← #27354945
Subgroups — #27354945
Order 13568.
584 conjugacy classes of subgroups.
The subgroup lattice has 402 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #20283810 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20283791 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #20273594 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #20273573 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #20273559 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #20273552 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #20273478 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #20273188 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #20273184 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #20273007 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C53×#3167 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #16810754 | — | 2 | 2 | no | — |
| 13 | #16810754 | C22 | 1 | 2 | yes | — |
| 14 | Q8×#88322 | C22 | 1 | 2 | yes | — |
| 15 | #16810701 | C22 | 1 | 2 | yes | — |
| 16 | #16810695 | — | 2 | 2 | no | — |
| 17 | D4×#88322 | C22 | 1 | 2 | yes | — |
| 18 | #16810684 | — | 2 | 2 | no | — |
| 19 | #16810680 | C22 | 1 | 1 | yes | characteristic |
| 20 | #16810680 | C22 | 1 | 1 | yes | characteristic |
| 21 | #16810676 | C22 | 1 | 1 | yes | characteristic |
| 22 | #16810676 | C22 | 1 | 1 | yes | characteristic |
| 23 | #16810590 | — | 2 | 2 | no | — |
| 24 | #16810376 | C22 | 1 | 2 | yes | — |
| 25 | #16810374 | C22 | 1 | 2 | yes | — |
| 26 | Q8⋊#88322 | C22 | 1 | 2 | yes | — |
| 27 | Q8⋊#88322 | C22 | 1 | 2 | yes | — |
| 28 | D4⋊#88322 | C22 | 1 | 2 | yes | — |
| 29 | D4⋊#88322 | C22 | 1 | 2 | yes | — |
| 30 | #16810345 | C22 | 1 | 1 | yes | characteristic |
| 31 | #16810345 | C22 | 1 | 1 | yes | characteristic |
| 32 | #16810345 | C22 | 1 | 1 | yes | characteristic |
| 33 | #16810345 | C22 | 1 | 1 | yes | characteristic |
| 34 | C53×#533 | C22 | 1 | 1 | yes | characteristic |
| 35 | C53×#532 | C22 | 1 | 1 | yes | characteristic |
| 36 | C53×#498 | C4 | 1 | 1 | yes | characteristic |
| 37 | C53×#492 | C4 | 1 | 1 | yes | characteristic |
| 38 | C53×#487 | C4 | 1 | 1 | yes | characteristic |
| 39 | C53×#486 | C4 | 1 | 1 | yes | characteristic |
| 40 | C53×#465 | C4 | 1 | 2 | yes | — |
| 41 | C53×#465 | C4 | 1 | 2 | yes | — |
| 42 | C4×SD16×C53 | C22 | 1 | 2 | yes | — |
| 43 | C4×SD16×C53 | C22 | 1 | 2 | yes | — |
| 44 | C2×C4×C8×C53 | C22 | 1 | 1 | yes | characteristic |
| 45 | C2×#11719917 | — | 2 | 2 | no | — |
| 46 | C22×#88322 | — | 2 | 2 | no | — |
| 47 | C4⋊#88322 | — | 2 | 1 | no | — |
| 48 | C4⋊#88322 | — | 2 | 2 | no | — |
| 49 | C4⋊#88322 | — | 2 | 2 | no | — |
| 50 | C4⋊#88322 | D4 | 1 | 2 | yes | — |
| 51 | C4⋊#88322 | C23 | 1 | 2 | yes | — |
| 52 | C4⋊#88322 | C23 | 1 | 2 | yes | — |
| 53 | C22⋊#88322 | — | 2 | 2 | no | — |
| 54 | C22⋊#88322 | — | 2 | 2 | no | — |
| 55 | C22⋊#88322 | — | 2 | 1 | no | — |
| 56 | C22⋊#88322 | — | 2 | 1 | no | — |
| 57 | C22⋊#88322 | — | 2 | 1 | no | — |
| 58 | C22⋊#88322 | D4 | 1 | 2 | yes | — |
