← #31989031
Subgroups — #31989031
Order 18176.
602 conjugacy classes of subgroups.
The subgroup lattice has 384 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | D8×Dic142 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22600617 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22587934 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22587889 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22587734 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22587707 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #22587610 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #22587601 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #22587225 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C8×#11765855 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C71×#3393 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | D4×Dic142 | C22 | 1 | 2 | yes | — |
| 13 | #17986404 | C22 | 1 | 1 | yes | characteristic |
| 14 | #17986403 | — | 2 | 1 | no | — |
| 15 | #17986395 | C22 | 1 | 2 | yes | — |
| 16 | #17986351 | C22 | 1 | 2 | yes | — |
| 17 | #17986340 | — | 2 | 2 | no | — |
| 18 | #17986281 | C22 | 1 | 2 | yes | — |
| 19 | #17986279 | C22 | 1 | 2 | yes | — |
| 20 | #17986277 | — | 2 | 2 | no | — |
| 21 | #17986255 | — | 2 | 2 | no | — |
| 22 | #17986209 | C22 | 1 | 2 | yes | — |
| 23 | #17986154 | — | 2 | 2 | no | — |
| 24 | C8×Dic142 | C22 | 1 | 1 | yes | characteristic |
| 25 | C4×#11765855 | C22 | 1 | 1 | yes | characteristic |
| 26 | D8×Dic71 | — | 2 | 1 | no | — |
| 27 | #17986077 | C22 | 1 | 2 | yes | — |
| 28 | #17986007 | — | 2 | 2 | no | — |
| 29 | #17985752 | C22 | 1 | 1 | yes | characteristic |
| 30 | #17985751 | C22 | 1 | 1 | yes | characteristic |
| 31 | #17985745 | C22 | 1 | 2 | yes | — |
| 32 | #17985744 | C22 | 1 | 2 | yes | — |
| 33 | Q8⋊(C71⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 34 | #17985729 | C22 | 1 | 1 | yes | characteristic |
| 35 | D4⋊(C71⋊C8) | C22 | 1 | 2 | yes | — |
| 36 | C8×C71⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 37 | #556×C71 | C22 | 1 | 2 | yes | — |
| 38 | #495×C71 | — | 2 | 1 | no | — |
| 39 | #494×C71 | C22 | 1 | 1 | yes | characteristic |
| 40 | #464×C71 | — | 2 | 2 | no | — |
| 41 | #461×C71 | C22 | 1 | 2 | yes | — |
| 42 | C8×Q8×C71 | C22 | 1 | 1 | yes | characteristic |
| 43 | C4×Q16×C71 | — | 2 | 1 | no | — |
| 44 | C4×D8×C71 | C22 | 1 | 1 | yes | characteristic |
| 45 | C22×Dic142 | — | 2 | 2 | no | — |
| 46 | C2×#11765855 | — | 2 | 2 | no | — |
| 47 | C2×#11765855 | D4 | 1 | 1 | yes | characteristic |
| 48 | C2×#11765849 | — | 2 | 2 | no | — |
| 49 | #14556128 | C23 | 1 | 2 | yes | — |
| 50 | #14556127 | — | 2 | 2 | no | — |
| 51 | #14556107 | — | 2 | 2 | no | — |
| 52 | #14556105 | — | 4 | 2 | no | — |
| 53 | C4×Dic142 | C23 | 1 | 1 | yes | characteristic |
