← C71×#19534 #31840406
Subgroups — C71×#19534 #31840406
Order 18176.
540 conjugacy classes of subgroups.
The subgroup lattice has 396 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C71×#3255 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C71×#3249 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C71×#3231 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C71×#2985 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C71×#1700 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C71×#1692 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C71×#1684 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C71×#1674 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C71×#1571 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C71×#1559 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | C71×#1552 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #533×C71 | C22 | 1 | 1 | yes | characteristic |
| 13 | #533×C71 | C22 | 1 | 1 | yes | characteristic |
| 14 | #533×C71 | C22 | 1 | 1 | yes | characteristic |
| 15 | #500×C71 | C22 | 1 | 1 | yes | characteristic |
| 16 | #498×C71 | C22 | 1 | 1 | yes | characteristic |
| 17 | #487×C71 | C22 | 1 | 1 | yes | characteristic |
| 18 | #487×C71 | C22 | 1 | 1 | yes | characteristic |
| 19 | #485×C71 | — | 2 | 2 | no | — |
| 20 | #479×C71 | — | 2 | 2 | no | — |
| 21 | #477×C71 | — | 2 | 1 | no | — |
| 22 | #477×C71 | C22 | 1 | 2 | yes | — |
| 23 | #475×C71 | — | 2 | 1 | no | — |
| 24 | #475×C71 | C22 | 1 | 2 | yes | — |
| 25 | #470×C71 | — | 2 | 2 | no | — |
| 26 | #467×C71 | — | 2 | 2 | no | — |
| 27 | #462×C71 | — | 2 | 1 | no | — |
| 28 | #462×C71 | — | 2 | 1 | no | — |
| 29 | #462×C71 | C22 | 1 | 2 | yes | — |
| 30 | #462×C71 | C22 | 1 | 2 | yes | — |
| 31 | #446×C71 | — | 2 | 2 | no | — |
| 32 | #446×C71 | C22 | 1 | 2 | yes | — |
| 33 | C8×Q8×C71 | C22 | 1 | 2 | yes | — |
| 34 | #433×C71 | — | 2 | 2 | no | — |
| 35 | #432×C71 | C22 | 1 | 1 | yes | characteristic |
| 36 | #431×C71 | C22 | 1 | 1 | yes | characteristic |
| 37 | #423×C71 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×C4⋊C8×C71 | C22 | 1 | 1 | yes | characteristic |
| 39 | #335×C71 | C22 | 1 | 2 | yes | — |
| 40 | #335×C71 | C22 | 1 | 2 | yes | — |
| 41 | #333×C71 | C22 | 1 | 2 | yes | — |
| 42 | #332×C71 | C22 | 1 | 2 | yes | — |
| 43 | #332×C71 | C22 | 1 | 2 | yes | — |
| 44 | #332×C71 | C22 | 1 | 2 | yes | — |
| 45 | C2×Q16×C71 | — | 2 | 2 | no | — |
| 46 | C2×Q16×C71 | — | 2 | 2 | no | — |
| 47 | C2×M16×C71 | — | 2 | 1 | no | — |
| 48 | C22×C8×C71 | — | 2 | 1 | no | — |
| 49 | C4⋊Q8×C71 | D4 | 1 | 1 | yes | characteristic |
| 50 | C4⋊Q8×C71 | D4 | 1 | 1 | yes | characteristic |
| 51 | C4⋊Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 52 | C4⋊Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 53 | C4⋊Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 54 | C4⋊Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 55 | #125×C71 | — | 2 | 1 | no | — |
| 56 | #125×C71 | — | 2 | 1 | no | — |
