Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1664 conjugacy classes of subgroups.
The subgroup lattice has 600 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11744099 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | Q8×#1159 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C7×#3359 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11741141 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | Q8×#1142 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11739072 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #11739055 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #11738488 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #11738462 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #11737862 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #11737856 | C2 | 1 | 3 | yes | maximal |
| 12 | Q8×Dic28 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #11737366 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #11737100 | C2 | 1 | 3 | yes | maximal |
| 15 | #11737079 | C2 | 1 | 3 | yes | maximal, complemented |
| 16 | C7×#557 | C22 | 1 | 1 | yes | characteristic |
| 17 | C7×D4×Q8 | C22 | 1 | 1 | yes | characteristic |
| 18 | Q8×C22⋊D7 | — | 2 | 1 | no | — |
| 19 | C2×Q8×Dic7 | — | 2 | 1 | no | — |
| 20 | #90419 | C22 | 1 | 3 | yes | — |
| 21 | #90419 | C22 | 1 | 3 | yes | — |
| 22 | #90412 | C22 | 1 | 3 | yes | — |
| 23 | #90412 | C22 | 1 | 3 | yes | — |
| 24 | #90380 | — | 2 | 3 | no | — |
| 25 | #90376 | — | 2 | 3 | no | — |
| 26 | #90326 | — | 2 | 3 | no | — |
| 27 | #90313 | — | 2 | 3 | no | — |
| 28 | #90269 | C22 | 1 | 3 | yes | — |
| 29 | #90263 | — | 2 | 1 | no | — |
| 30 | C4×Q8×D7 | C22 | 1 | 1 | yes | characteristic |
| 31 | #90261 | — | 2 | 1 | no | — |
| 32 | Q8×Dic14 | C22 | 1 | 3 | yes | — |
| 33 | Q8×Dic14 | C22 | 1 | 1 | yes | characteristic |
| 34 | Q8×Dic14 | C22 | 1 | 1 | yes | characteristic |
| 35 | #90234 | C22 | 1 | 3 | yes | — |
| 36 | C4×#1159 | C22 | 1 | 3 | yes | — |
| 37 | C7×#487 | C22 | 1 | 3 | yes | — |
| 38 | C7×#475 | C22 | 1 | 3 | yes | — |
| 39 | C7×#461 | C22 | 1 | 3 | yes | — |
| 40 | C7×C8×Q8 | C22 | 1 | 1 | yes | characteristic |
| 41 | C4×C7×SD16 | C22 | 1 | 3 | yes | — |
| 42 | #89945 | C22 | 1 | 3 | yes | — |
| 43 | #89936 | C22 | 1 | 6 | yes | — |
| 44 | #89934 | C22 | 1 | 3 | yes | — |
| 45 | #89866 | C22 | 1 | 3 | yes | — |
| 46 | #89862 | C22 | 1 | 3 | yes | — |
| 47 | #89853 | C22 | 1 | 3 | yes | — |
| 48 | #89851 | C22 | 1 | 3 | yes | — |
| 49 | C4×#1144 | C22 | 1 | 3 | yes | — |
| 50 | Q8×C7⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 51 | #89793 | C22 | 1 | 3 | yes | — |
| 52 | C4×#1142 | C22 | 1 | 3 | yes | — |
| 53 | #89780 | C22 | 1 | 3 | yes | — |
| 54 | #89639 | C22 | 1 | 3 | yes | — |
| 55 | #89628 | C22 | 1 | 6 | yes | — |
| 56 | #89626 | C22 | 1 | 3 | yes | — |
| 57 | #89622 | C22 | 1 | 3 | yes | — |
| 58 | #89622 | C22 | 1 | 3 | yes | — |
| 59 | #89607 | C22 | 1 | 3 | yes | — |
| 60 | #89603 | C22 | 1 | 3 | yes | — |
| 61 | #89586 | C22 | 1 | 6 | yes | — |
| 62 | #89586 | C22 | 1 | 3 | yes | — |
| 63 | #89569 | C22 | 1 | 6 | yes | — |
| 64 | #89568 | C22 | 1 | 6 | yes | — |
| 65 | #89568 | C22 | 1 | 6 | yes | — |
