← #16796378
Subgroups — #16796378
Order 3328.
644 conjugacy classes of subgroups.
The subgroup lattice has 334 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13131680 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #13130485 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #13130463 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #13130429 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13130397 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13130170 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13130046 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C4×#88173 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | C2×#88173 | C4 | 1 | 1 | yes | characteristic |
| 10 | C4×#6131 | C22 | 1 | 2 | yes | — |
| 11 | Q8×#1057 | C22 | 1 | 4 | yes | — |
| 12 | #11719076 | — | 2 | 4 | no | — |
| 13 | #11719076 | C22 | 1 | 4 | yes | — |
| 14 | #11719054 | — | 2 | 2 | no | — |
| 15 | #11719054 | C22 | 1 | 2 | yes | — |
| 16 | #11719051 | C22 | 1 | 1 | yes | characteristic |
| 17 | C4×#6118 | — | 2 | 2 | no | — |
| 18 | C4×#6118 | C22 | 1 | 1 | yes | characteristic |
| 19 | C4×C13×Q16 | C4 | 1 | 1 | yes | characteristic |
| 20 | Q16×Dic13 | C22 | 1 | 1 | yes | characteristic |
| 21 | C4×#6106 | C4 | 1 | 2 | yes | — |
| 22 | #11718541 | C4 | 1 | 1 | yes | characteristic |
| 23 | #11718533 | C22 | 1 | 1 | yes | characteristic |
| 24 | #11718465 | C4 | 1 | 2 | yes | — |
| 25 | #11718449 | C22 | 1 | 2 | yes | — |
| 26 | C4×D104 | C4 | 1 | 1 | yes | characteristic |
| 27 | C4×C8×D13 | C22 | 1 | 1 | yes | characteristic |
| 28 | Q8⋊#1057 | C22 | 1 | 4 | yes | — |
| 29 | #11718254 | C22 | 1 | 2 | yes | — |
| 30 | #11718253 | C22 | 1 | 2 | yes | — |
| 31 | #1057⋊C8 | C22 | 1 | 2 | yes | — |
| 32 | #11718251 | C22 | 1 | 2 | yes | — |
| 33 | #11718243 | C22 | 1 | 4 | yes | — |
| 34 | C2×#6131 | C2×C4 | 1 | 2 | yes | — |
| 35 | C2×#6118 | — | 2 | 4 | no | — |
| 36 | C2×#6118 | D4 | 1 | 2 | yes | — |
| 37 | C2×C13×Q16 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | C4×Q8×C13 | C2×C4 | 1 | 2 | yes | — |
| 39 | Q8×Dic13 | C23 | 1 | 2 | yes | — |
| 40 | C2×#6106 | C2×C4 | 1 | 2 | yes | — |
| 41 | #88173 | — | 2 | 4 | no | — |
| 42 | C2×D104 | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | C2×C8×D13 | C2×C4 | 1 | 1 | yes | characteristic |
| 44 | C2×C8×D13 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | #88147 | — | 2 | 2 | no | — |
| 46 | #88147 | C23 | 1 | 2 | yes | — |
| 47 | #88146 | — | 2 | 2 | no | — |
| 48 | #88146 | C2×C4 | 1 | 2 | yes | — |
| 49 | C4×D52 | — | 2 | 2 | no | — |
| 50 | C4×D52 | C2×C4 | 1 | 2 | yes | — |
| 51 | C42×D13 | — | 2 | 2 | no | — |
| 52 | C42×D13 | C23 | 1 | 1 | yes | characteristic |
| 53 | #88111 | — | 2 | 2 | no | — |
| 54 | #88111 | — | 2 | 1 | no | — |
| 55 | #88111 | — | 2 | 4 | no | — |
| 56 | #88110 | — | 2 | 2 | no | — |
| 57 | #88110 | D4 | 1 | 2 | yes | — |
