Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1928 conjugacy classes of subgroups.
The subgroup lattice has 644 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13128606 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | Q8×#6131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13127756 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #13127740 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | Q8×#6104 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13127563 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #13127542 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #13127507 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #13127472 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #13126032 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #13125973 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #13124990 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | #13124894 | C2 | 1 | 3 | yes | maximal, complemented |
| 14 | #13123924 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | Q8×C13×SD16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#88254 | — | 2 | 1 | no | — |
| 17 | Q82×C13 | C22 | 1 | 1 | yes | characteristic |
| 18 | D4×Q8×C13 | C22 | 1 | 1 | yes | characteristic |
| 19 | #11719522 | — | 2 | 1 | no | — |
| 20 | #11719435 | — | 2 | 3 | no | — |
| 21 | #11719435 | C22 | 1 | 3 | yes | — |
| 22 | #11719433 | — | 2 | 3 | no | — |
| 23 | #11719433 | C22 | 1 | 3 | yes | — |
| 24 | #11719432 | C22 | 1 | 3 | yes | — |
| 25 | #11719430 | C22 | 1 | 3 | yes | — |
| 26 | #11719338 | — | 2 | 3 | no | — |
| 27 | #11719334 | — | 2 | 3 | no | — |
| 28 | #11719282 | C22 | 1 | 1 | yes | characteristic |
| 29 | Q8×D52 | — | 2 | 1 | no | — |
| 30 | Q8×D52 | C22 | 1 | 1 | yes | characteristic |
| 31 | C4×#6131 | C22 | 1 | 3 | yes | — |
| 32 | C4×Q8×D13 | — | 2 | 1 | no | — |
| 33 | C4×Q8×D13 | C22 | 1 | 1 | yes | characteristic |
| 34 | #11719275 | C22 | 1 | 3 | yes | — |
| 35 | #11719258 | C22 | 1 | 3 | yes | — |
| 36 | #11719253 | C22 | 1 | 3 | yes | — |
| 37 | C13×#498 | C22 | 1 | 3 | yes | — |
| 38 | C13×#476 | C22 | 1 | 3 | yes | — |
| 39 | C13×#475 | C22 | 1 | 3 | yes | — |
| 40 | C8×Q8×C13 | C22 | 1 | 1 | yes | characteristic |
| 41 | C4×C13×SD16 | C22 | 1 | 3 | yes | — |
| 42 | #11718833 | C22 | 1 | 1 | yes | characteristic |
| 43 | #11718824 | C22 | 1 | 3 | yes | — |
| 44 | #11718749 | C22 | 1 | 3 | yes | — |
| 45 | #11718748 | C22 | 1 | 3 | yes | — |
| 46 | #11718745 | C22 | 1 | 3 | yes | — |
| 47 | #11718739 | C22 | 1 | 3 | yes | — |
| 48 | #11718688 | C22 | 1 | 3 | yes | — |
| 49 | C4×#6106 | C22 | 1 | 3 | yes | — |
| 50 | Q8×#1055 | C22 | 1 | 1 | yes | characteristic |
| 51 | C4×#6104 | C22 | 1 | 3 | yes | — |
| 52 | #11718668 | C22 | 1 | 3 | yes | — |
| 53 | #11718532 | C22 | 1 | 6 | yes | — |
| 54 | #11718532 | C22 | 1 | 6 | yes | — |
| 55 | #11718531 | C22 | 1 | 3 | yes | — |
| 56 | #11718530 | C22 | 1 | 6 | yes | — |
| 57 | #11718527 | C22 | 1 | 3 | yes | — |
| 58 | #11718527 | C22 | 1 | 6 | yes | — |
| 59 | #11718517 | C22 | 1 | 6 | yes | — |
| 60 | #11718507 | C22 | 1 | 3 | yes | — |
| 61 | #11718504 | C22 | 1 | 3 | yes | — |
| 62 | #11718496 | C22 | 1 | 3 | yes | — |
| 63 | #11718492 | C22 | 1 | 3 | yes | — |
| 64 | #11718478 | C22 | 1 | 6 | yes | — |
| 65 | #11718472 | C22 | 1 | 3 | yes | — |
| 66 | #11718455 | C22 | 1 | 3 | yes | — |
| 67 | #11718447 | C22 | 1 | 3 | yes | — |
| 68 | #11718445 | C22 | 1 | 3 | yes | — |