| 54 | D4×Dic71 | — | 2 | 2 | no | — |
| 55 | #14556062 | — | 2 | 1 | no | — |
| 56 | #14556062 | — | 2 | 1 | no | — |
| 57 | #14556061 | — | 2 | 2 | no | — |
| 58 | #14556061 | D4 | 1 | 1 | yes | characteristic |
| 59 | #14556059 | — | 2 | 2 | no | — |
| 60 | #14556059 | — | 4 | 2 | no | — |
| 61 | C4⋊(C71⋊C8) | C23 | 1 | 2 | yes | — |
| 62 | C4⋊(C71⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 63 | Dic71⋊C8 | — | 2 | 1 | no | — |
| 64 | #14556052 | D4 | 1 | 1 | yes | characteristic |
| 65 | #14556051 | — | 2 | 2 | no | — |
| 66 | #14556051 | — | 2 | 2 | no | — |
| 67 | #14556051 | — | 2 | 2 | no | — |
| 68 | #14556051 | — | 2 | 2 | no | — |
| 69 | #14556051 | D4 | 1 | 1 | yes | characteristic |
| 70 | #14556049 | — | 2 | 2 | no | — |
| 71 | C22⋊(C71⋊C8) | — | 2 | 2 | no | — |
| 72 | C4×C71⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 73 | C4×C71⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 74 | C8×Dic71 | — | 2 | 1 | no | — |
| 75 | C2×Q16×C71 | — | 2 | 1 | no | — |
| 76 | C2×Q16×C71 | — | 2 | 1 | no | — |
| 77 | C2×SD16×C71 | — | 2 | 2 | no | — |
| 78 | C2×D8×C71 | D4 | 1 | 1 | yes | characteristic |
| 79 | C4⋊Q8×C71 | C23 | 1 | 2 | yes | — |
| 80 | #126×C71 | — | 4 | 2 | no | — |
| 81 | #124×C71 | — | 2 | 2 | no | — |
| 82 | C22⋊Q8×C71 | — | 2 | 2 | no | — |
| 83 | C4×Q8×C71 | — | 2 | 2 | no | — |
| 84 | C4×Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 85 | C4×D4×C71 | C23 | 1 | 2 | yes | — |
| 86 | #117×C71 | — | 2 | 2 | no | — |
| 87 | #107×C71 | D4 | 1 | 1 | yes | characteristic |
| 88 | C4⋊C8×C71 | — | 2 | 1 | no | — |
| 89 | C4⋊C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 90 | #103×C71 | — | 2 | 2 | no | — |
| 91 | #102×C71 | D4 | 1 | 2 | yes | — |
| 92 | C4×C8×C71 | — | 2 | 1 | no | — |
| 93 | C4×C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×Dic142 | — | 2 | 2 | no | — |
| 95 | C2×Dic142 | — | 4 | 4 | no | — |
| 96 | C2×Dic142 | — | 4 | 2 | no | — |
| 97 | C2×Dic142 | — | 8 | 2 | no | — |
| 98 | C2×Dic142 | C2×D4 | 1 | 1 | yes | characteristic |
| 99 | C22×Dic71 | — | 4 | 2 | no | — |
| 100 | #11765855 | — | 2 | 2 | no | — |
| 101 | #11765855 | — | 8 | 2 | no | — |
| 102 | #11765849 | — | 8 | 2 | no | — |
| 103 | C2×C71⋊C8 | — | 2 | 1 | no | — |
| 104 | C2×C71⋊C8 | — | 2 | 1 | no | — |
| 105 | C2×C71⋊C8 | — | 2 | 2 | no | — |
| 106 | C2×C71⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 107 | C2×C71⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 108 | C4⋊Dic71 | — | 2 | 2 | no | — |
| 109 | C4⋊Dic71 | — | 2 | 2 | no | — |
| 110 | C4⋊Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 111 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 112 | Dic71⋊C4 | — | 4 | 2 | no | — |
| 113 | C22⋊Dic71 | — | 4 | 2 | no | — |
| 114 | C4×Dic71 | — | 2 | 1 | no | — |
