Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2064 conjugacy classes of subgroups.
The subgroup lattice has 658 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11744084 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D4×Q8×D7 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C7×#3359 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11741133 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11741007 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11739067 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #11739046 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #11738483 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #11738457 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #11737873 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #11737861 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #11737369 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | Q8×#1131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C4×#6477 | C2 | 1 | 3 | yes | maximal, complemented |
| 15 | #11737074 | C2 | 1 | 3 | yes | maximal, complemented |
| 16 | C22×Q8×D7 | — | 2 | 1 | no | — |
| 17 | C7×#557 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C7×D4×Q8 | C22 | 1 | 1 | yes | characteristic |
| 19 | Q8×C22⋊D7 | — | 2 | 1 | no | — |
| 20 | C2×#6477 | C22 | 1 | 3 | yes | — |
| 21 | #90423 | C22 | 1 | 3 | yes | complemented |
| 22 | #90418 | C22 | 1 | 3 | yes | — |
| 23 | #90416 | C22 | 1 | 3 | yes | — |
| 24 | D7×C4⋊Q8 | C22 | 1 | 3 | yes | — |
| 25 | #90386 | — | 2 | 3 | no | — |
| 26 | #90382 | — | 2 | 3 | no | — |
| 27 | #90323 | — | 2 | 3 | no | — |
| 28 | D7×C22⋊Q8 | — | 2 | 3 | no | — |
| 29 | #90276 | C22 | 1 | 3 | yes | complemented |
| 30 | #90268 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #90267 | — | 2 | 1 | no | — |
| 32 | Q8×D28 | C22 | 1 | 1 | yes | characteristic |
| 33 | C4×#1161 | — | 2 | 1 | no | — |
| 34 | C4×#1161 | C22 | 1 | 3 | yes | — |
| 35 | C4×Q8×D7 | C22 | 1 | 1 | yes | characteristic |
| 36 | C4×D4×D7 | C22 | 1 | 3 | yes | — |
| 37 | D4×Dic14 | C22 | 1 | 3 | yes | — |
| 38 | C7×#487 | C22 | 1 | 3 | yes | complemented |
| 39 | C7×#475 | C22 | 1 | 3 | yes | complemented |
| 40 | C7×#461 | C22 | 1 | 3 | yes | — |
| 41 | C7×C8×Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | C4×C7×SD16 | C22 | 1 | 3 | yes | — |
| 43 | #89937 | C22 | 1 | 6 | yes | — |
| 44 | #89936 | C22 | 1 | 3 | yes | — |
| 45 | #89860 | C22 | 1 | 3 | yes | complemented |
| 46 | #89859 | C22 | 1 | 3 | yes | complemented |
| 47 | #89855 | C22 | 1 | 3 | yes | — |
| 48 | #89853 | C22 | 1 | 3 | yes | complemented |
| 49 | C4×#1143 | C22 | 1 | 3 | yes | — |
| 50 | Q8×C7⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | #89792 | C22 | 1 | 3 | yes | complemented |
| 52 | #89787 | C22 | 1 | 3 | yes | — |
| 53 | C4×#1141 | C22 | 1 | 3 | yes | — |
| 54 | #89642 | C22 | 1 | 6 | yes | complemented |
| 55 | #89641 | C22 | 1 | 3 | yes | — |
| 56 | #89633 | C22 | 1 | 3 | yes | — |
| 57 | #89618 | C22 | 1 | 3 | yes | complemented |
| 58 | #89615 | C22 | 1 | 3 | yes | — |
| 59 | #89609 | C22 | 1 | 3 | yes | — |
| 60 | #89603 | C22 | 1 | 3 | yes | complemented |
| 61 | #89591 | C22 | 1 | 6 | yes | — |
| 62 | #89589 | C22 | 1 | 3 | yes | — |
| 63 | #89575 | C22 | 1 | 3 | yes | — |
| 64 | #89575 | C22 | 1 | 6 | yes | — |
| 65 | #89567 | C22 | 1 | 6 | yes | complemented |
| 66 | #89567 | C22 | 1 | 6 | yes | complemented |
| 67 | #89566 | C22 | 1 | 6 | yes | complemented |
| 68 | #89557 | C22 | 1 | 3 | yes | — |
| 69 | #89542 | C22 | 1 | 1 | yes | characteristic |
| 70 | #89466 | C22 | 1 | 3 | yes | complemented |