| 59 | #13133128 | — | 2 | 1 | no | — |
| 60 | #13133128 | — | 2 | 1 | no | — |
| 61 | #13133128 | — | 2 | 2 | no | — |
| 62 | C4×#88322 | — | 2 | 2 | no | — |
| 63 | C4×#88322 | C23 | 1 | 1 | yes | characteristic |
| 64 | C4×#88322 | C23 | 1 | 1 | yes | characteristic |
| 65 | C4×#88322 | C23 | 1 | 1 | yes | characteristic |
| 66 | C4×#88322 | C23 | 1 | 1 | yes | characteristic |
| 67 | C2×#41×C53 | — | 2 | 1 | no | — |
| 68 | C2×SD16×C53 | C2×C4 | 1 | 2 | yes | — |
| 69 | C2×SD16×C53 | C2×C4 | 1 | 2 | yes | — |
| 70 | C22×C8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 71 | C22×C8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 72 | C4⋊Q8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 73 | C4⋊Q8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 74 | C4⋊Q8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 75 | #127×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 76 | #125×C53 | — | 2 | 1 | no | — |
| 77 | #124×C53 | — | 2 | 1 | no | — |
| 78 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 79 | C22⋊Q8×C53 | C2×C4 | 1 | 2 | yes | — |
| 80 | #121×C53 | — | 2 | 1 | no | — |
| 81 | #121×C53 | C2×C4 | 1 | 2 | yes | — |
| 82 | C4×Q8×C53 | — | 2 | 1 | no | — |
| 83 | C4×Q8×C53 | C23 | 1 | 2 | yes | — |
| 84 | C4×D4×C53 | — | 2 | 1 | no | — |
| 85 | C4×D4×C53 | C23 | 1 | 2 | yes | — |
| 86 | #117×C53 | — | 2 | 1 | no | — |
| 87 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 88 | #106×C53 | C2×C4 | 1 | 2 | yes | — |
| 89 | #106×C53 | C2×C4 | 1 | 2 | yes | — |
| 90 | #103×C53 | C2×C4 | 1 | 2 | yes | — |
| 91 | #103×C53 | C2×C4 | 1 | 2 | yes | — |
| 92 | #102×C53 | C2×C4 | 1 | 2 | yes | — |
| 93 | #102×C53 | C2×C4 | 1 | 2 | yes | — |
| 94 | C4×C8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 95 | C4×C8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 96 | C4×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 97 | C4×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 98 | #41×C53 | — | 8 | 2 | no | — |
| 99 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 100 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 101 | C2×Q8×C53 | C22×C4 | 1 | 2 | yes | — |
| 102 | C2×D4×C53 | — | 2 | 2 | no | — |
| 103 | C2×D4×C53 | — | 2 | 1 | no | — |
| 104 | C2×D4×C53 | — | 2 | 1 | no | — |
| 105 | C2×D4×C53 | C22×C4 | 1 | 2 | yes | — |
| 106 | C22×C4×C53 | — | 2 | 2 | no | — |
| 107 | C22×C4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 108 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | C22×C4×C53 | #41 | 1 | 1 | yes | characteristic |
| 110 | SD16×C53 | — | 4 | 2 | no | — |
| 111 | SD16×C53 | — | 4 | 2 | no | — |
| 112 | C2×C8×C53 | — | 4 | 1 | no | — |
| 113 | C2×C8×C53 | — | 4 | 1 | no | — |
| 114 | C2×C8×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 115 | C2×C8×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 116 | C2×C8×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 117 | C2×C8×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 118 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 119 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 120 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 121 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 122 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 123 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 124 | C4⋊C4×C53 | C22×C4 | 1 | 2 | yes | — |
