← #13403584
Subgroups — #13403584
Order 1792.
680 conjugacy classes of subgroups.
The subgroup lattice has 640 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#89954 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11736398 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #11736394 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11735989 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C7×#1979 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #11729824 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #11728471 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #11728449 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #11728094 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #11728091 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #11727862 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #11727860 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #11727852 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | Dic7×#101 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | #11727645 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | C22×C7×Q16 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×Q8×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#6507 | C22 | 1 | 1 | yes | characteristic |
| 19 | C22×#1144 | C22 | 1 | 1 | yes | characteristic |
| 20 | #90208 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×C7×#108 | C22 | 1 | 1 | yes | characteristic |
| 22 | C7×#419 | C22 | 1 | 1 | yes | characteristic |
| 23 | C7×#419 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×C7×#101 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×C7×#101 | C22 | 1 | 1 | yes | characteristic |
| 26 | C7×#405 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#6410 | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×#6410 | C22 | 1 | 1 | yes | characteristic |
| 29 | #89997 | C22 | 1 | 1 | yes | characteristic |
| 30 | #89997 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#6409 | C22 | 1 | 1 | yes | characteristic |
| 32 | #89954 | — | 2 | 1 | no | — |
| 33 | #89954 | — | 2 | 1 | no | — |
| 34 | #89954 | — | 2 | 1 | no | — |
| 35 | #89954 | — | 2 | 1 | no | — |
| 36 | C2×#6398 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×#6398 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×#6396 | C22 | 1 | 1 | yes | characteristic |
| 39 | #89894 | C22 | 1 | 1 | yes | characteristic |
| 40 | #89893 | C22 | 1 | 1 | yes | characteristic |
| 41 | #89892 | C22 | 1 | 1 | yes | characteristic |
| 42 | #89890 | C22 | 1 | 1 | yes | characteristic |
| 43 | M16×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 44 | M16×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 45 | C2×#6390 | C22 | 1 | 1 | yes | characteristic |
| 46 | #89874 | C22 | 1 | 1 | yes | characteristic |
| 47 | C2×Dic7⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 48 | #89776 | C22 | 1 | 1 | yes | characteristic |
| 49 | #89771 | C22 | 1 | 1 | yes | characteristic |
| 50 | #89767 | C22 | 1 | 1 | yes | characteristic |
| 51 | #89571 | — | 2 | 1 | no | — |
| 52 | #89569 | — | 2 | 1 | no | — |
| 53 | #89569 | — | 2 | 1 | no | — |
| 54 | #89568 | — | 2 | 1 | no | — |
| 55 | #89566 | — | 2 | 1 | no | — |
| 56 | #89564 | — | 2 | 1 | no | — |
| 57 | #89564 | — | 2 | 1 | no | — |
| 58 | #89563 | — | 2 | 1 | no | — |
| 59 | #89473 | — | 2 | 1 | no | — |
| 60 | #89473 | — | 2 | 1 | no | — |
| 61 | #89451 | — | 2 | 1 | no | — |
| 62 | C8×Dic14 | — | 2 | 1 | no | — |
