Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2008 conjugacy classes of subgroups.
The subgroup lattice has 554 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C7×#3499 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11743299 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11741562 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | D4×#1144 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #11740999 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #11740974 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11740955 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #11740858 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #11740723 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11740667 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #11739979 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×C7×2−1+4 | C22 | 1 | 2 | yes | — |
| 13 | C7×D4×Q8 | C22 | 1 | 4 | yes | — |
| 14 | C7×#547 | — | 2 | 4 | no | — |
| 15 | C7×#547 | C22 | 1 | 4 | yes | — |
| 16 | C7×#536 | — | 2 | 2 | no | — |
| 17 | C7×#536 | C22 | 1 | 2 | yes | — |
| 18 | C7×#532 | — | 2 | 1 | no | — |
| 19 | C7×#532 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×C7×C4⋊Q8 | — | 2 | 1 | no | — |
| 21 | C2×C7×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 22 | C4×C7×#41 | C22 | 1 | 1 | yes | characteristic |
| 23 | #90516 | C22 | 1 | 4 | yes | — |
| 24 | C2×#6514 | C22 | 1 | 4 | yes | — |
| 25 | C22×#1144 | C22 | 1 | 4 | yes | — |
| 26 | #90413 | — | 2 | 1 | no | — |
| 27 | #90404 | — | 2 | 1 | no | — |
| 28 | #90363 | — | 2 | 2 | no | — |
| 29 | #90294 | — | 2 | 4 | no | — |
| 30 | #90233 | C22 | 1 | 4 | yes | — |
| 31 | D4×Dic14 | C22 | 1 | 4 | yes | — |
| 32 | #90161 | C22 | 1 | 2 | yes | — |
| 33 | #90011 | C22 | 1 | 8 | yes | — |
| 34 | #90011 | C22 | 1 | 4 | yes | — |
| 35 | #90006 | C22 | 1 | 4 | yes | — |
| 36 | #90005 | C22 | 1 | 4 | yes | — |
| 37 | #90000 | C22 | 1 | 8 | yes | — |
| 38 | #90000 | C22 | 1 | 8 | yes | — |
| 39 | #89997 | C22 | 1 | 4 | yes | — |
| 40 | #89864 | C22 | 1 | 4 | yes | — |
| 41 | #89862 | C22 | 1 | 4 | yes | — |
| 42 | #89862 | C22 | 1 | 4 | yes | — |
| 43 | #89853 | C22 | 1 | 4 | yes | — |
| 44 | #89824 | C22 | 1 | 8 | yes | — |
| 45 | #89823 | C22 | 1 | 8 | yes | — |
| 46 | #89822 | C22 | 1 | 8 | yes | — |
| 47 | #89817 | C22 | 1 | 8 | yes | — |
| 48 | #89803 | C22 | 1 | 2 | yes | — |
| 49 | C4×#1144 | C22 | 1 | 4 | yes | — |
| 50 | #89792 | C22 | 1 | 2 | yes | — |
| 51 | #89791 | C22 | 1 | 2 | yes | — |
| 52 | C4×#1142 | C22 | 1 | 4 | yes | — |
| 53 | #89784 | C22 | 1 | 4 | yes | — |
| 54 | D4×C7⋊C8 | C22 | 1 | 4 | yes | — |
| 55 | #89779 | C22 | 1 | 2 | yes | — |
| 56 | #89768 | C22 | 1 | 4 | yes | — |
| 57 | #89697 | C22 | 1 | 2 | yes | — |
| 58 | #61665 | — | 7 | 1 | no | maximal, Sylow |
| 59 | C7×2−1+4 | — | 4 | 4 | no | — |
| 60 | C7×2−1+4 | — | 4 | 4 | no | — |
| 61 | C2×C7×#41 | — | 2 | 2 | no | — |
| 62 | C2×C7×#41 | — | 2 | 4 | no | — |