| 58 | C4⋊#1057 | — | 2 | 4 | no | — |
| 59 | C4⋊#1057 | — | 2 | 1 | no | — |
| 60 | C4⋊#1057 | C23 | 1 | 4 | yes | — |
| 61 | C4×#1057 | — | 2 | 4 | no | — |
| 62 | C4×#1057 | C23 | 1 | 2 | yes | — |
| 63 | C4×#1057 | C23 | 1 | 2 | yes | — |
| 64 | C13×#107 | C2×C4 | 1 | 1 | yes | characteristic |
| 65 | C13×#103 | C2×C4 | 1 | 2 | yes | — |
| 66 | C4×C8×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 67 | #88075 | C2×C4 | 1 | 2 | yes | — |
| 68 | #88061 | C2×C4 | 1 | 2 | yes | — |
| 69 | #88058 | C2×C4 | 1 | 1 | yes | characteristic |
| 70 | C8×Dic13 | C23 | 1 | 1 | yes | characteristic |
| 71 | C8×Dic13 | C23 | 1 | 1 | yes | characteristic |
| 72 | #88049 | C2×C4 | 1 | 2 | yes | — |
| 73 | #88048 | C2×C4 | 1 | 2 | yes | — |
| 74 | C4×#1055 | C2×C4 | 1 | 1 | yes | characteristic |
| 75 | #18043 | — | 13 | 1 | no | maximal, Sylow |
| 76 | C2×Q8×C13 | C22×C4 | 1 | 2 | yes | — |
| 77 | #6131 | — | 2 | 4 | no | — |
| 78 | #6131 | — | 4 | 2 | no | — |
| 79 | C2×D52 | — | 2 | 2 | no | — |
| 80 | C2×D52 | C22×C4 | 1 | 2 | yes | — |
| 81 | C2×C4×D13 | — | 2 | 2 | no | — |
| 82 | C2×C4×D13 | — | 2 | 2 | no | — |
| 83 | C2×C4×D13 | — | 2 | 2 | no | — |
| 84 | C2×C4×D13 | C22×C4 | 1 | 1 | yes | characteristic |
| 85 | C2×C4×D13 | C2×D4 | 1 | 1 | yes | characteristic |
| 86 | C2×C4×D13 | #41 | 1 | 1 | yes | characteristic |
| 87 | C2×#1057 | — | 2 | 4 | no | — |
| 88 | C2×#1057 | — | 2 | 2 | no | — |
| 89 | C2×#1057 | C2×D4 | 1 | 4 | yes | — |
| 90 | #6118 | — | 4 | 2 | no | — |
| 91 | #6118 | — | 4 | 8 | no | — |
| 92 | C13×Q16 | M16 | 1 | 4 | yes | complemented |
| 93 | C2×C8×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 94 | C2×C8×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 95 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 96 | C13×C4⋊C4 | C22×C4 | 1 | 2 | yes | — |
| 97 | C42×C13 | — | 2 | 2 | no | — |
| 98 | C42×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 99 | #6106 | — | 2 | 4 | no | — |
| 100 | #6103 | — | 2 | 2 | no | — |
| 101 | #6103 | — | 2 | 2 | no | — |
| 102 | #6103 | — | 2 | 2 | no | — |
| 103 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 104 | C4⋊Dic13 | C22×C4 | 1 | 2 | yes | — |
| 105 | C4×Dic13 | — | 2 | 2 | no | — |
| 106 | C4×Dic13 | — | 2 | 2 | no | — |
| 107 | C4×Dic13 | C2×D4 | 1 | 1 | yes | characteristic |
| 108 | C4×Dic13 | #41 | 1 | 1 | yes | characteristic |
| 109 | C4×Dic13 | C24 | 1 | 1 | yes | characteristic |
| 110 | C2×#1055 | C22×C4 | 1 | 1 | yes | characteristic |
| 111 | C2×#1055 | C22×C4 | 1 | 1 | yes | characteristic |
| 112 | D104 | — | 2 | 2 | no | — |
| 113 | C8×D13 | — | 2 | 2 | no | — |
| 114 | C8×D13 | — | 4 | 1 | no | — |
| 115 | #2971 | — | 13 | 2 | no | — |
| 116 | C4×#135 | — | 13 | 1 | no | — |
| 117 | #1594 | — | 13 | 2 | no | — |
| 118 | #1588 | — | 13 | 4 | no | — |
| 119 | #1579 | — | 13 | 2 | no | — |
| 120 | #1568 | — | 13 | 1 | no | — |
