← #13320657
Subgroups — #13320657
Order 1792.
1284 conjugacy classes of subgroups.
The subgroup lattice has 406 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #41×D28 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C7×C8×#41 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11739957 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11728516 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #11728512 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #11727489 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C2×#89254 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C2×D7×#41 | — | 2 | 1 | no | — |
| 9 | C4×C7×#41 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#6511 | — | 2 | 1 | no | — |
| 11 | #90268 | C4 | 1 | 1 | yes | characteristic |
| 12 | #90267 | — | 2 | 1 | no | — |
| 13 | Q8×D28 | C4 | 1 | 1 | yes | characteristic |
| 14 | #90246 | C4 | 1 | 3 | yes | — |
| 15 | #90245 | — | 2 | 3 | no | — |
| 16 | D4×D28 | C4 | 1 | 3 | yes | — |
| 17 | #90215 | — | 2 | 3 | no | — |
| 18 | #90168 | C22 | 1 | 3 | yes | — |
| 19 | C2×C4×D28 | C22 | 1 | 3 | yes | — |
| 20 | C7×C8×Q8 | — | 2 | 1 | no | — |
| 21 | C7×C8×D4 | — | 2 | 3 | no | — |
| 22 | C7×#431 | C22 | 1 | 3 | yes | complemented |
| 23 | C2×C4×C7×C8 | C22 | 1 | 3 | yes | complemented |
| 24 | #89771 | — | 2 | 3 | no | — |
| 25 | #89696 | C22 | 1 | 3 | yes | complemented |
| 26 | C2×C4⋊(C7⋊C8) | C22 | 1 | 3 | yes | complemented |
| 27 | #89254 | C22 | 1 | 1 | yes | characteristic |
| 28 | #89254 | C22 | 1 | 3 | yes | — |
| 29 | #89254 | C22 | 1 | 3 | yes | complemented |
| 30 | #89254 | C22 | 1 | 3 | yes | complemented |
| 31 | #89254 | C22 | 1 | 6 | yes | complemented |
| 32 | #17507 | — | 7 | 1 | no | maximal, Sylow |
| 33 | C2×C7×#41 | D4 | 1 | 1 | yes | characteristic |
| 34 | D7×#41 | — | 4 | 4 | no | — |
| 35 | D7×#41 | — | 4 | 4 | no | — |
| 36 | C2×#1161 | — | 2 | 1 | no | — |
| 37 | C2×Q8×D7 | — | 2 | 1 | no | — |
| 38 | C2×#1159 | — | 2 | 3 | no | — |
| 39 | C2×D4×D7 | — | 2 | 3 | no | — |
| 40 | C2×#1157 | — | 2 | 3 | no | — |
| 41 | C22×D28 | C2×C4 | 1 | 3 | yes | — |
| 42 | C22×C4×D7 | — | 2 | 3 | no | — |
| 43 | C22×C7×C8 | — | 2 | 3 | no | — |
| 44 | C4×C7×Q8 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | C4×C7×Q8 | D4 | 1 | 1 | yes | characteristic |
| 46 | C4×C7×D4 | C2×C4 | 1 | 3 | yes | — |
| 47 | C4×C7×D4 | D4 | 1 | 3 | yes | — |
| 48 | C7×#117 | D4 | 1 | 3 | yes | — |
| 49 | C2×C42×C7 | C23 | 1 | 3 | yes | — |