| 63 | #89353 | C22 | 1 | 1 | yes | characteristic |
| 64 | #89349 | C22 | 1 | 1 | yes | characteristic |
| 65 | #89349 | C22 | 1 | 1 | yes | characteristic |
| 66 | #89347 | C22 | 1 | 1 | yes | characteristic |
| 67 | #25314 | — | 7 | 1 | no | maximal, Sylow |
| 68 | C22×C7×Q8 | C23 | 1 | 1 | yes | characteristic |
| 69 | C22×C7×Q8 | C23 | 1 | 1 | yes | characteristic |
| 70 | C22×Dic14 | C23 | 1 | 1 | yes | characteristic |
| 71 | C2×C7×Q16 | — | 2 | 2 | no | — |
| 72 | C2×C7×Q16 | — | 2 | 1 | no | — |
| 73 | C2×C7×Q16 | — | 2 | 1 | no | — |
| 74 | C2×C7×Q16 | — | 4 | 1 | no | — |
| 75 | C2×C7×M16 | C23 | 1 | 1 | yes | characteristic |
| 76 | C2×C7×M16 | C23 | 1 | 1 | yes | characteristic |
| 77 | C2×C7×M16 | C23 | 1 | 1 | yes | characteristic |
| 78 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 79 | C7×#117 | C23 | 1 | 1 | yes | characteristic |
| 80 | Q8×Dic7 | — | 2 | 1 | no | — |
| 81 | Q8×Dic7 | — | 2 | 1 | no | — |
| 82 | Q8×Dic7 | — | 2 | 1 | no | — |
| 83 | Q8×Dic7 | — | 2 | 1 | no | — |
| 84 | #6507 | — | 2 | 1 | no | — |
| 85 | #6507 | — | 2 | 1 | no | — |
| 86 | #6507 | — | 2 | 1 | no | — |
| 87 | #6507 | — | 2 | 1 | no | — |
| 88 | C2×#1144 | — | 2 | 2 | no | — |
| 89 | C2×#1144 | — | 2 | 1 | no | — |
| 90 | C2×#1144 | — | 2 | 1 | no | — |
| 91 | C2×#1144 | — | 4 | 1 | no | — |
| 92 | #6489 | C23 | 1 | 1 | yes | characteristic |
| 93 | C2×C4⋊Dic7 | — | 2 | 1 | no | — |
| 94 | C2×C4⋊Dic7 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×Dic7⋊C4 | — | 2 | 1 | no | — |
| 96 | C2×Dic7⋊C4 | — | 2 | 1 | no | — |
| 97 | C2×C4×Dic7 | — | 2 | 1 | no | — |
| 98 | C2×C4×Dic7 | C23 | 1 | 1 | yes | characteristic |
| 99 | C2×#1136 | C23 | 1 | 1 | yes | characteristic |
| 100 | C2×#1136 | C23 | 1 | 1 | yes | characteristic |
| 101 | C2×#1136 | C23 | 1 | 1 | yes | characteristic |
| 102 | C22×C7⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 103 | #6453 | D4 | 1 | 1 | yes | characteristic |
| 104 | #6453 | D4 | 1 | 1 | yes | characteristic |
| 105 | #6451 | D4 | 1 | 1 | yes | characteristic |
| 106 | #6451 | D4 | 1 | 1 | yes | characteristic |
| 107 | #6441 | — | 2 | 1 | no | — |
| 108 | #6441 | — | 2 | 1 | no | — |
| 109 | C4×Dic14 | — | 2 | 1 | no | — |
| 110 | C4×Dic14 | — | 2 | 1 | no | — |
| 111 | C7×#108 | — | 4 | 1 | no | — |
| 112 | C7×#103 | — | 2 | 1 | no | — |
| 113 | C7×#103 | — | 2 | 1 | no | — |
| 114 | C7×#103 | — | 2 | 1 | no | — |
| 115 | C7×#103 | — | 2 | 1 | no | — |
| 116 | C7×#101 | — | 2 | 2 | no | — |
| 117 | C7×#101 | — | 2 | 2 | no | — |
| 118 | C7×#97 | — | 2 | 1 | no | — |
| 119 | C4×C7×C8 | — | 2 | 1 | no | — |
| 120 | #6410 | — | 2 | 2 | no | — |
| 121 | #6410 | — | 4 | 1 | no | — |
| 122 | #6409 | — | 2 | 1 | no | — |
| 123 | #6409 | — | 2 | 1 | no | — |
| 124 | #6409 | — | 2 | 1 | no | — |
| 125 | #6409 | — | 2 | 1 | no | — |
| 126 | #6409 | — | 2 | 1 | no | — |
| 127 | #6409 | — | 2 | 1 | no | — |
| 128 | #6398 | — | 2 | 2 | no | — |
| 129 | #6398 | — | 4 | 1 | no | — |
| 130 | #6396 | — | 4 | 1 | no | — |
| 131 | #6392 | — | 2 | 1 | no | — |
| 132 | #6391 | — | 2 | 1 | no | — |
| 133 | #6390 | — | 2 | 1 | no | — |
| 134 | #6390 | — | 2 | 1 | no | — |
| 135 | #6390 | — | 2 | 1 | no | — |
| 136 | #6390 | — | 2 | 1 | no | — |
| 137 | #6389 | — | 2 | 1 | no | — |
| 138 | #6389 | — | 2 | 1 | no | — |
| 139 | #6389 | — | 2 | 1 | no | — |
| 140 | Dic7⋊C8 | — | 2 | 1 | no | — |
| 141 | Dic7⋊C8 | — | 2 | 1 | no | — |
| 142 | Dic7⋊C8 | — | 2 | 1 | no | — |