| 71 | C4×D56 | C22 | 1 | 3 | yes | — |
| 72 | C4×#1131 | C22 | 1 | 3 | yes | — |
| 73 | #89451 | C22 | 1 | 3 | yes | complemented |
| 74 | #61317 | — | 7 | 1 | no | maximal, Sylow |
| 75 | C22×C7×Q8 | — | 2 | 1 | no | — |
| 76 | C2×#1161 | — | 2 | 1 | no | — |
| 77 | C2×#1161 | C23 | 1 | 3 | yes | — |
| 78 | C2×Q8×D7 | — | 2 | 1 | no | — |
| 79 | C2×Q8×D7 | — | 2 | 3 | no | — |
| 80 | C2×Q8×D7 | — | 2 | 3 | no | — |
| 81 | C2×Q8×D7 | — | 4 | 8 | no | — |
| 82 | C2×Q8×D7 | D4 | 1 | 1 | yes | characteristic |
| 83 | C2×D4×D7 | C23 | 1 | 1 | yes | characteristic |
| 84 | C22×C4×D7 | — | 2 | 3 | no | — |
| 85 | C22×Dic14 | — | 2 | 3 | no | — |
| 86 | C2×C7×SD16 | C23 | 1 | 3 | yes | — |
| 87 | C7×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 88 | C7×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 89 | C7×#125 | — | 2 | 3 | no | — |
| 90 | C7×C22⋊Q8 | — | 2 | 3 | no | — |
| 91 | C4×C7×Q8 | — | 2 | 1 | no | — |
| 92 | C4×C7×Q8 | C23 | 1 | 3 | yes | — |
| 93 | C4×C7×Q8 | C23 | 1 | 1 | yes | characteristic |
| 94 | C4×C7×D4 | C23 | 1 | 3 | yes | — |
| 95 | #6510 | C23 | 1 | 6 | yes | — |
| 96 | #6509 | — | 2 | 3 | no | — |
| 97 | Q8×Dic7 | D4 | 1 | 1 | yes | characteristic |
| 98 | Q8×Dic7 | C23 | 1 | 3 | yes | — |
| 99 | #6507 | — | 2 | 3 | no | — |
| 100 | C2×#1143 | C23 | 1 | 3 | yes | — |
| 101 | D4×Dic7 | C23 | 1 | 3 | yes | — |
| 102 | C2×#1141 | C23 | 1 | 3 | yes | — |
| 103 | C4×C22⋊D7 | — | 2 | 3 | no | — |
| 104 | #6487 | — | 2 | 3 | no | — |
| 105 | #6477 | — | 2 | 12 | no | — |
| 106 | C2×D56 | C23 | 1 | 3 | yes | — |
| 107 | C2×#1131 | C23 | 1 | 3 | yes | — |
| 108 | C2×#1131 | C23 | 1 | 1 | yes | characteristic |
| 109 | #6461 | — | 2 | 6 | no | — |
| 110 | #6460 | — | 2 | 3 | no | — |
| 111 | #6460 | — | 2 | 3 | no | — |
| 112 | #6459 | — | 2 | 6 | no | — |
| 113 | #6458 | — | 2 | 3 | no | — |
| 114 | #6458 | — | 2 | 3 | no | — |
| 115 | #6458 | — | 2 | 3 | no | — |
| 116 | #6457 | — | 2 | 6 | no | — |
| 117 | #6456 | — | 2 | 3 | no | — |
| 118 | #6456 | — | 2 | 3 | no | — |
| 119 | #6456 | — | 2 | 3 | no | — |
| 120 | #6456 | C23 | 1 | 3 | yes | — |
| 121 | #6456 | C23 | 1 | 3 | yes | — |
| 122 | #6455 | — | 2 | 3 | no | — |
| 123 | #6455 | — | 2 | 3 | no | — |
| 124 | #6455 | C23 | 1 | 1 | yes | characteristic |
| 125 | D7×C4⋊C4 | — | 2 | 3 | no | — |
| 126 | D7×C4⋊C4 | D4 | 1 | 3 | yes | — |
| 127 | D7×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 128 | #6451 | — | 2 | 3 | no | — |
| 129 | #6451 | C23 | 1 | 6 | yes | — |
| 130 | #6450 | D4 | 1 | 3 | yes | — |
| 131 | (C22⋊D7)⋊C4 | — | 2 | 3 | no | — |
| 132 | D7×C22⋊C4 | — | 2 | 3 | no | — |
| 133 | #6441 | — | 2 | 6 | no | — |
| 134 | #6438 | — | 2 | 3 | no | — |
| 135 | #6437 | C23 | 1 | 3 | yes | — |
| 136 | C4×D28 | — | 2 | 3 | no | — |
| 137 | C4×D28 | — | 2 | 3 | no | — |
| 138 | C4×D28 | C23 | 1 | 3 | yes | — |
| 139 | C4×D28 | C23 | 1 | 3 | yes | — |
| 140 | C42×D7 | — | 2 | 3 | no | — |
| 141 | C42×D7 | C23 | 1 | 3 | yes | — |
| 142 | #6432 | C23 | 1 | 3 | yes | — |
| 143 | C4×Dic14 | C23 | 1 | 3 | yes | — |
| 144 | C7×#106 | C23 | 1 | 3 | yes | — |
| 145 | C7×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 146 | C7×#103 | C23 | 1 | 6 | yes | — |
| 147 | C7×#103 | C23 | 1 | 3 | yes | — |
| 148 | C7×#102 | C23 | 1 | 1 | yes | characteristic |
| 149 | C4×C7×C8 | C23 | 1 | 3 | yes | — |
| 150 | #6409 | C23 | 1 | 3 | yes | — |
| 151 | #6409 | C23 | 1 | 6 | yes | — |
| 152 | #6406 | C23 | 1 | 1 | yes | characteristic |
| 153 | #6395 | C23 | 1 | 6 | yes | — |
| 154 | #6395 | C23 | 1 | 1 | yes | characteristic |
| 155 | #6395 | C23 | 1 | 3 | yes | — |
| 156 | #6392 | C23 | 1 | 3 | yes | — |
