← #13412699
Subgroups — #13412699
Order 1792.
674 conjugacy classes of subgroups.
The subgroup lattice has 432 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C7×#2913 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11740005 | C2 | 1 | 2 | yes | maximal |
| 3 | #11736618 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11729770 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #11729762 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #11729419 | C2 | 1 | 2 | yes | maximal |
| 7 | #11728425 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11728421 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11728416 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11728379 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11728361 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×C7×#131 | C22 | 1 | 1 | yes | characteristic |
| 13 | C7×#520 | C22 | 1 | 2 | yes | — |
| 14 | #90210 | C22 | 1 | 2 | yes | — |
| 15 | C7×#428 | — | 2 | 2 | no | — |
| 16 | C7×#428 | C22 | 1 | 2 | yes | — |
| 17 | C7×#427 | — | 2 | 1 | no | — |
| 18 | C7×#427 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×C7×#107 | — | 2 | 1 | no | — |
| 20 | C2×C7×#107 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#6411 | C22 | 1 | 1 | yes | characteristic |
| 22 | #90005 | C22 | 1 | 1 | yes | characteristic |
| 23 | #90004 | C22 | 1 | 2 | yes | — |
| 24 | C2×#6393 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#6392 | C22 | 1 | 1 | yes | characteristic |
| 26 | #89873 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×C8×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 28 | #89794 | — | 2 | 2 | no | — |
| 29 | #89792 | — | 2 | 2 | no | — |
| 30 | #89781 | — | 2 | 2 | no | — |
| 31 | #89780 | — | 2 | 2 | no | — |
| 32 | #89771 | C22 | 1 | 2 | yes | — |
| 33 | #89767 | C22 | 1 | 2 | yes | — |
| 34 | #89749 | C22 | 1 | 2 | yes | — |
| 35 | #89736 | C22 | 1 | 2 | yes | — |
| 36 | C2×#6382 | C22 | 1 | 2 | yes | — |
| 37 | #89650 | — | 2 | 1 | no | — |
| 38 | #89646 | — | 2 | 1 | no | — |
| 39 | #89628 | — | 2 | 2 | no | — |
| 40 | #89353 | C22 | 1 | 1 | yes | characteristic |
| 41 | #89350 | C22 | 1 | 1 | yes | characteristic |
| 42 | #89349 | C22 | 1 | 2 | yes | — |
| 43 | #89327 | C22 | 1 | 2 | yes | — |
| 44 | #89325 | C22 | 1 | 2 | yes | — |
| 45 | #26082 | — | 7 | 1 | no | maximal, Sylow |
| 46 | C2×C7×#41 | C23 | 1 | 1 | yes | characteristic |
| 47 | C7×#131 | — | 2 | 2 | no | — |
| 48 | C7×#131 | Q8 | 1 | 4 | yes | complemented |
| 49 | C2×C7×M16 | — | 2 | 1 | no | — |
| 50 | C2×C7×M16 | C23 | 1 | 1 | yes | characteristic |
| 51 | C22×C7×C8 | — | 2 | 1 | no | — |
