← #14223479
Subgroups — #14223479
Order 1792.
1762 conjugacy classes of subgroups.
The subgroup lattice has 370 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C7×#3504 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11742897 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #11740918 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #11740917 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #11740787 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #11740784 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #11740460 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C2×#89836 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #11740007 | C2 | 1 | 2 | yes | maximal |
| 10 | #11740006 | C2 | 1 | 2 | yes | maximal |
| 11 | C4×#6511 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C7×#557 | — | 2 | 2 | no | — |
| 13 | C7×#554 | — | 2 | 6 | no | — |
| 14 | C7×#544 | C22 | 1 | 6 | yes | — |
| 15 | C7×#533 | C22 | 1 | 3 | yes | — |
| 16 | C2×C7×#125 | C22 | 1 | 3 | yes | — |
| 17 | C7×#520 | C22 | 1 | 2 | yes | — |
| 18 | C4×C7×#41 | C22 | 1 | 1 | yes | characteristic |
| 19 | #90518 | C22 | 1 | 2 | yes | — |
| 20 | C2×#6511 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#6511 | C22 | 1 | 1 | yes | characteristic |
| 22 | #90260 | — | 2 | 2 | no | — |
| 23 | #90230 | — | 2 | 6 | no | — |
| 24 | #90210 | C22 | 1 | 6 | yes | — |
| 25 | #90161 | C22 | 1 | 3 | yes | — |
| 26 | C2×#6433 | C22 | 1 | 3 | yes | — |
| 27 | #89852 | C22 | 1 | 12 | yes | — |
| 28 | #89851 | C22 | 1 | 6 | yes | — |
| 29 | #89850 | C22 | 1 | 6 | yes | — |
| 30 | #89837 | C22 | 1 | 12 | yes | — |
| 31 | #89836 | C22 | 1 | 3 | yes | — |
| 32 | #89836 | C22 | 1 | 6 | yes | — |
| 33 | #89836 | C22 | 1 | 6 | yes | — |
| 34 | #89836 | C22 | 1 | 6 | yes | — |
| 35 | #89836 | C22 | 1 | 3 | yes | — |
| 36 | #89836 | C22 | 1 | 1 | yes | characteristic |
| 37 | #89836 | C22 | 1 | 3 | yes | — |
| 38 | #89770 | C22 | 1 | 6 | yes | — |
| 39 | #89770 | C22 | 1 | 6 | yes | — |
| 40 | #89769 | C22 | 1 | 3 | yes | — |
| 41 | #89769 | C22 | 1 | 3 | yes | — |
| 42 | #89767 | C22 | 1 | 6 | yes | — |
| 43 | #89767 | C22 | 1 | 6 | yes | — |
| 44 | #89736 | C22 | 1 | 6 | yes | — |
| 45 | #89736 | C22 | 1 | 6 | yes | — |
| 46 | C2×#6382 | C22 | 1 | 6 | yes | — |
| 47 | C2×#6381 | C22 | 1 | 6 | yes | — |
| 48 | C4×#1136 | C22 | 1 | 3 | yes | — |
| 49 | C2×C4×C7⋊C8 | C22 | 1 | 3 | yes | — |
| 50 | #60666 | — | 7 | 1 | no | maximal, Sylow |
| 51 | C2×C7×#41 | C23 | 1 | 1 | yes | characteristic |
| 52 | C7×C4⋊Q8 | — | 2 | 6 | no | — |
| 53 | C7×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 54 | C7×#125 | — | 2 | 6 | no | — |