| 57 | #125×C71 | — | 2 | 1 | no | — |
| 58 | C22⋊Q8×C71 | — | 2 | 1 | no | — |
| 59 | C22⋊Q8×C71 | — | 2 | 1 | no | — |
| 60 | C22⋊Q8×C71 | — | 2 | 1 | no | — |
| 61 | C22⋊Q8×C71 | — | 2 | 1 | no | — |
| 62 | C22⋊Q8×C71 | — | 2 | 1 | no | — |
| 63 | C22⋊Q8×C71 | D4 | 1 | 2 | yes | — |
| 64 | C4×Q8×C71 | — | 2 | 1 | no | — |
| 65 | C4×Q8×C71 | — | 2 | 1 | no | — |
| 66 | C4×Q8×C71 | — | 2 | 1 | no | — |
| 67 | C4×Q8×C71 | — | 2 | 1 | no | — |
| 68 | C4×Q8×C71 | — | 2 | 1 | no | — |
| 69 | C4×Q8×C71 | C23 | 1 | 2 | yes | — |
| 70 | #117×C71 | — | 2 | 1 | no | — |
| 71 | #117×C71 | — | 2 | 1 | no | — |
| 72 | #117×C71 | — | 2 | 1 | no | — |
| 73 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 74 | #107×C71 | — | 2 | 2 | no | — |
| 75 | #107×C71 | — | 2 | 2 | no | — |
| 76 | #106×C71 | — | 2 | 2 | no | — |
| 77 | #106×C71 | — | 2 | 2 | no | — |
| 78 | C4⋊C8×C71 | — | 2 | 2 | no | — |
| 79 | C4⋊C8×C71 | — | 2 | 2 | no | — |
| 80 | C4⋊C8×C71 | — | 2 | 1 | no | — |
| 81 | C4⋊C8×C71 | — | 2 | 1 | no | — |
| 82 | C4⋊C8×C71 | D4 | 1 | 2 | yes | — |
| 83 | C4⋊C8×C71 | C23 | 1 | 2 | yes | — |
| 84 | C4⋊C8×C71 | C23 | 1 | 2 | yes | — |
| 85 | C4⋊C8×C71 | C23 | 1 | 2 | yes | — |
| 86 | #103×C71 | — | 2 | 2 | no | — |
| 87 | #103×C71 | — | 2 | 2 | no | — |
| 88 | #103×C71 | — | 2 | 2 | no | — |
| 89 | #103×C71 | — | 2 | 2 | no | — |
| 90 | #103×C71 | — | 2 | 2 | no | — |
| 91 | #103×C71 | — | 2 | 2 | no | — |
| 92 | C22⋊C8×C71 | — | 2 | 1 | no | — |
| 93 | C22⋊C8×C71 | D4 | 1 | 2 | yes | — |
| 94 | #97×C71 | — | 2 | 2 | no | — |
| 95 | #97×C71 | — | 2 | 1 | no | — |
| 96 | C4×C8×C71 | — | 2 | 2 | no | — |
| 97 | C4×C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 98 | C4×C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 99 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 100 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 101 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 102 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 103 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 104 | C2×Q8×C71 | C2×D4 | 1 | 2 | yes | — |
| 105 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 106 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 107 | C22×C4×C71 | #41 | 1 | 1 | yes | characteristic |
| 108 | Q16×C71 | — | 8 | 2 | no | — |
| 109 | Q16×C71 | — | 8 | 2 | no | — |
| 110 | M16×C71 | — | 8 | 1 | no | — |
| 111 | C2×C8×C71 | — | 2 | 2 | no | — |
| 112 | C2×C8×C71 | — | 2 | 2 | no | — |
| 113 | C2×C8×C71 | — | 2 | 2 | no | — |
| 114 | C2×C8×C71 | — | 8 | 1 | no | — |
| 115 | C2×C8×C71 | C2×D4 | 1 | 2 | yes | — |
| 116 | C2×C8×C71 | C2×D4 | 1 | 2 | yes | — |
