
| 253 | C2×SD16 | — | 106 | 2 | no | — |
| 254 | #131 | — | 2 | 1 | no | — |
| 255 | #131 | — | 2 | 1 | no | — |
| 256 | #131 | — | 2 | 1 | no | — |
| 257 | #131 | — | 2 | 1 | no | — |
| 258 | C2×M16 | — | 2 | 1 | no | — |
| 259 | C2×M16 | — | 53 | 2 | no | — |
| 260 | C2×M16 | — | 53 | 2 | no | — |
| 261 | C2×M16 | C22×D53 | 1 | 1 | yes | characteristic |
| 262 | C2×M16 | C22×D53 | 1 | 1 | yes | characteristic |
| 263 | C2×M16 | C22×D53 | 1 | 1 | yes | characteristic |
| 264 | C22×C8 | — | 2 | 1 | no | — |
| 265 | C22×C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 266 | C4×Q8 | — | 106 | 4 | no | — |
| 267 | C4×Q8 | — | 212 | 2 | no | — |
| 268 | #117 | — | 53 | 2 | no | — |
| 269 | #117 | — | 106 | 4 | no | — |
| 270 | #117 | C22×D53 | 1 | 1 | yes | characteristic |
| 271 | #117 | C22×D53 | 1 | 1 | yes | characteristic |
| 272 | #108 | — | 106 | 1 | no | — |
| 273 | #108 | — | 106 | 1 | no | — |
| 274 | #108 | — | 106 | 1 | no | — |
| 275 | #108 | — | 106 | 1 | no | — |
| 276 | #108 | — | 212 | 2 | no | — |
| 277 | #107 | — | 106 | 1 | no | — |
| 278 | #106 | — | 106 | 1 | no | — |
| 279 | #104 | — | 212 | 2 | no | — |
| 280 | #103 | — | 106 | 4 | no | — |
| 281 | #103 | — | 212 | 2 | no | — |
| 282 | #101 | — | 2 | 1 | no | — |
| 283 | #101 | — | 106 | 4 | no | — |
| 284 | #101 | — | 212 | 2 | no | — |
| 285 | #100 | — | 2 | 1 | no | — |
| 286 | #99 | — | 2 | 2 | no | — |
| 287 | #97 | — | 2 | 1 | no | — |
| 288 | #97 | — | 2 | 1 | no | — |
| 289 | C4×C8 | — | 2 | 1 | no | — |
| 290 | C4×C8 | — | 2 | 1 | no | — |
| 291 | #41 | — | 2 | 1 | no | — |
| 292 | #41 | — | 2 | 1 | no | — |
| 293 | #41 | — | 2 | 1 | no | — |
| 294 | #41 | — | 2 | 1 | no | — |
| 295 | C2×Q8 | — | 53 | 4 | no | — |
| 296 | C2×Q8 | — | 106 | 2 | no | — |
| 297 | C2×Q8 | — | 106 | 2 | no | — |
| 298 | C2×Q8 | — | 106 | 2 | no | — |
| 299 | C2×Q8 | — | 106 | 2 | no | — |
| 300 | C2×Q8 | — | 106 | 2 | no | — |
| 301 | C2×Q8 | #11719945 | 1 | 1 | yes | characteristic |
| 302 | C2×D4 | — | 2 | 1 | no | — |
| 303 | C2×D4 | #11719945 | 1 | 1 | yes | characteristic |
| 304 | C22×C4 | — | 2 | 1 | no | — |
| 305 | C22×C4 | — | 106 | 2 | no | — |
| 306 | C22×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 307 | Q16 | — | 106 | 2 | no | — |
| 308 | Q16 | — | 106 | 2 | no | — |
| 309 | Q16 | — | 106 | 2 | no | — |
| 310 | Q16 | — | 106 | 2 | no | — |
| 311 | Q16 | — | 212 | 4 | no | — |
| 312 | SD16 | — | 212 | 4 | no | — |
| 313 | M16 | — | 2 | 1 | no | — |
| 314 | M16 | — | 2 | 1 | no | — |
| 315 | M16 | — | 2 | 1 | no | — |
| 316 | M16 | — | 2 | 1 | no | — |
| 317 | M16 | — | 2 | 1 | no | — |
| 318 | M16 | — | 2 | 1 | no | — |
| 319 | M16 | — | 4 | 1 | no | — |
| 320 | M16 | — | 4 | 1 | no | — |
| 321 | M16 | — | 106 | 2 | no | — |
| 322 | M16 | — | 106 | 2 | no | — |
| 323 | M16 | — | 106 | 2 | no | — |
| 324 | M16 | — | 106 | 2 | no | — |
| 325 | C2×C8 | — | 2 | 1 | no | — |
| 326 | C2×C8 | — | 2 | 1 | no | — |
| 327 | C2×C8 | — | 2 | 1 | no | — |
| 328 | C2×C8 | — | 4 | 1 | no | — |
| 329 | C2×C8 | — | 4 | 1 | no | — |
| 330 | C2×C8 | — | 106 | 2 | no | — |
| 331 | C2×C8 | — | 106 | 2 | no | — |
| 332 | C2×C8 | #11719945 | 1 | 1 | yes | characteristic |
