← #14238635
Subgroups — #14238635
Order 1792.
2234 conjugacy classes of subgroups.
The subgroup lattice has 692 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#90241 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11742834 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C7×#2973 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11736948 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | #11736940 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | #11736796 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11736789 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11736087 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11736085 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #11736062 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C2×#89503 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C22×#1157 | C22 | 1 | 1 | yes | characteristic |
| 13 | C23×D28 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C4×C7×D4 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#6500 | — | 2 | 1 | no | — |
| 16 | #90489 | — | 2 | 1 | no | — |
| 17 | C2×#6493 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#6487 | C22 | 1 | 2 | yes | — |
| 19 | C2×#6487 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#6487 | C22 | 1 | 2 | yes | complemented |
| 21 | C2×#6472 | C22 | 1 | 4 | yes | complemented |
| 22 | C22×#1132 | C22 | 1 | 4 | yes | complemented |
| 23 | #90241 | — | 2 | 4 | no | — |
| 24 | #90241 | C22 | 1 | 8 | yes | — |
| 25 | #90234 | C22 | 1 | 4 | yes | complemented |
| 26 | #90230 | — | 2 | 4 | no | — |
| 27 | D4×Dic14 | C22 | 1 | 4 | yes | complemented |
| 28 | C2×#6457 | — | 2 | 1 | no | — |
| 29 | #90191 | — | 2 | 1 | no | — |
| 30 | C2×#6447 | — | 2 | 1 | no | — |
| 31 | C2×D7×C22⋊C4 | — | 2 | 1 | no | — |
| 32 | #90174 | — | 2 | 1 | no | — |
| 33 | #90174 | — | 2 | 1 | no | — |
| 34 | C2×#6438 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×C4×D28 | C22 | 1 | 1 | yes | characteristic |
| 36 | #90161 | C22 | 1 | 2 | yes | complemented |
| 37 | C7×#435 | C22 | 1 | 8 | yes | complemented |
| 38 | C7×#432 | C22 | 1 | 2 | yes | complemented |
| 39 | C7×#407 | C22 | 1 | 2 | yes | complemented |
| 40 | C2×C7×C22⋊C8 | C22 | 1 | 2 | yes | — |
| 41 | #89906 | C22 | 1 | 8 | yes | complemented |
| 42 | #89905 | C22 | 1 | 4 | yes | complemented |
| 43 | #89888 | C22 | 1 | 8 | yes | complemented |
| 44 | C2×#6395 | C22 | 1 | 4 | yes | complemented |
| 45 | #89618 | C22 | 1 | 4 | yes | complemented |
| 46 | #89617 | C22 | 1 | 8 | yes | complemented |
| 47 | #89613 | C22 | 1 | 4 | yes | complemented |
| 48 | #89511 | C22 | 1 | 4 | yes | complemented |
| 49 | #89511 | C22 | 1 | 4 | yes | complemented |
| 50 | #89510 | C22 | 1 | 4 | yes | complemented |
| 51 | #89508 | C22 | 1 | 4 | yes | complemented |
| 52 | #89505 | C22 | 1 | 8 | yes | complemented |
| 53 | #89503 | C22 | 1 | 4 | yes | — |
| 54 | #89503 | C22 | 1 | 4 | yes | — |
| 55 | #89503 | C22 | 1 | 8 | yes | complemented |
| 56 | #89494 | C22 | 1 | 4 | yes | complemented |
| 57 | #89494 | C22 | 1 | 4 | yes | complemented |
| 58 | #89487 | C22 | 1 | 4 | yes | complemented |
| 59 | #89486 | C22 | 1 | 4 | yes | complemented |
| 60 | #89482 | C22 | 1 | 8 | yes | complemented |
| 61 | #61570 | — | 7 | 1 | no | maximal, Sylow |
| 62 | C24×D7 | — | 2 | 1 | no | — |
| 63 | C22×C7×D4 | D4 | 1 | 1 | yes | characteristic |
| 64 | C23×C4×C7 | C23 | 1 | 1 | yes | characteristic |
| 65 | C23×C4×C7 | C23 | 1 | 1 | yes | characteristic |
| 66 | C22×C22⋊D7 | — | 2 | 1 | no | — |
| 67 | C22×C22⋊D7 | — | 2 | 1 | no | — |
| 68 | C2×#1157 | — | 2 | 2 | no | — |
| 69 | C2×#1157 | — | 4 | 4 | no | — |