| 63 | C2×C7×#41 | C23 | 1 | 1 | yes | characteristic |
| 64 | C2×C7×#41 | C23 | 1 | 4 | yes | — |
| 65 | C2×C7×#41 | C23 | 1 | 2 | yes | — |
| 66 | C22×C7×Q8 | — | 2 | 2 | no | — |
| 67 | C22×C7×Q8 | C23 | 1 | 4 | yes | — |
| 68 | C22×C7×Q8 | C23 | 1 | 2 | yes | — |
| 69 | C22×Dic14 | C23 | 1 | 4 | yes | — |
| 70 | C7×C4⋊Q8 | — | 2 | 2 | no | — |
| 71 | C7×C4⋊Q8 | — | 2 | 4 | no | — |
| 72 | C7×C4⋊Q8 | — | 2 | 1 | no | — |
| 73 | C7×C4⋊Q8 | — | 2 | 1 | no | — |
| 74 | C7×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 75 | C7×C4⋊Q8 | C23 | 1 | 4 | yes | — |
| 76 | C7×#127 | D4 | 1 | 1 | yes | characteristic |
| 77 | C7×#124 | — | 2 | 2 | no | — |
| 78 | C7×#124 | D4 | 1 | 2 | yes | — |
| 79 | C7×#123 | — | 2 | 4 | no | — |
| 80 | C7×#123 | — | 2 | 8 | no | — |
| 81 | C7×C22⋊Q8 | — | 2 | 8 | no | — |
| 82 | C7×C22⋊Q8 | C23 | 1 | 8 | yes | — |
| 83 | C7×#121 | — | 2 | 4 | no | — |
| 84 | C7×#121 | D4 | 1 | 4 | yes | — |
| 85 | C4×C7×Q8 | C23 | 1 | 2 | yes | — |
| 86 | C4×C7×D4 | — | 2 | 4 | no | — |
| 87 | C4×C7×D4 | — | 2 | 2 | no | — |
| 88 | C4×C7×D4 | C23 | 1 | 2 | yes | — |
| 89 | C4×C7×D4 | C23 | 1 | 4 | yes | — |
| 90 | C7×#117 | — | 2 | 1 | no | — |
| 91 | C7×#117 | C23 | 1 | 1 | yes | characteristic |
| 92 | C2×C7×C4⋊C4 | — | 2 | 2 | no | — |
| 93 | C2×C7×C4⋊C4 | — | 2 | 4 | no | — |
| 94 | C2×C42×C7 | — | 2 | 1 | no | — |
| 95 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 96 | #6514 | — | 4 | 8 | no | — |
| 97 | #6507 | — | 2 | 4 | no | — |
| 98 | C2×#1144 | — | 4 | 8 | no | — |
| 99 | C2×#1144 | C23 | 1 | 4 | yes | — |
| 100 | C2×#1144 | C23 | 1 | 8 | yes | — |
| 101 | C2×#1144 | C23 | 1 | 8 | yes | — |
| 102 | #6499 | — | 2 | 4 | no | — |
| 103 | #6499 | — | 2 | 4 | no | — |
| 104 | #6498 | — | 2 | 4 | no | — |
| 105 | #6498 | — | 2 | 4 | no | — |
| 106 | D4×Dic7 | — | 2 | 4 | no | — |
| 107 | C2×#1142 | C23 | 1 | 4 | yes | — |
| 108 | #6489 | — | 2 | 2 | no | — |
| 109 | #6489 | C23 | 1 | 4 | yes | — |
| 110 | #6487 | — | 2 | 2 | no | — |
| 111 | #6487 | C23 | 1 | 4 | yes | — |
| 112 | #6487 | C23 | 1 | 8 | yes | — |
| 113 | C2×#1136 | C23 | 1 | 4 | yes | — |
| 114 | C22×C7⋊C8 | C23 | 1 | 4 | yes | — |
| 115 | #6451 | — | 2 | 4 | no | — |
| 116 | #6450 | — | 2 | 4 | no | — |
| 117 | #6442 | — | 2 | 8 | no | — |
| 118 | #6441 | — | 2 | 8 | no | — |
| 119 | #6433 | — | 2 | 2 | no | — |
| 120 | #6432 | C23 | 1 | 2 | yes | — |
| 121 | #6432 | C23 | 1 | 2 | yes | — |
| 122 | C4×Dic14 | — | 2 | 2 | no | — |
| 123 | C4×Dic14 | C23 | 1 | 4 | yes | — |
| 124 | #6409 | C23 | 1 | 8 | yes | — |
| 125 | #6409 | C23 | 1 | 8 | yes | — |
| 126 | #6409 | C23 | 1 | 4 | yes | — |
| 127 | #6406 | C23 | 1 | 4 | yes | — |
| 128 | C22⋊(C7⋊C8) | C23 | 1 | 4 | yes | — |
| 129 | C22⋊(C7⋊C8) | C23 | 1 | 8 | yes | — |
| 130 | #6384 | C23 | 1 | 4 | yes | — |
| 131 | #6384 | C23 | 1 | 4 | yes | — |
| 132 | #6382 | C23 | 1 | 4 | yes | — |
| 133 | #6381 | C23 | 1 | 4 | yes | — |
