← #30826711
Subgroups — #30826711
Order 17152.
576 conjugacy classes of subgroups.
The subgroup lattice has 362 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22570779 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22569360 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22559082 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22559075 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22559054 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22559047 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22558965 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #22558675 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C67×#1452 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #16863930 | C22 | 1 | 2 | yes | — |
| 11 | #16863798 | C4 | 1 | 1 | yes | characteristic |
| 12 | #16863780 | C4 | 1 | 1 | yes | characteristic |
| 13 | #16863751 | C4 | 1 | 2 | yes | — |
| 14 | #16863637 | C4 | 1 | 1 | yes | characteristic |
| 15 | #16863632 | C4 | 1 | 1 | yes | characteristic |
| 16 | #16863625 | C4 | 1 | 2 | yes | — |
| 17 | #16863526 | C22 | 1 | 2 | yes | — |
| 18 | C8×Dic134 | C22 | 1 | 2 | yes | — |
| 19 | C4×Dic268 | C22 | 1 | 1 | yes | characteristic |
| 20 | C4×#11761617 | C22 | 1 | 2 | yes | — |
| 21 | C4×D536 | C22 | 1 | 1 | yes | characteristic |
| 22 | #16863475 | C22 | 1 | 2 | yes | — |
| 23 | #16863471 | — | 2 | 2 | no | — |
| 24 | #16863470 | — | 2 | 2 | no | — |
| 25 | C8×D268 | C22 | 1 | 2 | yes | — |
| 26 | #16863456 | — | 2 | 2 | no | — |
| 27 | #16863421 | — | 2 | 2 | no | — |
| 28 | #16863420 | C22 | 1 | 2 | yes | — |
| 29 | #16863147 | C22 | 1 | 1 | yes | characteristic |
| 30 | #16863147 | C22 | 1 | 1 | yes | characteristic |
| 31 | #16863147 | C22 | 1 | 2 | yes | — |
| 32 | #16863128 | C22 | 1 | 2 | yes | — |
| 33 | #16863128 | C22 | 1 | 2 | yes | — |
| 34 | #16863125 | C22 | 1 | 2 | yes | — |
| 35 | #16863125 | C22 | 1 | 2 | yes | — |
| 36 | #431×C67 | C22 | 1 | 1 | yes | characteristic |
| 37 | #431×C67 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×C4×C8×C67 | C22 | 1 | 1 | yes | characteristic |
| 39 | #322×C67 | C22 | 1 | 2 | yes | — |
| 40 | #322×C67 | C22 | 1 | 2 | yes | — |
| 41 | C2×Dic268 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | C2×#11761617 | C2×C4 | 1 | 2 | yes | — |
| 43 | C2×D536 | C2×C4 | 1 | 1 | yes | characteristic |
| 44 | C2×#11761612 | — | 2 | 2 | no | — |
| 45 | C2×#11761611 | — | 2 | 2 | no | — |
| 46 | C2×C8×D67 | — | 2 | 2 | no | — |
| 47 | #14524037 | — | 2 | 2 | no | — |
| 48 | #14524035 | C2×C4 | 1 | 2 | yes | — |
| 49 | #14524031 | C2×C4 | 1 | 2 | yes | — |
| 50 | #14524026 | — | 2 | 2 | no | — |
| 51 | #14524022 | C2×C4 | 1 | 2 | yes | — |
| 52 | #14524017 | C2×C4 | 1 | 2 | yes | — |