| 117 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 118 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 119 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 120 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 121 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 122 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 123 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 124 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 125 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 126 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 127 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 128 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 129 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 130 | C4⋊C4×C71 | — | 4 | 1 | no | — |
| 131 | C4⋊C4×C71 | — | 4 | 1 | no | — |
| 132 | C4⋊C4×C71 | — | 4 | 1 | no | — |
| 133 | C4⋊C4×C71 | — | 4 | 1 | no | — |
| 134 | C4⋊C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 135 | C22⋊C4×C71 | — | 2 | 2 | no | — |
| 136 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 137 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 138 | C42×C71 | — | 2 | 2 | no | — |
| 139 | C42×C71 | — | 4 | 1 | no | — |
| 140 | C42×C71 | — | 4 | 1 | no | — |
| 141 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 142 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 143 | C42×C71 | #41 | 1 | 1 | yes | characteristic |
| 144 | C42×C71 | C24 | 1 | 1 | yes | characteristic |
| 145 | C23×C71 | #121 | 1 | 1 | yes | characteristic |
| 146 | Q8×C71 | — | 2 | 2 | no | — |
| 147 | Q8×C71 | — | 2 | 2 | no | — |
| 148 | Q8×C71 | — | 4 | 1 | no | — |
| 149 | Q8×C71 | — | 4 | 1 | no | — |
| 150 | Q8×C71 | — | 4 | 2 | no | — |
| 151 | Q8×C71 | — | 4 | 1 | no | — |
| 152 | Q8×C71 | — | 4 | 1 | no | — |
| 153 | Q8×C71 | — | 8 | 1 | no | — |
| 154 | Q8×C71 | — | 8 | 1 | no | — |
| 155 | C2×C4×C71 | — | 2 | 1 | no | — |
| 156 | C2×C4×C71 | — | 2 | 2 | no | — |
| 157 | C2×C4×C71 | — | 2 | 1 | no | — |
| 158 | C2×C4×C71 | — | 2 | 2 | no | — |
| 159 | C2×C4×C71 | — | 2 | 2 | no | — |
| 160 | C2×C4×C71 | — | 4 | 1 | no | — |
| 161 | C2×C4×C71 | — | 4 | 1 | no | — |
| 162 | C2×C4×C71 | — | 4 | 1 | no | — |
| 163 | C2×C4×C71 | — | 4 | 1 | no | — |
| 164 | C2×C4×C71 | — | 4 | 1 | no | — |
| 165 | C2×C4×C71 | #121 | 1 | 1 | yes | characteristic |
| 166 | C2×C4×C71 | #121 | 1 | 1 | yes | characteristic |
| 167 | C2×C4×C71 | #121 | 1 | 1 | yes | characteristic |
| 168 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 169 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 170 | C2×C4×C71 | C2×#41 | 1 | 1 | yes | characteristic |
| 171 | C8×C71 | — | 2 | 2 | no | — |
| 172 | C8×C71 | — | 2 | 2 | no | — |
| 173 | C8×C71 | — | 4 | 2 | no | — |
| 174 | C8×C71 | — | 4 | 2 | no | — |
| 175 | C8×C71 | — | 4 | 2 | no | — |
| 176 | C22×C71 | — | 2 | 1 | no | — |
| 177 | C22×C71 | — | 2 | 1 | no | — |
| 178 | C22×C71 | — | 2 | 1 | no | — |
| 179 | C22×C71 | C2×#121 | 1 | 1 | yes | characteristic |
| 180 | C4×C71 | — | 2 | 1 | no | — |
| 181 | C4×C71 | — | 2 | 1 | no | — |
| 182 | C4×C71 | — | 2 | 1 | no | — |
| 183 | C4×C71 | — | 2 | 1 | no | — |
| 184 | C4×C71 | — | 4 | 2 | no | — |
| 185 | C4×C71 | — | 4 | 2 | no | — |
| 186 | C4×C71 | — | 8 | 1 | no | — |
| 187 | C4×C71 | — | 8 | 1 | no | — |