| 66 | #89565 | C22 | 1 | 3 | yes | — |
| 67 | #89561 | C22 | 1 | 6 | yes | — |
| 68 | #89555 | C22 | 1 | 1 | yes | characteristic |
| 69 | #89531 | C22 | 1 | 3 | yes | — |
| 70 | C4×Dic28 | C22 | 1 | 3 | yes | — |
| 71 | #89457 | C22 | 1 | 3 | yes | — |
| 72 | #89454 | C22 | 1 | 3 | yes | — |
| 73 | #89451 | C22 | 1 | 3 | yes | — |
| 74 | #61846 | — | 7 | 1 | no | maximal, Sylow |
| 75 | C22×C7×Q8 | — | 2 | 1 | no | — |
| 76 | C2×Q8×D7 | D4 | 1 | 1 | yes | characteristic |
| 77 | C2×#1159 | C23 | 1 | 1 | yes | characteristic |
| 78 | C2×C7×SD16 | C23 | 1 | 3 | yes | — |
| 79 | C7×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 80 | C7×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 81 | C7×#125 | — | 2 | 3 | no | — |
| 82 | C7×C22⋊Q8 | — | 2 | 3 | no | — |
| 83 | C4×C7×Q8 | — | 2 | 1 | no | — |
| 84 | C4×C7×Q8 | C23 | 1 | 3 | yes | — |
| 85 | C4×C7×Q8 | C23 | 1 | 1 | yes | characteristic |
| 86 | C4×C7×D4 | C23 | 1 | 3 | yes | — |
| 87 | #6509 | — | 2 | 3 | no | — |
| 88 | #6509 | C23 | 1 | 3 | yes | — |
| 89 | Q8×Dic7 | — | 2 | 1 | no | — |
| 90 | Q8×Dic7 | — | 2 | 1 | no | — |
| 91 | Q8×Dic7 | — | 2 | 3 | no | — |
| 92 | Q8×Dic7 | — | 2 | 3 | no | — |
| 93 | Q8×Dic7 | D4 | 1 | 1 | yes | characteristic |
| 94 | Q8×Dic7 | C23 | 1 | 6 | yes | — |
| 95 | #6507 | — | 2 | 3 | no | — |
| 96 | #6507 | C23 | 1 | 3 | yes | — |
| 97 | C2×#1144 | C23 | 1 | 3 | yes | — |
| 98 | D4×Dic7 | C23 | 1 | 3 | yes | — |
| 99 | C2×#1142 | C23 | 1 | 1 | yes | characteristic |
| 100 | C4×C22⋊D7 | — | 2 | 3 | no | — |
| 101 | C2×C4⋊Dic7 | — | 2 | 3 | no | — |
| 102 | #6487 | — | 2 | 3 | no | — |
| 103 | C2×C4×Dic7 | — | 2 | 3 | no | — |
| 104 | C2×Dic28 | C23 | 1 | 1 | yes | characteristic |
| 105 | #6460 | — | 2 | 3 | no | — |
| 106 | #6460 | — | 2 | 3 | no | — |
| 107 | #6460 | C23 | 1 | 1 | yes | characteristic |
| 108 | #6459 | — | 2 | 3 | no | — |
| 109 | #6455 | — | 2 | 3 | no | — |
| 110 | #6455 | C23 | 1 | 3 | yes | — |
| 111 | D7×C4⋊C4 | D4 | 1 | 3 | yes | — |
| 112 | #6453 | — | 2 | 3 | no | — |
| 113 | #6453 | — | 2 | 3 | no | — |
| 114 | #6453 | C23 | 1 | 6 | yes | — |
| 115 | #6452 | — | 2 | 6 | no | — |
| 116 | #6452 | — | 2 | 6 | no | — |
| 117 | #6452 | — | 2 | 3 | no | — |
| 118 | #6451 | — | 2 | 3 | no | — |
| 119 | #6451 | — | 2 | 3 | no | — |
| 120 | #6451 | — | 2 | 6 | no | — |
| 121 | #6451 | C23 | 1 | 3 | yes | — |
| 122 | #6450 | — | 2 | 3 | no | — |
| 123 | #6450 | — | 2 | 3 | no | — |
| 124 | #6450 | — | 2 | 3 | no | — |
| 125 | #6450 | D4 | 1 | 3 | yes | — |
| 126 | #6450 | C23 | 1 | 3 | yes | — |
| 127 | (C22⋊D7)⋊C4 | — | 2 | 3 | no | — |
| 128 | #6441 | — | 2 | 6 | no | — |
| 129 | #6440 | — | 2 | 3 | no | — |
| 130 | #6435 | — | 2 | 3 | no | — |
| 131 | C42×D7 | C23 | 1 | 3 | yes | — |
| 132 | #6432 | — | 2 | 3 | no | — |
| 133 | #6432 | C23 | 1 | 3 | yes | — |
| 134 | #6432 | C23 | 1 | 3 | yes | — |
| 135 | C4×Dic14 | — | 2 | 3 | no | — |
| 136 | C4×Dic14 | — | 2 | 3 | no | — |
| 137 | C4×Dic14 | C23 | 1 | 3 | yes | — |
| 138 | C4×Dic14 | C23 | 1 | 3 | yes | — |
| 139 | C4×Dic14 | C23 | 1 | 3 | yes | — |
| 140 | C7×#106 | C23 | 1 | 3 | yes | — |
| 141 | C7×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 142 | C7×#103 | C23 | 1 | 6 | yes | — |
