Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1294 conjugacy classes of subgroups.
The subgroup lattice has 572 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11743291 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C7×#3151 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11740633 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11740604 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11729848 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #11729842 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11729572 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C4×#6397 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11727622 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×C7×AGL(1,ℤ/8) | C22 | 1 | 4 | yes | — |
| 11 | C7×#532 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C7×#127 | C22 | 1 | 1 | yes | characteristic |
| 13 | #90521 | C22 | 1 | 2 | yes | — |
| 14 | #90518 | C22 | 1 | 2 | yes | — |
| 15 | C2×#6503 | C22 | 1 | 2 | yes | — |
| 16 | C2×#6501 | — | 2 | 2 | no | — |
| 17 | #90423 | — | 2 | 1 | no | — |
| 18 | #90409 | — | 2 | 1 | no | — |
| 19 | #90372 | — | 2 | 2 | no | — |
| 20 | #90308 | — | 2 | 2 | no | — |
| 21 | #90297 | — | 2 | 2 | no | — |
| 22 | #90256 | — | 2 | 2 | no | — |
| 23 | #90254 | — | 2 | 1 | no | — |
| 24 | #90246 | — | 2 | 1 | no | — |
| 25 | C2×C4×D28 | C22 | 1 | 1 | yes | characteristic |
| 26 | #90161 | C22 | 1 | 1 | yes | characteristic |
| 27 | C7×#496 | — | 2 | 2 | no | — |
| 28 | C7×#493 | — | 2 | 1 | no | — |
| 29 | C7×#492 | — | 2 | 1 | no | — |
| 30 | C4×C7×M16 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#6411 | C22 | 1 | 4 | yes | — |
| 32 | #89995 | — | 2 | 2 | no | — |
| 33 | #89993 | C22 | 1 | 2 | yes | — |
| 34 | #89987 | C22 | 1 | 4 | yes | — |
| 35 | C2×#6397 | C22 | 1 | 2 | yes | — |
| 36 | #89843 | — | 2 | 2 | no | — |
| 37 | #89842 | — | 2 | 1 | no | — |
| 38 | #89842 | — | 2 | 1 | no | — |
| 39 | C4×C4⋊Dic7 | C22 | 1 | 1 | yes | characteristic |
| 40 | C4×#1136 | C22 | 1 | 1 | yes | characteristic |
| 41 | #89350 | C22 | 1 | 4 | yes | — |
| 42 | #89349 | C22 | 1 | 2 | yes | — |
| 43 | #25622 | — | 7 | 1 | no | maximal, Sylow |
| 44 | C2×C7×#41 | C23 | 1 | 2 | yes | — |
| 45 | C22×C7×D4 | — | 2 | 1 | no | — |
| 46 | C22×C7×D4 | — | 2 | 1 | no | — |
| 47 | C22×C7×D4 | C23 | 1 | 2 | yes | — |
| 48 | C22×C22⋊D7 | — | 2 | 4 | no | — |
| 49 | C2×#1159 | — | 2 | 2 | no | — |
| 50 | C22×D28 | C23 | 1 | 1 | yes | characteristic |
| 51 | C22×C4×D7 | D4 | 1 | 2 | yes | — |
| 52 | C7×AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 53 | C7×AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 54 | C2×C7×SD16 | — | 2 | 4 | no | — |
| 55 | C2×C7×D8 | — | 2 | 4 | no | — |
| 56 | C2×C7×M16 | C23 | 1 | 2 | yes | — |
| 57 | C7×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic, complemented |
| 58 | C7×#127 | — | 2 | 1 | no | — |
| 59 | C7×#127 | — | 2 | 1 | no | — |
| 60 | C7×#127 | — | 2 | 1 | no | — |
| 61 | C7×#127 | — | 2 | 1 | no | — |
| 62 | C7×#127 | D4 | 1 | 1 | yes | characteristic, complemented |