| 53 | C4×Dic134 | C23 | 1 | 2 | yes | — |
| 54 | C4×D268 | C23 | 1 | 2 | yes | — |
| 55 | C4×C22⋊D67 | — | 2 | 2 | no | — |
| 56 | #14524000 | — | 2 | 2 | no | — |
| 57 | #14523977 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | #14523977 | C2×C4 | 1 | 1 | yes | characteristic |
| 59 | #14523975 | C2×C4 | 1 | 2 | yes | — |
| 60 | C4⋊(C67⋊C8) | — | 2 | 2 | no | — |
| 61 | C4⋊(C67⋊C8) | C23 | 1 | 2 | yes | — |
| 62 | C4⋊(C67⋊C8) | C23 | 1 | 2 | yes | — |
| 63 | Dic67⋊C8 | — | 2 | 2 | no | — |
| 64 | Dic67⋊C8 | — | 2 | 2 | no | — |
| 65 | #14523968 | C2×C4 | 1 | 2 | yes | — |
| 66 | #14523968 | C2×C4 | 1 | 2 | yes | — |
| 67 | #14523965 | C2×C4 | 1 | 2 | yes | — |
| 68 | #14523965 | C2×C4 | 1 | 2 | yes | — |
| 69 | (C2×D67)⋊C8 | — | 2 | 2 | no | — |
| 70 | (C2×D67)⋊C8 | — | 2 | 2 | no | — |
| 71 | #14523953 | — | 2 | 2 | no | — |
| 72 | C8×Dic67 | — | 2 | 2 | no | — |
| 73 | C22×C8×C67 | C2×C4 | 1 | 1 | yes | characteristic |
| 74 | C22×C8×C67 | C2×C4 | 1 | 1 | yes | characteristic |
| 75 | C2×C42×C67 | C23 | 1 | 1 | yes | characteristic |
| 76 | C4⋊C8×C67 | — | 2 | 1 | no | — |
| 77 | C4⋊C8×C67 | D4 | 1 | 2 | yes | — |
| 78 | C22⋊C8×C67 | — | 2 | 1 | no | — |
| 79 | C22⋊C8×C67 | D4 | 1 | 1 | yes | characteristic |
| 80 | C22⋊C8×C67 | D4 | 1 | 1 | yes | characteristic |
| 81 | C4×C8×C67 | C2×C4 | 1 | 1 | yes | characteristic |
| 82 | C4×C8×C67 | C2×C4 | 1 | 1 | yes | characteristic |
| 83 | C4×C8×C67 | C23 | 1 | 2 | yes | — |
| 84 | C4×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 85 | C4×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 86 | C4×C8×C67 | C23 | 1 | 2 | yes | — |
| 87 | C2×Dic134 | C22×C4 | 1 | 2 | yes | — |
| 88 | C2×D268 | C22×C4 | 1 | 2 | yes | — |
| 89 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 90 | C2×C4×D67 | — | 2 | 2 | no | — |
| 91 | Dic268 | — | 4 | 1 | no | — |
| 92 | #11761617 | — | 4 | 2 | no | — |
| 93 | D536 | — | 4 | 1 | no | — |
| 94 | #11761612 | — | 8 | 2 | no | — |
| 95 | #11761611 | — | 8 | 2 | no | — |
| 96 | C2×C67⋊C8 | — | 2 | 2 | no | — |
| 97 | C2×C67⋊C8 | — | 2 | 2 | no | — |
| 98 | C8×D67 | — | 8 | 2 | no | — |
| 99 | C4⋊Dic67 | C22×C4 | 1 | 2 | yes | — |
| 100 | C4⋊Dic67 | C22×C4 | 1 | 2 | yes | — |
| 101 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 102 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 103 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 104 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 105 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 106 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 107 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 108 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 109 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 110 | C4×Dic67 | — | 2 | 2 | no | — |
