← #14224374
Subgroups — #14224374
Order 1792.
2394 conjugacy classes of subgroups.
The subgroup lattice has 700 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#90318 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C7×#3189 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11740181 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11738927 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #11738912 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #11738210 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11738203 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #11737633 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #11737627 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #11736056 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C2×D7×C22⋊C8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C22×#1161 | C22 | 1 | 2 | yes | complemented |
| 13 | C23×C4×D7 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C7×C22⋊Q8 | C22 | 1 | 2 | yes | — |
| 15 | C2×#6509 | C22 | 1 | 2 | yes | complemented |
| 16 | C2×#6493 | C22 | 1 | 2 | yes | — |
| 17 | C2×#6482 | C22 | 1 | 4 | yes | complemented |
| 18 | C22×C8×D7 | C22 | 1 | 2 | yes | complemented |
| 19 | #90318 | — | 2 | 2 | no | — |
| 20 | #90318 | — | 2 | 2 | no | — |
| 21 | #90318 | — | 2 | 2 | no | — |
| 22 | #90318 | — | 2 | 2 | no | — |
| 23 | #90318 | C22 | 1 | 4 | yes | — |
| 24 | #90318 | C22 | 1 | 4 | yes | — |
| 25 | #90318 | C22 | 1 | 4 | yes | complemented |
| 26 | #90318 | C22 | 1 | 4 | yes | complemented |
| 27 | C2×#6458 | C22 | 1 | 2 | yes | complemented |
| 28 | C2×#6457 | — | 2 | 2 | no | — |
| 29 | C2×#6456 | — | 2 | 2 | no | — |
| 30 | C2×#6455 | C22 | 1 | 2 | yes | complemented |
| 31 | C2×#6445 | — | 2 | 2 | no | — |
| 32 | C2×(C22⋊D7)⋊C4 | — | 2 | 2 | no | — |
| 33 | C7×#484 | C22 | 1 | 4 | yes | complemented |
| 34 | C7×#467 | C22 | 1 | 4 | yes | complemented |
| 35 | C7×#451 | C22 | 1 | 4 | yes | complemented |
| 36 | C2×C7×C22⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 37 | #89999 | C22 | 1 | 4 | yes | complemented |
| 38 | C2×C22⋊(C7⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 39 | #89960 | C22 | 1 | 4 | yes | complemented |
| 40 | #89959 | C22 | 1 | 8 | yes | complemented |
| 41 | #89887 | C22 | 1 | 4 | yes | complemented |
| 42 | C2×(C2×D7)⋊C8 | C22 | 1 | 2 | yes | complemented |
| 43 | #89820 | C22 | 1 | 8 | yes | complemented |
| 44 | #89818 | C22 | 1 | 4 | yes | complemented |
| 45 | #89815 | C22 | 1 | 4 | yes | complemented |
| 46 | #89740 | C22 | 1 | 4 | yes | complemented |
| 47 | #89657 | C22 | 1 | 8 | yes | complemented |
| 48 | #89655 | C22 | 1 | 4 | yes | complemented |
| 49 | #89652 | C22 | 1 | 4 | yes | complemented |
| 50 | #89586 | C22 | 1 | 8 | yes | complemented |
| 51 | #89583 | C22 | 1 | 8 | yes | complemented |
| 52 | #89579 | C22 | 1 | 8 | yes | complemented |
| 53 | #89576 | C22 | 1 | 8 | yes | complemented |
| 54 | #89508 | C22 | 1 | 4 | yes | complemented |
| 55 | #89504 | C22 | 1 | 4 | yes | complemented |
| 56 | D7×C22⋊C8 | C22 | 1 | 4 | yes | complemented |
| 57 | D7×C22⋊C8 | C22 | 1 | 4 | yes | complemented |
| 58 | #60734 | — | 7 | 1 | no | maximal, Sylow |
| 59 | C24×D7 | D4 | 1 | 1 | yes | characteristic |
| 60 | C22×C7×Q8 | C23 | 1 | 2 | yes | — |
| 61 | C23×C4×C7 | C23 | 1 | 1 | yes | characteristic |
| 62 | C22×C22⋊D7 | — | 2 | 2 | no | — |
| 63 | C23×Dic7 | D4 | 1 | 1 | yes | characteristic |
| 64 | C2×#1161 | — | 2 | 2 | no | — |
| 65 | C2×#1161 | — | 2 | 2 | no | — |
| 66 | C2×#1161 | — | 4 | 8 | no | — |
| 67 | C2×#1161 | C23 | 1 | 4 | yes | — |
