Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
808 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 155 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C13⋊#564 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13126028 | C2 | 1 | 2 | yes | maximal |
| 3 | #13125239 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #13114165 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #13114139 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #13113439 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C13×#1534 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×C13×#125 | C22 | 1 | 1 | yes | characteristic |
| 9 | C13⋊#564 | — | 2 | 2 | no | — |
| 10 | C13⋊#564 | — | 2 | 4 | no | — |
| 11 | C13⋊#564 | C22 | 1 | 4 | yes | — |
| 12 | C2×#88144 | — | 2 | 2 | no | — |
| 13 | C2×#88143 | — | 2 | 2 | no | — |
| 14 | C2×#88143 | — | 2 | 2 | no | — |
| 15 | #11719182 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#88124 | C22 | 1 | 2 | yes | — |
| 17 | C13×#432 | C22 | 1 | 2 | yes | — |
| 18 | #11718730 | C22 | 1 | 2 | yes | — |
| 19 | #11718729 | — | 2 | 2 | no | — |
| 20 | #11718728 | C22 | 1 | 2 | yes | — |
| 21 | #11718627 | — | 2 | 2 | no | — |
| 22 | C4×#6099 | C22 | 1 | 1 | yes | characteristic |
| 23 | #11718508 | — | 2 | 4 | no | — |
| 24 | #11718397 | — | 2 | 2 | no | — |
| 25 | #11718396 | — | 2 | 2 | no | — |
| 26 | #11718374 | C22 | 1 | 4 | yes | — |
| 27 | #11718363 | C22 | 1 | 4 | yes | — |
| 28 | C13×#330 | C22 | 1 | 4 | yes | — |
| 29 | #11718057 | C22 | 1 | 8 | yes | — |
| 30 | C2×#6127 | — | 2 | 1 | no | — |
| 31 | C13×#125 | — | 2 | 2 | no | — |
| 32 | C13×#125 | D4 | 1 | 2 | yes | — |
| 33 | C13×#125 | C23 | 1 | 2 | yes | — |
| 34 | C2×C13×C4⋊C4 | — | 2 | 2 | no | — |
| 35 | C2×C13×C4⋊C4 | D4 | 1 | 2 | yes | — |
| 36 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 37 | #88184 | — | 2 | 2 | no | — |
| 38 | C2×C4⋊Dic13 | — | 2 | 2 | no | — |
| 39 | C2×C4⋊Dic13 | D4 | 1 | 2 | yes | — |
| 40 | C2×C4⋊Dic13 | D4 | 1 | 2 | yes | — |
| 41 | C2×#6101 | — | 2 | 2 | no | — |
| 42 | C2×#6101 | — | 2 | 2 | no | — |
| 43 | C2×#6101 | — | 2 | 2 | no | — |
| 44 | C2×#6101 | — | 2 | 2 | no | — |
| 45 | C2×C4×Dic13 | — | 2 | 2 | no | — |
| 46 | C2×#6099 | — | 2 | 1 | no | — |
| 47 | #88144 | — | 2 | 8 | no | — |
| 48 | #88144 | — | 2 | 8 | no | — |
| 49 | #88143 | — | 2 | 8 | no | — |
| 50 | #88143 | — | 2 | 8 | no | — |
| 51 | #88143 | — | 2 | 8 | no | — |
| 52 | #88143 | — | 2 | 8 | no | — |
| 53 | #88129 | — | 2 | 1 | no | — |
| 54 | #88128 | C23 | 1 | 1 | yes | characteristic |