| 111 | C22×C4×C67 | C22×C4 | 1 | 1 | yes | characteristic |
| 112 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 113 | C22×C4×C67 | #41 | 1 | 1 | yes | characteristic |
| 114 | C2×C8×C67 | — | 2 | 2 | no | — |
| 115 | C2×C8×C67 | — | 4 | 1 | no | — |
| 116 | C2×C8×C67 | — | 4 | 1 | no | — |
| 117 | C2×C8×C67 | C22×C4 | 1 | 1 | yes | characteristic |
| 118 | C2×C8×C67 | C22×C4 | 1 | 1 | yes | characteristic |
| 119 | C2×C8×C67 | C22×C4 | 1 | 1 | yes | characteristic |
| 120 | C2×C8×C67 | C22×C4 | 1 | 1 | yes | characteristic |
| 121 | C2×C8×C67 | C2×D4 | 1 | 2 | yes | — |
| 122 | C2×C8×C67 | C2×D4 | 1 | 2 | yes | — |
| 123 | C42×C67 | C22×C4 | 1 | 1 | yes | characteristic |
| 124 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 125 | C42×C67 | #41 | 1 | 1 | yes | characteristic |
| 126 | C42×C67 | C24 | 1 | 1 | yes | characteristic |
| 127 | C23×C67 | C4×D4 | 1 | 1 | yes | characteristic |
| 128 | C22×D67 | — | 2 | 2 | no | — |
| 129 | C2×C4×C67 | — | 2 | 1 | no | — |
| 130 | C2×C4×C67 | — | 2 | 1 | no | — |
| 131 | C2×C4×C67 | — | 2 | 2 | no | — |
| 132 | C2×C4×C67 | — | 4 | 1 | no | — |
| 133 | C2×C4×C67 | C4×D4 | 1 | 1 | yes | characteristic |
| 134 | C2×C4×C67 | C4×D4 | 1 | 1 | yes | characteristic |
| 135 | C2×C4×C67 | C4×D4 | 1 | 1 | yes | characteristic |
| 136 | C2×C4×C67 | C23×C4 | 1 | 1 | yes | characteristic |
| 137 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 138 | C2×C4×C67 | C2×#41 | 1 | 1 | yes | characteristic |
| 139 | C22⋊D67 | — | 8 | 2 | no | — |
| 140 | C2×Dic67 | — | 2 | 2 | no | — |
| 141 | C2×Dic67 | — | 2 | 2 | no | — |
| 142 | C2×Dic67 | — | 2 | 2 | no | — |
| 143 | D268 | — | 2 | 2 | no | — |
| 144 | D268 | — | 2 | 2 | no | — |
| 145 | C4×D67 | — | 4 | 2 | no | — |
| 146 | C4×D67 | — | 4 | 2 | no | — |
| 147 | Dic134 | — | 2 | 2 | no | — |
| 148 | Dic134 | — | 2 | 2 | no | — |
| 149 | C8×C67 | — | 2 | 1 | no | — |
| 150 | C8×C67 | — | 2 | 1 | no | — |
| 151 | C8×C67 | — | 2 | 1 | no | — |
| 152 | C8×C67 | — | 2 | 1 | no | — |
| 153 | C8×C67 | — | 2 | 2 | no | — |
| 154 | C8×C67 | — | 2 | 2 | no | — |
| 155 | C8×C67 | — | 4 | 2 | no | — |
| 156 | C67⋊C8 | — | 4 | 2 | no | — |
| 157 | C67⋊C8 | — | 4 | 2 | no | — |
| 158 | C22×C67 | — | 2 | 1 | no | — |
| 159 | C22×C67 | — | 2 | 1 | no | — |
| 160 | C22×C67 | — | 2 | 1 | no | — |
| 161 | C22×C67 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 162 | C2×D67 | — | 4 | 2 | no | — |
| 163 | C2×D67 | — | 4 | 2 | no | — |
| 164 | C2×D67 | — | 4 | 2 | no | — |
| 165 | C4×C67 | — | 2 | 1 | no | — |
| 166 | C4×C67 | — | 2 | 1 | no | — |
| 167 | C4×C67 | — | 2 | 1 | no | — |
| 168 | C4×C67 | — | 2 | 1 | no | — |