| 50 | #6511 | — | 4 | 4 | no | — |
| 51 | #6493 | — | 2 | 3 | no | — |
| 52 | #6493 | C2×C4 | 1 | 6 | yes | — |
| 53 | C2×(C2×D7)⋊C4 | — | 2 | 3 | no | — |
| 54 | C2×C4⋊Dic7 | C2×C4 | 1 | 3 | yes | — |
| 55 | C2×#1136 | — | 2 | 3 | no | — |
| 56 | C22×C7⋊C8 | — | 2 | 3 | no | — |
| 57 | #6460 | — | 2 | 3 | no | — |
| 58 | #6460 | — | 2 | 3 | no | — |
| 59 | #6458 | — | 2 | 3 | no | — |
| 60 | #6458 | — | 2 | 3 | no | — |
| 61 | #6449 | — | 2 | 6 | no | — |
| 62 | #6445 | — | 2 | 6 | no | — |
| 63 | #6438 | — | 2 | 3 | no | — |
| 64 | #6437 | C2×C4 | 1 | 3 | yes | — |
| 65 | C4×D28 | — | 2 | 3 | no | — |
| 66 | C4×D28 | — | 2 | 3 | no | — |
| 67 | C4×D28 | — | 2 | 3 | no | — |
| 68 | C4×D28 | C2×C4 | 1 | 3 | yes | — |
| 69 | C4×D28 | C2×C4 | 1 | 3 | yes | — |
| 70 | C4×D28 | C23 | 1 | 1 | yes | characteristic |
| 71 | C4×D28 | C23 | 1 | 3 | yes | — |
| 72 | #6432 | C2×C4 | 1 | 3 | yes | — |
| 73 | C7×C4⋊C8 | — | 2 | 3 | no | — |
| 74 | C7×C22⋊C8 | — | 2 | 3 | no | — |
| 75 | C4×C7×C8 | — | 2 | 3 | no | — |
| 76 | C4×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 77 | C4×C7×C8 | C23 | 1 | 3 | yes | — |
| 78 | C4⋊(C7⋊C8) | — | 2 | 3 | no | — |
| 79 | C4⋊(C7⋊C8) | — | 2 | 3 | no | — |
| 80 | C4⋊(C7⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 81 | C4⋊(C7⋊C8) | C23 | 1 | 3 | yes | — |
| 82 | D4×#41 | — | 7 | 1 | no | — |
| 83 | C8×#41 | D7 | 1 | 1 | yes | characteristic, complemented |
| 84 | #2906 | — | 7 | 1 | no | — |
| 85 | #1492 | — | 7 | 3 | no | — |
| 86 | #1486 | — | 7 | 3 | no | — |
| 87 | #1480 | — | 7 | 3 | no | — |
| 88 | C2×D4⋊C8 | — | 7 | 3 | no | — |
| 89 | C23×D7 | — | 2 | 3 | no | — |
| 90 | C7×#41 | D8 | 1 | 4 | yes | — |
| 91 | C7×#41 | SD16 | 1 | 4 | yes | — |
| 92 | C2×C7×Q8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 93 | C2×C7×D4 | C22⋊C4 | 1 | 3 | yes | — |
| 94 | C22×C4×C7 | C22×C4 | 1 | 3 | yes | — |
| 95 | C22×C4×C7 | C2×D4 | 1 | 3 | yes | — |
| 96 | C22×C4×C7 | C2×D4 | 1 | 3 | yes | — |
| 97 | C2×C22⋊D7 | — | 2 | 6 | no | — |
| 98 | C22×Dic7 | — | 2 | 3 | no | — |
| 99 | #1161 | — | 4 | 4 | no | — |
| 100 | Q8×D7 | — | 4 | 4 | no | — |
| 101 | #1159 | — | 4 | 12 | no | — |
| 102 | D4×D7 | — | 4 | 12 | no | — |
| 103 | #1157 | — | 4 | 6 | no | — |
| 104 | #1157 | — | 4 | 6 | no | — |
| 105 | C2×D28 | — | 2 | 6 | no | — |
| 106 | C2×D28 | — | 2 | 3 | no | — |
| 107 | C2×D28 | — | 2 | 3 | no | — |
| 108 | C2×D28 | — | 2 | 3 | no | — |
