← #14224161
Subgroups — #14224161
Order 1792.
1870 conjugacy classes of subgroups.
The subgroup lattice has 518 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #11743295 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C7×#3147 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11741362 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11741361 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11741344 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11741343 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11740729 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11739257 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #11739254 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #11739238 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #11739221 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #11739198 | C2 | 1 | 4 | yes | maximal, complemented |
| 13 | C4×#6464 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C2×#89455 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C2×C7×#135 | C22 | 1 | 2 | yes | — |
| 16 | C2×C7×#135 | C22 | 1 | 2 | yes | — |
| 17 | C7×#532 | C22 | 1 | 2 | yes | — |
| 18 | #90524 | C22 | 1 | 4 | yes | — |
| 19 | #90518 | C22 | 1 | 4 | yes | — |
| 20 | C2×#6464 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#6464 | C22 | 1 | 1 | yes | characteristic |
| 22 | #90422 | C22 | 1 | 4 | yes | — |
| 23 | #90410 | C22 | 1 | 4 | yes | — |
| 24 | #90371 | C22 | 1 | 8 | yes | — |
| 25 | #90292 | — | 2 | 8 | no | — |
| 26 | #90256 | — | 2 | 4 | no | — |
| 27 | #90232 | — | 2 | 4 | no | — |
| 28 | C4×#1157 | C22 | 1 | 1 | yes | characteristic |
| 29 | C2×#6433 | C22 | 1 | 2 | yes | — |
| 30 | C7×#495 | C22 | 1 | 2 | yes | — |
| 31 | C7×#495 | C22 | 1 | 2 | yes | — |
| 32 | C7×#494 | C22 | 1 | 1 | yes | characteristic |
| 33 | C7×#493 | C22 | 1 | 1 | yes | characteristic |
| 34 | C7×#492 | C22 | 1 | 2 | yes | — |
| 35 | C2×C4×C7×C8 | C22 | 1 | 1 | yes | characteristic |
| 36 | #90004 | C22 | 1 | 4 | yes | — |
| 37 | #90004 | C22 | 1 | 4 | yes | — |
| 38 | #89961 | C22 | 1 | 4 | yes | — |
| 39 | #89960 | C22 | 1 | 4 | yes | — |
| 40 | #89956 | C22 | 1 | 4 | yes | — |
| 41 | Q16×Dic7 | C22 | 1 | 4 | yes | — |
| 42 | #89946 | C22 | 1 | 8 | yes | — |
| 43 | #89943 | C22 | 1 | 8 | yes | — |
| 44 | #89936 | C22 | 1 | 8 | yes | — |
| 45 | SD16×Dic7 | C22 | 1 | 8 | yes | — |
| 46 | #89931 | C22 | 1 | 4 | yes | — |
| 47 | #89929 | C22 | 1 | 4 | yes | — |
| 48 | #89924 | C22 | 1 | 4 | yes | — |
| 49 | D8×Dic7 | C22 | 1 | 4 | yes | — |
| 50 | C2×#6392 | C22 | 1 | 2 | yes | — |
| 51 | C2×#6391 | C22 | 1 | 2 | yes | — |
| 52 | #89873 | C22 | 1 | 1 | yes | characteristic |
| 53 | #89873 | C22 | 1 | 1 | yes | characteristic |