| 52 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 53 | C4×C7×Q8 | — | 2 | 2 | no | — |
| 54 | C4×C7×D4 | — | 2 | 2 | no | — |
| 55 | C4×C7×D4 | — | 4 | 2 | no | — |
| 56 | C7×#117 | — | 2 | 2 | no | — |
| 57 | C7×#117 | C23 | 1 | 2 | yes | — |
| 58 | C2×C7×C4⋊C4 | — | 2 | 2 | no | — |
| 59 | C2×C7×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 60 | #6489 | C23 | 1 | 1 | yes | characteristic |
| 61 | C2×C4⋊Dic7 | C23 | 1 | 2 | yes | — |
| 62 | C2×C4×Dic7 | C23 | 1 | 1 | yes | characteristic |
| 63 | C2×#1136 | C23 | 1 | 2 | yes | — |
| 64 | C2×#1136 | C23 | 1 | 1 | yes | characteristic |
| 65 | C22×C7⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 66 | #6453 | — | 2 | 2 | no | — |
| 67 | #6451 | — | 2 | 2 | no | — |
| 68 | #6441 | — | 4 | 2 | no | — |
| 69 | #6433 | — | 2 | 2 | no | — |
| 70 | #6432 | — | 2 | 2 | no | — |
| 71 | C7×#107 | — | 2 | 1 | no | — |
| 72 | C7×#107 | — | 2 | 1 | no | — |
| 73 | C7×#107 | — | 2 | 2 | no | — |
| 74 | C7×#107 | D4 | 1 | 1 | yes | characteristic |
| 75 | C7×#107 | D4 | 1 | 1 | yes | characteristic |
| 76 | C7×#106 | — | 2 | 2 | no | — |
| 77 | C7×#106 | D4 | 1 | 2 | yes | — |
| 78 | #6411 | Q8 | 1 | 4 | yes | complemented |
| 79 | #6409 | — | 2 | 2 | no | — |
| 80 | #6409 | D4 | 1 | 1 | yes | characteristic |
| 81 | #6409 | D4 | 1 | 1 | yes | characteristic |
| 82 | #6406 | — | 2 | 2 | no | — |
| 83 | #6406 | D4 | 1 | 1 | yes | characteristic |
| 84 | #6406 | D4 | 1 | 1 | yes | characteristic |
| 85 | C7⋊#95 | — | 4 | 2 | no | — |
| 86 | #6393 | — | 2 | 2 | no | — |
| 87 | #6392 | — | 2 | 1 | no | — |
| 88 | #6392 | — | 2 | 1 | no | — |
| 89 | #6389 | — | 2 | 1 | no | — |
| 90 | C8×Dic7 | — | 2 | 1 | no | — |
| 91 | C8×Dic7 | — | 2 | 2 | no | — |
| 92 | #6382 | — | 2 | 2 | no | — |
| 93 | #6382 | — | 2 | 2 | no | — |
| 94 | #6382 | — | 2 | 2 | no | — |
| 95 | #6382 | — | 2 | 2 | no | — |
| 96 | #6381 | — | 2 | 2 | no | — |
| 97 | #6381 | — | 2 | 2 | no | — |
| 98 | C4⋊(C7⋊C8) | — | 2 | 2 | no | — |
| 99 | C4⋊(C7⋊C8) | — | 2 | 2 | no | — |
| 100 | #3164 | — | 7 | 1 | no | — |
| 101 | #3084 | — | 7 | 2 | no | — |
| 102 | #2913 | D7 | 1 | 1 | yes | characteristic |
| 103 | #2090 | — | 7 | 2 | no | — |
| 104 | #2061 | — | 7 | 2 | no | — |
| 105 | #1952 | — | 7 | 1 | no | — |
| 106 | #1945 | — | 7 | 1 | no | — |
| 107 | #1860 | — | 7 | 2 | no | — |
| 108 | #1846 | — | 7 | 1 | no | — |
| 109 | #1816 | — | 7 | 1 | no | — |
| 110 | #1764 | — | 7 | 1 | no | — |
| 111 | C7×#41 | — | 2 | 1 | no | — |
| 112 | C7×#41 | — | 2 | 1 | no | — |
| 113 | C7×#41 | C2×Q8 | 1 | 2 | yes | — |
| 114 | C7×#41 | C2×Q8 | 1 | 2 | yes | — |
| 115 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C2×C7×D4 | — | 2 | 1 | no | — |