| 143 | Dic7⋊C8 | — | 2 | 1 | no | — |
| 144 | Dic7⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 145 | Dic7⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 146 | Dic7⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 147 | Dic7⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 148 | C8×Dic7 | — | 2 | 1 | no | — |
| 149 | C8×Dic7 | — | 2 | 1 | no | — |
| 150 | C8×Dic7 | — | 2 | 1 | no | — |
| 151 | #6384 | — | 2 | 1 | no | — |
| 152 | #6384 | — | 2 | 1 | no | — |
| 153 | #6382 | — | 2 | 1 | no | — |
| 154 | #6381 | — | 2 | 1 | no | — |
| 155 | C4⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 156 | C4⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 157 | #3139 | — | 7 | 1 | no | — |
| 158 | #3078 | — | 7 | 1 | no | — |
| 159 | C2×#462 | — | 7 | 1 | no | — |
| 160 | #2962 | — | 7 | 1 | no | — |
| 161 | #2064 | — | 7 | 1 | no | — |
| 162 | #2064 | — | 7 | 1 | no | — |
| 163 | #2047 | — | 7 | 1 | no | — |
| 164 | #2047 | — | 7 | 1 | no | — |
| 165 | #1979 | — | 7 | 1 | no | — |
| 166 | #1979 | D7 | 1 | 1 | yes | characteristic |
| 167 | #1966 | — | 7 | 1 | no | — |
| 168 | #1950 | — | 7 | 1 | no | — |
| 169 | #1930 | — | 7 | 1 | no | — |
| 170 | #1930 | — | 7 | 1 | no | — |
| 171 | C4×#101 | — | 7 | 1 | no | — |
| 172 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 173 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 174 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 175 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 176 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 177 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 178 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 179 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 180 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 181 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 182 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 183 | C2×C7×Q8 | #41 | 1 | 2 | yes | — |
| 184 | C22×C4×C7 | — | 2 | 1 | no | — |
| 185 | C22×C4×C7 | — | 2 | 1 | no | — |
| 186 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 187 | C22×Dic7 | — | 2 | 1 | no | — |
| 188 | C22×Dic7 | — | 2 | 1 | no | — |
| 189 | C22×Dic7 | #41 | 1 | 1 | yes | characteristic |
| 190 | C22×Dic7 | #41 | 1 | 1 | yes | characteristic |
| 191 | C2×Dic14 | — | 2 | 1 | no | — |
| 192 | C2×Dic14 | — | 2 | 1 | no | — |
| 193 | C2×Dic14 | — | 2 | 1 | no | — |
| 194 | C2×Dic14 | — | 2 | 1 | no | — |
| 195 | C2×Dic14 | — | 2 | 1 | no | — |
| 196 | C2×Dic14 | — | 2 | 1 | no | — |
| 197 | C2×Dic14 | — | 2 | 1 | no | — |
| 198 | C2×Dic14 | — | 2 | 1 | no | — |
| 199 | C7×Q16 | — | 4 | 2 | no | — |
| 200 | C7×Q16 | — | 4 | 2 | no | — |
| 201 | C7×M16 | — | 2 | 1 | no | — |
| 202 | C7×M16 | — | 2 | 1 | no | — |
| 203 | C7×M16 | — | 2 | 1 | no | — |
| 204 | C7×M16 | — | 2 | 1 | no | — |
| 205 | C7×M16 | — | 2 | 1 | no | — |
| 206 | C7×M16 | #41 | 1 | 2 | yes | — |
| 207 | C2×C7×C8 | — | 2 | 1 | no | — |
| 208 | C2×C7×C8 | — | 2 | 1 | no | — |
| 209 | C2×C7×C8 | — | 2 | 1 | no | — |
| 210 | C2×C7×C8 | — | 2 | 1 | no | — |
| 211 | C2×C7×C8 | — | 2 | 1 | no | — |
| 212 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 213 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 214 | C7×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 215 | C7×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 216 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 217 | C42×C7 | — | 2 | 1 | no | — |