| 54 | #89854 | C22 | 1 | 4 | yes | — |
| 55 | #89843 | C22 | 1 | 4 | yes | — |
| 56 | #89828 | C22 | 1 | 8 | yes | — |
| 57 | C4×#1136 | C22 | 1 | 1 | yes | characteristic |
| 58 | #89461 | C22 | 1 | 2 | yes | — |
| 59 | #89461 | C22 | 1 | 2 | yes | — |
| 60 | C4×#1131 | C22 | 1 | 2 | yes | — |
| 61 | C4×C8×D7 | C22 | 1 | 2 | yes | — |
| 62 | #89455 | C22 | 1 | 2 | yes | — |
| 63 | #89455 | C22 | 1 | 2 | yes | — |
| 64 | #89455 | C22 | 1 | 2 | yes | — |
| 65 | #89455 | C22 | 1 | 2 | yes | — |
| 66 | #60717 | — | 7 | 1 | no | maximal, Sylow |
| 67 | C2×C7×#41 | C23 | 1 | 4 | yes | — |
| 68 | C2×#1157 | C23 | 1 | 1 | yes | characteristic |
| 69 | C7×#135 | — | 2 | 8 | no | — |
| 70 | C7×#135 | — | 2 | 8 | no | — |
| 71 | C2×C7×Q16 | C23 | 1 | 2 | yes | — |
| 72 | C2×C7×Q16 | C23 | 1 | 2 | yes | — |
| 73 | C2×C7×SD16 | C23 | 1 | 4 | yes | — |
| 74 | C2×C7×SD16 | C23 | 1 | 4 | yes | — |
| 75 | C2×C7×D8 | C23 | 1 | 2 | yes | — |
| 76 | C2×C7×D8 | C23 | 1 | 2 | yes | — |
| 77 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 78 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 79 | C7×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 80 | C7×#127 | C23 | 1 | 2 | yes | — |
| 81 | C7×#124 | C23 | 1 | 4 | yes | — |
| 82 | C7×#121 | — | 2 | 4 | no | — |
| 83 | C4×C7×D4 | — | 2 | 4 | no | — |
| 84 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 85 | #6509 | C23 | 1 | 8 | yes | — |
| 86 | Q8×Dic7 | C23 | 1 | 8 | yes | — |
| 87 | #6502 | — | 2 | 8 | no | — |
| 88 | #6502 | — | 2 | 8 | no | — |
| 89 | #6501 | C23 | 1 | 8 | yes | — |
| 90 | #6498 | — | 2 | 8 | no | — |
| 91 | D4×Dic7 | — | 2 | 8 | no | — |
| 92 | D4×Dic7 | C23 | 1 | 8 | yes | — |
| 93 | #6493 | — | 2 | 4 | no | — |
| 94 | C4×C22⋊D7 | D4 | 1 | 4 | yes | — |
| 95 | #6489 | — | 2 | 4 | no | — |
| 96 | #6489 | C23 | 1 | 1 | yes | characteristic |
| 97 | C2×C4⋊Dic7 | — | 2 | 4 | no | — |
| 98 | C2×C4⋊Dic7 | C23 | 1 | 4 | yes | — |
| 99 | #6487 | — | 2 | 4 | no | — |
| 100 | C2×Dic7⋊C4 | — | 2 | 4 | no | — |
| 101 | C2×#1136 | C23 | 1 | 1 | yes | characteristic |
| 102 | C2×#1136 | C23 | 1 | 1 | yes | characteristic |
| 103 | #6464 | — | 2 | 4 | no | — |
| 104 | #6464 | — | 2 | 4 | no | — |
| 105 | C2×#1131 | C23 | 1 | 2 | yes | — |
| 106 | C2×#1131 | C23 | 1 | 2 | yes | — |
| 107 | C2×C8×D7 | C23 | 1 | 2 | yes | — |
| 108 | C2×C8×D7 | C23 | 1 | 2 | yes | — |
| 109 | #6461 | — | 2 | 8 | no | — |
| 110 | #6452 | — | 2 | 8 | no | — |
| 111 | #6446 | — | 2 | 8 | no | — |
| 112 | (C22⋊D7)⋊C4 | — | 2 | 8 | no | — |
| 113 | #6442 | — | 2 | 8 | no | — |
| 114 | #6440 | — | 2 | 8 | no | — |
| 115 | C4×D28 | D4 | 1 | 2 | yes | — |
| 116 | #6435 | C23 | 1 | 2 | yes | — |
| 117 | C42×D7 | C23 | 1 | 2 | yes | — |