| 169 | C4×C67 | #568 | 1 | 1 | yes | characteristic |
| 170 | C4×C67 | #568 | 1 | 1 | yes | characteristic |
| 171 | C4×C67 | #577 | 1 | 2 | yes | — |
| 172 | Dic67 | — | 4 | 2 | no | — |
| 173 | Dic67 | — | 4 | 2 | no | — |
| 174 | Dic67 | — | 4 | 2 | no | — |
| 175 | #17993 | — | 67 | 1 | no | maximal, Sylow |
| 176 | C2×C67 | — | 4 | 1 | no | — |
| 177 | C2×C67 | #2932 | 1 | 1 | yes | characteristic |
| 178 | C2×C67 | #2952 | 1 | 1 | yes | characteristic |
| 179 | C2×C67 | #2957 | 1 | 1 | yes | characteristic |
| 180 | D67 | — | 8 | 2 | no | — |
| 181 | #3168 | — | 67 | 1 | no | — |
| 182 | #2993 | — | 67 | 2 | no | — |
| 183 | #1587 | — | 67 | 2 | no | — |
| 184 | #1586 | — | 67 | 2 | no | — |
| 185 | #1583 | — | 67 | 2 | no | — |
| 186 | #1582 | — | 67 | 2 | no | — |
| 187 | #1566 | — | 67 | 1 | no | — |
| 188 | #1495 | — | 67 | 2 | no | — |
| 189 | #1452 | D67 | 1 | 1 | yes | characteristic, complemented |
| 190 | C67 | #17993 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 191 | #529 | — | 67 | 2 | no | — |
| 192 | #499 | — | 67 | 1 | no | — |
| 193 | #495 | — | 67 | 1 | no | — |
| 194 | #488 | — | 67 | 2 | no | — |
| 195 | #467 | — | 67 | 1 | no | — |
| 196 | #466 | — | 67 | 1 | no | — |
| 197 | #465 | — | 67 | 2 | no | — |
| 198 | #446 | — | 67 | 2 | no | — |
| 199 | C8×Q8 | — | 67 | 2 | no | — |
| 200 | C4×Q16 | — | 67 | 1 | no | — |
| 201 | C4×SD16 | — | 67 | 2 | no | — |
| 202 | C4×D8 | — | 67 | 1 | no | — |
| 203 | #436 | — | 67 | 2 | no | — |
| 204 | #436 | — | 134 | 2 | no | — |
| 205 | #435 | — | 134 | 2 | no | — |
| 206 | C8×D4 | — | 67 | 2 | no | — |
| 207 | #433 | — | 134 | 2 | no | — |
| 208 | #431 | C2×D67 | 1 | 1 | yes | characteristic |
| 209 | #431 | C2×D67 | 1 | 1 | yes | characteristic |
| 210 | #424 | — | 134 | 2 | no | — |
| 211 | #423 | — | 67 | 2 | no | — |
| 212 | C2×C4×C8 | C2×D67 | 1 | 1 | yes | characteristic |
| 213 | #334 | — | 67 | 1 | no | — |
| 214 | #334 | — | 67 | 1 | no | — |
| 215 | #334 | — | 67 | 2 | no | — |
| 216 | Q8⋊C8 | — | 67 | 2 | no | — |
| 217 | Q8⋊C8 | — | 67 | 2 | no | — |
| 218 | D4⋊C8 | — | 67 | 2 | no | — |
| 219 | D4⋊C8 | — | 67 | 2 | no | — |
| 220 | #322 | C2×D67 | 1 | 2 | yes | — |
| 221 | #322 | C2×D67 | 1 | 2 | yes | — |
| 222 | C2×Q16 | — | 67 | 1 | no | — |
| 223 | C2×SD16 | — | 67 | 2 | no | — |
| 224 | C2×D8 | — | 67 | 1 | no | — |
| 225 | C2×M16 | — | 134 | 2 | no | — |
| 226 | C2×M16 | — | 134 | 2 | no | — |
| 227 | C22×C8 | — | 134 | 2 | no | — |
| 228 | C22×C8 | C4×D67 | 1 | 1 | yes | characteristic |
| 229 | C22×C8 | C4×D67 | 1 | 1 | yes | characteristic |
| 230 | #126 | — | 134 | 2 | no | — |
| 231 | #125 | — | 67 | 2 | no | — |
| 232 | #124 | — | 67 | 2 | no | — |
| 233 | #123 | — | 134 | 2 | no | — |