| 55 | C7×#125 | — | 2 | 6 | no | — |
| 56 | C7×#125 | C23 | 1 | 3 | yes | — |
| 57 | C7×#125 | C23 | 1 | 6 | yes | — |
| 58 | C7×#125 | C23 | 1 | 1 | yes | characteristic |
| 59 | C7×C22⋊Q8 | — | 2 | 6 | no | — |
| 60 | C7×C22⋊Q8 | — | 2 | 12 | no | — |
| 61 | C4×C7×Q8 | — | 2 | 2 | no | — |
| 62 | C4×C7×Q8 | — | 2 | 6 | no | — |
| 63 | C4×C7×Q8 | D4 | 1 | 2 | yes | — |
| 64 | C4×C7×D4 | — | 2 | 6 | no | — |
| 65 | C4×C7×D4 | D4 | 1 | 6 | yes | — |
| 66 | C7×#117 | C23 | 1 | 6 | yes | — |
| 67 | C7×#117 | C23 | 1 | 3 | yes | — |
| 68 | C2×C7×C4⋊C4 | — | 2 | 6 | no | — |
| 69 | C2×C7×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 70 | C2×C42×C7 | C23 | 1 | 3 | yes | — |
| 71 | #6511 | Q8 | 1 | 8 | yes | complemented |
| 72 | #6511 | Q8 | 1 | 8 | yes | complemented |
| 73 | Q8×Dic7 | — | 2 | 2 | no | — |
| 74 | D4×Dic7 | — | 2 | 6 | no | — |
| 75 | #6489 | C23 | 1 | 6 | yes | — |
| 76 | C2×C4⋊Dic7 | C23 | 1 | 6 | yes | — |
| 77 | #6487 | — | 2 | 6 | no | — |
| 78 | C2×Dic7⋊C4 | — | 2 | 6 | no | — |
| 79 | C2×#1136 | C23 | 1 | 3 | yes | — |
| 80 | C2×#1136 | C23 | 1 | 3 | yes | — |
| 81 | C22×C7⋊C8 | C23 | 1 | 3 | yes | — |
| 82 | C22×C7⋊C8 | C23 | 1 | 3 | yes | — |
| 83 | #6453 | — | 2 | 6 | no | — |
| 84 | #6451 | — | 2 | 6 | no | — |
| 85 | #6441 | — | 2 | 12 | no | — |
| 86 | #6433 | — | 2 | 6 | no | — |
| 87 | #6433 | C23 | 1 | 3 | yes | — |
| 88 | #6433 | C23 | 1 | 6 | yes | — |
| 89 | #6433 | C23 | 1 | 1 | yes | characteristic |
| 90 | #6432 | C23 | 1 | 6 | yes | — |
| 91 | C4×Dic14 | — | 2 | 6 | no | — |
| 92 | #6382 | C23 | 1 | 6 | yes | — |
| 93 | #6382 | C23 | 1 | 12 | yes | — |
| 94 | #6382 | C23 | 1 | 6 | yes | — |
| 95 | #6382 | C23 | 1 | 6 | yes | — |
| 96 | #6382 | C23 | 1 | 2 | yes | — |
| 97 | #6381 | C23 | 1 | 6 | yes | — |
| 98 | #6381 | C23 | 1 | 12 | yes | — |
| 99 | #6381 | C23 | 1 | 6 | yes | — |
| 100 | #6381 | C23 | 1 | 6 | yes | — |
| 101 | #6381 | C23 | 1 | 2 | yes | — |
| 102 | #6377 | C23 | 1 | 6 | yes | — |
| 103 | C4×C7⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 104 | C4×C7⋊C8 | C23 | 1 | 3 | yes | — |
| 105 | C4×C7⋊C8 | C23 | 1 | 3 | yes | — |
| 106 | C4×C7⋊C8 | C23 | 1 | 3 | yes | — |
| 107 | #3504 | — | 7 | 1 | no | — |
| 108 | #3504 | D7 | 1 | 1 | yes | characteristic |
| 109 | #3166 | — | 7 | 3 | no | — |
| 110 | #3166 | — | 7 | 3 | no | — |
| 111 | #3164 | — | 7 | 6 | no | — |
| 112 | #3163 | — | 7 | 6 | no | — |
| 113 | #3160 | — | 7 | 3 | no | — |
| 114 | C2×#499 | — | 7 | 3 | no | — |
| 115 | #2913 | — | 7 | 2 | no | — |
| 116 | #2912 | — | 7 | 2 | no | — |