| 69 | #11718425 | C22 | 1 | 6 | yes | — |
| 70 | #11718355 | C22 | 1 | 3 | yes | — |
| 71 | C4×D104 | C22 | 1 | 3 | yes | — |
| 72 | #11718346 | C22 | 1 | 3 | yes | — |
| 73 | #11718340 | C22 | 1 | 3 | yes | — |
| 74 | C22×Q8×C13 | — | 2 | 1 | no | — |
| 75 | #88254 | — | 4 | 8 | no | — |
| 76 | C2×#6131 | — | 2 | 1 | no | — |
| 77 | C2×#6131 | — | 2 | 3 | no | — |
| 78 | C2×#6131 | C23 | 1 | 1 | yes | characteristic |
| 79 | C2×Q8×D13 | — | 2 | 1 | no | — |
| 80 | C2×Q8×D13 | — | 2 | 3 | no | — |
| 81 | C2×Q8×D13 | D4 | 1 | 1 | yes | characteristic |
| 82 | C2×#6127 | — | 2 | 3 | no | — |
| 83 | C2×#6127 | — | 2 | 3 | no | — |
| 84 | C2×C13×SD16 | C23 | 1 | 1 | yes | characteristic |
| 85 | C13×C4⋊Q8 | — | 2 | 3 | no | — |
| 86 | C13×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 87 | C13×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 88 | C13×C22⋊Q8 | — | 2 | 3 | no | — |
| 89 | C4×Q8×C13 | — | 2 | 1 | no | — |
| 90 | C4×Q8×C13 | C23 | 1 | 3 | yes | — |
| 91 | C4×Q8×C13 | C23 | 1 | 1 | yes | characteristic |
| 92 | C4×D4×C13 | C23 | 1 | 3 | yes | — |
| 93 | #88201 | — | 2 | 3 | no | — |
| 94 | #88200 | — | 2 | 3 | no | — |
| 95 | #88200 | — | 2 | 3 | no | — |
| 96 | #88200 | — | 2 | 6 | no | — |
| 97 | Q8×Dic13 | — | 2 | 3 | no | — |
| 98 | Q8×Dic13 | D4 | 1 | 1 | yes | characteristic |
| 99 | Q8×Dic13 | C23 | 1 | 3 | yes | — |
| 100 | C2×#6106 | C23 | 1 | 3 | yes | — |
| 101 | #88194 | C23 | 1 | 3 | yes | — |
| 102 | #88192 | C23 | 1 | 1 | yes | characteristic |
| 103 | C2×#6104 | C23 | 1 | 1 | yes | characteristic |
| 104 | #88184 | — | 2 | 3 | no | — |
| 105 | C4×C22⋊D13 | — | 2 | 3 | no | — |
| 106 | C2×D104 | C23 | 1 | 3 | yes | — |
| 107 | #88151 | — | 2 | 3 | no | — |
| 108 | #88151 | — | 2 | 3 | no | — |
| 109 | #88151 | — | 2 | 3 | no | — |
| 110 | #88150 | — | 2 | 6 | no | — |
| 111 | #88149 | — | 2 | 3 | no | — |
| 112 | #88149 | — | 2 | 3 | no | — |
| 113 | #88149 | C23 | 1 | 3 | yes | — |
| 114 | #88147 | — | 2 | 3 | no | — |
| 115 | #88147 | — | 2 | 3 | no | — |
| 116 | #88147 | C23 | 1 | 6 | yes | — |
| 117 | #88147 | C23 | 1 | 3 | yes | — |
| 118 | #88146 | — | 2 | 3 | no | — |
| 119 | #88146 | C23 | 1 | 3 | yes | — |
| 120 | C4⋊C4×D13 | — | 2 | 3 | no | — |
| 121 | C4⋊C4×D13 | D4 | 1 | 3 | yes | — |
| 122 | #88144 | — | 2 | 6 | no | — |
| 123 | #88144 | C23 | 1 | 6 | yes | — |
| 124 | #88142 | C23 | 1 | 3 | yes | — |
| 125 | #88141 | — | 2 | 3 | no | — |
| 126 | #88141 | D4 | 1 | 3 | yes | — |
| 127 | #88139 | — | 2 | 3 | no | — |
| 128 | #88138 | — | 2 | 3 | no | — |
| 129 | #88138 | — | 2 | 6 | no | — |
| 130 | #88128 | C23 | 1 | 3 | yes | — |
| 131 | C4×D52 | — | 2 | 3 | no | — |
| 132 | C4×D52 | C23 | 1 | 3 | yes | — |
| 133 | C4×D52 | C23 | 1 | 3 | yes | — |
| 134 | C42×D13 | — | 2 | 3 | no | — |
| 135 | C42×D13 | C23 | 1 | 3 | yes | — |
| 136 | #88123 | — | 2 | 3 | no | — |
| 137 | #88123 | C23 | 1 | 3 | yes | — |
| 138 | C4×Dic26 | — | 2 | 3 | no | — |
| 139 | C4×Dic26 | C23 | 1 | 3 | yes | — |
| 140 | C13×#106 | C23 | 1 | 3 | yes | — |
| 141 | C13×#106 | C23 | 1 | 6 | yes | — |
| 142 | C13×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 143 | C13×#103 | C23 | 1 | 3 | yes | — |
| 144 | C13×#102 | C23 | 1 | 3 | yes | — |
| 145 | C4×C8×C13 | C23 | 1 | 3 | yes | — |
| 146 | #88075 | C23 | 1 | 1 | yes | characteristic |
| 147 | #88072 | C23 | 1 | 3 | yes | — |
| 148 | #88061 | C23 | 1 | 6 | yes | — |
| 149 | #88061 | C23 | 1 | 3 | yes | — |
| 150 | #88061 | C23 | 1 | 1 | yes | characteristic |