| 115 | C2×Q8×C71 | — | 2 | 2 | no | — |
| 116 | C2×Q8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 117 | C2×D4×C71 | C2×D4 | 1 | 2 | yes | — |
| 118 | C22×C4×C71 | — | 2 | 2 | no | — |
| 119 | Q16×C71 | — | 4 | 2 | no | — |
| 120 | Q16×C71 | — | 8 | 1 | no | — |
| 121 | SD16×C71 | — | 8 | 2 | no | — |
| 122 | D8×C71 | — | 2 | 2 | no | — |
| 123 | C2×C8×C71 | — | 2 | 1 | no | — |
| 124 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 125 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 126 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 127 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 128 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 129 | C4⋊C4×C71 | — | 4 | 2 | no | — |
| 130 | C4⋊C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 131 | C4⋊C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 132 | C22⋊C4×C71 | — | 2 | 2 | no | — |
| 133 | C22⋊C4×C71 | — | 4 | 2 | no | — |
| 134 | C22⋊C4×C71 | — | 4 | 2 | no | — |
| 135 | C42×C71 | — | 2 | 1 | no | — |
| 136 | C42×C71 | — | 4 | 2 | no | — |
| 137 | C42×C71 | C24 | 1 | 1 | yes | characteristic |
| 138 | C23×C71 | — | 2 | 2 | no | — |
| 139 | Q8×C71 | — | 2 | 1 | no | — |
| 140 | Q8×C71 | — | 2 | 1 | no | — |
| 141 | Q8×C71 | — | 4 | 2 | no | — |
| 142 | Q8×C71 | — | 4 | 2 | no | — |
| 143 | D4×C71 | — | 2 | 2 | no | — |
| 144 | D4×C71 | — | 2 | 2 | no | — |
| 145 | C2×C4×C71 | — | 2 | 1 | no | — |
| 146 | C2×C4×C71 | — | 2 | 1 | no | — |
| 147 | C2×C4×C71 | — | 2 | 2 | no | — |
| 148 | C2×C4×C71 | — | 4 | 2 | no | — |
| 149 | C2×C4×C71 | — | 4 | 2 | no | — |
| 150 | C2×C4×C71 | — | 4 | 2 | no | — |
| 151 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 152 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 153 | C2×C4×C71 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 154 | C2×Dic71 | — | 2 | 1 | no | — |
| 155 | C2×Dic71 | — | 2 | 1 | no | — |
| 156 | C2×Dic71 | — | 4 | 2 | no | — |
| 157 | C2×Dic71 | — | 8 | 4 | no | — |
| 158 | Dic142 | — | 2 | 1 | no | — |
| 159 | Dic142 | — | 4 | 2 | no | — |
| 160 | Dic142 | — | 4 | 2 | no | — |
| 161 | Dic142 | — | 8 | 4 | no | — |
| 162 | Dic142 | #135 | 1 | 2 | yes | — |
| 163 | C8×C71 | — | 2 | 1 | no | — |
| 164 | C8×C71 | — | 4 | 1 | no | — |
| 165 | C8×C71 | #137 | 1 | 2 | yes | — |
| 166 | C71⋊C8 | — | 2 | 2 | no | — |
| 167 | C71⋊C8 | — | 2 | 1 | no | — |
| 168 | C71⋊C8 | — | 2 | 1 | no | — |
| 169 | C71⋊C8 | — | 4 | 2 | no | — |
| 170 | C71⋊C8 | — | 4 | 1 | no | — |
| 171 | C22×C71 | — | 4 | 2 | no | — |
| 172 | C22×C71 | — | 4 | 2 | no | — |
| 173 | C22×C71 | — | 4 | 2 | no | — |
| 174 | C22×C71 | D42 | 1 | 1 | yes | characteristic |
| 175 | C4×C71 | — | 2 | 1 | no | — |
| 176 | C4×C71 | — | 4 | 2 | no | — |
| 177 | C4×C71 | — | 4 | 1 | no | — |
| 178 | C4×C71 | — | 4 | 1 | no | — |