| 218 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 219 | #1144 | — | 4 | 2 | no | — |
| 220 | #1144 | — | 4 | 2 | no | — |
| 221 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 222 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 223 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 224 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 225 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 226 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 227 | C4⋊Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 228 | C4⋊Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 229 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 230 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 231 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 232 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 233 | Dic7⋊C4 | — | 4 | 1 | no | — |
| 234 | Dic7⋊C4 | — | 4 | 1 | no | — |
| 235 | Dic7⋊C4 | — | 4 | 1 | no | — |
| 236 | Dic7⋊C4 | — | 4 | 1 | no | — |
| 237 | C4×Dic7 | — | 2 | 1 | no | — |
| 238 | C4×Dic7 | — | 4 | 1 | no | — |
| 239 | C4×Dic7 | — | 4 | 1 | no | — |
| 240 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 241 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 242 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 243 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 244 | #1136 | — | 2 | 1 | no | — |
| 245 | #1136 | — | 2 | 1 | no | — |
| 246 | #1136 | — | 2 | 1 | no | — |
| 247 | #1136 | — | 2 | 1 | no | — |
| 248 | #1136 | — | 2 | 1 | no | — |
| 249 | #1136 | — | 2 | 1 | no | — |
| 250 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 251 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 252 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 253 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 254 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 255 | C2×C7⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 256 | C2×C7⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 257 | C22×Q16 | — | 7 | 1 | no | — |
| 258 | C22×Q16 | C2×D7 | 1 | 1 | yes | characteristic |
| 259 | #533 | — | 7 | 1 | no | — |
| 260 | C2×C4⋊Q8 | — | 7 | 1 | no | — |
| 261 | C2×C4×Q8 | — | 7 | 1 | no | — |
| 262 | #491 | — | 14 | 1 | no | — |
| 263 | #491 | — | 14 | 1 | no | — |
| 264 | #487 | — | 14 | 1 | no | — |
| 265 | #487 | — | 14 | 1 | no | — |
| 266 | #479 | — | 14 | 1 | no | — |
| 267 | #479 | — | 14 | 1 | no | — |
| 268 | #477 | — | 14 | 1 | no | — |
| 269 | #475 | — | 14 | 1 | no | — |
| 270 | #462 | — | 14 | 1 | no | — |
| 271 | #462 | — | 14 | 1 | no | — |
| 272 | #462 | — | 14 | 1 | no | — |
| 273 | #462 | — | 14 | 1 | no | — |
| 274 | #446 | — | 14 | 1 | no | — |
| 275 | #446 | — | 14 | 1 | no | — |
| 276 | #446 | — | 14 | 1 | no | — |
| 277 | C8×Q8 | — | 14 | 1 | no | — |
| 278 | C2×#108 | — | 7 | 1 | no | — |
| 279 | C2×#108 | C2×D7 | 1 | 1 | yes | characteristic |
| 280 | #428 | — | 7 | 1 | no | — |
| 281 | #428 | — | 7 | 1 | no | — |
| 282 | #424 | — | 7 | 1 | no | — |
| 283 | #424 | — | 7 | 1 | no | — |
| 284 | #423 | — | 7 | 1 | no | — |
| 285 | C2×C4⋊C8 | — | 7 | 1 | no | — |
| 286 | #419 | — | 7 | 1 | no | — |
| 287 | #419 | — | 7 | 1 | no | — |
| 288 | #419 | — | 7 | 1 | no | — |
| 289 | #419 | — | 7 | 1 | no | — |
| 290 | #419 | C2×D7 | 1 | 1 | yes | characteristic |
| 291 | #419 | C2×D7 | 1 | 1 | yes | characteristic |
| 292 | C2×#103 | — | 7 | 1 | no | — |
| 293 | C2×#103 | — | 7 | 1 | no | — |
| 294 | C2×#101 | — | 7 | 1 | no | — |
| 295 | C2×#101 | — | 7 | 1 | no | — |