| 134 | C4⋊(C7⋊C8) | C23 | 1 | 2 | yes | — |
| 135 | C4⋊(C7⋊C8) | C23 | 1 | 2 | yes | — |
| 136 | C4×C7⋊C8 | C23 | 1 | 4 | yes | — |
| 137 | #3550 | — | 7 | 1 | no | — |
| 138 | #3499 | D7 | 1 | 1 | yes | characteristic |
| 139 | #3328 | — | 7 | 4 | no | — |
| 140 | #3302 | — | 7 | 4 | no | — |
| 141 | D4×Q16 | — | 7 | 4 | no | — |
| 142 | #3276 | — | 7 | 4 | no | — |
| 143 | #3209 | — | 7 | 2 | no | — |
| 144 | #3202 | — | 7 | 4 | no | — |
| 145 | #3107 | — | 7 | 2 | no | — |
| 146 | #3011 | — | 7 | 4 | no | — |
| 147 | #2979 | — | 7 | 1 | no | — |
| 148 | C7×#41 | — | 2 | 2 | no | — |
| 149 | C7×#41 | — | 2 | 2 | no | — |
| 150 | C7×#41 | — | 2 | 8 | no | — |
| 151 | C7×#41 | — | 4 | 2 | no | — |
| 152 | C7×#41 | — | 4 | 2 | no | — |
| 153 | C7×#41 | — | 4 | 4 | no | — |
| 154 | C7×#41 | — | 4 | 8 | no | — |
| 155 | C7×#41 | — | 4 | 16 | no | — |
| 156 | C2×C7×Q8 | — | 2 | 4 | no | — |
| 157 | C2×C7×Q8 | — | 2 | 2 | no | — |
| 158 | C2×C7×Q8 | — | 2 | 8 | no | — |
| 159 | C2×C7×Q8 | — | 4 | 4 | no | — |
| 160 | C2×C7×Q8 | — | 4 | 2 | no | — |
| 161 | C2×C7×Q8 | — | 4 | 2 | no | — |
| 162 | C2×C7×Q8 | — | 4 | 8 | no | — |
| 163 | C2×C7×Q8 | C2×D4 | 1 | 2 | yes | — |
| 164 | C2×C7×Q8 | C24 | 1 | 4 | yes | — |
| 165 | C2×C7×Q8 | C24 | 1 | 1 | yes | characteristic |
| 166 | C2×C7×D4 | — | 2 | 1 | no | — |
| 167 | C2×C7×D4 | — | 2 | 4 | no | — |
| 168 | C2×C7×D4 | C2×D4 | 1 | 4 | yes | — |
| 169 | C2×C7×D4 | C2×D4 | 1 | 2 | yes | — |
| 170 | C2×C7×D4 | C2×D4 | 1 | 4 | yes | — |
| 171 | C2×C7×D4 | C24 | 1 | 1 | yes | characteristic |
| 172 | C22×C4×C7 | — | 2 | 1 | no | — |
| 173 | C22×C4×C7 | — | 2 | 2 | no | — |
| 174 | C22×C4×C7 | — | 2 | 4 | no | — |
| 175 | C22×C4×C7 | — | 2 | 2 | no | — |
| 176 | C22×C4×C7 | — | 2 | 4 | no | — |
| 177 | C22×C4×C7 | C2×D4 | 1 | 2 | yes | — |
| 178 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 179 | C22×C4×C7 | C24 | 1 | 4 | yes | — |
| 180 | C22×Dic7 | — | 2 | 4 | no | — |
| 181 | C2×Dic14 | — | 2 | 2 | no | — |
| 182 | C2×Dic14 | — | 2 | 4 | no | — |
| 183 | C2×Dic14 | — | 4 | 4 | no | — |
| 184 | C2×Dic14 | — | 4 | 4 | no | — |
| 185 | C2×Dic14 | C24 | 1 | 4 | yes | — |
| 186 | C7×C4⋊C4 | — | 2 | 4 | no | — |
| 187 | C7×C4⋊C4 | — | 2 | 4 | no | — |
| 188 | C7×C4⋊C4 | — | 2 | 8 | no | — |
| 189 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 190 | C7×C4⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 191 | C7×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 192 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 193 | C7×C22⋊C4 | — | 2 | 8 | no | — |
| 194 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 195 | C7×C22⋊C4 | C2×D4 | 1 | 8 | yes | — |
| 196 | C42×C7 | — | 2 | 1 | no | — |
| 197 | C42×C7 | — | 2 | 2 | no | — |
| 198 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 199 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 200 | C42×C7 | C24 | 1 | 2 | yes | — |
| 201 | C22⋊Dic7 | — | 2 | 8 | no | — |
| 202 | C22⋊Dic7 | — | 2 | 4 | no | — |