| 118 | #6433 | — | 2 | 4 | no | — |
| 119 | #6433 | C23 | 1 | 4 | yes | — |
| 120 | #6433 | C23 | 1 | 4 | yes | — |
| 121 | C4×Dic14 | D4 | 1 | 2 | yes | — |
| 122 | C4×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 123 | C4×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 124 | C4×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 125 | C4×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 126 | #6409 | C23 | 1 | 8 | yes | — |
| 127 | #6409 | C23 | 1 | 8 | yes | — |
| 128 | #6406 | C23 | 1 | 8 | yes | — |
| 129 | #6406 | C23 | 1 | 8 | yes | — |
| 130 | #6392 | C23 | 1 | 4 | yes | — |
| 131 | #6392 | C23 | 1 | 4 | yes | — |
| 132 | #6391 | C23 | 1 | 4 | yes | — |
| 133 | #6391 | C23 | 1 | 4 | yes | — |
| 134 | #6389 | C23 | 1 | 2 | yes | — |
| 135 | #6389 | C23 | 1 | 2 | yes | — |
| 136 | C8×Dic7 | C23 | 1 | 2 | yes | — |
| 137 | C8×Dic7 | C23 | 1 | 2 | yes | — |
| 138 | #6377 | C23 | 1 | 2 | yes | — |
| 139 | C4×C7⋊C8 | C23 | 1 | 2 | yes | — |
| 140 | #3512 | — | 7 | 2 | no | — |
| 141 | #3183 | — | 7 | 4 | no | — |
| 142 | #3177 | — | 7 | 2 | no | — |
| 143 | #3176 | — | 7 | 2 | no | — |
| 144 | #3174 | — | 7 | 4 | no | — |
| 145 | #3168 | — | 7 | 4 | no | — |
| 146 | C2×#499 | — | 7 | 1 | no | — |
| 147 | #3147 | D7 | 1 | 1 | yes | characteristic, complemented |
| 148 | #3142 | — | 7 | 2 | no | — |
| 149 | #3061 | — | 7 | 2 | no | — |
| 150 | #3060 | — | 7 | 2 | no | — |
| 151 | #2952 | — | 7 | 2 | no | — |
| 152 | #2951 | — | 7 | 2 | no | — |
| 153 | C4×#131 | — | 7 | 1 | no | — |
| 154 | C7×#41 | — | 2 | 8 | no | — |
| 155 | C7×#41 | — | 2 | 8 | no | — |
| 156 | C2×C7×Q8 | C24 | 1 | 4 | yes | — |
| 157 | C2×C7×D4 | — | 2 | 4 | no | — |
| 158 | C2×C7×D4 | — | 2 | 4 | no | — |
| 159 | C2×C7×D4 | C24 | 1 | 4 | yes | — |
| 160 | C22×C4×C7 | — | 2 | 4 | no | — |
| 161 | C22×C4×C7 | C2×D4 | 1 | 2 | yes | — |
| 162 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 163 | C2×C22⋊D7 | — | 2 | 8 | no | — |
| 164 | C2×C22⋊D7 | C2×D4 | 1 | 2 | yes | — |
| 165 | C22×Dic7 | — | 2 | 4 | no | — |
| 166 | C22×Dic7 | — | 2 | 8 | no | — |
| 167 | #1157 | — | 2 | 2 | no | — |
| 168 | #1157 | — | 2 | 2 | no | — |
| 169 | C2×D28 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | C2×C4×D7 | C2×D4 | 1 | 4 | yes | — |
| 171 | C2×C4×D7 | C24 | 1 | 2 | yes | — |
| 172 | C2×Dic14 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | C7×Q16 | — | 2 | 4 | no | — |
| 174 | C7×Q16 | — | 2 | 4 | no | — |
| 175 | C7×SD16 | — | 2 | 8 | no | — |
| 176 | C7×SD16 | — | 2 | 8 | no | — |
| 177 | C7×D8 | — | 2 | 4 | no | — |
| 178 | C7×D8 | — | 2 | 4 | no | — |
| 179 | C2×C7×C8 | #41 | 1 | 4 | yes | — |
| 180 | C2×C7×C8 | #41 | 1 | 4 | yes | — |
| 181 | C2×C7×C8 | C24 | 1 | 1 | yes | characteristic |