| 70 | C2×#1157 | C23 | 1 | 4 | yes | — |
| 71 | C22×D28 | — | 2 | 1 | no | — |
| 72 | C22×D28 | — | 2 | 2 | no | — |
| 73 | C22×D28 | — | 4 | 4 | no | — |
| 74 | C22×D28 | C23 | 1 | 1 | yes | characteristic |
| 75 | C22×D28 | C23 | 1 | 4 | yes | — |
| 76 | C22×D28 | C23 | 1 | 1 | yes | characteristic |
| 77 | C22×C4×D7 | — | 2 | 1 | no | — |
| 78 | C22×C4×D7 | — | 2 | 1 | no | — |
| 79 | C22×Dic14 | C23 | 1 | 1 | yes | characteristic |
| 80 | C22×Dic14 | C23 | 1 | 2 | yes | — |
| 81 | C22×Dic14 | C23 | 1 | 2 | yes | complemented |
| 82 | C2×C7×M16 | C23 | 1 | 4 | yes | complemented |
| 83 | C22×C7×C8 | C23 | 1 | 4 | yes | — |
| 84 | C4×C7×D4 | D4 | 1 | 4 | yes | — |
| 85 | C4×C7×D4 | C23 | 1 | 4 | yes | — |
| 86 | C2×C7×C4⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 87 | C2×C7×C22⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 88 | C2×C7×C22⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 89 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 90 | C2×C22⋊Dic7 | — | 2 | 2 | no | — |
| 91 | C2×C22⋊Dic7 | — | 2 | 2 | no | — |
| 92 | C2×C22⋊Dic7 | — | 2 | 1 | no | — |
| 93 | #6500 | — | 2 | 8 | no | — |
| 94 | D4×Dic7 | — | 2 | 4 | no | — |
| 95 | D4×Dic7 | — | 2 | 4 | no | — |
| 96 | #6493 | — | 2 | 2 | no | — |
| 97 | #6493 | C23 | 1 | 4 | yes | — |
| 98 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 99 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 100 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 101 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 102 | #6489 | — | 2 | 2 | no | — |
| 103 | C2×C4⋊Dic7 | C23 | 1 | 2 | yes | — |
| 104 | C2×C4⋊Dic7 | C23 | 1 | 1 | yes | characteristic |
| 105 | C2×C4⋊Dic7 | C23 | 1 | 2 | yes | complemented |
| 106 | #6487 | — | 2 | 2 | no | — |
| 107 | #6487 | — | 2 | 2 | no | — |
| 108 | #6487 | — | 2 | 2 | no | — |
| 109 | #6487 | — | 2 | 2 | no | — |
| 110 | #6487 | — | 2 | 2 | no | — |
| 111 | #6487 | — | 2 | 2 | no | — |
| 112 | #6487 | C23 | 1 | 4 | yes | — |
| 113 | #6487 | C23 | 1 | 4 | yes | — |
| 114 | #6487 | C23 | 1 | 4 | yes | — |
| 115 | #6487 | C23 | 1 | 4 | yes | complemented |
| 116 | C2×Dic7⋊C4 | — | 2 | 1 | no | — |
| 117 | C2×Dic7⋊C4 | — | 2 | 2 | no | — |
| 118 | C2×Dic7⋊C4 | — | 2 | 2 | no | — |
| 119 | #6472 | — | 4 | 8 | no | — |
| 120 | C2×Dic28 | C23 | 1 | 8 | yes | complemented |
| 121 | C2×#1132 | — | 4 | 8 | no | — |
| 122 | C2×#1132 | C23 | 1 | 8 | yes | — |
| 123 | C2×#1132 | C23 | 1 | 8 | yes | — |
| 124 | #6457 | — | 2 | 8 | no | — |
| 125 | #6453 | — | 2 | 4 | no | — |
| 126 | #6451 | — | 2 | 4 | no | — |
| 127 | #6447 | — | 2 | 8 | no | — |
| 128 | D7×C22⋊C4 | — | 2 | 8 | no | — |
| 129 | #6441 | — | 2 | 4 | no | — |
| 130 | #6441 | — | 2 | 4 | no | — |
| 131 | #6441 | — | 2 | 4 | no | — |
| 132 | #6441 | — | 2 | 4 | no | — |
| 133 | #6438 | — | 2 | 2 | no | — |
| 134 | #6438 | C23 | 1 | 4 | yes | — |
| 135 | C4×D28 | — | 2 | 2 | no | — |
| 136 | C4×D28 | C23 | 1 | 4 | yes | — |
| 137 | #6433 | — | 2 | 2 | no | — |
| 138 | #6432 | C23 | 1 | 2 | yes | complemented |
| 139 | #6432 | C23 | 1 | 2 | yes | complemented |
| 140 | C4×Dic14 | — | 2 | 2 | no | — |
| 141 | C4×Dic14 | C23 | 1 | 4 | yes | complemented |
| 142 | C7×C4⋊C8 | C23 | 1 | 4 | yes | complemented |
| 143 | C7×C22⋊C8 | C23 | 1 | 4 | yes | — |
| 144 | C7×C22⋊C8 | C23 | 1 | 4 | yes | — |
| 145 | C7×C22⋊C8 | C23 | 1 | 4 | yes | complemented |
| 146 | C7×#97 | C23 | 1 | 4 | yes | complemented |
| 147 | #6395 | C23 | 1 | 8 | yes | — |
| 148 | #6395 | C23 | 1 | 8 | yes | — |
| 149 | #6392 | C23 | 1 | 8 | yes | complemented |
| 150 | #6390 | C23 | 1 | 8 | yes | complemented |
| 151 | #6390 | C23 | 1 | 8 | yes | complemented |