| 203 | C22⋊Dic7 | — | 2 | 4 | no | — |
| 204 | #1144 | — | 2 | 8 | no | — |
| 205 | #1144 | — | 4 | 8 | no | — |
| 206 | #1144 | — | 4 | 8 | no | — |
| 207 | #1142 | — | 2 | 8 | no | — |
| 208 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 209 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 210 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 211 | C4⋊Dic7 | C24 | 1 | 4 | yes | — |
| 212 | Dic7⋊C4 | — | 2 | 4 | no | — |
| 213 | Dic7⋊C4 | — | 2 | 4 | no | — |
| 214 | Dic7⋊C4 | — | 2 | 8 | no | — |
| 215 | C4×Dic7 | — | 2 | 4 | no | — |
| 216 | C4×Dic7 | — | 2 | 4 | no | — |
| 217 | #1136 | — | 4 | 4 | no | — |
| 218 | C2×C7⋊C8 | — | 4 | 4 | no | — |
| 219 | C2×C7⋊C8 | C24 | 1 | 4 | yes | — |
| 220 | C2×C7⋊C8 | C24 | 1 | 4 | yes | — |
| 221 | C2×2−1+4 | C2×D7 | 1 | 2 | yes | — |
| 222 | C2×#137 | — | 7 | 4 | no | — |
| 223 | C22×Q16 | — | 7 | 4 | no | — |
| 224 | #563 | — | 14 | 2 | no | — |
| 225 | #559 | — | 14 | 1 | no | — |
| 226 | Q82 | — | 14 | 1 | no | — |
| 227 | #556 | — | 7 | 4 | no | — |
| 228 | D4×Q8 | — | 7 | 4 | no | — |
| 229 | D4×Q8 | C2×D7 | 1 | 4 | yes | — |
| 230 | #547 | — | 2 | 4 | no | — |
| 231 | #547 | C2×D7 | 1 | 4 | yes | — |
| 232 | #542 | — | 14 | 4 | no | — |
| 233 | #536 | — | 2 | 2 | no | — |
| 234 | #536 | — | 7 | 4 | no | — |
| 235 | #536 | C2×D7 | 1 | 2 | yes | — |
| 236 | #533 | — | 7 | 2 | no | — |
| 237 | #532 | — | 2 | 1 | no | — |
| 238 | #532 | C2×D7 | 1 | 1 | yes | characteristic |
| 239 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 240 | C2×C4⋊Q8 | C2×D7 | 1 | 1 | yes | characteristic |
| 241 | C4×#41 | C2×D7 | 1 | 1 | yes | characteristic |
| 242 | #494 | — | 7 | 4 | no | — |
| 243 | #487 | — | 7 | 4 | no | — |
| 244 | #485 | — | 7 | 8 | no | — |
| 245 | #485 | — | 7 | 4 | no | — |
| 246 | #475 | — | 7 | 2 | no | — |
| 247 | #474 | — | 7 | 2 | no | — |
| 248 | #470 | — | 7 | 8 | no | — |
| 249 | #467 | — | 7 | 8 | no | — |
| 250 | #462 | — | 7 | 4 | no | — |
| 251 | #462 | — | 7 | 4 | no | — |
| 252 | #462 | — | 7 | 2 | no | — |
| 253 | #461 | — | 7 | 2 | no | — |
| 254 | #452 | — | 7 | 4 | no | — |
| 255 | #452 | — | 7 | 8 | no | — |
| 256 | #451 | — | 7 | 8 | no | — |
| 257 | #451 | — | 7 | 8 | no | — |
| 258 | #451 | — | 7 | 8 | no | — |
| 259 | C4×Q16 | — | 7 | 4 | no | — |
| 260 | C4×SD16 | — | 7 | 4 | no | — |
| 261 | #436 | — | 7 | 4 | no | — |
| 262 | C8×D4 | — | 7 | 4 | no | — |
| 263 | #431 | — | 7 | 2 | no | — |
| 264 | #419 | — | 7 | 4 | no | — |
| 265 | #416 | — | 7 | 4 | no | — |
| 266 | #408 | — | 7 | 4 | no | — |
| 267 | C23×C7 | — | 2 | 1 | no | — |
| 268 | C23×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 269 | C23×C7 | C22×D4 | 1 | 4 | yes | — |
| 270 | C7×Q8 | — | 2 | 1 | no | — |
| 271 | C7×Q8 | — | 2 | 4 | no | — |
| 272 | C7×Q8 | — | 2 | 4 | no | — |
| 273 | C7×Q8 | — | 4 | 2 | no | — |
| 274 | C7×Q8 | — | 4 | 8 | no | — |
| 275 | C7×Q8 | — | 4 | 4 | no | — |
| 276 | C7×Q8 | H(5,𝔽2) | 1 | 2 | yes | — |