| 151 | #88060 | C23 | 1 | 3 | yes | — |
| 152 | #88060 | C23 | 1 | 1 | yes | characteristic |
| 153 | #88058 | C23 | 1 | 3 | yes | — |
| 154 | #88055 | C23 | 1 | 6 | yes | — |
| 155 | #88054 | C23 | 1 | 3 | yes | — |
| 156 | #88054 | C23 | 1 | 3 | yes | — |
| 157 | #88049 | C23 | 1 | 3 | yes | — |
| 158 | #88049 | C23 | 1 | 6 | yes | — |
| 159 | #88049 | C23 | 1 | 3 | yes | — |
| 160 | #88048 | C23 | 1 | 3 | yes | — |
| 161 | #88047 | C23 | 1 | 6 | yes | — |
| 162 | #88047 | C23 | 1 | 3 | yes | — |
| 163 | C4⋊#1055 | C23 | 1 | 3 | yes | — |
| 164 | C4×#1055 | C23 | 1 | 3 | yes | — |
| 165 | #61840 | — | 13 | 1 | no | maximal, Sylow |
| 166 | C2×Q8×C13 | — | 2 | 3 | no | — |
| 167 | C2×Q8×C13 | — | 2 | 3 | no | — |
| 168 | C2×Q8×C13 | — | 4 | 4 | no | — |
| 169 | C2×Q8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | C2×Q8×C13 | C24 | 1 | 1 | yes | characteristic |
| 171 | C2×D4×C13 | C24 | 1 | 1 | yes | characteristic |
| 172 | C22×C4×C13 | — | 2 | 3 | no | — |
| 173 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 174 | C2×C22⋊D13 | — | 2 | 3 | no | — |
| 175 | C2×C22⋊D13 | — | 2 | 3 | no | — |
| 176 | #6131 | — | 2 | 2 | no | — |
| 177 | #6131 | — | 2 | 2 | no | — |
| 178 | #6131 | — | 4 | 12 | no | — |
| 179 | #6131 | — | 4 | 4 | no | — |
| 180 | Q8×D13 | — | 2 | 4 | no | — |
| 181 | Q8×D13 | — | 4 | 12 | no | — |
| 182 | Q8×D13 | — | 4 | 4 | no | — |
| 183 | #6127 | — | 4 | 12 | no | — |
| 184 | #6127 | — | 4 | 12 | no | — |
| 185 | C2×D52 | — | 2 | 1 | no | — |
| 186 | C2×D52 | — | 2 | 3 | no | — |
| 187 | C2×D52 | — | 2 | 3 | no | — |
| 188 | C2×D52 | — | 2 | 3 | no | — |
| 189 | C2×D52 | C24 | 1 | 3 | yes | — |
| 190 | C2×D52 | C24 | 1 | 1 | yes | characteristic |
| 191 | C2×C4×D13 | — | 2 | 1 | no | — |
| 192 | C2×C4×D13 | — | 2 | 3 | no | — |
| 193 | C2×C4×D13 | — | 2 | 3 | no | — |
| 194 | C2×C4×D13 | — | 2 | 6 | no | — |
| 195 | C2×C4×D13 | — | 2 | 3 | no | — |
| 196 | C2×C4×D13 | C2×D4 | 1 | 3 | yes | — |
| 197 | C2×C4×D13 | C2×D4 | 1 | 3 | yes | — |
| 198 | C2×C4×D13 | C24 | 1 | 1 | yes | characteristic |
| 199 | C2×Dic26 | — | 2 | 3 | no | — |
| 200 | C2×Dic26 | — | 2 | 3 | no | — |
| 201 | C2×Dic26 | C2×D4 | 1 | 3 | yes | — |
| 202 | C13×SD16 | — | 2 | 2 | no | — |
| 203 | C2×C8×C13 | C24 | 1 | 1 | yes | characteristic |
| 204 | C2×C8×C13 | C24 | 1 | 3 | yes | — |
| 205 | C13×C4⋊C4 | — | 2 | 3 | no | — |
| 206 | C13×C4⋊C4 | — | 2 | 3 | no | — |
| 207 | C13×C4⋊C4 | — | 2 | 3 | no | — |
| 208 | C13×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 209 | C13×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 210 | C13×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 211 | C13×C22⋊C4 | — | 2 | 3 | no | — |
| 212 | C42×C13 | — | 2 | 3 | no | — |
| 213 | C42×C13 | C24 | 1 | 3 | yes | — |
| 214 | C22⋊Dic13 | — | 2 | 1 | no | — |
| 215 | #6106 | — | 2 | 6 | no | — |
| 216 | #6104 | — | 2 | 2 | no | — |
| 217 | #6103 | — | 2 | 3 | no | — |
| 218 | #6103 | — | 2 | 3 | no | — |
| 219 | #6103 | — | 2 | 3 | no | — |
| 220 | #6103 | — | 2 | 3 | no | — |
| 221 | #6103 | — | 2 | 6 | no | — |
| 222 | #6103 | — | 2 | 3 | no | — |
| 223 | C4⋊Dic13 | — | 2 | 3 | no | — |
| 224 | C4⋊Dic13 | — | 2 | 3 | no | — |
| 225 | C4⋊Dic13 | — | 2 | 6 | no | — |
| 226 | C4⋊Dic13 | C2×D4 | 1 | 3 | yes | — |
| 227 | C4⋊Dic13 | C24 | 1 | 3 | yes | — |
| 228 | C4⋊Dic13 | C24 | 1 | 1 | yes | characteristic |
| 229 | #6101 | — | 2 | 6 | no | — |
| 230 | #6101 | — | 2 | 3 | no | — |