| 63 | C7×#124 | D4 | 1 | 2 | yes | complemented |
| 64 | C7×#121 | — | 2 | 1 | no | — |
| 65 | C7×#121 | — | 2 | 1 | no | — |
| 66 | C4×C7×D4 | — | 2 | 1 | no | — |
| 67 | C4×C7×D4 | — | 2 | 1 | no | — |
| 68 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×C22⋊Dic7 | — | 2 | 4 | no | — |
| 70 | #6510 | — | 2 | 2 | no | — |
| 71 | Q8×Dic7 | — | 2 | 2 | no | — |
| 72 | #6503 | — | 2 | 2 | no | — |
| 73 | #6503 | — | 4 | 4 | no | — |
| 74 | #6502 | — | 2 | 4 | no | — |
| 75 | #6501 | — | 2 | 2 | no | — |
| 76 | #6501 | — | 4 | 8 | no | — |
| 77 | #6500 | — | 2 | 4 | no | — |
| 78 | D4×Dic7 | — | 2 | 2 | no | — |
| 79 | D4×Dic7 | — | 2 | 4 | no | — |
| 80 | #6493 | — | 2 | 2 | no | — |
| 81 | #6493 | — | 2 | 2 | no | — |
| 82 | C2×(C2×D7)⋊C4 | D4 | 1 | 2 | yes | — |
| 83 | #6489 | — | 2 | 2 | no | — |
| 84 | #6489 | C23 | 1 | 2 | yes | — |
| 85 | C2×C4⋊Dic7 | — | 2 | 1 | no | — |
| 86 | C2×C4⋊Dic7 | — | 2 | 2 | no | — |
| 87 | C2×C4⋊Dic7 | C23 | 1 | 1 | yes | characteristic |
| 88 | #6487 | — | 2 | 1 | no | — |
| 89 | #6487 | — | 2 | 1 | no | — |
| 90 | C2×C4×Dic7 | C23 | 1 | 2 | yes | — |
| 91 | C2×#1136 | C23 | 1 | 2 | yes | — |
| 92 | #6461 | — | 2 | 4 | no | — |
| 93 | #6460 | — | 2 | 2 | no | — |
| 94 | #6455 | — | 2 | 2 | no | — |
| 95 | #6449 | — | 2 | 4 | no | — |
| 96 | #6448 | — | 2 | 4 | no | — |
| 97 | #6446 | — | 2 | 4 | no | — |
| 98 | (C22⋊D7)⋊C4 | — | 2 | 4 | no | — |
| 99 | C4×D28 | — | 2 | 1 | no | — |
| 100 | C4×D28 | — | 2 | 1 | no | — |
| 101 | C4×D28 | — | 2 | 1 | no | — |
| 102 | C4×D28 | — | 2 | 1 | no | — |
| 103 | #6433 | D4 | 1 | 2 | yes | complemented |
| 104 | #6432 | D4 | 1 | 1 | yes | characteristic, complemented |
| 105 | #6432 | D4 | 1 | 1 | yes | characteristic, complemented |
| 106 | C4×Dic14 | — | 2 | 1 | no | — |
| 107 | C4×Dic14 | — | 2 | 1 | no | — |
| 108 | C7×#97 | — | 2 | 1 | no | — |
| 109 | C4×C7×C8 | — | 2 | 1 | no | — |
| 110 | #6411 | — | 4 | 4 | no | — |
| 111 | #6406 | — | 2 | 4 | no | — |
| 112 | #6406 | — | 2 | 4 | no | — |
| 113 | C7⋊#95 | — | 2 | 1 | no | — |
| 114 | #6397 | — | 2 | 4 | no | — |
| 115 | #6377 | — | 2 | 1 | no | — |
| 116 | C4×C7⋊C8 | — | 2 | 1 | no | — |
| 117 | #3506 | — | 7 | 1 | no | — |
| 118 | #3151 | D7 | 1 | 1 | yes | characteristic, complemented |
| 119 | #3138 | — | 7 | 1 | no | — |
| 120 | #2541 | — | 7 | 1 | no | — |
| 121 | #2002 | — | 7 | 4 | no | — |
| 122 | #1986 | — | 7 | 1 | no | — |
| 123 | #1980 | — | 7 | 1 | no | — |
| 124 | #1883 | — | 7 | 4 | no | — |
| 125 | C4×#100 | — | 7 | 1 | no | — |
| 126 | C24×C7 | — | 2 | 2 | no | — |
| 127 | C23×D7 | C2×D4 | 1 | 2 | yes | — |
| 128 | C7×#41 | — | 2 | 4 | no | — |
| 129 | C7×#41 | — | 2 | 4 | no | — |
| 130 | C2×C7×Q8 | C2×D4 | 1 | 2 | yes | — |
| 131 | C2×C7×D4 | — | 2 | 2 | no | — |
| 132 | C2×C7×D4 | — | 2 | 1 | no | — |
| 133 | C2×C7×D4 | — | 2 | 1 | no | — |
| 134 | C2×C7×D4 | — | 2 | 2 | no | — |
| 135 | C2×C7×D4 | — | 2 | 2 | no | — |
| 136 | C2×C7×D4 | — | 2 | 4 | no | — |
| 137 | C2×C7×D4 | — | 2 | 4 | no | — |
| 138 | C2×C7×D4 | — | 4 | 4 | no | — |
| 139 | C2×C7×D4 | — | 4 | 1 | no | — |
| 140 | C2×C7×D4 | — | 4 | 1 | no | — |