| 55 | C4×D52 | — | 2 | 2 | no | — |
| 56 | #88124 | — | 2 | 2 | no | — |
| 57 | #88124 | — | 2 | 2 | no | — |
| 58 | #88124 | D4 | 1 | 4 | yes | — |
| 59 | #88124 | C23 | 1 | 4 | yes | — |
| 60 | #88123 | C23 | 1 | 1 | yes | characteristic |
| 61 | C13×C4⋊C8 | — | 2 | 2 | no | — |
| 62 | C13×C22⋊C8 | — | 2 | 2 | no | — |
| 63 | C13×#97 | C23 | 1 | 4 | yes | — |
| 64 | #88061 | — | 2 | 4 | no | — |
| 65 | #88061 | — | 2 | 4 | no | — |
| 66 | #88058 | — | 2 | 4 | no | — |
| 67 | #88057 | — | 2 | 4 | no | — |
| 68 | #88050 | — | 2 | 4 | no | — |
| 69 | #88049 | — | 2 | 4 | no | — |
| 70 | #88043 | C23 | 1 | 2 | yes | — |
| 71 | C4×#1055 | — | 2 | 1 | no | — |
| 72 | #19003 | — | 13 | 1 | no | maximal, Sylow |
| 73 | C22×C4×C13 | — | 2 | 2 | no | — |
| 74 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 75 | C22×C4×C13 | C2×D4 | 1 | 2 | yes | — |
| 76 | C2×C22⋊D13 | — | 4 | 1 | no | — |
| 77 | C22×Dic13 | — | 2 | 2 | no | — |
| 78 | C22×Dic13 | — | 2 | 2 | no | — |
| 79 | #6127 | — | 4 | 4 | no | — |
| 80 | C2×D52 | — | 2 | 2 | no | — |
| 81 | C2×D52 | — | 2 | 1 | no | — |
| 82 | C2×C4×D13 | — | 4 | 1 | no | — |
| 83 | C2×Dic26 | — | 2 | 1 | no | — |
| 84 | C2×C8×C13 | — | 2 | 4 | no | — |
| 85 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 86 | C13×C4⋊C4 | — | 2 | 4 | no | — |
| 87 | C13×C4⋊C4 | — | 2 | 4 | no | — |
| 88 | C13×C4⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 89 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 90 | C42×C13 | C2×D4 | 1 | 2 | yes | — |
| 91 | C42×C13 | C24 | 1 | 1 | yes | characteristic |
| 92 | #6103 | — | 4 | 2 | no | — |
| 93 | C4⋊Dic13 | — | 2 | 8 | no | — |
| 94 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 95 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 96 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 97 | C4⋊Dic13 | C2×D4 | 1 | 4 | yes | — |
| 98 | C4⋊Dic13 | C2×D4 | 1 | 4 | yes | — |
| 99 | #6101 | — | 2 | 8 | no | — |
| 100 | #6101 | — | 2 | 8 | no | — |
| 101 | #6101 | — | 2 | 4 | no | — |
| 102 | #6101 | — | 2 | 4 | no | — |
| 103 | #6101 | — | 2 | 4 | no | — |
| 104 | #6101 | — | 2 | 4 | no | — |
| 105 | C4×Dic13 | — | 2 | 8 | no | — |
| 106 | #6099 | — | 4 | 2 | no | — |
| 107 | C2×#1055 | — | 2 | 2 | no | — |
| 108 | C2×#564 | — | 13 | 1 | no | — |
| 109 | #3234 | — | 13 | 2 | no | — |
| 110 | #3142 | — | 13 | 1 | no | — |
| 111 | #1663 | — | 13 | 4 | no | — |
| 112 | #1658 | — | 13 | 4 | no | — |
| 113 | #1534 | D13 | 1 | 1 | yes | characteristic, complemented |