| 125 | C4⋊C4×C53 | C22×C4 | 1 | 2 | yes | — |
| 126 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 127 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 128 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 129 | C42×C53 | — | 2 | 2 | no | — |
| 130 | C42×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 131 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 132 | C42×C53 | #41 | 1 | 1 | yes | characteristic |
| 133 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 134 | #11719917 | — | 8 | 2 | no | — |
| 135 | C2×#88322 | — | 2 | 2 | no | — |
| 136 | C2×#88322 | — | 2 | 2 | no | — |
| 137 | C2×#88322 | — | 2 | 1 | no | — |
| 138 | C2×#88322 | — | 2 | 1 | no | — |
| 139 | C2×#88322 | — | 8 | 2 | no | — |
| 140 | C2×#88322 | C2×D4 | 1 | 2 | yes | — |
| 141 | C2×#88322 | C2×D4 | 1 | 2 | yes | — |
| 142 | C23×C53 | — | 2 | 2 | no | — |
| 143 | C23×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 144 | Q8×C53 | — | 2 | 2 | no | — |
| 145 | Q8×C53 | — | 2 | 2 | no | — |
| 146 | Q8×C53 | — | 8 | 1 | no | — |
| 147 | Q8×C53 | — | 8 | 1 | no | — |
| 148 | D4×C53 | — | 2 | 2 | no | — |
| 149 | D4×C53 | — | 2 | 2 | no | — |
| 150 | D4×C53 | — | 8 | 1 | no | — |
| 151 | D4×C53 | — | 8 | 1 | no | — |
| 152 | D4×C53 | — | 8 | 2 | no | — |
| 153 | C2×C4×C53 | — | 2 | 1 | no | — |
| 154 | C2×C4×C53 | — | 2 | 1 | no | — |
| 155 | C2×C4×C53 | — | 2 | 2 | no | — |
| 156 | C2×C4×C53 | — | 2 | 2 | no | — |
| 157 | C2×C4×C53 | — | 2 | 2 | no | — |
| 158 | C2×C4×C53 | — | 2 | 2 | no | — |
| 159 | C2×C4×C53 | — | 4 | 1 | no | — |
| 160 | C2×C4×C53 | — | 4 | 2 | no | — |
| 161 | C2×C4×C53 | — | 4 | 2 | no | — |
| 162 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 163 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 164 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 165 | C2×C4×C53 | C23×C4 | 1 | 1 | yes | characteristic |
| 166 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 167 | C2×C4×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 168 | C8×C53 | — | 2 | 1 | no | — |
| 169 | C8×C53 | — | 2 | 1 | no | — |
| 170 | C8×C53 | — | 2 | 1 | no | — |
| 171 | C8×C53 | — | 2 | 1 | no | — |
| 172 | #88322 | — | 2 | 2 | no | — |
| 173 | #88322 | — | 2 | 2 | no | — |
| 174 | #88322 | — | 4 | 1 | no | — |
| 175 | #88322 | — | 4 | 1 | no | — |
| 176 | #88322 | — | 4 | 2 | no | — |
| 177 | #88322 | — | 4 | 2 | no | — |
| 178 | #17990 | — | 53 | 1 | no | maximal, Sylow |
| 179 | C22×C53 | — | 2 | 1 | no | — |
| 180 | C22×C53 | — | 2 | 1 | no | — |
| 181 | C22×C53 | — | 2 | 1 | no | — |
| 182 | C22×C53 | — | 4 | 2 | no | — |
| 183 | C22×C53 | — | 4 | 2 | no | — |
| 184 | C22×C53 | — | 4 | 2 | no | — |
| 185 | C22×C53 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 186 | C4×C53 | — | 2 | 1 | no | — |