| 117 | C2×C7×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | C22×C4×C7 | — | 2 | 1 | no | — |
| 119 | C22×C4×C7 | — | 2 | 2 | no | — |
| 120 | C22×C4×C7 | — | 4 | 2 | no | — |
| 121 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 122 | C22×Dic7 | — | 2 | 1 | no | — |
| 123 | C22×Dic7 | — | 2 | 2 | no | — |
| 124 | C2×Dic14 | — | 4 | 2 | no | — |
| 125 | C7×M16 | — | 2 | 1 | no | — |
| 126 | C7×M16 | — | 2 | 4 | no | — |
| 127 | C7×M16 | C2×Q8 | 1 | 2 | yes | — |
| 128 | C2×C7×C8 | — | 2 | 1 | no | — |
| 129 | C2×C7×C8 | — | 2 | 4 | no | — |
| 130 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 131 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 132 | C2×C7×C8 | C2×Q8 | 1 | 2 | yes | — |
| 133 | C2×C7×C8 | #41 | 1 | 2 | yes | — |
| 134 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 135 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 136 | C7×C4⋊C4 | — | 4 | 2 | no | — |
| 137 | C7×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 138 | C7×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 139 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 140 | C7×C22⋊C4 | — | 4 | 2 | no | — |
| 141 | C42×C7 | — | 2 | 2 | no | — |
| 142 | C42×C7 | — | 4 | 2 | no | — |
| 143 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 144 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 145 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 146 | C4⋊Dic7 | — | 4 | 2 | no | — |
| 147 | C4⋊Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 148 | C4⋊Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 149 | Dic7⋊C4 | — | 4 | 2 | no | — |
| 150 | Dic7⋊C4 | — | 4 | 2 | no | — |
| 151 | C4×Dic7 | — | 2 | 1 | no | — |
| 152 | C4×Dic7 | — | 2 | 1 | no | — |
| 153 | C4×Dic7 | C2×Q8 | 1 | 2 | yes | — |
| 154 | #1136 | — | 2 | 1 | no | — |
| 155 | #1136 | — | 2 | 2 | no | — |
| 156 | #1136 | — | 2 | 2 | no | — |
| 157 | #1136 | C2×Q8 | 1 | 2 | yes | — |
| 158 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 159 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 160 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 161 | C2×C7⋊C8 | — | 2 | 2 | no | — |
| 162 | C2×C7⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 163 | C2×C7⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | C2×#131 | C2×D7 | 1 | 1 | yes | characteristic |
| 165 | #544 | — | 7 | 2 | no | — |
| 166 | #520 | C2×D7 | 1 | 2 | yes | — |
| 167 | #501 | — | 14 | 2 | no | — |
| 168 | #500 | — | 14 | 1 | no | — |
| 169 | #499 | — | 14 | 1 | no | — |
| 170 | #479 | — | 14 | 2 | no | — |
| 171 | #478 | — | 14 | 2 | no | — |
| 172 | #476 | — | 14 | 2 | no | — |
| 173 | #475 | — | 14 | 2 | no | — |