| 277 | C7×D4 | — | 2 | 4 | no | — |
| 278 | C7×D4 | — | 2 | 8 | no | — |
| 279 | C7×D4 | — | 2 | 1 | no | — |
| 280 | C7×D4 | — | 4 | 4 | no | — |
| 281 | C7×D4 | — | 4 | 2 | no | — |
| 282 | C7×D4 | — | 4 | 8 | no | — |
| 283 | C7×D4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 284 | C2×C4×C7 | — | 2 | 4 | no | — |
| 285 | C2×C4×C7 | — | 2 | 1 | no | — |
| 286 | C2×C4×C7 | — | 2 | 4 | no | — |
| 287 | C2×C4×C7 | — | 2 | 4 | no | — |
| 288 | C2×C4×C7 | — | 2 | 4 | no | — |
| 289 | C2×C4×C7 | — | 2 | 1 | no | — |
| 290 | C2×C4×C7 | — | 2 | 1 | no | — |
| 291 | C2×C4×C7 | — | 2 | 2 | no | — |
| 292 | C2×C4×C7 | — | 2 | 4 | no | — |
| 293 | C2×C4×C7 | — | 4 | 8 | no | — |
| 294 | C2×C4×C7 | — | 4 | 8 | no | — |
| 295 | C2×C4×C7 | — | 4 | 4 | no | — |
| 296 | C2×C4×C7 | — | 4 | 4 | no | — |
| 297 | C2×C4×C7 | C22×D4 | 1 | 4 | yes | — |
| 298 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 299 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 300 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 301 | C2×C4×C7 | C25 | 1 | 1 | yes | characteristic |
| 302 | C2×Dic7 | — | 2 | 4 | no | — |
| 303 | C2×Dic7 | — | 2 | 4 | no | — |
| 304 | C2×Dic7 | — | 8 | 4 | no | — |
| 305 | Dic14 | — | 2 | 4 | no | — |
| 306 | Dic14 | — | 2 | 4 | no | — |
| 307 | Dic14 | — | 4 | 4 | no | — |
| 308 | Dic14 | — | 8 | 4 | no | — |
| 309 | C7⋊C8 | — | 2 | 4 | no | — |
| 310 | C7⋊C8 | — | 2 | 4 | no | — |
| 311 | 2−1+4 | — | 4 | 4 | no | — |
| 312 | 2−1+4 | — | 4 | 4 | no | — |
| 313 | C2×#41 | — | 2 | 2 | no | — |
| 314 | C2×#41 | — | 2 | 4 | no | — |
| 315 | C2×#41 | C22×D7 | 1 | 1 | yes | characteristic |
| 316 | C2×#41 | C22×D7 | 1 | 4 | yes | — |
| 317 | C2×#41 | C22×D7 | 1 | 2 | yes | — |
| 318 | C22×Q8 | — | 2 | 2 | no | — |
| 319 | C22×Q8 | — | 7 | 4 | no | — |
| 320 | C22×Q8 | C22×D7 | 1 | 4 | yes | — |
| 321 | C22×Q8 | C22×D7 | 1 | 2 | yes | — |
| 322 | #137 | — | 28 | 8 | no | — |
| 323 | C2×Q16 | — | 7 | 4 | no | — |
| 324 | C2×Q16 | — | 7 | 8 | no | — |
| 325 | C2×Q16 | — | 7 | 8 | no | — |
| 326 | C2×Q16 | — | 28 | 8 | no | — |
| 327 | C2×SD16 | — | 7 | 4 | no | — |
| 328 | C2×M16 | — | 7 | 4 | no | — |
| 329 | C22×C8 | — | 7 | 4 | no | — |
| 330 | C4⋊Q8 | — | 2 | 2 | no | — |
| 331 | C4⋊Q8 | — | 2 | 4 | no | — |
| 332 | C4⋊Q8 | — | 2 | 1 | no | — |
| 333 | C4⋊Q8 | — | 2 | 1 | no | — |
| 334 | C4⋊Q8 | — | 7 | 2 | no | — |
| 335 | C4⋊Q8 | — | 7 | 2 | no | — |
| 336 | C4⋊Q8 | — | 14 | 4 | no | — |
| 337 | C4⋊Q8 | — | 14 | 4 | no | — |
| 338 | C4⋊Q8 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 339 | C4⋊Q8 | C22×D7 | 1 | 4 | yes | — |
| 340 | #127 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 341 | #126 | — | 14 | 8 | no | — |
| 342 | #125 | — | 14 | 2 | no | — |
| 343 | #124 | — | 2 | 2 | no | — |
| 344 | #124 | — | 14 | 4 | no | — |
| 345 | #124 | — | 14 | 4 | no | — |
| 346 | #124 | C22⋊D7 | 1 | 2 | yes | — |
| 347 | #123 | — | 2 | 4 | no | — |