| 157 | #6389 | C23 | 1 | 3 | yes | — |
| 158 | #6389 | C23 | 1 | 3 | yes | — |
| 159 | Dic7⋊C8 | C23 | 1 | 6 | yes | — |
| 160 | #6383 | C23 | 1 | 6 | yes | — |
| 161 | #6383 | C23 | 1 | 3 | yes | — |
| 162 | #6383 | C23 | 1 | 1 | yes | characteristic |
| 163 | #6382 | C23 | 1 | 3 | yes | — |
| 164 | #6381 | C23 | 1 | 3 | yes | — |
| 165 | C4⋊(C7⋊C8) | C23 | 1 | 3 | yes | — |
| 166 | C4×C7⋊C8 | C23 | 1 | 3 | yes | — |
| 167 | #3480 | — | 7 | 1 | no | — |
| 168 | C2×D4×Q8 | — | 7 | 1 | no | — |
| 169 | #3373 | — | 7 | 3 | no | — |
| 170 | #3373 | — | 7 | 3 | no | — |
| 171 | #3367 | — | 7 | 3 | no | — |
| 172 | #3367 | — | 7 | 3 | no | — |
| 173 | #3359 | — | 7 | 1 | no | — |
| 174 | #3359 | D7 | 1 | 1 | yes | characteristic, complemented |
| 175 | #3358 | — | 7 | 1 | no | — |
| 176 | #3358 | — | 7 | 1 | no | — |
| 177 | #3141 | — | 7 | 3 | no | — |
| 178 | #3079 | — | 7 | 3 | no | — |
| 179 | #3036 | — | 7 | 3 | no | — |
| 180 | Q8×M16 | — | 7 | 1 | no | — |
| 181 | C4×AGL(1,ℤ/8) | — | 7 | 3 | no | — |
| 182 | C23×D7 | — | 2 | 1 | no | — |
| 183 | C2×C7×Q8 | — | 2 | 3 | no | — |
| 184 | C2×C7×Q8 | — | 4 | 4 | no | — |
| 185 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 186 | C2×C7×Q8 | C24 | 1 | 3 | yes | — |
| 187 | C2×C7×D4 | C24 | 1 | 1 | yes | characteristic |
| 188 | C22×C4×C7 | — | 2 | 3 | no | — |
| 189 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 190 | C22×Dic7 | — | 2 | 3 | no | — |
| 191 | #1161 | — | 2 | 6 | no | — |
| 192 | #1161 | — | 2 | 6 | no | — |
| 193 | #1161 | — | 4 | 4 | no | — |
| 194 | Q8×D7 | — | 2 | 4 | no | — |
| 195 | Q8×D7 | — | 4 | 12 | no | — |
| 196 | Q8×D7 | — | 4 | 12 | no | — |
| 197 | Q8×D7 | — | 4 | 4 | no | — |
| 198 | D4×D7 | — | 2 | 2 | no | — |
| 199 | D4×D7 | #41 | 1 | 4 | yes | complemented |
| 200 | C2×D28 | — | 2 | 3 | no | — |
| 201 | C2×D28 | — | 2 | 3 | no | — |
| 202 | C2×D28 | — | 2 | 3 | no | — |
| 203 | C2×D28 | C24 | 1 | 3 | yes | — |
| 204 | C2×D28 | C24 | 1 | 1 | yes | characteristic |
| 205 | C2×C4×D7 | — | 2 | 3 | no | — |
| 206 | C2×C4×D7 | — | 2 | 3 | no | — |
| 207 | C2×C4×D7 | — | 2 | 3 | no | — |
| 208 | C2×C4×D7 | — | 2 | 3 | no | — |
| 209 | C2×C4×D7 | — | 2 | 3 | no | — |
| 210 | C2×C4×D7 | — | 2 | 3 | no | — |
| 211 | C2×C4×D7 | — | 4 | 12 | no | — |
| 212 | C2×C4×D7 | C2×D4 | 1 | 3 | yes | — |
| 213 | C2×C4×D7 | C2×D4 | 1 | 3 | yes | — |
| 214 | C2×C4×D7 | C24 | 1 | 1 | yes | characteristic |
| 215 | C2×Dic14 | — | 2 | 3 | no | — |
| 216 | C2×Dic14 | — | 2 | 6 | no | — |
| 217 | C2×Dic14 | — | 4 | 12 | no | — |
| 218 | C2×Dic14 | C2×D4 | 1 | 3 | yes | — |
| 219 | C7×SD16 | — | 2 | 6 | no | — |
| 220 | C2×C7×C8 | C24 | 1 | 1 | yes | characteristic |
| 221 | C2×C7×C8 | C24 | 1 | 3 | yes | — |
| 222 | C7×C4⋊C4 | — | 2 | 3 | no | — |
| 223 | C7×C4⋊C4 | — | 2 | 3 | no | — |
| 224 | C7×C4⋊C4 | — | 2 | 3 | no | — |
| 225 | C7×C4⋊C4 | — | 2 | 3 | no | — |
| 226 | C7×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 227 | C7×C4⋊C4 | C24 | 1 | 1 | yes | characteristic |
| 228 | C7×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 229 | C7×C22⋊C4 | — | 2 | 3 | no | — |
| 230 | C42×C7 | — | 2 | 3 | no | — |
| 231 | C42×C7 | C24 | 1 | 3 | yes | — |
| 232 | C22⋊Dic7 | — | 2 | 3 | no | — |
| 233 | #1143 | — | 2 | 6 | no | — |
| 234 | #1141 | — | 2 | 6 | no | — |
| 235 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 236 | (C2×D7)⋊C4 | — | 2 | 3 | no | — |
| 237 | (C2×D7)⋊C4 | — | 2 | 3 | no | — |
| 238 | (C2×D7)⋊C4 | — | 2 | 3 | no | — |
| 239 | (C2×D7)⋊C4 | — | 2 | 6 | no | — |
| 240 | (C2×D7)⋊C4 | — | 2 | 6 | no | — |
| 241 | (C2×D7)⋊C4 | — | 2 | 3 | no | — |