| 234 | C22⋊Q8 | — | 67 | 2 | no | — |
| 235 | #121 | — | 67 | 2 | no | — |
| 236 | C4×Q8 | — | 67 | 2 | no | — |
| 237 | C4×D4 | — | 67 | 2 | no | — |
| 238 | C4×D4 | — | 134 | 2 | no | — |
| 239 | #117 | — | 134 | 2 | no | — |
| 240 | C2×C42 | C22×D67 | 1 | 1 | yes | characteristic |
| 241 | #107 | — | 67 | 1 | no | — |
| 242 | #107 | — | 67 | 1 | no | — |
| 243 | #106 | — | 67 | 2 | no | — |
| 244 | C4⋊C8 | — | 2 | 1 | no | — |
| 245 | C4⋊C8 | — | 67 | 2 | no | — |
| 246 | C4⋊C8 | — | 67 | 2 | no | — |
| 247 | C4⋊C8 | — | 134 | 2 | no | — |
| 248 | C4⋊C8 | — | 134 | 2 | no | — |
| 249 | C4⋊C8 | — | 134 | 2 | no | — |
| 250 | C4⋊C8 | D268 | 1 | 2 | yes | — |
| 251 | #103 | — | 67 | 2 | no | — |
| 252 | #103 | — | 67 | 2 | no | — |
| 253 | #102 | — | 67 | 2 | no | — |
| 254 | #102 | — | 67 | 2 | no | — |
| 255 | C22⋊C8 | — | 2 | 1 | no | — |
| 256 | C22⋊C8 | — | 134 | 2 | no | — |
| 257 | C22⋊C8 | — | 134 | 2 | no | — |
| 258 | C22⋊C8 | D268 | 1 | 1 | yes | characteristic |
| 259 | C22⋊C8 | D268 | 1 | 1 | yes | characteristic |
| 260 | #97 | — | 134 | 2 | no | — |
| 261 | C4×C8 | — | 134 | 2 | no | — |
| 262 | C4×C8 | C4×D67 | 1 | 1 | yes | characteristic |
| 263 | C4×C8 | C4×D67 | 1 | 1 | yes | characteristic |
| 264 | C4×C8 | C22×D67 | 1 | 2 | yes | — |
| 265 | C4×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 266 | C4×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 267 | C4×C8 | C22×D67 | 1 | 2 | yes | — |
| 268 | C2×Q8 | — | 67 | 2 | no | — |
| 269 | C2×D4 | — | 67 | 2 | no | — |
| 270 | C2×D4 | — | 134 | 2 | no | — |
| 271 | C22×C4 | — | 134 | 2 | no | — |
| 272 | C22×C4 | C2×C4×D67 | 1 | 1 | yes | characteristic |
| 273 | C22×C4 | C2×D268 | 1 | 1 | yes | characteristic |
| 274 | C22×C4 | #11761628 | 1 | 1 | yes | characteristic |
| 275 | Q16 | — | 268 | 1 | no | — |
| 276 | SD16 | — | 268 | 2 | no | — |
| 277 | D8 | — | 268 | 1 | no | — |
| 278 | M16 | — | 536 | 2 | no | — |
| 279 | M16 | — | 536 | 2 | no | — |
| 280 | C2×C8 | — | 2 | 2 | no | — |
| 281 | C2×C8 | — | 4 | 1 | no | — |
| 282 | C2×C8 | — | 4 | 1 | no | — |
| 283 | C2×C8 | — | 536 | 2 | no | — |
| 284 | C2×C8 | — | 134 | 2 | no | — |
| 285 | C2×C8 | — | 134 | 2 | no | — |
| 286 | C2×C8 | C2×C4×D67 | 1 | 1 | yes | characteristic |
| 287 | C2×C8 | C2×C4×D67 | 1 | 1 | yes | characteristic |
| 288 | C2×C8 | C2×C4×D67 | 1 | 1 | yes | characteristic |
| 289 | C2×C8 | C2×C4×D67 | 1 | 1 | yes | characteristic |
| 290 | C2×C8 | C2×D268 | 1 | 2 | yes | — |
| 291 | C2×C8 | C2×D268 | 1 | 2 | yes | — |
| 292 | C4⋊C4 | — | 67 | 2 | no | — |
| 293 | C4⋊C4 | — | 67 | 2 | no | — |
| 294 | C4⋊C4 | — | 134 | 2 | no | — |
| 295 | C4⋊C4 | — | 134 | 2 | no | — |
| 296 | C4⋊C4 | — | 134 | 2 | no | — |
