← #13372804
Subgroups — #13372804
Order 1792.
622 conjugacy classes of subgroups.
The subgroup lattice has 544 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #11736491 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#89600 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | M16×Dic14 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C7×#1950 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #11728449 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #11728449 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #11728446 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | Dic7×#108 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #11728271 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #11728228 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #11727627 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #11726683 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #11726682 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #11726674 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | #11726674 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | C2×C4×Dic14 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C7×#108 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C7×#108 | C22 | 1 | 1 | yes | characteristic |
| 19 | C7×#423 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×C7×C4⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 21 | C4×C7×M16 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#6396 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#6396 | C22 | 1 | 1 | yes | characteristic |
| 24 | #89890 | C22 | 1 | 1 | yes | characteristic |
| 25 | #89890 | C22 | 1 | 1 | yes | characteristic |
| 26 | #89890 | C22 | 1 | 1 | yes | characteristic |
| 27 | #89890 | C22 | 1 | 1 | yes | characteristic |
| 28 | M16×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 29 | M16×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 30 | M16×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 31 | M16×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×#6393 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×#6393 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×#6389 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×Dic7⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 36 | C2×Dic7⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×C8×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 38 | #89696 | C22 | 1 | 1 | yes | characteristic |
| 39 | C4×#1136 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×#6377 | C22 | 1 | 1 | yes | characteristic |
| 41 | #89603 | — | 2 | 1 | no | — |
| 42 | #89602 | — | 2 | 1 | no | — |
| 43 | #89600 | — | 2 | 1 | no | — |
| 44 | #89600 | — | 2 | 1 | no | — |
| 45 | #89600 | C4 | 1 | 2 | yes | — |
| 46 | #89600 | C4 | 1 | 2 | yes | — |
| 47 | #89600 | C4 | 1 | 2 | yes | — |
| 48 | #89600 | C4 | 1 | 2 | yes | — |
| 49 | #89473 | — | 2 | 1 | no | — |
| 50 | #89473 | — | 2 | 1 | no | — |
| 51 | #89451 | — | 2 | 1 | no | — |
| 52 | C8×Dic14 | — | 2 | 1 | no | — |
| 53 | C7×#341 | C22 | 1 | 1 | yes | characteristic |