| 242 | C4⋊Dic7 | — | 2 | 3 | no | — |
| 243 | C4⋊Dic7 | — | 2 | 3 | no | — |
| 244 | C4⋊Dic7 | C2×D4 | 1 | 3 | yes | — |
| 245 | C4⋊Dic7 | C24 | 1 | 1 | yes | characteristic |
| 246 | C4⋊Dic7 | C24 | 1 | 3 | yes | — |
| 247 | Dic7⋊C4 | — | 2 | 6 | no | — |
| 248 | Dic7⋊C4 | — | 2 | 3 | no | — |
| 249 | Dic7⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 250 | C4×Dic7 | — | 2 | 1 | no | — |
| 251 | C4×Dic7 | — | 2 | 3 | no | — |
| 252 | C4×Dic7 | C2×D4 | 1 | 3 | yes | — |
| 253 | C4×Dic7 | C2×D4 | 1 | 3 | yes | — |
| 254 | C4×Dic7 | C24 | 1 | 3 | yes | — |
| 255 | C2×C7⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 256 | C2×C7⋊C8 | C24 | 1 | 3 | yes | — |
| 257 | D56 | — | 2 | 6 | no | — |
| 258 | #1131 | — | 2 | 6 | no | — |
| 259 | #1131 | — | 2 | 2 | no | — |
| 260 | C23×Q8 | — | 14 | 1 | no | — |
| 261 | C2×AGL(1,ℤ/8) | — | 7 | 3 | no | — |
| 262 | #559 | — | 7 | 3 | no | — |
| 263 | #557 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 264 | #556 | — | 7 | 3 | no | — |
| 265 | #553 | — | 14 | 3 | no | — |
| 266 | #550 | — | 7 | 1 | no | — |
| 267 | D4×Q8 | — | 7 | 3 | no | — |
| 268 | D4×Q8 | — | 7 | 1 | no | — |
| 269 | D4×Q8 | — | 7 | 3 | no | — |
| 270 | D4×Q8 | — | 14 | 3 | no | — |
| 271 | D4×Q8 | — | 14 | 1 | no | — |
| 272 | D4×Q8 | C2×D7 | 1 | 1 | yes | characteristic |
| 273 | #548 | — | 14 | 1 | no | — |
| 274 | #532 | — | 7 | 3 | no | — |
| 275 | C2×C4⋊Q8 | — | 7 | 3 | no | — |
| 276 | #529 | — | 14 | 3 | no | — |
| 277 | C2×C22⋊Q8 | — | 14 | 3 | no | — |
| 278 | C4×#41 | — | 7 | 3 | no | — |
| 279 | C4×#41 | — | 14 | 1 | no | — |
| 280 | C2×C4×Q8 | — | 7 | 1 | no | — |
| 281 | C2×C4×D4 | — | 7 | 3 | no | — |
| 282 | #489 | — | 7 | 6 | no | — |
| 283 | #489 | — | 7 | 6 | no | — |
| 284 | #487 | — | 7 | 3 | no | — |
| 285 | #487 | C2×D7 | 1 | 3 | yes | complemented |
| 286 | #486 | — | 7 | 3 | no | — |
| 287 | #486 | — | 7 | 3 | no | — |
| 288 | #477 | — | 7 | 6 | no | — |
| 289 | #476 | — | 7 | 6 | no | — |
| 290 | #475 | — | 7 | 3 | no | — |
| 291 | #475 | C2×D7 | 1 | 3 | yes | complemented |
| 292 | #474 | — | 7 | 3 | no | — |
| 293 | #474 | — | 7 | 3 | no | — |
| 294 | #463 | — | 7 | 6 | no | — |
| 295 | #463 | — | 7 | 6 | no | — |
| 296 | #461 | — | 7 | 3 | no | — |
| 297 | #461 | C2×D7 | 1 | 3 | yes | — |
| 298 | #459 | — | 7 | 3 | no | — |
| 299 | #459 | — | 7 | 3 | no | — |
| 300 | #446 | — | 7 | 3 | no | — |
| 301 | #446 | — | 7 | 3 | no | — |
| 302 | C8×Q8 | — | 7 | 1 | no | — |
| 303 | C8×Q8 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 304 | #442 | — | 7 | 3 | no | — |
| 305 | #442 | — | 7 | 3 | no | — |
| 306 | #440 | — | 7 | 3 | no | — |
| 307 | #440 | — | 7 | 3 | no | — |
| 308 | C4×SD16 | — | 7 | 3 | no | — |
| 309 | C4×SD16 | C2×D7 | 1 | 3 | yes | — |
| 310 | C4×D8 | — | 7 | 3 | no | — |
| 311 | C4×D8 | — | 7 | 3 | no | — |
| 312 | #428 | — | 7 | 3 | no | — |
| 313 | #423 | — | 7 | 3 | no | — |
| 314 | #418 | — | 7 | 1 | no | — |
| 315 | #417 | — | 7 | 6 | no | — |
| 316 | #417 | — | 7 | 3 | no | — |
| 317 | C4×M16 | — | 7 | 3 | no | — |
| 318 | C23×C7 | — | 2 | 1 | no | — |
| 319 | C22×D7 | — | 2 | 1 | no | — |
| 320 | C22×D7 | — | 2 | 4 | no | — |
| 321 | C22×D7 | — | 2 | 3 | no | — |
| 322 | C22×D7 | — | 4 | 2 | no | — |
| 323 | C22×D7 | — | 4 | 2 | no | — |
| 324 | C22×D7 | C22×D4 | 1 | 1 | yes | characteristic |
| 325 | C7×Q8 | — | 2 | 3 | no | — |
| 326 | C7×Q8 | — | 2 | 3 | no | — |
| 327 | C7×Q8 | — | 4 | 6 | no | — |
| 328 | C7×Q8 | AGL(1,ℤ/8) | 1 | 4 | yes | complemented |
| 329 | C7×D4 | — | 2 | 1 | no | — |
| 330 | C7×D4 | C2×#41 | 1 | 2 | yes | — |
| 331 | C2×C4×C7 | — | 2 | 3 | no | — |
| 332 | C2×C4×C7 | — | 2 | 1 | no | — |