| 109 | C2×D28 | — | 4 | 3 | no | — |
| 110 | C2×D28 | C22×C4 | 1 | 3 | yes | — |
| 111 | C2×D28 | C22×C4 | 1 | 1 | yes | characteristic |
| 112 | C2×C4×D7 | — | 2 | 3 | no | — |
| 113 | C2×C4×D7 | — | 2 | 3 | no | — |
| 114 | C2×C4×D7 | — | 2 | 1 | no | — |
| 115 | C2×C4×D7 | — | 2 | 3 | no | — |
| 116 | C2×C4×D7 | — | 4 | 6 | no | — |
| 117 | C2×C4×D7 | — | 4 | 6 | no | — |
| 118 | C2×Dic14 | — | 2 | 3 | no | — |
| 119 | C2×C7×C8 | — | 2 | 1 | no | — |
| 120 | C2×C7×C8 | — | 2 | 3 | no | — |
| 121 | C2×C7×C8 | — | 4 | 6 | no | — |
| 122 | C7×C4⋊C4 | C22⋊C4 | 1 | 3 | yes | — |
| 123 | C7×C4⋊C4 | C22⋊C4 | 1 | 3 | yes | — |
| 124 | C7×C22⋊C4 | C22⋊C4 | 1 | 6 | yes | — |
| 125 | C42×C7 | C22×C4 | 1 | 3 | yes | — |
| 126 | C42×C7 | C2×D4 | 1 | 3 | yes | — |
| 127 | C42×C7 | C2×D4 | 1 | 3 | yes | — |
| 128 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 129 | (C2×D7)⋊C4 | — | 2 | 3 | no | — |
| 130 | (C2×D7)⋊C4 | — | 2 | 3 | no | — |
| 131 | (C2×D7)⋊C4 | — | 2 | 6 | no | — |
| 132 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 133 | (C2×D7)⋊C4 | — | 2 | 3 | no | — |
| 134 | C4⋊Dic7 | — | 2 | 3 | no | — |
| 135 | C4⋊Dic7 | — | 2 | 3 | no | — |
| 136 | C4⋊Dic7 | C22×C4 | 1 | 3 | yes | — |
| 137 | C4⋊Dic7 | C22×C4 | 1 | 1 | yes | characteristic |
| 138 | #1136 | — | 4 | 6 | no | — |
| 139 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 140 | C2×C7⋊C8 | — | 2 | 3 | no | — |
| 141 | C2×C7⋊C8 | — | 4 | 6 | no | — |
| 142 | C22×#41 | — | 14 | 1 | no | — |
| 143 | C2×#131 | — | 14 | 1 | no | — |
| 144 | #550 | — | 7 | 1 | no | — |
| 145 | D4×Q8 | — | 7 | 1 | no | — |
| 146 | #548 | — | 14 | 1 | no | — |
| 147 | #547 | — | 7 | 3 | no | — |
| 148 | #546 | — | 14 | 3 | no | — |
| 149 | D42 | — | 7 | 3 | no | — |
| 150 | #532 | — | 7 | 3 | no | — |
| 151 | #525 | — | 14 | 3 | no | — |
| 152 | C4×#41 | C2×D7 | 1 | 1 | yes | characteristic |
| 153 | C2×C4×D4 | — | 7 | 3 | no | — |
| 154 | C8×Q8 | — | 2 | 1 | no | — |
| 155 | C8×D4 | — | 2 | 3 | no | — |
| 156 | #431 | C2×D7 | 1 | 3 | yes | complemented |
| 157 | #424 | — | 14 | 3 | no | — |
| 158 | #423 | — | 7 | 3 | no | — |
| 159 | C2×C4⋊C8 | — | 7 | 3 | no | — |
| 160 | C2×C4×C8 | C2×D7 | 1 | 3 | yes | complemented |
| 161 | D4⋊C8 | — | 7 | 1 | no | — |
| 162 | D4⋊C8 | — | 7 | 3 | no | — |
| 163 | D4⋊C8 | — | 7 | 3 | no | — |
| 164 | D4⋊C8 | — | 7 | 3 | no | — |
| 165 | D4⋊C8 | — | 7 | 6 | no | — |
| 166 | C23×C7 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 167 | C22×D7 | — | 2 | 1 | no | — |