| 68 | C2×#1161 | C23 | 1 | 4 | yes | — |
| 69 | C22×D28 | — | 2 | 2 | no | — |
| 70 | C22×D28 | — | 2 | 2 | no | — |
| 71 | C22×D28 | C23 | 1 | 2 | yes | — |
| 72 | C22×C4×D7 | — | 2 | 2 | no | — |
| 73 | C22×C4×D7 | — | 4 | 4 | no | — |
| 74 | C22×C4×D7 | D4 | 1 | 2 | yes | — |
| 75 | C22×C4×D7 | D4 | 1 | 2 | yes | — |
| 76 | C22×C4×D7 | D4 | 1 | 1 | yes | characteristic |
| 77 | C22×C4×D7 | D4 | 1 | 1 | yes | characteristic |
| 78 | C22×C4×D7 | C23 | 1 | 1 | yes | characteristic |
| 79 | C22×C4×D7 | C23 | 1 | 2 | yes | — |
| 80 | C22×C4×D7 | C23 | 1 | 1 | yes | characteristic |
| 81 | C22×C4×D7 | C23 | 1 | 2 | yes | — |
| 82 | C2×C7×Q16 | C23 | 1 | 4 | yes | complemented |
| 83 | C22×C7×C8 | C23 | 1 | 2 | yes | — |
| 84 | C7×C22⋊Q8 | — | 2 | 2 | no | — |
| 85 | C7×C22⋊Q8 | — | 2 | 2 | no | — |
| 86 | C7×C22⋊Q8 | C23 | 1 | 4 | yes | — |
| 87 | C7×C22⋊Q8 | C23 | 1 | 4 | yes | — |
| 88 | C2×C7×C4⋊C4 | — | 2 | 2 | no | — |
| 89 | C2×C7×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 90 | C2×C7×C22⋊C4 | — | 2 | 2 | no | — |
| 91 | #6509 | — | 2 | 2 | no | — |
| 92 | #6509 | — | 2 | 2 | no | — |
| 93 | #6509 | C23 | 1 | 4 | yes | — |
| 94 | #6509 | C23 | 1 | 4 | yes | — |
| 95 | C2×#1143 | C23 | 1 | 8 | yes | complemented |
| 96 | #6493 | — | 2 | 2 | no | — |
| 97 | #6493 | — | 2 | 2 | no | — |
| 98 | #6493 | C23 | 1 | 4 | yes | — |
| 99 | #6493 | C23 | 1 | 4 | yes | — |
| 100 | C2×(C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 101 | C2×(C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 102 | C2×(C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 103 | C2×(C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 104 | C2×C4⋊Dic7 | C23 | 1 | 2 | yes | — |
| 105 | C2×Dic7⋊C4 | — | 2 | 2 | no | — |
| 106 | C2×C4×Dic7 | — | 2 | 2 | no | — |
| 107 | C22×C7⋊C8 | C23 | 1 | 2 | yes | — |
| 108 | #6482 | — | 4 | 8 | no | — |
| 109 | C2×D56 | C23 | 1 | 4 | yes | complemented |
| 110 | C2×C8×D7 | — | 4 | 4 | no | — |
| 111 | C2×C8×D7 | C23 | 1 | 4 | yes | — |
| 112 | C2×C8×D7 | C23 | 1 | 4 | yes | — |
| 113 | #6458 | — | 2 | 2 | no | — |
| 114 | #6458 | — | 2 | 2 | no | — |
| 115 | #6458 | C23 | 1 | 4 | yes | — |
| 116 | #6458 | C23 | 1 | 4 | yes | — |
| 117 | #6457 | — | 2 | 4 | no | — |
| 118 | #6457 | — | 2 | 4 | no | — |
| 119 | #6457 | — | 2 | 4 | no | — |
| 120 | #6457 | — | 2 | 4 | no | — |
| 121 | #6456 | — | 2 | 4 | no | — |
| 122 | #6456 | — | 2 | 4 | no | — |
| 123 | #6456 | — | 2 | 4 | no | — |
| 124 | #6456 | — | 2 | 4 | no | — |
| 125 | #6455 | — | 2 | 2 | no | — |
| 126 | #6455 | — | 2 | 2 | no | — |
| 127 | #6455 | C23 | 1 | 4 | yes | — |
| 128 | #6455 | C23 | 1 | 4 | yes | — |
| 129 | #6445 | — | 2 | 4 | no | — |
| 130 | #6445 | — | 2 | 4 | no | — |
| 131 | #6445 | — | 2 | 4 | no | — |
| 132 | #6445 | — | 2 | 4 | no | — |
| 133 | (C22⋊D7)⋊C4 | — | 2 | 4 | no | — |
| 134 | (C22⋊D7)⋊C4 | — | 2 | 4 | no | — |
| 135 | (C22⋊D7)⋊C4 | — | 2 | 4 | no | — |
| 136 | (C22⋊D7)⋊C4 | — | 2 | 4 | no | — |
| 137 | C7×#107 | C23 | 1 | 4 | yes | complemented |
| 138 | C7×#103 | C23 | 1 | 8 | yes | complemented |
| 139 | C7×C22⋊C8 | C23 | 1 | 4 | yes | — |
| 140 | #6409 | C23 | 1 | 8 | yes | complemented |
| 141 | C22⋊(C7⋊C8) | C23 | 1 | 4 | yes | — |
| 142 | #6395 | C23 | 1 | 8 | yes | complemented |
| 143 | (C2×D7)⋊C8 | C23 | 1 | 8 | yes | — |
| 144 | #6392 | C23 | 1 | 4 | yes | complemented |
| 145 | #6383 | C23 | 1 | 8 | yes | complemented |
| 146 | #6382 | C23 | 1 | 8 | yes | complemented |
| 147 | C2×#525 | — | 7 | 2 | no | — |
| 148 | #3191 | — | 7 | 4 | no | — |
| 149 | #3190 | — | 7 | 4 | no | — |