| 152 | #3501 | — | 7 | 1 | no | — |
| 153 | C2×#546 | — | 7 | 1 | no | — |
| 154 | #3314 | — | 7 | 8 | no | — |
| 155 | #3266 | — | 7 | 8 | no | — |
| 156 | #3215 | — | 7 | 2 | no | — |
| 157 | #3193 | — | 7 | 2 | no | — |
| 158 | #3189 | — | 7 | 2 | no | — |
| 159 | #3110 | — | 7 | 2 | no | — |
| 160 | #3007 | — | 7 | 2 | no | — |
| 161 | C2×#450 | — | 7 | 2 | no | — |
| 162 | #2973 | D7 | 1 | 1 | yes | characteristic, complemented |
| 163 | C24×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | C24×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 165 | C23×D7 | — | 2 | 1 | no | — |
| 166 | C23×D7 | — | 2 | 1 | no | — |
| 167 | C23×D7 | — | 2 | 4 | no | — |
| 168 | C23×D7 | — | 4 | 4 | no | — |
| 169 | C23×D7 | — | 4 | 4 | no | — |
| 170 | C23×D7 | — | 8 | 2 | no | — |
| 171 | C2×C7×D4 | — | 2 | 4 | no | — |
| 172 | C2×C7×D4 | C2×D4 | 1 | 4 | yes | — |
| 173 | C22×C4×C7 | — | 4 | 2 | no | — |
| 174 | C22×C4×C7 | — | 4 | 2 | no | — |
| 175 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 177 | C22×C4×C7 | C2×D4 | 1 | 2 | yes | — |
| 178 | C22×C4×C7 | C2×D4 | 1 | 2 | yes | — |
| 179 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 180 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 182 | C22×C4×C7 | C24 | 1 | 2 | yes | — |
| 183 | C22×C4×C7 | C24 | 1 | 2 | yes | — |
| 184 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 185 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 186 | C2×C22⋊D7 | — | 4 | 4 | no | — |
| 187 | C2×C22⋊D7 | — | 8 | 2 | no | — |
| 188 | C22×Dic7 | — | 2 | 1 | no | — |
| 189 | C22×Dic7 | — | 2 | 1 | no | — |
| 190 | C22×Dic7 | — | 2 | 2 | no | — |
| 191 | C22×Dic7 | — | 2 | 2 | no | — |
| 192 | C22×Dic7 | — | 2 | 2 | no | — |
| 193 | C22×Dic7 | — | 2 | 2 | no | — |
| 194 | #1157 | — | 2 | 8 | no | — |
| 195 | #1157 | — | 4 | 4 | no | — |
| 196 | #1157 | — | 4 | 8 | no | — |
| 197 | C2×D28 | — | 2 | 1 | no | — |
| 198 | C2×D28 | — | 2 | 4 | no | — |
| 199 | C2×D28 | — | 2 | 8 | no | — |
| 200 | C2×D28 | — | 2 | 1 | no | — |
| 201 | C2×D28 | — | 2 | 4 | no | — |
| 202 | C2×D28 | — | 4 | 4 | no | — |
| 203 | C2×D28 | — | 4 | 2 | no | — |
| 204 | C2×D28 | — | 4 | 8 | no | — |
| 205 | C2×D28 | — | 4 | 4 | no | — |
| 206 | C2×D28 | C24 | 1 | 2 | yes | — |
| 207 | C2×D28 | C24 | 1 | 2 | yes | — |
| 208 | C2×C4×D7 | — | 2 | 4 | no | — |
| 209 | C2×C4×D7 | — | 2 | 4 | no | — |
| 210 | C2×C4×D7 | — | 4 | 4 | no | — |
| 211 | C2×C4×D7 | — | 8 | 2 | no | — |
| 212 | C2×Dic14 | — | 2 | 1 | no | — |
| 213 | C2×Dic14 | — | 2 | 2 | no | — |
| 214 | C2×Dic14 | — | 2 | 2 | no | — |
| 215 | C2×Dic14 | — | 2 | 2 | no | — |
| 216 | C2×Dic14 | — | 4 | 2 | no | — |
| 217 | C2×Dic14 | — | 4 | 4 | no | — |
| 218 | C2×Dic14 | — | 4 | 4 | no | — |
| 219 | C2×Dic14 | C24 | 1 | 4 | yes | — |
| 220 | C2×Dic14 | C24 | 1 | 2 | yes | — |
| 221 | C7×M16 | — | 4 | 4 | no | — |
| 222 | C2×C7×C8 | — | 4 | 4 | no | — |
| 223 | C2×C7×C8 | C24 | 1 | 8 | yes | — |
| 224 | C7×C4⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 225 | C7×C22⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 226 | C7×C22⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 227 | C42×C7 | C2×D4 | 1 | 2 | yes | — |
| 228 | C42×C7 | C24 | 1 | 2 | yes | — |
| 229 | C22⋊Dic7 | — | 2 | 4 | no | — |
| 230 | C22⋊Dic7 | — | 2 | 4 | no | — |
| 231 | C22⋊Dic7 | — | 2 | 4 | no | — |
| 232 | C22⋊Dic7 | — | 2 | 4 | no | — |