| 333 | C2×C8 | #11719945 | 1 | 1 | yes | characteristic |
| 334 | C2×C8 | D4×D53 | 1 | 1 | yes | characteristic |
| 335 | C2×C8 | D4×D53 | 1 | 1 | yes | characteristic |
| 336 | C2×C8 | #11719947 | 1 | 1 | yes | characteristic |
| 337 | C2×C8 | #11719947 | 1 | 1 | yes | characteristic |
| 338 | C4⋊C4 | — | 2 | 1 | no | — |
| 339 | C4⋊C4 | — | 2 | 1 | no | — |
| 340 | C4⋊C4 | — | 106 | 2 | no | — |
| 341 | C4⋊C4 | — | 212 | 4 | no | — |
| 342 | C22⋊C4 | — | 2 | 1 | no | — |
| 343 | C22⋊C4 | — | 106 | 2 | no | — |
| 344 | C22⋊C4 | #11719945 | 1 | 2 | yes | — |
| 345 | C42 | — | 2 | 1 | no | — |
| 346 | C42 | — | 2 | 1 | no | — |
| 347 | C42 | — | 106 | 2 | no | — |
| 348 | C42 | — | 212 | 4 | no | — |
| 349 | C23 | — | 2 | 1 | no | — |
| 350 | C23 | C2×#11719945 | 1 | 1 | yes | characteristic |
| 351 | Q8 | — | 2 | 1 | no | — |
| 352 | Q8 | — | 2 | 1 | no | — |
| 353 | Q8 | — | 106 | 4 | no | — |
| 354 | Q8 | — | 106 | 4 | no | — |
| 355 | Q8 | — | 212 | 2 | no | — |
| 356 | Q8 | — | 212 | 2 | no | — |
| 357 | D4 | — | 2 | 1 | no | — |
| 358 | D4 | — | 2 | 1 | no | — |
| 359 | D4 | — | 4 | 1 | no | — |
| 360 | D4 | — | 4 | 1 | no | — |
| 361 | C2×C4 | — | 2 | 2 | no | — |
| 362 | C2×C4 | — | 2 | 1 | no | — |
| 363 | C2×C4 | — | 4 | 1 | no | — |
| 364 | C2×C4 | — | 4 | 1 | no | — |
| 365 | C2×C4 | — | 4 | 1 | no | — |
| 366 | C2×C4 | — | 106 | 4 | no | — |
| 367 | C2×C4 | — | 212 | 2 | no | — |
| 368 | C2×C4 | — | 212 | 2 | no | — |
| 369 | C2×C4 | — | 212 | 2 | no | — |
| 370 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 371 | C2×C4 | C2×#11719947 | 1 | 1 | yes | characteristic |
| 372 | C2×C4 | C2×#11719945 | 1 | 1 | yes | characteristic |
| 373 | C2×C4 | C2×#11719945 | 1 | 1 | yes | characteristic |
| 374 | C2×C4 | #13133263 | 1 | 1 | yes | characteristic |
| 375 | C2×C4 | #13133263 | 1 | 1 | yes | characteristic |
| 376 | C8 | — | 4 | 1 | no | — |
| 377 | C8 | — | 4 | 1 | no | — |
| 378 | C8 | — | 4 | 1 | no | — |
| 379 | C8 | — | 212 | 2 | no | — |
| 380 | C8 | — | 212 | 2 | no | — |
| 381 | C8 | #13133199 | 1 | 1 | yes | characteristic |
| 382 | C8 | #13133199 | 1 | 1 | yes | characteristic |
| 383 | C8 | #13133199 | 1 | 1 | yes | characteristic |
| 384 | C8 | #13133199 | 1 | 1 | yes | characteristic |
| 385 | C22 | — | 4 | 1 | no | — |
| 386 | C22 | — | 4 | 1 | no | — |
| 387 | C22 | — | 8 | 1 | no | — |
| 388 | C22 | #16811157 | 1 | 1 | yes | characteristic |
| 389 | C22 | #16811269 | 1 | 1 | yes | characteristic |
| 390 | C22 | #16811338 | 1 | 1 | yes | characteristic |
| 391 | C4 | — | 4 | 2 | no | — |
| 392 | C4 | — | 4 | 1 | no | — |
| 393 | C4 | — | 8 | 1 | no | — |
| 394 | C4 | — | 424 | 2 | no | — |
| 395 | C4 | — | 212 | 4 | no | — |
| 396 | C4 | C2×#13133199 | 1 | 1 | yes | characteristic |
| 397 | C4 | #16811228 | 1 | 1 | yes | characteristic |
| 398 | C4 | #16811269 | 1 | 1 | yes | characteristic |
| 399 | C4 | #16811319 | 1 | 1 | yes | characteristic |
| 400 | C2 | — | 2 | 1 | no | — |
| 401 | C2 | — | 2 | 1 | no | — |
| 402 | C2 | — | 2 | 1 | no | — |
| 403 | C2 | — | 8 | 1 | no | — |
| 404 | C2 | #20278207 | 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