| 114 | #1528 | — | 13 | 2 | no | — |
| 115 | C23×C13 | #120 | 1 | 1 | yes | characteristic |
| 116 | C22×D13 | — | 4 | 1 | no | — |
| 117 | C2×C4×C13 | — | 2 | 2 | no | — |
| 118 | C2×C4×C13 | — | 2 | 4 | no | — |
| 119 | C2×C4×C13 | — | 4 | 2 | no | — |
| 120 | C2×C4×C13 | — | 4 | 4 | no | — |
| 121 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 122 | C2×C4×C13 | #120 | 1 | 2 | yes | — |
| 123 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 124 | C2×C4×C13 | C22×D4 | 1 | 2 | yes | — |
| 125 | C22⋊D13 | — | 8 | 2 | no | — |
| 126 | C2×Dic13 | — | 2 | 4 | no | — |
| 127 | C2×Dic13 | — | 2 | 4 | no | — |
| 128 | C2×Dic13 | — | 4 | 4 | no | — |
| 129 | C2×Dic13 | — | 4 | 4 | no | — |
| 130 | C2×Dic13 | — | 4 | 1 | no | — |
| 131 | D52 | — | 4 | 4 | no | — |
| 132 | D52 | — | 4 | 2 | no | — |
| 133 | C4×D13 | — | 8 | 2 | no | — |
| 134 | Dic26 | — | 4 | 2 | no | — |
| 135 | C8×C13 | — | 4 | 4 | no | — |
| 136 | #1055 | — | 4 | 2 | no | — |
| 137 | #564 | — | 13 | 4 | no | — |
| 138 | #564 | — | 26 | 4 | no | — |
| 139 | #564 | — | 26 | 2 | no | — |
| 140 | #532 | — | 13 | 1 | no | — |
| 141 | C2×#125 | — | 13 | 2 | no | — |
| 142 | C2×#125 | — | 26 | 2 | no | — |
| 143 | C2×#125 | — | 26 | 2 | no | — |
| 144 | C2×#125 | — | 26 | 2 | no | — |
| 145 | C2×#125 | C2×D13 | 1 | 1 | yes | characteristic |
| 146 | #501 | — | 13 | 4 | no | — |
| 147 | #491 | — | 13 | 2 | no | — |
| 148 | #490 | — | 13 | 2 | no | — |
| 149 | #490 | — | 13 | 4 | no | — |
| 150 | #488 | — | 26 | 2 | no | — |
| 151 | #481 | — | 26 | 2 | no | — |
| 152 | #480 | — | 26 | 2 | no | — |
| 153 | #478 | — | 26 | 4 | no | — |
| 154 | #432 | C2×D13 | 1 | 2 | yes | — |
| 155 | #417 | — | 26 | 2 | no | — |
| 156 | C4×M16 | — | 13 | 1 | no | — |
| 157 | #330 | — | 13 | 8 | no | — |
| 158 | #330 | C2×D13 | 1 | 4 | yes | — |
| 159 | C22×C13 | — | 2 | 2 | no | — |
| 160 | C22×C13 | #454 | 1 | 2 | yes | — |
| 161 | C22×C13 | C2×#120 | 1 | 1 | yes | characteristic |
| 162 | C2×D13 | — | 8 | 1 | no | — |
| 163 | C2×D13 | — | 8 | 2 | no | — |
| 164 | C4×C13 | — | 2 | 1 | no | — |
| 165 | C4×C13 | — | 2 | 1 | no | — |
| 166 | C4×C13 | — | 2 | 2 | no | — |
| 167 | C4×C13 | — | 2 | 2 | no | — |
| 168 | C4×C13 | — | 4 | 4 | no | — |
| 169 | Dic13 | — | 4 | 4 | no | — |
| 170 | Dic13 | — | 4 | 4 | no | — |
| 171 | Dic13 | — | 8 | 1 | no | — |
| 172 | C2×#41 | — | 26 | 1 | no | — |
| 173 | C2×M16 | — | 26 | 1 | no | — |
| 174 | C4⋊Q8 | — | 13 | 1 | no | — |
| 175 | #127 | — | 13 | 1 | no | — |
| 176 | #125 | — | 2 | 2 | no | — |