| 54 | C7×#341 | C22 | 1 | 1 | yes | characteristic |
| 55 | #89353 | C22 | 1 | 1 | yes | characteristic |
| 56 | #89353 | C22 | 1 | 1 | yes | characteristic |
| 57 | #89353 | C22 | 1 | 1 | yes | characteristic |
| 58 | #89353 | C22 | 1 | 1 | yes | characteristic |
| 59 | #89353 | C22 | 1 | 1 | yes | characteristic |
| 60 | #89353 | C22 | 1 | 1 | yes | characteristic |
| 61 | #89347 | C22 | 1 | 1 | yes | characteristic |
| 62 | #89347 | C22 | 1 | 1 | yes | characteristic |
| 63 | #22747 | — | 7 | 1 | no | maximal, Sylow |
| 64 | C22×Dic14 | Q8 | 1 | 1 | yes | characteristic |
| 65 | C2×C7×M16 | C23 | 1 | 1 | yes | characteristic |
| 66 | C2×C7×M16 | C23 | 1 | 1 | yes | characteristic |
| 67 | C2×C7×M16 | C23 | 1 | 1 | yes | characteristic |
| 68 | C2×C7×M16 | C23 | 1 | 1 | yes | characteristic |
| 69 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 70 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 71 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 72 | C2×C4⋊Dic7 | Q8 | 1 | 1 | yes | characteristic |
| 73 | C2×Dic7⋊C4 | Q8 | 1 | 1 | yes | characteristic |
| 74 | C2×Dic7⋊C4 | Q8 | 1 | 1 | yes | characteristic |
| 75 | C2×C4×Dic7 | C23 | 1 | 1 | yes | characteristic |
| 76 | C2×C4×Dic7 | C23 | 1 | 1 | yes | characteristic |
| 77 | C2×#1136 | C23 | 1 | 1 | yes | characteristic |
| 78 | C2×#1136 | C23 | 1 | 1 | yes | characteristic |
| 79 | C2×#1136 | C23 | 1 | 1 | yes | characteristic |
| 80 | C2×#1136 | C23 | 1 | 1 | yes | characteristic |
| 81 | C22×C7⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 82 | C22×C7⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 83 | C4×Dic14 | C2×C4 | 1 | 1 | yes | characteristic |
| 84 | C4×Dic14 | C2×C4 | 1 | 1 | yes | characteristic |
| 85 | C4×Dic14 | C2×C4 | 1 | 1 | yes | characteristic |
| 86 | C4×Dic14 | C2×C4 | 1 | 1 | yes | characteristic |
| 87 | C4×Dic14 | D4 | 1 | 1 | yes | characteristic |
| 88 | C4×Dic14 | D4 | 1 | 1 | yes | characteristic |
| 89 | C4×Dic14 | D4 | 1 | 1 | yes | characteristic |
| 90 | C4×Dic14 | D4 | 1 | 1 | yes | characteristic |
| 91 | C7×#108 | — | 2 | 2 | no | — |
| 92 | C7×#108 | — | 2 | 2 | no | — |
| 93 | C7×C4⋊C8 | — | 2 | 1 | no | — |
| 94 | C7×C4⋊C8 | — | 2 | 1 | no | — |
| 95 | C7×C4⋊C8 | C2×C4 | 1 | 2 | yes | — |
| 96 | C7×C4⋊C8 | C2×C4 | 1 | 2 | yes | — |
| 97 | C7×#97 | — | 2 | 1 | no | — |
| 98 | C4×C7×C8 | — | 2 | 1 | no | — |
| 99 | #6396 | — | 2 | 2 | no | — |
| 100 | #6396 | — | 2 | 2 | no | — |
| 101 | #6393 | — | 2 | 2 | no | — |
| 102 | #6393 | — | 2 | 2 | no | — |
| 103 | #6389 | — | 2 | 1 | no | — |
| 104 | #6389 | — | 2 | 1 | no | — |
| 105 | #6389 | — | 2 | 1 | no | — |
| 106 | #6389 | — | 2 | 1 | no | — |
| 107 | #6389 | C2×C4 | 1 | 2 | yes | — |
| 108 | #6389 | C2×C4 | 1 | 2 | yes | — |
| 109 | Dic7⋊C8 | — | 2 | 1 | no | — |
| 110 | Dic7⋊C8 | — | 2 | 1 | no | — |
| 111 | Dic7⋊C8 | — | 2 | 1 | no | — |
| 112 | Dic7⋊C8 | — | 2 | 1 | no | — |
| 113 | Dic7⋊C8 | — | 2 | 1 | no | — |
| 114 | Dic7⋊C8 | — | 2 | 1 | no | — |
| 115 | Dic7⋊C8 | — | 2 | 1 | no | — |
| 116 | Dic7⋊C8 | — | 2 | 1 | no | — |
| 117 | Dic7⋊C8 | C2×C4 | 1 | 2 | yes | — |