| 174 | C2×#108 | — | 7 | 1 | no | — |
| 175 | #428 | — | 2 | 2 | no | — |
| 176 | #428 | — | 7 | 2 | no | — |
| 177 | #428 | — | 7 | 2 | no | — |
| 178 | #428 | C2×D7 | 1 | 2 | yes | — |
| 179 | #427 | — | 2 | 1 | no | — |
| 180 | #427 | C2×D7 | 1 | 1 | yes | characteristic |
| 181 | C2×#107 | — | 2 | 1 | no | — |
| 182 | C2×#107 | — | 7 | 1 | no | — |
| 183 | C2×#107 | C2×D7 | 1 | 1 | yes | characteristic |
| 184 | C2×#106 | — | 7 | 2 | no | — |
| 185 | #424 | — | 7 | 2 | no | — |
| 186 | C2×#104 | — | 7 | 1 | no | — |
| 187 | #417 | — | 7 | 2 | no | — |
| 188 | #416 | — | 7 | 1 | no | — |
| 189 | #405 | — | 7 | 1 | no | — |
| 190 | C2×C4×C8 | — | 7 | 1 | no | — |
| 191 | #382 | — | 7 | 2 | no | — |
| 192 | #343 | — | 7 | 2 | no | — |
| 193 | #343 | — | 7 | 2 | no | — |
| 194 | #341 | — | 7 | 1 | no | — |
| 195 | #339 | — | 7 | 1 | no | — |
| 196 | #339 | — | 7 | 2 | no | — |
| 197 | C23×C7 | — | 2 | 1 | no | — |
| 198 | C23×C7 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 199 | C7×Q8 | — | 2 | 1 | no | — |
| 200 | C7×Q8 | C4⋊Q8 | 1 | 2 | yes | — |
| 201 | C7×D4 | — | 2 | 2 | no | — |
| 202 | C7×D4 | — | 2 | 2 | no | — |
| 203 | C7×D4 | — | 2 | 1 | no | — |
| 204 | C7×D4 | C4⋊Q8 | 1 | 2 | yes | — |
| 205 | C2×C4×C7 | — | 2 | 1 | no | — |
| 206 | C2×C4×C7 | — | 2 | 2 | no | — |
| 207 | C2×C4×C7 | — | 2 | 2 | no | — |
| 208 | C2×C4×C7 | — | 2 | 2 | no | — |
| 209 | C2×C4×C7 | — | 2 | 2 | no | — |
| 210 | C2×C4×C7 | — | 4 | 2 | no | — |
| 211 | C2×C4×C7 | — | 8 | 2 | no | — |
| 212 | C2×C4×C7 | — | 16 | 2 | no | — |
| 213 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 214 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 215 | C2×C4×C7 | C22×Q8 | 1 | 1 | yes | characteristic |
| 216 | C2×C4×C7 | C22×Q8 | 1 | 1 | yes | characteristic |
| 217 | C2×C4×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 218 | C2×C4×C7 | 2−1+4 | 1 | 1 | yes | characteristic |
| 219 | C2×Dic7 | — | 2 | 1 | no | — |
| 220 | C2×Dic7 | — | 2 | 1 | no | — |
| 221 | C2×Dic7 | — | 2 | 2 | no | — |
| 222 | C2×Dic7 | — | 4 | 1 | no | — |
| 223 | C2×Dic7 | — | 4 | 1 | no | — |
| 224 | C2×Dic7 | — | 4 | 2 | no | — |
| 225 | C2×Dic7 | — | 8 | 2 | no | — |
| 226 | Dic14 | — | 16 | 2 | no | — |
| 227 | C7×C8 | — | 2 | 2 | no | — |
| 228 | C7×C8 | C22⋊Q8 | 1 | 2 | yes | — |
| 229 | C7×C8 | C22⋊Q8 | 1 | 2 | yes | — |
| 230 | C7⋊C8 | — | 2 | 1 | no | — |
| 231 | C7⋊C8 | — | 2 | 1 | no | — |
| 232 | C7⋊C8 | — | 2 | 2 | no | — |
| 233 | C7⋊C8 | — | 4 | 2 | no | — |
| 234 | C2×#41 | C22×D7 | 1 | 1 | yes | characteristic |
| 235 | #131 | — | 2 | 2 | no | — |
| 236 | #131 | Dic14 | 1 | 4 | yes | complemented |
| 237 | C2×M16 | — | 2 | 1 | no | — |