| 177 | #125 | — | 13 | 4 | no | — |
| 178 | #125 | — | 13 | 4 | no | — |
| 179 | #125 | — | 26 | 8 | no | — |
| 180 | #125 | — | 26 | 8 | no | — |
| 181 | #125 | — | 26 | 8 | no | — |
| 182 | #125 | — | 26 | 8 | no | — |
| 183 | #125 | — | 26 | 8 | no | — |
| 184 | #125 | — | 26 | 8 | no | — |
| 185 | #125 | — | 26 | 2 | no | — |
| 186 | #125 | — | 26 | 2 | no | — |
| 187 | #125 | D52 | 1 | 2 | yes | — |
| 188 | #125 | C22×D13 | 1 | 2 | yes | — |
| 189 | #124 | — | 26 | 1 | no | — |
| 190 | #121 | — | 26 | 2 | no | — |
| 191 | C4×D4 | — | 26 | 2 | no | — |
| 192 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 193 | C2×C4⋊C4 | — | 13 | 2 | no | — |
| 194 | C2×C4⋊C4 | — | 13 | 2 | no | — |
| 195 | C2×C4⋊C4 | — | 26 | 2 | no | — |
| 196 | C2×C4⋊C4 | — | 26 | 2 | no | — |
| 197 | C2×C4⋊C4 | — | 26 | 2 | no | — |
| 198 | C2×C4⋊C4 | — | 26 | 2 | no | — |
| 199 | C2×C4⋊C4 | — | 26 | 2 | no | — |
| 200 | C2×C4⋊C4 | D52 | 1 | 2 | yes | — |
| 201 | C2×C42 | — | 26 | 2 | no | — |
| 202 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 203 | #107 | — | 26 | 4 | no | — |
| 204 | #106 | — | 26 | 4 | no | — |
| 205 | C4⋊C8 | — | 2 | 2 | no | — |
| 206 | #103 | — | 26 | 4 | no | — |
| 207 | #102 | — | 26 | 4 | no | — |
| 208 | #102 | — | 26 | 4 | no | — |
| 209 | #102 | — | 26 | 4 | no | — |
| 210 | C22⋊C8 | — | 2 | 2 | no | — |
| 211 | #97 | — | 13 | 2 | no | — |
| 212 | #97 | C22×D13 | 1 | 4 | yes | — |
| 213 | C4×C8 | — | 26 | 1 | no | — |
| 214 | C2×C13 | — | 2 | 2 | no | — |
| 215 | C2×C13 | C2×#454 | 1 | 1 | yes | characteristic |
| 216 | C2×C13 | #3020 | 1 | 2 | yes | — |
| 217 | D13 | — | 16 | 1 | no | — |
| 218 | #41 | — | 52 | 4 | no | — |
| 219 | C2×Q8 | — | 26 | 1 | no | — |
| 220 | C2×D4 | — | 26 | 1 | no | — |
| 221 | C2×D4 | — | 26 | 2 | no | — |
| 222 | C2×D4 | — | 52 | 1 | no | — |
| 223 | C22×C4 | — | 2 | 2 | no | — |
| 224 | C22×C4 | — | 26 | 2 | no | — |
| 225 | C22×C4 | — | 26 | 2 | no | — |
| 226 | C22×C4 | — | 52 | 1 | no | — |
| 227 | C22×C4 | C2×D52 | 1 | 1 | yes | characteristic |
| 228 | C22×C4 | D4×D13 | 1 | 2 | yes | — |
| 229 | M16 | — | 52 | 2 | no | — |
| 230 | C2×C8 | — | 2 | 4 | no | — |
| 231 | C2×C8 | — | 26 | 2 | no | — |
| 232 | C4⋊C4 | — | 2 | 4 | no | — |
| 233 | C4⋊C4 | — | 2 | 2 | no | — |
| 234 | C4⋊C4 | — | 2 | 4 | no | — |
| 235 | C4⋊C4 | — | 13 | 4 | no | — |
| 236 | C4⋊C4 | — | 13 | 4 | no | — |
| 237 | C4⋊C4 | — | 26 | 8 | no | — |
| 238 | C4⋊C4 | — | 26 | 8 | no | — |
| 239 | C4⋊C4 | — | 26 | 8 | no | — |
| 240 | C4⋊C4 | — | 26 | 2 | no | — |