| 179 | C4×C71 | — | 8 | 2 | no | — |
| 180 | C4×C71 | C2×#135 | 1 | 1 | yes | characteristic |
| 181 | C4×C71 | C2×#137 | 1 | 1 | yes | characteristic |
| 182 | C4×C71 | #576 | 1 | 1 | yes | characteristic |
| 183 | C4×C71 | #577 | 1 | 1 | yes | characteristic |
| 184 | Dic71 | — | 2 | 2 | no | — |
| 185 | Dic71 | — | 4 | 1 | no | — |
| 186 | Dic71 | — | 8 | 2 | no | — |
| 187 | #19907 | — | 71 | 1 | no | maximal, Sylow |
| 188 | C2×C71 | — | 8 | 2 | no | — |
| 189 | C2×C71 | #3278 | 1 | 1 | yes | characteristic |
| 190 | C2×C71 | #3280 | 1 | 1 | yes | characteristic |
| 191 | C2×C71 | #3293 | 1 | 1 | yes | characteristic |
| 192 | #3393 | D71 | 1 | 1 | yes | characteristic |
| 193 | Q8×D8 | — | 71 | 1 | no | — |
| 194 | #3328 | — | 71 | 2 | no | — |
| 195 | #1707 | — | 71 | 1 | no | — |
| 196 | #1699 | — | 71 | 2 | no | — |
| 197 | #1674 | — | 71 | 1 | no | — |
| 198 | #1670 | — | 71 | 1 | no | — |
| 199 | #1652 | — | 71 | 2 | no | — |
| 200 | #1651 | — | 71 | 2 | no | — |
| 201 | #1589 | — | 71 | 1 | no | — |
| 202 | C8×Q16 | — | 71 | 1 | no | — |
| 203 | C71 | #19907 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 204 | #556 | C2×D71 | 1 | 2 | yes | — |
| 205 | D4×Q8 | — | 71 | 2 | no | — |
| 206 | #500 | — | 71 | 1 | no | — |
| 207 | #500 | — | 142 | 1 | no | — |
| 208 | #498 | — | 71 | 2 | no | — |
| 209 | #495 | — | 2 | 1 | no | — |
| 210 | #494 | C2×D71 | 1 | 1 | yes | characteristic |
| 211 | #487 | — | 71 | 2 | no | — |
| 212 | #485 | — | 142 | 2 | no | — |
| 213 | #475 | — | 71 | 2 | no | — |
| 214 | #474 | — | 71 | 2 | no | — |
| 215 | #474 | — | 142 | 2 | no | — |
| 216 | #470 | — | 142 | 2 | no | — |
| 217 | #464 | — | 2 | 2 | no | — |
| 218 | #462 | — | 71 | 2 | no | — |
| 219 | #461 | C2×D71 | 1 | 2 | yes | — |
| 220 | #451 | — | 142 | 2 | no | — |
| 221 | C8×Q8 | — | 71 | 1 | no | — |
| 222 | C8×Q8 | C2×D71 | 1 | 1 | yes | characteristic |
| 223 | C4×Q16 | — | 2 | 1 | no | — |
| 224 | C4×Q16 | — | 71 | 1 | no | — |
| 225 | C4×D8 | — | 142 | 1 | no | — |
| 226 | C4×D8 | C2×D71 | 1 | 1 | yes | characteristic |
| 227 | #436 | — | 71 | 2 | no | — |
| 228 | #419 | — | 142 | 2 | no | — |
| 229 | #335 | — | 71 | 1 | no | — |
| 230 | #335 | — | 71 | 1 | no | — |
| 231 | #332 | — | 71 | 2 | no | — |
| 232 | #332 | — | 71 | 2 | no | — |
| 233 | Q8⋊C8 | — | 71 | 1 | no | — |
| 234 | Q8⋊C8 | — | 71 | 1 | no | — |
| 235 | D4⋊C8 | — | 71 | 2 | no | — |
| 236 | C82 | — | 71 | 1 | no | — |
| 237 | C22×Q8 | — | 142 | 2 | no | — |
| 238 | C2×Q16 | — | 2 | 1 | no | — |
| 239 | C2×Q16 | — | 2 | 1 | no | — |
| 240 | C2×Q16 | — | 71 | 1 | no | — |
| 241 | C2×Q16 | — | 142 | 2 | no | — |
| 242 | C2×SD16 | — | 2 | 2 | no | — |
| 243 | C2×D8 | C22⋊D71 | 1 | 1 | yes | characteristic |
| 244 | C2×M16 | — | 142 | 2 | no | — |
| 245 | C4⋊Q8 | — | 71 | 2 | no | — |