| 150 | #3189 | D7 | 1 | 1 | yes | characteristic, complemented |
| 151 | #3188 | — | 7 | 4 | no | — |
| 152 | #3187 | — | 7 | 2 | no | — |
| 153 | #3186 | — | 7 | 1 | no | — |
| 154 | #3091 | — | 7 | 4 | no | — |
| 155 | #3050 | — | 7 | 4 | no | — |
| 156 | #3002 | — | 7 | 4 | no | — |
| 157 | C22×C22⋊C8 | — | 7 | 1 | no | — |
| 158 | C24×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 159 | C23×D7 | — | 2 | 4 | no | — |
| 160 | C23×D7 | — | 2 | 2 | no | — |
| 161 | C23×D7 | — | 4 | 2 | no | — |
| 162 | C23×D7 | — | 4 | 2 | no | — |
| 163 | C23×D7 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | C23×D7 | C2×D4 | 1 | 2 | yes | — |
| 165 | C23×D7 | C2×D4 | 1 | 2 | yes | — |
| 166 | C23×D7 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C2×C7×Q8 | — | 2 | 2 | no | — |
| 168 | C2×C7×Q8 | — | 4 | 4 | no | — |
| 169 | C2×C7×Q8 | C24 | 1 | 4 | yes | — |
| 170 | C22×C4×C7 | — | 2 | 2 | no | — |
| 171 | C22×C4×C7 | — | 2 | 2 | no | — |
| 172 | C22×C4×C7 | — | 4 | 2 | no | — |
| 173 | C22×C4×C7 | C2×D4 | 1 | 2 | yes | — |
| 174 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | C22×C4×C7 | C24 | 1 | 2 | yes | — |
| 176 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 177 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 178 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 179 | C2×C22⋊D7 | — | 4 | 8 | no | — |
| 180 | C22×Dic7 | — | 2 | 2 | no | — |
| 181 | C22×Dic7 | — | 4 | 2 | no | — |
| 182 | C22×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 183 | C22×Dic7 | C2×D4 | 1 | 2 | yes | — |
| 184 | C22×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 185 | C22×Dic7 | C2×D4 | 1 | 2 | yes | — |
| 186 | #1161 | — | 2 | 16 | no | — |
| 187 | #1161 | — | 4 | 8 | no | — |
| 188 | #1161 | — | 4 | 8 | no | — |
| 189 | #1161 | — | 4 | 8 | no | — |
| 190 | C2×D28 | — | 2 | 4 | no | — |
| 191 | C2×D28 | — | 2 | 4 | no | — |
| 192 | C2×D28 | — | 2 | 4 | no | — |
| 193 | C2×D28 | — | 2 | 4 | no | — |
| 194 | C2×D28 | — | 2 | 2 | no | — |
| 195 | C2×D28 | — | 4 | 4 | no | — |
| 196 | C2×D28 | — | 4 | 8 | no | — |
| 197 | C2×D28 | — | 4 | 8 | no | — |
| 198 | C2×D28 | C24 | 1 | 4 | yes | — |
| 199 | C2×C4×D7 | — | 2 | 4 | no | — |
| 200 | C2×C4×D7 | — | 2 | 8 | no | — |
| 201 | C2×C4×D7 | — | 2 | 4 | no | — |
| 202 | C2×C4×D7 | — | 2 | 4 | no | — |
| 203 | C2×C4×D7 | — | 4 | 4 | no | — |
| 204 | C2×C4×D7 | — | 4 | 2 | no | — |
| 205 | C2×C4×D7 | — | 4 | 4 | no | — |
| 206 | C2×C4×D7 | — | 4 | 2 | no | — |
| 207 | C2×C4×D7 | — | 4 | 4 | no | — |
| 208 | C2×C4×D7 | — | 4 | 2 | no | — |
| 209 | C2×C4×D7 | — | 4 | 8 | no | — |
| 210 | C2×C4×D7 | C2×D4 | 1 | 2 | yes | — |
| 211 | C2×C4×D7 | C2×D4 | 1 | 2 | yes | — |
| 212 | C2×C4×D7 | C2×D4 | 1 | 1 | yes | characteristic |
| 213 | C2×C4×D7 | C2×D4 | 1 | 1 | yes | characteristic |
| 214 | C2×C4×D7 | C2×D4 | 1 | 2 | yes | — |
| 215 | C2×C4×D7 | C2×D4 | 1 | 2 | yes | — |
| 216 | C2×C4×D7 | C2×D4 | 1 | 2 | yes | — |
| 217 | C2×C4×D7 | C24 | 1 | 2 | yes | — |
| 218 | C2×C4×D7 | C24 | 1 | 1 | yes | characteristic |
| 219 | C2×C4×D7 | C24 | 1 | 1 | yes | characteristic |
| 220 | C7×Q16 | — | 4 | 4 | no | — |
| 221 | C2×C7×C8 | — | 4 | 2 | no | — |
| 222 | C2×C7×C8 | C24 | 1 | 4 | yes | — |
| 223 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 224 | C7×C4⋊C4 | — | 2 | 4 | no | — |
| 225 | C7×C4⋊C4 | — | 2 | 4 | no | — |
| 226 | C7×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 227 | C7×C22⋊C4 | — | 2 | 4 | no | — |
| 228 | C7×C22⋊C4 | — | 2 | 4 | no | — |
| 229 | #1143 | — | 4 | 8 | no | — |