| 333 | C2×C4×C7 | — | 2 | 3 | no | — |
| 334 | C2×C4×C7 | — | 4 | 6 | no | — |
| 335 | C2×C4×C7 | C22×D4 | 1 | 3 | yes | — |
| 336 | C2×C4×C7 | C22×D4 | 1 | 3 | yes | — |
| 337 | C2×C4×C7 | C25 | 1 | 1 | yes | characteristic |
| 338 | C22⋊D7 | — | 2 | 4 | no | — |
| 339 | C2×Dic7 | — | 2 | 1 | no | — |
| 340 | C2×Dic7 | — | 2 | 3 | no | — |
| 341 | C2×Dic7 | — | 4 | 6 | no | — |
| 342 | C2×Dic7 | C22×D4 | 1 | 3 | yes | — |
| 343 | C2×Dic7 | C22×D4 | 1 | 3 | yes | — |
| 344 | C2×Dic7 | C22×D4 | 1 | 1 | yes | characteristic |
| 345 | D28 | — | 2 | 3 | no | — |
| 346 | D28 | — | 2 | 1 | no | — |
| 347 | D28 | — | 2 | 3 | no | — |
| 348 | D28 | — | 4 | 6 | no | — |
| 349 | D28 | — | 4 | 6 | no | — |
| 350 | D28 | — | 8 | 3 | no | — |
| 351 | D28 | C2×#41 | 1 | 2 | yes | — |
| 352 | C4×D7 | — | 2 | 6 | no | — |
| 353 | C4×D7 | — | 4 | 3 | no | — |
| 354 | C4×D7 | — | 4 | 6 | no | — |
| 355 | C4×D7 | — | 4 | 6 | no | — |
| 356 | C4×D7 | — | 4 | 6 | no | — |
| 357 | C4×D7 | — | 4 | 6 | no | — |
| 358 | C4×D7 | — | 4 | 6 | no | — |
| 359 | C4×D7 | — | 8 | 3 | no | — |
| 360 | C4×D7 | C2×#41 | 1 | 2 | yes | — |
| 361 | C4×D7 | 2−1+4 | 1 | 2 | yes | — |
| 362 | Dic14 | — | 2 | 6 | no | — |
| 363 | Dic14 | — | 4 | 12 | no | — |
| 364 | Dic14 | — | 4 | 6 | no | — |
| 365 | C7×C8 | — | 2 | 3 | no | — |
| 366 | C7×C8 | — | 2 | 1 | no | — |
| 367 | C7⋊C8 | — | 2 | 3 | no | — |
| 368 | C7⋊C8 | — | 2 | 1 | no | — |
| 369 | C2×#41 | — | 7 | 3 | no | — |
| 370 | C2×#41 | — | 14 | 1 | no | — |
| 371 | C22×Q8 | — | 2 | 1 | no | — |
| 372 | C22×Q8 | — | 7 | 1 | no | — |
| 373 | C22×Q8 | — | 14 | 3 | no | — |
| 374 | C22×Q8 | — | 14 | 3 | no | — |
| 375 | C22×Q8 | — | 14 | 3 | no | — |
| 376 | C22×Q8 | — | 14 | 1 | no | — |
| 377 | C22×Q8 | — | 28 | 8 | no | — |
| 378 | C22×D4 | — | 7 | 1 | no | — |
| 379 | C23×C4 | — | 14 | 3 | no | — |
| 380 | AGL(1,ℤ/8) | — | 14 | 12 | no | — |
| 381 | C2×SD16 | — | 7 | 3 | no | — |
| 382 | C2×SD16 | C22×D7 | 1 | 3 | yes | — |
| 383 | C2×D8 | — | 7 | 3 | no | — |
| 384 | C2×D8 | — | 7 | 3 | no | — |
| 385 | C2×M16 | — | 7 | 3 | no | — |
| 386 | C2×M16 | — | 7 | 1 | no | — |
| 387 | C4⋊Q8 | — | 7 | 6 | no | — |
| 388 | C4⋊Q8 | — | 7 | 3 | no | — |
| 389 | C4⋊Q8 | — | 14 | 3 | no | — |
| 390 | C4⋊Q8 | — | 14 | 3 | no | — |
| 391 | C4⋊Q8 | C22×D7 | 1 | 3 | yes | — |
| 392 | C4⋊Q8 | C22×D7 | 1 | 3 | yes | — |
| 393 | #127 | — | 7 | 3 | no | — |
| 394 | #126 | — | 14 | 6 | no | — |
| 395 | #125 | — | 2 | 3 | no | — |
| 396 | #124 | — | 7 | 6 | no | — |
| 397 | #124 | — | 14 | 3 | no | — |
| 398 | #123 | — | 14 | 6 | no | — |
| 399 | C22⋊Q8 | — | 2 | 3 | no | — |
| 400 | C22⋊Q8 | — | 14 | 6 | no | — |
| 401 | C22⋊Q8 | — | 14 | 6 | no | — |
| 402 | C22⋊Q8 | — | 14 | 3 | no | — |
| 403 | C22⋊Q8 | — | 14 | 3 | no | — |
| 404 | C22⋊Q8 | — | 14 | 3 | no | — |
| 405 | C22⋊Q8 | — | 14 | 3 | no | — |
| 406 | #121 | — | 14 | 3 | no | — |
| 407 | #121 | — | 14 | 3 | no | — |
| 408 | #121 | — | 14 | 3 | no | — |
| 409 | C4×Q8 | — | 2 | 1 | no | — |
| 410 | C4×Q8 | — | 7 | 1 | no | — |
| 411 | C4×Q8 | — | 7 | 3 | no | — |
| 412 | C4×Q8 | — | 7 | 3 | no | — |
| 413 | C4×Q8 | — | 7 | 3 | no | — |
| 414 | C4×Q8 | C22×D7 | 1 | 3 | yes | — |
| 415 | C4×Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 416 | C4×D4 | — | 7 | 3 | no | — |
| 417 | C4×D4 | — | 7 | 3 | no | — |
| 418 | C4×D4 | — | 7 | 3 | no | — |
| 419 | C4×D4 | — | 7 | 3 | no | — |
| 420 | C4×D4 | — | 7 | 3 | no | — |
| 421 | C4×D4 | — | 14 | 3 | no | — |
| 422 | C4×D4 | — | 14 | 3 | no | — |
| 423 | C4×D4 | — | 14 | 3 | no | — |
| 424 | C4×D4 | — | 14 | 3 | no | — |
| 425 | C4×D4 | — | 14 | 3 | no | — |