| 296 | C2×#101 | — | 7 | 1 | no | — |
| 297 | C2×#101 | — | 7 | 1 | no | — |
| 298 | C2×#101 | C2×D7 | 1 | 1 | yes | characteristic |
| 299 | C2×#101 | C2×D7 | 1 | 1 | yes | characteristic |
| 300 | #405 | — | 7 | 1 | no | — |
| 301 | #405 | C2×D7 | 1 | 1 | yes | characteristic |
| 302 | C4×M16 | — | 7 | 1 | no | — |
| 303 | C4×M16 | — | 7 | 1 | no | — |
| 304 | #343 | — | 7 | 1 | no | — |
| 305 | #343 | — | 7 | 1 | no | — |
| 306 | #341 | — | 7 | 1 | no | — |
| 307 | #341 | — | 7 | 1 | no | — |
| 308 | C23×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 309 | C7×Q8 | — | 2 | 2 | no | — |
| 310 | C7×Q8 | — | 2 | 2 | no | — |
| 311 | C7×Q8 | — | 4 | 1 | no | — |
| 312 | C7×Q8 | — | 4 | 1 | no | — |
| 313 | C7×Q8 | — | 4 | 1 | no | — |
| 314 | C7×Q8 | — | 4 | 1 | no | — |
| 315 | C7×Q8 | — | 4 | 1 | no | — |
| 316 | C7×Q8 | — | 4 | 1 | no | — |
| 317 | C2×C4×C7 | — | 2 | 1 | no | — |
| 318 | C2×C4×C7 | — | 2 | 1 | no | — |
| 319 | C2×C4×C7 | — | 2 | 2 | no | — |
| 320 | C2×C4×C7 | — | 4 | 1 | no | — |
| 321 | C2×C4×C7 | — | 4 | 1 | no | — |
| 322 | C2×C4×C7 | — | 4 | 1 | no | — |
| 323 | C2×C4×C7 | — | 4 | 1 | no | — |
| 324 | C2×C4×C7 | — | 4 | 1 | no | — |
| 325 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 326 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 327 | C2×C4×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 328 | C2×C4×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 329 | C2×C4×C7 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 330 | C2×C4×C7 | 2−1+4 | 1 | 1 | yes | characteristic |
| 331 | C2×Dic7 | — | 2 | 2 | no | — |
| 332 | C2×Dic7 | — | 2 | 1 | no | — |
| 333 | C2×Dic7 | — | 2 | 1 | no | — |
| 334 | C2×Dic7 | — | 4 | 1 | no | — |
| 335 | C2×Dic7 | — | 4 | 1 | no | — |
| 336 | C2×Dic7 | — | 4 | 1 | no | — |
| 337 | C2×Dic7 | — | 4 | 1 | no | — |
| 338 | C2×Dic7 | — | 4 | 1 | no | — |
| 339 | C2×Dic7 | — | 8 | 1 | no | — |
| 340 | C2×Dic7 | #121 | 1 | 1 | yes | characteristic |
| 341 | C2×Dic7 | #121 | 1 | 1 | yes | characteristic |
| 342 | C2×Dic7 | #121 | 1 | 1 | yes | characteristic |
| 343 | C2×Dic7 | #121 | 1 | 1 | yes | characteristic |
| 344 | Dic14 | — | 4 | 2 | no | — |
| 345 | Dic14 | — | 4 | 1 | no | — |
| 346 | Dic14 | — | 4 | 1 | no | — |
| 347 | Dic14 | — | 4 | 1 | no | — |
| 348 | Dic14 | — | 4 | 1 | no | — |
| 349 | Dic14 | — | 8 | 1 | no | — |
| 350 | C7×C8 | — | 2 | 1 | no | — |
| 351 | C7×C8 | — | 2 | 1 | no | — |
| 352 | C7×C8 | — | 2 | 2 | no | — |
| 353 | C7×C8 | — | 4 | 1 | no | — |
| 354 | C7×C8 | — | 4 | 1 | no | — |
| 355 | C7⋊C8 | — | 2 | 1 | no | — |
| 356 | C7⋊C8 | — | 2 | 1 | no | — |
| 357 | C7⋊C8 | — | 4 | 1 | no | — |
| 358 | C7⋊C8 | — | 4 | 1 | no | — |
| 359 | C7⋊C8 | — | 4 | 1 | no | — |
| 360 | C22×Q8 | — | 7 | 1 | no | — |
| 361 | C22×Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 362 | C22×Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 363 | C2×Q16 | — | 2 | 2 | no | — |
| 364 | C2×Q16 | — | 2 | 1 | no | — |
| 365 | C2×Q16 | — | 2 | 1 | no | — |
| 366 | C2×Q16 | — | 4 | 1 | no | — |
| 367 | C2×Q16 | — | 14 | 1 | no | — |
| 368 | C2×Q16 | — | 14 | 1 | no | — |
| 369 | C2×Q16 | — | 14 | 2 | no | — |
| 370 | C2×Q16 | — | 28 | 1 | no | — |
| 371 | C2×M16 | — | 7 | 1 | no | — |
| 372 | C2×M16 | — | 7 | 1 | no | — |
| 373 | C2×M16 | — | 7 | 1 | no | — |
| 374 | C2×M16 | C22×D7 | 1 | 1 | yes | characteristic |
| 375 | C2×M16 | C22×D7 | 1 | 1 | yes | characteristic |
| 376 | C2×M16 | C22×D7 | 1 | 1 | yes | characteristic |