| 187 | C4×C53 | — | 2 | 1 | no | — |
| 188 | C4×C53 | — | 2 | 1 | no | — |
| 189 | C4×C53 | — | 2 | 1 | no | — |
| 190 | C4×C53 | — | 4 | 2 | no | — |
| 191 | C4×C53 | — | 4 | 2 | no | — |
| 192 | C4×C53 | — | 4 | 2 | no | — |
| 193 | C4×C53 | #568 | 1 | 1 | yes | characteristic |
| 194 | C4×C53 | #568 | 1 | 1 | yes | characteristic |
| 195 | C4×C53 | #577 | 1 | 2 | yes | — |
| 196 | #3167 | D53 | 1 | 1 | yes | characteristic |
| 197 | #2985 | — | 53 | 1 | no | — |
| 198 | #2981 | — | 53 | 1 | no | — |
| 199 | #1588 | — | 53 | 2 | no | — |
| 200 | #1585 | — | 53 | 2 | no | — |
| 201 | #1583 | — | 53 | 2 | no | — |
| 202 | #1582 | — | 53 | 2 | no | — |
| 203 | #1568 | — | 53 | 1 | no | — |
| 204 | #1497 | — | 53 | 1 | no | — |
| 205 | #1496 | — | 53 | 1 | no | — |
| 206 | #1452 | — | 53 | 1 | no | — |
| 207 | C2×C53 | — | 4 | 1 | no | — |
| 208 | C2×C53 | — | 8 | 2 | no | — |
| 209 | C2×C53 | #2932 | 1 | 1 | yes | characteristic |
| 210 | C2×C53 | #2949 | 1 | 1 | yes | characteristic |
| 211 | C2×C53 | #2957 | 1 | 1 | yes | characteristic |
| 212 | #533 | C2×D53 | 1 | 1 | yes | characteristic |
| 213 | #532 | C2×D53 | 1 | 1 | yes | characteristic |
| 214 | #498 | Dic53 | 1 | 1 | yes | characteristic |
| 215 | #492 | Dic53 | 1 | 1 | yes | characteristic |
| 216 | #487 | Dic53 | 1 | 1 | yes | characteristic |
| 217 | #486 | Dic53 | 1 | 1 | yes | characteristic |
| 218 | #465 | Dic53 | 1 | 2 | yes | — |
| 219 | #465 | Dic53 | 1 | 2 | yes | — |
| 220 | #446 | — | 53 | 2 | no | — |
| 221 | #446 | — | 106 | 2 | no | — |
| 222 | C8×Q8 | — | 53 | 2 | no | — |
| 223 | C4×SD16 | C2×D53 | 1 | 2 | yes | — |
| 224 | C4×SD16 | C2×D53 | 1 | 2 | yes | — |
| 225 | #436 | — | 53 | 2 | no | — |
| 226 | #435 | — | 106 | 2 | no | — |
| 227 | C8×D4 | — | 53 | 2 | no | — |
| 228 | #433 | — | 106 | 2 | no | — |
| 229 | #432 | — | 53 | 1 | no | — |
| 230 | #432 | — | 53 | 1 | no | — |
| 231 | #431 | — | 53 | 1 | no | — |
| 232 | #431 | — | 53 | 1 | no | — |
| 233 | #408 | — | 106 | 2 | no | — |
| 234 | C2×C4×C8 | C2×D53 | 1 | 1 | yes | characteristic |
| 235 | #335 | — | 53 | 2 | no | — |
| 236 | #334 | — | 53 | 2 | no | — |
| 237 | Q8⋊C8 | — | 53 | 2 | no | — |
| 238 | Q8⋊C8 | — | 53 | 2 | no | — |
| 239 | D4⋊C8 | — | 53 | 2 | no | — |
| 240 | D4⋊C8 | — | 53 | 2 | no | — |
| 241 | #322 | — | 53 | 1 | no | — |
| 242 | #322 | — | 53 | 1 | no | — |
| 243 | #322 | — | 53 | 1 | no | — |
| 244 | #322 | — | 53 | 1 | no | — |
| 245 | C53 | #17990 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 246 | C2×#41 | — | 2 | 1 | no | — |
| 247 | C2×SD16 | C2×Dic53 | 1 | 2 | yes | — |
| 248 | C2×SD16 | C2×Dic53 | 1 | 2 | yes | — |
| 249 | C2×M16 | — | 106 | 2 | no | — |
| 250 | C22×C8 | — | 106 | 2 | no | — |
| 251 | C22×C8 | C2×Dic53 | 1 | 1 | yes | characteristic |
| 252 | C22×C8 | C2×Dic53 | 1 | 1 | yes | characteristic |
| 253 | C4⋊Q8 | C2×Dic53 | 1 | 1 | yes | characteristic |
| 254 | C4⋊Q8 | C2×Dic53 | 1 | 1 | yes | characteristic |
| 255 | C4⋊Q8 | C2×Dic53 | 1 | 1 | yes | characteristic |