| 348 | #123 | — | 2 | 8 | no | — |
| 349 | #123 | — | 14 | 4 | no | — |
| 350 | #123 | — | 14 | 4 | no | — |
| 351 | C22⋊Q8 | — | 2 | 8 | no | — |
| 352 | C22⋊Q8 | — | 7 | 4 | no | — |
| 353 | C22⋊Q8 | — | 7 | 8 | no | — |
| 354 | C22⋊Q8 | — | 14 | 2 | no | — |
| 355 | C22⋊Q8 | — | 14 | 8 | no | — |
| 356 | C22⋊Q8 | C22×D7 | 1 | 8 | yes | — |
| 357 | #121 | — | 2 | 4 | no | — |
| 358 | #121 | C22⋊D7 | 1 | 4 | yes | — |
| 359 | C4×Q8 | — | 7 | 4 | no | — |
| 360 | C4×Q8 | — | 14 | 4 | no | — |
| 361 | C4×Q8 | — | 14 | 2 | no | — |
| 362 | C4×Q8 | C22×D7 | 1 | 2 | yes | — |
| 363 | C4×D4 | — | 2 | 4 | no | — |
| 364 | C4×D4 | — | 2 | 2 | no | — |
| 365 | C4×D4 | — | 14 | 4 | no | — |
| 366 | C4×D4 | C22×D7 | 1 | 2 | yes | — |
| 367 | C4×D4 | C22×D7 | 1 | 4 | yes | — |
| 368 | #117 | — | 2 | 1 | no | — |
| 369 | #117 | — | 7 | 4 | no | — |
| 370 | #117 | — | 14 | 2 | no | — |
| 371 | #117 | C22×D7 | 1 | 1 | yes | characteristic |
| 372 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 373 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 374 | C2×C42 | — | 2 | 1 | no | — |
| 375 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 376 | #107 | — | 7 | 4 | no | — |
| 377 | #106 | — | 7 | 4 | no | — |
| 378 | C4⋊C8 | — | 7 | 2 | no | — |
| 379 | C4⋊C8 | — | 7 | 2 | no | — |
| 380 | #103 | — | 7 | 8 | no | — |
| 381 | #103 | — | 7 | 4 | no | — |
| 382 | #103 | — | 7 | 8 | no | — |
| 383 | #103 | — | 7 | 4 | no | — |
| 384 | #103 | — | 7 | 4 | no | — |
| 385 | #102 | — | 7 | 4 | no | — |
| 386 | C22⋊C8 | — | 7 | 4 | no | — |
| 387 | C22⋊C8 | — | 7 | 8 | no | — |
| 388 | C4×C8 | — | 7 | 4 | no | — |
| 389 | C22×C7 | — | 2 | 4 | no | — |
| 390 | C22×C7 | — | 2 | 1 | no | — |
| 391 | C22×C7 | — | 2 | 2 | no | — |
| 392 | C22×C7 | — | 2 | 2 | no | — |
| 393 | C22×C7 | — | 2 | 8 | no | — |
| 394 | C22×C7 | — | 4 | 2 | no | — |
| 395 | C22×C7 | C23×D4 | 1 | 1 | yes | characteristic |
| 396 | C4×C7 | — | 2 | 4 | no | — |
| 397 | C4×C7 | — | 2 | 1 | no | — |
| 398 | C4×C7 | — | 2 | 2 | no | — |
| 399 | C4×C7 | — | 2 | 2 | no | — |
| 400 | C4×C7 | — | 4 | 4 | no | — |
| 401 | C4×C7 | — | 4 | 2 | no | — |
| 402 | C4×C7 | #578 | 1 | 4 | yes | — |
| 403 | C4×C7 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 404 | C4×C7 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 405 | Dic7 | — | 4 | 4 | no | — |
| 406 | Dic7 | — | 4 | 4 | no | — |
| 407 | #41 | — | 2 | 2 | no | — |
| 408 | #41 | — | 2 | 2 | no | — |
| 409 | #41 | — | 2 | 8 | no | — |
| 410 | #41 | — | 4 | 2 | no | — |
| 411 | #41 | — | 4 | 2 | no | — |
| 412 | #41 | — | 4 | 4 | no | — |
| 413 | #41 | — | 4 | 8 | no | — |
| 414 | #41 | — | 4 | 16 | no | — |
| 415 | C2×Q8 | — | 2 | 4 | no | — |
| 416 | C2×Q8 | — | 2 | 2 | no | — |
| 417 | C2×Q8 | — | 2 | 8 | no | — |
| 418 | C2×Q8 | — | 4 | 4 | no | — |
| 419 | C2×Q8 | — | 4 | 2 | no | — |
| 420 | C2×Q8 | — | 4 | 2 | no | — |
| 421 | C2×Q8 | — | 4 | 8 | no | — |
| 422 | C2×Q8 | — | 7 | 4 | no | — |