| 118 | Dic7⋊C8 | C2×C4 | 1 | 2 | yes | — |
| 119 | Dic7⋊C8 | C2×C4 | 1 | 2 | yes | — |
| 120 | Dic7⋊C8 | C2×C4 | 1 | 2 | yes | — |
| 121 | C8×Dic7 | — | 2 | 1 | no | — |
| 122 | C8×Dic7 | — | 2 | 1 | no | — |
| 123 | C8×Dic7 | — | 2 | 1 | no | — |
| 124 | C8×Dic7 | — | 2 | 1 | no | — |
| 125 | C8×Dic7 | C2×C4 | 1 | 2 | yes | — |
| 126 | C8×Dic7 | C2×C4 | 1 | 2 | yes | — |
| 127 | C4⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 128 | C4⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 129 | #6377 | — | 2 | 1 | no | — |
| 130 | #6377 | C2×C4 | 1 | 2 | yes | — |
| 131 | #6377 | C2×C4 | 1 | 2 | yes | — |
| 132 | C4×C7⋊C8 | — | 2 | 1 | no | — |
| 133 | Q8×M16 | — | 7 | 1 | no | — |
| 134 | Q8×M16 | — | 7 | 1 | no | — |
| 135 | C2×#446 | — | 7 | 1 | no | — |
| 136 | #1950 | — | 7 | 1 | no | — |
| 137 | #1950 | — | 7 | 1 | no | — |
| 138 | #1950 | — | 7 | 1 | no | — |
| 139 | #1950 | — | 7 | 1 | no | — |
| 140 | #1950 | — | 7 | 1 | no | — |
| 141 | #1950 | D7 | 1 | 1 | yes | characteristic |
| 142 | #1838 | — | 7 | 1 | no | — |
| 143 | #1838 | — | 7 | 1 | no | — |
| 144 | #1837 | — | 7 | 1 | no | — |
| 145 | #1778 | — | 7 | 1 | no | — |
| 146 | #1778 | — | 7 | 1 | no | — |
| 147 | C4×#108 | — | 7 | 1 | no | — |
| 148 | C22×C4×C7 | C2×Q8 | 1 | 1 | yes | characteristic |
| 149 | C22×C4×C7 | C2×Q8 | 1 | 1 | yes | characteristic |
| 150 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 151 | C22×Dic7 | C2×Q8 | 1 | 1 | yes | characteristic |
| 152 | C22×Dic7 | C2×Q8 | 1 | 1 | yes | characteristic |
| 153 | C22×Dic7 | C2×Q8 | 1 | 1 | yes | characteristic |
| 154 | C22×Dic7 | C2×Q8 | 1 | 1 | yes | characteristic |
| 155 | C2×Dic14 | — | 4 | 2 | no | — |
| 156 | C2×Dic14 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 157 | C2×Dic14 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 158 | C2×Dic14 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 159 | C2×Dic14 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 160 | C7×M16 | — | 2 | 1 | no | — |
| 161 | C7×M16 | — | 2 | 1 | no | — |
| 162 | C7×M16 | — | 2 | 1 | no | — |
| 163 | C7×M16 | — | 2 | 1 | no | — |
| 164 | C7×M16 | — | 2 | 1 | no | — |
| 165 | C7×M16 | — | 2 | 1 | no | — |
| 166 | C7×M16 | — | 2 | 1 | no | — |
| 167 | C7×M16 | #41 | 1 | 2 | yes | — |
| 168 | C2×C7×C8 | — | 2 | 1 | no | — |
| 169 | C2×C7×C8 | — | 2 | 1 | no | — |
| 170 | C2×C7×C8 | — | 2 | 1 | no | — |
| 171 | C2×C7×C8 | — | 2 | 1 | no | — |
| 172 | C2×C7×C8 | — | 2 | 1 | no | — |
| 173 | C2×C7×C8 | — | 2 | 1 | no | — |
| 174 | C2×C7×C8 | — | 2 | 1 | no | — |
| 175 | C2×C7×C8 | — | 2 | 1 | no | — |
| 176 | C2×C7×C8 | C22×C4 | 1 | 2 | yes | — |
| 177 | C2×C7×C8 | C22×C4 | 1 | 2 | yes | — |
| 178 | C42×C7 | C22×C4 | 1 | 1 | yes | characteristic |
| 179 | C42×C7 | C22×C4 | 1 | 1 | yes | characteristic |