| 230 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 231 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 232 | (C2×D7)⋊C4 | — | 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 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 238 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 239 | C4⋊Dic7 | C24 | 1 | 4 | yes | — |
| 240 | Dic7⋊C4 | — | 2 | 4 | no | — |
| 241 | Dic7⋊C4 | — | 2 | 4 | no | — |
| 242 | C4×Dic7 | — | 2 | 4 | no | — |
| 243 | C4×Dic7 | — | 2 | 4 | no | — |
| 244 | C2×C7⋊C8 | — | 4 | 2 | no | — |
| 245 | C2×C7⋊C8 | C24 | 1 | 4 | yes | — |
| 246 | D56 | — | 4 | 4 | no | — |
| 247 | C8×D7 | — | 2 | 8 | no | — |
| 248 | C8×D7 | — | 4 | 4 | no | — |
| 249 | C22×#41 | — | 7 | 2 | no | — |
| 250 | C24×C4 | — | 7 | 1 | no | — |
| 251 | C2×#135 | — | 7 | 4 | no | — |
| 252 | C23×C8 | — | 7 | 2 | no | — |
| 253 | #525 | — | 7 | 4 | no | — |
| 254 | #525 | — | 7 | 4 | no | — |
| 255 | #525 | — | 7 | 4 | no | — |
| 256 | #525 | — | 7 | 4 | no | — |
| 257 | #525 | — | 14 | 2 | no | — |
| 258 | #525 | — | 14 | 2 | no | — |
| 259 | #525 | — | 14 | 2 | no | — |
| 260 | #525 | — | 14 | 2 | no | — |
| 261 | C2×#123 | — | 14 | 2 | no | — |
| 262 | C2×C22⋊Q8 | — | 7 | 2 | no | — |
| 263 | C2×C22⋊Q8 | C2×D7 | 1 | 2 | yes | — |
| 264 | C2×#121 | — | 7 | 2 | no | — |
| 265 | C2×#121 | — | 7 | 2 | no | — |
| 266 | C2×#120 | — | 14 | 2 | no | — |
| 267 | C2×C4×D4 | — | 14 | 2 | no | — |
| 268 | C2×C4×D4 | — | 14 | 2 | no | — |
| 269 | C2×#117 | — | 7 | 2 | no | — |
| 270 | #485 | — | 7 | 8 | no | — |
| 271 | #484 | C2×D7 | 1 | 4 | yes | complemented |
| 272 | #483 | — | 7 | 4 | no | — |
| 273 | #482 | — | 7 | 8 | no | — |
| 274 | #481 | — | 7 | 4 | no | — |
| 275 | #480 | — | 7 | 4 | no | — |
| 276 | #467 | — | 7 | 4 | no | — |
| 277 | #467 | C2×D7 | 1 | 4 | yes | complemented |
| 278 | #466 | — | 7 | 4 | no | — |
| 279 | #466 | — | 7 | 4 | no | — |
| 280 | #465 | — | 7 | 8 | no | — |
| 281 | #465 | — | 7 | 8 | no | — |
| 282 | #452 | — | 7 | 8 | no | — |
| 283 | #451 | C2×D7 | 1 | 4 | yes | complemented |
| 284 | #450 | — | 7 | 4 | no | — |
| 285 | #449 | — | 7 | 8 | no | — |
| 286 | #448 | — | 7 | 4 | no | — |
| 287 | #447 | — | 7 | 4 | no | — |
| 288 | #427 | — | 7 | 4 | no | — |
| 289 | #416 | — | 7 | 8 | no | — |
| 290 | C2×C22⋊C8 | — | 7 | 1 | no | — |
| 291 | C2×C22⋊C8 | — | 7 | 2 | no | — |
| 292 | C2×C22⋊C8 | — | 7 | 4 | no | — |
| 293 | C2×C22⋊C8 | — | 7 | 4 | no | — |
| 294 | C2×C22⋊C8 | C2×D7 | 1 | 1 | yes | characteristic |
| 295 | C23×C7 | — | 4 | 1 | no | — |
| 296 | C23×C7 | — | 4 | 1 | no | — |
| 297 | C23×C7 | #135 | 1 | 4 | yes | complemented |
| 298 | C23×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 299 | C23×C7 | C22×D4 | 1 | 2 | yes | — |
| 300 | C22×D7 | — | 2 | 2 | no | — |
| 301 | C22×D7 | — | 2 | 2 | no | — |
| 302 | C22×D7 | — | 2 | 2 | no | — |
| 303 | C22×D7 | — | 2 | 4 | no | — |
| 304 | C22×D7 | — | 2 | 4 | no | — |
| 305 | C22×D7 | — | 2 | 2 | no | — |
| 306 | C22×D7 | — | 2 | 4 | no | — |
| 307 | C22×D7 | — | 2 | 4 | no | — |
| 308 | C22×D7 | — | 2 | 4 | no | — |
| 309 | C22×D7 | — | 4 | 2 | no | — |
| 310 | C22×D7 | — | 4 | 1 | no | — |
| 311 | C22×D7 | — | 4 | 2 | no | — |
| 312 | C22×D7 | — | 4 | 1 | no | — |
| 313 | C22×D7 | — | 4 | 16 | no | — |
| 314 | C22×D7 | — | 4 | 4 | no | — |
| 315 | C22×D7 | — | 4 | 4 | no | — |
| 316 | C22×D7 | — | 4 | 4 | no | — |
| 317 | C22×D7 | C22×D4 | 1 | 2 | yes | — |
| 318 | C22×D7 | C22×D4 | 1 | 1 | yes | characteristic |
| 319 | C22×D7 | C22×D4 | 1 | 1 | yes | characteristic |
| 320 | C7×Q8 | — | 2 | 8 | no | — |
| 321 | C7×Q8 | — | 4 | 4 | no | — |
| 322 | C2×C4×C7 | — | 2 | 2 | no | — |
| 323 | C2×C4×C7 | — | 2 | 4 | no | — |