| 233 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 234 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 235 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 236 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 237 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 238 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 239 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 240 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 241 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 242 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 243 | C4⋊Dic7 | C24 | 1 | 4 | yes | — |
| 244 | C4⋊Dic7 | C24 | 1 | 2 | yes | — |
| 245 | Dic7⋊C4 | — | 2 | 4 | no | — |
| 246 | Dic7⋊C4 | — | 2 | 4 | no | — |
| 247 | Dic7⋊C4 | — | 2 | 4 | no | — |
| 248 | Dic7⋊C4 | — | 2 | 4 | no | — |
| 249 | Dic7⋊C4 | — | 2 | 4 | no | — |
| 250 | C4×Dic7 | — | 2 | 4 | no | — |
| 251 | Dic28 | — | 4 | 8 | no | — |
| 252 | #1132 | — | 2 | 16 | no | — |
| 253 | #1132 | — | 4 | 8 | no | — |
| 254 | C22×#41 | — | 7 | 1 | no | — |
| 255 | C23×D4 | — | 7 | 1 | no | — |
| 256 | C2×#137 | — | 7 | 4 | no | — |
| 257 | C22×SD16 | — | 7 | 4 | no | — |
| 258 | #554 | — | 7 | 4 | no | — |
| 259 | #554 | — | 14 | 4 | no | — |
| 260 | D4×Q8 | — | 7 | 4 | no | — |
| 261 | #546 | — | 7 | 8 | no | — |
| 262 | #546 | — | 14 | 4 | no | — |
| 263 | #544 | — | 14 | 1 | no | — |
| 264 | #543 | — | 14 | 1 | no | — |
| 265 | #543 | — | 14 | 1 | no | — |
| 266 | #533 | — | 7 | 2 | no | — |
| 267 | C2×#124 | — | 7 | 1 | no | — |
| 268 | C2×#123 | — | 14 | 1 | no | — |
| 269 | C2×C22⋊Q8 | — | 7 | 1 | no | — |
| 270 | C2×C22⋊Q8 | — | 7 | 2 | no | — |
| 271 | C2×C22⋊Q8 | — | 7 | 2 | no | — |
| 272 | C2×#121 | — | 7 | 1 | no | — |
| 273 | C2×#121 | — | 14 | 1 | no | — |
| 274 | C2×#120 | — | 14 | 1 | no | — |
| 275 | #518 | — | 14 | 1 | no | — |
| 276 | C2×C4×D4 | — | 7 | 1 | no | — |
| 277 | C2×C4×D4 | C2×D7 | 1 | 1 | yes | characteristic |
| 278 | C22×C22⋊C4 | — | 14 | 1 | no | — |
| 279 | #497 | — | 7 | 4 | no | — |
| 280 | #489 | — | 7 | 4 | no | — |
| 281 | #484 | — | 7 | 4 | no | — |
| 282 | #484 | — | 7 | 4 | no | — |
| 283 | #480 | — | 7 | 4 | no | — |
| 284 | #474 | — | 7 | 4 | no | — |
| 285 | #468 | — | 7 | 8 | no | — |
| 286 | #467 | — | 7 | 8 | no | — |
| 287 | #464 | — | 7 | 8 | no | — |
| 288 | #461 | — | 7 | 4 | no | — |
| 289 | #452 | — | 7 | 8 | no | — |
| 290 | #451 | — | 7 | 4 | no | — |
| 291 | #451 | — | 7 | 4 | no | — |
| 292 | #450 | — | 7 | 4 | no | — |
| 293 | #450 | — | 7 | 4 | no | — |
| 294 | #450 | — | 7 | 8 | no | — |
| 295 | #448 | — | 7 | 4 | no | — |
| 296 | #440 | — | 7 | 8 | no | — |
| 297 | #435 | C2×D7 | 1 | 8 | yes | complemented |
| 298 | #432 | C2×D7 | 1 | 2 | yes | complemented |
| 299 | #417 | — | 7 | 4 | no | — |
| 300 | C2×#102 | — | 7 | 4 | no | — |
| 301 | #407 | C2×D7 | 1 | 2 | yes | complemented |
| 302 | C2×C22⋊C8 | C2×D7 | 1 | 2 | yes | — |
| 303 | C23×C7 | — | 2 | 2 | no | — |
| 304 | C23×C7 | — | 4 | 1 | no | — |
| 305 | C23×C7 | — | 4 | 1 | no | — |
| 306 | C23×C7 | — | 4 | 1 | no | — |
| 307 | C23×C7 | — | 4 | 1 | no | — |
| 308 | C23×C7 | #137 | 1 | 4 | yes | complemented |
| 309 | C23×C7 | C22×D4 | 1 | 2 | yes | — |
| 310 | C23×C7 | C22×D4 | 1 | 2 | yes | — |
| 311 | C23×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 312 | C22×D7 | — | 2 | 4 | no | — |
| 313 | C22×D7 | — | 2 | 2 | no | — |
| 314 | C22×D7 | — | 2 | 2 | no | — |
| 315 | C22×D7 | — | 4 | 8 | no | — |
| 316 | C22×D7 | — | 4 | 2 | no | — |
| 317 | C22×D7 | — | 4 | 2 | no | — |
| 318 | C22×D7 | — | 4 | 2 | no | — |
| 319 | C22×D7 | — | 4 | 2 | no | — |
| 320 | C22×D7 | — | 4 | 8 | no | — |
| 321 | C22×D7 | — | 4 | 2 | no | — |
| 322 | C22×D7 | — | 8 | 4 | no | — |
| 323 | C22×D7 | — | 8 | 16 | no | — |
| 324 | C7×D4 | — | 2 | 8 | no | — |
| 325 | C2×C4×C7 | — | 2 | 2 | no | — |
| 326 | C2×C4×C7 | — | 2 | 4 | no | — |