| 180 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 182 | C4⋊Dic7 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 183 | C4⋊Dic7 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 184 | C4⋊Dic7 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 185 | C4⋊Dic7 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 186 | Dic7⋊C4 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 187 | Dic7⋊C4 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 188 | Dic7⋊C4 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 189 | Dic7⋊C4 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 190 | Dic7⋊C4 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 191 | Dic7⋊C4 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 192 | Dic7⋊C4 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 193 | Dic7⋊C4 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 194 | C4×Dic7 | C22×C4 | 1 | 1 | yes | characteristic |
| 195 | C4×Dic7 | C22×C4 | 1 | 1 | yes | characteristic |
| 196 | C4×Dic7 | C22×C4 | 1 | 1 | yes | characteristic |
| 197 | C4×Dic7 | C22×C4 | 1 | 1 | yes | characteristic |
| 198 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 199 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 200 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 201 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 202 | #1136 | — | 2 | 1 | no | — |
| 203 | #1136 | — | 2 | 1 | no | — |
| 204 | #1136 | — | 2 | 1 | no | — |
| 205 | #1136 | — | 2 | 1 | no | — |
| 206 | #1136 | — | 2 | 1 | no | — |
| 207 | #1136 | — | 2 | 1 | no | — |
| 208 | #1136 | — | 2 | 1 | no | — |
| 209 | #1136 | #41 | 1 | 2 | yes | — |
| 210 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 211 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 212 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 213 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 214 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 215 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 216 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 217 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 218 | C2×C7⋊C8 | C22×C4 | 1 | 2 | yes | — |
| 219 | C2×C7⋊C8 | C22×C4 | 1 | 2 | yes | — |
| 220 | C2×C4×Q8 | — | 7 | 1 | no | — |
| 221 | #446 | — | 7 | 2 | no | — |
| 222 | #446 | — | 7 | 2 | no | — |
| 223 | #446 | — | 7 | 2 | no | — |
| 224 | #446 | — | 7 | 2 | no | — |
| 225 | #446 | — | 14 | 1 | no | — |
| 226 | #446 | — | 14 | 1 | no | — |
| 227 | #446 | — | 14 | 1 | no | — |
| 228 | #446 | — | 14 | 1 | no | — |
| 229 | #446 | — | 14 | 1 | no | — |
| 230 | #446 | — | 14 | 1 | no | — |
| 231 | C8×Q8 | — | 14 | 1 | no | — |
| 232 | C8×Q8 | — | 14 | 1 | no | — |
| 233 | C2×#108 | — | 7 | 1 | no | — |
| 234 | C2×#108 | — | 7 | 1 | no | — |
| 235 | C2×#108 | — | 7 | 1 | no | — |
| 236 | C2×#108 | — | 7 | 1 | no | — |
| 237 | C2×#108 | C2×D7 | 1 | 1 | yes | characteristic |
| 238 | C2×#108 | C2×D7 | 1 | 1 | yes | characteristic |
| 239 | #423 | — | 7 | 1 | no | — |
| 240 | #423 | — | 7 | 1 | no | — |
| 241 | #423 | — | 7 | 1 | no | — |
| 242 | #423 | — | 7 | 1 | no | — |
| 243 | #423 | — | 7 | 1 | no | — |
| 244 | #423 | C2×D7 | 1 | 1 | yes | characteristic |
| 245 | C2×C4⋊C8 | — | 7 | 1 | no | — |
| 246 | C2×C4⋊C8 | — | 7 | 1 | no | — |
| 247 | C2×C4⋊C8 | C2×D7 | 1 | 1 | yes | characteristic |
| 248 | C4×M16 | — | 7 | 1 | no | — |