| 121 | #1488 | — | 13 | 2 | no | — |
| 122 | #1451 | — | 13 | 1 | no | — |
| 123 | C22×D13 | — | 2 | 2 | no | — |
| 124 | C22×D13 | C4×D4 | 1 | 1 | yes | characteristic |
| 125 | Q8×C13 | — | 2 | 2 | no | — |
| 126 | Q8×C13 | C2×M16 | 1 | 4 | yes | — |
| 127 | C2×C4×C13 | — | 2 | 2 | no | — |
| 128 | C2×C4×C13 | — | 2 | 2 | no | — |
| 129 | C2×C4×C13 | C4×D4 | 1 | 1 | yes | characteristic |
| 130 | C2×C4×C13 | C4×D4 | 1 | 1 | yes | characteristic |
| 131 | C2×C4×C13 | C23×C4 | 1 | 1 | yes | characteristic |
| 132 | C2×Dic13 | — | 2 | 2 | no | — |
| 133 | C2×Dic13 | C4×D4 | 1 | 1 | yes | characteristic |
| 134 | C2×Dic13 | C22×D4 | 1 | 1 | yes | characteristic |
| 135 | C2×Dic13 | C2×#41 | 1 | 1 | yes | characteristic |
| 136 | D52 | — | 2 | 2 | no | — |
| 137 | D52 | — | 2 | 2 | no | — |
| 138 | D52 | — | 4 | 4 | no | — |
| 139 | C4×D13 | — | 2 | 1 | no | — |
| 140 | C4×D13 | — | 2 | 1 | no | — |
| 141 | C4×D13 | — | 2 | 2 | no | — |
| 142 | C4×D13 | — | 4 | 1 | no | — |
| 143 | C4×D13 | — | 4 | 4 | no | — |
| 144 | C4×D13 | — | 4 | 4 | no | — |
| 145 | C4×D13 | — | 8 | 2 | no | — |
| 146 | #1057 | — | 2 | 4 | no | — |
| 147 | #1057 | — | 4 | 2 | no | — |
| 148 | #1057 | — | 4 | 4 | no | — |
| 149 | C8×C13 | — | 2 | 1 | no | — |
| 150 | C8×C13 | C2×M16 | 1 | 2 | yes | — |
| 151 | #1055 | — | 2 | 1 | no | — |
| 152 | #1055 | — | 2 | 1 | no | — |
| 153 | C2×#135 | — | 13 | 1 | no | — |
| 154 | C4×#41 | — | 13 | 2 | no | — |
| 155 | C8×Q8 | — | 13 | 4 | no | — |
| 156 | C4×Q16 | — | 13 | 1 | no | — |
| 157 | C4×Q16 | #261 | 1 | 1 | yes | characteristic |
| 158 | C4×SD16 | — | 13 | 2 | no | — |
| 159 | C4×SD16 | — | 13 | 2 | no | — |
| 160 | C4×D8 | — | 13 | 1 | no | — |
| 161 | C4×D8 | — | 13 | 1 | no | — |
| 162 | #436 | — | 13 | 4 | no | — |
| 163 | #436 | — | 26 | 4 | no | — |
| 164 | #432 | — | 13 | 2 | no | — |
| 165 | #432 | — | 26 | 2 | no | — |
| 166 | #431 | — | 13 | 1 | no | — |
| 167 | #427 | — | 13 | 1 | no | — |
| 168 | #416 | — | 13 | 2 | no | — |
| 169 | C4×M16 | — | 13 | 1 | no | — |
| 170 | C4×M16 | — | 26 | 2 | no | — |
| 171 | C2×C4×C8 | — | 13 | 1 | no | — |
| 172 | #335 | — | 13 | 2 | no | — |
| 173 | #334 | — | 13 | 2 | no | — |
| 174 | Q8⋊C8 | — | 13 | 4 | no | — |
| 175 | D4⋊C8 | — | 13 | 4 | no | — |
| 176 | #322 | — | 13 | 2 | no | — |
| 177 | #322 | — | 13 | 2 | no | — |
| 178 | C22×C13 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 179 | C2×D13 | — | 2 | 1 | no | — |
| 180 | C2×D13 | — | 2 | 1 | no | — |
| 181 | C2×D13 | — | 2 | 1 | no | — |
| 182 | C2×D13 | — | 4 | 2 | no | — |
| 183 | C2×D13 | — | 4 | 2 | no | — |
| 184 | C2×D13 | — | 4 | 2 | no | — |
| 185 | C4×C13 | — | 2 | 4 | no | — |
| 186 | C4×C13 | — | 2 | 1 | no | — |
| 187 | C4×C13 | — | 2 | 1 | no | — |
| 188 | C4×C13 | — | 4 | 2 | no | — |
| 189 | C4×C13 | C22×M16 | 1 | 1 | yes | characteristic |