| 327 | C2×C4×C7 | — | 2 | 4 | no | — |
| 328 | C2×C4×C7 | — | 2 | 2 | no | — |
| 329 | C2×C4×C7 | — | 4 | 1 | no | — |
| 330 | C2×C4×C7 | — | 4 | 1 | no | — |
| 331 | C2×C4×C7 | — | 4 | 2 | no | — |
| 332 | C2×C4×C7 | — | 4 | 1 | no | — |
| 333 | C2×C4×C7 | — | 4 | 2 | no | — |
| 334 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 335 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 336 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 337 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 338 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 339 | C2×C4×C7 | C25 | 1 | 1 | yes | characteristic |
| 340 | C22⋊D7 | — | 4 | 8 | no | — |
| 341 | C22⋊D7 | — | 8 | 4 | no | — |
| 342 | C2×Dic7 | — | 2 | 4 | no | — |
| 343 | C2×Dic7 | — | 2 | 4 | no | — |
| 344 | C2×Dic7 | — | 2 | 2 | no | — |
| 345 | C2×Dic7 | — | 2 | 2 | no | — |
| 346 | C2×Dic7 | — | 4 | 2 | no | — |
| 347 | C2×Dic7 | — | 4 | 2 | no | — |
| 348 | C2×Dic7 | — | 8 | 2 | no | — |
| 349 | C2×Dic7 | — | 8 | 2 | no | — |
| 350 | C2×Dic7 | — | 8 | 2 | no | — |
| 351 | C2×Dic7 | — | 8 | 2 | no | — |
| 352 | D28 | — | 2 | 4 | no | — |
| 353 | D28 | — | 2 | 2 | no | — |
| 354 | D28 | — | 2 | 4 | no | — |
| 355 | D28 | — | 4 | 8 | no | — |
| 356 | D28 | — | 4 | 2 | no | — |
| 357 | D28 | H(5,𝔽2) | 1 | 4 | yes | — |
| 358 | C4×D7 | — | 4 | 8 | no | — |
| 359 | C4×D7 | — | 8 | 4 | no | — |
| 360 | Dic14 | — | 2 | 8 | no | — |
| 361 | Dic14 | — | 2 | 4 | no | — |
| 362 | Dic14 | — | 4 | 2 | no | — |
| 363 | Dic14 | — | 8 | 2 | no | — |
| 364 | Dic14 | — | 8 | 2 | no | — |
| 365 | Dic14 | — | 8 | 2 | no | — |
| 366 | C7×C8 | — | 2 | 8 | no | — |
| 367 | C25 | — | 14 | 1 | no | — |
| 368 | C2×#41 | — | 7 | 4 | no | — |
| 369 | C2×#41 | — | 14 | 2 | no | — |
| 370 | C2×#41 | — | 28 | 4 | no | — |
| 371 | C22×Q8 | — | 7 | 1 | no | — |
| 372 | C22×Q8 | — | 7 | 2 | no | — |
| 373 | C22×Q8 | — | 7 | 2 | no | — |
| 374 | C22×D4 | — | 7 | 1 | no | — |
| 375 | C22×D4 | — | 7 | 4 | no | — |
| 376 | C22×D4 | — | 7 | 1 | no | — |
| 377 | C22×D4 | — | 14 | 1 | no | — |
| 378 | C22×D4 | — | 14 | 1 | no | — |
| 379 | C22×D4 | — | 14 | 1 | no | — |
| 380 | C22×D4 | — | 14 | 2 | no | — |
| 381 | C22×D4 | — | 28 | 4 | no | — |
| 382 | C22×D4 | D28 | 1 | 1 | yes | characteristic |
| 383 | C23×C4 | — | 14 | 1 | no | — |
| 384 | C23×C4 | — | 14 | 1 | no | — |
| 385 | C23×C4 | C22×D7 | 1 | 1 | yes | characteristic |
| 386 | C23×C4 | C22×D7 | 1 | 1 | yes | characteristic |
| 387 | #137 | — | 28 | 8 | no | — |
| 388 | C2×Q16 | — | 7 | 8 | no | — |
| 389 | C2×SD16 | — | 7 | 8 | no | — |
| 390 | C2×SD16 | — | 7 | 8 | no | — |
| 391 | C2×SD16 | — | 28 | 8 | no | — |
| 392 | C2×M16 | C22×D7 | 1 | 4 | yes | complemented |
| 393 | C22×C8 | C22×D7 | 1 | 4 | yes | — |
| 394 | C4⋊Q8 | — | 7 | 2 | no | — |
| 395 | C4⋊Q8 | — | 7 | 2 | no | — |
| 396 | C4⋊Q8 | — | 14 | 4 | no | — |
| 397 | #125 | — | 14 | 4 | no | — |
| 398 | #125 | — | 14 | 2 | no | — |
| 399 | #124 | — | 7 | 4 | no | — |
| 400 | #124 | — | 14 | 2 | no | — |
| 401 | #123 | — | 14 | 8 | no | — |
| 402 | C22⋊Q8 | — | 7 | 4 | no | — |
| 403 | C22⋊Q8 | — | 7 | 4 | no | — |
| 404 | C22⋊Q8 | — | 7 | 4 | no | — |
| 405 | C22⋊Q8 | — | 7 | 4 | no | — |
| 406 | C22⋊Q8 | — | 14 | 2 | no | — |
| 407 | C22⋊Q8 | — | 14 | 2 | no | — |
| 408 | C22⋊Q8 | — | 14 | 2 | no | — |
| 409 | C22⋊Q8 | — | 14 | 2 | no | — |
| 410 | C22⋊Q8 | — | 14 | 2 | no | — |
| 411 | C22⋊Q8 | — | 14 | 2 | no | — |
| 412 | C22⋊Q8 | — | 14 | 4 | no | — |
| 413 | C22⋊Q8 | — | 14 | 4 | no | — |
| 414 | C22⋊Q8 | — | 14 | 4 | no | — |
| 415 | C22⋊Q8 | — | 14 | 4 | no | — |
| 416 | #121 | — | 7 | 4 | no | — |
| 417 | #121 | — | 14 | 2 | no | — |