| 168 | C22×D7 | — | 2 | 3 | no | — |
| 169 | C22×D7 | — | 4 | 6 | no | — |
| 170 | C22×D7 | — | 4 | 6 | no | — |
| 171 | C22×D7 | — | 8 | 3 | no | — |
| 172 | C7×Q8 | #102 | 1 | 4 | yes | — |
| 173 | C7×D4 | #102 | 1 | 12 | yes | — |
| 174 | C2×C4×C7 | — | 2 | 3 | no | — |
| 175 | C2×C4×C7 | — | 2 | 3 | no | — |
| 176 | C2×C4×C7 | — | 4 | 3 | no | — |
| 177 | C2×C4×C7 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 178 | C2×C4×C7 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 179 | C2×C4×C7 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 180 | C2×C4×C7 | C2×D8 | 1 | 6 | yes | — |
| 181 | C2×C4×C7 | C2×SD16 | 1 | 6 | yes | — |
| 182 | C2×C4×C7 | C23×C4 | 1 | 1 | yes | characteristic |
| 183 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 184 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 185 | C22⋊D7 | — | 4 | 12 | no | — |
| 186 | C2×Dic7 | — | 2 | 3 | no | — |
| 187 | C2×Dic7 | — | 2 | 1 | no | — |
| 188 | C2×Dic7 | — | 4 | 6 | no | — |
| 189 | D28 | — | 2 | 3 | no | — |
| 190 | D28 | — | 2 | 1 | no | — |
| 191 | D28 | — | 2 | 3 | no | — |
| 192 | D28 | — | 4 | 6 | no | — |
| 193 | D28 | — | 4 | 6 | no | — |
| 194 | D28 | — | 8 | 3 | no | — |
| 195 | D28 | #131 | 1 | 2 | yes | complemented |
| 196 | C4×D7 | — | 4 | 1 | no | — |
| 197 | C4×D7 | — | 4 | 3 | no | — |
| 198 | C4×D7 | — | 4 | 1 | no | — |
| 199 | C4×D7 | — | 4 | 3 | no | — |
| 200 | C4×D7 | — | 4 | 6 | no | — |
| 201 | C4×D7 | — | 4 | 6 | no | — |
| 202 | Dic14 | — | 4 | 6 | no | — |
| 203 | C7×C8 | — | 2 | 2 | no | — |
| 204 | C7×C8 | — | 4 | 3 | no | — |
| 205 | C7⋊C8 | — | 4 | 1 | no | — |
| 206 | C7⋊C8 | — | 4 | 3 | no | — |
| 207 | C2×#41 | — | 14 | 1 | no | — |
| 208 | C2×#41 | — | 14 | 3 | no | — |
| 209 | C2×#41 | — | 14 | 3 | no | — |
| 210 | C2×#41 | — | 28 | 4 | no | — |
| 211 | C2×#41 | — | 28 | 4 | no | — |
| 212 | C2×#41 | D28 | 1 | 1 | yes | characteristic |
| 213 | C22×Q8 | — | 14 | 1 | no | — |
| 214 | C22×D4 | — | 7 | 3 | no | — |
| 215 | C22×D4 | — | 14 | 3 | no | — |
| 216 | C23×C4 | — | 14 | 3 | no | — |
| 217 | #131 | — | 28 | 4 | no | — |
| 218 | C2×M16 | — | 14 | 3 | no | — |
| 219 | C22×C8 | — | 2 | 3 | no | — |
| 220 | C22×C8 | — | 14 | 3 | no | — |
| 221 | C4⋊Q8 | — | 7 | 3 | no | — |
| 222 | #127 | — | 7 | 3 | no | — |
| 223 | #124 | — | 14 | 3 | no | — |
| 224 | #123 | — | 14 | 6 | no | — |
| 225 | C22⋊Q8 | — | 14 | 3 | no | — |
| 226 | C22⋊Q8 | — | 14 | 3 | no | — |