| 190 | C4×C13 | #568 | 1 | 1 | yes | characteristic |
| 191 | Dic13 | — | 2 | 1 | no | — |
| 192 | Dic13 | — | 2 | 1 | no | — |
| 193 | Dic13 | — | 4 | 2 | no | — |
| 194 | Dic13 | #575 | 1 | 2 | yes | — |
| 195 | C2×#41 | — | 13 | 2 | no | — |
| 196 | #135 | — | 26 | 4 | no | — |
| 197 | C2×Q16 | C2×#261 | 1 | 1 | yes | characteristic |
| 198 | C2×SD16 | — | 13 | 2 | no | — |
| 199 | C2×D8 | — | 13 | 1 | no | — |
| 200 | C2×M16 | — | 13 | 2 | no | — |
| 201 | C2×M16 | — | 26 | 4 | no | — |
| 202 | C22×C8 | — | 13 | 1 | no | — |
| 203 | C22×C8 | — | 13 | 1 | no | — |
| 204 | C4×Q8 | — | 13 | 2 | no | — |
| 205 | C4×Q8 | C2×#261 | 1 | 2 | yes | — |
| 206 | C4×D4 | — | 13 | 2 | no | — |
| 207 | C4×D4 | — | 13 | 2 | no | — |
| 208 | C4×D4 | — | 26 | 2 | no | — |
| 209 | C4×D4 | — | 26 | 2 | no | — |
| 210 | #117 | — | 13 | 2 | no | — |
| 211 | #117 | — | 26 | 2 | no | — |
| 212 | C2×C42 | — | 13 | 1 | no | — |
| 213 | C2×C42 | — | 26 | 2 | no | — |
| 214 | #107 | — | 13 | 1 | no | — |
| 215 | #107 | C2×#261 | 1 | 1 | yes | characteristic |
| 216 | #106 | — | 13 | 2 | no | — |
| 217 | C4⋊C8 | — | 13 | 4 | no | — |
| 218 | C4⋊C8 | — | 26 | 1 | no | — |
| 219 | C4⋊C8 | — | 26 | 4 | no | — |
| 220 | #103 | — | 13 | 2 | no | — |
| 221 | #103 | C2×#261 | 1 | 2 | yes | — |
| 222 | #102 | — | 13 | 2 | no | — |
| 223 | #102 | — | 13 | 2 | no | — |
| 224 | C22⋊C8 | — | 26 | 4 | no | — |
| 225 | C22⋊C8 | — | 26 | 1 | no | — |
| 226 | C22⋊C8 | — | 26 | 2 | no | — |
| 227 | #97 | — | 13 | 2 | no | — |
| 228 | #97 | — | 26 | 2 | no | — |
| 229 | C4×C8 | — | 13 | 2 | no | — |
| 230 | C4×C8 | — | 13 | 1 | no | — |
| 231 | C4×C8 | — | 13 | 1 | no | — |
| 232 | C4×C8 | — | 13 | 2 | no | — |
| 233 | C4×C8 | — | 13 | 1 | no | — |
| 234 | C4×C8 | — | 26 | 4 | no | — |
| 235 | C4×C8 | C2×#261 | 1 | 1 | yes | characteristic |
| 236 | C2×C13 | D4×M16 | 1 | 1 | yes | characteristic |
| 237 | C2×C13 | #2943 | 1 | 1 | yes | characteristic |
| 238 | C2×C13 | #2957 | 1 | 1 | yes | characteristic |
| 239 | D13 | — | 4 | 1 | no | — |
| 240 | D13 | — | 8 | 2 | no | — |
| 241 | #41 | — | 26 | 4 | no | — |
| 242 | #41 | — | 52 | 2 | no | — |
| 243 | C2×Q8 | C22×#261 | 1 | 2 | yes | — |
| 244 | C2×D4 | — | 13 | 2 | no | — |
| 245 | C2×D4 | — | 26 | 2 | no | — |
| 246 | C22×C4 | — | 13 | 1 | no | — |
| 247 | C22×C4 | — | 13 | 1 | no | — |
| 248 | C22×C4 | — | 13 | 1 | no | — |
| 249 | C22×C4 | — | 26 | 2 | no | — |
| 250 | C22×C4 | — | 26 | 2 | no | — |
| 251 | C22×C4 | — | 26 | 2 | no | — |
| 252 | Q16 | #6118 | 1 | 4 | yes | complemented |
| 253 | SD16 | — | 26 | 4 | no | — |
| 254 | D8 | — | 26 | 2 | no | — |
| 255 | M16 | — | 52 | 2 | no | — |
| 256 | M16 | — | 52 | 8 | no | — |
| 257 | C2×C8 | — | 13 | 4 | no | — |
| 258 | C2×C8 | — | 13 | 1 | no | — |
| 259 | C2×C8 | — | 13 | 1 | no | — |
| 260 | C2×C8 | — | 26 | 2 | no | — |
| 261 | C2×C8 | — | 26 | 2 | no | — |
| 262 | C2×C8 | — | 26 | 4 | no | — |