| 141 | C2×C7×D4 | — | 4 | 1 | no | — |
| 142 | C2×C7×D4 | — | 4 | 1 | no | — |
| 143 | C2×C7×D4 | — | 8 | 2 | no | — |
| 144 | C2×C7×D4 | C2×D4 | 1 | 2 | yes | — |
| 145 | C22×C4×C7 | — | 2 | 2 | no | — |
| 146 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 147 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 148 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 149 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 150 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 151 | C2×C22⋊D7 | — | 4 | 8 | no | — |
| 152 | C2×C22⋊D7 | — | 4 | 8 | no | — |
| 153 | C2×C22⋊D7 | — | 8 | 4 | no | — |
| 154 | C22×Dic7 | — | 2 | 2 | no | — |
| 155 | C22×Dic7 | — | 2 | 4 | no | — |
| 156 | C22×Dic7 | C2×D4 | 1 | 2 | yes | — |
| 157 | #1159 | — | 8 | 4 | no | — |
| 158 | C2×D28 | — | 2 | 1 | no | — |
| 159 | C2×D28 | — | 2 | 1 | no | — |
| 160 | C2×D28 | — | 2 | 2 | no | — |
| 161 | C2×D28 | — | 2 | 2 | no | — |
| 162 | C2×C4×D7 | — | 2 | 2 | no | — |
| 163 | C2×C4×D7 | — | 2 | 2 | no | — |
| 164 | C2×C4×D7 | — | 4 | 4 | no | — |
| 165 | C2×Dic14 | — | 2 | 1 | no | — |
| 166 | C2×Dic14 | — | 2 | 1 | no | — |
| 167 | C7×SD16 | — | 4 | 8 | no | — |
| 168 | C7×D8 | — | 4 | 8 | no | — |
| 169 | C7×M16 | — | 2 | 2 | no | — |
| 170 | C7×M16 | #41 | 1 | 4 | yes | complemented |
| 171 | C2×C7×C8 | — | 2 | 2 | no | — |
| 172 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 173 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 174 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 175 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 176 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 177 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 178 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 179 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 180 | C22⋊Dic7 | — | 2 | 4 | no | — |
| 181 | C22⋊Dic7 | — | 2 | 2 | no | — |
| 182 | C22⋊Dic7 | — | 4 | 8 | no | — |
| 183 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 184 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 185 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 186 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 187 | C4⋊Dic7 | — | 2 | 4 | no | — |
| 188 | C4⋊Dic7 | — | 2 | 4 | no | — |
| 189 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 190 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 191 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 192 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 193 | C4⋊Dic7 | C2×D4 | 1 | 2 | yes | — |
| 194 | C4⋊Dic7 | C2×D4 | 1 | 2 | yes | — |
| 195 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 196 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 197 | C4×Dic7 | — | 2 | 4 | no | — |
| 198 | C4×Dic7 | — | 2 | 2 | no | — |
| 199 | C4×Dic7 | — | 2 | 4 | no | — |
| 200 | #1136 | — | 2 | 2 | no | — |
| 201 | #1136 | — | 2 | 2 | no | — |
| 202 | C2×C7⋊C8 | — | 2 | 2 | no | — |
| 203 | C2×AGL(1,ℤ/8) | C2×D7 | 1 | 4 | yes | — |
| 204 | #559 | — | 14 | 2 | no | — |
| 205 | #556 | — | 14 | 1 | no | — |
| 206 | #555 | — | 14 | 1 | no | — |
| 207 | #553 | — | 14 | 2 | no | — |