| 227 | #121 | — | 7 | 6 | no | — |
| 228 | #121 | — | 14 | 3 | no | — |
| 229 | #121 | — | 14 | 3 | no | — |
| 230 | #121 | — | 14 | 3 | no | — |
| 231 | #120 | — | 14 | 6 | no | — |
| 232 | C4×Q8 | C4×D7 | 1 | 1 | yes | characteristic |
| 233 | C4×Q8 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 234 | C4×D4 | — | 7 | 3 | no | — |
| 235 | C4×D4 | — | 7 | 3 | no | — |
| 236 | C4×D4 | — | 7 | 1 | no | — |
| 237 | C4×D4 | — | 7 | 3 | no | — |
| 238 | C4×D4 | — | 14 | 3 | no | — |
| 239 | C4×D4 | — | 14 | 3 | no | — |
| 240 | C4×D4 | — | 14 | 3 | no | — |
| 241 | C4×D4 | C4×D7 | 1 | 3 | yes | — |
| 242 | C4×D4 | C22⋊D7 | 1 | 3 | yes | — |
| 243 | #117 | D28 | 1 | 3 | yes | — |
| 244 | C2×C4⋊C4 | — | 7 | 3 | no | — |
| 245 | C2×C22⋊C4 | — | 14 | 3 | no | — |
| 246 | C2×C42 | C22×D7 | 1 | 3 | yes | — |
| 247 | C4⋊C8 | — | 2 | 3 | no | — |
| 248 | C4⋊C8 | — | 7 | 1 | no | — |
| 249 | C4⋊C8 | — | 7 | 3 | no | — |
| 250 | C4⋊C8 | — | 14 | 3 | no | — |
| 251 | C4⋊C8 | — | 14 | 3 | no | — |
| 252 | C22⋊C8 | — | 2 | 3 | no | — |
| 253 | C4×C8 | — | 2 | 3 | no | — |
| 254 | C4×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 255 | C4×C8 | C22×D7 | 1 | 3 | yes | — |
| 256 | C22×C7 | — | 2 | 3 | no | — |
| 257 | C22×C7 | — | 2 | 3 | no | — |
| 258 | C22×C7 | C2×#102 | 1 | 6 | yes | — |
| 259 | C22×C7 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 260 | C2×D7 | — | 2 | 2 | no | — |
| 261 | C2×D7 | — | 4 | 1 | no | — |
| 262 | C2×D7 | — | 4 | 1 | no | — |
| 263 | C2×D7 | — | 4 | 3 | no | — |
| 264 | C2×D7 | — | 4 | 3 | no | — |
| 265 | C2×D7 | — | 4 | 3 | no | — |
| 266 | C2×D7 | — | 8 | 12 | no | — |
| 267 | C4×C7 | — | 2 | 3 | no | — |
| 268 | C4×C7 | — | 2 | 1 | no | — |
| 269 | C4×C7 | — | 2 | 3 | no | — |
| 270 | C4×C7 | C2×#102 | 1 | 6 | yes | — |
| 271 | C4×C7 | C2×#131 | 1 | 1 | yes | characteristic |
| 272 | C4×C7 | #568 | 1 | 1 | yes | characteristic |
| 273 | C4×C7 | C22×D8 | 1 | 1 | yes | characteristic |
| 274 | C4×C7 | C22×SD16 | 1 | 1 | yes | characteristic |
| 275 | Dic7 | — | 4 | 3 | no | — |
| 276 | Dic7 | — | 4 | 1 | no | — |
| 277 | C24 | — | 14 | 3 | no | — |
| 278 | #41 | — | 28 | 4 | no | — |
| 279 | #41 | — | 28 | 12 | no | — |
| 280 | #41 | — | 28 | 6 | no | — |
| 281 | #41 | — | 28 | 6 | no | — |
| 282 | #41 | #1132 | 1 | 4 | yes | — |
| 283 | #41 | D56 | 1 | 4 | yes | — |
| 284 | C2×Q8 | — | 14 | 3 | no | — |
| 285 | C2×Q8 | — | 28 | 4 | no | — |