| 182 | C2×C7×C8 | C24 | 1 | 1 | yes | characteristic |
| 183 | C2×C7×C8 | C24 | 1 | 1 | yes | characteristic |
| 184 | C2×C7×C8 | C24 | 1 | 1 | yes | characteristic |
| 185 | C7×C4⋊C4 | — | 2 | 4 | no | — |
| 186 | C7×C22⋊C4 | — | 2 | 4 | no | — |
| 187 | C7×C22⋊C4 | — | 2 | 4 | no | — |
| 188 | C42×C7 | C2×D4 | 1 | 2 | yes | — |
| 189 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 190 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 191 | C22⋊Dic7 | — | 2 | 8 | no | — |
| 192 | C22⋊Dic7 | — | 2 | 8 | no | — |
| 193 | C22⋊Dic7 | C2×D4 | 1 | 2 | yes | — |
| 194 | (C2×D7)⋊C4 | — | 2 | 8 | no | — |
| 195 | (C2×D7)⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 196 | C4⋊Dic7 | — | 2 | 4 | no | — |
| 197 | C4⋊Dic7 | — | 2 | 8 | no | — |
| 198 | C4⋊Dic7 | C2×D4 | 1 | 2 | yes | — |
| 199 | C4⋊Dic7 | C24 | 1 | 8 | yes | — |
| 200 | Dic7⋊C4 | — | 2 | 8 | no | — |
| 201 | Dic7⋊C4 | — | 2 | 8 | no | — |
| 202 | Dic7⋊C4 | — | 2 | 8 | no | — |
| 203 | Dic7⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 204 | C4×Dic7 | — | 2 | 8 | no | — |
| 205 | C4×Dic7 | C2×D4 | 1 | 4 | yes | — |
| 206 | C4×Dic7 | C24 | 1 | 2 | yes | — |
| 207 | #1136 | — | 2 | 2 | no | — |
| 208 | #1136 | — | 2 | 2 | no | — |
| 209 | C2×C7⋊C8 | C24 | 1 | 2 | yes | — |
| 210 | C2×C7⋊C8 | C24 | 1 | 2 | yes | — |
| 211 | #1131 | — | 2 | 4 | no | — |
| 212 | #1131 | — | 2 | 4 | no | — |
| 213 | C8×D7 | — | 2 | 4 | no | — |
| 214 | C8×D7 | — | 2 | 4 | no | — |
| 215 | C2×#135 | C2×D7 | 1 | 2 | yes | — |
| 216 | C2×#135 | C2×D7 | 1 | 2 | yes | — |
| 217 | C2×#131 | — | 7 | 1 | no | — |
| 218 | C2×#131 | — | 7 | 1 | no | — |
| 219 | #553 | — | 14 | 4 | no | — |
| 220 | #553 | — | 14 | 8 | no | — |
| 221 | #552 | — | 14 | 4 | no | — |
| 222 | #541 | — | 7 | 4 | no | — |
| 223 | #540 | — | 7 | 4 | no | — |
| 224 | #537 | — | 7 | 4 | no | — |
| 225 | #532 | C2×D7 | 1 | 2 | yes | — |
| 226 | #529 | — | 7 | 8 | no | — |
| 227 | C2×#125 | — | 7 | 2 | no | — |
| 228 | #520 | — | 7 | 4 | no | — |
| 229 | C4×#41 | — | 7 | 1 | no | — |
| 230 | #499 | — | 7 | 2 | no | — |
| 231 | #499 | — | 7 | 2 | no | — |
| 232 | #499 | — | 7 | 2 | no | — |
| 233 | #499 | — | 7 | 2 | no | — |
| 234 | #495 | C2×D7 | 1 | 2 | yes | — |
| 235 | #495 | C2×D7 | 1 | 2 | yes | — |
| 236 | #494 | C2×D7 | 1 | 1 | yes | characteristic |
| 237 | #493 | C2×D7 | 1 | 1 | yes | characteristic |
| 238 | #492 | C2×D7 | 1 | 2 | yes | — |
| 239 | #491 | — | 7 | 4 | no | — |
| 240 | #490 | — | 7 | 4 | no | — |
| 241 | #488 | — | 7 | 8 | no | — |
| 242 | #470 | — | 7 | 4 | no | — |
| 243 | #469 | — | 7 | 4 | no | — |
| 244 | #468 | — | 7 | 8 | no | — |
| 245 | #467 | — | 7 | 4 | no | — |
| 246 | #466 | — | 7 | 4 | no | — |