| 377 | C22×C8 | — | 7 | 1 | no | — |
| 378 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 379 | C4⋊Q8 | — | 7 | 1 | no | — |
| 380 | C4⋊Q8 | — | 7 | 1 | no | — |
| 381 | C4⋊Q8 | — | 14 | 1 | no | — |
| 382 | C4⋊Q8 | — | 14 | 1 | no | — |
| 383 | C4⋊Q8 | — | 14 | 1 | no | — |
| 384 | C4⋊Q8 | — | 14 | 1 | no | — |
| 385 | #125 | — | 7 | 1 | no | — |
| 386 | #125 | — | 7 | 1 | no | — |
| 387 | C22⋊Q8 | — | 14 | 1 | no | — |
| 388 | C22⋊Q8 | — | 14 | 1 | no | — |
| 389 | C4×Q8 | — | 14 | 1 | no | — |
| 390 | C4×Q8 | — | 14 | 1 | no | — |
| 391 | C4×Q8 | — | 14 | 1 | no | — |
| 392 | C4×Q8 | — | 14 | 1 | no | — |
| 393 | C4×Q8 | — | 14 | 1 | no | — |
| 394 | C4×Q8 | — | 14 | 1 | no | — |
| 395 | #117 | — | 7 | 1 | no | — |
| 396 | #117 | C22×D7 | 1 | 1 | yes | characteristic |
| 397 | C2×C4⋊C4 | — | 7 | 1 | no | — |
| 398 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 399 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 400 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 401 | C2×C42 | — | 7 | 1 | no | — |
| 402 | C2×C42 | — | 14 | 1 | no | — |
| 403 | #108 | — | 4 | 1 | no | — |
| 404 | #108 | — | 28 | 1 | no | — |
| 405 | #107 | — | 14 | 1 | no | — |
| 406 | #107 | — | 14 | 1 | no | — |
| 407 | #106 | — | 14 | 1 | no | — |
| 408 | #106 | — | 14 | 1 | no | — |
| 409 | C4⋊C8 | — | 7 | 1 | no | — |
| 410 | C4⋊C8 | — | 7 | 1 | no | — |
| 411 | C4⋊C8 | — | 7 | 1 | no | — |
| 412 | C4⋊C8 | — | 7 | 1 | no | — |
| 413 | C4⋊C8 | — | 14 | 1 | no | — |
| 414 | C4⋊C8 | — | 14 | 1 | no | — |
| 415 | C4⋊C8 | — | 14 | 1 | no | — |
| 416 | C4⋊C8 | — | 14 | 1 | no | — |
| 417 | C4⋊C8 | — | 14 | 1 | no | — |
| 418 | C4⋊C8 | — | 14 | 1 | no | — |
| 419 | #103 | — | 2 | 1 | no | — |
| 420 | #103 | — | 2 | 1 | no | — |
| 421 | #103 | — | 2 | 1 | no | — |
| 422 | #103 | — | 2 | 1 | no | — |
| 423 | #103 | — | 14 | 1 | no | — |
| 424 | #103 | — | 14 | 1 | no | — |
| 425 | #103 | — | 14 | 1 | no | — |
| 426 | #103 | — | 14 | 1 | no | — |
| 427 | #103 | — | 14 | 1 | no | — |
| 428 | #103 | — | 14 | 1 | no | — |
| 429 | #103 | — | 14 | 1 | no | — |
| 430 | #103 | — | 14 | 1 | no | — |
| 431 | #103 | — | 14 | 1 | no | — |
| 432 | #103 | — | 14 | 1 | no | — |
| 433 | #103 | — | 14 | 1 | no | — |
| 434 | #103 | — | 14 | 1 | no | — |
| 435 | #101 | — | 2 | 2 | no | — |
| 436 | #101 | — | 2 | 2 | no | — |
| 437 | #101 | — | 14 | 2 | no | — |
| 438 | #101 | — | 14 | 2 | no | — |
| 439 | #101 | — | 28 | 1 | no | — |
| 440 | #101 | — | 28 | 1 | no | — |
| 441 | #97 | — | 2 | 1 | no | — |
| 442 | #97 | — | 14 | 1 | no | — |
| 443 | #97 | — | 14 | 1 | no | — |
| 444 | #97 | — | 14 | 1 | no | — |
| 445 | C4×C8 | — | 2 | 1 | no | — |
| 446 | C4×C8 | — | 14 | 1 | no | — |
| 447 | C4×C8 | — | 14 | 1 | no | — |
| 448 | C4×C8 | — | 14 | 1 | no | — |
| 449 | C22×C7 | — | 2 | 1 | no | — |
| 450 | C22×C7 | — | 2 | 1 | no | — |
| 451 | C22×C7 | C2×#121 | 1 | 1 | yes | characteristic |
| 452 | C22×C7 | #529 | 1 | 1 | yes | characteristic |
| 453 | C22×C7 | #542 | 1 | 1 | yes | characteristic |
| 454 | C4×C7 | — | 4 | 2 | no | — |
| 455 | C4×C7 | — | 4 | 1 | no | — |
| 456 | C4×C7 | — | 4 | 1 | no | — |
| 457 | C4×C7 | — | 8 | 1 | no | — |
| 458 | C4×C7 | #546 | 1 | 1 | yes | characteristic |
| 459 | C4×C7 | #548 | 1 | 1 | yes | characteristic |
| 460 | C4×C7 | #548 | 1 | 1 | yes | characteristic |
| 461 | C4×C7 | #550 | 1 | 1 | yes | characteristic |
| 462 | Dic7 | — | 2 | 1 | no | — |
| 463 | Dic7 | — | 2 | 1 | no | — |