| 208 | #550 | — | 14 | 1 | no | — |
| 209 | #547 | — | 14 | 1 | no | — |
| 210 | #538 | — | 14 | 2 | no | — |
| 211 | #535 | — | 7 | 2 | no | — |
| 212 | #533 | — | 7 | 1 | no | — |
| 213 | #532 | C2×D7 | 1 | 1 | yes | characteristic |
| 214 | C2×#127 | — | 7 | 2 | no | — |
| 215 | C2×#127 | C2×D7 | 1 | 1 | yes | characteristic |
| 216 | #525 | — | 14 | 2 | no | — |
| 217 | C2×#121 | — | 14 | 2 | no | — |
| 218 | #520 | — | 7 | 2 | no | — |
| 219 | C2×C4×D4 | — | 7 | 1 | no | — |
| 220 | #496 | — | 2 | 2 | no | — |
| 221 | #493 | — | 2 | 1 | no | — |
| 222 | #492 | — | 2 | 1 | no | — |
| 223 | #490 | — | 14 | 2 | no | — |
| 224 | #486 | — | 14 | 1 | no | — |
| 225 | #486 | — | 14 | 1 | no | — |
| 226 | C2×#104 | — | 7 | 4 | no | — |
| 227 | #418 | — | 7 | 4 | no | — |
| 228 | C2×#100 | — | 7 | 2 | no | — |
| 229 | C4×M16 | — | 7 | 1 | no | — |
| 230 | C4×M16 | C2×D7 | 1 | 1 | yes | characteristic |
| 231 | #392 | — | 14 | 2 | no | — |
| 232 | #390 | — | 7 | 2 | no | — |
| 233 | C4×C4⋊C4 | — | 7 | 1 | no | — |
| 234 | #343 | — | 7 | 2 | no | — |
| 235 | #339 | — | 7 | 4 | no | — |
| 236 | C23×C7 | — | 2 | 2 | no | — |
| 237 | C23×C7 | — | 4 | 4 | no | — |
| 238 | C23×C7 | — | 4 | 4 | no | — |
| 239 | C23×C7 | — | 4 | 2 | no | — |
| 240 | C23×C7 | — | 4 | 2 | no | — |
| 241 | C23×C7 | — | 4 | 2 | no | — |
| 242 | C23×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 243 | C22×D7 | — | 2 | 2 | no | — |
| 244 | C22×D7 | — | 2 | 2 | no | — |
| 245 | C22×D7 | — | 2 | 2 | no | — |
| 246 | C22×D7 | — | 4 | 2 | no | — |
| 247 | C22×D7 | — | 4 | 2 | no | — |
| 248 | C7×Q8 | — | 2 | 4 | no | — |
| 249 | C7×D4 | — | 2 | 4 | no | — |
| 250 | C7×D4 | — | 4 | 2 | no | — |
| 251 | C7×D4 | — | 4 | 2 | no | — |
| 252 | C7×D4 | — | 4 | 4 | no | — |
| 253 | C7×D4 | — | 4 | 4 | no | — |
| 254 | C7×D4 | — | 4 | 2 | no | — |
| 255 | C7×D4 | — | 8 | 1 | no | — |
| 256 | C7×D4 | — | 8 | 2 | no | — |
| 257 | C7×D4 | — | 8 | 2 | no | — |
| 258 | C7×D4 | — | 8 | 2 | no | — |
| 259 | C7×D4 | — | 8 | 2 | no | — |
| 260 | C2×C4×C7 | — | 2 | 2 | no | — |
| 261 | C2×C4×C7 | — | 2 | 2 | no | — |
| 262 | C2×C4×C7 | — | 4 | 1 | no | — |
| 263 | C2×C4×C7 | — | 4 | 4 | no | — |
| 264 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 265 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 266 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 267 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 268 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 269 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 270 | C2×C4×C7 | C2×#41 | 1 | 2 | yes | — |
| 271 | C2×C4×C7 | H(5,𝔽2) | 1 | 2 | yes | — |
| 272 | C22⋊D7 | — | 8 | 4 | no | — |
| 273 | C22⋊D7 | — | 8 | 4 | no | — |
| 274 | C22⋊D7 | — | 8 | 16 | no | — |
| 275 | C2×Dic7 | — | 2 | 4 | no | — |
| 276 | C2×Dic7 | — | 2 | 2 | no | — |
| 277 | C2×Dic7 | — | 2 | 2 | no | — |
| 278 | C2×Dic7 | — | 2 | 2 | no | — |
| 279 | C2×Dic7 | — | 4 | 2 | no | — |
| 280 | C2×Dic7 | — | 4 | 2 | no | — |
| 281 | C2×Dic7 | — | 4 | 2 | no | — |
| 282 | C2×Dic7 | — | 8 | 4 | no | — |
| 283 | D28 | — | 4 | 2 | no | — |
| 284 | D28 | — | 4 | 2 | no | — |
| 285 | C4×D7 | — | 4 | 4 | no | — |
| 286 | C4×D7 | — | 8 | 2 | no | — |
| 287 | Dic14 | — | 4 | 2 | no | — |
| 288 | Dic14 | — | 8 | 1 | no | — |
| 289 | C7×C8 | — | 2 | 4 | no | — |
| 290 | C7⋊C8 | — | 4 | 2 | no | — |
| 291 | C2×#41 | — | 14 | 2 | no | — |
| 292 | C2×#41 | C22×D7 | 1 | 2 | yes | — |
| 293 | C22×D4 | — | 2 | 1 | no | — |
| 294 | C22×D4 | — | 2 | 1 | no | — |
| 295 | C22×D4 | — | 7 | 1 | no | — |
| 296 | C22×D4 | — | 14 | 4 | no | — |
| 297 | C22×D4 | C22×D7 | 1 | 2 | yes | — |
| 298 | C23×C4 | — | 7 | 2 | no | — |
| 299 | AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 300 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 301 | C2×SD16 | — | 2 | 4 | no | — |
| 302 | C2×D8 | — | 2 | 4 | no | — |
| 303 | C2×M16 | — | 7 | 2 | no | — |
| 304 | C2×M16 | C22×D7 | 1 | 2 | yes | — |
| 305 | C4⋊Q8 | — | 7 | 1 | no | — |
| 306 | C4⋊Q8 | — | 7 | 1 | no | — |
| 307 | C4⋊Q8 | C22⋊D7 | 1 | 1 | yes | characteristic, complemented |
| 308 | #127 | — | 2 | 1 | no | — |
| 309 | #127 | — | 2 | 1 | no | — |
| 310 | #127 | — | 2 | 1 | no | — |
| 311 | #127 | — | 2 | 1 | no | — |
| 312 | #127 | — | 14 | 2 | no | — |
| 313 | #127 | — | 28 | 4 | no | — |
| 314 | #127 | C22⋊D7 | 1 | 1 | yes | characteristic, complemented |
| 315 | #126 | — | 14 | 4 | no | — |
| 316 | #125 | — | 7 | 2 | no | — |
| 317 | #124 | — | 14 | 4 | no | — |
| 318 | #124 | — | 14 | 2 | no | — |
| 319 | #124 | C22⋊D7 | 1 | 2 | yes | complemented |
| 320 | #123 | — | 14 | 4 | no | — |
| 321 | #123 | — | 14 | 4 | no | — |
| 322 | C22⋊Q8 | — | 14 | 2 | no | — |
| 323 | C22⋊Q8 | — | 14 | 1 | no | — |
| 324 | C22⋊Q8 | — | 14 | 1 | no | — |
| 325 | #121 | — | 2 | 1 | no | — |
| 326 | #121 | — | 2 | 1 | no | — |
| 327 | #121 | — | 14 | 2 | no | — |
| 328 | #121 | — | 14 | 2 | no | — |
| 329 | #121 | — | 14 | 2 | no | — |
| 330 | #121 | — | 14 | 4 | no | — |
| 331 | #121 | — | 28 | 8 | no | — |
| 332 | #120 | — | 14 | 4 | no | — |
| 333 | C4×Q8 | — | 14 | 2 | no | — |
| 334 | C4×Q8 | — | 14 | 1 | no | — |
| 335 | C4×Q8 | — | 14 | 1 | no | — |
| 336 | C4×D4 | — | 2 | 1 | no | — |
| 337 | C4×D4 | — | 2 | 1 | no | — |
| 338 | C4×D4 | — | 14 | 4 | no | — |
| 339 | C4×D4 | — | 14 | 4 | no | — |
| 340 | C4×D4 | — | 14 | 2 | no | — |
| 341 | C4×D4 | — | 14 | 1 | no | — |
| 342 | C4×D4 | — | 14 | 1 | no | — |
| 343 | C4×D4 | — | 14 | 1 | no | — |
| 344 | C4×D4 | — | 14 | 1 | no | — |
| 345 | #117 | — | 7 | 2 | no | — |
| 346 | #117 | — | 14 | 2 | no | — |
| 347 | #117 | — | 14 | 2 | no | — |
| 348 | C2×C4⋊C4 | — | 7 | 1 | no | — |
| 349 | C2×C4⋊C4 | — | 14 | 2 | no | — |
| 350 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 351 | C2×C22⋊C4 | — | 7 | 2 | no | — |
| 352 | C2×C22⋊C4 | — | 14 | 4 | no | — |
| 353 | C2×C42 | — | 7 | 2 | no | — |
| 354 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 355 | #104 | — | 28 | 4 | no | — |
| 356 | #102 | — | 14 | 4 | no | — |
| 357 | #102 | — | 14 | 4 | no | — |
| 358 | #100 | — | 14 | 4 | no | — |
| 359 | #97 | — | 2 | 1 | no | — |
| 360 | #97 | — | 14 | 1 | no | — |
| 361 | C4×C8 | — | 2 | 1 | no | — |
| 362 | C4×C8 | — | 14 | 1 | no | — |
| 363 | #95 | — | 14 | 1 | no | — |
| 364 | C22×C7 | — | 2 | 1 | no | — |
| 365 | C22×C7 | — | 2 | 1 | no | — |
| 366 | C22×C7 | — | 4 | 2 | no | — |
| 367 | C22×C7 | — | 4 | 2 | no | — |
| 368 | C22×C7 | — | 4 | 2 | no | — |
| 369 | C22×C7 | — | 8 | 4 | no | — |
| 370 | C22×C7 | — | 8 | 4 | no | — |
| 371 | C22×C7 | — | 8 | 2 | no | — |
| 372 | C22×C7 | — | 8 | 2 | no | — |
| 373 | C22×C7 | — | 8 | 2 | no | — |
| 374 | C22×C7 | C2×#120 | 1 | 1 | yes | characteristic |
| 375 | C22×C7 | #532 | 1 | 1 | yes | characteristic |
| 376 | C22×C7 | #535 | 1 | 1 | yes | characteristic |
| 377 | C2×D7 | — | 4 | 4 | no | — |
| 378 | C2×D7 | — | 4 | 2 | no | — |
| 379 | C2×D7 | — | 4 | 2 | no | — |
| 380 | C2×D7 | — | 4 | 2 | no | — |
| 381 | C2×D7 | — | 8 | 2 | no | — |
| 382 | C4×C7 | — | 2 | 1 | no | — |
| 383 | C4×C7 | — | 2 | 1 | no | — |
| 384 | C4×C7 | — | 2 | 1 | no | — |
| 385 | C4×C7 | — | 4 | 2 | no | — |
| 386 | C4×C7 | #453 | 1 | 2 | yes | — |
| 387 | C4×C7 | #546 | 1 | 2 | yes | — |
| 388 | C4×C7 | #550 | 1 | 2 | yes | — |
| 389 | Dic7 | — | 4 | 4 | no | — |
| 390 | Dic7 | — | 4 | 2 | no | — |
| 391 | Dic7 | — | 4 | 2 | no | — |
| 392 | Dic7 | — | 4 | 2 | no | — |
| 393 | C24 | — | 2 | 2 | no | — |
| 394 | C24 | — | 7 | 2 | no | — |
| 395 | #41 | — | 2 | 4 | no | — |
| 396 | #41 | — | 2 | 4 | no | — |
| 397 | #41 | — | 56 | 4 | no | — |
| 398 | C2×Q8 | — | 14 | 1 | no | — |
| 399 | C2×Q8 | — | 14 | 1 | no | — |
| 400 | C2×Q8 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 401 | C2×D4 | — | 2 | 2 | no | — |
| 402 | C2×D4 | — | 2 | 1 | no | — |
| 403 | C2×D4 | — | 2 | 1 | no | — |
| 404 | C2×D4 | — | 2 | 2 | no | — |
| 405 | C2×D4 | — | 2 | 4 | no | — |
| 406 | C2×D4 | — | 2 | 4 | no | — |
| 407 | C2×D4 | — | 2 | 2 | no | — |
| 408 | C2×D4 | — | 4 | 4 | no | — |
| 409 | C2×D4 | — | 4 | 1 | no | — |
| 410 | C2×D4 | — | 4 | 1 | no | — |
| 411 | C2×D4 | — | 4 | 1 | no | — |
| 412 | C2×D4 | — | 4 | 1 | no | — |
| 413 | C2×D4 | — | 8 | 2 | no | — |
| 414 | C2×D4 | — | 14 | 4 | no | — |
| 415 | C2×D4 | — | 14 | 4 | no | — |
| 416 | C2×D4 | — | 14 | 1 | no | — |
| 417 | C2×D4 | — | 14 | 2 | no | — |
| 418 | C2×D4 | — | 14 | 2 | no | — |
| 419 | C2×D4 | — | 14 | 1 | no | — |
| 420 | C2×D4 | — | 28 | 8 | no | — |
| 421 | C2×D4 | — | 28 | 8 | no | — |
| 422 | C2×D4 | — | 56 | 4 | no | — |
| 423 | C2×D4 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 424 | C22×C4 | — | 2 | 2 | no | — |
| 425 | C22×C4 | — | 7 | 2 | no | — |
| 426 | C22×C4 | — | 14 | 2 | no | — |
| 427 | C22×C4 | — | 14 | 4 | no | — |
| 428 | C22×C4 | — | 14 | 2 | no | — |
| 429 | C22×C4 | — | 14 | 2 | no | — |
| 430 | C22×C4 | — | 28 | 4 | no | — |
| 431 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 432 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 433 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 434 | SD16 | — | 4 | 8 | no | — |
| 435 | D8 | — | 4 | 8 | no | — |
| 436 | M16 | — | 2 | 2 | no | — |
| 437 | M16 | — | 14 | 2 | no | — |
| 438 | M16 | — | 14 | 2 | no | — |
| 439 | M16 | #1159 | 1 | 4 | yes | complemented |