| 249 | C4×M16 | — | 7 | 1 | no | — |
| 250 | C4×M16 | — | 7 | 1 | no | — |
| 251 | C4×M16 | — | 7 | 1 | no | — |
| 252 | C4×M16 | — | 7 | 1 | no | — |
| 253 | C4×M16 | C2×D7 | 1 | 1 | yes | characteristic |
| 254 | C2×#97 | — | 7 | 1 | no | — |
| 255 | C2×#97 | — | 7 | 1 | no | — |
| 256 | C2×C4×C8 | — | 7 | 1 | no | — |
| 257 | #341 | — | 7 | 1 | no | — |
| 258 | #341 | — | 7 | 1 | no | — |
| 259 | #341 | — | 7 | 1 | no | — |
| 260 | #341 | — | 7 | 1 | no | — |
| 261 | #341 | — | 7 | 1 | no | — |
| 262 | #341 | — | 7 | 1 | no | — |
| 263 | #341 | — | 7 | 1 | no | — |
| 264 | #341 | — | 7 | 1 | no | — |
| 265 | #341 | C2×D7 | 1 | 1 | yes | characteristic |
| 266 | #341 | C2×D7 | 1 | 1 | yes | characteristic |
| 267 | C23×C7 | C22×Q8 | 1 | 1 | yes | characteristic |
| 268 | C2×C4×C7 | — | 4 | 1 | no | — |
| 269 | C2×C4×C7 | — | 4 | 1 | no | — |
| 270 | C2×C4×C7 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 271 | C2×C4×C7 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 272 | C2×C4×C7 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 273 | C2×C4×C7 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 274 | C2×C4×C7 | C23×C4 | 1 | 1 | yes | characteristic |
| 275 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 276 | C2×C4×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 277 | C2×C4×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 278 | C2×C4×C7 | 2−1+4 | 1 | 1 | yes | characteristic |
| 279 | C2×C4×C7 | 2−1+4 | 1 | 1 | yes | characteristic |
| 280 | C2×Dic7 | — | 2 | 2 | no | — |
| 281 | C2×Dic7 | — | 4 | 1 | no | — |
| 282 | C2×Dic7 | — | 4 | 1 | no | — |
| 283 | C2×Dic7 | — | 4 | 1 | no | — |
| 284 | C2×Dic7 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 285 | C2×Dic7 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 286 | C2×Dic7 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 287 | C2×Dic7 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 288 | C2×Dic7 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 289 | C2×Dic7 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 290 | C2×Dic7 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 291 | C2×Dic7 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 292 | Dic14 | — | 2 | 2 | no | — |
| 293 | Dic14 | — | 2 | 2 | no | — |
| 294 | Dic14 | — | 4 | 1 | no | — |
| 295 | Dic14 | — | 4 | 1 | no | — |
| 296 | C7×C8 | — | 2 | 2 | no | — |
| 297 | C7×C8 | — | 2 | 2 | no | — |
| 298 | C7×C8 | — | 2 | 2 | no | — |
| 299 | C7×C8 | — | 4 | 1 | no | — |
| 300 | C7×C8 | — | 4 | 1 | no | — |
| 301 | C7×C8 | — | 4 | 1 | no | — |
| 302 | C7⋊C8 | — | 2 | 2 | no | — |
| 303 | C7⋊C8 | — | 2 | 2 | no | — |
| 304 | C7⋊C8 | — | 2 | 2 | no | — |
| 305 | C7⋊C8 | — | 4 | 1 | no | — |
| 306 | C7⋊C8 | — | 4 | 1 | no | — |
| 307 | C7⋊C8 | — | 4 | 1 | no | — |
| 308 | C22×Q8 | — | 7 | 1 | no | — |
| 309 | C2×M16 | — | 7 | 1 | no | — |
| 310 | C2×M16 | — | 7 | 1 | no | — |
| 311 | C2×M16 | — | 7 | 1 | no | — |
| 312 | C2×M16 | — | 7 | 1 | no | — |
| 313 | C2×M16 | C22×D7 | 1 | 1 | yes | characteristic |
| 314 | C2×M16 | C22×D7 | 1 | 1 | yes | characteristic |
