Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1630 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1630 conjugacy classes of subgroups — too many to draw. Only its 171 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×#11719422 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13125210 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13124936 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #13114016 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | #13113278 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C13×#1555 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C22×D4×D13 | — | 2 | 2 | no | — |
| 8 | C2×C13×#127 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#88192 | — | 2 | 2 | no | — |
| 10 | C2×#88191 | — | 2 | 2 | no | — |
| 11 | #11719422 | — | 2 | 2 | no | — |
| 12 | #11719422 | — | 2 | 4 | no | — |
| 13 | #11719422 | C22 | 1 | 4 | yes | — |
| 14 | C2×C4×D52 | C22 | 1 | 2 | yes | — |
| 15 | #11719175 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C13×#432 | C22 | 1 | 2 | yes | complemented |
| 17 | #11718876 | — | 2 | 2 | no | — |
| 18 | #11718732 | — | 2 | 2 | no | — |
| 19 | #11718731 | C22 | 1 | 4 | yes | complemented |
| 20 | C4×#6099 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #11718507 | C22 | 1 | 4 | yes | complemented |
| 22 | #11718502 | C22 | 1 | 4 | yes | complemented |
| 23 | #11718392 | — | 2 | 2 | no | — |
| 24 | #11718383 | — | 2 | 2 | no | — |
| 25 | #11718371 | — | 2 | 4 | no | — |
| 26 | C13×#331 | C22 | 1 | 4 | yes | complemented |
| 27 | #11718075 | C22 | 1 | 8 | yes | complemented |
| 28 | C24×D13 | — | 2 | 2 | no | — |
| 29 | C22×D4×C13 | — | 2 | 2 | no | — |
| 30 | C22×D4×C13 | D4 | 1 | 2 | yes | — |
| 31 | C22×C22⋊D13 | — | 2 | 4 | no | — |
| 32 | C2×D4×D13 | — | 2 | 8 | no | — |
| 33 | C2×D4×D13 | — | 2 | 8 | no | — |
| 34 | C2×D4×D13 | — | 4 | 16 | no | — |
| 35 | C22×D52 | D4 | 1 | 2 | yes | — |
| 36 | C22×C4×D13 | — | 2 | 2 | no | — |
| 37 | C13×#127 | — | 2 | 2 | no | — |
| 38 | C13×#127 | D4 | 1 | 2 | yes | — |
| 39 | C13×#127 | C23 | 1 | 2 | yes | — |
| 40 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 41 | C2×C22⋊Dic13 | — | 2 | 2 | no | — |
| 42 | #88192 | — | 2 | 8 | no | — |
| 43 | #88192 | — | 2 | 8 | no | — |
| 44 | #88191 | — | 2 | 8 | no | — |
| 45 | #88191 | — | 2 | 8 | no | — |
| 46 | C2×#6103 | — | 2 | 2 | no | — |
| 47 | #88180 | — | 2 | 1 | no | — |
| 48 | C2×C4⋊Dic13 | D4 | 1 | 2 | yes | — |
| 49 | #88178 | — | 2 | 2 | no | — |
| 50 | C2×#6099 | — | 2 | 1 | no | — |
| 51 | C2×#6095 | — | 2 | 4 | no | — |
| 52 | C4×D52 | — | 2 | 2 | no | — |
| 53 | C4×D52 | — | 2 | 2 | no | — |
| 54 | C4×D52 | D4 | 1 | 4 | yes | — |
| 55 | C4×D52 | C23 | 1 | 4 | yes | — |