| 117 | C4×#131 | — | 7 | 1 | no | — |
| 118 | C7×#41 | C2×Q8 | 1 | 4 | yes | — |
| 119 | C7×#41 | C2×Q8 | 1 | 4 | yes | — |
| 120 | C2×C7×Q8 | — | 2 | 6 | no | — |
| 121 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | C2×C7×D4 | C2×D4 | 1 | 3 | yes | — |
| 123 | C22×C4×C7 | — | 2 | 6 | no | — |
| 124 | C22×C4×C7 | C2×D4 | 1 | 6 | yes | — |
| 125 | C22×C4×C7 | C24 | 1 | 3 | yes | — |
| 126 | C22×Dic7 | — | 2 | 6 | no | — |
| 127 | C2×Dic14 | — | 2 | 6 | no | — |
| 128 | C7×C4⋊C4 | — | 2 | 6 | no | — |
| 129 | C7×C4⋊C4 | — | 2 | 12 | no | — |
| 130 | C7×C4⋊C4 | — | 2 | 6 | no | — |
| 131 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 132 | C7×C4⋊C4 | — | 2 | 6 | no | — |
| 133 | C7×C4⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 134 | C7×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 135 | C7×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 136 | C7×C22⋊C4 | — | 2 | 6 | no | — |
| 137 | C7×C22⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 138 | C42×C7 | — | 2 | 6 | no | — |
| 139 | C42×C7 | C2×D4 | 1 | 6 | yes | — |
| 140 | C42×C7 | C24 | 1 | 3 | yes | — |
| 141 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 142 | C22⋊Dic7 | — | 2 | 6 | no | — |
| 143 | C4⋊Dic7 | — | 2 | 6 | no | — |
| 144 | C4⋊Dic7 | — | 2 | 6 | no | — |
| 145 | C4⋊Dic7 | C24 | 1 | 2 | yes | — |
| 146 | C4⋊Dic7 | C24 | 1 | 6 | yes | — |
| 147 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 148 | Dic7⋊C4 | — | 2 | 6 | no | — |
| 149 | Dic7⋊C4 | — | 2 | 12 | no | — |
| 150 | C4×Dic7 | — | 2 | 6 | no | — |
| 151 | #1136 | C2×Q8 | 1 | 12 | yes | — |
| 152 | #1136 | C2×Q8 | 1 | 12 | yes | — |
| 153 | C2×C7⋊C8 | C2×Q8 | 1 | 12 | yes | — |
| 154 | C2×C7⋊C8 | C2×Q8 | 1 | 12 | yes | — |
| 155 | C2×C7⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 156 | C2×C7⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 157 | C2×C7⋊C8 | C24 | 1 | 3 | yes | — |
| 158 | C2×C7⋊C8 | C24 | 1 | 3 | yes | — |
| 159 | C2×#131 | — | 7 | 1 | no | — |
| 160 | C2×#131 | — | 7 | 1 | no | — |
| 161 | #557 | — | 2 | 2 | no | — |
| 162 | #557 | — | 14 | 2 | no | — |
| 163 | #554 | — | 2 | 6 | no | — |
| 164 | #554 | — | 14 | 6 | no | — |
| 165 | #544 | — | 7 | 6 | no | — |
| 166 | #544 | C2×D7 | 1 | 6 | yes | — |
| 167 | #533 | — | 7 | 3 | no | — |
| 168 | #533 | C2×D7 | 1 | 3 | yes | — |
| 169 | C2×#125 | — | 7 | 3 | no | — |
| 170 | C2×#125 | C2×D7 | 1 | 3 | yes | — |
| 171 | #520 | — | 7 | 2 | no | — |
| 172 | #520 | C2×D7 | 1 | 2 | yes | — |
| 173 | C4×#41 | C2×D7 | 1 | 1 | yes | characteristic |
| 174 | #501 | — | 7 | 12 | no | — |
| 175 | #501 | — | 7 | 12 | no | — |