| 188 | C4×C71 | — | 8 | 1 | no | — |
| 189 | C4×C71 | — | 8 | 1 | no | — |
| 190 | C4×C71 | #576 | 1 | 1 | yes | characteristic |
| 191 | C4×C71 | #578 | 1 | 2 | yes | — |
| 192 | C4×C71 | #578 | 1 | 1 | yes | characteristic |
| 193 | #19534 | C71 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 194 | C2×C71 | — | 4 | 1 | no | — |
| 195 | C2×C71 | #3044 | 1 | 1 | yes | characteristic |
| 196 | C2×C71 | #3061 | 1 | 1 | yes | characteristic |
| 197 | C2×C71 | #3069 | 1 | 1 | yes | characteristic |
| 198 | #3255 | C2×C71 | 1 | 1 | yes | characteristic |
| 199 | #3249 | C2×C71 | 1 | 1 | yes | characteristic |
| 200 | #3231 | C2×C71 | 1 | 1 | yes | characteristic |
| 201 | #2985 | C2×C71 | 1 | 1 | yes | characteristic |
| 202 | #1700 | C2×C71 | 1 | 2 | yes | complemented |
| 203 | #1692 | C2×C71 | 1 | 2 | yes | complemented |
| 204 | #1684 | C2×C71 | 1 | 2 | yes | complemented |
| 205 | #1674 | C2×C71 | 1 | 2 | yes | complemented |
| 206 | #1571 | C2×C71 | 1 | 1 | yes | characteristic |
| 207 | #1559 | C2×C71 | 1 | 1 | yes | characteristic |
| 208 | #1552 | C2×C71 | 1 | 1 | yes | characteristic |
| 209 | C71 | #19534 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 210 | #533 | C22×C71 | 1 | 1 | yes | characteristic |
| 211 | #533 | C22×C71 | 1 | 1 | yes | characteristic |
| 212 | #533 | C22×C71 | 1 | 1 | yes | characteristic |
| 213 | #500 | C22×C71 | 1 | 1 | yes | characteristic |
| 214 | #498 | C22×C71 | 1 | 1 | yes | characteristic |
| 215 | #487 | C22×C71 | 1 | 1 | yes | characteristic |
| 216 | #487 | C22×C71 | 1 | 1 | yes | characteristic |
| 217 | #485 | — | 2 | 2 | no | — |
| 218 | #479 | — | 2 | 2 | no | — |
| 219 | #477 | — | 2 | 1 | no | — |
| 220 | #477 | C22×C71 | 1 | 2 | yes | — |
| 221 | #475 | — | 2 | 1 | no | — |
| 222 | #475 | C22×C71 | 1 | 2 | yes | — |
| 223 | #470 | — | 2 | 2 | no | — |
| 224 | #467 | — | 2 | 2 | no | — |
| 225 | #462 | — | 2 | 1 | no | — |
| 226 | #462 | — | 2 | 1 | no | — |
| 227 | #462 | C22×C71 | 1 | 2 | yes | — |
| 228 | #462 | C22×C71 | 1 | 2 | yes | — |
| 229 | #446 | — | 2 | 2 | no | — |
| 230 | #446 | C22×C71 | 1 | 2 | yes | — |
| 231 | C8×Q8 | C22×C71 | 1 | 2 | yes | — |
| 232 | #433 | — | 2 | 2 | no | — |
| 233 | #432 | C22×C71 | 1 | 1 | yes | characteristic |
| 234 | #431 | C22×C71 | 1 | 1 | yes | characteristic |
| 235 | #423 | C22×C71 | 1 | 1 | yes | characteristic |
| 236 | C2×C4⋊C8 | C22×C71 | 1 | 1 | yes | characteristic |
| 237 | #335 | C22×C71 | 1 | 2 | yes | — |
| 238 | #335 | C22×C71 | 1 | 2 | yes | — |
| 239 | #333 | C22×C71 | 1 | 2 | yes | — |
| 240 | #332 | C22×C71 | 1 | 2 | yes | — |
| 241 | #332 | C22×C71 | 1 | 2 | yes | — |
| 242 | #332 | C22×C71 | 1 | 2 | yes | — |
| 243 | C2×Q16 | — | 2 | 2 | no | — |
| 244 | C2×Q16 | — | 2 | 2 | no | — |
| 245 | C2×M16 | — | 2 | 1 | no | — |
| 246 | C22×C8 | — | 2 | 1 | no | — |
| 247 | C4⋊Q8 | D4×C71 | 1 | 1 | yes | characteristic |
| 248 | C4⋊Q8 | D4×C71 | 1 | 1 | yes | characteristic |
| 249 | C4⋊Q8 | C23×C71 | 1 | 1 | yes | characteristic |