| 56 | #88124 | — | 2 | 1 | no | — |
| 57 | #88123 | C23 | 1 | 2 | yes | complemented |
| 58 | C4×Dic26 | — | 2 | 2 | no | — |
| 59 | C13×C4⋊C8 | C23 | 1 | 4 | yes | complemented |
| 60 | C13×C22⋊C8 | — | 2 | 2 | no | — |
| 61 | C13×#97 | — | 2 | 2 | no | — |
| 62 | #88072 | — | 2 | 8 | no | — |
| 63 | #88061 | — | 2 | 4 | no | — |
| 64 | #88058 | — | 2 | 4 | no | — |
| 65 | #88056 | — | 2 | 4 | no | — |
| 66 | #88043 | — | 2 | 1 | no | — |
| 67 | C4×#1055 | C23 | 1 | 2 | yes | complemented |
| 68 | #18529 | — | 13 | 1 | no | maximal, Sylow |
| 69 | C24×C13 | — | 2 | 2 | no | — |
| 70 | C23×D13 | — | 2 | 2 | no | — |
| 71 | C23×D13 | — | 2 | 8 | no | — |
| 72 | C23×D13 | — | 4 | 16 | no | — |
| 73 | C23×D13 | — | 8 | 4 | no | — |
| 74 | C2×D4×C13 | — | 2 | 4 | no | — |
| 75 | C2×D4×C13 | — | 2 | 2 | no | — |
| 76 | C2×D4×C13 | — | 2 | 4 | no | — |
| 77 | C2×D4×C13 | — | 4 | 8 | no | — |
| 78 | C2×D4×C13 | — | 4 | 4 | no | — |
| 79 | C2×D4×C13 | C2×D4 | 1 | 4 | yes | — |
| 80 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 81 | C22×C4×C13 | C2×D4 | 1 | 2 | yes | — |
| 82 | C2×C22⋊D13 | — | 2 | 16 | no | — |
| 83 | C2×C22⋊D13 | — | 4 | 16 | no | — |
| 84 | C22×Dic13 | — | 2 | 2 | no | — |
| 85 | D4×D13 | — | 4 | 32 | no | — |
| 86 | D4×D13 | — | 4 | 16 | no | — |
| 87 | D4×D13 | — | 4 | 16 | no | — |
| 88 | C2×D52 | — | 2 | 2 | no | — |
| 89 | C2×D52 | — | 2 | 8 | no | — |
| 90 | C2×D52 | C2×D4 | 1 | 4 | yes | — |
| 91 | C2×C4×D13 | — | 2 | 4 | no | — |
| 92 | C2×C4×D13 | — | 2 | 4 | no | — |
| 93 | C2×C4×D13 | — | 4 | 8 | no | — |
| 94 | C2×Dic26 | — | 2 | 2 | no | — |
| 95 | C2×C8×C13 | — | 2 | 4 | no | — |
| 96 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | C42×C13 | C2×D4 | 1 | 2 | yes | — |
| 98 | C42×C13 | C24 | 1 | 1 | yes | characteristic |
| 99 | C22⋊Dic13 | — | 2 | 8 | no | — |
| 100 | C22⋊Dic13 | — | 4 | 1 | no | — |
| 101 | #6103 | — | 2 | 4 | no | — |
| 102 | #6103 | — | 2 | 4 | no | — |
| 103 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 104 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 105 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 106 | C4⋊Dic13 | C2×D4 | 1 | 4 | yes | — |
| 107 | #6101 | — | 4 | 2 | no | — |
| 108 | C4×Dic13 | — | 4 | 1 | no | — |
| 109 | #6099 | — | 4 | 2 | no | — |
| 110 | C2×#1055 | — | 2 | 2 | no | — |
| 111 | #6095 | — | 4 | 8 | no | — |
| 112 | C2×D42 | — | 13 | 1 | no | — |
| 113 | #3138 | — | 13 | 1 | no | — |
| 114 | #3110 | — | 13 | 2 | no | — |
| 115 | #1639 | — | 13 | 8 | no | — |
| 116 | #1555 | D13 | 1 | 1 | yes | characteristic, complemented |
| 117 | #1490 | — | 13 | 2 | no | — |
| 118 | C23×C13 | — | 2 | 4 | no | — |
| 119 | C23×C13 | — | 4 | 8 | no | — |
| 120 | C23×C13 | — | 4 | 4 | no | — |