| 464 | Dic7 | — | 2 | 1 | no | — |
| 465 | Dic7 | — | 4 | 1 | no | — |
| 466 | Dic7 | — | 4 | 1 | no | — |
| 467 | Dic7 | — | 8 | 1 | no | — |
| 468 | Dic7 | — | 8 | 1 | no | — |
| 469 | Dic7 | #473 | 1 | 2 | yes | — |
| 470 | C2×Q8 | — | 2 | 1 | no | — |
| 471 | C2×Q8 | — | 2 | 1 | no | — |
| 472 | C2×Q8 | — | 2 | 1 | no | — |
| 473 | C2×Q8 | — | 2 | 1 | no | — |
| 474 | C2×Q8 | — | 2 | 1 | no | — |
| 475 | C2×Q8 | — | 2 | 1 | no | — |
| 476 | C2×Q8 | — | 2 | 1 | no | — |
| 477 | C2×Q8 | — | 2 | 1 | no | — |
| 478 | C2×Q8 | — | 2 | 1 | no | — |
| 479 | C2×Q8 | — | 2 | 1 | no | — |
| 480 | C2×Q8 | — | 2 | 1 | no | — |
| 481 | C2×Q8 | — | 14 | 1 | no | — |
| 482 | C2×Q8 | — | 14 | 1 | no | — |
| 483 | C2×Q8 | — | 14 | 1 | no | — |
| 484 | C2×Q8 | — | 14 | 1 | no | — |
| 485 | C2×Q8 | — | 14 | 1 | no | — |
| 486 | C2×Q8 | — | 14 | 1 | no | — |
| 487 | C2×Q8 | — | 14 | 1 | no | — |
| 488 | C2×Q8 | — | 14 | 1 | no | — |
| 489 | C2×Q8 | #1157 | 1 | 2 | yes | — |
| 490 | C22×C4 | — | 2 | 1 | no | — |
| 491 | C22×C4 | — | 2 | 1 | no | — |
| 492 | C22×C4 | — | 7 | 1 | no | — |
| 493 | C22×C4 | — | 7 | 1 | no | — |
| 494 | C22×C4 | — | 14 | 1 | no | — |
| 495 | C22×C4 | — | 14 | 1 | no | — |
| 496 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 497 | Q16 | — | 4 | 2 | no | — |
| 498 | Q16 | — | 4 | 2 | no | — |
| 499 | Q16 | — | 28 | 2 | no | — |
| 500 | Q16 | — | 28 | 2 | no | — |
| 501 | M16 | — | 2 | 1 | no | — |
| 502 | M16 | — | 2 | 1 | no | — |
| 503 | M16 | — | 2 | 1 | no | — |
| 504 | M16 | — | 2 | 1 | no | — |
| 505 | M16 | — | 2 | 1 | no | — |
| 506 | M16 | — | 14 | 1 | no | — |
| 507 | M16 | — | 14 | 1 | no | — |
| 508 | M16 | — | 14 | 1 | no | — |
| 509 | M16 | — | 14 | 1 | no | — |
| 510 | M16 | — | 14 | 1 | no | — |
| 511 | M16 | — | 14 | 1 | no | — |
| 512 | M16 | #1159 | 1 | 2 | yes | — |
| 513 | C2×C8 | — | 2 | 1 | no | — |
| 514 | C2×C8 | — | 2 | 1 | no | — |
| 515 | C2×C8 | — | 2 | 1 | no | — |
| 516 | C2×C8 | — | 2 | 1 | no | — |
| 517 | C2×C8 | — | 2 | 1 | no | — |
| 518 | C2×C8 | — | 7 | 1 | no | — |
| 519 | C2×C8 | — | 7 | 1 | no | — |
| 520 | C2×C8 | — | 14 | 1 | no | — |
| 521 | C2×C8 | — | 14 | 1 | no | — |
| 522 | C2×C8 | — | 14 | 1 | no | — |
| 523 | C2×C8 | — | 14 | 1 | no | — |
| 524 | C2×C8 | — | 14 | 1 | no | — |
| 525 | C2×C8 | D4×D7 | 1 | 1 | yes | characteristic |
| 526 | C2×C8 | D4×D7 | 1 | 1 | yes | characteristic |
| 527 | C4⋊C4 | — | 7 | 1 | no | — |
| 528 | C4⋊C4 | — | 7 | 1 | no | — |
| 529 | C4⋊C4 | — | 14 | 1 | no | — |
| 530 | C4⋊C4 | — | 14 | 1 | no | — |
| 531 | C4⋊C4 | — | 14 | 1 | no | — |
| 532 | C4⋊C4 | — | 14 | 1 | no | — |
| 533 | C4⋊C4 | — | 14 | 1 | no | — |
| 534 | C4⋊C4 | — | 14 | 1 | no | — |
| 535 | C4⋊C4 | — | 14 | 1 | no | — |
| 536 | C4⋊C4 | — | 14 | 1 | no | — |
| 537 | C4⋊C4 | — | 28 | 1 | no | — |
| 538 | C4⋊C4 | — | 28 | 1 | no | — |
| 539 | C4⋊C4 | — | 28 | 1 | no | — |
| 540 | C4⋊C4 | — | 28 | 1 | no | — |
| 541 | C4⋊C4 | — | 28 | 1 | no | — |
| 542 | C4⋊C4 | — | 28 | 1 | no | — |
| 543 | C4⋊C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 544 | C4⋊C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 545 | C22⋊C4 | — | 2 | 1 | no | — |
| 546 | C22⋊C4 | — | 14 | 1 | no | — |
| 547 | C42 | — | 2 | 1 | no | — |
| 548 | C42 | — | 7 | 1 | no | — |
| 549 | C42 | — | 7 | 1 | no | — |
| 550 | C42 | — | 7 | 1 | no | — |
| 551 | C42 | — | 7 | 1 | no | — |
| 552 | C42 | — | 14 | 1 | no | — |
| 553 | C42 | — | 28 | 1 | no | — |