| 250 | C4⋊Q8 | C23×C71 | 1 | 1 | yes | characteristic |
| 251 | C4⋊Q8 | C23×C71 | 1 | 1 | yes | characteristic |
| 252 | C4⋊Q8 | C23×C71 | 1 | 1 | yes | characteristic |
| 253 | #125 | — | 2 | 1 | no | — |
| 254 | #125 | — | 2 | 1 | no | — |
| 255 | #125 | — | 2 | 1 | no | — |
| 256 | C22⋊Q8 | — | 2 | 1 | no | — |
| 257 | C22⋊Q8 | — | 2 | 1 | no | — |
| 258 | C22⋊Q8 | — | 2 | 1 | no | — |
| 259 | C22⋊Q8 | — | 2 | 1 | no | — |
| 260 | C22⋊Q8 | — | 2 | 1 | no | — |
| 261 | C22⋊Q8 | D4×C71 | 1 | 2 | yes | — |
| 262 | C4×Q8 | — | 2 | 1 | no | — |
| 263 | C4×Q8 | — | 2 | 1 | no | — |
| 264 | C4×Q8 | — | 2 | 1 | no | — |
| 265 | C4×Q8 | — | 2 | 1 | no | — |
| 266 | C4×Q8 | — | 2 | 1 | no | — |
| 267 | C4×Q8 | C23×C71 | 1 | 2 | yes | — |
| 268 | #117 | — | 2 | 1 | no | — |
| 269 | #117 | — | 2 | 1 | no | — |
| 270 | #117 | — | 2 | 1 | no | — |
| 271 | C2×C42 | C23×C71 | 1 | 1 | yes | characteristic |
| 272 | #107 | — | 2 | 2 | no | — |
| 273 | #107 | — | 2 | 2 | no | — |
| 274 | #106 | — | 2 | 2 | no | — |
| 275 | #106 | — | 2 | 2 | no | — |
| 276 | C4⋊C8 | — | 2 | 2 | no | — |
| 277 | C4⋊C8 | — | 2 | 2 | no | — |
| 278 | C4⋊C8 | — | 2 | 1 | no | — |
| 279 | C4⋊C8 | — | 2 | 1 | no | — |
| 280 | C4⋊C8 | D4×C71 | 1 | 2 | yes | — |
| 281 | C4⋊C8 | C23×C71 | 1 | 2 | yes | — |
| 282 | C4⋊C8 | C23×C71 | 1 | 2 | yes | — |
| 283 | C4⋊C8 | C23×C71 | 1 | 2 | yes | — |
| 284 | #103 | — | 2 | 2 | no | — |
| 285 | #103 | — | 2 | 2 | no | — |
| 286 | #103 | — | 2 | 2 | no | — |
| 287 | #103 | — | 2 | 2 | no | — |
| 288 | #103 | — | 2 | 2 | no | — |
| 289 | #103 | — | 2 | 2 | no | — |
| 290 | C22⋊C8 | — | 2 | 1 | no | — |
| 291 | C22⋊C8 | D4×C71 | 1 | 2 | yes | — |
| 292 | #97 | — | 2 | 2 | no | — |
| 293 | #97 | — | 2 | 1 | no | — |
| 294 | C4×C8 | — | 2 | 2 | no | — |
| 295 | C4×C8 | C23×C71 | 1 | 1 | yes | characteristic |
| 296 | C4×C8 | C23×C71 | 1 | 1 | yes | characteristic |
| 297 | C2×Q8 | — | 2 | 1 | no | — |
| 298 | C2×Q8 | — | 2 | 1 | no | — |
| 299 | C2×Q8 | — | 2 | 1 | no | — |
| 300 | C2×Q8 | — | 2 | 1 | no | — |
| 301 | C2×Q8 | — | 2 | 1 | no | — |
| 302 | C2×Q8 | C2×D4×C71 | 1 | 2 | yes | — |
| 303 | C22×C4 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 304 | C22×C4 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 305 | C22×C4 | #41×C71 | 1 | 1 | yes | characteristic |
| 306 | Q16 | — | 8 | 2 | no | — |
| 307 | Q16 | — | 8 | 2 | no | — |
| 308 | M16 | — | 8 | 1 | no | — |
| 309 | C2×C8 | — | 2 | 2 | no | — |
| 310 | C2×C8 | — | 2 | 2 | no | — |
| 311 | C2×C8 | — | 2 | 2 | no | — |
| 312 | C2×C8 | — | 8 | 1 | no | — |
| 313 | C2×C8 | C2×D4×C71 | 1 | 2 | yes | — |
| 314 | C2×C8 | C2×D4×C71 | 1 | 2 | yes | — |
| 315 | C4⋊C4 | — | 2 | 1 | no | — |
| 316 | C4⋊C4 | — | 2 | 1 | no | — |
| 317 | C4⋊C4 | — | 2 | 1 | no | — |
| 318 | C4⋊C4 | — | 2 | 2 | no | — |
| 319 | C4⋊C4 | — | 2 | 2 | no | — |
| 320 | C4⋊C4 | — | 2 | 1 | no | — |
| 321 | C4⋊C4 | — | 2 | 1 | no | — |
| 322 | C4⋊C4 | — | 2 | 1 | no | — |