| 238 | C2×M16 | — | 7 | 1 | no | — |
| 239 | C2×M16 | — | 7 | 2 | no | — |
| 240 | C2×M16 | C22×D7 | 1 | 1 | yes | characteristic |
| 241 | C22×C8 | — | 2 | 1 | no | — |
| 242 | C22×C8 | — | 7 | 1 | no | — |
| 243 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 244 | C4⋊Q8 | — | 14 | 2 | no | — |
| 245 | C4⋊Q8 | — | 14 | 2 | no | — |
| 246 | #125 | — | 14 | 2 | no | — |
| 247 | #125 | — | 14 | 2 | no | — |
| 248 | C22⋊Q8 | — | 28 | 2 | no | — |
| 249 | C4×Q8 | — | 2 | 2 | no | — |
| 250 | C4×D4 | — | 2 | 2 | no | — |
| 251 | C4×D4 | — | 4 | 2 | no | — |
| 252 | #117 | — | 2 | 2 | no | — |
| 253 | #117 | — | 7 | 1 | no | — |
| 254 | #117 | C22×D7 | 1 | 2 | yes | — |
| 255 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 256 | C2×C4⋊C4 | — | 7 | 2 | no | — |
| 257 | C2×C4⋊C4 | C22×D7 | 1 | 2 | yes | — |
| 258 | C2×C42 | — | 7 | 1 | no | — |
| 259 | #108 | — | 14 | 2 | no | — |
| 260 | #107 | — | 2 | 1 | no | — |
| 261 | #107 | — | 2 | 1 | no | — |
| 262 | #107 | — | 2 | 2 | no | — |
| 263 | #107 | — | 14 | 2 | no | — |
| 264 | #107 | — | 14 | 1 | no | — |
| 265 | #107 | — | 14 | 1 | no | — |
| 266 | #107 | — | 14 | 2 | no | — |
| 267 | #107 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 268 | #107 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 269 | #106 | — | 2 | 2 | no | — |
| 270 | #106 | — | 14 | 2 | no | — |
| 271 | #106 | — | 14 | 2 | no | — |
| 272 | #106 | — | 14 | 2 | no | — |
| 273 | #106 | — | 14 | 2 | no | — |
| 274 | #106 | C22⋊D7 | 1 | 2 | yes | — |
| 275 | C4⋊C8 | — | 14 | 2 | no | — |
| 276 | C4⋊C8 | — | 14 | 2 | no | — |
| 277 | #104 | — | 7 | 4 | no | — |
| 278 | #103 | — | 7 | 1 | no | — |
| 279 | #103 | — | 7 | 1 | no | — |
| 280 | #103 | — | 14 | 2 | no | — |
| 281 | #102 | — | 7 | 1 | no | — |
| 282 | #102 | — | 7 | 1 | no | — |
| 283 | #102 | — | 14 | 2 | no | — |
| 284 | #97 | — | 14 | 1 | no | — |
| 285 | C4×C8 | — | 14 | 2 | no | — |
| 286 | C4×C8 | — | 14 | 1 | no | — |
| 287 | #95 | — | 28 | 2 | no | — |
| 288 | C22×C7 | — | 2 | 1 | no | — |
| 289 | C22×C7 | — | 2 | 1 | no | — |
| 290 | C22×C7 | — | 2 | 2 | no | — |
| 291 | C22×C7 | — | 4 | 1 | no | — |
| 292 | C22×C7 | — | 4 | 1 | no | — |
| 293 | C22×C7 | #544 | 1 | 1 | yes | characteristic |
| 294 | C22×C7 | D42 | 1 | 1 | yes | characteristic |
| 295 | C22×C7 | #554 | 1 | 1 | yes | characteristic |
| 296 | C4×C7 | — | 2 | 2 | no | — |
| 297 | C4×C7 | — | 4 | 2 | no | — |
| 298 | C4×C7 | — | 4 | 2 | no | — |
| 299 | C4×C7 | — | 8 | 2 | no | — |
| 300 | C4×C7 | C2×C22⋊Q8 | 1 | 1 | yes | characteristic |
| 301 | C4×C7 | C2×C4⋊Q8 | 1 | 1 | yes | characteristic |
| 302 | C4×C7 | #547 | 1 | 1 | yes | characteristic |