| 297 | C4⋊C4 | — | 134 | 2 | no | — |
| 298 | C22⋊C4 | — | 134 | 2 | no | — |
| 299 | C22⋊C4 | — | 134 | 2 | no | — |
| 300 | C22⋊C4 | — | 134 | 2 | no | — |
| 301 | C22⋊C4 | — | 134 | 2 | no | — |
| 302 | C22⋊C4 | — | 134 | 2 | no | — |
| 303 | C42 | — | 134 | 2 | no | — |
| 304 | C42 | C2×C4×D67 | 1 | 1 | yes | characteristic |
| 305 | C42 | C2×D268 | 1 | 1 | yes | characteristic |
| 306 | C42 | #11761628 | 1 | 1 | yes | characteristic |
| 307 | C42 | C23×D67 | 1 | 1 | yes | characteristic |
| 308 | C23 | — | 134 | 2 | no | — |
| 309 | C23 | C4×D268 | 1 | 1 | yes | characteristic |
| 310 | Q8 | — | 134 | 2 | no | — |
| 311 | Q8 | — | 134 | 2 | no | — |
| 312 | D4 | — | 536 | 2 | no | — |
| 313 | D4 | — | 134 | 2 | no | — |
| 314 | D4 | — | 134 | 2 | no | — |
| 315 | C2×C4 | — | 2 | 1 | no | — |
| 316 | C2×C4 | — | 2 | 1 | no | — |
| 317 | C2×C4 | — | 2 | 2 | no | — |
| 318 | C2×C4 | — | 4 | 1 | no | — |
| 319 | C2×C4 | — | 268 | 2 | no | — |
| 320 | C2×C4 | — | 268 | 2 | no | — |
| 321 | C2×C4 | — | 134 | 2 | no | — |
| 322 | C2×C4 | — | 134 | 2 | no | — |
| 323 | C2×C4 | — | 134 | 2 | no | — |
| 324 | C2×C4 | C4×D268 | 1 | 1 | yes | characteristic |
| 325 | C2×C4 | C4×D268 | 1 | 1 | yes | characteristic |
| 326 | C2×C4 | C4×D268 | 1 | 1 | yes | characteristic |
| 327 | C2×C4 | C22×C4×D67 | 1 | 1 | yes | characteristic |
| 328 | C2×C4 | C22×D268 | 1 | 1 | yes | characteristic |
| 329 | C2×C4 | C2×#11761628 | 1 | 1 | yes | characteristic |
| 330 | C8 | — | 2 | 1 | no | — |
| 331 | C8 | — | 2 | 1 | no | — |
| 332 | C8 | — | 2 | 1 | no | — |
| 333 | C8 | — | 2 | 1 | no | — |
| 334 | C8 | — | 2 | 2 | no | — |
| 335 | C8 | — | 2 | 2 | no | — |
| 336 | C8 | — | 4 | 2 | no | — |
| 337 | C8 | — | 268 | 2 | no | — |
| 338 | C8 | — | 268 | 2 | no | — |
| 339 | C22 | — | 2 | 1 | no | — |
| 340 | C22 | — | 2 | 1 | no | — |
| 341 | C22 | — | 2 | 1 | no | — |
| 342 | C22 | — | 268 | 2 | no | — |
| 343 | C22 | — | 268 | 2 | no | — |
| 344 | C22 | — | 268 | 2 | no | — |
| 345 | C22 | C2×C4×D268 | 1 | 1 | yes | characteristic |
| 346 | C4 | — | 2 | 1 | no | — |
| 347 | C4 | — | 2 | 1 | no | — |
| 348 | C4 | — | 2 | 1 | no | — |
| 349 | C4 | — | 2 | 1 | no | — |
| 350 | C4 | — | 268 | 2 | no | — |
| 351 | C4 | — | 268 | 2 | no | — |
| 352 | C4 | — | 268 | 2 | no | — |
| 353 | C4 | #16864162 | 1 | 1 | yes | characteristic |
| 354 | C4 | #16864162 | 1 | 1 | yes | characteristic |
| 355 | C4 | #16864208 | 1 | 2 | yes | — |
| 356 | C2 | — | 4 | 1 | no | — |
| 357 | C2 | — | 536 | 2 | no | — |
| 358 | C2 | #22568928 | 1 | 1 | yes | characteristic |
| 359 | C2 | #22569094 | 1 | 1 | yes | characteristic |
| 360 | C2 | #22569127 | 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