| 256 | #127 | C2×Dic53 | 1 | 1 | yes | characteristic |
| 257 | #125 | — | 2 | 1 | no | — |
| 258 | #124 | — | 2 | 1 | no | — |
| 259 | C22⋊Q8 | — | 2 | 1 | no | — |
| 260 | C22⋊Q8 | C2×Dic53 | 1 | 2 | yes | — |
| 261 | #121 | — | 2 | 1 | no | — |
| 262 | #121 | C2×Dic53 | 1 | 2 | yes | — |
| 263 | C4×Q8 | — | 2 | 1 | no | — |
| 264 | C4×Q8 | C22×D53 | 1 | 2 | yes | — |
| 265 | C4×D4 | — | 2 | 1 | no | — |
| 266 | C4×D4 | C22×D53 | 1 | 2 | yes | — |
| 267 | #117 | — | 2 | 1 | no | — |
| 268 | C2×C42 | C22×D53 | 1 | 1 | yes | characteristic |
| 269 | #106 | C2×Dic53 | 1 | 2 | yes | — |
| 270 | #106 | C2×Dic53 | 1 | 2 | yes | — |
| 271 | C4⋊C8 | — | 53 | 2 | no | — |
| 272 | C4⋊C8 | — | 53 | 2 | no | — |
| 273 | C4⋊C8 | — | 53 | 2 | no | — |
| 274 | C4⋊C8 | — | 106 | 2 | no | — |
| 275 | C4⋊C8 | — | 106 | 2 | no | — |
| 276 | C4⋊C8 | — | 106 | 1 | no | — |
| 277 | #103 | C2×Dic53 | 1 | 2 | yes | — |
| 278 | #103 | C2×Dic53 | 1 | 2 | yes | — |
| 279 | #102 | C2×Dic53 | 1 | 2 | yes | — |
| 280 | #102 | C2×Dic53 | 1 | 2 | yes | — |
| 281 | C22⋊C8 | — | 53 | 2 | no | — |
| 282 | C22⋊C8 | — | 106 | 2 | no | — |
| 283 | C22⋊C8 | — | 106 | 2 | no | — |
| 284 | C22⋊C8 | — | 106 | 1 | no | — |
| 285 | C22⋊C8 | — | 106 | 1 | no | — |
| 286 | C22⋊C8 | — | 106 | 1 | no | — |
| 287 | #97 | — | 106 | 2 | no | — |
| 288 | #97 | — | 106 | 1 | no | — |
| 289 | #97 | — | 106 | 1 | no | — |
| 290 | C4×C8 | — | 53 | 1 | no | — |
| 291 | C4×C8 | — | 53 | 1 | no | — |
| 292 | C4×C8 | — | 53 | 1 | no | — |
| 293 | C4×C8 | — | 53 | 1 | no | — |
| 294 | C4×C8 | — | 106 | 2 | no | — |
| 295 | C4×C8 | C2×Dic53 | 1 | 1 | yes | characteristic |
| 296 | C4×C8 | C2×Dic53 | 1 | 1 | yes | characteristic |
| 297 | C4×C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 298 | C4×C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 299 | #41 | — | 8 | 2 | no | — |
| 300 | C2×Q8 | — | 2 | 1 | no | — |
| 301 | C2×Q8 | — | 2 | 1 | no | — |
| 302 | C2×Q8 | C22×Dic53 | 1 | 2 | yes | — |
| 303 | C2×D4 | — | 2 | 2 | no | — |
| 304 | C2×D4 | — | 2 | 1 | no | — |
| 305 | C2×D4 | — | 2 | 1 | no | — |
| 306 | C2×D4 | C22×Dic53 | 1 | 2 | yes | — |
| 307 | C22×C4 | — | 2 | 2 | no | — |
| 308 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 309 | C22×C4 | #11719947 | 1 | 1 | yes | characteristic |
| 310 | C22×C4 | C22×Dic53 | 1 | 1 | yes | characteristic |
| 311 | SD16 | — | 4 | 2 | no | — |
| 312 | SD16 | — | 4 | 2 | no | — |
| 313 | M16 | — | 424 | 2 | no | — |
| 314 | C2×C8 | — | 4 | 1 | no | — |
| 315 | C2×C8 | — | 4 | 1 | no | — |
| 316 | C2×C8 | — | 53 | 2 | no | — |
| 317 | C2×C8 | — | 53 | 2 | no | — |
| 318 | C2×C8 | — | 106 | 2 | no | — |
| 319 | C2×C8 | — | 106 | 2 | no | — |
| 320 | C2×C8 | — | 106 | 1 | no | — |
| 321 | C2×C8 | — | 106 | 1 | no | — |
| 322 | C2×C8 | — | 424 | 2 | no | — |
| 323 | C2×C8 | C22×Dic53 | 1 | 1 | yes | characteristic |
| 324 | C2×C8 | C22×Dic53 | 1 | 1 | yes | characteristic |
| 325 | C2×C8 | C22×Dic53 | 1 | 1 | yes | characteristic |
| 326 | C2×C8 | C22×Dic53 | 1 | 1 | yes | characteristic |