| 303 | C4×C7 | D4×Q8 | 1 | 1 | yes | characteristic |
| 304 | Dic7 | — | 4 | 2 | no | — |
| 305 | Dic7 | — | 4 | 1 | no | — |
| 306 | Dic7 | — | 4 | 1 | no | — |
| 307 | Dic7 | — | 8 | 2 | no | — |
| 308 | #41 | — | 2 | 1 | no | — |
| 309 | #41 | — | 2 | 1 | no | — |
| 310 | #41 | C2×Dic14 | 1 | 2 | yes | — |
| 311 | #41 | Q8×D7 | 1 | 2 | yes | — |
| 312 | C2×Q8 | — | 28 | 2 | no | — |
| 313 | C2×Q8 | D4×D7 | 1 | 1 | yes | characteristic |
| 314 | C2×D4 | — | 2 | 1 | no | — |
| 315 | C2×D4 | D4×D7 | 1 | 1 | yes | characteristic |
| 316 | C22×C4 | — | 2 | 1 | no | — |
| 317 | C22×C4 | — | 2 | 2 | no | — |
| 318 | C22×C4 | — | 4 | 2 | no | — |
| 319 | C22×C4 | — | 14 | 1 | no | — |
| 320 | C22×C4 | — | 14 | 2 | no | — |
| 321 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 322 | M16 | — | 2 | 1 | no | — |
| 323 | M16 | — | 2 | 4 | no | — |
| 324 | M16 | — | 7 | 2 | no | — |
| 325 | M16 | — | 14 | 1 | no | — |
| 326 | M16 | — | 14 | 2 | no | — |
| 327 | M16 | — | 14 | 2 | no | — |
| 328 | M16 | C2×Dic14 | 1 | 2 | yes | — |
| 329 | C2×C8 | — | 2 | 1 | no | — |
| 330 | C2×C8 | — | 2 | 4 | no | — |
| 331 | C2×C8 | — | 7 | 1 | no | — |
| 332 | C2×C8 | — | 7 | 1 | no | — |
| 333 | C2×C8 | — | 14 | 1 | no | — |
| 334 | C2×C8 | — | 14 | 1 | no | — |
| 335 | C2×C8 | — | 14 | 1 | no | — |
| 336 | C2×C8 | — | 14 | 2 | no | — |
| 337 | C2×C8 | C2×Dic14 | 1 | 2 | yes | — |
| 338 | C2×C8 | #1157 | 1 | 2 | yes | — |
| 339 | C2×C8 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 340 | C2×C8 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 341 | C4⋊C4 | — | 2 | 2 | no | — |
| 342 | C4⋊C4 | — | 2 | 2 | no | — |
| 343 | C4⋊C4 | — | 4 | 2 | no | — |
| 344 | C4⋊C4 | — | 7 | 1 | no | — |
| 345 | C4⋊C4 | — | 7 | 1 | no | — |
| 346 | C4⋊C4 | — | 14 | 2 | no | — |
| 347 | C4⋊C4 | — | 14 | 2 | no | — |
| 348 | C4⋊C4 | — | 28 | 2 | no | — |
| 349 | C4⋊C4 | — | 28 | 2 | no | — |
| 350 | C4⋊C4 | — | 28 | 2 | no | — |
| 351 | C4⋊C4 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 352 | C4⋊C4 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 353 | C22⋊C4 | — | 2 | 2 | no | — |
| 354 | C22⋊C4 | — | 4 | 2 | no | — |
| 355 | C22⋊C4 | — | 14 | 1 | no | — |
| 356 | C42 | — | 2 | 2 | no | — |
| 357 | C42 | — | 4 | 2 | no | — |
| 358 | C42 | — | 7 | 2 | no | — |
| 359 | C42 | — | 14 | 1 | no | — |
| 360 | C42 | — | 14 | 1 | no | — |
| 361 | C2×C7 | — | 2 | 1 | no | — |
| 362 | C2×C7 | — | 2 | 1 | no | — |
| 363 | C2×C7 | — | 4 | 2 | no | — |
| 364 | C2×C7 | #2440 | 1 | 1 | yes | characteristic |
| 365 | C2×C7 | #3290 | 1 | 1 | yes | characteristic |
| 366 | C2×C7 | #3290 | 1 | 1 | yes | characteristic |
| 367 | C23 | — | 2 | 1 | no | — |