| 231 | #6101 | C2×D4 | 1 | 6 | yes | — |
| 232 | C4×Dic13 | — | 2 | 3 | no | — |
| 233 | C4×Dic13 | — | 2 | 3 | no | — |
| 234 | C4×Dic13 | C2×D4 | 1 | 3 | yes | — |
| 235 | C4×Dic13 | C2×D4 | 1 | 3 | yes | — |
| 236 | C4×Dic13 | C24 | 1 | 3 | yes | — |
| 237 | C2×#1055 | C24 | 1 | 3 | yes | — |
| 238 | C2×#1055 | C24 | 1 | 1 | yes | characteristic |
| 239 | D104 | — | 2 | 6 | no | — |
| 240 | #3497 | — | 13 | 1 | no | — |
| 241 | Q8×#41 | — | 13 | 1 | no | — |
| 242 | #3386 | — | 13 | 3 | no | — |
| 243 | #3384 | — | 13 | 3 | no | — |
| 244 | Q8×SD16 | D13 | 1 | 1 | yes | characteristic, complemented |
| 245 | Q8×D8 | — | 13 | 1 | no | — |
| 246 | #3368 | — | 13 | 3 | no | — |
| 247 | #3366 | — | 13 | 3 | no | — |
| 248 | #3362 | — | 13 | 1 | no | — |
| 249 | #3358 | — | 13 | 1 | no | — |
| 250 | #3235 | — | 13 | 3 | no | — |
| 251 | #3228 | — | 13 | 3 | no | — |
| 252 | #3115 | — | 13 | 3 | no | — |
| 253 | #3106 | — | 13 | 3 | no | — |
| 254 | #2984 | — | 13 | 1 | no | — |
| 255 | C23×C13 | — | 2 | 1 | no | — |
| 256 | C22×D13 | — | 2 | 1 | no | — |
| 257 | C22×D13 | — | 2 | 3 | no | — |
| 258 | C22×D13 | C22×D4 | 1 | 1 | yes | characteristic |
| 259 | Q8×C13 | — | 2 | 1 | no | — |
| 260 | Q8×C13 | — | 4 | 6 | no | — |
| 261 | Q8×C13 | — | 8 | 3 | no | — |
| 262 | Q8×C13 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 263 | Q8×C13 | 2−1+4 | 1 | 2 | yes | complemented |
| 264 | D4×C13 | — | 2 | 1 | no | — |
| 265 | D4×C13 | — | 2 | 1 | no | — |
| 266 | C2×C4×C13 | — | 2 | 1 | no | — |
| 267 | C2×C4×C13 | — | 2 | 3 | no | — |
| 268 | C2×C4×C13 | — | 2 | 3 | no | — |
| 269 | C2×C4×C13 | — | 4 | 6 | no | — |
| 270 | C2×C4×C13 | C22×D4 | 1 | 3 | yes | — |
| 271 | C2×C4×C13 | C22×D4 | 1 | 3 | yes | — |
| 272 | C2×C4×C13 | C25 | 1 | 1 | yes | characteristic |
| 273 | C22⋊D13 | — | 4 | 6 | no | — |
| 274 | C22⋊D13 | — | 4 | 2 | no | — |
| 275 | C22⋊D13 | — | 8 | 3 | no | — |
| 276 | C2×Dic13 | — | 2 | 3 | no | — |
| 277 | C2×Dic13 | — | 2 | 1 | no | — |
| 278 | C2×Dic13 | C22×D4 | 1 | 1 | yes | characteristic |
| 279 | C2×Dic13 | C22×D4 | 1 | 3 | yes | — |
| 280 | C2×Dic13 | C22×D4 | 1 | 3 | yes | — |
| 281 | D52 | — | 2 | 4 | no | — |
| 282 | D52 | — | 2 | 1 | no | — |
| 283 | D52 | — | 2 | 3 | no | — |
| 284 | D52 | — | 2 | 3 | no | — |
| 285 | D52 | — | 4 | 6 | no | — |
| 286 | D52 | — | 4 | 6 | no | — |
| 287 | D52 | — | 8 | 3 | no | — |
| 288 | D52 | 2−1+4 | 1 | 2 | yes | complemented |
| 289 | C4×D13 | — | 2 | 4 | no | — |
| 290 | C4×D13 | — | 2 | 6 | no | — |
| 291 | C4×D13 | — | 2 | 1 | no | — |
| 292 | C4×D13 | — | 2 | 1 | no | — |
| 293 | C4×D13 | — | 4 | 3 | no | — |
| 294 | C4×D13 | — | 4 | 12 | no | — |
| 295 | C4×D13 | — | 4 | 6 | no | — |
| 296 | C4×D13 | — | 4 | 6 | no | — |
| 297 | C4×D13 | — | 8 | 3 | no | — |
| 298 | Dic26 | — | 2 | 6 | no | — |
| 299 | Dic26 | — | 4 | 6 | no | — |
| 300 | Dic26 | — | 4 | 6 | no | — |
| 301 | C8×C13 | — | 2 | 3 | no | — |
| 302 | C8×C13 | — | 2 | 1 | no | — |
| 303 | #1055 | — | 2 | 1 | no | — |
| 304 | #1055 | — | 2 | 3 | no | — |
| 305 | C2×2−1+4 | — | 26 | 1 | no | — |
| 306 | Q82 | C2×D13 | 1 | 1 | yes | characteristic |
| 307 | #557 | — | 13 | 3 | no | — |
| 308 | #554 | — | 13 | 3 | no | — |
| 309 | #554 | — | 26 | 3 | no | — |
| 310 | #550 | — | 13 | 1 | no | — |
| 311 | #550 | — | 13 | 3 | no | — |
| 312 | D4×Q8 | — | 13 | 3 | no | — |
| 313 | D4×Q8 | — | 13 | 1 | no | — |
| 314 | D4×Q8 | — | 26 | 1 | no | — |
| 315 | D4×Q8 | C2×D13 | 1 | 1 | yes | characteristic |