| 315 | C2×M16 | C22×D7 | 1 | 1 | yes | characteristic |
| 316 | C2×M16 | C22×D7 | 1 | 1 | yes | characteristic |
| 317 | C22×C8 | — | 7 | 1 | no | — |
| 318 | C22×C8 | — | 7 | 1 | no | — |
| 319 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 320 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 321 | C4×Q8 | — | 7 | 1 | no | — |
| 322 | C4×Q8 | — | 7 | 1 | no | — |
| 323 | C4×Q8 | — | 7 | 1 | no | — |
| 324 | C4×Q8 | — | 7 | 1 | no | — |
| 325 | C4×Q8 | — | 7 | 1 | no | — |
| 326 | C4×Q8 | — | 7 | 1 | no | — |
| 327 | C4×Q8 | — | 7 | 1 | no | — |
| 328 | C4×Q8 | — | 7 | 1 | no | — |
| 329 | C2×C4⋊C4 | — | 7 | 1 | no | — |
| 330 | C2×C4⋊C4 | — | 7 | 1 | no | — |
| 331 | C2×C4⋊C4 | — | 7 | 1 | no | — |
| 332 | C2×C42 | — | 7 | 1 | no | — |
| 333 | C2×C42 | — | 7 | 1 | no | — |
| 334 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 335 | #108 | — | 2 | 2 | no | — |
| 336 | #108 | — | 2 | 2 | no | — |
| 337 | #108 | — | 14 | 2 | no | — |
| 338 | #108 | — | 14 | 2 | no | — |
| 339 | #108 | — | 14 | 2 | no | — |
| 340 | #108 | — | 14 | 2 | no | — |
| 341 | C4⋊C8 | — | 2 | 1 | no | — |
| 342 | C4⋊C8 | — | 2 | 1 | no | — |
| 343 | C4⋊C8 | — | 7 | 2 | no | — |
| 344 | C4⋊C8 | — | 7 | 2 | no | — |
| 345 | C4⋊C8 | — | 7 | 2 | no | — |
| 346 | C4⋊C8 | — | 7 | 2 | no | — |
| 347 | C4⋊C8 | — | 14 | 1 | no | — |
| 348 | C4⋊C8 | — | 14 | 1 | no | — |
| 349 | C4⋊C8 | — | 14 | 1 | no | — |
| 350 | C4⋊C8 | — | 14 | 1 | no | — |
| 351 | C4⋊C8 | — | 14 | 1 | no | — |
| 352 | C4⋊C8 | — | 14 | 1 | no | — |
| 353 | C4⋊C8 | — | 14 | 1 | no | — |
| 354 | C4⋊C8 | — | 14 | 1 | no | — |
| 355 | C4⋊C8 | — | 14 | 1 | no | — |
| 356 | C4⋊C8 | — | 14 | 1 | no | — |
| 357 | C4⋊C8 | C4×D7 | 1 | 2 | yes | — |
| 358 | C4⋊C8 | C4×D7 | 1 | 2 | yes | — |
| 359 | #97 | — | 2 | 1 | no | — |
| 360 | #97 | — | 7 | 2 | no | — |
| 361 | #97 | — | 7 | 2 | no | — |
| 362 | #97 | — | 7 | 2 | no | — |
| 363 | #97 | — | 7 | 2 | no | — |
| 364 | #97 | — | 14 | 1 | no | — |
| 365 | #97 | — | 14 | 1 | no | — |
| 366 | #97 | — | 14 | 1 | no | — |
| 367 | #97 | — | 14 | 1 | no | — |
| 368 | #97 | — | 14 | 1 | no | — |
| 369 | C4×C8 | — | 2 | 1 | no | — |
| 370 | C4×C8 | — | 7 | 2 | no | — |
| 371 | C4×C8 | — | 7 | 2 | no | — |
| 372 | C4×C8 | — | 14 | 1 | no | — |
| 373 | C4×C8 | — | 14 | 1 | no | — |
| 374 | C4×C8 | — | 14 | 1 | no | — |
| 375 | C4×C8 | — | 14 | 1 | no | — |
| 376 | C4×C8 | — | 14 | 1 | no | — |
| 377 | C22×C7 | — | 2 | 1 | no | — |
| 378 | C22×C7 | — | 2 | 1 | no | — |
| 379 | C22×C7 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 380 | C22×C7 | #557 | 1 | 1 | yes | characteristic |
| 381 | C22×C7 | #557 | 1 | 1 | yes | characteristic |
| 382 | C4×C7 | — | 2 | 1 | no | — |
| 383 | C4×C7 | — | 2 | 1 | no | — |
| 384 | C4×C7 | — | 2 | 1 | no | — |
| 385 | C4×C7 | — | 2 | 1 | no | — |
| 386 | C4×C7 | C4×#41 | 1 | 1 | yes | characteristic |
| 387 | C4×C7 | #519 | 1 | 1 | yes | characteristic |
| 388 | C4×C7 | #548 | 1 | 1 | yes | characteristic |
| 389 | C4×C7 | #548 | 1 | 1 | yes | characteristic |
| 390 | Dic7 | — | 2 | 1 | no | — |