| 426 | C4×D4 | — | 14 | 3 | no | — |
| 427 | C4×D4 | — | 14 | 3 | no | — |
| 428 | C4×D4 | C22×D7 | 1 | 3 | yes | — |
| 429 | #117 | — | 7 | 1 | no | — |
| 430 | #117 | — | 14 | 3 | no | — |
| 431 | #117 | — | 14 | 3 | no | — |
| 432 | C2×C4⋊C4 | — | 7 | 3 | no | — |
| 433 | C2×C4⋊C4 | — | 7 | 3 | no | — |
| 434 | C2×C4⋊C4 | — | 14 | 3 | no | — |
| 435 | C2×C22⋊C4 | — | 14 | 3 | no | — |
| 436 | C2×C42 | — | 7 | 3 | no | — |
| 437 | C2×C42 | — | 14 | 3 | no | — |
| 438 | #107 | — | 7 | 3 | no | — |
| 439 | #107 | — | 7 | 3 | no | — |
| 440 | #106 | — | 7 | 3 | no | — |
| 441 | #106 | C22×D7 | 1 | 3 | yes | — |
| 442 | C4⋊C8 | — | 7 | 6 | no | — |
| 443 | C4⋊C8 | — | 7 | 3 | no | — |
| 444 | C4⋊C8 | C22×D7 | 1 | 3 | yes | — |
| 445 | #103 | — | 7 | 3 | no | — |
| 446 | #103 | — | 7 | 6 | no | — |
| 447 | #103 | C22×D7 | 1 | 3 | yes | — |
| 448 | #103 | C22×D7 | 1 | 6 | yes | — |
| 449 | #102 | — | 7 | 1 | no | — |
| 450 | #102 | — | 7 | 3 | no | — |
| 451 | #102 | — | 7 | 6 | no | — |
| 452 | #102 | — | 7 | 1 | no | — |
| 453 | #102 | — | 7 | 3 | no | — |
| 454 | #102 | — | 7 | 6 | no | — |
| 455 | #102 | — | 7 | 1 | no | — |
| 456 | #102 | C22×D7 | 1 | 1 | yes | characteristic |
| 457 | #97 | — | 7 | 3 | no | — |
| 458 | #97 | — | 7 | 3 | no | — |
| 459 | C4×C8 | — | 7 | 3 | no | — |
| 460 | C4×C8 | C22×D7 | 1 | 3 | yes | — |
| 461 | C22×C7 | — | 2 | 2 | no | — |
| 462 | C22×C7 | — | 4 | 1 | no | — |
| 463 | C22×C7 | — | 4 | 1 | no | — |
| 464 | C22×C7 | C23×D4 | 1 | 1 | yes | characteristic |
| 465 | C2×D7 | — | 2 | 1 | no | — |
| 466 | C2×D7 | — | 2 | 1 | no | — |
| 467 | C2×D7 | — | 2 | 2 | no | — |
| 468 | C2×D7 | — | 4 | 8 | no | — |
| 469 | C2×D7 | — | 4 | 1 | no | — |
| 470 | C2×D7 | — | 4 | 1 | no | — |
| 471 | C2×D7 | — | 4 | 3 | no | — |
| 472 | C2×D7 | — | 4 | 3 | no | — |
| 473 | C2×D7 | — | 4 | 3 | no | — |
| 474 | C2×D7 | #548 | 1 | 2 | yes | — |
| 475 | C4×C7 | — | 2 | 3 | no | — |
| 476 | C4×C7 | — | 4 | 1 | no | — |
| 477 | C4×C7 | — | 4 | 3 | no | — |
| 478 | C4×C7 | — | 4 | 3 | no | — |
| 479 | C4×C7 | C2×AGL(1,ℤ/8) | 1 | 6 | yes | — |
| 480 | C4×C7 | C22×#41 | 1 | 1 | yes | characteristic |
| 481 | C4×C7 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 482 | Dic7 | — | 2 | 3 | no | — |
| 483 | Dic7 | — | 2 | 3 | no | — |
| 484 | Dic7 | — | 4 | 3 | no | — |
| 485 | Dic7 | — | 4 | 1 | no | — |
| 486 | Dic7 | #548 | 1 | 2 | yes | — |
| 487 | C24 | — | 14 | 1 | no | — |
| 488 | #41 | — | 14 | 6 | no | — |
| 489 | #41 | — | 14 | 6 | no | — |
| 490 | #41 | — | 28 | 4 | no | — |
| 491 | C2×Q8 | — | 2 | 3 | no | — |
| 492 | C2×Q8 | — | 4 | 4 | no | — |
| 493 | C2×Q8 | — | 7 | 3 | no | — |
| 494 | C2×Q8 | — | 14 | 6 | no | — |
| 495 | C2×Q8 | — | 14 | 4 | no | — |
| 496 | C2×Q8 | — | 14 | 3 | no | — |
| 497 | C2×Q8 | — | 28 | 12 | no | — |
| 498 | C2×Q8 | — | 28 | 12 | no | — |
| 499 | C2×Q8 | — | 28 | 12 | no | — |
| 500 | C2×Q8 | — | 28 | 4 | no | — |
| 501 | C2×Q8 | D4×D7 | 1 | 1 | yes | characteristic |
| 502 | C2×Q8 | C23×D7 | 1 | 3 | yes | — |
| 503 | C2×D4 | — | 7 | 4 | no | — |
| 504 | C2×D4 | — | 7 | 1 | no | — |
| 505 | C2×D4 | — | 7 | 3 | no | — |
| 506 | C2×D4 | — | 14 | 3 | no | — |
| 507 | C2×D4 | — | 14 | 2 | no | — |
| 508 | C2×D4 | — | 14 | 1 | no | — |
| 509 | C2×D4 | — | 14 | 3 | no | — |
| 510 | C2×D4 | — | 14 | 3 | no | — |
| 511 | C2×D4 | C23×D7 | 1 | 1 | yes | characteristic |
| 512 | C22×C4 | — | 2 | 3 | no | — |
| 513 | C22×C4 | — | 7 | 1 | no | — |
| 514 | C22×C4 | — | 7 | 3 | no | — |
| 515 | C22×C4 | — | 7 | 3 | no | — |
| 516 | C22×C4 | — | 14 | 3 | no | — |
| 517 | C22×C4 | — | 14 | 3 | no | — |