| 554 | C42 | — | 28 | 1 | no | — |
| 555 | C2×C7 | — | 2 | 1 | no | — |
| 556 | C2×C7 | — | 2 | 1 | no | — |
| 557 | C2×C7 | #2426 | 1 | 1 | yes | characteristic |
| 558 | C2×C7 | C2×#473 | 1 | 1 | yes | characteristic |
| 559 | C2×C7 | #3069 | 1 | 1 | yes | characteristic |
| 560 | C23 | D7×#41 | 1 | 1 | yes | characteristic |
| 561 | Q8 | — | 2 | 2 | no | — |
| 562 | Q8 | — | 2 | 2 | no | — |
| 563 | Q8 | — | 4 | 1 | no | — |
| 564 | Q8 | — | 4 | 1 | no | — |
| 565 | Q8 | — | 4 | 1 | no | — |
| 566 | Q8 | — | 4 | 1 | no | — |
| 567 | Q8 | — | 4 | 1 | no | — |
| 568 | Q8 | — | 4 | 1 | no | — |
| 569 | Q8 | — | 28 | 2 | no | — |
| 570 | Q8 | — | 28 | 1 | no | — |
| 571 | Q8 | — | 28 | 1 | no | — |
| 572 | Q8 | — | 28 | 1 | no | — |
| 573 | Q8 | — | 28 | 1 | no | — |
| 574 | Q8 | — | 56 | 1 | no | — |
| 575 | C2×C4 | — | 2 | 2 | no | — |
| 576 | C2×C4 | — | 2 | 1 | no | — |
| 577 | C2×C4 | — | 2 | 1 | no | — |
| 578 | C2×C4 | — | 4 | 1 | no | — |
| 579 | C2×C4 | — | 4 | 1 | no | — |
| 580 | C2×C4 | — | 4 | 1 | no | — |
| 581 | C2×C4 | — | 4 | 1 | no | — |
| 582 | C2×C4 | — | 4 | 1 | no | — |
| 583 | C2×C4 | — | 7 | 1 | no | — |
| 584 | C2×C4 | — | 7 | 1 | no | — |
| 585 | C2×C4 | — | 7 | 1 | no | — |
| 586 | C2×C4 | — | 7 | 1 | no | — |
| 587 | C2×C4 | — | 14 | 2 | no | — |
| 588 | C2×C4 | — | 14 | 1 | no | — |
| 589 | C2×C4 | — | 14 | 1 | no | — |
| 590 | C2×C4 | — | 28 | 1 | no | — |
| 591 | C2×C4 | — | 28 | 1 | no | — |
| 592 | C2×C4 | — | 28 | 1 | no | — |
| 593 | C2×C4 | — | 28 | 1 | no | — |
| 594 | C2×C4 | — | 28 | 1 | no | — |
| 595 | C2×C4 | — | 56 | 1 | no | — |
| 596 | C2×C4 | C2×#1157 | 1 | 1 | yes | characteristic |
| 597 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 598 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 599 | C2×C4 | C2×#1159 | 1 | 1 | yes | characteristic |
| 600 | C2×C4 | #6548 | 1 | 1 | yes | characteristic |
| 601 | C2×C4 | #6554 | 1 | 1 | yes | characteristic |
| 602 | C8 | — | 2 | 1 | no | — |
| 603 | C8 | — | 2 | 1 | no | — |
| 604 | C8 | — | 2 | 2 | no | — |
| 605 | C8 | — | 4 | 1 | no | — |
| 606 | C8 | — | 4 | 1 | no | — |
| 607 | C8 | — | 14 | 1 | no | — |
| 608 | C8 | — | 14 | 1 | no | — |
| 609 | C8 | — | 28 | 1 | no | — |
| 610 | C8 | — | 28 | 1 | no | — |
| 611 | C8 | — | 28 | 1 | no | — |
| 612 | C7 | #25314 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 613 | C22 | — | 2 | 1 | no | — |
| 614 | C22 | — | 2 | 1 | no | — |
| 615 | C22 | #90229 | 1 | 1 | yes | characteristic |
| 616 | C22 | D7×#121 | 1 | 1 | yes | characteristic |
| 617 | C22 | #90360 | 1 | 1 | yes | characteristic |
| 618 | C4 | — | 4 | 1 | no | — |
| 619 | C4 | — | 4 | 1 | no | — |
| 620 | C4 | — | 4 | 2 | no | — |
| 621 | C4 | — | 7 | 2 | no | — |
| 622 | C4 | — | 8 | 1 | no | — |
| 623 | C4 | — | 14 | 1 | no | — |
| 624 | C4 | — | 14 | 1 | no | — |
| 625 | C4 | — | 14 | 1 | no | — |
| 626 | C4 | — | 28 | 1 | no | — |
| 627 | C4 | — | 28 | 1 | no | — |
| 628 | C4 | — | 56 | 1 | no | — |
| 629 | C4 | — | 56 | 1 | no | — |
| 630 | C4 | #90181 | 1 | 1 | yes | characteristic |
| 631 | C4 | #90243 | 1 | 1 | yes | characteristic |
| 632 | C4 | #90289 | 1 | 1 | yes | characteristic |
| 633 | C4 | #90409 | 1 | 1 | yes | characteristic |
| 634 | C2 | — | 2 | 1 | no | — |
| 635 | C2 | — | 2 | 1 | no | — |
| 636 | C2 | #11733757 | 1 | 1 | yes | characteristic |
| 637 | C2 | D7×#473 | 1 | 1 | yes | characteristic |
| 638 | C2 | #11738389 | 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