| 316 | #548 | — | 26 | 3 | no | — |
| 317 | #548 | — | 26 | 1 | no | — |
| 318 | #537 | — | 26 | 3 | no | — |
| 319 | #533 | — | 13 | 3 | no | — |
| 320 | #533 | — | 26 | 3 | no | — |
| 321 | #532 | — | 13 | 3 | no | — |
| 322 | #532 | — | 13 | 3 | no | — |
| 323 | C4×#41 | — | 13 | 3 | no | — |
| 324 | C2×C4×Q8 | — | 13 | 1 | no | — |
| 325 | C2×C4×Q8 | — | 26 | 1 | no | — |
| 326 | #501 | — | 13 | 6 | no | — |
| 327 | #500 | — | 13 | 3 | no | — |
| 328 | #498 | C2×D13 | 1 | 3 | yes | — |
| 329 | #490 | — | 13 | 6 | no | — |
| 330 | #486 | — | 13 | 3 | no | — |
| 331 | #486 | — | 13 | 3 | no | — |
| 332 | #482 | — | 13 | 3 | no | — |
| 333 | #482 | — | 13 | 6 | no | — |
| 334 | #482 | — | 13 | 3 | no | — |
| 335 | #478 | — | 13 | 6 | no | — |
| 336 | #478 | — | 13 | 6 | no | — |
| 337 | #477 | — | 13 | 3 | no | — |
| 338 | #476 | — | 13 | 3 | no | — |
| 339 | #476 | — | 13 | 3 | no | — |
| 340 | #476 | C2×D13 | 1 | 3 | yes | — |
| 341 | #475 | C2×D13 | 1 | 3 | yes | — |
| 342 | #474 | — | 13 | 3 | no | — |
| 343 | #474 | — | 13 | 3 | no | — |
| 344 | #474 | — | 13 | 3 | no | — |
| 345 | #460 | — | 13 | 3 | no | — |
| 346 | #460 | — | 13 | 3 | no | — |
| 347 | #459 | — | 13 | 3 | no | — |
| 348 | #459 | — | 13 | 3 | no | — |
| 349 | #449 | — | 13 | 1 | no | — |
| 350 | #449 | — | 13 | 3 | no | — |
| 351 | #446 | — | 13 | 3 | no | — |
| 352 | #446 | — | 13 | 3 | no | — |
| 353 | C8×Q8 | — | 13 | 1 | no | — |
| 354 | C8×Q8 | C2×D13 | 1 | 1 | yes | characteristic |
| 355 | #442 | — | 13 | 6 | no | — |
| 356 | #440 | — | 13 | 6 | no | — |
| 357 | C4×SD16 | — | 13 | 3 | no | — |
| 358 | C4×SD16 | C2×D13 | 1 | 3 | yes | — |
| 359 | C4×D8 | — | 13 | 3 | no | — |
| 360 | C4×D8 | — | 13 | 3 | no | — |
| 361 | #432 | — | 13 | 3 | no | — |
| 362 | #431 | — | 13 | 3 | no | — |
| 363 | C22×C13 | — | 4 | 1 | no | — |
| 364 | C22×C13 | — | 4 | 1 | no | — |
| 365 | C22×C13 | — | 4 | 1 | no | — |
| 366 | C22×C13 | C23×D4 | 1 | 1 | yes | characteristic |
| 367 | C2×D13 | — | 2 | 1 | no | — |
| 368 | C2×D13 | — | 2 | 1 | no | — |
| 369 | C2×D13 | — | 2 | 2 | no | — |
| 370 | C2×D13 | — | 2 | 1 | no | — |
| 371 | C2×D13 | — | 4 | 1 | no | — |
| 372 | C2×D13 | — | 4 | 1 | no | — |
| 373 | C2×D13 | — | 4 | 3 | no | — |
| 374 | C2×D13 | — | 4 | 3 | no | — |
| 375 | C2×D13 | — | 4 | 3 | no | — |
| 376 | C4×C13 | — | 2 | 3 | no | — |
| 377 | C4×C13 | — | 2 | 2 | no | — |
| 378 | C4×C13 | — | 4 | 3 | no | — |
| 379 | C4×C13 | — | 4 | 3 | no | — |
| 380 | C4×C13 | C2×AGL(1,ℤ/8) | 1 | 6 | yes | — |
| 381 | C4×C13 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 382 | C4×C13 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 383 | Dic13 | — | 2 | 3 | no | — |
| 384 | Dic13 | — | 2 | 1 | no | — |
| 385 | Dic13 | — | 2 | 3 | no | — |
| 386 | Dic13 | — | 4 | 1 | no | — |
| 387 | Dic13 | — | 4 | 3 | no | — |
| 388 | 2−1+4 | — | 52 | 8 | no | — |
| 389 | C2×#41 | — | 13 | 1 | no | — |
| 390 | C2×#41 | — | 26 | 3 | no | — |
| 391 | C2×#41 | — | 26 | 3 | no | — |
| 392 | C2×#41 | — | 26 | 3 | no | — |
| 393 | C2×#41 | — | 26 | 1 | no | — |
| 394 | C22×Q8 | — | 2 | 1 | no | — |
| 395 | C22×Q8 | — | 13 | 1 | no | — |
| 396 | C22×Q8 | — | 26 | 3 | no | — |
| 397 | C22×Q8 | — | 26 | 1 | no | — |
| 398 | C2×SD16 | — | 13 | 3 | no | — |
| 399 | C2×SD16 | C22×D13 | 1 | 1 | yes | characteristic |
| 400 | C2×D8 | — | 13 | 1 | no | — |
| 401 | C2×D8 | — | 13 | 3 | no | — |
| 402 | C4⋊Q8 | — | 2 | 3 | no | — |