| 391 | Dic7 | — | 2 | 1 | no | — |
| 392 | Dic7 | — | 2 | 1 | no | — |
| 393 | Dic7 | — | 2 | 1 | no | — |
| 394 | Dic7 | — | 2 | 1 | no | — |
| 395 | Dic7 | — | 2 | 1 | no | — |
| 396 | Dic7 | — | 2 | 1 | no | — |
| 397 | Dic7 | #430 | 1 | 2 | yes | — |
| 398 | C2×Q8 | — | 7 | 1 | no | — |
| 399 | C2×Q8 | — | 7 | 1 | no | — |
| 400 | C2×Q8 | — | 7 | 1 | no | — |
| 401 | C2×Q8 | — | 7 | 1 | no | — |
| 402 | C2×Q8 | — | 28 | 2 | no | — |
| 403 | C22×C4 | — | 7 | 1 | no | — |
| 404 | C22×C4 | — | 7 | 1 | no | — |
| 405 | C22×C4 | — | 7 | 1 | no | — |
| 406 | C22×C4 | — | 7 | 1 | no | — |
| 407 | C22×C4 | Q8×D7 | 1 | 1 | yes | characteristic |
| 408 | C22×C4 | Q8×D7 | 1 | 1 | yes | characteristic |
| 409 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 410 | M16 | — | 2 | 1 | no | — |
| 411 | M16 | — | 2 | 1 | no | — |
| 412 | M16 | — | 2 | 1 | no | — |
| 413 | M16 | — | 2 | 1 | no | — |
| 414 | M16 | — | 2 | 1 | no | — |
| 415 | M16 | — | 2 | 1 | no | — |
| 416 | M16 | — | 2 | 1 | no | — |
| 417 | M16 | — | 7 | 2 | no | — |
| 418 | M16 | — | 14 | 1 | no | — |
| 419 | M16 | — | 14 | 1 | no | — |
| 420 | M16 | — | 14 | 1 | no | — |
| 421 | M16 | — | 14 | 1 | no | — |
| 422 | M16 | — | 14 | 1 | no | — |
| 423 | M16 | — | 14 | 1 | no | — |
| 424 | M16 | — | 14 | 1 | no | — |
| 425 | M16 | #1159 | 1 | 2 | yes | — |
| 426 | C2×C8 | — | 2 | 1 | no | — |
| 427 | C2×C8 | — | 2 | 1 | no | — |
| 428 | C2×C8 | — | 2 | 1 | no | — |
| 429 | C2×C8 | — | 2 | 1 | no | — |
| 430 | C2×C8 | — | 2 | 1 | no | — |
| 431 | C2×C8 | — | 2 | 1 | no | — |
| 432 | C2×C8 | — | 2 | 1 | no | — |
| 433 | C2×C8 | — | 2 | 1 | no | — |
| 434 | C2×C8 | — | 7 | 2 | no | — |
| 435 | C2×C8 | — | 7 | 2 | no | — |
| 436 | C2×C8 | — | 14 | 1 | no | — |
| 437 | C2×C8 | — | 14 | 1 | no | — |
| 438 | C2×C8 | — | 14 | 1 | no | — |
| 439 | C2×C8 | — | 14 | 1 | no | — |
| 440 | C2×C8 | — | 14 | 1 | no | — |
| 441 | C2×C8 | — | 14 | 1 | no | — |
| 442 | C2×C8 | — | 14 | 1 | no | — |
| 443 | C2×C8 | — | 14 | 1 | no | — |
| 444 | C2×C8 | C2×C4×D7 | 1 | 2 | yes | — |
| 445 | C2×C8 | C2×C4×D7 | 1 | 2 | yes | — |
| 446 | C4⋊C4 | — | 7 | 1 | no | — |
| 447 | C4⋊C4 | — | 7 | 1 | no | — |
| 448 | C4⋊C4 | — | 7 | 1 | no | — |
| 449 | C4⋊C4 | — | 7 | 1 | no | — |
| 450 | C4⋊C4 | — | 7 | 1 | no | — |
| 451 | C4⋊C4 | — | 7 | 1 | no | — |
| 452 | C4⋊C4 | — | 7 | 1 | no | — |
| 453 | C4⋊C4 | — | 7 | 1 | no | — |
| 454 | C4⋊C4 | — | 7 | 1 | no | — |
| 455 | C4⋊C4 | — | 7 | 1 | no | — |
| 456 | C4⋊C4 | — | 7 | 1 | no | — |
| 457 | C4⋊C4 | — | 7 | 1 | no | — |
| 458 | C42 | — | 7 | 1 | no | — |
| 459 | C42 | — | 7 | 1 | no | — |
| 460 | C42 | — | 7 | 1 | no | — |
| 461 | C42 | — | 7 | 1 | no | — |
| 462 | C42 | — | 7 | 1 | no | — |
| 463 | C42 | — | 7 | 1 | no | — |
| 464 | C42 | — | 7 | 1 | no | — |
| 465 | C42 | — | 7 | 1 | no | — |
| 466 | C42 | C2×C4×D7 | 1 | 1 | yes | characteristic |
| 467 | C42 | C2×C4×D7 | 1 | 1 | yes | characteristic |
| 468 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 469 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 470 | C2×C7 | — | 2 | 1 | no | — |