| 368 | C23 | #6548 | 1 | 1 | yes | characteristic |
| 369 | Q8 | — | 2 | 1 | no | — |
| 370 | Q8 | — | 112 | 2 | no | — |
| 371 | Q8 | #6451 | 1 | 2 | yes | — |
| 372 | D4 | — | 2 | 2 | no | — |
| 373 | D4 | — | 2 | 2 | no | — |
| 374 | D4 | — | 2 | 1 | no | — |
| 375 | D4 | #6451 | 1 | 2 | yes | — |
| 376 | C2×C4 | — | 2 | 1 | no | — |
| 377 | C2×C4 | — | 2 | 2 | no | — |
| 378 | C2×C4 | — | 2 | 2 | no | — |
| 379 | C2×C4 | — | 2 | 2 | no | — |
| 380 | C2×C4 | — | 2 | 2 | no | — |
| 381 | C2×C4 | — | 4 | 2 | no | — |
| 382 | C2×C4 | — | 8 | 2 | no | — |
| 383 | C2×C4 | — | 14 | 2 | no | — |
| 384 | C2×C4 | — | 14 | 1 | no | — |
| 385 | C2×C4 | — | 14 | 1 | no | — |
| 386 | C2×C4 | — | 16 | 2 | no | — |
| 387 | C2×C4 | — | 28 | 1 | no | — |
| 388 | C2×C4 | — | 28 | 1 | no | — |
| 389 | C2×C4 | — | 28 | 2 | no | — |
| 390 | C2×C4 | — | 56 | 2 | no | — |
| 391 | C2×C4 | C22×Dic14 | 1 | 1 | yes | characteristic |
| 392 | C2×C4 | C2×#1157 | 1 | 1 | yes | characteristic |
| 393 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 394 | C2×C4 | C2×Q8×D7 | 1 | 1 | yes | characteristic |
| 395 | C2×C4 | #6551 | 1 | 1 | yes | characteristic |
| 396 | C2×C4 | C22×C22⋊D7 | 1 | 1 | yes | characteristic |
| 397 | C8 | — | 2 | 2 | no | — |
| 398 | C8 | — | 14 | 1 | no | — |
| 399 | C8 | — | 14 | 1 | no | — |
| 400 | C8 | — | 14 | 2 | no | — |
| 401 | C8 | — | 28 | 2 | no | — |
| 402 | C8 | #6487 | 1 | 2 | yes | — |
| 403 | C8 | #6487 | 1 | 2 | yes | — |
| 404 | C7 | #26082 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 405 | C22 | — | 2 | 1 | no | — |
| 406 | C22 | — | 2 | 1 | no | — |
| 407 | C22 | — | 2 | 2 | no | — |
| 408 | C22 | — | 4 | 1 | no | — |
| 409 | C22 | — | 4 | 1 | no | — |
| 410 | C22 | #90191 | 1 | 1 | yes | characteristic |
| 411 | C22 | #90202 | 1 | 1 | yes | characteristic |
| 412 | C22 | D4×C22⋊D7 | 1 | 1 | yes | characteristic |
| 413 | C4 | — | 2 | 2 | no | — |
| 414 | C4 | — | 4 | 2 | no | — |
| 415 | C4 | — | 4 | 2 | no | — |
| 416 | C4 | — | 8 | 2 | no | — |
| 417 | C4 | — | 28 | 2 | no | — |
| 418 | C4 | — | 28 | 1 | no | — |
| 419 | C4 | — | 28 | 1 | no | — |
| 420 | C4 | — | 56 | 2 | no | — |
| 421 | C4 | C2×#6451 | 1 | 1 | yes | characteristic |
| 422 | C4 | #90198 | 1 | 1 | yes | characteristic |
| 423 | C4 | C2×#6487 | 1 | 1 | yes | characteristic |
| 424 | C4 | Q8×C22⋊D7 | 1 | 1 | yes | characteristic |
| 425 | C2 | — | 2 | 1 | no | — |
| 426 | C2 | — | 2 | 1 | no | — |
| 427 | C2 | — | 4 | 2 | no | — |
| 428 | C2 | #11739616 | 1 | 1 | yes | characteristic |
| 429 | C2 | #11741456 | 1 | 1 | yes | characteristic |
| 430 | C2 | #11741465 | 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