| 143 | C7×#103 | C23 | 1 | 3 | yes | — |
| 144 | C7×#102 | C23 | 1 | 1 | yes | characteristic |
| 145 | C4×C7×C8 | C23 | 1 | 3 | yes | — |
| 146 | #6409 | C23 | 1 | 6 | yes | — |
| 147 | #6409 | C23 | 1 | 3 | yes | — |
| 148 | #6406 | C23 | 1 | 3 | yes | — |
| 149 | (C2×D7)⋊C8 | C23 | 1 | 3 | yes | — |
| 150 | (C2×D7)⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 151 | #6392 | C23 | 1 | 6 | yes | — |
| 152 | #6392 | C23 | 1 | 3 | yes | — |
| 153 | #6390 | C23 | 1 | 3 | yes | — |
| 154 | #6390 | C23 | 1 | 3 | yes | — |
| 155 | #6389 | C23 | 1 | 6 | yes | — |
| 156 | Dic7⋊C8 | C23 | 1 | 3 | yes | — |
| 157 | Dic7⋊C8 | C23 | 1 | 3 | yes | — |
| 158 | #6384 | C23 | 1 | 3 | yes | — |
| 159 | #6384 | C23 | 1 | 1 | yes | characteristic |
| 160 | #6382 | C23 | 1 | 6 | yes | — |
| 161 | #6382 | C23 | 1 | 3 | yes | — |
| 162 | #6381 | C23 | 1 | 3 | yes | — |
| 163 | C4⋊(C7⋊C8) | C23 | 1 | 3 | yes | — |
| 164 | C4×C7⋊C8 | C23 | 1 | 3 | yes | — |
| 165 | #3502 | — | 7 | 1 | no | — |
| 166 | Q8×#41 | — | 7 | 1 | no | — |
| 167 | #3387 | — | 7 | 3 | no | — |
| 168 | #3385 | — | 7 | 3 | no | — |
| 169 | Q8×Q16 | — | 7 | 1 | no | — |
| 170 | Q8×SD16 | — | 7 | 1 | no | — |
| 171 | #3374 | — | 7 | 3 | no | — |
| 172 | #3372 | — | 7 | 3 | no | — |
| 173 | #3363 | — | 7 | 1 | no | — |
| 174 | #3359 | D7 | 1 | 1 | yes | characteristic, complemented |
| 175 | #3237 | — | 7 | 3 | no | — |
| 176 | #3231 | — | 7 | 3 | no | — |
| 177 | #3116 | — | 7 | 3 | no | — |
| 178 | #3107 | — | 7 | 3 | no | — |
| 179 | #2984 | — | 7 | 1 | no | — |
| 180 | C2×C7×Q8 | — | 2 | 3 | no | — |
| 181 | C2×C7×Q8 | — | 4 | 4 | no | — |
| 182 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 183 | C2×C7×Q8 | C24 | 1 | 3 | yes | — |
| 184 | C2×C7×D4 | C24 | 1 | 1 | yes | characteristic |
| 185 | C22×C4×C7 | — | 2 | 3 | no | — |
| 186 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 187 | C22×Dic7 | — | 2 | 1 | no | — |
| 188 | C22×Dic7 | — | 2 | 3 | no | — |
| 189 | Q8×D7 | — | 2 | 4 | no | — |
| 190 | #1159 | — | 2 | 2 | no | — |
| 191 | #1159 | — | 2 | 2 | no | — |
| 192 | C2×C4×D7 | C2×D4 | 1 | 3 | yes | — |
| 193 | C2×C4×D7 | C2×D4 | 1 | 3 | yes | — |
| 194 | C2×C4×D7 | C24 | 1 | 1 | yes | characteristic |
| 195 | C2×Dic14 | — | 2 | 3 | no | — |
| 196 | C2×Dic14 | — | 2 | 3 | no | — |
| 197 | C2×Dic14 | — | 2 | 3 | no | — |
| 198 | C2×Dic14 | C2×D4 | 1 | 3 | yes | — |
| 199 | C2×Dic14 | C24 | 1 | 1 | yes | characteristic |
| 200 | C2×Dic14 | C24 | 1 | 1 | yes | characteristic |
| 201 | C7×SD16 | — | 2 | 6 | no | — |
| 202 | C2×C7×C8 | C24 | 1 | 1 | yes | characteristic |
| 203 | C2×C7×C8 | C24 | 1 | 3 | yes | — |
| 204 | C7×C4⋊C4 | — | 2 | 3 | no | — |
| 205 | C7×C4⋊C4 | — | 2 | 3 | no | — |
| 206 | C7×C4⋊C4 | — | 2 | 3 | no | — |
| 207 | C7×C4⋊C4 | — | 2 | 3 | no | — |
| 208 | C7×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 209 | C7×C4⋊C4 | C24 | 1 | 1 | yes | characteristic |
| 210 | C7×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 211 | C7×C22⋊C4 | — | 2 | 3 | no | — |
| 212 | C42×C7 | — | 2 | 3 | no | — |
| 213 | C42×C7 | C24 | 1 | 3 | yes | — |
| 214 | C22⋊Dic7 | — | 2 | 3 | no | — |