| 176 | #500 | — | 7 | 6 | no | — |
| 177 | #499 | — | 7 | 3 | no | — |
| 178 | #499 | — | 7 | 6 | no | — |
| 179 | #499 | — | 7 | 6 | no | — |
| 180 | #499 | — | 7 | 6 | no | — |
| 181 | #499 | — | 7 | 1 | no | — |
| 182 | #499 | — | 7 | 3 | no | — |
| 183 | #499 | — | 7 | 3 | no | — |
| 184 | #498 | — | 7 | 6 | no | — |
| 185 | #428 | — | 7 | 6 | no | — |
| 186 | #428 | — | 7 | 6 | no | — |
| 187 | #428 | — | 7 | 6 | no | — |
| 188 | #428 | — | 7 | 6 | no | — |
| 189 | #427 | — | 7 | 6 | no | — |
| 190 | #427 | — | 7 | 6 | no | — |
| 191 | C2×#107 | — | 7 | 6 | no | — |
| 192 | C2×#106 | — | 7 | 6 | no | — |
| 193 | #405 | — | 7 | 3 | no | — |
| 194 | #405 | — | 7 | 3 | no | — |
| 195 | C4×M16 | — | 7 | 3 | no | — |
| 196 | C2×C4×C8 | — | 7 | 3 | no | — |
| 197 | C23×C7 | C22×D4 | 1 | 3 | yes | — |
| 198 | C7×Q8 | — | 8 | 6 | no | — |
| 199 | C7×Q8 | C4⋊Q8 | 1 | 4 | yes | — |
| 200 | C7×D4 | C4⋊Q8 | 1 | 12 | yes | — |
| 201 | C2×C4×C7 | — | 2 | 2 | no | — |
| 202 | C2×C4×C7 | — | 2 | 6 | no | — |
| 203 | C2×C4×C7 | — | 4 | 6 | no | — |
| 204 | C2×C4×C7 | — | 8 | 6 | no | — |
| 205 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 206 | C2×C4×C7 | C22×D4 | 1 | 6 | yes | — |
| 207 | C2×C4×C7 | C22×D4 | 1 | 3 | yes | — |
| 208 | C2×C4×C7 | C22×Q8 | 1 | 6 | yes | — |
| 209 | C2×C4×C7 | C22×Q8 | 1 | 6 | yes | — |
| 210 | C2×C4×C7 | C25 | 1 | 1 | yes | characteristic |
| 211 | C2×Dic7 | — | 2 | 2 | no | — |
| 212 | C2×Dic7 | — | 2 | 6 | no | — |
| 213 | C2×Dic7 | — | 8 | 6 | no | — |
| 214 | Dic14 | — | 8 | 6 | no | — |
| 215 | C7⋊C8 | C22×Q8 | 1 | 2 | yes | — |
| 216 | C7⋊C8 | C22×Q8 | 1 | 2 | yes | — |
| 217 | C7⋊C8 | C22×Q8 | 1 | 6 | yes | — |
| 218 | C7⋊C8 | C22×Q8 | 1 | 6 | yes | — |
| 219 | C2×#41 | C22×D7 | 1 | 1 | yes | characteristic |
| 220 | #131 | — | 7 | 8 | no | — |
| 221 | #131 | — | 7 | 8 | no | — |
| 222 | C2×M16 | — | 7 | 3 | no | — |
| 223 | C2×M16 | — | 7 | 3 | no | — |
| 224 | C22×C8 | — | 7 | 3 | no | — |
| 225 | C22×C8 | — | 7 | 3 | no | — |
| 226 | C4⋊Q8 | — | 2 | 6 | no | — |
| 227 | C4⋊Q8 | — | 7 | 6 | no | — |
| 228 | C4⋊Q8 | — | 14 | 6 | no | — |
| 229 | C4⋊Q8 | C22×D7 | 1 | 6 | yes | — |
| 230 | #125 | — | 2 | 6 | no | — |
| 231 | #125 | — | 2 | 6 | no | — |
| 232 | #125 | — | 7 | 3 | no | — |
| 233 | #125 | — | 7 | 6 | no | — |
| 234 | #125 | — | 7 | 1 | no | — |
| 235 | #125 | — | 14 | 6 | no | — |
| 236 | #125 | — | 14 | 6 | no | — |
| 237 | #125 | C22×D7 | 1 | 3 | yes | — |
| 238 | #125 | C22×D7 | 1 | 6 | yes | — |
| 239 | #125 | C22×D7 | 1 | 1 | yes | characteristic |
| 240 | C22⋊Q8 | — | 2 | 6 | no | — |
| 241 | C22⋊Q8 | — | 2 | 12 | no | — |