| 324 | C2×C4×C7 | — | 2 | 4 | no | — |
| 325 | C2×C4×C7 | — | 2 | 4 | no | — |
| 326 | C2×C4×C7 | — | 4 | 1 | no | — |
| 327 | C2×C4×C7 | — | 4 | 2 | no | — |
| 328 | C2×C4×C7 | — | 4 | 4 | no | — |
| 329 | C2×C4×C7 | — | 4 | 4 | no | — |
| 330 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 331 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 332 | C2×C4×C7 | C25 | 1 | 1 | yes | characteristic |
| 333 | C22⋊D7 | — | 4 | 8 | no | — |
| 334 | C22⋊D7 | — | 4 | 8 | no | — |
| 335 | C2×Dic7 | — | 2 | 4 | no | — |
| 336 | C2×Dic7 | — | 2 | 2 | no | — |
| 337 | C2×Dic7 | — | 2 | 4 | no | — |
| 338 | C2×Dic7 | — | 4 | 1 | no | — |
| 339 | C2×Dic7 | — | 4 | 2 | no | — |
| 340 | C2×Dic7 | — | 4 | 4 | no | — |
| 341 | C2×Dic7 | C22×D4 | 1 | 2 | yes | — |
| 342 | C2×Dic7 | C22×D4 | 1 | 1 | yes | characteristic |
| 343 | C2×Dic7 | C22×D4 | 1 | 1 | yes | characteristic |
| 344 | D28 | — | 2 | 8 | no | — |
| 345 | D28 | — | 4 | 4 | no | — |
| 346 | D28 | — | 4 | 8 | no | — |
| 347 | D28 | — | 4 | 8 | no | — |
| 348 | D28 | — | 4 | 8 | no | — |
| 349 | D28 | — | 4 | 8 | no | — |
| 350 | C4×D7 | — | 2 | 2 | no | — |
| 351 | C4×D7 | — | 2 | 4 | no | — |
| 352 | C4×D7 | — | 2 | 2 | no | — |
| 353 | C4×D7 | — | 2 | 4 | no | — |
| 354 | C4×D7 | — | 2 | 2 | no | — |
| 355 | C4×D7 | — | 2 | 4 | no | — |
| 356 | C4×D7 | — | 4 | 2 | no | — |
| 357 | C4×D7 | — | 4 | 2 | no | — |
| 358 | C4×D7 | — | 4 | 2 | no | — |
| 359 | C4×D7 | — | 4 | 8 | no | — |
| 360 | C4×D7 | — | 4 | 8 | no | — |
| 361 | C4×D7 | H(5,𝔽2) | 1 | 4 | yes | — |
| 362 | C7×C8 | — | 2 | 4 | no | — |
| 363 | C7⋊C8 | — | 2 | 4 | no | — |
| 364 | C25 | — | 7 | 1 | no | — |
| 365 | C2×#41 | — | 7 | 4 | no | — |
| 366 | C2×#41 | — | 7 | 4 | no | — |
| 367 | C2×#41 | — | 14 | 2 | no | — |
| 368 | C2×#41 | — | 14 | 2 | no | — |
| 369 | C2×#41 | — | 28 | 8 | no | — |
| 370 | C22×Q8 | C22×D7 | 1 | 2 | yes | — |
| 371 | C22×D4 | — | 7 | 2 | no | — |
| 372 | C22×D4 | — | 14 | 2 | no | — |
| 373 | C22×D4 | — | 14 | 2 | no | — |
| 374 | C22×D4 | — | 14 | 2 | no | — |
| 375 | C23×C4 | — | 7 | 1 | no | — |
| 376 | C23×C4 | — | 7 | 2 | no | — |
| 377 | C23×C4 | — | 7 | 1 | no | — |
| 378 | C23×C4 | — | 7 | 2 | no | — |
| 379 | C23×C4 | — | 7 | 2 | no | — |
| 380 | C23×C4 | — | 7 | 1 | no | — |
| 381 | C23×C4 | — | 7 | 1 | no | — |
| 382 | C23×C4 | — | 7 | 2 | no | — |
| 383 | C23×C4 | — | 7 | 1 | no | — |
| 384 | C23×C4 | — | 14 | 2 | no | — |
| 385 | C23×C4 | — | 28 | 4 | no | — |
| 386 | C23×C4 | C22×D7 | 1 | 1 | yes | characteristic |
| 387 | #135 | — | 28 | 8 | no | — |
| 388 | C2×Q16 | C22×D7 | 1 | 4 | yes | complemented |
| 389 | C2×SD16 | — | 7 | 8 | no | — |
| 390 | C2×D8 | — | 7 | 4 | no | — |
| 391 | C22×C8 | — | 7 | 2 | no | — |
| 392 | C22×C8 | — | 7 | 4 | no | — |
| 393 | C22×C8 | — | 7 | 4 | no | — |
| 394 | C22×C8 | — | 28 | 4 | no | — |
| 395 | C22×C8 | C22×D7 | 1 | 2 | yes | — |
| 396 | #123 | — | 14 | 4 | no | — |
| 397 | #123 | — | 14 | 4 | no | — |
| 398 | #123 | — | 14 | 4 | no | — |
| 399 | #123 | — | 14 | 4 | no | — |
| 400 | C22⋊Q8 | — | 2 | 2 | no | — |
| 401 | C22⋊Q8 | — | 2 | 2 | no | — |
| 402 | C22⋊Q8 | — | 7 | 4 | no | — |
| 403 | C22⋊Q8 | — | 7 | 4 | no | — |
| 404 | C22⋊Q8 | — | 14 | 2 | no | — |
| 405 | C22⋊Q8 | — | 14 | 2 | no | — |
| 406 | C22⋊Q8 | C22×D7 | 1 | 4 | yes | — |
| 407 | C22⋊Q8 | C22×D7 | 1 | 4 | yes | — |
| 408 | #121 | — | 7 | 4 | no | — |
| 409 | #121 | — | 7 | 4 | no | — |
| 410 | #121 | — | 7 | 4 | no | — |
| 411 | #121 | — | 7 | 4 | no | — |
| 412 | #121 | — | 14 | 2 | no | — |
| 413 | #121 | — | 14 | 2 | no | — |
| 414 | #121 | — | 14 | 2 | no | — |