| 440 | C2×C8 | — | 2 | 2 | no | — |
| 441 | C2×C8 | — | 14 | 2 | no | — |
| 442 | C4⋊C4 | — | 2 | 1 | no | — |
| 443 | C4⋊C4 | — | 2 | 1 | no | — |
| 444 | C4⋊C4 | — | 7 | 2 | no | — |
| 445 | C4⋊C4 | — | 7 | 2 | no | — |
| 446 | C4⋊C4 | — | 14 | 4 | no | — |
| 447 | C4⋊C4 | — | 14 | 4 | no | — |
| 448 | C4⋊C4 | — | 14 | 2 | no | — |
| 449 | C4⋊C4 | — | 14 | 2 | no | — |
| 450 | C4⋊C4 | — | 14 | 1 | no | — |
| 451 | C4⋊C4 | — | 14 | 1 | no | — |
| 452 | C4⋊C4 | — | 14 | 1 | no | — |
| 453 | C4⋊C4 | — | 14 | 1 | no | — |
| 454 | C22⋊C4 | — | 2 | 2 | no | — |
| 455 | C22⋊C4 | — | 2 | 2 | no | — |
| 456 | C22⋊C4 | — | 14 | 4 | no | — |
| 457 | C22⋊C4 | — | 14 | 4 | no | — |
| 458 | C22⋊C4 | — | 14 | 4 | no | — |
| 459 | C22⋊C4 | — | 14 | 2 | no | — |
| 460 | C22⋊C4 | — | 14 | 2 | no | — |
| 461 | C22⋊C4 | — | 14 | 2 | no | — |
| 462 | C22⋊C4 | — | 28 | 8 | no | — |
| 463 | C42 | — | 14 | 4 | no | — |
| 464 | C42 | — | 14 | 2 | no | — |
| 465 | C42 | — | 14 | 4 | no | — |
| 466 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 467 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 468 | C42 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 469 | C42 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 470 | C2×C7 | — | 2 | 1 | no | — |
| 471 | C2×C7 | — | 2 | 1 | no | — |
| 472 | C2×C7 | — | 8 | 2 | no | — |
| 473 | C2×C7 | — | 16 | 2 | no | — |
| 474 | C2×C7 | #2431 | 1 | 1 | yes | characteristic |
| 475 | C2×C7 | C2×#453 | 1 | 1 | yes | characteristic |
| 476 | C2×C7 | #3021 | 1 | 1 | yes | characteristic |
| 477 | D7 | — | 8 | 2 | no | — |
| 478 | C23 | — | 2 | 2 | no | — |
| 479 | C23 | — | 4 | 4 | no | — |
| 480 | C23 | — | 4 | 4 | no | — |
| 481 | C23 | — | 4 | 2 | no | — |
| 482 | C23 | — | 4 | 2 | no | — |
| 483 | C23 | — | 4 | 2 | no | — |
| 484 | C23 | — | 14 | 2 | no | — |
| 485 | C23 | — | 14 | 2 | no | — |
| 486 | C23 | — | 14 | 2 | no | — |
| 487 | C23 | — | 28 | 2 | no | — |
| 488 | C23 | — | 28 | 2 | no | — |
| 489 | C23 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 490 | Q8 | — | 2 | 4 | no | — |
| 491 | Q8 | — | 28 | 2 | no | — |
| 492 | Q8 | — | 56 | 1 | no | — |
| 493 | D4 | — | 2 | 4 | no | — |
| 494 | D4 | — | 4 | 2 | no | — |
| 495 | D4 | — | 4 | 2 | no | — |
| 496 | D4 | — | 4 | 4 | no | — |
| 497 | D4 | — | 4 | 2 | no | — |
| 498 | D4 | — | 4 | 4 | no | — |
| 499 | D4 | — | 8 | 1 | no | — |
| 500 | D4 | — | 8 | 2 | no | — |
| 501 | D4 | — | 8 | 2 | no | — |
| 502 | D4 | — | 8 | 2 | no | — |
| 503 | D4 | — | 8 | 2 | no | — |
| 504 | D4 | — | 28 | 2 | no | — |
| 505 | D4 | — | 28 | 2 | no | — |
| 506 | D4 | — | 56 | 4 | no | — |
| 507 | D4 | — | 56 | 4 | no | — |
| 508 | D4 | — | 56 | 16 | no | — |
| 509 | C2×C4 | — | 2 | 2 | no | — |
| 510 | C2×C4 | — | 2 | 2 | no | — |
| 511 | C2×C4 | — | 4 | 1 | no | — |
| 512 | C2×C4 | — | 4 | 4 | no | — |
| 513 | C2×C4 | — | 14 | 4 | no | — |
| 514 | C2×C4 | — | 14 | 2 | no | — |
| 515 | C2×C4 | — | 14 | 2 | no | — |
| 516 | C2×C4 | — | 14 | 2 | no | — |
| 517 | C2×C4 | — | 28 | 2 | no | — |
| 518 | C2×C4 | — | 28 | 2 | no | — |
| 519 | C2×C4 | — | 28 | 4 | no | — |