| 323 | C4⋊C4 | — | 2 | 1 | no | — |
| 324 | C4⋊C4 | — | 2 | 1 | no | — |
| 325 | C4⋊C4 | — | 2 | 1 | no | — |
| 326 | C4⋊C4 | — | 2 | 1 | no | — |
| 327 | C4⋊C4 | — | 2 | 1 | no | — |
| 328 | C4⋊C4 | — | 4 | 1 | no | — |
| 329 | C4⋊C4 | — | 4 | 1 | no | — |
| 330 | C4⋊C4 | — | 4 | 1 | no | — |
| 331 | C4⋊C4 | — | 4 | 1 | no | — |
| 332 | C4⋊C4 | C2×D4×C71 | 1 | 2 | yes | — |
| 333 | C22⋊C4 | — | 2 | 2 | no | — |
| 334 | C22⋊C4 | — | 4 | 1 | no | — |
| 335 | C22⋊C4 | — | 4 | 1 | no | — |
| 336 | C42 | — | 2 | 2 | no | — |
| 337 | C42 | — | 4 | 1 | no | — |
| 338 | C42 | — | 4 | 1 | no | — |
| 339 | C42 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 340 | C42 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 341 | C42 | #41×C71 | 1 | 1 | yes | characteristic |
| 342 | C42 | C24×C71 | 1 | 1 | yes | characteristic |
| 343 | C23 | #121×C71 | 1 | 1 | yes | characteristic |
| 344 | Q8 | — | 2 | 2 | no | — |
| 345 | Q8 | — | 2 | 2 | no | — |
| 346 | Q8 | — | 4 | 1 | no | — |
| 347 | Q8 | — | 4 | 1 | no | — |
| 348 | Q8 | — | 4 | 2 | no | — |
| 349 | Q8 | — | 4 | 1 | no | — |
| 350 | Q8 | — | 4 | 1 | no | — |
| 351 | Q8 | — | 8 | 1 | no | — |
| 352 | Q8 | — | 8 | 1 | no | — |
| 353 | C2×C4 | — | 2 | 1 | no | — |
| 354 | C2×C4 | — | 2 | 2 | no | — |
| 355 | C2×C4 | — | 2 | 1 | no | — |
| 356 | C2×C4 | — | 2 | 2 | no | — |
| 357 | C2×C4 | — | 2 | 2 | no | — |
| 358 | C2×C4 | — | 4 | 1 | no | — |
| 359 | C2×C4 | — | 4 | 1 | no | — |
| 360 | C2×C4 | — | 4 | 1 | no | — |
| 361 | C2×C4 | — | 4 | 1 | no | — |
| 362 | C2×C4 | — | 4 | 1 | no | — |
| 363 | C2×C4 | #121×C71 | 1 | 1 | yes | characteristic |
| 364 | C2×C4 | #121×C71 | 1 | 1 | yes | characteristic |
| 365 | C2×C4 | #121×C71 | 1 | 1 | yes | characteristic |
| 366 | C2×C4 | C22×D4×C71 | 1 | 1 | yes | characteristic |
| 367 | C2×C4 | C22×D4×C71 | 1 | 1 | yes | characteristic |
| 368 | C2×C4 | C2×#41×C71 | 1 | 1 | yes | characteristic |
| 369 | C8 | — | 2 | 2 | no | — |
| 370 | C8 | — | 2 | 2 | no | — |
| 371 | C8 | — | 4 | 2 | no | — |
| 372 | C8 | — | 4 | 2 | no | — |
| 373 | C8 | — | 4 | 2 | no | — |
| 374 | C22 | — | 2 | 1 | no | — |
| 375 | C22 | — | 2 | 1 | no | — |
| 376 | C22 | — | 2 | 1 | no | — |
| 377 | C22 | C2×#121×C71 | 1 | 1 | yes | characteristic |
| 378 | C4 | — | 2 | 1 | no | — |
| 379 | C4 | — | 2 | 1 | no | — |
| 380 | C4 | — | 2 | 1 | no | — |
| 381 | C4 | — | 2 | 1 | no | — |
| 382 | C4 | — | 4 | 2 | no | — |
| 383 | C4 | — | 4 | 2 | no | — |
| 384 | C4 | — | 8 | 1 | no | — |
| 385 | C4 | — | 8 | 1 | no | — |
| 386 | C4 | — | 8 | 1 | no | — |
| 387 | C4 | — | 8 | 1 | no | — |
| 388 | C4 | #576×C71 | 1 | 1 | yes | characteristic |
| 389 | C4 | #578×C71 | 1 | 2 | yes | — |
| 390 | C4 | #578×C71 | 1 | 1 | yes | characteristic |
| 391 | C2 | — | 4 | 1 | no | — |
| 392 | C2 | C71×#3044 | 1 | 1 | yes | characteristic |
| 393 | C2 | C71×#3061 | 1 | 1 | yes | characteristic |
| 394 | C2 | C71×#3069 | 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