| 121 | C23×C13 | #120 | 1 | 1 | yes | characteristic |
| 122 | C22×D13 | — | 2 | 8 | no | — |
| 123 | C22×D13 | — | 2 | 4 | no | — |
| 124 | C22×D13 | — | 4 | 32 | no | — |
| 125 | C22×D13 | — | 4 | 4 | no | — |
| 126 | C22×D13 | — | 4 | 4 | no | — |
| 127 | C22×D13 | — | 8 | 8 | no | — |
| 128 | C22×D13 | — | 8 | 32 | no | — |
| 129 | D4×C13 | — | 4 | 8 | no | — |
| 130 | D4×C13 | — | 4 | 4 | no | — |
| 131 | D4×C13 | — | 4 | 8 | no | — |
| 132 | D4×C13 | — | 8 | 2 | no | — |
| 133 | C2×C4×C13 | — | 2 | 2 | no | — |
| 134 | C2×C4×C13 | — | 2 | 4 | no | — |
| 135 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 136 | C2×C4×C13 | #120 | 1 | 2 | yes | — |
| 137 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 138 | C2×C4×C13 | C22×D4 | 1 | 2 | yes | — |
| 139 | C22⋊D13 | — | 4 | 32 | no | — |
| 140 | C2×Dic13 | — | 2 | 4 | no | — |
| 141 | C2×Dic13 | — | 4 | 4 | no | — |
| 142 | C2×Dic13 | — | 4 | 2 | no | — |
| 143 | D52 | — | 2 | 8 | no | — |
| 144 | D52 | — | 2 | 4 | no | — |
| 145 | D52 | AGL(1,ℤ/8) | 1 | 8 | yes | — |
| 146 | C4×D13 | — | 4 | 8 | no | — |
| 147 | C4×D13 | — | 4 | 8 | no | — |
| 148 | Dic26 | — | 4 | 4 | no | — |
| 149 | C8×C13 | — | 4 | 4 | no | — |
| 150 | #1055 | — | 4 | 2 | no | — |
| 151 | C23×D4 | — | 26 | 2 | no | — |
| 152 | D42 | — | 13 | 4 | no | — |
| 153 | D42 | — | 26 | 4 | no | — |
| 154 | D42 | — | 26 | 2 | no | — |
| 155 | #533 | — | 13 | 1 | no | — |
| 156 | C2×#127 | C2×D13 | 1 | 1 | yes | characteristic |
| 157 | C2×#121 | — | 26 | 2 | no | — |
| 158 | C2×#120 | — | 26 | 2 | no | — |
| 159 | C2×C4×D4 | — | 13 | 2 | no | — |
| 160 | #490 | — | 26 | 2 | no | — |
| 161 | #486 | — | 13 | 4 | no | — |
| 162 | #484 | — | 26 | 2 | no | — |
| 163 | #474 | — | 13 | 4 | no | — |
| 164 | #461 | — | 13 | 4 | no | — |
| 165 | #450 | — | 26 | 2 | no | — |
| 166 | #440 | — | 26 | 4 | no | — |
| 167 | #432 | C2×D13 | 1 | 2 | yes | complemented |
| 168 | #418 | — | 26 | 2 | no | — |
| 169 | C4×M16 | — | 13 | 1 | no | — |
| 170 | #331 | C2×D13 | 1 | 4 | yes | complemented |
| 171 | D4⋊C8 | — | 13 | 8 | no | — |
| 172 | C22×C13 | — | 2 | 2 | no | — |
| 173 | C22×C13 | — | 4 | 8 | no | — |
| 174 | C22×C13 | — | 4 | 4 | no | — |
| 175 | C22×C13 | — | 8 | 8 | no | — |
| 176 | C22×C13 | #455 | 1 | 2 | yes | — |
| 177 | C22×C13 | C2×#120 | 1 | 1 | yes | characteristic |
| 178 | C2×D13 | — | 2 | 8 | no | — |
| 179 | C2×D13 | — | 4 | 16 | no | — |
| 180 | C2×D13 | — | 4 | 4 | no | — |
| 181 | C2×D13 | — | 4 | 4 | no | — |
| 182 | C2×D13 | — | 8 | 32 | no | — |
| 183 | C4×C13 | — | 2 | 2 | no | — |
| 184 | C4×C13 | — | 2 | 1 | no | — |
| 185 | C4×C13 | — | 2 | 1 | no | — |
| 186 | C4×C13 | C2×AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 187 | Dic13 | — | 4 | 4 | no | — |