| 246 | C4⋊Q8 | — | 142 | 2 | no | — |
| 247 | C4⋊Q8 | C22×D71 | 1 | 2 | yes | — |
| 248 | #126 | — | 4 | 2 | no | — |
| 249 | #124 | — | 2 | 2 | no | — |
| 250 | C22⋊Q8 | — | 2 | 2 | no | — |
| 251 | C22⋊Q8 | — | 284 | 2 | no | — |
| 252 | C22⋊Q8 | — | 142 | 2 | no | — |
| 253 | C4×Q8 | — | 2 | 2 | no | — |
| 254 | C4×Q8 | — | 71 | 1 | no | — |
| 255 | C4×Q8 | C22×D71 | 1 | 1 | yes | characteristic |
| 256 | C4×D4 | — | 142 | 2 | no | — |
| 257 | C4×D4 | C22×D71 | 1 | 2 | yes | — |
| 258 | #117 | — | 2 | 2 | no | — |
| 259 | #107 | — | 71 | 1 | no | — |
| 260 | #107 | — | 142 | 1 | no | — |
| 261 | #107 | — | 142 | 1 | no | — |
| 262 | #107 | — | 142 | 2 | no | — |
| 263 | #107 | C22⋊D71 | 1 | 1 | yes | characteristic |
| 264 | #106 | — | 284 | 2 | no | — |
| 265 | #106 | — | 142 | 2 | no | — |
| 266 | C4⋊C8 | — | 2 | 1 | no | — |
| 267 | C4⋊C8 | — | 71 | 2 | no | — |
| 268 | C4⋊C8 | — | 71 | 1 | no | — |
| 269 | C4⋊C8 | — | 142 | 1 | no | — |
| 270 | C4⋊C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 271 | #103 | — | 2 | 2 | no | — |
| 272 | #103 | — | 71 | 1 | no | — |
| 273 | #103 | — | 71 | 1 | no | — |
| 274 | #103 | — | 142 | 2 | no | — |
| 275 | #103 | — | 142 | 2 | no | — |
| 276 | #103 | — | 142 | 2 | no | — |
| 277 | #103 | — | 142 | 2 | no | — |
| 278 | #102 | — | 142 | 2 | no | — |
| 279 | #102 | C22⋊D71 | 1 | 2 | yes | — |
| 280 | C22⋊C8 | — | 142 | 2 | no | — |
| 281 | C4×C8 | — | 2 | 1 | no | — |
| 282 | C4×C8 | — | 71 | 1 | no | — |
| 283 | C4×C8 | — | 71 | 1 | no | — |
| 284 | C4×C8 | — | 142 | 1 | no | — |
| 285 | C4×C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 286 | C2×Q8 | — | 2 | 2 | no | — |
| 287 | C2×Q8 | — | 284 | 2 | no | — |
| 288 | C2×Q8 | — | 284 | 4 | no | — |
| 289 | C2×Q8 | — | 568 | 2 | no | — |
| 290 | C2×Q8 | — | 71 | 1 | no | — |
| 291 | C2×Q8 | — | 142 | 2 | no | — |
| 292 | C2×Q8 | D4×D71 | 1 | 1 | yes | characteristic |
| 293 | C2×D4 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 294 | C22×C4 | — | 2 | 2 | no | — |
| 295 | C22×C4 | — | 284 | 2 | no | — |
| 296 | Q16 | — | 4 | 2 | no | — |
| 297 | Q16 | — | 8 | 1 | no | — |
| 298 | Q16 | — | 568 | 2 | no | — |
| 299 | Q16 | — | 142 | 2 | no | — |
| 300 | SD16 | — | 8 | 2 | no | — |
| 301 | D8 | — | 2 | 2 | no | — |
| 302 | M16 | — | 568 | 2 | no | — |
| 303 | C2×C8 | — | 2 | 1 | no | — |
| 304 | C2×C8 | — | 71 | 1 | no | — |
| 305 | C2×C8 | — | 71 | 1 | no | — |
| 306 | C2×C8 | — | 142 | 2 | no | — |
| 307 | C2×C8 | — | 142 | 1 | no | — |
| 308 | C2×C8 | — | 142 | 1 | no | — |
| 309 | C2×C8 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 310 | C2×C8 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 311 | C4⋊C4 | — | 2 | 1 | no | — |
| 312 | C4⋊C4 | — | 2 | 2 | no | — |
| 313 | C4⋊C4 | — | 2 | 2 | no | — |
| 314 | C4⋊C4 | — | 4 | 2 | no | — |