| 520 | C2×C4 | — | 28 | 2 | no | — |
| 521 | C2×C4 | — | 56 | 2 | no | — |
| 522 | C2×C4 | — | 56 | 4 | no | — |
| 523 | C2×C4 | #6500 | 1 | 1 | yes | characteristic |
| 524 | C2×C4 | #6500 | 1 | 1 | yes | characteristic |
| 525 | C2×C4 | #6500 | 1 | 1 | yes | characteristic |
| 526 | C2×C4 | #6500 | 1 | 1 | yes | characteristic |
| 527 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 528 | C2×C4 | C2×#1159 | 1 | 2 | yes | — |
| 529 | C2×C4 | #6548 | 1 | 2 | yes | — |
| 530 | C2×C4 | C22×C22⋊D7 | 1 | 1 | yes | characteristic |
| 531 | C8 | — | 2 | 4 | no | — |
| 532 | C8 | — | 28 | 2 | no | — |
| 533 | C7 | #25622 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 534 | C22 | — | 2 | 1 | no | — |
| 535 | C22 | — | 2 | 1 | no | — |
| 536 | C22 | — | 4 | 2 | no | — |
| 537 | C22 | — | 4 | 2 | no | — |
| 538 | C22 | — | 4 | 2 | no | — |
| 539 | C22 | — | 8 | 4 | no | — |
| 540 | C22 | — | 8 | 4 | no | — |
| 541 | C22 | — | 8 | 2 | no | — |
| 542 | C22 | — | 8 | 2 | no | — |
| 543 | C22 | — | 8 | 2 | no | — |
| 544 | C22 | — | 28 | 4 | no | — |
| 545 | C22 | — | 28 | 2 | no | — |
| 546 | C22 | — | 28 | 2 | no | — |
| 547 | C22 | — | 28 | 2 | no | — |
| 548 | C22 | — | 56 | 2 | no | — |
| 549 | C22 | #90406 | 1 | 1 | yes | characteristic |
| 550 | C22 | #90407 | 1 | 1 | yes | characteristic |
| 551 | C22 | C2×#6500 | 1 | 1 | yes | characteristic |
| 552 | C4 | — | 2 | 1 | no | — |
| 553 | C4 | — | 2 | 1 | no | — |
| 554 | C4 | — | 2 | 1 | no | — |
| 555 | C4 | — | 4 | 2 | no | — |
| 556 | C4 | — | 28 | 4 | no | — |
| 557 | C4 | — | 28 | 2 | no | — |
| 558 | C4 | — | 28 | 2 | no | — |
| 559 | C4 | — | 28 | 2 | no | — |
| 560 | C4 | #89970 | 1 | 2 | yes | — |
| 561 | C4 | #90409 | 1 | 2 | yes | — |
| 562 | C4 | #90497 | 1 | 2 | yes | — |
| 563 | C2 | — | 2 | 1 | no | — |
| 564 | C2 | — | 2 | 1 | no | — |
| 565 | C2 | — | 8 | 2 | no | — |
| 566 | C2 | — | 16 | 2 | no | — |
| 567 | C2 | — | 56 | 2 | no | — |
| 568 | C2 | #11740632 | 1 | 1 | yes | characteristic |
| 569 | C2 | C2×#89970 | 1 | 1 | yes | characteristic |
| 570 | C2 | #11741402 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11743291 | C2 | semidirect |
| 2. C7×#3151 | C2 | semidirect |
| 3. #11740633 | C2 | semidirect |
| 4. #11740604 | C2 | semidirect |
| 5. #11729848 | C2 | semidirect |
| 6. #11729842 | C2 | semidirect |
| 7. #11729572 | C2 | semidirect |
| 8. C4×#6397 | C2 | semidirect |
| 9. #11727622 | C2 | semidirect |
| 57. C7×C4⋊Q8 | D4 | semidirect |
| 62. C7×#127 | D4 | semidirect |
| 63. C7×#124 | D4 | semidirect |
| 103. #6433 | D4 | semidirect |
| 104. #6432 | D4 | semidirect |
| 105. #6432 | D4 | semidirect |
| 118. #3151 | D7 | semidirect |
| 170. C7×M16 | #41 | semidirect |
| 307. C4⋊Q8 | C22⋊D7 | semidirect |
| 314. #127 | C22⋊D7 | semidirect |
| 319. #124 | C22⋊D7 | semidirect |
| 439. M16 | #1159 | semidirect |
| 533. C7 | #25622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11743291 | 2 |
| C7×#3151 | 2 |
| #11740633 | 2 |
| #11740604 | 2 |
| #11729848 | 2 |
| #11729842 | 2 |
| #11729572 | 2 |
| C4×#6397 | 2 |
| #11727622 | 2 |
| #25622 | 7 |