| 263 | C2×C8 | — | 52 | 1 | no | — |
| 264 | C2×C8 | C22×#261 | 1 | 1 | yes | characteristic |
| 265 | C2×C8 | C22×#261 | 1 | 1 | yes | characteristic |
| 266 | C4⋊C4 | — | 2 | 2 | no | — |
| 267 | C4⋊C4 | — | 13 | 2 | no | — |
| 268 | C4⋊C4 | — | 26 | 2 | no | — |
| 269 | C4⋊C4 | C22×#261 | 1 | 2 | yes | — |
| 270 | C22⋊C4 | — | 26 | 2 | no | — |
| 271 | C22⋊C4 | — | 26 | 2 | no | — |
| 272 | C22⋊C4 | — | 26 | 2 | no | — |
| 273 | C42 | — | 2 | 2 | no | — |
| 274 | C42 | — | 13 | 1 | no | — |
| 275 | C42 | — | 13 | 1 | no | — |
| 276 | C42 | — | 13 | 1 | no | — |
| 277 | C42 | — | 26 | 2 | no | — |
| 278 | C42 | — | 26 | 2 | no | — |
| 279 | C42 | C22×#261 | 1 | 1 | yes | characteristic |
| 280 | C13 | #18043 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 281 | C23 | — | 13 | 1 | no | — |
| 282 | C23 | — | 26 | 2 | no | — |
| 283 | Q8 | — | 2 | 2 | no | — |
| 284 | Q8 | C2×#6118 | 1 | 4 | yes | — |
| 285 | D4 | — | 26 | 2 | no | — |
| 286 | D4 | — | 26 | 2 | no | — |
| 287 | D4 | — | 52 | 4 | no | — |
| 288 | C2×C4 | — | 2 | 2 | no | — |
| 289 | C2×C4 | — | 2 | 2 | no | — |
| 290 | C2×C4 | — | 13 | 1 | no | — |
| 291 | C2×C4 | — | 13 | 1 | no | — |
| 292 | C2×C4 | — | 13 | 1 | no | — |
| 293 | C2×C4 | — | 26 | 2 | no | — |
| 294 | C2×C4 | — | 26 | 1 | no | — |
| 295 | C2×C4 | — | 26 | 1 | no | — |
| 296 | C2×C4 | — | 26 | 2 | no | — |
| 297 | C2×C4 | — | 52 | 1 | no | — |
| 298 | C2×C4 | — | 52 | 4 | no | — |
| 299 | C2×C4 | — | 52 | 4 | no | — |
| 300 | C2×C4 | — | 104 | 2 | no | — |
| 301 | C2×C4 | D4×#261 | 1 | 1 | yes | characteristic |
| 302 | C2×C4 | D4×#261 | 1 | 1 | yes | characteristic |
| 303 | C2×C4 | C23×#261 | 1 | 1 | yes | characteristic |
| 304 | C8 | — | 2 | 1 | no | — |
| 305 | C8 | — | 26 | 4 | no | — |
| 306 | C8 | — | 26 | 1 | no | — |
| 307 | C8 | — | 26 | 1 | no | — |
| 308 | C8 | — | 52 | 4 | no | — |
| 309 | C8 | — | 52 | 2 | no | — |
| 310 | C8 | C2×#6118 | 1 | 2 | yes | — |
| 311 | C22 | — | 26 | 1 | no | — |
| 312 | C22 | — | 26 | 1 | no | — |
| 313 | C22 | — | 26 | 1 | no | — |
| 314 | C22 | — | 52 | 2 | no | — |
| 315 | C22 | — | 52 | 2 | no | — |
| 316 | C22 | — | 52 | 2 | no | — |
| 317 | C22 | C2×D4×#261 | 1 | 1 | yes | characteristic |
| 318 | C4 | — | 2 | 4 | no | — |
| 319 | C4 | — | 2 | 1 | no | — |
| 320 | C4 | — | 2 | 1 | no | — |
| 321 | C4 | — | 4 | 2 | no | — |
| 322 | C4 | — | 13 | 2 | no | — |
| 323 | C4 | — | 26 | 1 | no | — |
| 324 | C4 | — | 26 | 1 | no | — |
| 325 | C4 | — | 52 | 2 | no | — |
| 326 | C4 | C22×#6118 | 1 | 1 | yes | characteristic |
| 327 | C4 | #11719629 | 1 | 1 | yes | characteristic |
| 328 | C2 | — | 52 | 1 | no | — |
| 329 | C2 | — | 104 | 2 | no | — |
| 330 | C2 | D4×#6118 | 1 | 1 | yes | characteristic |
| 331 | C2 | #13131590 | 1 | 1 | yes | characteristic |
| 332 | C2 | #13131616 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta