← #26193012
Subgroups — #26193012
Order 12032.
898 conjugacy classes of subgroups.
The subgroup lattice has 616 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #20254615 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #20253935 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#15689333 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20242665 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #20242658 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #20242637 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #20242630 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #20242088 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #20241835 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #20241801 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | C47×#3523 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C22×#10625337 | — | 2 | 1 | no | — |
| 13 | C2×#13094024 | C22 | 1 | 1 | yes | characteristic |
| 14 | #15689533 | — | 2 | 1 | no | — |
| 15 | #15689533 | — | 2 | 2 | no | — |
| 16 | #15689526 | C22 | 1 | 2 | yes | — |
| 17 | #15689519 | C22 | 1 | 2 | yes | — |
| 18 | #15689482 | — | 2 | 1 | no | — |
| 19 | #15689456 | — | 2 | 1 | no | — |
| 20 | #15689439 | — | 2 | 1 | no | — |
| 21 | #15689408 | C22 | 1 | 2 | yes | — |
| 22 | #15689403 | C22 | 1 | 2 | yes | — |
| 23 | #15689333 | — | 2 | 1 | no | — |
| 24 | #15689333 | — | 2 | 1 | no | — |
| 25 | #15689333 | C22 | 1 | 2 | yes | — |
| 26 | #15689333 | C22 | 1 | 2 | yes | — |
| 27 | #15689180 | C22 | 1 | 1 | yes | characteristic |
| 28 | #15689166 | — | 2 | 2 | no | — |
| 29 | C2×C4⋊(C47⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×#13093947 | — | 2 | 1 | no | — |
| 31 | C4×#10625329 | C22 | 1 | 1 | yes | characteristic |
| 32 | #15688869 | C22 | 1 | 2 | yes | — |
| 33 | #15688869 | C22 | 1 | 2 | yes | — |
| 34 | Q8⋊(C47⋊C8) | C22 | 1 | 2 | yes | — |
| 35 | Q8⋊(C47⋊C8) | C22 | 1 | 2 | yes | — |
| 36 | Q8⋊(C47⋊C8) | C22 | 1 | 2 | yes | — |
| 37 | D4⋊(C47⋊C8) | C22 | 1 | 2 | yes | — |
| 38 | C47×#557 | — | 2 | 1 | no | — |
| 39 | C47×#557 | C22 | 1 | 1 | yes | characteristic |
| 40 | C47×#557 | C22 | 1 | 1 | yes | characteristic |
| 41 | C47×#556 | — | 2 | 1 | no | — |
| 42 | C47×#556 | C22 | 1 | 1 | yes | characteristic |
| 43 | C47×#552 | — | 2 | 2 | no | — |
| 44 | C47×#552 | — | 2 | 1 | no | — |
| 45 | D4×Q8×C47 | — | 2 | 1 | no | — |
| 46 | D4×Q8×C47 | C22 | 1 | 1 | yes | characteristic |
| 47 | C47×#541 | — | 2 | 2 | no | — |
| 48 | C47×#541 | — | 2 | 1 | no | — |
| 49 | C47×#533 | — | 2 | 1 | no | — |
| 50 | C47×#533 | C22 | 1 | 1 | yes | characteristic |
| 51 | C47×#529 | — | 2 | 1 | no | — |
| 52 | C47×#529 | C22 | 1 | 1 | yes | characteristic |
| 53 | C47×#519 | — | 2 | 1 | no | — |
| 54 | C2×C4×Q8×C47 | C22 | 1 | 1 | yes | characteristic |
| 55 | C22×Dic94 | — | 2 | 1 | no | — |
| 56 | C2×#10625337 | — | 2 | 2 | no | — |
| 57 | C2×#10625337 | — | 2 | 2 | no | — |
| 58 | C2×#10625337 | — | 4 | 4 | no | — |
| 59 | C2×#10625329 | — | 2 | 1 | no | — |
| 60 | C22×C47⋊C8 | — | 2 | 1 | no | — |
| 61 | #13094024 | — | 2 | 1 | no | — |
| 62 | #13094024 | — | 2 | 1 | no | — |
| 63 | #13094024 | — | 2 | 1 | no | — |
| 64 | #13094024 | C23 | 1 | 2 | yes | — |
| 65 | C2×C4⋊Dic47 | — | 2 | 1 | no | — |
| 66 | C2×C4⋊Dic47 | — | 2 | 1 | no | — |
| 67 | #13093957 | — | 2 | 4 | no | — |
| 68 | #13093957 | — | 2 | 2 | no | — |
| 69 | #13093955 | — | 2 | 4 | no | — |
| 70 | #13093955 | — | 2 | 2 | no | — |
| 71 | C4⋊(C47⋊C8) | — | 2 | 1 | no | — |
| 72 | C4⋊(C47⋊C8) | C23 | 1 | 2 | yes | — |
| 73 | C4⋊(C47⋊C8) | C23 | 1 | 2 | yes | — |
| 74 | #13093948 | — | 2 | 2 | no | — |
| 75 | #13093947 | — | 2 | 2 | no | — |
| 76 | #13093947 | — | 2 | 2 | no | — |
| 77 | #13093945 | — | 2 | 2 | no | — |
| 78 | C22⋊(C47⋊C8) | — | 2 | 1 | no | — |
| 79 | #13093935 | — | 2 | 1 | no | — |
| 80 | #13093935 | — | 2 | 1 | no | — |
| 81 | C4×C47⋊C8 | C23 | 1 | 2 | yes | — |
| 82 | C22×Q8×C47 | — | 2 | 1 | no | — |
| 83 | C22×Q8×C47 | D4 | 1 | 1 | yes | characteristic |
| 84 | C4⋊Q8×C47 | — | 2 | 2 | no | — |
| 85 | C4⋊Q8×C47 | — | 2 | 1 | no | — |
| 86 | C4⋊Q8×C47 | — | 2 | 1 | no | — |
| 87 | C4⋊Q8×C47 | — | 2 | 1 | no | — |
| 88 | C4⋊Q8×C47 | C23 | 1 | 1 | yes | characteristic |
| 89 | C4⋊Q8×C47 | C23 | 1 | 1 | yes | characteristic |
| 90 | #126×C47 | — | 2 | 2 | no | — |
| 91 | #126×C47 | — | 2 | 2 | no | — |
| 92 | #126×C47 | — | 2 | 2 | no | — |
| 93 | #126×C47 | — | 2 | 2 | no | — |
| 94 | #126×C47 | — | 2 | 1 | no | — |
| 95 | #125×C47 | — | 2 | 2 | no | — |
| 96 | #125×C47 | — | 2 | 2 | no | — |
| 97 | #125×C47 | — | 2 | 2 | no | — |
| 98 | #125×C47 | — | 2 | 1 | no | — |
| 99 | #125×C47 | — | 2 | 2 | no | — |
| 100 | #125×C47 | — | 2 | 2 | no | — |
| 101 | #125×C47 | — | 2 | 1 | no | — |
| 102 | #125×C47 | D4 | 1 | 1 | yes | characteristic |
| 103 | #125×C47 | D4 | 1 | 2 | yes | — |
| 104 | #124×C47 | — | 2 | 1 | no | — |
| 105 | #124×C47 | D4 | 1 | 1 | yes | characteristic |
| 106 | #123×C47 | — | 2 | 2 | no | — |
| 107 | #123×C47 | — | 2 | 1 | no | — |
| 108 | C22⋊Q8×C47 | — | 2 | 2 | no | — |
| 109 | C22⋊Q8×C47 | — | 2 | 2 | no | — |
| 110 | C22⋊Q8×C47 | — | 2 | 1 | no | — |
| 111 | C22⋊Q8×C47 | — | 2 | 1 | no | — |
| 112 | C22⋊Q8×C47 | — | 2 | 1 | no | — |
| 113 | C22⋊Q8×C47 | — | 2 | 1 | no | — |
| 114 | C22⋊Q8×C47 | — | 2 | 2 | no | — |
| 115 | C22⋊Q8×C47 | D4 | 1 | 1 | yes | characteristic |
| 116 | #121×C47 | D4 | 1 | 1 | yes | characteristic |
| 117 | C4×Q8×C47 | — | 2 | 2 | no | — |
| 118 | C4×Q8×C47 | — | 2 | 2 | no | — |
| 119 | C4×Q8×C47 | — | 2 | 1 | no | — |
| 120 | C4×Q8×C47 | — | 2 | 1 | no | — |
| 121 | C4×Q8×C47 | — | 2 | 1 | no | — |
| 122 | C4×Q8×C47 | — | 2 | 1 | no | — |
| 123 | C4×Q8×C47 | — | 2 | 1 | no | — |
| 124 | C4×Q8×C47 | — | 2 | 1 | no | — |
| 125 | C4×Q8×C47 | — | 2 | 1 | no | — |
| 126 | C4×Q8×C47 | — | 2 | 1 | no | — |
| 127 | C4×Q8×C47 | — | 2 | 1 | no | — |
| 128 | C4×Q8×C47 | D4 | 1 | 1 | yes | characteristic |
| 129 | C4×Q8×C47 | D4 | 1 | 1 | yes | characteristic |
| 130 | C4×Q8×C47 | C23 | 1 | 1 | yes | characteristic |
| 131 | C4×Q8×C47 | C23 | 1 | 1 | yes | characteristic |
| 132 | C4×Q8×C47 | C23 | 1 | 1 | yes | characteristic |
| 133 | C4×D4×C47 | — | 2 | 2 | no | — |
| 134 | C4×D4×C47 | — | 2 | 1 | no | — |
| 135 | C4×D4×C47 | — | 2 | 1 | no | — |
| 136 | C4×D4×C47 | C23 | 1 | 1 | yes | characteristic |
| 137 | #117×C47 | — | 2 | 2 | no | — |
| 138 | #117×C47 | — | 2 | 2 | no | — |
| 139 | #117×C47 | — | 2 | 2 | no | — |
| 140 | #117×C47 | — | 2 | 1 | no | — |
| 141 | #117×C47 | — | 2 | 1 | no | — |
| 142 | #117×C47 | D4 | 1 | 2 | yes | — |
| 143 | C2×C4⋊C4×C47 | — | 2 | 1 | no | — |
| 144 | C2×C4⋊C4×C47 | D4 | 1 | 1 | yes | characteristic |
| 145 | C2×C42×C47 | — | 2 | 1 | no | — |
| 146 | C2×C42×C47 | C23 | 1 | 1 | yes | characteristic |
| 147 | C2×Q8×C47 | — | 2 | 2 | no | — |
| 148 | C2×Q8×C47 | — | 2 | 1 | no | — |
| 149 | C2×Q8×C47 | — | 2 | 1 | no | — |
| 150 | C2×Q8×C47 | — | 2 | 1 | no | — |
| 151 | C2×Q8×C47 | — | 2 | 2 | no | — |
| 152 | C2×Q8×C47 | — | 4 | 1 | no | — |
| 153 | C2×Q8×C47 | — | 4 | 2 | no | — |
| 154 | C2×Q8×C47 | — | 4 | 2 | no | — |
| 155 | C2×Q8×C47 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | C2×Q8×C47 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | C2×Q8×C47 | C2×D4 | 1 | 1 | yes | characteristic |
| 158 | C2×D4×C47 | — | 2 | 1 | no | — |
| 159 | C2×D4×C47 | C2×D4 | 1 | 1 | yes | characteristic |
| 160 | C22×C4×C47 | — | 2 | 2 | no | — |
| 161 | C22×C4×C47 | — | 2 | 1 | no | — |
| 162 | C22×C4×C47 | — | 2 | 1 | no | — |
| 163 | C22×C4×C47 | — | 2 | 1 | no | — |
| 164 | C22×C4×C47 | C2×D4 | 1 | 1 | yes | characteristic |
| 165 | C22×C4×C47 | C2×D4 | 1 | 1 | yes | characteristic |
| 166 | C22×C4×C47 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C22×Dic47 | — | 4 | 1 | no | — |
| 168 | C2×Dic94 | — | 2 | 2 | no | — |
| 169 | C2×Dic94 | — | 4 | 2 | no | — |
| 170 | C2×Dic94 | — | 4 | 2 | no | — |
| 171 | C2×Dic94 | — | 4 | 1 | no | — |
| 172 | C4⋊C4×C47 | — | 2 | 2 | no | — |
| 173 | C4⋊C4×C47 | — | 2 | 2 | no | — |
| 174 | C4⋊C4×C47 | — | 2 | 2 | no | — |
| 175 | C4⋊C4×C47 | — | 2 | 2 | no | — |
| 176 | C4⋊C4×C47 | — | 2 | 2 | no | — |
| 177 | C4⋊C4×C47 | — | 2 | 2 | no | — |
| 178 | C4⋊C4×C47 | — | 2 | 2 | no | — |
| 179 | C4⋊C4×C47 | — | 2 | 2 | no | — |
| 180 | C4⋊C4×C47 | — | 2 | 1 | no | — |
| 181 | C4⋊C4×C47 | — | 2 | 1 | no | — |
| 182 | C4⋊C4×C47 | — | 2 | 1 | no | — |
| 183 | C4⋊C4×C47 | — | 2 | 2 | no | — |
| 184 | C4⋊C4×C47 | — | 2 | 1 | no | — |
| 185 | C4⋊C4×C47 | — | 2 | 1 | no | — |
| 186 | C4⋊C4×C47 | — | 2 | 1 | no | — |
| 187 | C4⋊C4×C47 | — | 2 | 2 | no | — |
| 188 | C4⋊C4×C47 | — | 2 | 1 | no | — |
| 189 | C4⋊C4×C47 | — | 2 | 1 | no | — |
| 190 | C4⋊C4×C47 | — | 2 | 1 | no | — |
| 191 | C4⋊C4×C47 | — | 2 | 1 | no | — |
| 192 | C4⋊C4×C47 | — | 2 | 1 | no | — |
| 193 | C4⋊C4×C47 | C2×D4 | 1 | 1 | yes | characteristic |
| 194 | C4⋊C4×C47 | C2×D4 | 1 | 1 | yes | characteristic |
| 195 | C4⋊C4×C47 | C2×D4 | 1 | 2 | yes | — |
| 196 | C4⋊C4×C47 | C2×D4 | 1 | 2 | yes | — |
| 197 | C4⋊C4×C47 | C2×D4 | 1 | 1 | yes | characteristic |
| 198 | C4⋊C4×C47 | C2×D4 | 1 | 1 | yes | characteristic |
| 199 | C22⋊C4×C47 | — | 2 | 2 | no | — |
| 200 | C22⋊C4×C47 | — | 2 | 2 | no | — |
| 201 | C22⋊C4×C47 | — | 2 | 2 | no | — |
| 202 | C22⋊C4×C47 | — | 2 | 1 | no | — |
| 203 | C22⋊C4×C47 | — | 2 | 2 | no | — |
| 204 | C22⋊C4×C47 | — | 2 | 1 | no | — |
| 205 | C22⋊C4×C47 | — | 2 | 1 | no | — |
| 206 | C22⋊C4×C47 | — | 2 | 1 | no | — |
| 207 | C22⋊C4×C47 | — | 2 | 1 | no | — |
| 208 | C42×C47 | — | 2 | 2 | no | — |
| 209 | C42×C47 | — | 2 | 2 | no | — |
| 210 | C42×C47 | — | 2 | 2 | no | — |
| 211 | C42×C47 | — | 2 | 1 | no | — |
| 212 | C42×C47 | — | 2 | 1 | no | — |
| 213 | C42×C47 | — | 2 | 2 | no | — |
| 214 | C42×C47 | — | 2 | 1 | no | — |
| 215 | C42×C47 | — | 2 | 1 | no | — |
| 216 | C42×C47 | — | 2 | 1 | no | — |
| 217 | C42×C47 | C2×D4 | 1 | 1 | yes | characteristic |
| 218 | C42×C47 | C2×D4 | 1 | 1 | yes | characteristic |
| 219 | C42×C47 | C2×D4 | 1 | 1 | yes | characteristic |
| 220 | C42×C47 | C24 | 1 | 1 | yes | characteristic |
| 221 | #10625337 | — | 4 | 4 | no | — |
| 222 | #10625337 | — | 4 | 4 | no | — |
| 223 | C4⋊Dic47 | — | 2 | 2 | no | — |
| 224 | C4⋊Dic47 | — | 2 | 2 | no | — |
| 225 | C4⋊Dic47 | — | 4 | 1 | no | — |
| 226 | C4⋊Dic47 | — | 4 | 1 | no | — |
| 227 | #10625329 | — | 2 | 4 | no | — |
| 228 | C2×C47⋊C8 | — | 2 | 2 | no | — |
| 229 | C2×C47⋊C8 | — | 2 | 2 | no | — |
| 230 | C2×C47⋊C8 | — | 2 | 2 | no | — |
| 231 | C2×C47⋊C8 | — | 4 | 2 | no | — |
| 232 | C23×C47 | — | 2 | 1 | no | — |
| 233 | C23×C47 | #120 | 1 | 1 | yes | characteristic |
| 234 | Q8×C47 | — | 2 | 1 | no | — |
| 235 | Q8×C47 | — | 2 | 1 | no | — |
| 236 | Q8×C47 | — | 2 | 1 | no | — |
| 237 | Q8×C47 | — | 2 | 2 | no | — |
| 238 | Q8×C47 | — | 4 | 2 | no | — |
| 239 | Q8×C47 | — | 4 | 4 | no | — |
| 240 | Q8×C47 | — | 4 | 1 | no | — |
| 241 | Q8×C47 | — | 4 | 1 | no | — |
| 242 | Q8×C47 | — | 4 | 2 | no | — |
| 243 | Q8×C47 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 244 | D4×C47 | — | 2 | 2 | no | — |
| 245 | D4×C47 | — | 4 | 2 | no | — |
| 246 | C2×C4×C47 | — | 2 | 1 | no | — |
| 247 | C2×C4×C47 | — | 2 | 2 | no | — |
| 248 | C2×C4×C47 | — | 2 | 1 | no | — |
| 249 | C2×C4×C47 | — | 2 | 1 | no | — |
| 250 | C2×C4×C47 | — | 2 | 2 | no | — |
| 251 | C2×C4×C47 | — | 2 | 1 | no | — |
| 252 | C2×C4×C47 | — | 2 | 1 | no | — |
| 253 | C2×C4×C47 | — | 2 | 2 | no | — |
| 254 | C2×C4×C47 | — | 2 | 1 | no | — |
| 255 | C2×C4×C47 | — | 2 | 1 | no | — |
| 256 | C2×C4×C47 | — | 2 | 1 | no | — |
| 257 | C2×C4×C47 | — | 2 | 1 | no | — |
| 258 | C2×C4×C47 | — | 2 | 2 | no | — |
| 259 | C2×C4×C47 | — | 4 | 2 | no | — |
| 260 | C2×C4×C47 | — | 4 | 4 | no | — |
| 261 | C2×C4×C47 | — | 4 | 2 | no | — |
| 262 | C2×C4×C47 | — | 4 | 1 | no | — |
| 263 | C2×C4×C47 | — | 4 | 1 | no | — |
| 264 | C2×C4×C47 | #120 | 1 | 1 | yes | characteristic |
| 265 | C2×C4×C47 | #120 | 1 | 1 | yes | characteristic |
| 266 | C2×C4×C47 | #120 | 1 | 1 | yes | characteristic |
| 267 | C2×C4×C47 | C22×D4 | 1 | 1 | yes | characteristic |
| 268 | C2×C4×C47 | C22×D4 | 1 | 1 | yes | characteristic |
| 269 | C2×C4×C47 | C22×D4 | 1 | 1 | yes | characteristic |
| 270 | C2×Dic47 | — | 4 | 2 | no | — |
| 271 | C2×Dic47 | — | 8 | 2 | no | — |
| 272 | Dic94 | — | 4 | 2 | no | — |
| 273 | Dic94 | — | 4 | 2 | no | — |
| 274 | Dic94 | — | 8 | 2 | no | — |
| 275 | C47⋊C8 | — | 2 | 4 | no | — |
| 276 | C47⋊C8 | — | 4 | 2 | no | — |
| 277 | C47⋊C8 | — | 4 | 2 | no | — |
| 278 | #18588 | — | 47 | 1 | no | maximal, Sylow |
| 279 | C22×C47 | — | 2 | 1 | no | — |
| 280 | C22×C47 | — | 2 | 1 | no | — |
| 281 | C22×C47 | — | 4 | 1 | no | — |
| 282 | C22×C47 | — | 4 | 1 | no | — |
| 283 | C22×C47 | — | 4 | 1 | no | — |
| 284 | C22×C47 | #456 | 1 | 2 | yes | — |
| 285 | C22×C47 | C2×#120 | 1 | 1 | yes | characteristic |
| 286 | C4×C47 | — | 2 | 1 | no | — |
| 287 | C4×C47 | — | 2 | 2 | no | — |
| 288 | C4×C47 | — | 2 | 1 | no | — |
| 289 | C4×C47 | — | 2 | 1 | no | — |
| 290 | C4×C47 | — | 2 | 1 | no | — |
| 291 | C4×C47 | — | 4 | 1 | no | — |
| 292 | C4×C47 | — | 4 | 2 | no | — |
| 293 | C4×C47 | — | 4 | 1 | no | — |
| 294 | C4×C47 | — | 4 | 1 | no | — |
| 295 | C4×C47 | — | 4 | 2 | no | — |
| 296 | C4×C47 | — | 4 | 1 | no | — |
| 297 | C4×C47 | — | 4 | 1 | no | — |
| 298 | C4×C47 | — | 4 | 1 | no | — |
| 299 | C4×C47 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 300 | C4×C47 | #575 | 1 | 1 | yes | characteristic |
| 301 | C4×C47 | #578 | 1 | 2 | yes | — |
| 302 | Dic47 | — | 8 | 2 | no | — |
| 303 | #3523 | D47 | 1 | 1 | yes | characteristic |
| 304 | #3239 | — | 47 | 1 | no | — |
| 305 | #3165 | — | 47 | 1 | no | — |
| 306 | C2×#462 | — | 47 | 1 | no | — |
| 307 | #1653 | — | 47 | 2 | no | — |
| 308 | #1652 | — | 47 | 2 | no | — |
| 309 | #1649 | — | 47 | 2 | no | — |
| 310 | #1648 | — | 47 | 2 | no | — |
| 311 | #1552 | — | 47 | 1 | no | — |
| 312 | #1491 | — | 47 | 1 | no | — |
| 313 | #1483 | — | 47 | 1 | no | — |
| 314 | C2×C47 | — | 2 | 2 | no | — |
| 315 | C2×C47 | — | 8 | 1 | no | — |
| 316 | C2×C47 | #3006 | 1 | 1 | yes | characteristic |
| 317 | C2×C47 | #3011 | 1 | 1 | yes | characteristic |
| 318 | C2×C47 | C2×#456 | 1 | 1 | yes | characteristic |
| 319 | C22×Q16 | — | 94 | 1 | no | — |
| 320 | #557 | — | 2 | 1 | no | — |
| 321 | #557 | C2×D47 | 1 | 1 | yes | characteristic |
| 322 | #557 | C2×D47 | 1 | 1 | yes | characteristic |
| 323 | #556 | — | 2 | 1 | no | — |
| 324 | #556 | C2×D47 | 1 | 1 | yes | characteristic |
| 325 | #552 | — | 2 | 2 | no | — |
| 326 | #552 | — | 2 | 1 | no | — |
| 327 | D4×Q8 | — | 2 | 1 | no | — |
| 328 | D4×Q8 | C2×D47 | 1 | 1 | yes | characteristic |
| 329 | #541 | — | 2 | 2 | no | — |
| 330 | #541 | — | 2 | 1 | no | — |
| 331 | #533 | — | 2 | 1 | no | — |
| 332 | #533 | C2×D47 | 1 | 1 | yes | characteristic |
| 333 | C2×C4⋊Q8 | — | 47 | 1 | no | — |
| 334 | #529 | — | 2 | 1 | no | — |
| 335 | #529 | C2×D47 | 1 | 1 | yes | characteristic |
| 336 | #519 | — | 2 | 1 | no | — |
| 337 | C2×C4×Q8 | C2×D47 | 1 | 1 | yes | characteristic |
| 338 | #501 | — | 94 | 2 | no | — |
| 339 | #501 | — | 94 | 1 | no | — |
| 340 | #500 | — | 47 | 2 | no | — |
| 341 | #498 | — | 47 | 2 | no | — |
| 342 | #489 | — | 94 | 1 | no | — |
| 343 | #484 | — | 94 | 1 | no | — |
| 344 | #481 | — | 94 | 1 | no | — |
| 345 | #475 | — | 47 | 2 | no | — |
| 346 | #474 | — | 47 | 2 | no | — |
| 347 | #462 | — | 47 | 2 | no | — |
| 348 | #462 | — | 47 | 2 | no | — |
| 349 | #462 | — | 94 | 1 | no | — |
| 350 | #462 | — | 94 | 1 | no | — |
| 351 | #432 | — | 47 | 1 | no | — |
| 352 | #428 | — | 94 | 2 | no | — |
| 353 | C2×C4⋊C8 | — | 47 | 1 | no | — |
| 354 | C2×#103 | — | 94 | 1 | no | — |
| 355 | C4×M16 | — | 47 | 1 | no | — |
| 356 | #332 | — | 47 | 2 | no | — |
| 357 | #332 | — | 47 | 2 | no | — |
| 358 | Q8⋊C8 | — | 47 | 2 | no | — |
| 359 | Q8⋊C8 | — | 47 | 2 | no | — |
| 360 | Q8⋊C8 | — | 47 | 2 | no | — |
| 361 | D4⋊C8 | — | 47 | 2 | no | — |
| 362 | C47 | #18588 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 363 | C22×Q8 | — | 2 | 1 | no | — |
| 364 | C22×Q8 | — | 94 | 1 | no | — |
| 365 | C22×Q8 | C22⋊D47 | 1 | 1 | yes | characteristic |
| 366 | C2×Q16 | — | 94 | 2 | no | — |
| 367 | C2×Q16 | — | 94 | 2 | no | — |
| 368 | C2×Q16 | — | 188 | 4 | no | — |
| 369 | C2×M16 | — | 94 | 1 | no | — |
| 370 | C22×C8 | — | 94 | 1 | no | — |
| 371 | C4⋊Q8 | — | 2 | 2 | no | — |
| 372 | C4⋊Q8 | — | 2 | 1 | no | — |
| 373 | C4⋊Q8 | — | 2 | 1 | no | — |
| 374 | C4⋊Q8 | — | 2 | 1 | no | — |
| 375 | C4⋊Q8 | — | 47 | 2 | no | — |
| 376 | C4⋊Q8 | — | 94 | 1 | no | — |
| 377 | C4⋊Q8 | — | 94 | 1 | no | — |
| 378 | C4⋊Q8 | — | 94 | 1 | no | — |
| 379 | C4⋊Q8 | C22×D47 | 1 | 1 | yes | characteristic |
| 380 | C4⋊Q8 | C22×D47 | 1 | 1 | yes | characteristic |
| 381 | #126 | — | 2 | 2 | no | — |
| 382 | #126 | — | 2 | 2 | no | — |
| 383 | #126 | — | 2 | 2 | no | — |
| 384 | #126 | — | 2 | 2 | no | — |
| 385 | #126 | — | 2 | 1 | no | — |
| 386 | #125 | — | 2 | 2 | no | — |
| 387 | #125 | — | 2 | 2 | no | — |
| 388 | #125 | — | 2 | 2 | no | — |
| 389 | #125 | — | 2 | 1 | no | — |
| 390 | #125 | — | 2 | 2 | no | — |
| 391 | #125 | — | 2 | 2 | no | — |
| 392 | #125 | — | 2 | 1 | no | — |
| 393 | #125 | C22⋊D47 | 1 | 1 | yes | characteristic |
| 394 | #125 | C22⋊D47 | 1 | 2 | yes | — |
| 395 | #124 | — | 2 | 1 | no | — |
| 396 | #124 | C22⋊D47 | 1 | 1 | yes | characteristic |
| 397 | #123 | — | 2 | 2 | no | — |
| 398 | #123 | — | 2 | 1 | no | — |
| 399 | C22⋊Q8 | — | 2 | 2 | no | — |
| 400 | C22⋊Q8 | — | 2 | 2 | no | — |
| 401 | C22⋊Q8 | — | 2 | 1 | no | — |
| 402 | C22⋊Q8 | — | 2 | 1 | no | — |
| 403 | C22⋊Q8 | — | 2 | 1 | no | — |
| 404 | C22⋊Q8 | — | 2 | 1 | no | — |
| 405 | C22⋊Q8 | — | 2 | 2 | no | — |
| 406 | C22⋊Q8 | C22⋊D47 | 1 | 1 | yes | characteristic |
| 407 | #121 | C22⋊D47 | 1 | 1 | yes | characteristic |
| 408 | C4×Q8 | — | 2 | 2 | no | — |
| 409 | C4×Q8 | — | 2 | 2 | no | — |
| 410 | C4×Q8 | — | 2 | 1 | no | — |
| 411 | C4×Q8 | — | 2 | 1 | no | — |
| 412 | C4×Q8 | — | 2 | 1 | no | — |
| 413 | C4×Q8 | — | 2 | 1 | no | — |
| 414 | C4×Q8 | — | 2 | 1 | no | — |
| 415 | C4×Q8 | — | 2 | 1 | no | — |
| 416 | C4×Q8 | — | 2 | 1 | no | — |
| 417 | C4×Q8 | — | 2 | 1 | no | — |
| 418 | C4×Q8 | — | 2 | 1 | no | — |
| 419 | C4×Q8 | C22⋊D47 | 1 | 1 | yes | characteristic |
| 420 | C4×Q8 | C22⋊D47 | 1 | 1 | yes | characteristic |
| 421 | C4×Q8 | C22×D47 | 1 | 1 | yes | characteristic |
| 422 | C4×Q8 | C22×D47 | 1 | 1 | yes | characteristic |
| 423 | C4×Q8 | C22×D47 | 1 | 1 | yes | characteristic |
| 424 | C4×D4 | — | 2 | 2 | no | — |
| 425 | C4×D4 | — | 2 | 1 | no | — |
| 426 | C4×D4 | — | 2 | 1 | no | — |
| 427 | C4×D4 | C22×D47 | 1 | 1 | yes | characteristic |
| 428 | #117 | — | 2 | 2 | no | — |
| 429 | #117 | — | 2 | 2 | no | — |
| 430 | #117 | — | 2 | 2 | no | — |
| 431 | #117 | — | 2 | 1 | no | — |
| 432 | #117 | — | 2 | 1 | no | — |
| 433 | #117 | C22⋊D47 | 1 | 2 | yes | — |
| 434 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 435 | C2×C4⋊C4 | — | 94 | 1 | no | — |
| 436 | C2×C4⋊C4 | — | 94 | 1 | no | — |
| 437 | C2×C4⋊C4 | C22⋊D47 | 1 | 1 | yes | characteristic |
| 438 | C2×C42 | — | 2 | 1 | no | — |
| 439 | C2×C42 | C22×D47 | 1 | 1 | yes | characteristic |
| 440 | #107 | — | 94 | 4 | no | — |
| 441 | #107 | — | 94 | 2 | no | — |
| 442 | #106 | — | 94 | 4 | no | — |
| 443 | #106 | — | 94 | 2 | no | — |
| 444 | C4⋊C8 | — | 47 | 2 | no | — |
| 445 | C4⋊C8 | — | 47 | 2 | no | — |
| 446 | C4⋊C8 | — | 94 | 1 | no | — |
| 447 | #103 | — | 94 | 2 | no | — |
| 448 | #103 | — | 94 | 2 | no | — |
| 449 | #103 | — | 94 | 2 | no | — |
| 450 | #102 | — | 94 | 2 | no | — |
| 451 | C22⋊C8 | — | 94 | 1 | no | — |
| 452 | #97 | — | 94 | 1 | no | — |