| 418 | #121 | — | 14 | 8 | no | — |
| 419 | #120 | — | 14 | 8 | no | — |
| 420 | C4×Q8 | — | 7 | 4 | no | — |
| 421 | C4×Q8 | — | 14 | 2 | no | — |
| 422 | C4×D4 | — | 7 | 4 | no | — |
| 423 | C4×D4 | — | 14 | 4 | no | — |
| 424 | C4×D4 | — | 14 | 4 | no | — |
| 425 | C4×D4 | — | 14 | 2 | no | — |
| 426 | C4×D4 | D28 | 1 | 4 | yes | — |
| 427 | C4×D4 | C22×D7 | 1 | 4 | yes | — |
| 428 | #117 | — | 14 | 2 | no | — |
| 429 | C2×C4⋊C4 | — | 7 | 1 | no | — |
| 430 | C2×C4⋊C4 | — | 7 | 2 | no | — |
| 431 | C2×C4⋊C4 | — | 7 | 2 | no | — |
| 432 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 433 | C2×C4⋊C4 | — | 14 | 2 | no | — |
| 434 | C2×C4⋊C4 | — | 14 | 2 | no | — |
| 435 | C2×C4⋊C4 | D28 | 1 | 1 | yes | characteristic |
| 436 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 437 | C2×C22⋊C4 | — | 14 | 2 | no | — |
| 438 | C2×C22⋊C4 | — | 14 | 2 | no | — |
| 439 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 440 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 441 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 442 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 443 | C2×C22⋊C4 | — | 14 | 8 | no | — |
| 444 | C2×C22⋊C4 | D28 | 1 | 1 | yes | characteristic |
| 445 | C2×C22⋊C4 | D28 | 1 | 1 | yes | characteristic |
| 446 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 447 | #107 | — | 7 | 8 | no | — |
| 448 | C4⋊C8 | C22×D7 | 1 | 4 | yes | complemented |
| 449 | #103 | — | 7 | 8 | no | — |
| 450 | #103 | — | 7 | 8 | no | — |
| 451 | #102 | — | 7 | 8 | no | — |
| 452 | #102 | — | 7 | 8 | no | — |
| 453 | C22⋊C8 | C22×D7 | 1 | 4 | yes | — |
| 454 | C22⋊C8 | C22×D7 | 1 | 4 | yes | — |
| 455 | C22⋊C8 | C22×D7 | 1 | 4 | yes | complemented |
| 456 | #97 | C22×D7 | 1 | 4 | yes | complemented |
| 457 | C22×C7 | — | 2 | 1 | no | — |
| 458 | C22×C7 | — | 2 | 2 | no | — |
| 459 | C22×C7 | — | 2 | 1 | no | — |
| 460 | C22×C7 | — | 2 | 2 | no | — |
| 461 | C22×C7 | — | 2 | 2 | no | — |
| 462 | C22×C7 | — | 2 | 2 | no | — |
| 463 | C22×C7 | — | 2 | 2 | no | — |
| 464 | C22×C7 | — | 4 | 4 | no | — |
| 465 | C22×C7 | — | 8 | 2 | no | — |
| 466 | C22×C7 | C2×#137 | 1 | 2 | yes | — |
| 467 | C22×C7 | C2×#137 | 1 | 4 | yes | — |
| 468 | C22×C7 | C23×D4 | 1 | 1 | yes | characteristic |
| 469 | C2×D7 | — | 2 | 4 | no | — |
| 470 | C2×D7 | — | 4 | 8 | no | — |
| 471 | C2×D7 | — | 4 | 2 | no | — |
| 472 | C2×D7 | — | 4 | 2 | no | — |
| 473 | C2×D7 | — | 4 | 2 | no | — |
| 474 | C2×D7 | — | 4 | 2 | no | — |
| 475 | C2×D7 | — | 4 | 2 | no | — |
| 476 | C2×D7 | — | 8 | 16 | no | — |
| 477 | C2×D7 | — | 8 | 4 | no | — |
| 478 | C4×C7 | — | 2 | 2 | no | — |
| 479 | C4×C7 | — | 2 | 1 | no | — |
| 480 | C4×C7 | — | 2 | 2 | no | — |
| 481 | C4×C7 | — | 2 | 2 | no | — |
| 482 | C4×C7 | — | 2 | 2 | no | — |
| 483 | C4×C7 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 484 | Dic7 | — | 4 | 4 | no | — |
| 485 | Dic7 | — | 4 | 2 | no | — |
| 486 | Dic7 | — | 4 | 2 | no | — |
| 487 | Dic7 | — | 4 | 4 | no | — |
| 488 | C24 | — | 14 | 1 | no | — |
| 489 | C24 | — | 14 | 1 | no | — |
| 490 | C24 | — | 14 | 4 | no | — |
| 491 | C24 | — | 28 | 4 | no | — |
| 492 | C24 | — | 28 | 4 | no | — |
| 493 | C24 | — | 56 | 2 | no | — |
| 494 | C24 | C2×D28 | 1 | 1 | yes | characteristic |
| 495 | C24 | C2×D28 | 1 | 1 | yes | characteristic |
| 496 | #41 | — | 14 | 8 | no | — |
| 497 | #41 | — | 28 | 4 | no | — |
| 498 | #41 | — | 28 | 8 | no | — |
| 499 | C2×Q8 | — | 7 | 2 | no | — |
| 500 | C2×Q8 | — | 7 | 4 | no | — |
| 501 | C2×Q8 | — | 14 | 1 | no | — |
| 502 | C2×Q8 | — | 14 | 2 | no | — |
| 503 | C2×Q8 | — | 14 | 2 | no | — |
| 504 | C2×Q8 | — | 14 | 2 | no | — |
| 505 | C2×Q8 | — | 28 | 2 | no | — |