| 471 | C2×C7 | — | 2 | 1 | no | — |
| 472 | C2×C7 | #2351 | 1 | 1 | yes | characteristic |
| 473 | C2×C7 | C2×#430 | 1 | 1 | yes | characteristic |
| 474 | C2×C7 | #2916 | 1 | 1 | yes | characteristic |
| 475 | C23 | C2×Q8×D7 | 1 | 1 | yes | characteristic |
| 476 | Q8 | — | 14 | 2 | no | — |
| 477 | Q8 | — | 14 | 2 | no | — |
| 478 | Q8 | — | 28 | 1 | no | — |
| 479 | Q8 | — | 28 | 1 | no | — |
| 480 | C2×C4 | — | 4 | 1 | no | — |
| 481 | C2×C4 | — | 4 | 1 | no | — |
| 482 | C2×C4 | — | 7 | 1 | no | — |
| 483 | C2×C4 | — | 7 | 1 | no | — |
| 484 | C2×C4 | — | 7 | 1 | no | — |
| 485 | C2×C4 | — | 7 | 1 | no | — |
| 486 | C2×C4 | — | 7 | 1 | no | — |
| 487 | C2×C4 | — | 7 | 1 | no | — |
| 488 | C2×C4 | — | 7 | 1 | no | — |
| 489 | C2×C4 | — | 7 | 1 | no | — |
| 490 | C2×C4 | — | 14 | 2 | no | — |
| 491 | C2×C4 | — | 28 | 1 | no | — |
| 492 | C2×C4 | — | 28 | 1 | no | — |
| 493 | C2×C4 | — | 28 | 1 | no | — |
| 494 | C2×C4 | D7×C4⋊C4 | 1 | 1 | yes | characteristic |
| 495 | C2×C4 | D7×C4⋊C4 | 1 | 1 | yes | characteristic |
| 496 | C2×C4 | D7×C4⋊C4 | 1 | 1 | yes | characteristic |
| 497 | C2×C4 | D7×C4⋊C4 | 1 | 1 | yes | characteristic |
| 498 | C2×C4 | C22×C4×D7 | 1 | 1 | yes | characteristic |
| 499 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 500 | C2×C4 | C2×#1159 | 1 | 1 | yes | characteristic |
| 501 | C2×C4 | #6551 | 1 | 1 | yes | characteristic |
| 502 | C2×C4 | D7×#41 | 1 | 1 | yes | characteristic |
| 503 | C2×C4 | #6554 | 1 | 1 | yes | characteristic |
| 504 | C8 | — | 2 | 2 | no | — |
| 505 | C8 | — | 2 | 2 | no | — |
| 506 | C8 | — | 2 | 2 | no | — |
| 507 | C8 | — | 4 | 1 | no | — |
| 508 | C8 | — | 4 | 1 | no | — |
| 509 | C8 | — | 4 | 1 | no | — |
| 510 | C8 | — | 14 | 2 | no | — |
| 511 | C8 | — | 14 | 2 | no | — |
| 512 | C8 | — | 14 | 2 | no | — |
| 513 | C8 | — | 28 | 1 | no | — |
| 514 | C8 | — | 28 | 1 | no | — |
| 515 | C8 | — | 28 | 1 | no | — |
| 516 | C7 | #22747 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 517 | C22 | — | 2 | 1 | no | — |
| 518 | C22 | — | 2 | 1 | no | — |
| 519 | C22 | C2×D7×C4⋊C4 | 1 | 1 | yes | characteristic |
| 520 | C22 | #90376 | 1 | 1 | yes | characteristic |
| 521 | C22 | #90412 | 1 | 1 | yes | characteristic |
| 522 | C4 | — | 2 | 1 | no | — |
| 523 | C4 | — | 2 | 1 | no | — |
| 524 | C4 | — | 2 | 1 | no | — |
| 525 | C4 | — | 2 | 1 | no | — |
| 526 | C4 | — | 7 | 2 | no | — |
| 527 | C4 | — | 14 | 1 | no | — |
| 528 | C4 | — | 14 | 1 | no | — |
| 529 | C4 | — | 14 | 1 | no | — |
| 530 | C4 | — | 14 | 1 | no | — |
| 531 | C4 | — | 14 | 1 | no | — |
| 532 | C4 | — | 14 | 1 | no | — |
| 533 | C4 | — | 14 | 1 | no | — |
| 534 | C4 | C4×#1159 | 1 | 1 | yes | characteristic |
| 535 | C4 | #90263 | 1 | 1 | yes | characteristic |
| 536 | C4 | #90289 | 1 | 1 | yes | characteristic |
| 537 | C4 | #90324 | 1 | 1 | yes | characteristic |
| 538 | C2 | — | 2 | 1 | no | — |
| 539 | C2 | — | 2 | 1 | no | — |
| 540 | C2 | #11733427 | 1 | 1 | yes | characteristic |
| 541 | C2 | #11736697 | 1 | 1 | yes | characteristic |
| 542 | C2 | D7×#430 | 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