| 423 | C2×Q8 | — | 14 | 2 | no | — |
| 424 | C2×Q8 | — | 14 | 4 | no | — |
| 425 | C2×Q8 | — | 28 | 4 | no | — |
| 426 | C2×Q8 | — | 28 | 4 | no | — |
| 427 | C2×Q8 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 428 | C2×Q8 | C23×D7 | 1 | 4 | yes | — |
| 429 | C2×Q8 | C23×D7 | 1 | 1 | yes | characteristic |
| 430 | C2×D4 | — | 2 | 1 | no | — |
| 431 | C2×D4 | — | 2 | 4 | no | — |
| 432 | C2×D4 | C2×C22⋊D7 | 1 | 4 | yes | — |
| 433 | C2×D4 | C2×C22⋊D7 | 1 | 4 | yes | — |
| 434 | C2×D4 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 435 | C2×D4 | C23×D7 | 1 | 1 | yes | characteristic |
| 436 | C22×C4 | — | 2 | 1 | no | — |
| 437 | C22×C4 | — | 2 | 2 | no | — |
| 438 | C22×C4 | — | 2 | 4 | no | — |
| 439 | C22×C4 | — | 2 | 2 | no | — |
| 440 | C22×C4 | — | 2 | 4 | no | — |
| 441 | C22×C4 | — | 14 | 4 | no | — |
| 442 | C22×C4 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 443 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 444 | C22×C4 | C23×D7 | 1 | 4 | yes | — |
| 445 | Q16 | — | 14 | 8 | no | — |
| 446 | Q16 | — | 28 | 8 | no | — |
| 447 | Q16 | — | 28 | 8 | no | — |
| 448 | SD16 | — | 14 | 8 | no | — |
| 449 | M16 | — | 28 | 4 | no | — |
| 450 | C2×C8 | — | 7 | 4 | no | — |
| 451 | C2×C8 | — | 7 | 4 | no | — |
| 452 | C2×C8 | — | 28 | 4 | no | — |
| 453 | C4⋊C4 | — | 2 | 4 | no | — |
| 454 | C4⋊C4 | — | 2 | 4 | no | — |
| 455 | C4⋊C4 | — | 2 | 8 | no | — |
| 456 | C4⋊C4 | — | 2 | 2 | no | — |
| 457 | C4⋊C4 | — | 7 | 4 | no | — |
| 458 | C4⋊C4 | — | 14 | 4 | no | — |
| 459 | C4⋊C4 | — | 14 | 8 | no | — |
| 460 | C4⋊C4 | — | 14 | 4 | no | — |
| 461 | C4⋊C4 | — | 14 | 2 | no | — |
| 462 | C4⋊C4 | — | 14 | 2 | no | — |
| 463 | C4⋊C4 | — | 14 | 2 | no | — |
| 464 | C4⋊C4 | C2×C22⋊D7 | 1 | 4 | yes | — |
| 465 | C4⋊C4 | C23×D7 | 1 | 2 | yes | — |
| 466 | C22⋊C4 | — | 2 | 1 | no | — |
| 467 | C22⋊C4 | — | 2 | 8 | no | — |
| 468 | C22⋊C4 | — | 2 | 2 | no | — |
| 469 | C22⋊C4 | — | 14 | 4 | no | — |
| 470 | C22⋊C4 | — | 14 | 4 | no | — |
| 471 | C22⋊C4 | — | 14 | 8 | no | — |
| 472 | C22⋊C4 | C2×C22⋊D7 | 1 | 8 | yes | — |
| 473 | C42 | — | 2 | 1 | no | — |
| 474 | C42 | — | 2 | 2 | no | — |
| 475 | C42 | — | 14 | 4 | no | — |
| 476 | C42 | — | 14 | 4 | no | — |
| 477 | C42 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 478 | C42 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 479 | C42 | C23×D7 | 1 | 2 | yes | — |
| 480 | C2×C7 | — | 4 | 4 | no | — |
| 481 | C2×C7 | — | 4 | 1 | no | — |
| 482 | C2×C7 | — | 4 | 2 | no | — |
| 483 | C2×C7 | #3484 | 1 | 1 | yes | characteristic |
| 484 | C2×C7 | C2×#578 | 1 | 2 | yes | — |
| 485 | C23 | — | 2 | 1 | no | — |
| 486 | C23 | C22×C22⋊D7 | 1 | 4 | yes | — |
| 487 | C23 | C22×C22⋊D7 | 1 | 1 | yes | characteristic |
| 488 | Q8 | — | 2 | 1 | no | — |
| 489 | Q8 | — | 2 | 4 | no | — |
| 490 | Q8 | — | 2 | 4 | no | — |
| 491 | Q8 | — | 4 | 2 | no | — |
| 492 | Q8 | — | 4 | 8 | no | — |
| 493 | Q8 | — | 4 | 4 | no | — |