| 506 | C2×Q8 | — | 28 | 4 | no | — |
| 507 | C2×Q8 | — | 28 | 4 | no | — |
| 508 | C2×D4 | — | 2 | 4 | no | — |
| 509 | C2×D4 | — | 7 | 2 | no | — |
| 510 | C2×D4 | — | 7 | 2 | no | — |
| 511 | C2×D4 | — | 14 | 4 | no | — |
| 512 | C2×D4 | — | 14 | 8 | no | — |
| 513 | C2×D4 | — | 14 | 4 | no | — |
| 514 | C2×D4 | — | 14 | 4 | no | — |
| 515 | C2×D4 | — | 14 | 1 | no | — |
| 516 | C2×D4 | — | 14 | 4 | no | — |
| 517 | C2×D4 | — | 14 | 1 | no | — |
| 518 | C2×D4 | — | 28 | 4 | no | — |
| 519 | C2×D4 | — | 28 | 2 | no | — |
| 520 | C2×D4 | — | 28 | 8 | no | — |
| 521 | C2×D4 | — | 28 | 4 | no | — |
| 522 | C2×D4 | — | 28 | 4 | no | — |
| 523 | C2×D4 | — | 56 | 2 | no | — |
| 524 | C2×D4 | C2×D28 | 1 | 4 | yes | — |
| 525 | C22×C4 | — | 4 | 2 | no | — |
| 526 | C22×C4 | — | 4 | 2 | no | — |
| 527 | C22×C4 | — | 14 | 1 | no | — |
| 528 | C22×C4 | — | 14 | 1 | no | — |
| 529 | C22×C4 | — | 14 | 2 | no | — |
| 530 | C22×C4 | — | 14 | 2 | no | — |
| 531 | C22×C4 | — | 14 | 2 | no | — |
| 532 | C22×C4 | — | 14 | 2 | no | — |
| 533 | C22×C4 | — | 14 | 4 | no | — |
| 534 | C22×C4 | — | 14 | 4 | no | — |
| 535 | C22×C4 | — | 28 | 4 | no | — |
| 536 | C22×C4 | — | 56 | 2 | no | — |
| 537 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 538 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 539 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 540 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 541 | C22×C4 | C2×D28 | 1 | 2 | yes | — |
| 542 | C22×C4 | C2×D28 | 1 | 2 | yes | — |
| 543 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 544 | C22×C4 | C23×D7 | 1 | 2 | yes | — |
| 545 | C22×C4 | C23×D7 | 1 | 2 | yes | — |
| 546 | Q16 | — | 28 | 8 | no | — |
| 547 | SD16 | — | 14 | 16 | no | — |
| 548 | SD16 | — | 28 | 8 | no | — |
| 549 | M16 | — | 4 | 4 | no | — |
| 550 | C2×C8 | — | 4 | 4 | no | — |
| 551 | C2×C8 | C23×D7 | 1 | 8 | yes | — |
| 552 | C4⋊C4 | — | 7 | 4 | no | — |
| 553 | C4⋊C4 | — | 7 | 2 | no | — |
| 554 | C4⋊C4 | — | 14 | 4 | no | — |
| 555 | C4⋊C4 | — | 14 | 4 | no | — |
| 556 | C4⋊C4 | — | 14 | 4 | no | — |
| 557 | C4⋊C4 | — | 14 | 4 | no | — |
| 558 | C4⋊C4 | — | 14 | 4 | no | — |
| 559 | C4⋊C4 | — | 14 | 1 | no | — |
| 560 | C4⋊C4 | — | 14 | 2 | no | — |
| 561 | C4⋊C4 | — | 14 | 2 | no | — |
| 562 | C4⋊C4 | — | 14 | 2 | no | — |
| 563 | C4⋊C4 | — | 14 | 2 | no | — |
| 564 | C4⋊C4 | — | 14 | 2 | no | — |
| 565 | C4⋊C4 | C2×D28 | 1 | 4 | yes | — |
| 566 | C22⋊C4 | — | 14 | 4 | no | — |
| 567 | C22⋊C4 | — | 14 | 4 | no | — |
| 568 | C22⋊C4 | — | 14 | 4 | no | — |
| 569 | C22⋊C4 | — | 14 | 4 | no | — |
| 570 | C22⋊C4 | — | 14 | 4 | no | — |
| 571 | C22⋊C4 | — | 14 | 4 | no | — |
| 572 | C22⋊C4 | — | 14 | 4 | no | — |
| 573 | C22⋊C4 | — | 14 | 4 | no | — |
| 574 | C22⋊C4 | C2×D28 | 1 | 4 | yes | — |
| 575 | C22⋊C4 | C2×D28 | 1 | 4 | yes | — |
| 576 | C42 | — | 14 | 4 | no | — |
| 577 | C42 | C2×D28 | 1 | 2 | yes | — |
| 578 | C42 | C23×D7 | 1 | 2 | yes | — |
| 579 | C2×C7 | — | 2 | 2 | no | — |
| 580 | C2×C7 | — | 2 | 4 | no | — |
| 581 | C2×C7 | — | 4 | 2 | no | — |
| 582 | C2×C7 | #3484 | 1 | 1 | yes | characteristic |
| 583 | C2×C7 | C22×#137 | 1 | 1 | yes | characteristic |
| 584 | C2×C7 | #3585 | 1 | 1 | yes | characteristic |
| 585 | D7 | — | 4 | 4 | no | — |
| 586 | D7 | — | 8 | 2 | no | — |
| 587 | C23 | — | 2 | 2 | no | — |
| 588 | C23 | — | 4 | 1 | no | — |
| 589 | C23 | — | 4 | 1 | no | — |
| 590 | C23 | — | 4 | 1 | no | — |
| 591 | C23 | — | 4 | 1 | no | — |
| 592 | C23 | — | 14 | 4 | no | — |
| 593 | C23 | — | 14 | 2 | no | — |
| 594 | C23 | — | 14 | 2 | no | — |
| 595 | C23 | — | 28 | 8 | no | — |
| 596 | C23 | — | 28 | 2 | no | — |