| 315 | C4⋊C4 | — | 284 | 2 | no | — |
| 316 | C4⋊C4 | — | 71 | 1 | no | — |
| 317 | C4⋊C4 | — | 142 | 2 | no | — |
| 318 | C4⋊C4 | — | 142 | 2 | no | — |
| 319 | C4⋊C4 | — | 142 | 1 | no | — |
| 320 | C4⋊C4 | D4×D71 | 1 | 1 | yes | characteristic |
| 321 | C4⋊C4 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 322 | C22⋊C4 | — | 2 | 2 | no | — |
| 323 | C22⋊C4 | — | 4 | 2 | no | — |
| 324 | C22⋊C4 | — | 4 | 2 | no | — |
| 325 | C22⋊C4 | — | 284 | 2 | no | — |
| 326 | C42 | — | 2 | 1 | no | — |
| 327 | C42 | — | 4 | 2 | no | — |
| 328 | C42 | — | 142 | 1 | no | — |
| 329 | C42 | C23×D71 | 1 | 1 | yes | characteristic |
| 330 | C23 | — | 2 | 2 | no | — |
| 331 | Q8 | — | 2 | 1 | no | — |
| 332 | Q8 | — | 2 | 1 | no | — |
| 333 | Q8 | — | 4 | 2 | no | — |
| 334 | Q8 | — | 4 | 2 | no | — |
| 335 | Q8 | — | 284 | 2 | no | — |
| 336 | Q8 | — | 284 | 2 | no | — |
| 337 | Q8 | — | 568 | 4 | no | — |
| 338 | Q8 | — | 71 | 2 | no | — |
| 339 | Q8 | — | 142 | 1 | no | — |
| 340 | D4 | — | 2 | 2 | no | — |
| 341 | D4 | — | 2 | 2 | no | — |
| 342 | C2×C4 | — | 2 | 1 | no | — |
| 343 | C2×C4 | — | 2 | 1 | no | — |
| 344 | C2×C4 | — | 2 | 2 | no | — |
| 345 | C2×C4 | — | 4 | 2 | no | — |
| 346 | C2×C4 | — | 4 | 2 | no | — |
| 347 | C2×C4 | — | 4 | 2 | no | — |
| 348 | C2×C4 | — | 284 | 2 | no | — |
| 349 | C2×C4 | — | 568 | 4 | no | — |
| 350 | C2×C4 | — | 142 | 1 | no | — |
| 351 | C2×C4 | — | 142 | 1 | no | — |
| 352 | C2×C4 | C2×D4×D71 | 1 | 1 | yes | characteristic |
| 353 | C2×C4 | C22×C22⋊D71 | 1 | 1 | yes | characteristic |
| 354 | C2×C4 | #14556173 | 1 | 1 | yes | characteristic |
| 355 | C8 | — | 2 | 1 | no | — |
| 356 | C8 | — | 4 | 1 | no | — |
| 357 | C8 | — | 284 | 2 | no | — |
| 358 | C8 | — | 284 | 1 | no | — |
| 359 | C8 | — | 142 | 2 | no | — |
| 360 | C8 | — | 142 | 1 | no | — |
| 361 | C8 | — | 142 | 1 | no | — |
| 362 | C8 | #14556158 | 1 | 2 | yes | — |
| 363 | C22 | — | 4 | 2 | no | — |
| 364 | C22 | — | 4 | 2 | no | — |
| 365 | C22 | — | 4 | 2 | no | — |
| 366 | C22 | D4×C22⋊D71 | 1 | 1 | yes | characteristic |
| 367 | C4 | — | 2 | 1 | no | — |
| 368 | C4 | — | 4 | 2 | no | — |
| 369 | C4 | — | 4 | 1 | no | — |
| 370 | C4 | — | 4 | 1 | no | — |
| 371 | C4 | — | 8 | 2 | no | — |
| 372 | C4 | — | 284 | 1 | no | — |
| 373 | C4 | — | 568 | 2 | no | — |
| 374 | C4 | — | 142 | 2 | no | — |
| 375 | C4 | #135×D71 | 1 | 1 | yes | characteristic |
| 376 | C4 | C2×#14556158 | 1 | 1 | yes | characteristic |
| 377 | C4 | #17986801 | 1 | 1 | yes | characteristic |
| 378 | C4 | #17986810 | 1 | 1 | yes | characteristic |
| 379 | C2 | — | 8 | 2 | no | — |
| 380 | C2 | #22600006 | 1 | 1 | yes | characteristic |
| 381 | C2 | #22600019 | 1 | 1 | yes | characteristic |
| 382 | C2 | #22600142 | 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