| 327 | C4⋊C4 | — | 2 | 1 | no | — |
| 328 | C4⋊C4 | — | 2 | 1 | no | — |
| 329 | C4⋊C4 | — | 2 | 1 | no | — |
| 330 | C4⋊C4 | — | 2 | 1 | no | — |
| 331 | C4⋊C4 | — | 2 | 2 | no | — |
| 332 | C4⋊C4 | — | 2 | 2 | no | — |
| 333 | C4⋊C4 | C22×Dic53 | 1 | 2 | yes | — |
| 334 | C4⋊C4 | C22×Dic53 | 1 | 2 | yes | — |
| 335 | C22⋊C4 | — | 2 | 2 | no | — |
| 336 | C22⋊C4 | — | 2 | 2 | no | — |
| 337 | C22⋊C4 | — | 2 | 2 | no | — |
| 338 | C42 | — | 2 | 2 | no | — |
| 339 | C42 | D4×D53 | 1 | 1 | yes | characteristic |
| 340 | C42 | #11719947 | 1 | 1 | yes | characteristic |
| 341 | C42 | C22×Dic53 | 1 | 1 | yes | characteristic |
| 342 | C42 | C23×D53 | 1 | 1 | yes | characteristic |
| 343 | C23 | — | 2 | 2 | no | — |
| 344 | C23 | D4×Dic53 | 1 | 1 | yes | characteristic |
| 345 | Q8 | — | 2 | 2 | no | — |
| 346 | Q8 | — | 2 | 2 | no | — |
| 347 | Q8 | — | 8 | 1 | no | — |
| 348 | Q8 | — | 8 | 1 | no | — |
| 349 | D4 | — | 2 | 2 | no | — |
| 350 | D4 | — | 2 | 2 | no | — |
| 351 | D4 | — | 8 | 1 | no | — |
| 352 | D4 | — | 8 | 1 | no | — |
| 353 | D4 | — | 8 | 2 | no | — |
| 354 | C2×C4 | — | 2 | 1 | no | — |
| 355 | C2×C4 | — | 2 | 1 | no | — |
| 356 | C2×C4 | — | 2 | 2 | no | — |
| 357 | C2×C4 | — | 2 | 2 | no | — |
| 358 | C2×C4 | — | 2 | 2 | no | — |
| 359 | C2×C4 | — | 2 | 2 | no | — |
| 360 | C2×C4 | — | 4 | 1 | no | — |
| 361 | C2×C4 | — | 4 | 2 | no | — |
| 362 | C2×C4 | — | 4 | 2 | no | — |
| 363 | C2×C4 | D4×Dic53 | 1 | 1 | yes | characteristic |
| 364 | C2×C4 | D4×Dic53 | 1 | 1 | yes | characteristic |
| 365 | C2×C4 | D4×Dic53 | 1 | 1 | yes | characteristic |
| 366 | C2×C4 | C23×Dic53 | 1 | 1 | yes | characteristic |
| 367 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 368 | C2×C4 | C2×#11719947 | 1 | 1 | yes | characteristic |
| 369 | C8 | — | 2 | 1 | no | — |
| 370 | C8 | — | 2 | 1 | no | — |
| 371 | C8 | — | 2 | 1 | no | — |
| 372 | C8 | — | 2 | 1 | no | — |
| 373 | C8 | — | 106 | 2 | no | — |
| 374 | C8 | — | 106 | 2 | no | — |
| 375 | C8 | — | 212 | 1 | no | — |
| 376 | C8 | — | 212 | 1 | no | — |
| 377 | C8 | — | 212 | 2 | no | — |
| 378 | C8 | — | 212 | 2 | no | — |
| 379 | C22 | — | 2 | 1 | no | — |
| 380 | C22 | — | 2 | 1 | no | — |
| 381 | C22 | — | 2 | 1 | no | — |
| 382 | C22 | — | 4 | 2 | no | — |
| 383 | C22 | — | 4 | 2 | no | — |
| 384 | C22 | — | 4 | 2 | no | — |
| 385 | C22 | C2×D4×Dic53 | 1 | 1 | yes | characteristic |
| 386 | C4 | — | 2 | 1 | no | — |
| 387 | C4 | — | 2 | 1 | no | — |
| 388 | C4 | — | 2 | 1 | no | — |
| 389 | C4 | — | 2 | 1 | no | — |
| 390 | C4 | — | 4 | 2 | no | — |
| 391 | C4 | — | 4 | 2 | no | — |
| 392 | C4 | — | 4 | 2 | no | — |
| 393 | C4 | #16811390 | 1 | 1 | yes | characteristic |
| 394 | C4 | #16811390 | 1 | 1 | yes | characteristic |
| 395 | C4 | #16811429 | 1 | 2 | yes | — |
| 396 | C2 | — | 4 | 1 | no | — |
| 397 | C2 | — | 8 | 2 | no | — |
| 398 | C2 | #20283433 | 1 | 1 | yes | characteristic |
| 399 | C2 | #20283575 | 1 | 1 | yes | characteristic |
| 400 | C2 | #20283632 | 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