| 403 | C4⋊Q8 | — | 13 | 3 | no | — |
| 404 | C4⋊Q8 | — | 13 | 3 | no | — |
| 405 | C4⋊Q8 | — | 26 | 3 | no | — |
| 406 | C4⋊Q8 | C22×D13 | 1 | 3 | yes | — |
| 407 | C4⋊Q8 | C22×D13 | 1 | 3 | yes | — |
| 408 | #127 | — | 13 | 3 | no | — |
| 409 | #127 | — | 13 | 3 | no | — |
| 410 | #125 | — | 13 | 6 | no | — |
| 411 | #125 | — | 26 | 6 | no | — |
| 412 | #124 | — | 26 | 3 | no | — |
| 413 | #124 | — | 26 | 3 | no | — |
| 414 | C22⋊Q8 | — | 2 | 3 | no | — |
| 415 | C22⋊Q8 | — | 26 | 6 | no | — |
| 416 | C22⋊Q8 | — | 26 | 3 | no | — |
| 417 | C22⋊Q8 | — | 26 | 3 | no | — |
| 418 | C22⋊Q8 | — | 26 | 6 | no | — |
| 419 | C22⋊Q8 | — | 26 | 3 | no | — |
| 420 | C22⋊Q8 | — | 26 | 3 | no | — |
| 421 | C22⋊Q8 | — | 26 | 3 | no | — |
| 422 | #121 | — | 13 | 1 | no | — |
| 423 | #121 | — | 13 | 3 | no | — |
| 424 | #121 | — | 26 | 6 | no | — |
| 425 | #121 | — | 26 | 3 | no | — |
| 426 | #121 | — | 26 | 3 | no | — |
| 427 | #121 | — | 26 | 3 | no | — |
| 428 | #121 | — | 26 | 3 | no | — |
| 429 | C4×Q8 | — | 2 | 1 | no | — |
| 430 | C4×Q8 | — | 13 | 1 | no | — |
| 431 | C4×Q8 | — | 13 | 3 | no | — |
| 432 | C4×Q8 | — | 13 | 3 | no | — |
| 433 | C4×Q8 | — | 13 | 3 | no | — |
| 434 | C4×Q8 | — | 26 | 3 | no | — |
| 435 | C4×Q8 | — | 26 | 3 | no | — |
| 436 | C4×Q8 | — | 26 | 3 | no | — |
| 437 | C4×Q8 | C22×D13 | 1 | 3 | yes | — |
| 438 | C4×Q8 | C22×D13 | 1 | 1 | yes | characteristic |
| 439 | C4×D4 | — | 13 | 3 | no | — |
| 440 | C4×D4 | — | 13 | 6 | no | — |
| 441 | C4×D4 | — | 13 | 3 | no | — |
| 442 | C4×D4 | — | 13 | 3 | no | — |
| 443 | C4×D4 | — | 26 | 3 | no | — |
| 444 | C4×D4 | — | 26 | 3 | no | — |
| 445 | C4×D4 | — | 26 | 3 | no | — |
| 446 | C4×D4 | — | 26 | 3 | no | — |
| 447 | C4×D4 | C22×D13 | 1 | 3 | yes | — |
| 448 | #117 | — | 13 | 3 | no | — |
| 449 | #117 | — | 26 | 3 | no | — |
| 450 | C2×C4⋊C4 | — | 13 | 3 | no | — |
| 451 | C2×C4⋊C4 | — | 26 | 3 | no | — |
| 452 | C2×C42 | — | 13 | 3 | no | — |
| 453 | C2×C42 | — | 26 | 3 | no | — |
| 454 | #107 | — | 13 | 3 | no | — |
| 455 | #107 | — | 13 | 3 | no | — |
| 456 | #107 | — | 13 | 6 | no | — |
| 457 | #106 | — | 13 | 3 | no | — |
| 458 | #106 | C22×D13 | 1 | 3 | yes | — |
| 459 | #106 | C22×D13 | 1 | 6 | yes | — |
| 460 | C4⋊C8 | — | 13 | 3 | no | — |
| 461 | C4⋊C8 | — | 13 | 3 | no | — |
| 462 | C4⋊C8 | — | 13 | 3 | no | — |
| 463 | C4⋊C8 | C22×D13 | 1 | 3 | yes | — |
| 464 | #103 | — | 13 | 1 | no | — |
| 465 | #103 | C22×D13 | 1 | 3 | yes | — |
| 466 | #102 | — | 13 | 3 | no | — |
| 467 | #102 | — | 13 | 1 | no | — |
| 468 | #102 | — | 13 | 3 | no | — |
| 469 | #102 | — | 13 | 6 | no | — |
| 470 | #102 | — | 13 | 3 | no | — |
| 471 | #102 | — | 13 | 3 | no | — |
| 472 | #102 | — | 13 | 6 | no | — |
| 473 | #102 | C22×D13 | 1 | 3 | yes | — |
| 474 | C22⋊C8 | — | 13 | 1 | no | — |
| 475 | C22⋊C8 | — | 13 | 3 | no | — |
| 476 | #97 | — | 13 | 6 | no | — |
| 477 | C4×C8 | — | 13 | 3 | no | — |
| 478 | C4×C8 | C22×D13 | 1 | 3 | yes | — |
| 479 | C2×C13 | — | 8 | 1 | no | — |
| 480 | C2×C13 | #3486 | 1 | 1 | yes | characteristic |
| 481 | C2×C13 | C22×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 482 | C2×C13 | #3584 | 1 | 1 | yes | characteristic |
| 483 | D13 | — | 4 | 1 | no | — |
| 484 | D13 | — | 4 | 2 | no | — |
| 485 | D13 | — | 8 | 3 | no | — |
| 486 | #41 | — | 26 | 2 | no | — |
| 487 | #41 | — | 26 | 2 | no | — |
| 488 | #41 | — | 52 | 12 | no | — |
| 489 | #41 | — | 52 | 12 | no | — |
| 490 | #41 | — | 52 | 12 | no | — |