| 415 | #121 | — | 14 | 2 | no | — |
| 416 | #120 | — | 14 | 4 | no | — |
| 417 | #120 | — | 14 | 4 | no | — |
| 418 | #120 | — | 14 | 4 | no | — |
| 419 | #120 | — | 14 | 4 | no | — |
| 420 | C4×D4 | — | 14 | 4 | no | — |
| 421 | C4×D4 | — | 14 | 4 | no | — |
| 422 | C4×D4 | — | 14 | 4 | no | — |
| 423 | C4×D4 | — | 14 | 4 | no | — |
| 424 | C4×D4 | — | 14 | 4 | no | — |
| 425 | C4×D4 | — | 14 | 4 | no | — |
| 426 | C4×D4 | — | 14 | 4 | no | — |
| 427 | C4×D4 | — | 14 | 4 | no | — |
| 428 | #117 | — | 7 | 4 | no | — |
| 429 | #117 | — | 7 | 4 | no | — |
| 430 | #117 | — | 14 | 2 | no | — |
| 431 | #117 | — | 14 | 2 | no | — |
| 432 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 433 | C2×C4⋊C4 | — | 7 | 2 | no | — |
| 434 | C2×C4⋊C4 | — | 14 | 2 | no | — |
| 435 | C2×C4⋊C4 | C22×D7 | 1 | 2 | yes | — |
| 436 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 437 | C2×C22⋊C4 | — | 14 | 2 | no | — |
| 438 | C2×C22⋊C4 | — | 14 | 2 | no | — |
| 439 | C2×C22⋊C4 | — | 14 | 2 | no | — |
| 440 | C2×C22⋊C4 | — | 14 | 2 | no | — |
| 441 | C2×C42 | — | 14 | 2 | no | — |
| 442 | #107 | — | 7 | 4 | no | — |
| 443 | #107 | C22×D7 | 1 | 4 | yes | complemented |
| 444 | #106 | — | 7 | 8 | no | — |
| 445 | #103 | — | 7 | 8 | no | — |
| 446 | #103 | C22×D7 | 1 | 8 | yes | complemented |
| 447 | #102 | — | 7 | 8 | no | — |
| 448 | #102 | — | 7 | 8 | no | — |
| 449 | C22⋊C8 | — | 7 | 4 | no | — |
| 450 | C22⋊C8 | — | 7 | 8 | no | — |
| 451 | C22⋊C8 | C22×D7 | 1 | 4 | yes | — |
| 452 | C22×C7 | — | 2 | 2 | no | — |
| 453 | C22×C7 | — | 2 | 1 | no | — |
| 454 | C22×C7 | — | 2 | 2 | no | — |
| 455 | C22×C7 | — | 2 | 1 | no | — |
| 456 | C22×C7 | — | 4 | 4 | no | — |
| 457 | C22×C7 | C2×#135 | 1 | 4 | yes | — |
| 458 | C22×C7 | C2×#135 | 1 | 2 | yes | — |
| 459 | C22×C7 | C23×D4 | 1 | 1 | yes | characteristic |
| 460 | C2×D7 | — | 2 | 8 | no | — |
| 461 | C2×D7 | — | 2 | 1 | no | — |
| 462 | C2×D7 | — | 2 | 1 | no | — |
| 463 | C2×D7 | — | 2 | 1 | no | — |
| 464 | C2×D7 | — | 2 | 1 | no | — |
| 465 | C2×D7 | — | 2 | 2 | no | — |
| 466 | C2×D7 | — | 2 | 2 | no | — |
| 467 | C2×D7 | — | 2 | 2 | no | — |
| 468 | C2×D7 | — | 4 | 8 | no | — |
| 469 | C2×D7 | — | 4 | 8 | no | — |
| 470 | C2×D7 | — | 4 | 4 | no | — |
| 471 | C2×D7 | — | 4 | 4 | no | — |
| 472 | C2×D7 | — | 4 | 4 | no | — |
| 473 | C2×D7 | — | 4 | 4 | no | — |
| 474 | C2×D7 | — | 8 | 8 | no | — |
| 475 | C2×D7 | #534 | 1 | 2 | yes | — |
| 476 | C2×D7 | #575 | 1 | 2 | yes | — |
| 477 | C4×C7 | — | 2 | 2 | no | — |
| 478 | C4×C7 | — | 2 | 1 | no | — |
| 479 | C4×C7 | — | 4 | 4 | no | — |
| 480 | C4×C7 | — | 4 | 4 | no | — |
| 481 | C4×C7 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 482 | Dic7 | — | 2 | 2 | no | — |
| 483 | Dic7 | — | 2 | 1 | no | — |
| 484 | Dic7 | — | 4 | 4 | no | — |
| 485 | Dic7 | #534 | 1 | 2 | yes | — |
| 486 | C24 | — | 7 | 1 | no | — |
| 487 | C24 | — | 7 | 2 | no | — |
| 488 | C24 | — | 7 | 2 | no | — |
| 489 | C24 | — | 7 | 1 | no | — |
| 490 | C24 | — | 14 | 4 | no | — |
| 491 | C24 | — | 14 | 2 | no | — |
| 492 | C24 | — | 28 | 2 | no | — |
| 493 | C24 | — | 28 | 2 | no | — |
| 494 | C24 | D4×D7 | 1 | 1 | yes | characteristic |
| 495 | #41 | — | 14 | 16 | no | — |
| 496 | #41 | — | 28 | 8 | no | — |
| 497 | #41 | — | 28 | 8 | no | — |
| 498 | #41 | — | 28 | 8 | no | — |
| 499 | C2×Q8 | — | 2 | 2 | no | — |
| 500 | C2×Q8 | — | 4 | 4 | no | — |
| 501 | C2×Q8 | C23×D7 | 1 | 4 | yes | — |
| 502 | C2×D4 | — | 7 | 4 | no | — |
| 503 | C2×D4 | — | 14 | 4 | no | — |
| 504 | C2×D4 | — | 14 | 4 | no | — |
| 505 | C2×D4 | — | 14 | 4 | no | — |
| 506 | C2×D4 | — | 14 | 4 | no | — |