| 286 | C2×Q8 | (C2×D7)⋊C4 | 1 | 1 | yes | characteristic |
| 287 | C2×D4 | — | 7 | 1 | no | — |
| 288 | C2×D4 | — | 7 | 3 | no | — |
| 289 | C2×D4 | — | 14 | 6 | no | — |
| 290 | C2×D4 | — | 14 | 6 | no | — |
| 291 | C2×D4 | — | 14 | 3 | no | — |
| 292 | C2×D4 | — | 14 | 3 | no | — |
| 293 | C2×D4 | — | 14 | 3 | no | — |
| 294 | C2×D4 | — | 28 | 3 | no | — |
| 295 | C2×D4 | — | 28 | 12 | no | — |
| 296 | C2×D4 | (C2×D7)⋊C4 | 1 | 3 | yes | — |
| 297 | C22×C4 | — | 14 | 3 | no | — |
| 298 | C22×C4 | — | 14 | 3 | no | — |
| 299 | C22×C4 | — | 14 | 3 | no | — |
| 300 | C22×C4 | — | 14 | 1 | no | — |
| 301 | C22×C4 | — | 14 | 3 | no | — |
| 302 | C22×C4 | — | 28 | 6 | no | — |
| 303 | C22×C4 | — | 28 | 6 | no | — |
| 304 | C22×C4 | C2×C4×D7 | 1 | 3 | yes | — |
| 305 | C22×C4 | C2×D28 | 1 | 3 | yes | — |
| 306 | C22×C4 | C2×C22⋊D7 | 1 | 3 | yes | — |
| 307 | M16 | — | 28 | 6 | no | — |
| 308 | C2×C8 | — | 2 | 1 | no | — |
| 309 | C2×C8 | — | 2 | 3 | no | — |
| 310 | C2×C8 | — | 4 | 6 | no | — |
| 311 | C2×C8 | — | 14 | 1 | no | — |
| 312 | C2×C8 | — | 14 | 3 | no | — |
| 313 | C2×C8 | — | 28 | 6 | no | — |
| 314 | C4⋊C4 | — | 7 | 1 | no | — |
| 315 | C4⋊C4 | — | 7 | 3 | no | — |
| 316 | C4⋊C4 | — | 14 | 3 | no | — |
| 317 | C4⋊C4 | — | 14 | 3 | no | — |
| 318 | C4⋊C4 | (C2×D7)⋊C4 | 1 | 3 | yes | — |
| 319 | C4⋊C4 | (C2×D7)⋊C4 | 1 | 3 | yes | — |
| 320 | C22⋊C4 | — | 14 | 3 | no | — |
| 321 | C22⋊C4 | — | 14 | 3 | no | — |
| 322 | C22⋊C4 | — | 14 | 6 | no | — |
| 323 | C22⋊C4 | — | 14 | 1 | no | — |
| 324 | C22⋊C4 | — | 14 | 3 | no | — |
| 325 | C22⋊C4 | (C2×D7)⋊C4 | 1 | 6 | yes | — |
| 326 | C42 | C2×C4×D7 | 1 | 3 | yes | — |
| 327 | C42 | C2×D28 | 1 | 3 | yes | — |
| 328 | C42 | C2×C22⋊D7 | 1 | 3 | yes | — |
| 329 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 330 | C2×C7 | — | 2 | 6 | no | — |
| 331 | C2×C7 | #2880 | 1 | 1 | yes | characteristic |
| 332 | C2×C7 | C22×#102 | 1 | 1 | yes | characteristic |
| 333 | C2×C7 | #2901 | 1 | 1 | yes | characteristic |
| 334 | D7 | — | 4 | 2 | no | — |
| 335 | D7 | — | 8 | 3 | no | — |
| 336 | C23 | — | 14 | 1 | no | — |
| 337 | C23 | — | 14 | 3 | no | — |
| 338 | C23 | — | 28 | 6 | no | — |
| 339 | C23 | — | 28 | 6 | no | — |
| 340 | C23 | — | 56 | 3 | no | — |
| 341 | C23 | C2×(C2×D7)⋊C4 | 1 | 3 | yes | — |
| 342 | Q8 | — | 28 | 6 | no | — |
| 343 | Q8 | #6395 | 1 | 4 | yes | — |
| 344 | D4 | — | 7 | 2 | no | — |
| 345 | D4 | — | 14 | 3 | no | — |
| 346 | D4 | — | 14 | 1 | no | — |