| 491 | #41 | — | 52 | 4 | no | — |
| 492 | C2×Q8 | — | 2 | 3 | no | — |
| 493 | C2×Q8 | — | 2 | 3 | no | — |
| 494 | C2×Q8 | — | 4 | 4 | no | — |
| 495 | C2×Q8 | — | 13 | 3 | no | — |
| 496 | C2×Q8 | — | 26 | 3 | no | — |
| 497 | C2×Q8 | — | 26 | 4 | no | — |
| 498 | C2×Q8 | — | 26 | 3 | no | — |
| 499 | C2×Q8 | — | 52 | 12 | no | — |
| 500 | C2×Q8 | — | 52 | 4 | no | — |
| 501 | C2×Q8 | D4×D13 | 1 | 1 | yes | characteristic |
| 502 | C2×Q8 | C23×D13 | 1 | 1 | yes | characteristic |
| 503 | C2×D4 | — | 13 | 1 | no | — |
| 504 | C2×D4 | — | 13 | 3 | no | — |
| 505 | C2×D4 | — | 26 | 1 | no | — |
| 506 | C2×D4 | — | 26 | 3 | no | — |
| 507 | C2×D4 | — | 26 | 3 | no | — |
| 508 | C2×D4 | — | 26 | 3 | no | — |
| 509 | C2×D4 | — | 26 | 1 | no | — |
| 510 | C2×D4 | — | 26 | 3 | no | — |
| 511 | C2×D4 | — | 26 | 3 | no | — |
| 512 | C2×D4 | C23×D13 | 1 | 1 | yes | characteristic |
| 513 | C22×C4 | — | 2 | 3 | no | — |
| 514 | C22×C4 | — | 13 | 3 | no | — |
| 515 | C22×C4 | — | 13 | 1 | no | — |
| 516 | C22×C4 | — | 13 | 3 | no | — |
| 517 | C22×C4 | — | 26 | 1 | no | — |
| 518 | C22×C4 | — | 26 | 6 | no | — |
| 519 | C22×C4 | — | 26 | 3 | no | — |
| 520 | C22×C4 | — | 26 | 3 | no | — |
| 521 | C22×C4 | — | 26 | 3 | no | — |
| 522 | SD16 | — | 2 | 2 | no | — |
| 523 | SD16 | — | 26 | 6 | no | — |
| 524 | D8 | — | 26 | 6 | no | — |
| 525 | D8 | — | 26 | 2 | no | — |
| 526 | C2×C8 | — | 13 | 1 | no | — |
| 527 | C2×C8 | — | 13 | 3 | no | — |
| 528 | C2×C8 | C23×D13 | 1 | 1 | yes | characteristic |
| 529 | C2×C8 | C23×D13 | 1 | 3 | yes | — |
| 530 | C4⋊C4 | — | 2 | 3 | no | — |
| 531 | C4⋊C4 | — | 2 | 3 | no | — |
| 532 | C4⋊C4 | — | 2 | 3 | no | — |
| 533 | C4⋊C4 | — | 13 | 3 | no | — |
| 534 | C4⋊C4 | — | 13 | 6 | no | — |
| 535 | C4⋊C4 | — | 13 | 3 | no | — |
| 536 | C4⋊C4 | — | 13 | 1 | no | — |
| 537 | C4⋊C4 | — | 26 | 6 | no | — |
| 538 | C4⋊C4 | — | 26 | 3 | no | — |
| 539 | C4⋊C4 | — | 26 | 3 | no | — |
| 540 | C4⋊C4 | — | 26 | 6 | no | — |
| 541 | C4⋊C4 | — | 26 | 3 | no | — |
| 542 | C4⋊C4 | D4×D13 | 1 | 3 | yes | — |
| 543 | C4⋊C4 | C23×D13 | 1 | 3 | yes | — |
| 544 | C4⋊C4 | C23×D13 | 1 | 3 | yes | — |
| 545 | C22⋊C4 | — | 2 | 3 | no | — |
| 546 | C22⋊C4 | — | 26 | 3 | no | — |
| 547 | C22⋊C4 | — | 26 | 6 | no | — |
| 548 | C22⋊C4 | — | 26 | 3 | no | — |
| 549 | C22⋊C4 | — | 26 | 3 | no | — |
| 550 | C22⋊C4 | — | 26 | 1 | no | — |
| 551 | C22⋊C4 | — | 26 | 3 | no | — |
| 552 | C22⋊C4 | — | 26 | 3 | no | — |
| 553 | C42 | — | 2 | 3 | no | — |
| 554 | C42 | — | 13 | 3 | no | — |
| 555 | C42 | — | 13 | 3 | no | — |
| 556 | C42 | — | 13 | 3 | no | — |
| 557 | C42 | — | 26 | 3 | no | — |
| 558 | C42 | — | 26 | 3 | no | — |
| 559 | C42 | C23×D13 | 1 | 3 | yes | — |
| 560 | C13 | #61840 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 561 | C23 | — | 2 | 1 | no | — |
| 562 | C23 | — | 13 | 1 | no | — |
| 563 | C23 | — | 26 | 1 | no | — |
| 564 | C23 | — | 26 | 3 | no | — |
| 565 | Q8 | — | 2 | 1 | no | — |
| 566 | Q8 | — | 4 | 6 | no | — |
| 567 | Q8 | — | 8 | 3 | no | — |
| 568 | Q8 | — | 26 | 6 | no | — |
| 569 | Q8 | — | 52 | 6 | no | — |
| 570 | Q8 | — | 52 | 6 | no | — |
| 571 | Q8 | #88168 | 1 | 4 | yes | — |
| 572 | Q8 | #88254 | 1 | 2 | yes | complemented |
| 573 | D4 | — | 2 | 1 | no | — |
| 574 | D4 | — | 2 | 1 | no | — |
| 575 | D4 | — | 13 | 2 | no | — |
| 576 | D4 | — | 26 | 4 | no | — |
| 577 | D4 | — | 26 | 1 | no | — |
| 578 | D4 | — | 26 | 3 | no | — |
| 579 | D4 | — | 26 | 3 | no | — |