| 215 | #1144 | — | 2 | 6 | no | — |
| 216 | #1142 | — | 2 | 2 | no | — |
| 217 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 218 | (C2×D7)⋊C4 | — | 2 | 3 | no | — |
| 219 | (C2×D7)⋊C4 | — | 2 | 3 | no | — |
| 220 | C4⋊Dic7 | — | 2 | 3 | no | — |
| 221 | C4⋊Dic7 | — | 2 | 3 | no | — |
| 222 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 223 | C4⋊Dic7 | — | 2 | 6 | no | — |
| 224 | C4⋊Dic7 | — | 2 | 6 | no | — |
| 225 | C4⋊Dic7 | C2×D4 | 1 | 3 | yes | — |
| 226 | C4⋊Dic7 | C24 | 1 | 3 | yes | — |
| 227 | C4⋊Dic7 | C24 | 1 | 3 | yes | — |
| 228 | Dic7⋊C4 | — | 2 | 3 | no | — |
| 229 | Dic7⋊C4 | — | 2 | 3 | no | — |
| 230 | Dic7⋊C4 | — | 2 | 3 | no | — |
| 231 | Dic7⋊C4 | — | 2 | 3 | no | — |
| 232 | Dic7⋊C4 | — | 2 | 3 | no | — |
| 233 | Dic7⋊C4 | — | 2 | 3 | no | — |
| 234 | Dic7⋊C4 | — | 2 | 3 | no | — |
| 235 | Dic7⋊C4 | — | 2 | 6 | no | — |
| 236 | Dic7⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 237 | C4×Dic7 | — | 2 | 3 | no | — |
| 238 | C4×Dic7 | — | 2 | 3 | no | — |
| 239 | C4×Dic7 | — | 2 | 6 | no | — |
| 240 | C4×Dic7 | — | 2 | 3 | no | — |
| 241 | C4×Dic7 | — | 2 | 3 | no | — |
| 242 | C4×Dic7 | C2×D4 | 1 | 3 | yes | — |
| 243 | C4×Dic7 | C2×D4 | 1 | 3 | yes | — |
| 244 | C4×Dic7 | C24 | 1 | 3 | yes | — |
| 245 | C2×C7⋊C8 | C24 | 1 | 3 | yes | — |
| 246 | C2×C7⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 247 | Dic28 | — | 2 | 2 | no | — |
| 248 | Q82 | — | 7 | 3 | no | — |
| 249 | Q82 | — | 7 | 1 | no | — |
| 250 | Q82 | — | 7 | 1 | no | — |
| 251 | #557 | — | 7 | 3 | no | — |
| 252 | #557 | — | 7 | 3 | no | — |
| 253 | #557 | — | 14 | 1 | no | — |
| 254 | #557 | — | 14 | 3 | no | — |
| 255 | #557 | C2×D7 | 1 | 1 | yes | characteristic |
| 256 | #554 | — | 7 | 3 | no | — |
| 257 | #554 | — | 14 | 3 | no | — |
| 258 | D4×Q8 | — | 14 | 1 | no | — |
| 259 | D4×Q8 | C2×D7 | 1 | 1 | yes | characteristic |
| 260 | #544 | — | 14 | 3 | no | — |
| 261 | #533 | — | 7 | 3 | no | — |
| 262 | #533 | — | 7 | 3 | no | — |
| 263 | #533 | — | 7 | 3 | no | — |
| 264 | #533 | — | 14 | 3 | no | — |
| 265 | #519 | — | 14 | 1 | no | — |
| 266 | C4×#41 | — | 7 | 3 | no | — |
| 267 | C2×C4×Q8 | — | 7 | 1 | no | — |
| 268 | C2×C4×Q8 | — | 14 | 1 | no | — |
| 269 | #501 | — | 7 | 6 | no | — |
| 270 | #500 | — | 7 | 3 | no | — |
| 271 | #498 | — | 7 | 3 | no | — |
| 272 | #491 | — | 7 | 6 | no | — |
| 273 | #487 | — | 7 | 3 | no | — |
| 274 | #487 | C2×D7 | 1 | 3 | yes | — |
| 275 | #485 | — | 7 | 3 | no | — |
| 276 | #485 | — | 7 | 3 | no | — |
| 277 | #485 | — | 7 | 6 | no | — |
| 278 | #479 | — | 7 | 6 | no | — |
| 279 | #479 | — | 7 | 6 | no | — |
| 280 | #477 | — | 7 | 3 | no | — |
| 281 | #477 | — | 7 | 3 | no | — |
| 282 | #477 | — | 7 | 3 | no | — |
| 283 | #476 | — | 7 | 3 | no | — |
| 284 | #475 | — | 7 | 3 | no | — |
| 285 | #475 | — | 7 | 3 | no | — |
| 286 | #475 | C2×D7 | 1 | 3 | yes | — |
| 287 | #474 | — | 7 | 3 | no | — |
| 288 | #462 | — | 7 | 3 | no | — |
| 289 | #462 | — | 7 | 3 | no | — |
| 290 | #461 | — | 7 | 3 | no | — |
| 291 | #461 | C2×D7 | 1 | 3 | yes | — |
| 292 | #452 | — | 7 | 3 | no | — |
| 293 | #452 | — | 7 | 1 | no | — |
| 294 | #446 | — | 7 | 3 | no | — |