| 241 | C4⋊C4 | — | 26 | 2 | no | — |
| 242 | C4⋊C4 | — | 26 | 4 | no | — |
| 243 | C4⋊C4 | — | 26 | 4 | no | — |
| 244 | C4⋊C4 | — | 26 | 4 | no | — |
| 245 | C4⋊C4 | — | 26 | 4 | no | — |
| 246 | C4⋊C4 | — | 26 | 2 | no | — |
| 247 | C4⋊C4 | C2×D52 | 1 | 4 | yes | — |
| 248 | C22⋊C4 | — | 52 | 2 | no | — |
| 249 | C42 | — | 26 | 8 | no | — |
| 250 | C42 | C2×D52 | 1 | 1 | yes | characteristic |
| 251 | C42 | D4×D13 | 1 | 2 | yes | — |
| 252 | C42 | C23×D13 | 1 | 1 | yes | characteristic |
| 253 | C13 | #19003 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 254 | C23 | — | 52 | 1 | no | — |
| 255 | C23 | #88136 | 1 | 1 | yes | characteristic |
| 256 | Q8 | — | 52 | 2 | no | — |
| 257 | D4 | — | 52 | 4 | no | — |
| 258 | D4 | — | 52 | 2 | no | — |
| 259 | D4 | — | 104 | 2 | no | — |
| 260 | C2×C4 | — | 2 | 2 | no | — |
| 261 | C2×C4 | — | 2 | 4 | no | — |
| 262 | C2×C4 | — | 4 | 2 | no | — |
| 263 | C2×C4 | — | 4 | 4 | no | — |
| 264 | C2×C4 | — | 26 | 4 | no | — |
| 265 | C2×C4 | — | 26 | 4 | no | — |
| 266 | C2×C4 | — | 52 | 4 | no | — |
| 267 | C2×C4 | — | 52 | 4 | no | — |
| 268 | C2×C4 | — | 52 | 1 | no | — |
| 269 | C2×C4 | — | 104 | 2 | no | — |
| 270 | C2×C4 | #88136 | 1 | 2 | yes | — |
| 271 | C2×C4 | #88136 | 1 | 1 | yes | characteristic |
| 272 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 273 | C2×C4 | C2×D4×D13 | 1 | 2 | yes | — |
| 274 | C8 | — | 4 | 4 | no | — |
| 275 | C8 | — | 52 | 2 | no | — |
| 276 | C22 | — | 2 | 2 | no | — |
| 277 | C22 | — | 104 | 1 | no | — |
| 278 | C22 | — | 104 | 2 | no | — |
| 279 | C22 | #11718414 | 1 | 2 | yes | — |
| 280 | C22 | C2×#88136 | 1 | 1 | yes | characteristic |
| 281 | C4 | — | 2 | 1 | no | — |
| 282 | C4 | — | 2 | 1 | no | — |
| 283 | C4 | — | 2 | 2 | no | — |
| 284 | C4 | — | 2 | 2 | no | — |
| 285 | C4 | — | 4 | 4 | no | — |
| 286 | C4 | — | 52 | 4 | no | — |
| 287 | C4 | — | 52 | 4 | no | — |
| 288 | C4 | — | 104 | 1 | no | — |
| 289 | C2 | — | 2 | 2 | no | — |
| 290 | C2 | — | 208 | 1 | no | — |
| 291 | C2 | C2×#11718414 | 1 | 1 | yes | characteristic |
| 292 | C2 | #13124202 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C13⋊#564 | C2 | semidirect |
| 4. #13114165 | C2 | semidirect |
| 5. #13114139 | C2 | semidirect |
| 6. #13113439 | C2 | semidirect |
| 7. C13×#1534 | C2 | semidirect |
| 113. #1534 | D13 | semidirect |
| 253. C13 | #19003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13⋊#564 | 2 |
| #13126028 | 2 |
| #13125239 | 2 |
| #13114165 | 2 |
| #13114139 | 2 |
| #13113439 | 2 |
| C13×#1534 | 2 |
| #19003 | 13 |