| 580 | D4 | — | 52 | 6 | no | — |
| 581 | D4 | — | 52 | 6 | no | — |
| 582 | D4 | — | 52 | 2 | no | — |
| 583 | D4 | — | 52 | 6 | no | — |
| 584 | D4 | — | 104 | 3 | no | — |
| 585 | D4 | — | 104 | 3 | no | — |
| 586 | C2×C4 | — | 2 | 1 | no | — |
| 587 | C2×C4 | — | 2 | 3 | no | — |
| 588 | C2×C4 | — | 2 | 3 | no | — |
| 589 | C2×C4 | — | 4 | 6 | no | — |
| 590 | C2×C4 | — | 13 | 1 | no | — |
| 591 | C2×C4 | — | 13 | 3 | no | — |
| 592 | C2×C4 | — | 13 | 3 | no | — |
| 593 | C2×C4 | — | 26 | 4 | no | — |
| 594 | C2×C4 | — | 26 | 6 | no | — |
| 595 | C2×C4 | — | 26 | 1 | no | — |
| 596 | C2×C4 | — | 26 | 1 | no | — |
| 597 | C2×C4 | — | 26 | 3 | no | — |
| 598 | C2×C4 | — | 26 | 1 | no | — |
| 599 | C2×C4 | — | 52 | 3 | no | — |
| 600 | C2×C4 | — | 52 | 12 | no | — |
| 601 | C2×C4 | — | 52 | 6 | no | — |
| 602 | C2×C4 | — | 52 | 6 | no | — |
| 603 | C2×C4 | — | 104 | 3 | no | — |
| 604 | C2×C4 | C2×D4×D13 | 1 | 3 | yes | — |
| 605 | C2×C4 | C2×D4×D13 | 1 | 3 | yes | — |
| 606 | C2×C4 | C24×D13 | 1 | 1 | yes | characteristic |
| 607 | C8 | — | 2 | 1 | no | — |
| 608 | C8 | — | 2 | 3 | no | — |
| 609 | C8 | — | 26 | 3 | no | — |
| 610 | C8 | — | 26 | 1 | no | — |
| 611 | C22 | — | 4 | 1 | no | — |
| 612 | C22 | — | 4 | 1 | no | — |
| 613 | C22 | — | 4 | 1 | no | — |
| 614 | C22 | — | 26 | 2 | no | — |
| 615 | C22 | — | 26 | 1 | no | — |
| 616 | C22 | — | 26 | 1 | no | — |
| 617 | C22 | — | 26 | 1 | no | — |
| 618 | C22 | — | 52 | 1 | no | — |
| 619 | C22 | — | 52 | 1 | no | — |
| 620 | C22 | — | 52 | 3 | no | — |
| 621 | C22 | — | 52 | 3 | no | — |
| 622 | C22 | — | 52 | 3 | no | — |
| 623 | C22 | C22×D4×D13 | 1 | 1 | yes | characteristic |
| 624 | C4 | — | 2 | 2 | no | — |
| 625 | C4 | — | 2 | 3 | no | — |
| 626 | C4 | — | 4 | 3 | no | — |
| 627 | C4 | — | 4 | 3 | no | — |
| 628 | C4 | — | 26 | 1 | no | — |
| 629 | C4 | — | 26 | 3 | no | — |
| 630 | C4 | — | 26 | 3 | no | — |
| 631 | C4 | — | 52 | 1 | no | — |
| 632 | C4 | — | 52 | 3 | no | — |
| 633 | C4 | C2×#88168 | 1 | 6 | yes | — |
| 634 | C4 | C2×#88254 | 1 | 1 | yes | characteristic |
| 635 | C4 | D13×2−1+4 | 1 | 1 | yes | characteristic |
| 636 | C2 | — | 8 | 1 | no | — |
| 637 | C2 | — | 52 | 1 | no | — |
| 638 | C2 | — | 52 | 2 | no | — |
| 639 | C2 | — | 104 | 3 | no | — |
| 640 | C2 | #13128486 | 1 | 1 | yes | characteristic |
| 641 | C2 | C22×#88168 | 1 | 1 | yes | characteristic |
| 642 | C2 | #13129608 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13128606 | C2 | semidirect |
| 2. Q8×#6131 | C2 | semidirect |
| 3. #13127756 | C2 | semidirect |
| 4. #13127740 | C2 | semidirect |
| 5. Q8×#6104 | C2 | semidirect |
| 6. #13127563 | C2 | semidirect |
| 7. #13127542 | C2 | semidirect |
| 8. #13127507 | C2 | semidirect |
| 9. #13127472 | C2 | semidirect |
| 10. #13126032 | C2 | semidirect |
| 11. #13125973 | C2 | semidirect |
| 12. #13124990 | C2 | semidirect |
| 13. #13124894 | C2 | semidirect |
| 14. #13123924 | C2 | semidirect |
| 15. Q8×C13×SD16 | C2 | semidirect |
| 244. Q8×SD16 | D13 | semidirect |
| 263. Q8×C13 | 2−1+4 | semidirect |
| 288. D52 | 2−1+4 | semidirect |
| 560. C13 | #61840 | semidirect |
| 572. Q8 | #88254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13128606 | 2 |
| Q8×#6131 | 2 |
| #13127756 | 2 |
| #13127740 | 2 |
| Q8×#6104 | 2 |
| #13127563 | 2 |
| #13127542 | 2 |
| #13127507 | 2 |
| #13127472 | 2 |
| #13126032 | 2 |
| #13125973 | 2 |
| #13124990 | 2 |
| #13124894 | 2 |
| #13123924 | 2 |
| Q8×C13×SD16 | 2 |
| #61840 | 13 |