| 295 | #446 | — | 7 | 3 | no | — |
| 296 | C8×Q8 | — | 7 | 1 | no | — |
| 297 | C8×Q8 | C2×D7 | 1 | 1 | yes | characteristic |
| 298 | #441 | — | 7 | 6 | no | — |
| 299 | #440 | — | 7 | 6 | no | — |
| 300 | C4×Q16 | — | 7 | 3 | no | — |
| 301 | C4×Q16 | — | 7 | 3 | no | — |
| 302 | C4×SD16 | — | 7 | 3 | no | — |
| 303 | C4×SD16 | C2×D7 | 1 | 3 | yes | — |
| 304 | #432 | — | 7 | 3 | no | — |
| 305 | #431 | — | 7 | 3 | no | — |
| 306 | C23×C7 | — | 2 | 1 | no | — |
| 307 | C22×D7 | C22×D4 | 1 | 1 | yes | characteristic |
| 308 | C7×Q8 | — | 2 | 3 | no | — |
| 309 | C7×Q8 | — | 2 | 3 | no | — |
| 310 | C7×Q8 | — | 4 | 6 | no | — |
| 311 | C7×Q8 | #137 | 1 | 4 | yes | — |
| 312 | C7×D4 | — | 2 | 1 | no | — |
| 313 | C7×D4 | 2−1+4 | 1 | 2 | yes | — |
| 314 | C2×C4×C7 | — | 2 | 3 | no | — |
| 315 | C2×C4×C7 | — | 2 | 3 | no | — |
| 316 | C2×C4×C7 | — | 2 | 1 | no | — |
| 317 | C2×C4×C7 | — | 4 | 6 | no | — |
| 318 | C2×C4×C7 | C22×D4 | 1 | 3 | yes | — |
| 319 | C2×C4×C7 | C22×D4 | 1 | 3 | yes | — |
| 320 | C2×C4×C7 | C25 | 1 | 1 | yes | characteristic |
| 321 | C22⋊D7 | — | 2 | 4 | no | — |
| 322 | C2×Dic7 | — | 2 | 4 | no | — |
| 323 | C2×Dic7 | — | 2 | 1 | no | — |
| 324 | C2×Dic7 | — | 2 | 1 | no | — |
| 325 | C2×Dic7 | — | 2 | 3 | no | — |
| 326 | C2×Dic7 | — | 2 | 3 | no | — |
| 327 | C2×Dic7 | — | 8 | 3 | no | — |
| 328 | C2×Dic7 | C22×D4 | 1 | 1 | yes | characteristic |
| 329 | C2×Dic7 | C22×D4 | 1 | 3 | yes | — |
| 330 | C2×Dic7 | C22×D4 | 1 | 3 | yes | — |
| 331 | C4×D7 | — | 2 | 6 | no | — |
| 332 | C4×D7 | — | 2 | 1 | no | — |
| 333 | C4×D7 | — | 2 | 1 | no | — |
| 334 | C4×D7 | — | 4 | 3 | no | — |
| 335 | Dic14 | — | 2 | 6 | no | — |
| 336 | Dic14 | — | 2 | 1 | no | — |
| 337 | Dic14 | — | 2 | 1 | no | — |
| 338 | Dic14 | — | 2 | 1 | no | — |
| 339 | Dic14 | — | 8 | 3 | no | — |
| 340 | Dic14 | — | 8 | 3 | no | — |
| 341 | Dic14 | — | 8 | 3 | no | — |
| 342 | Dic14 | 2−1+4 | 1 | 2 | yes | — |
| 343 | C7×C8 | — | 2 | 1 | no | — |
| 344 | C7×C8 | — | 2 | 3 | no | — |
| 345 | C7⋊C8 | — | 2 | 1 | no | — |
| 346 | C7⋊C8 | — | 2 | 3 | no | — |
| 347 | C2×#41 | — | 7 | 1 | no | — |
| 348 | C22×Q8 | — | 2 | 1 | no | — |
| 349 | C22×Q8 | — | 7 | 1 | no | — |
| 350 | C2×Q16 | — | 7 | 3 | no | — |
| 351 | C2×Q16 | — | 7 | 1 | no | — |
| 352 | C2×SD16 | — | 7 | 1 | no | — |
| 353 | C2×SD16 | C22×D7 | 1 | 3 | yes | — |
| 354 | C4⋊Q8 | — | 7 | 3 | no | — |
| 355 | C4⋊Q8 | — | 7 | 3 | no | — |
| 356 | C4⋊Q8 | — | 7 | 3 | no | — |
| 357 | C4⋊Q8 | — | 7 | 3 | no | — |
| 358 | C4⋊Q8 | — | 14 | 3 | no | — |
| 359 | C4⋊Q8 | — | 14 | 6 | no | — |
| 360 | C4⋊Q8 | — | 14 | 3 | no | — |
| 361 | C4⋊Q8 | — | 14 | 3 | no | — |
| 362 | C4⋊Q8 | — | 14 | 3 | no | — |
| 363 | C4⋊Q8 | C22×D7 | 1 | 3 | yes | — |
| 364 | C4⋊Q8 | C22×D7 | 1 | 3 | yes | — |
| 365 | #125 | — | 2 | 3 | no | — |
| 366 | #125 | — | 7 | 6 | no | — |
| 367 | #125 | — | 14 | 3 | no | — |
| 368 | #125 | — | 14 | 3 | no | — |
| 369 | #125 | — | 14 | 6 | no | — |
| 370 | #125 | — | 14 | 6 | no | — |
| 371 | #125 | — | 14 | 3 | no | — |
| 372 | C22⋊Q8 | — | 2 | 3 | no | — |
| 373 | C22⋊Q8 | — | 7 | 3 | no | — |
| 374 | C22⋊Q8 | — | 7 | 1 | no | — |
| 375 | C22⋊Q8 | — | 14 | 6 | no | — |