| 597 | C23 | — | 28 | 2 | no | — |
| 598 | C23 | — | 28 | 2 | no | — |
| 599 | C23 | — | 28 | 2 | no | — |
| 600 | C23 | — | 28 | 8 | no | — |
| 601 | C23 | — | 28 | 2 | no | — |
| 602 | C23 | — | 56 | 4 | no | — |
| 603 | C23 | — | 56 | 16 | no | — |
| 604 | C23 | #6472 | 1 | 4 | yes | complemented |
| 605 | C23 | C22×D28 | 1 | 2 | yes | — |
| 606 | C23 | C22×D28 | 1 | 2 | yes | — |
| 607 | C23 | C22×D28 | 1 | 1 | yes | characteristic |
| 608 | Q8 | — | 14 | 8 | no | — |
| 609 | Q8 | — | 14 | 4 | no | — |
| 610 | Q8 | — | 28 | 2 | no | — |
| 611 | Q8 | — | 56 | 2 | no | — |
| 612 | Q8 | — | 56 | 2 | no | — |
| 613 | Q8 | — | 56 | 2 | no | — |
| 614 | D4 | — | 2 | 8 | no | — |
| 615 | D4 | — | 7 | 4 | no | — |
| 616 | D4 | — | 14 | 4 | no | — |
| 617 | D4 | — | 14 | 2 | no | — |
| 618 | D4 | — | 14 | 4 | no | — |
| 619 | D4 | — | 28 | 8 | no | — |
| 620 | D4 | — | 28 | 2 | no | — |
| 621 | D4 | — | 28 | 8 | no | — |
| 622 | D4 | — | 56 | 4 | no | — |
| 623 | C2×C4 | — | 2 | 2 | no | — |
| 624 | C2×C4 | — | 2 | 4 | no | — |
| 625 | C2×C4 | — | 2 | 4 | no | — |
| 626 | C2×C4 | — | 2 | 2 | no | — |
| 627 | C2×C4 | — | 4 | 1 | no | — |
| 628 | C2×C4 | — | 4 | 2 | no | — |
| 629 | C2×C4 | — | 4 | 1 | no | — |
| 630 | C2×C4 | — | 4 | 2 | no | — |
| 631 | C2×C4 | — | 4 | 1 | no | — |
| 632 | C2×C4 | — | 14 | 4 | no | — |
| 633 | C2×C4 | — | 14 | 4 | no | — |
| 634 | C2×C4 | — | 14 | 2 | no | — |
| 635 | C2×C4 | — | 14 | 2 | no | — |
| 636 | C2×C4 | — | 28 | 8 | no | — |
| 637 | C2×C4 | — | 28 | 2 | no | — |
| 638 | C2×C4 | — | 28 | 2 | no | — |
| 639 | C2×C4 | — | 56 | 4 | no | — |
| 640 | C2×C4 | — | 56 | 2 | no | — |
| 641 | C2×C4 | — | 56 | 2 | no | — |
| 642 | C2×C4 | — | 56 | 2 | no | — |
| 643 | C2×C4 | — | 56 | 2 | no | — |
| 644 | C2×C4 | C22×D28 | 1 | 2 | yes | — |
| 645 | C2×C4 | C22×D28 | 1 | 1 | yes | characteristic |
| 646 | C2×C4 | C22×D28 | 1 | 2 | yes | — |
| 647 | C2×C4 | C22×D28 | 1 | 2 | yes | — |
| 648 | C2×C4 | C22×D28 | 1 | 2 | yes | — |
| 649 | C2×C4 | C24×D7 | 1 | 1 | yes | characteristic |
| 650 | C8 | — | 2 | 8 | no | — |
| 651 | C7 | #61570 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 652 | C22 | — | 2 | 1 | no | — |
| 653 | C22 | — | 2 | 2 | no | — |
| 654 | C22 | — | 2 | 1 | no | — |
| 655 | C22 | — | 2 | 2 | no | — |
| 656 | C22 | — | 2 | 2 | no | — |
| 657 | C22 | — | 2 | 2 | no | — |
| 658 | C22 | — | 2 | 2 | no | — |
| 659 | C22 | — | 4 | 4 | no | — |
| 660 | C22 | — | 8 | 2 | no | — |
| 661 | C22 | — | 14 | 4 | no | — |
| 662 | C22 | — | 28 | 8 | no | — |
| 663 | C22 | — | 28 | 2 | no | — |
| 664 | C22 | — | 28 | 2 | no | — |
| 665 | C22 | — | 28 | 2 | no | — |
| 666 | C22 | — | 28 | 2 | no | — |
| 667 | C22 | — | 28 | 2 | no | — |
| 668 | C22 | — | 56 | 16 | no | — |
| 669 | C22 | — | 56 | 4 | no | — |
| 670 | C22 | C2×#6472 | 1 | 2 | yes | — |
| 671 | C22 | C2×#6472 | 1 | 4 | yes | — |
| 672 | C22 | C23×D28 | 1 | 1 | yes | characteristic |
| 673 | C4 | — | 2 | 1 | no | — |
| 674 | C4 | — | 2 | 2 | no | — |
| 675 | C4 | — | 2 | 2 | no | — |
| 676 | C4 | — | 2 | 2 | no | — |
| 677 | C4 | — | 2 | 2 | no | — |
| 678 | C4 | — | 28 | 2 | no | — |
| 679 | C4 | — | 28 | 4 | no | — |
| 680 | C4 | — | 28 | 2 | no | — |
| 681 | C4 | — | 28 | 4 | no | — |
| 682 | C4 | D7×H(5,𝔽2) | 1 | 2 | yes | — |
| 683 | C2 | — | 2 | 2 | no | — |
| 684 | C2 | — | 2 | 4 | no | — |
| 685 | C2 | — | 4 | 2 | no | — |
| 686 | C2 | — | 28 | 4 | no | — |
| 687 | C2 | — | 56 | 2 | no | — |
| 688 | C2 | #11742935 | 1 | 1 | yes | characteristic |
| 689 | C2 | C22×#6472 | 1 | 1 | yes | characteristic |
| 690 | C2 | #11744235 | 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