| 494 | Q8 | — | 14 | 4 | no | — |
| 495 | Q8 | — | 14 | 4 | no | — |
| 496 | Q8 | — | 28 | 4 | no | — |
| 497 | Q8 | — | 56 | 4 | no | — |
| 498 | Q8 | #6548 | 1 | 2 | yes | — |
| 499 | D4 | — | 2 | 4 | no | — |
| 500 | D4 | — | 2 | 8 | no | — |
| 501 | D4 | — | 2 | 1 | no | — |
| 502 | D4 | — | 4 | 2 | no | — |
| 503 | D4 | — | 4 | 4 | no | — |
| 504 | D4 | — | 4 | 8 | no | — |
| 505 | D4 | #6548 | 1 | 2 | yes | — |
| 506 | C2×C4 | — | 2 | 4 | no | — |
| 507 | C2×C4 | — | 2 | 1 | no | — |
| 508 | C2×C4 | — | 2 | 4 | no | — |
| 509 | C2×C4 | — | 2 | 4 | no | — |
| 510 | C2×C4 | — | 2 | 4 | no | — |
| 511 | C2×C4 | — | 2 | 1 | no | — |
| 512 | C2×C4 | — | 2 | 1 | no | — |
| 513 | C2×C4 | — | 2 | 2 | no | — |
| 514 | C2×C4 | — | 2 | 4 | no | — |
| 515 | C2×C4 | — | 4 | 8 | no | — |
| 516 | C2×C4 | — | 4 | 8 | no | — |
| 517 | C2×C4 | — | 4 | 4 | no | — |
| 518 | C2×C4 | — | 4 | 4 | no | — |
| 519 | C2×C4 | — | 14 | 4 | no | — |
| 520 | C2×C4 | — | 14 | 4 | no | — |
| 521 | C2×C4 | — | 56 | 4 | no | — |
| 522 | C2×C4 | C22×C22⋊D7 | 1 | 1 | yes | characteristic |
| 523 | C2×C4 | C22×C22⋊D7 | 1 | 4 | yes | — |
| 524 | C2×C4 | C22×C22⋊D7 | 1 | 2 | yes | — |
| 525 | C2×C4 | C22×C22⋊D7 | 1 | 2 | yes | — |
| 526 | C2×C4 | C24×D7 | 1 | 1 | yes | characteristic |
| 527 | C8 | — | 14 | 4 | no | — |
| 528 | C8 | — | 14 | 4 | no | — |
| 529 | C7 | #61665 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 530 | C22 | — | 2 | 1 | no | — |
| 531 | C22 | — | 2 | 2 | no | — |
| 532 | C22 | — | 2 | 4 | no | — |
| 533 | C22 | — | 2 | 2 | no | — |
| 534 | C22 | — | 2 | 8 | no | — |
| 535 | C22 | — | 4 | 2 | no | — |
| 536 | C22 | C23×C22⋊D7 | 1 | 1 | yes | characteristic |
| 537 | C4 | — | 2 | 1 | no | — |
| 538 | C4 | — | 2 | 2 | no | — |
| 539 | C4 | — | 2 | 4 | no | — |
| 540 | C4 | — | 2 | 2 | no | — |
| 541 | C4 | — | 4 | 4 | no | — |
| 542 | C4 | — | 4 | 2 | no | — |
| 543 | C4 | — | 28 | 4 | no | — |
| 544 | C4 | — | 28 | 4 | no | — |
| 545 | C4 | #90529 | 1 | 4 | yes | — |
| 546 | C4 | C2×#6548 | 1 | 1 | yes | characteristic |
| 547 | C4 | C2×#6548 | 1 | 1 | yes | characteristic |
| 548 | C2 | — | 4 | 1 | no | — |
| 549 | C2 | — | 4 | 4 | no | — |
| 550 | C2 | — | 4 | 2 | no | — |
| 551 | C2 | #11744307 | 1 | 1 | yes | characteristic |
| 552 | C2 | C2×#90529 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11743299 | C2 | semidirect |
| 3. #11741562 | C2 | semidirect |
| 4. D4×#1144 | C2 | semidirect |
| 5. #11740999 | C2 | semidirect |
| 6. #11740974 | C2 | semidirect |
| 7. #11740955 | C2 | semidirect |
| 8. #11740858 | C2 | semidirect |
| 9. #11740723 | C2 | semidirect |
| 10. #11740667 | C2 | semidirect |
| 11. #11739979 | C2 | semidirect |
| 529. C7 | #61665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3499 | 2 |
| #11743299 | 2 |
| #11741562 | 2 |
| D4×#1144 | 2 |
| #11740999 | 2 |
| #11740974 | 2 |
| #11740955 | 2 |
| #11740858 | 2 |
| #11740723 | 2 |
| #11740667 | 2 |
| #11739979 | 2 |
| #61665 | 7 |