| 376 | C22⋊Q8 | — | 14 | 3 | no | — |
| 377 | C22⋊Q8 | — | 14 | 3 | no | — |
| 378 | C22⋊Q8 | — | 14 | 3 | no | — |
| 379 | C22⋊Q8 | — | 14 | 3 | no | — |
| 380 | C22⋊Q8 | — | 14 | 3 | no | — |
| 381 | C4×Q8 | — | 2 | 1 | no | — |
| 382 | C4×Q8 | — | 7 | 1 | no | — |
| 383 | C4×Q8 | — | 7 | 3 | no | — |
| 384 | C4×Q8 | — | 7 | 3 | no | — |
| 385 | C4×Q8 | — | 7 | 6 | no | — |
| 386 | C4×Q8 | — | 7 | 3 | no | — |
| 387 | C4×Q8 | — | 7 | 3 | no | — |
| 388 | C4×Q8 | — | 7 | 3 | no | — |
| 389 | C4×Q8 | — | 14 | 3 | no | — |
| 390 | C4×Q8 | — | 14 | 3 | no | — |
| 391 | C4×Q8 | — | 14 | 3 | no | — |
| 392 | C4×Q8 | — | 14 | 3 | no | — |
| 393 | C4×Q8 | — | 14 | 3 | no | — |
| 394 | C4×Q8 | — | 14 | 3 | no | — |
| 395 | C4×Q8 | — | 14 | 3 | no | — |
| 396 | C4×Q8 | — | 14 | 1 | no | — |
| 397 | C4×Q8 | — | 14 | 1 | no | — |
| 398 | C4×Q8 | C22×D7 | 1 | 3 | yes | — |
| 399 | C4×Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 400 | C4×D4 | — | 7 | 3 | no | — |
| 401 | C4×D4 | — | 14 | 3 | no | — |
| 402 | C4×D4 | — | 14 | 3 | no | — |
| 403 | C4×D4 | C22×D7 | 1 | 3 | yes | — |
| 404 | #117 | — | 7 | 3 | no | — |
| 405 | #117 | — | 14 | 3 | no | — |
| 406 | #117 | — | 14 | 3 | no | — |
| 407 | #117 | — | 14 | 3 | no | — |
| 408 | C2×C4⋊C4 | — | 7 | 3 | no | — |
| 409 | C2×C4⋊C4 | — | 14 | 3 | no | — |
| 410 | C2×C42 | — | 7 | 3 | no | — |
| 411 | C2×C42 | — | 14 | 3 | no | — |
| 412 | #107 | — | 7 | 3 | no | — |
| 413 | #107 | — | 7 | 6 | no | — |
| 414 | #107 | — | 7 | 3 | no | — |
| 415 | #106 | — | 7 | 3 | no | — |
| 416 | #106 | — | 7 | 6 | no | — |
| 417 | #106 | C22×D7 | 1 | 3 | yes | — |
| 418 | C4⋊C8 | — | 7 | 3 | no | — |
| 419 | C4⋊C8 | — | 7 | 3 | no | — |
| 420 | C4⋊C8 | — | 7 | 3 | no | — |
| 421 | C4⋊C8 | C22×D7 | 1 | 3 | yes | — |
| 422 | #103 | — | 7 | 3 | no | — |
| 423 | #103 | — | 7 | 6 | no | — |
| 424 | #103 | — | 7 | 3 | no | — |
| 425 | #103 | — | 7 | 3 | no | — |
| 426 | #103 | — | 7 | 3 | no | — |
| 427 | #103 | — | 7 | 1 | no | — |
| 428 | #103 | C22×D7 | 1 | 3 | yes | — |
| 429 | #103 | C22×D7 | 1 | 6 | yes | — |
| 430 | #102 | — | 7 | 3 | no | — |
| 431 | #102 | C22×D7 | 1 | 1 | yes | characteristic |
| 432 | C22⋊C8 | — | 7 | 1 | no | — |
| 433 | C22⋊C8 | — | 7 | 3 | no | — |
| 434 | #97 | — | 7 | 6 | no | — |
| 435 | C4×C8 | — | 7 | 3 | no | — |
| 436 | C4×C8 | C22×D7 | 1 | 3 | yes | — |
| 437 | C22×C7 | — | 2 | 2 | no | — |
| 438 | C22×C7 | — | 4 | 1 | no | — |
| 439 | C22×C7 | — | 4 | 1 | no | — |
| 440 | C22×C7 | C23×D4 | 1 | 1 | yes | characteristic |
| 441 | C2×D7 | — | 2 | 1 | no | — |
| 442 | C2×D7 | — | 2 | 1 | no | — |
| 443 | C2×D7 | — | 2 | 1 | no | — |
| 444 | C4×C7 | — | 2 | 3 | no | — |
| 445 | C4×C7 | — | 4 | 1 | no | — |
| 446 | C4×C7 | — | 4 | 3 | no | — |
| 447 | C4×C7 | — | 4 | 3 | no | — |
| 448 | C4×C7 | C2×#137 | 1 | 6 | yes | — |
| 449 | C4×C7 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 450 | C4×C7 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 451 | Dic7 | — | 2 | 3 | no | — |
| 452 | Dic7 | — | 2 | 2 | no | — |
| 453 | Dic7 | — | 2 | 1 | no | — |
| 454 | Dic7 | — | 2 | 3 | no | — |
| 455 | Dic7 | — | 4 | 3 | no | — |
| 456 | Dic7 | — | 4 | 3 | no | — |