| 347 | D4 | — | 14 | 3 | no | — |
| 348 | D4 | — | 28 | 6 | no | — |
| 349 | D4 | — | 28 | 12 | no | — |
| 350 | D4 | — | 28 | 6 | no | — |
| 351 | D4 | — | 56 | 3 | no | — |
| 352 | D4 | #6395 | 1 | 12 | yes | — |
| 353 | C2×C4 | — | 2 | 3 | no | — |
| 354 | C2×C4 | — | 2 | 3 | no | — |
| 355 | C2×C4 | — | 4 | 3 | no | — |
| 356 | C2×C4 | — | 14 | 1 | no | — |
| 357 | C2×C4 | — | 14 | 3 | no | — |
| 358 | C2×C4 | — | 28 | 6 | no | — |
| 359 | C2×C4 | — | 28 | 6 | no | — |
| 360 | C2×C4 | — | 28 | 6 | no | — |
| 361 | C2×C4 | — | 28 | 1 | no | — |
| 362 | C2×C4 | — | 28 | 3 | no | — |
| 363 | C2×C4 | — | 28 | 1 | no | — |
| 364 | C2×C4 | — | 28 | 3 | no | — |
| 365 | C2×C4 | C2×#1132 | 1 | 6 | yes | — |
| 366 | C2×C4 | C2×D56 | 1 | 6 | yes | — |
| 367 | C2×C4 | C2×(C2×D7)⋊C4 | 1 | 3 | yes | — |
| 368 | C2×C4 | C2×(C2×D7)⋊C4 | 1 | 3 | yes | — |
| 369 | C2×C4 | C2×(C2×D7)⋊C4 | 1 | 3 | yes | — |
| 370 | C2×C4 | C22×C4×D7 | 1 | 1 | yes | characteristic |
| 371 | C2×C4 | C22×D28 | 1 | 1 | yes | characteristic |
| 372 | C2×C4 | C22×C22⋊D7 | 1 | 1 | yes | characteristic |
| 373 | C8 | — | 2 | 2 | no | — |
| 374 | C8 | — | 4 | 3 | no | — |
| 375 | C8 | — | 28 | 1 | no | — |
| 376 | C8 | — | 28 | 3 | no | — |
| 377 | C7 | #17507 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 378 | C22 | — | 2 | 3 | no | — |
| 379 | C22 | — | 2 | 3 | no | — |
| 380 | C22 | — | 14 | 2 | no | — |
| 381 | C22 | — | 28 | 1 | no | — |
| 382 | C22 | — | 28 | 1 | no | — |
| 383 | C22 | — | 28 | 3 | no | — |
| 384 | C22 | — | 28 | 3 | no | — |
| 385 | C22 | — | 28 | 3 | no | — |
| 386 | C22 | — | 56 | 12 | no | — |
| 387 | C22 | C2×#6395 | 1 | 6 | yes | — |
| 388 | C22 | C22×(C2×D7)⋊C4 | 1 | 1 | yes | characteristic |
| 389 | C4 | — | 2 | 3 | no | — |
| 390 | C4 | — | 2 | 1 | no | — |
| 391 | C4 | — | 2 | 3 | no | — |
| 392 | C4 | — | 28 | 1 | no | — |
| 393 | C4 | — | 28 | 3 | no | — |
| 394 | C4 | C2×#6395 | 1 | 6 | yes | — |
| 395 | C4 | C22×#1132 | 1 | 1 | yes | characteristic |
| 396 | C4 | C22×D56 | 1 | 1 | yes | characteristic |
| 397 | C4 | D7×#131 | 1 | 1 | yes | characteristic |
| 398 | C4 | #90441 | 1 | 1 | yes | characteristic |
| 399 | C2 | — | 2 | 6 | no | — |
| 400 | C2 | — | 28 | 2 | no | — |
| 401 | C2 | — | 56 | 3 | no | — |
| 402 | C2 | #11739981 | 1 | 1 | yes | characteristic |
| 403 | C2 | C22×#6395 | 1 | 1 | yes | characteristic |
| 404 | C2 | #11741238 | 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