| 518 | C22×C4 | — | 14 | 3 | no | — |
| 519 | C22×C4 | — | 14 | 3 | no | — |
| 520 | C22×C4 | — | 14 | 3 | no | — |
| 521 | C22×C4 | — | 14 | 3 | no | — |
| 522 | C22×C4 | — | 14 | 3 | no | — |
| 523 | C22×C4 | — | 28 | 12 | no | — |
| 524 | SD16 | — | 2 | 6 | no | — |
| 525 | SD16 | — | 14 | 6 | no | — |
| 526 | D8 | — | 14 | 6 | no | — |
| 527 | D8 | — | 14 | 6 | no | — |
| 528 | M16 | — | 14 | 2 | no | — |
| 529 | M16 | — | 14 | 6 | no | — |
| 530 | C2×C8 | — | 7 | 1 | no | — |
| 531 | C2×C8 | — | 7 | 3 | no | — |
| 532 | C2×C8 | C23×D7 | 1 | 1 | yes | characteristic |
| 533 | C2×C8 | C23×D7 | 1 | 3 | yes | — |
| 534 | C4⋊C4 | — | 2 | 3 | no | — |
| 535 | C4⋊C4 | — | 2 | 3 | no | — |
| 536 | C4⋊C4 | — | 2 | 3 | no | — |
| 537 | C4⋊C4 | — | 2 | 3 | no | — |
| 538 | C4⋊C4 | — | 7 | 6 | no | — |
| 539 | C4⋊C4 | — | 7 | 3 | no | — |
| 540 | C4⋊C4 | — | 7 | 3 | no | — |
| 541 | C4⋊C4 | — | 7 | 1 | no | — |
| 542 | C4⋊C4 | — | 14 | 3 | no | — |
| 543 | C4⋊C4 | — | 14 | 6 | no | — |
| 544 | C4⋊C4 | — | 14 | 3 | no | — |
| 545 | C4⋊C4 | — | 14 | 3 | no | — |
| 546 | C4⋊C4 | D4×D7 | 1 | 3 | yes | — |
| 547 | C4⋊C4 | C23×D7 | 1 | 3 | yes | — |
| 548 | C4⋊C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 549 | C22⋊C4 | — | 2 | 3 | no | — |
| 550 | C22⋊C4 | — | 14 | 3 | no | — |
| 551 | C22⋊C4 | — | 14 | 3 | no | — |
| 552 | C22⋊C4 | — | 14 | 6 | no | — |
| 553 | C22⋊C4 | — | 14 | 6 | no | — |
| 554 | C22⋊C4 | — | 14 | 1 | no | — |
| 555 | C22⋊C4 | — | 14 | 3 | no | — |
| 556 | C22⋊C4 | — | 14 | 3 | no | — |
| 557 | C22⋊C4 | — | 14 | 3 | no | — |
| 558 | C42 | — | 2 | 3 | no | — |
| 559 | C42 | — | 7 | 3 | no | — |
| 560 | C42 | — | 7 | 3 | no | — |
| 561 | C42 | — | 7 | 3 | no | — |
| 562 | C42 | — | 14 | 1 | no | — |
| 563 | C42 | — | 14 | 3 | no | — |
| 564 | C42 | C23×D7 | 1 | 3 | yes | — |
| 565 | C2×C7 | — | 4 | 2 | no | — |
| 566 | C2×C7 | C2×#548 | 1 | 1 | yes | characteristic |
| 567 | C2×C7 | C22×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 568 | C2×C7 | #3586 | 1 | 1 | yes | characteristic |
| 569 | D7 | — | 2 | 2 | no | — |
| 570 | D7 | — | 4 | 2 | no | — |
| 571 | D7 | — | 8 | 3 | no | — |
| 572 | C23 | — | 2 | 1 | no | — |
| 573 | C23 | — | 7 | 1 | no | — |
| 574 | C23 | — | 14 | 4 | no | — |
| 575 | C23 | — | 14 | 1 | no | — |
| 576 | C23 | — | 14 | 3 | no | — |
| 577 | C23 | — | 28 | 2 | no | — |
| 578 | C23 | — | 28 | 2 | no | — |
| 579 | Q8 | — | 2 | 3 | no | — |
| 580 | Q8 | — | 2 | 3 | no | — |
| 581 | Q8 | — | 4 | 6 | no | — |
| 582 | Q8 | — | 14 | 6 | no | — |
| 583 | Q8 | — | 28 | 12 | no | — |
| 584 | Q8 | — | 28 | 6 | no | — |
| 585 | Q8 | #6477 | 1 | 4 | yes | complemented |
| 586 | D4 | — | 2 | 1 | no | — |
| 587 | D4 | — | 7 | 2 | no | — |
| 588 | D4 | — | 14 | 4 | no | — |
| 589 | D4 | — | 14 | 3 | no | — |
| 590 | D4 | — | 14 | 1 | no | — |
| 591 | D4 | — | 14 | 3 | no | — |
| 592 | D4 | — | 28 | 6 | no | — |
| 593 | D4 | — | 28 | 6 | no | — |
| 594 | D4 | — | 56 | 3 | no | — |
| 595 | D4 | D7×#41 | 1 | 2 | yes | — |
| 596 | C2×C4 | — | 2 | 1 | no | — |
| 597 | C2×C4 | — | 2 | 3 | no | — |
| 598 | C2×C4 | — | 2 | 3 | no | — |
| 599 | C2×C4 | — | 4 | 6 | no | — |
| 600 | C2×C4 | — | 7 | 1 | no | — |
| 601 | C2×C4 | — | 7 | 2 | no | — |
| 602 | C2×C4 | — | 7 | 2 | no | — |
| 603 | C2×C4 | — | 7 | 3 | no | — |
| 604 | C2×C4 | — | 7 | 3 | no | — |
| 605 | C2×C4 | — | 14 | 6 | no | — |
| 606 | C2×C4 | — | 14 | 1 | no | — |
| 607 | C2×C4 | — | 14 | 3 | no | — |
| 608 | C2×C4 | — | 28 | 3 | no | — |
| 609 | C2×C4 | — | 28 | 6 | no | — |
| 610 | C2×C4 | — | 28 | 6 | no | — |
| 611 | C2×C4 | — | 28 | 6 | no | — |
| 612 | C2×C4 | — | 28 | 6 | no | — |