| 457 | Dic7 | — | 4 | 1 | no | — |
| 458 | #41 | — | 14 | 2 | no | — |
| 459 | #41 | — | 14 | 2 | no | — |
| 460 | C2×Q8 | — | 2 | 3 | no | — |
| 461 | C2×Q8 | — | 4 | 4 | no | — |
| 462 | C2×Q8 | — | 7 | 3 | no | — |
| 463 | C2×Q8 | — | 7 | 1 | no | — |
| 464 | C2×Q8 | — | 7 | 1 | no | — |
| 465 | C2×Q8 | — | 14 | 3 | no | — |
| 466 | C2×Q8 | — | 14 | 4 | no | — |
| 467 | C2×Q8 | — | 14 | 3 | no | — |
| 468 | C2×Q8 | — | 14 | 3 | no | — |
| 469 | C2×Q8 | D4×D7 | 1 | 1 | yes | characteristic |
| 470 | C2×Q8 | C23×D7 | 1 | 3 | yes | — |
| 471 | C2×D4 | — | 14 | 1 | no | — |
| 472 | C2×D4 | C23×D7 | 1 | 1 | yes | characteristic |
| 473 | C22×C4 | — | 2 | 3 | no | — |
| 474 | C22×C4 | — | 7 | 3 | no | — |
| 475 | C22×C4 | — | 7 | 1 | no | — |
| 476 | C22×C4 | — | 7 | 3 | no | — |
| 477 | C22×C4 | — | 14 | 1 | no | — |
| 478 | C22×C4 | — | 14 | 3 | no | — |
| 479 | Q16 | — | 14 | 2 | no | — |
| 480 | Q16 | — | 14 | 6 | no | — |
| 481 | SD16 | — | 2 | 6 | no | — |
| 482 | SD16 | — | 14 | 2 | no | — |
| 483 | C2×C8 | — | 7 | 1 | no | — |
| 484 | C2×C8 | — | 7 | 3 | no | — |
| 485 | C2×C8 | C23×D7 | 1 | 1 | yes | characteristic |
| 486 | C2×C8 | C23×D7 | 1 | 3 | yes | — |
| 487 | C4⋊C4 | — | 2 | 3 | no | — |
| 488 | C4⋊C4 | — | 2 | 3 | no | — |
| 489 | C4⋊C4 | — | 2 | 3 | no | — |
| 490 | C4⋊C4 | — | 2 | 3 | no | — |
| 491 | C4⋊C4 | — | 7 | 6 | no | — |
| 492 | C4⋊C4 | — | 7 | 3 | no | — |
| 493 | C4⋊C4 | — | 7 | 3 | no | — |
| 494 | C4⋊C4 | — | 7 | 3 | no | — |
| 495 | C4⋊C4 | — | 14 | 3 | no | — |
| 496 | C4⋊C4 | — | 14 | 3 | no | — |
| 497 | C4⋊C4 | — | 14 | 3 | no | — |
| 498 | C4⋊C4 | — | 14 | 3 | no | — |
| 499 | C4⋊C4 | — | 14 | 6 | no | — |
| 500 | C4⋊C4 | — | 14 | 3 | no | — |
| 501 | C4⋊C4 | — | 14 | 6 | no | — |
| 502 | C4⋊C4 | — | 14 | 6 | no | — |
| 503 | C4⋊C4 | — | 14 | 1 | no | — |
| 504 | C4⋊C4 | — | 14 | 3 | no | — |
| 505 | C4⋊C4 | — | 14 | 3 | no | — |
| 506 | C4⋊C4 | — | 14 | 3 | no | — |
| 507 | C4⋊C4 | — | 14 | 3 | no | — |
| 508 | C4⋊C4 | D4×D7 | 1 | 3 | yes | — |
| 509 | C4⋊C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 510 | C4⋊C4 | C23×D7 | 1 | 3 | yes | — |
| 511 | C22⋊C4 | — | 2 | 3 | no | — |
| 512 | C22⋊C4 | — | 14 | 3 | no | — |
| 513 | C22⋊C4 | — | 14 | 1 | no | — |
| 514 | C22⋊C4 | — | 14 | 3 | no | — |
| 515 | C22⋊C4 | — | 14 | 3 | no | — |
| 516 | C42 | — | 2 | 3 | no | — |
| 517 | C42 | — | 7 | 3 | no | — |
| 518 | C42 | — | 7 | 3 | no | — |
| 519 | C42 | — | 7 | 3 | no | — |
| 520 | C42 | — | 14 | 3 | no | — |
| 521 | C42 | — | 14 | 3 | no | — |
| 522 | C42 | — | 14 | 6 | no | — |
| 523 | C42 | — | 14 | 3 | no | — |
| 524 | C42 | — | 14 | 3 | no | — |
| 525 | C42 | C23×D7 | 1 | 3 | yes | — |
| 526 | C2×C7 | — | 4 | 2 | no | — |
| 527 | C2×C7 | #3486 | 1 | 1 | yes | characteristic |
| 528 | C2×C7 | C22×#137 | 1 | 1 | yes | characteristic |
| 529 | C2×C7 | #3584 | 1 | 1 | yes | characteristic |
| 530 | D7 | — | 4 | 1 | no | — |
| 531 | C23 | — | 2 | 1 | no | — |
| 532 | C23 | — | 7 | 1 | no | — |
| 533 | Q8 | — | 2 | 3 | no | — |
| 534 | Q8 | — | 2 | 3 | no | — |
| 535 | Q8 | — | 4 | 6 | no | — |
| 536 | Q8 | — | 7 | 2 | no | — |
| 537 | Q8 | — | 14 | 6 | no | — |
| 538 | Q8 | — | 14 | 1 | no | — |