| 453 | #97 | — | 94 | 1 | no | — |
| 454 | C4×C8 | — | 47 | 2 | no | — |
| 455 | C2×Q8 | — | 2 | 2 | no | — |
| 456 | C2×Q8 | — | 2 | 1 | no | — |
| 457 | C2×Q8 | — | 2 | 1 | no | — |
| 458 | C2×Q8 | — | 2 | 1 | no | — |
| 459 | C2×Q8 | — | 2 | 2 | no | — |
| 460 | C2×Q8 | — | 4 | 1 | no | — |
| 461 | C2×Q8 | — | 4 | 2 | no | — |
| 462 | C2×Q8 | — | 4 | 2 | no | — |
| 463 | C2×Q8 | — | 94 | 2 | no | — |
| 464 | C2×Q8 | — | 188 | 2 | no | — |
| 465 | C2×Q8 | — | 188 | 2 | no | — |
| 466 | C2×Q8 | — | 188 | 1 | no | — |
| 467 | C2×Q8 | C2×C22⋊D47 | 1 | 1 | yes | characteristic |
| 468 | C2×Q8 | C2×C22⋊D47 | 1 | 1 | yes | characteristic |
| 469 | C2×Q8 | C2×C22⋊D47 | 1 | 1 | yes | characteristic |
| 470 | C2×D4 | — | 2 | 1 | no | — |
| 471 | C2×D4 | C2×C22⋊D47 | 1 | 1 | yes | characteristic |
| 472 | C22×C4 | — | 2 | 2 | no | — |
| 473 | C22×C4 | — | 2 | 1 | no | — |
| 474 | C22×C4 | — | 2 | 1 | no | — |
| 475 | C22×C4 | — | 2 | 1 | no | — |
| 476 | C22×C4 | — | 188 | 1 | no | — |
| 477 | C22×C4 | C2×C22⋊D47 | 1 | 1 | yes | characteristic |
| 478 | C22×C4 | C2×C22⋊D47 | 1 | 1 | yes | characteristic |
| 479 | C22×C4 | C2×C22⋊D47 | 1 | 1 | yes | characteristic |
| 480 | Q16 | — | 188 | 4 | no | — |
| 481 | Q16 | — | 188 | 4 | no | — |
| 482 | M16 | — | 94 | 4 | no | — |
| 483 | C2×C8 | — | 94 | 2 | no | — |
| 484 | C2×C8 | — | 94 | 2 | no | — |
| 485 | C2×C8 | — | 94 | 2 | no | — |
| 486 | C2×C8 | — | 188 | 2 | no | — |
| 487 | C4⋊C4 | — | 2 | 2 | no | — |
| 488 | C4⋊C4 | — | 2 | 2 | no | — |
| 489 | C4⋊C4 | — | 2 | 2 | no | — |
| 490 | C4⋊C4 | — | 2 | 2 | no | — |
| 491 | C4⋊C4 | — | 2 | 2 | no | — |
| 492 | C4⋊C4 | — | 2 | 2 | no | — |
| 493 | C4⋊C4 | — | 2 | 2 | no | — |
| 494 | C4⋊C4 | — | 2 | 2 | no | — |
| 495 | C4⋊C4 | — | 2 | 1 | no | — |
| 496 | C4⋊C4 | — | 2 | 1 | no | — |
| 497 | C4⋊C4 | — | 2 | 1 | no | — |
| 498 | C4⋊C4 | — | 2 | 2 | no | — |
| 499 | C4⋊C4 | — | 2 | 1 | no | — |
| 500 | C4⋊C4 | — | 2 | 1 | no | — |
| 501 | C4⋊C4 | — | 2 | 1 | no | — |
| 502 | C4⋊C4 | — | 2 | 2 | no | — |
| 503 | C4⋊C4 | — | 2 | 1 | no | — |
| 504 | C4⋊C4 | — | 2 | 1 | no | — |
| 505 | C4⋊C4 | — | 2 | 1 | no | — |
| 506 | C4⋊C4 | — | 2 | 1 | no | — |
| 507 | C4⋊C4 | — | 2 | 1 | no | — |
| 508 | C4⋊C4 | — | 94 | 2 | no | — |
| 509 | C4⋊C4 | — | 94 | 2 | no | — |
| 510 | C4⋊C4 | — | 188 | 1 | no | — |
| 511 | C4⋊C4 | — | 188 | 1 | no | — |
| 512 | C4⋊C4 | C2×C22⋊D47 | 1 | 1 | yes | characteristic |
| 513 | C4⋊C4 | C2×C22⋊D47 | 1 | 1 | yes | characteristic |
| 514 | C4⋊C4 | C2×C22⋊D47 | 1 | 2 | yes | — |
| 515 | C4⋊C4 | C2×C22⋊D47 | 1 | 1 | yes | characteristic |
| 516 | C4⋊C4 | C2×C22⋊D47 | 1 | 2 | yes | — |
| 517 | C4⋊C4 | C2×C22⋊D47 | 1 | 1 | yes | characteristic |
| 518 | C22⋊C4 | — | 2 | 2 | no | — |
| 519 | C22⋊C4 | — | 2 | 2 | no | — |
| 520 | C22⋊C4 | — | 2 | 2 | no | — |
| 521 | C22⋊C4 | — | 2 | 1 | no | — |
| 522 | C22⋊C4 | — | 2 | 2 | no | — |
| 523 | C22⋊C4 | — | 2 | 1 | no | — |
| 524 | C22⋊C4 | — | 2 | 1 | no | — |
| 525 | C22⋊C4 | — | 2 | 1 | no | — |
| 526 | C22⋊C4 | — | 2 | 1 | no | — |
| 527 | C42 | — | 2 | 2 | no | — |
| 528 | C42 | — | 2 | 2 | no | — |
| 529 | C42 | — | 2 | 2 | no | — |
| 530 | C42 | — | 2 | 1 | no | — |
| 531 | C42 | — | 2 | 1 | no | — |
| 532 | C42 | — | 2 | 2 | no | — |
| 533 | C42 | — | 2 | 1 | no | — |