| 507 | C2×D4 | — | 14 | 4 | no | — |
| 508 | C2×D4 | — | 14 | 4 | no | — |
| 509 | C2×D4 | — | 14 | 2 | no | — |
| 510 | C2×D4 | — | 28 | 4 | no | — |
| 511 | C2×D4 | — | 28 | 8 | no | — |
| 512 | C2×D4 | — | 28 | 8 | no | — |
| 513 | C2×D4 | — | 28 | 8 | no | — |
| 514 | C22×C4 | — | 2 | 2 | no | — |
| 515 | C22×C4 | — | 2 | 2 | no | — |
| 516 | C22×C4 | — | 4 | 2 | no | — |
| 517 | C22×C4 | — | 7 | 1 | no | — |
| 518 | C22×C4 | — | 7 | 2 | no | — |
| 519 | C22×C4 | — | 7 | 1 | no | — |
| 520 | C22×C4 | — | 7 | 2 | no | — |
| 521 | C22×C4 | — | 7 | 1 | no | — |
| 522 | C22×C4 | — | 7 | 2 | no | — |
| 523 | C22×C4 | — | 7 | 2 | no | — |
| 524 | C22×C4 | — | 7 | 1 | no | — |
| 525 | C22×C4 | — | 7 | 1 | no | — |
| 526 | C22×C4 | — | 7 | 2 | no | — |
| 527 | C22×C4 | — | 7 | 1 | no | — |
| 528 | C22×C4 | — | 7 | 2 | no | — |
| 529 | C22×C4 | — | 7 | 2 | no | — |
| 530 | C22×C4 | — | 7 | 2 | no | — |
| 531 | C22×C4 | — | 14 | 4 | no | — |
| 532 | C22×C4 | — | 14 | 8 | no | — |
| 533 | C22×C4 | — | 14 | 4 | no | — |
| 534 | C22×C4 | — | 14 | 4 | no | — |
| 535 | C22×C4 | — | 14 | 2 | no | — |
| 536 | C22×C4 | — | 28 | 2 | no | — |
| 537 | C22×C4 | — | 28 | 4 | no | — |
| 538 | C22×C4 | — | 28 | 4 | no | — |
| 539 | C22×C4 | — | 28 | 2 | no | — |
| 540 | C22×C4 | — | 28 | 4 | no | — |
| 541 | C22×C4 | — | 28 | 2 | no | — |
| 542 | C22×C4 | — | 28 | 8 | no | — |
| 543 | C22×C4 | — | 28 | 2 | no | — |
| 544 | C22×C4 | D4×D7 | 1 | 2 | yes | — |
| 545 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 546 | C22×C4 | C23×D7 | 1 | 2 | yes | — |
| 547 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 548 | Q16 | — | 4 | 4 | no | — |
| 549 | SD16 | — | 28 | 8 | no | — |
| 550 | D8 | — | 28 | 4 | no | — |
| 551 | C2×C8 | — | 4 | 2 | no | — |
| 552 | C2×C8 | — | 7 | 4 | no | — |
| 553 | C2×C8 | — | 14 | 8 | no | — |
| 554 | C2×C8 | — | 28 | 4 | no | — |
| 555 | C2×C8 | — | 28 | 2 | no | — |
| 556 | C2×C8 | C23×D7 | 1 | 4 | yes | — |
| 557 | C4⋊C4 | — | 2 | 4 | no | — |
| 558 | C4⋊C4 | — | 2 | 4 | no | — |
| 559 | C4⋊C4 | — | 2 | 2 | no | — |
| 560 | C4⋊C4 | — | 7 | 4 | no | — |
| 561 | C4⋊C4 | — | 14 | 4 | no | — |
| 562 | C4⋊C4 | — | 14 | 4 | no | — |
| 563 | C4⋊C4 | — | 14 | 2 | no | — |
| 564 | C4⋊C4 | C23×D7 | 1 | 4 | yes | — |
| 565 | C22⋊C4 | — | 2 | 4 | no | — |
| 566 | C22⋊C4 | — | 2 | 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 | — | 14 | 4 | no | — |
| 575 | C42 | — | 14 | 4 | no | — |
| 576 | C42 | — | 14 | 4 | no | — |
| 577 | C2×C7 | — | 2 | 2 | no | — |
| 578 | C2×C7 | — | 2 | 4 | no | — |
| 579 | C2×C7 | C2×#534 | 1 | 1 | yes | characteristic |
| 580 | C2×C7 | C22×#135 | 1 | 1 | yes | characteristic |
| 581 | C2×C7 | C2×#575 | 1 | 1 | yes | characteristic |
| 582 | D7 | — | 2 | 2 | no | — |
| 583 | D7 | — | 2 | 2 | no | — |
| 584 | D7 | — | 4 | 2 | no | — |
| 585 | D7 | — | 8 | 4 | no | — |
| 586 | C23 | — | 4 | 1 | no | — |
| 587 | C23 | — | 4 | 1 | no | — |
| 588 | C23 | — | 7 | 1 | no | — |
| 589 | C23 | — | 7 | 1 | no | — |
| 590 | C23 | — | 7 | 2 | no | — |
| 591 | C23 | — | 14 | 2 | no | — |
| 592 | C23 | — | 14 | 2 | no | — |
| 593 | C23 | — | 14 | 4 | no | — |
| 594 | C23 | — | 14 | 4 | no | — |
| 595 | C23 | — | 14 | 2 | no | — |
| 596 | C23 | — | 14 | 4 | no | — |
| 597 | C23 | — | 14 | 4 | no | — |
| 598 | C23 | — | 14 | 2 | no | — |
| 599 | C23 | — | 14 | 4 | no | — |
| 600 | C23 | — | 28 | 2 | no | — |
| 601 | C23 | — | 28 | 1 | no | — |
| 602 | C23 | — | 28 | 2 | no | — |
| 603 | C23 | — | 28 | 1 | no | — |
| 604 | C23 | — | 28 | 4 | no | — |
| 605 | C23 | — | 28 | 4 | no | — |