| 247 | #465 | — | 7 | 8 | no | — |
| 248 | #442 | — | 7 | 4 | no | — |
| 249 | #441 | — | 7 | 4 | no | — |
| 250 | #440 | — | 7 | 8 | no | — |
| 251 | C4×Q16 | — | 7 | 4 | no | — |
| 252 | C4×SD16 | — | 7 | 8 | no | — |
| 253 | C4×D8 | — | 7 | 4 | no | — |
| 254 | C2×#107 | — | 7 | 2 | no | — |
| 255 | C2×#106 | — | 7 | 2 | no | — |
| 256 | #417 | — | 7 | 4 | no | — |
| 257 | #417 | — | 7 | 4 | no | — |
| 258 | #405 | — | 7 | 1 | no | — |
| 259 | #405 | — | 7 | 1 | no | — |
| 260 | #405 | — | 7 | 2 | no | — |
| 261 | #405 | — | 7 | 2 | no | — |
| 262 | C4×M16 | — | 7 | 1 | no | — |
| 263 | C4×M16 | — | 7 | 2 | no | — |
| 264 | C2×C4×C8 | — | 7 | 2 | no | — |
| 265 | C2×C4×C8 | C2×D7 | 1 | 1 | yes | characteristic |
| 266 | C23×C7 | — | 2 | 4 | no | — |
| 267 | C23×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 268 | C22×D7 | C22×D4 | 1 | 2 | yes | — |
| 269 | C7×Q8 | — | 2 | 4 | no | — |
| 270 | C7×Q8 | — | 2 | 4 | no | — |
| 271 | C7×D4 | — | 2 | 4 | no | — |
| 272 | C7×D4 | — | 2 | 4 | no | — |
| 273 | C7×D4 | — | 4 | 8 | no | — |
| 274 | C7×D4 | — | 8 | 4 | no | — |
| 275 | C2×C4×C7 | — | 2 | 4 | no | — |
| 276 | C2×C4×C7 | — | 4 | 2 | no | — |
| 277 | C2×C4×C7 | — | 4 | 8 | no | — |
| 278 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 279 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 280 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 281 | C2×C4×C7 | C2×#41 | 1 | 2 | yes | — |
| 282 | C2×C4×C7 | C2×#41 | 1 | 2 | yes | — |
| 283 | C2×C4×C7 | C25 | 1 | 1 | yes | characteristic |
| 284 | C22⋊D7 | — | 2 | 4 | no | — |
| 285 | C22⋊D7 | — | 8 | 8 | no | — |
| 286 | C2×Dic7 | — | 2 | 8 | no | — |
| 287 | C2×Dic7 | — | 8 | 8 | no | — |
| 288 | C2×Dic7 | — | 8 | 4 | no | — |
| 289 | C2×Dic7 | C22×D4 | 1 | 4 | yes | — |
| 290 | C2×Dic7 | C22×D4 | 1 | 2 | yes | — |
| 291 | D28 | — | 2 | 2 | no | — |
| 292 | C4×D7 | — | 2 | 2 | no | — |
| 293 | C4×D7 | — | 2 | 2 | no | — |
| 294 | C4×D7 | — | 4 | 4 | no | — |
| 295 | Dic14 | — | 2 | 2 | no | — |
| 296 | C7×C8 | C2×#41 | 1 | 2 | yes | — |
| 297 | C7×C8 | C2×#41 | 1 | 2 | yes | — |
| 298 | C7×C8 | C2×#41 | 1 | 2 | yes | — |
| 299 | C7×C8 | C2×#41 | 1 | 2 | yes | — |
| 300 | C7⋊C8 | — | 2 | 2 | no | — |
| 301 | C7⋊C8 | — | 2 | 2 | no | — |
| 302 | C2×#41 | — | 7 | 1 | no | — |
| 303 | C2×#41 | C22×D7 | 1 | 4 | yes | — |
| 304 | #135 | — | 2 | 8 | no | — |
| 305 | #135 | — | 2 | 8 | no | — |
| 306 | C2×Q16 | C22×D7 | 1 | 2 | yes | — |
| 307 | C2×Q16 | C22×D7 | 1 | 2 | yes | — |
| 308 | C2×SD16 | C22×D7 | 1 | 4 | yes | — |
| 309 | C2×SD16 | C22×D7 | 1 | 4 | yes | — |
| 310 | C2×D8 | C22×D7 | 1 | 2 | yes | — |
| 311 | C2×D8 | C22×D7 | 1 | 2 | yes | — |
| 312 | #131 | — | 14 | 4 | no | — |
| 313 | #131 | — | 14 | 4 | no | — |
| 314 | C2×M16 | — | 7 | 1 | no | — |
| 315 | C2×M16 | — | 7 | 1 | no | — |
| 316 | C2×M16 | — | 7 | 2 | no | — |
| 317 | C2×M16 | — | 7 | 2 | no | — |
| 318 | C22×C8 | — | 7 | 2 | no | — |
| 319 | C22×C8 | — | 7 | 2 | no | — |
| 320 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 321 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 322 | C4⋊Q8 | C22×D7 | 1 | 2 | yes | — |
| 323 | #127 | C22×D7 | 1 | 2 | yes | — |
| 324 | #126 | — | 14 | 8 | no | — |
| 325 | #126 | — | 14 | 8 | no | — |
| 326 | #125 | — | 7 | 4 | no | — |
| 327 | #125 | — | 7 | 4 | no | — |
| 328 | #125 | — | 14 | 8 | no | — |
| 329 | #125 | — | 14 | 4 | no | — |
| 330 | #124 | C22×D7 | 1 | 4 | yes | — |
| 331 | #123 | — | 14 | 8 | no | — |
| 332 | #123 | — | 14 | 8 | no | — |
| 333 | C22⋊Q8 | — | 7 | 8 | no | — |
| 334 | C22⋊Q8 | — | 14 | 4 | no | — |
| 335 | #121 | — | 2 | 4 | no | — |
| 336 | #121 | — | 7 | 8 | no | — |
| 337 | #121 | — | 14 | 8 | no | — |
| 338 | #121 | — | 14 | 4 | no | — |
| 339 | #121 | — | 14 | 8 | no | — |
| 340 | C4×Q8 | — | 7 | 2 | no | — |
| 341 | C4×Q8 | — | 7 | 8 | no | — |
| 342 | C4×D4 | — | 2 | 4 | no | — |
| 343 | C4×D4 | — | 7 | 4 | no | — |
| 344 | C4×D4 | — | 7 | 8 | no | — |
| 345 | C4×D4 | — | 7 | 2 | no | — |
| 346 | C4×D4 | — | 14 | 8 | no | — |
| 347 | C4×D4 | — | 14 | 8 | no | — |
| 348 | #117 | — | 7 | 1 | no | — |
| 349 | #117 | — | 7 | 2 | no | — |
| 350 | #117 | — | 14 | 8 | no | — |
| 351 | #117 | — | 14 | 4 | no | — |
| 352 | C2×C4⋊C4 | — | 7 | 4 | no | — |
| 353 | C2×C4⋊C4 | — | 14 | 4 | no | — |
| 354 | C2×C4⋊C4 | — | 14 | 4 | no | — |
| 355 | C2×C42 | — | 7 | 2 | no | — |
| 356 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 357 | #107 | — | 7 | 4 | no | — |
| 358 | #107 | — | 7 | 4 | no | — |
| 359 | #106 | — | 7 | 4 | no | — |
| 360 | #106 | — | 7 | 4 | no | — |
| 361 | #103 | — | 7 | 8 | no | — |
| 362 | #103 | — | 7 | 8 | no | — |
| 363 | #102 | — | 7 | 8 | no | — |
| 364 | #102 | — | 7 | 8 | no | — |
| 365 | #97 | — | 7 | 2 | no | — |
| 366 | #97 | — | 7 | 2 | no | — |
| 367 | #97 | — | 7 | 2 | no | — |
| 368 | C4×C8 | — | 7 | 2 | no | — |
| 369 | C4×C8 | — | 7 | 2 | no | — |
| 370 | C4×C8 | — | 7 | 2 | no | — |
| 371 | C4×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 372 | C4×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 373 | C4×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 374 | C4×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 375 | C22×C7 | — | 2 | 2 | no | — |
| 376 | C22×C7 | — | 4 | 4 | no | — |
| 377 | C22×C7 | — | 4 | 4 | no | — |
| 378 | C22×C7 | — | 4 | 4 | no | — |
| 379 | C22×C7 | #532 | 1 | 2 | yes | — |
| 380 | C22×C7 | C23×D4 | 1 | 1 | yes | characteristic |
| 381 | C2×D7 | — | 2 | 4 | no | — |
| 382 | C2×D7 | — | 2 | 2 | no | — |
| 383 | C4×C7 | — | 2 | 2 | no | — |
| 384 | C4×C7 | — | 2 | 2 | no | — |
| 385 | C4×C7 | — | 4 | 4 | no | — |
| 386 | C4×C7 | #532 | 1 | 2 | yes | — |
| 387 | C4×C7 | C22×#41 | 1 | 1 | yes | characteristic |
| 388 | C4×C7 | C22×#41 | 1 | 1 | yes | characteristic |
| 389 | Dic7 | — | 2 | 4 | no | — |
| 390 | Dic7 | — | 2 | 2 | no | — |
| 391 | Dic7 | — | 4 | 8 | no | — |
| 392 | #41 | — | 2 | 8 | no | — |
| 393 | #41 | — | 2 | 8 | no | — |
| 394 | #41 | — | 14 | 2 | no | — |
| 395 | #41 | — | 14 | 2 | no | — |
| 396 | C2×Q8 | — | 7 | 1 | no | — |
| 397 | C2×Q8 | C23×D7 | 1 | 4 | yes | — |
| 398 | C2×D4 | — | 2 | 4 | no | — |
| 399 | C2×D4 | — | 2 | 4 | no | — |
| 400 | C2×D4 | — | 7 | 2 | no | — |
| 401 | C2×D4 | — | 7 | 1 | no | — |
| 402 | C2×D4 | — | 14 | 8 | no | — |
| 403 | C2×D4 | C23×D7 | 1 | 4 | yes | — |
| 404 | C22×C4 | — | 2 | 4 | no | — |
| 405 | C22×C4 | — | 7 | 2 | no | — |
| 406 | C22×C4 | — | 7 | 4 | no | — |
| 407 | C22×C4 | — | 14 | 8 | no | — |
| 408 | C22×C4 | — | 14 | 4 | no | — |
| 409 | C22×C4 | D4×D7 | 1 | 2 | yes | — |
| 410 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 411 | Q16 | — | 2 | 4 | no | — |
| 412 | Q16 | — | 2 | 4 | no | — |
| 413 | SD16 | — | 2 | 8 | no | — |
| 414 | SD16 | — | 2 | 8 | no | — |
| 415 | D8 | — | 2 | 4 | no | — |
| 416 | D8 | — | 2 | 4 | no | — |
| 417 | M16 | — | 14 | 2 | no | — |
| 418 | M16 | — | 14 | 2 | no | — |
| 419 | M16 | — | 14 | 4 | no | — |
| 420 | M16 | — | 14 | 4 | no | — |
| 421 | C2×C8 | — | 7 | 2 | no | — |
| 422 | C2×C8 | — | 7 | 2 | no | — |
| 423 | C2×C8 | — | 14 | 4 | no | — |
| 424 | C2×C8 | — | 14 | 4 | no | — |
| 425 | C2×C8 | #1159 | 1 | 4 | yes | — |
| 426 | C2×C8 | #1159 | 1 | 4 | yes | — |
| 427 | C2×C8 | C23×D7 | 1 | 1 | yes | characteristic |
| 428 | C2×C8 | C23×D7 | 1 | 1 | yes | characteristic |
| 429 | C2×C8 | C23×D7 | 1 | 1 | yes | characteristic |
| 430 | C2×C8 | C23×D7 | 1 | 1 | yes | characteristic |
| 431 | C4⋊C4 | — | 2 | 4 | no | — |
| 432 | C4⋊C4 | — | 7 | 4 | no | — |
| 433 | C4⋊C4 | — | 7 | 2 | no | — |
| 434 | C4⋊C4 | — | 7 | 8 | no | — |
| 435 | C4⋊C4 | — | 14 | 8 | no | — |
| 436 | C4⋊C4 | — | 14 | 8 | no | — |
| 437 | C4⋊C4 | — | 14 | 8 | no | — |
| 438 | C4⋊C4 | — | 14 | 8 | no | — |
| 439 | C4⋊C4 | — | 14 | 4 | no | — |
| 440 | C22⋊C4 | — | 2 | 4 | no | — |
| 441 | C22⋊C4 | — | 2 | 4 | no | — |
| 442 | C22⋊C4 | — | 7 | 2 | no | — |
| 443 | C22⋊C4 | — | 7 | 4 | no | — |
| 444 | C22⋊C4 | — | 14 | 8 | no | — |
| 445 | C22⋊C4 | — | 14 | 8 | no | — |
| 446 | C22⋊C4 | — | 14 | 8 | no | — |
| 447 | C42 | — | 7 | 4 | no | — |
| 448 | C42 | — | 7 | 2 | no | — |
| 449 | C42 | — | 14 | 8 | no | — |
| 450 | C42 | D4×D7 | 1 | 2 | yes | — |