| 539 | Q8 | — | 14 | 1 | no | — |
| 540 | Q8 | — | 14 | 1 | no | — |
| 541 | Q8 | — | 56 | 3 | no | — |
| 542 | Q8 | — | 56 | 3 | no | — |
| 543 | Q8 | — | 56 | 3 | no | — |
| 544 | Q8 | #6478 | 1 | 4 | yes | — |
| 545 | D4 | — | 2 | 1 | no | — |
| 546 | D4 | — | 14 | 4 | no | — |
| 547 | D4 | #6554 | 1 | 2 | yes | — |
| 548 | C2×C4 | — | 2 | 1 | no | — |
| 549 | C2×C4 | — | 2 | 3 | no | — |
| 550 | C2×C4 | — | 2 | 3 | no | — |
| 551 | C2×C4 | — | 4 | 6 | no | — |
| 552 | C2×C4 | — | 7 | 1 | no | — |
| 553 | C2×C4 | — | 7 | 3 | no | — |
| 554 | C2×C4 | — | 7 | 3 | no | — |
| 555 | C2×C4 | — | 14 | 4 | no | — |
| 556 | C2×C4 | — | 14 | 1 | no | — |
| 557 | C2×C4 | — | 14 | 6 | no | — |
| 558 | C2×C4 | — | 14 | 1 | no | — |
| 559 | C2×C4 | — | 14 | 1 | no | — |
| 560 | C2×C4 | — | 14 | 3 | no | — |
| 561 | C2×C4 | — | 14 | 1 | no | — |
| 562 | C2×C4 | — | 14 | 3 | no | — |
| 563 | C2×C4 | — | 28 | 3 | no | — |
| 564 | C2×C4 | — | 56 | 3 | no | — |
| 565 | C2×C4 | C2×D4×D7 | 1 | 3 | yes | — |
| 566 | C2×C4 | C2×D4×D7 | 1 | 3 | yes | — |
| 567 | C2×C4 | C24×D7 | 1 | 1 | yes | characteristic |
| 568 | C8 | — | 2 | 3 | no | — |
| 569 | C8 | — | 2 | 1 | no | — |
| 570 | C8 | — | 14 | 1 | no | — |
| 571 | C8 | — | 14 | 3 | no | — |
| 572 | C7 | #61846 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 573 | C22 | — | 2 | 2 | no | — |
| 574 | C22 | — | 4 | 1 | no | — |
| 575 | C22 | — | 4 | 1 | no | — |
| 576 | C22 | — | 14 | 1 | no | — |
| 577 | C22 | — | 14 | 1 | no | — |
| 578 | C22 | — | 14 | 1 | no | — |
| 579 | C22 | C22×D4×D7 | 1 | 1 | yes | characteristic |
| 580 | C4 | — | 2 | 3 | no | — |
| 581 | C4 | — | 4 | 1 | no | — |
| 582 | C4 | — | 4 | 3 | no | — |
| 583 | C4 | — | 4 | 3 | no | — |
| 584 | C4 | — | 14 | 3 | no | — |
| 585 | C4 | — | 14 | 1 | no | — |
| 586 | C4 | — | 14 | 2 | no | — |
| 587 | C4 | — | 14 | 3 | no | — |
| 588 | C4 | — | 28 | 3 | no | — |
| 589 | C4 | — | 28 | 3 | no | — |
| 590 | C4 | — | 28 | 1 | no | — |
| 591 | C4 | C2×#6478 | 1 | 6 | yes | — |
| 592 | C4 | C2×#6554 | 1 | 1 | yes | characteristic |
| 593 | C4 | D7×2−1+4 | 1 | 1 | yes | characteristic |
| 594 | C2 | — | 4 | 2 | no | — |
| 595 | C2 | — | 28 | 1 | no | — |
| 596 | C2 | #11743803 | 1 | 1 | yes | characteristic |
| 597 | C2 | C22×#6478 | 1 | 1 | yes | characteristic |
| 598 | C2 | #11744278 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11744099 | C2 | semidirect |
| 3. C7×#3359 | C2 | semidirect |
| 4. #11741141 | C2 | semidirect |
| 5. Q8×#1142 | C2 | semidirect |
| 6. #11739072 | C2 | semidirect |
| 7. #11739055 | C2 | semidirect |
| 8. #11738488 | C2 | semidirect |
| 9. #11738462 | C2 | semidirect |
| 10. #11737862 | C2 | semidirect |
| 12. Q8×Dic28 | C2 | semidirect |
| 13. #11737366 | C2 | semidirect |
| 15. #11737079 | C2 | semidirect |
| 174. #3359 | D7 | semidirect |
| 572. C7 | #61846 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11744099 | 2 |
| Q8×#1159 | 2 |
| C7×#3359 | 2 |
| #11741141 | 2 |
| Q8×#1142 | 2 |
| #11739072 | 2 |
| #11739055 | 2 |
| #11738488 | 2 |
| #11738462 | 2 |
| #11737862 | 2 |
| #11737856 | 2 |
| Q8×Dic28 | 2 |
| #11737366 | 2 |
| #11737100 | 2 |
| #11737079 | 2 |
| #61846 | 7 |