| 606 | C23 | — | 28 | 16 | no | — |
| 607 | C23 | — | 28 | 4 | no | — |
| 608 | C23 | #6482 | 1 | 4 | yes | complemented |
| 609 | C23 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 610 | C23 | C2×D4×D7 | 1 | 2 | yes | — |
| 611 | Q8 | — | 2 | 8 | no | — |
| 612 | Q8 | — | 4 | 4 | no | — |
| 613 | D4 | — | 14 | 8 | no | — |
| 614 | D4 | — | 28 | 4 | no | — |
| 615 | D4 | — | 28 | 8 | no | — |
| 616 | D4 | — | 28 | 8 | no | — |
| 617 | D4 | — | 28 | 8 | no | — |
| 618 | D4 | — | 28 | 8 | no | — |
| 619 | D4 | — | 28 | 8 | no | — |
| 620 | D4 | — | 28 | 8 | no | — |
| 621 | C2×C4 | — | 2 | 2 | no | — |
| 622 | C2×C4 | — | 2 | 4 | no | — |
| 623 | C2×C4 | — | 2 | 4 | no | — |
| 624 | C2×C4 | — | 2 | 4 | no | — |
| 625 | C2×C4 | — | 4 | 1 | no | — |
| 626 | C2×C4 | — | 4 | 2 | no | — |
| 627 | C2×C4 | — | 4 | 4 | no | — |
| 628 | C2×C4 | — | 4 | 4 | no | — |
| 629 | C2×C4 | — | 7 | 1 | no | — |
| 630 | C2×C4 | — | 7 | 4 | no | — |
| 631 | C2×C4 | — | 7 | 2 | no | — |
| 632 | C2×C4 | — | 7 | 1 | no | — |
| 633 | C2×C4 | — | 14 | 2 | no | — |
| 634 | C2×C4 | — | 14 | 4 | no | — |
| 635 | C2×C4 | — | 14 | 2 | no | — |
| 636 | C2×C4 | — | 14 | 4 | no | — |
| 637 | C2×C4 | — | 14 | 2 | no | — |
| 638 | C2×C4 | — | 14 | 4 | no | — |
| 639 | C2×C4 | — | 14 | 2 | no | — |
| 640 | C2×C4 | — | 14 | 4 | no | — |
| 641 | C2×C4 | — | 14 | 4 | no | — |
| 642 | C2×C4 | — | 28 | 2 | no | — |
| 643 | C2×C4 | — | 28 | 2 | no | — |
| 644 | C2×C4 | — | 28 | 2 | no | — |
| 645 | C2×C4 | — | 28 | 8 | no | — |
| 646 | C2×C4 | — | 28 | 8 | no | — |
| 647 | C2×C4 | — | 28 | 1 | no | — |
| 648 | C2×C4 | — | 28 | 2 | no | — |
| 649 | C2×C4 | — | 28 | 4 | no | — |
| 650 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 651 | C2×C4 | C2×D4×D7 | 1 | 2 | yes | — |
| 652 | C2×C4 | C24×D7 | 1 | 1 | yes | characteristic |
| 653 | C8 | — | 2 | 4 | no | — |
| 654 | C8 | — | 14 | 4 | no | — |
| 655 | C7 | #60734 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 656 | C22 | — | 2 | 2 | no | — |
| 657 | C22 | — | 2 | 1 | no | — |
| 658 | C22 | — | 2 | 2 | no | — |
| 659 | C22 | — | 2 | 1 | no | — |
| 660 | C22 | — | 4 | 4 | no | — |
| 661 | C22 | — | 7 | 2 | no | — |
| 662 | C22 | — | 7 | 2 | no | — |
| 663 | C22 | — | 14 | 8 | no | — |
| 664 | C22 | — | 14 | 1 | no | — |
| 665 | C22 | — | 14 | 1 | no | — |
| 666 | C22 | — | 14 | 1 | no | — |
| 667 | C22 | — | 14 | 1 | no | — |
| 668 | C22 | — | 14 | 2 | no | — |
| 669 | C22 | — | 14 | 2 | no | — |
| 670 | C22 | — | 14 | 2 | no | — |
| 671 | C22 | — | 28 | 8 | no | — |
| 672 | C22 | — | 28 | 8 | no | — |
| 673 | C22 | — | 28 | 4 | no | — |
| 674 | C22 | — | 28 | 4 | no | — |
| 675 | C22 | — | 28 | 4 | no | — |
| 676 | C22 | — | 28 | 4 | no | — |
| 677 | C22 | — | 56 | 8 | no | — |
| 678 | C22 | C2×#6482 | 1 | 4 | yes | — |
| 679 | C22 | C2×#6482 | 1 | 2 | yes | — |
| 680 | C22 | C22×D4×D7 | 1 | 1 | yes | characteristic |
| 681 | C4 | — | 2 | 2 | no | — |
| 682 | C4 | — | 2 | 1 | no | — |
| 683 | C4 | — | 4 | 4 | no | — |
| 684 | C4 | — | 4 | 4 | no | — |
| 685 | C4 | — | 7 | 2 | no | — |
| 686 | C4 | — | 14 | 2 | no | — |
| 687 | C4 | — | 14 | 1 | no | — |
| 688 | C4 | — | 28 | 4 | no | — |
| 689 | C4 | D7×H(5,𝔽2) | 1 | 2 | yes | — |
| 690 | C2 | — | 2 | 2 | no | — |
| 691 | C2 | — | 2 | 4 | no | — |
| 692 | C2 | — | 14 | 2 | no | — |
| 693 | C2 | — | 14 | 2 | no | — |
| 694 | C2 | — | 28 | 2 | no | — |
| 695 | C2 | — | 56 | 4 | no | — |
| 696 | C2 | D7×#534 | 1 | 1 | yes | characteristic |
| 697 | C2 | C22×#6482 | 1 | 1 | yes | characteristic |
| 698 | C2 | D7×#575 | 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