| 534 | C42 | — | 2 | 1 | no | — |
| 535 | C42 | — | 2 | 1 | no | — |
| 536 | C42 | C2×C22⋊D47 | 1 | 1 | yes | characteristic |
| 537 | C42 | C2×C22⋊D47 | 1 | 1 | yes | characteristic |
| 538 | C42 | C2×C22⋊D47 | 1 | 1 | yes | characteristic |
| 539 | C42 | C23×D47 | 1 | 1 | yes | characteristic |
| 540 | C23 | — | 2 | 1 | no | — |
| 541 | C23 | #13093993 | 1 | 1 | yes | characteristic |
| 542 | Q8 | — | 2 | 1 | no | — |
| 543 | Q8 | — | 2 | 1 | no | — |
| 544 | Q8 | — | 2 | 1 | no | — |
| 545 | Q8 | — | 2 | 2 | no | — |
| 546 | Q8 | — | 4 | 2 | no | — |
| 547 | Q8 | — | 4 | 4 | no | — |
| 548 | Q8 | — | 4 | 1 | no | — |
| 549 | Q8 | — | 4 | 1 | no | — |
| 550 | Q8 | — | 4 | 2 | no | — |
| 551 | Q8 | — | 376 | 2 | no | — |
| 552 | Q8 | — | 188 | 2 | no | — |
| 553 | Q8 | — | 188 | 2 | no | — |
| 554 | Q8 | #13094049 | 1 | 2 | yes | — |
| 555 | D4 | — | 2 | 2 | no | — |
| 556 | D4 | — | 4 | 2 | no | — |
| 557 | C2×C4 | — | 2 | 2 | no | — |
| 558 | C2×C4 | — | 2 | 1 | no | — |
| 559 | C2×C4 | — | 2 | 1 | no | — |
| 560 | C2×C4 | — | 2 | 1 | no | — |
| 561 | C2×C4 | — | 2 | 2 | no | — |
| 562 | C2×C4 | — | 2 | 1 | no | — |
| 563 | C2×C4 | — | 2 | 1 | no | — |
| 564 | C2×C4 | — | 2 | 2 | no | — |
| 565 | C2×C4 | — | 2 | 1 | no | — |
| 566 | C2×C4 | — | 2 | 1 | no | — |
| 567 | C2×C4 | — | 2 | 1 | no | — |
| 568 | C2×C4 | — | 2 | 1 | no | — |
| 569 | C2×C4 | — | 2 | 2 | no | — |
| 570 | C2×C4 | — | 4 | 2 | no | — |
| 571 | C2×C4 | — | 4 | 4 | no | — |
| 572 | C2×C4 | — | 4 | 2 | no | — |
| 573 | C2×C4 | — | 4 | 1 | no | — |
| 574 | C2×C4 | — | 4 | 1 | no | — |
| 575 | C2×C4 | — | 376 | 2 | no | — |
| 576 | C2×C4 | — | 188 | 2 | no | — |
| 577 | C2×C4 | #13093993 | 1 | 1 | yes | characteristic |
| 578 | C2×C4 | #13093993 | 1 | 1 | yes | characteristic |
| 579 | C2×C4 | #13093993 | 1 | 1 | yes | characteristic |
| 580 | C2×C4 | C22×C22⋊D47 | 1 | 1 | yes | characteristic |
| 581 | C2×C4 | C22×C22⋊D47 | 1 | 1 | yes | characteristic |
| 582 | C2×C4 | C22×C22⋊D47 | 1 | 1 | yes | characteristic |
| 583 | C8 | — | 94 | 4 | no | — |
| 584 | C8 | — | 188 | 2 | no | — |
| 585 | C8 | — | 188 | 2 | no | — |
| 586 | C22 | — | 2 | 1 | no | — |
| 587 | C22 | — | 2 | 1 | no | — |
| 588 | C22 | — | 4 | 1 | no | — |
| 589 | C22 | — | 4 | 1 | no | — |
| 590 | C22 | — | 4 | 1 | no | — |
| 591 | C22 | #15689306 | 1 | 2 | yes | — |
| 592 | C22 | C2×#13093993 | 1 | 1 | yes | characteristic |
| 593 | C4 | — | 2 | 1 | no | — |
| 594 | C4 | — | 2 | 1 | no | — |
| 595 | C4 | — | 2 | 1 | no | — |
| 596 | C4 | — | 2 | 1 | no | — |
| 597 | C4 | — | 2 | 2 | no | — |
| 598 | C4 | — | 4 | 1 | no | — |
| 599 | C4 | — | 4 | 2 | no | — |
| 600 | C4 | — | 4 | 1 | no | — |
| 601 | C4 | — | 4 | 1 | no | — |
| 602 | C4 | — | 4 | 1 | no | — |
| 603 | C4 | — | 4 | 1 | no | — |
| 604 | C4 | — | 4 | 2 | no | — |
| 605 | C4 | — | 4 | 1 | no | — |
| 606 | C4 | — | 376 | 2 | no | — |
| 607 | C4 | C2×#13094049 | 1 | 1 | yes | characteristic |
| 608 | C4 | #15689921 | 1 | 1 | yes | characteristic |
| 609 | C4 | #15689938 | 1 | 2 | yes | — |
| 610 | C2 | — | 2 | 2 | no | — |
| 611 | C2 | — | 8 | 1 | no | — |
| 612 | C2 | #20252640 | 1 | 1 | yes | characteristic |
| 613 | C2 | #20252683 | 1 | 1 | yes | characteristic |
| 614 | C2 | C2×#15689306 | 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