| 613 | C2×C4 | — | 28 | 6 | no | — |
| 614 | C2×C4 | — | 28 | 6 | no | — |
| 615 | C2×C4 | — | 56 | 3 | no | — |
| 616 | C2×C4 | C2×D4×D7 | 1 | 3 | yes | — |
| 617 | C2×C4 | C2×D4×D7 | 1 | 3 | yes | — |
| 618 | C2×C4 | C24×D7 | 1 | 1 | yes | characteristic |
| 619 | C8 | — | 2 | 3 | no | — |
| 620 | C8 | — | 2 | 1 | no | — |
| 621 | C8 | — | 14 | 3 | no | — |
| 622 | C8 | — | 14 | 1 | no | — |
| 623 | C7 | #61317 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 624 | C22 | — | 2 | 2 | no | — |
| 625 | C22 | — | 4 | 1 | no | — |
| 626 | C22 | — | 4 | 1 | no | — |
| 627 | C22 | — | 7 | 2 | no | — |
| 628 | C22 | — | 14 | 1 | no | — |
| 629 | C22 | — | 14 | 1 | no | — |
| 630 | C22 | — | 14 | 2 | no | — |
| 631 | C22 | — | 28 | 8 | no | — |
| 632 | C22 | — | 28 | 1 | no | — |
| 633 | C22 | — | 28 | 1 | no | — |
| 634 | C22 | — | 28 | 3 | no | — |
| 635 | C22 | — | 28 | 3 | no | — |
| 636 | C22 | — | 28 | 3 | no | — |
| 637 | C22 | C22×D4×D7 | 1 | 1 | yes | characteristic |
| 638 | C4 | — | 2 | 3 | no | — |
| 639 | C4 | — | 4 | 1 | no | — |
| 640 | C4 | — | 4 | 3 | no | — |
| 641 | C4 | — | 4 | 3 | no | — |
| 642 | C4 | — | 7 | 2 | no | — |
| 643 | C4 | — | 14 | 3 | no | — |
| 644 | C4 | — | 14 | 3 | no | — |
| 645 | C4 | — | 28 | 3 | no | — |
| 646 | C4 | — | 28 | 1 | no | — |
| 647 | C4 | C2×#6477 | 1 | 6 | yes | — |
| 648 | C4 | C2×D7×#41 | 1 | 1 | yes | characteristic |
| 649 | C4 | D7×2−1+4 | 1 | 1 | yes | characteristic |
| 650 | C2 | — | 4 | 2 | no | — |
| 651 | C2 | — | 14 | 2 | no | — |
| 652 | C2 | — | 28 | 2 | no | — |
| 653 | C2 | — | 56 | 3 | no | — |
| 654 | C2 | D7×#548 | 1 | 1 | yes | characteristic |
| 655 | C2 | C22×#6477 | 1 | 1 | yes | characteristic |
| 656 | C2 | #11744279 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11744084 | C2 | semidirect |
| 2. D4×Q8×D7 | C2 | semidirect |
| 3. C7×#3359 | C2 | semidirect |
| 4. #11741133 | C2 | semidirect |
| 5. #11741007 | C2 | semidirect |
| 6. #11739067 | C2 | semidirect |
| 7. #11739046 | C2 | semidirect |
| 8. #11738483 | C2 | semidirect |
| 9. #11738457 | C2 | semidirect |
| 10. #11737873 | C2 | semidirect |
| 11. #11737861 | C2 | semidirect |
| 12. #11737369 | C2 | semidirect |
| 13. Q8×#1131 | C2 | semidirect |
| 14. C4×#6477 | C2 | semidirect |
| 15. #11737074 | C2 | semidirect |
| 17. C7×#557 | C22 | semidirect |
| 21. #90423 | C22 | semidirect |
| 29. #90276 | C22 | semidirect |
| 30. #90268 | C22 | semidirect |
| 38. C7×#487 | C22 | semidirect |
| 39. C7×#475 | C22 | semidirect |
| 41. C7×C8×Q8 | C22 | semidirect |
| 45. #89860 | C22 | semidirect |
| 46. #89859 | C22 | semidirect |
| 48. #89853 | C22 | semidirect |
| 50. Q8×C7⋊C8 | C22 | semidirect |
| 51. #89792 | C22 | semidirect |
| 54. #89642 | C22 | semidirect |
| 57. #89618 | C22 | semidirect |
| 60. #89603 | C22 | semidirect |
| 65. #89567 | C22 | semidirect |
| 66. #89567 | C22 | semidirect |
| 67. #89566 | C22 | semidirect |
| 70. #89466 | C22 | semidirect |
| 73. #89451 | C22 | semidirect |
| 174. #3359 | D7 | semidirect |
| 199. D4×D7 | #41 | semidirect |
| 263. #557 | C2×D7 | semidirect |
| 285. #487 | C2×D7 | semidirect |
| 291. #475 | C2×D7 | semidirect |
| 303. C8×Q8 | C2×D7 | semidirect |
| 328. C7×Q8 | AGL(1,ℤ/8) | semidirect |
| 585. Q8 | #6477 | semidirect |
| 623. C7 | #61317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11744084 | 2 |
| D4×Q8×D7 | 2 |
| C7×#3359 | 2 |
| #11741133 | 2 |
| #11741007 | 2 |
| #11739067 | 2 |
| #11739046 | 2 |
| #11738483 | 2 |
| #11738457 | 2 |
| #11737873 | 2 |
| #11737861 | 2 |
| #11737369 | 2 |
| Q8×#1131 | 2 |
| C4×#6477 | 2 |
| #11737074 | 2 |
| #61317 | 7 |