| 242 | C22⋊Q8 | — | 14 | 6 | no | — |
| 243 | C22⋊Q8 | — | 14 | 12 | no | — |
| 244 | C4×Q8 | — | 2 | 2 | no | — |
| 245 | C4×Q8 | — | 2 | 6 | no | — |
| 246 | C4×Q8 | — | 14 | 2 | no | — |
| 247 | C4×Q8 | — | 14 | 6 | no | — |
| 248 | C4×Q8 | C22⋊D7 | 1 | 2 | yes | — |
| 249 | C4×D4 | — | 2 | 6 | no | — |
| 250 | C4×D4 | — | 14 | 6 | no | — |
| 251 | C4×D4 | C22⋊D7 | 1 | 6 | yes | — |
| 252 | #117 | — | 7 | 6 | no | — |
| 253 | #117 | C22×D7 | 1 | 6 | yes | — |
| 254 | #117 | C22×D7 | 1 | 3 | yes | — |
| 255 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 256 | C2×C4⋊C4 | — | 7 | 6 | no | — |
| 257 | C2×C4⋊C4 | — | 14 | 6 | no | — |
| 258 | C2×C4⋊C4 | C22×D7 | 1 | 6 | yes | — |
| 259 | C2×C42 | C22×D7 | 1 | 3 | yes | — |
| 260 | #107 | — | 7 | 6 | no | — |
| 261 | #107 | — | 7 | 12 | no | — |
| 262 | #107 | — | 7 | 2 | no | — |
| 263 | #107 | — | 7 | 6 | no | — |
| 264 | #107 | — | 7 | 6 | no | — |
| 265 | #106 | — | 7 | 6 | no | — |
| 266 | #106 | — | 7 | 12 | no | — |
| 267 | #106 | — | 7 | 2 | no | — |
| 268 | #106 | — | 7 | 6 | no | — |
| 269 | #106 | — | 7 | 6 | no | — |
| 270 | #97 | — | 7 | 6 | no | — |
| 271 | C4×C8 | — | 7 | 1 | no | — |
| 272 | C4×C8 | — | 7 | 3 | no | — |
| 273 | C4×C8 | — | 7 | 3 | no | — |
| 274 | C4×C8 | — | 7 | 3 | no | — |
| 275 | C22×C7 | — | 2 | 6 | no | — |
| 276 | C22×C7 | C2×C4⋊Q8 | 1 | 6 | yes | — |
| 277 | C22×C7 | C23×D4 | 1 | 1 | yes | characteristic |
| 278 | C4×C7 | — | 2 | 6 | no | — |
| 279 | C4×C7 | — | 2 | 2 | no | — |
| 280 | C4×C7 | — | 4 | 6 | no | — |
| 281 | C4×C7 | — | 4 | 2 | no | — |
| 282 | C4×C7 | C2×C4⋊Q8 | 1 | 6 | yes | — |
| 283 | C4×C7 | C23×Q8 | 1 | 1 | yes | characteristic |
| 284 | C4×C7 | C23×Q8 | 1 | 1 | yes | characteristic |
| 285 | Dic7 | — | 4 | 2 | no | — |
| 286 | Dic7 | — | 4 | 6 | no | — |
| 287 | #41 | Q8×D7 | 1 | 4 | yes | — |
| 288 | #41 | Q8×D7 | 1 | 4 | yes | — |
| 289 | C2×Q8 | — | 2 | 6 | no | — |
| 290 | C2×Q8 | — | 14 | 6 | no | — |
| 291 | C2×Q8 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 292 | C2×D4 | C2×C22⋊D7 | 1 | 3 | yes | — |
| 293 | C22×C4 | — | 2 | 6 | no | — |
| 294 | C22×C4 | — | 14 | 6 | no | — |
| 295 | C22×C4 | C2×C22⋊D7 | 1 | 6 | yes | — |
| 296 | C22×C4 | C23×D7 | 1 | 3 | yes | — |
| 297 | M16 | — | 7 | 12 | no | — |
| 298 | M16 | — | 7 | 12 | no | — |
| 299 | C2×C8 | — | 7 | 12 | no | — |
| 300 | C2×C8 | — | 7 | 12 | no | — |
| 301 | C2×C8 | — | 7 | 1 | no | — |
| 302 | C2×C8 | — | 7 | 1 | no | — |
| 303 | C2×C8 | — | 7 | 3 | no | — |
| 304 | C2×C8 | — | 7 | 3 | no | — |
| 305 | C4⋊C4 | — | 2 | 6 | no | — |
| 306 | C4⋊C4 | — | 2 | 12 | no | — |