| 451 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 452 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 453 | C2×C7 | — | 2 | 2 | no | — |
| 454 | C2×C7 | — | 8 | 4 | no | — |
| 455 | C2×C7 | C2×#532 | 1 | 1 | yes | characteristic |
| 456 | C2×C7 | #3584 | 1 | 2 | yes | — |
| 457 | D7 | — | 4 | 2 | no | — |
| 458 | C23 | — | 2 | 4 | no | — |
| 459 | C23 | — | 7 | 2 | no | — |
| 460 | C23 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 461 | Q8 | — | 2 | 4 | no | — |
| 462 | Q8 | — | 2 | 4 | no | — |
| 463 | Q8 | — | 14 | 2 | no | — |
| 464 | D4 | — | 2 | 4 | no | — |
| 465 | D4 | — | 2 | 4 | no | — |
| 466 | D4 | — | 4 | 8 | no | — |
| 467 | D4 | — | 8 | 4 | no | — |
| 468 | D4 | — | 14 | 4 | no | — |
| 469 | D4 | — | 14 | 2 | no | — |
| 470 | D4 | — | 56 | 8 | no | — |
| 471 | C2×C4 | — | 2 | 4 | no | — |
| 472 | C2×C4 | — | 4 | 2 | no | — |
| 473 | C2×C4 | — | 4 | 8 | no | — |
| 474 | C2×C4 | — | 7 | 4 | no | — |
| 475 | C2×C4 | — | 7 | 2 | no | — |
| 476 | C2×C4 | — | 14 | 2 | no | — |
| 477 | C2×C4 | — | 14 | 2 | no | — |
| 478 | C2×C4 | — | 14 | 8 | no | — |
| 479 | C2×C4 | — | 28 | 4 | no | — |
| 480 | C2×C4 | — | 56 | 8 | no | — |
| 481 | C2×C4 | — | 56 | 4 | no | — |
| 482 | C2×C4 | C2×D4×D7 | 1 | 2 | yes | — |
| 483 | C2×C4 | C2×D4×D7 | 1 | 2 | yes | — |
| 484 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 485 | C2×C4 | C2×#1159 | 1 | 2 | yes | — |
| 486 | C2×C4 | C2×#1159 | 1 | 2 | yes | — |
| 487 | C2×C4 | C24×D7 | 1 | 1 | yes | characteristic |
| 488 | C8 | — | 14 | 2 | no | — |
| 489 | C8 | — | 14 | 2 | no | — |
| 490 | C8 | C2×#1159 | 1 | 2 | yes | — |
| 491 | C8 | C2×#1159 | 1 | 2 | yes | — |
| 492 | C8 | C2×#1159 | 1 | 2 | yes | — |
| 493 | C8 | C2×#1159 | 1 | 2 | yes | — |
| 494 | C7 | #60717 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 495 | C22 | — | 2 | 2 | no | — |
| 496 | C22 | — | 4 | 4 | no | — |
| 497 | C22 | — | 4 | 4 | no | — |
| 498 | C22 | — | 4 | 4 | no | — |
| 499 | C22 | — | 14 | 2 | no | — |
| 500 | C22 | — | 14 | 4 | no | — |
| 501 | C22 | #90407 | 1 | 2 | yes | — |
| 502 | C22 | C22×D4×D7 | 1 | 1 | yes | characteristic |
| 503 | C4 | — | 2 | 2 | no | — |
| 504 | C4 | — | 2 | 2 | no | — |
| 505 | C4 | — | 4 | 4 | no | — |
| 506 | C4 | — | 14 | 2 | no | — |
| 507 | C4 | — | 14 | 4 | no | — |
| 508 | C4 | — | 28 | 8 | no | — |
| 509 | C4 | #90407 | 1 | 2 | yes | — |
| 510 | C4 | C22×#1159 | 1 | 1 | yes | characteristic |
| 511 | C4 | C22×#1159 | 1 | 1 | yes | characteristic |
| 512 | C2 | — | 2 | 2 | no | — |
| 513 | C2 | — | 8 | 4 | no | — |
| 514 | C2 | — | 28 | 2 | no | — |
| 515 | C2 | C2×#90407 | 1 | 1 | yes | characteristic |
| 516 | C2 | #11744255 | 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