| 307 | C4⋊C4 | — | 2 | 6 | no | — |
| 308 | C4⋊C4 | — | 2 | 2 | no | — |
| 309 | C4⋊C4 | — | 2 | 6 | no | — |
| 310 | C4⋊C4 | — | 7 | 6 | no | — |
| 311 | C4⋊C4 | — | 7 | 2 | no | — |
| 312 | C4⋊C4 | — | 14 | 6 | no | — |
| 313 | C4⋊C4 | — | 14 | 12 | no | — |
| 314 | C4⋊C4 | — | 14 | 2 | no | — |
| 315 | C4⋊C4 | — | 14 | 6 | no | — |
| 316 | C4⋊C4 | — | 14 | 6 | no | — |
| 317 | C4⋊C4 | C2×C22⋊D7 | 1 | 6 | yes | — |
| 318 | C4⋊C4 | C23×D7 | 1 | 6 | yes | — |
| 319 | C4⋊C4 | C23×D7 | 1 | 2 | yes | — |
| 320 | C22⋊C4 | — | 2 | 6 | no | — |
| 321 | C22⋊C4 | — | 14 | 6 | no | — |
| 322 | C22⋊C4 | C2×C22⋊D7 | 1 | 6 | yes | — |
| 323 | C42 | — | 2 | 6 | no | — |
| 324 | C42 | — | 14 | 6 | no | — |
| 325 | C42 | C2×C22⋊D7 | 1 | 6 | yes | — |
| 326 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 327 | C42 | C23×D7 | 1 | 3 | yes | — |
| 328 | C2×C7 | — | 2 | 6 | no | — |
| 329 | C2×C7 | C22×C4⋊Q8 | 1 | 1 | yes | characteristic |
| 330 | C2×C7 | #3584 | 1 | 2 | yes | — |
| 331 | C23 | C22×C22⋊D7 | 1 | 3 | yes | — |
| 332 | Q8 | — | 8 | 6 | no | — |
| 333 | Q8 | — | 56 | 6 | no | — |
| 334 | Q8 | #6507 | 1 | 4 | yes | — |
| 335 | D4 | #6507 | 1 | 12 | yes | — |
| 336 | C2×C4 | — | 2 | 2 | no | — |
| 337 | C2×C4 | — | 2 | 6 | no | — |
| 338 | C2×C4 | — | 4 | 6 | no | — |
| 339 | C2×C4 | — | 8 | 6 | no | — |
| 340 | C2×C4 | — | 14 | 2 | no | — |
| 341 | C2×C4 | — | 14 | 6 | no | — |
| 342 | C2×C4 | — | 56 | 6 | no | — |
| 343 | C2×C4 | C2×Q8×D7 | 1 | 6 | yes | — |
| 344 | C2×C4 | C2×Q8×D7 | 1 | 6 | yes | — |
| 345 | C2×C4 | C22×C22⋊D7 | 1 | 2 | yes | — |
| 346 | C2×C4 | C22×C22⋊D7 | 1 | 6 | yes | — |
| 347 | C2×C4 | C22×C22⋊D7 | 1 | 3 | yes | — |
| 348 | C2×C4 | C24×D7 | 1 | 1 | yes | characteristic |
| 349 | C8 | — | 7 | 2 | no | — |
| 350 | C8 | — | 7 | 2 | no | — |
| 351 | C8 | — | 7 | 6 | no | — |
| 352 | C8 | — | 7 | 6 | no | — |
| 353 | C7 | #60666 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 354 | C22 | — | 2 | 6 | no | — |
| 355 | C22 | C2×#6507 | 1 | 6 | yes | — |
| 356 | C22 | C23×C22⋊D7 | 1 | 1 | yes | characteristic |
| 357 | C4 | — | 2 | 2 | no | — |
| 358 | C4 | — | 2 | 6 | no | — |
| 359 | C4 | — | 4 | 6 | no | — |
| 360 | C4 | — | 4 | 2 | no | — |
| 361 | C4 | — | 28 | 6 | no | — |
| 362 | C4 | — | 28 | 2 | no | — |
| 363 | C4 | C2×#6507 | 1 | 6 | yes | — |
| 364 | C4 | C22×Q8×D7 | 1 | 1 | yes | characteristic |
| 365 | C4 | C22×Q8×D7 | 1 | 1 | yes | characteristic |
| 366 | C2 | — | 2 | 6 | no | — |
| 367 | C2 | C22×#6507 | 1 | 1 | yes | characteristic |
| 368 | C2 | #11744365 | 1 | 2 | yes | — |
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