| 188 | Dic13 | — | 8 | 2 | no | — |
| 189 | C25 | — | 26 | 2 | no | — |
| 190 | C22×D4 | — | 2 | 2 | no | — |
| 191 | C22×D4 | — | 13 | 2 | no | — |
| 192 | C22×D4 | — | 26 | 8 | no | — |
| 193 | C22×D4 | — | 26 | 8 | no | — |
| 194 | C22×D4 | — | 26 | 4 | no | — |
| 195 | C22×D4 | — | 52 | 16 | no | — |
| 196 | C22×D4 | D52 | 1 | 2 | yes | — |
| 197 | C23×C4 | — | 26 | 2 | no | — |
| 198 | C2×SD16 | — | 26 | 4 | no | — |
| 199 | C2×M16 | — | 26 | 1 | no | — |
| 200 | C4⋊Q8 | — | 13 | 2 | no | — |
| 201 | #127 | — | 2 | 2 | no | — |
| 202 | #127 | D52 | 1 | 2 | yes | — |
| 203 | #127 | C22×D13 | 1 | 2 | yes | — |
| 204 | #125 | — | 26 | 1 | no | — |
| 205 | C22⋊Q8 | — | 26 | 2 | no | — |
| 206 | #121 | — | 26 | 8 | no | — |
| 207 | #121 | — | 26 | 8 | no | — |
| 208 | #120 | — | 26 | 8 | no | — |
| 209 | #120 | — | 26 | 8 | no | — |
| 210 | C4×Q8 | — | 26 | 2 | no | — |
| 211 | C4×D4 | — | 13 | 4 | no | — |
| 212 | C4×D4 | — | 13 | 4 | no | — |
| 213 | C4×D4 | — | 26 | 2 | no | — |
| 214 | C4×D4 | — | 26 | 2 | no | — |
| 215 | #117 | — | 26 | 1 | no | — |
| 216 | C2×C4⋊C4 | — | 13 | 2 | no | — |
| 217 | C2×C22⋊C4 | — | 26 | 2 | no | — |
| 218 | C2×C22⋊C4 | — | 26 | 2 | no | — |
| 219 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 220 | #107 | — | 26 | 4 | no | — |
| 221 | C4⋊C8 | C22×D13 | 1 | 4 | yes | complemented |
| 222 | #103 | — | 26 | 4 | no | — |
| 223 | #102 | — | 26 | 4 | no | — |
| 224 | #102 | — | 26 | 8 | no | — |
| 225 | C22⋊C8 | — | 2 | 2 | no | — |
| 226 | #97 | — | 2 | 2 | no | — |
| 227 | #97 | — | 26 | 1 | no | — |
| 228 | C4×C8 | — | 13 | 2 | no | — |
| 229 | C2×C13 | — | 2 | 2 | no | — |
| 230 | C2×C13 | — | 8 | 4 | no | — |
| 231 | C2×C13 | #3003 | 1 | 2 | yes | — |
| 232 | C2×C13 | C2×#455 | 1 | 1 | yes | characteristic |
| 233 | D13 | — | 4 | 8 | no | — |
| 234 | C24 | — | 2 | 2 | no | — |
| 235 | C24 | — | 26 | 8 | no | — |
| 236 | C24 | — | 26 | 2 | no | — |
| 237 | C24 | — | 52 | 16 | no | — |
| 238 | C24 | — | 104 | 4 | no | — |
| 239 | C2×Q8 | — | 26 | 2 | no | — |
| 240 | C2×D4 | — | 2 | 4 | no | — |
| 241 | C2×D4 | — | 2 | 2 | no | — |
| 242 | C2×D4 | — | 2 | 4 | no | — |
| 243 | C2×D4 | — | 4 | 8 | no | — |
| 244 | C2×D4 | — | 4 | 4 | no | — |
| 245 | C2×D4 | — | 13 | 4 | no | — |
| 246 | C2×D4 | — | 26 | 8 | no | — |
| 247 | C2×D4 | — | 26 | 16 | no | — |
| 248 | C2×D4 | — | 26 | 2 | no | — |
| 249 | C2×D4 | — | 52 | 16 | no | — |
| 250 | C2×D4 | — | 52 | 32 | no | — |
| 251 | C2×D4 | — | 52 | 16 | no | — |
| 252 | C2×D4 | — | 52 | 16 | no | — |
| 253 | C2×D4 | C2×D52 | 1 | 4 | yes | — |
| 254 | C22×C4 | — | 26 | 2 | no | — |
| 255 | C22×C4 | — | 26 | 4 | no | — |
| 256 | C22×C4 | — | 26 | 4 | no | — |
| 257 | C22×C4 | — | 52 | 8 | no | — |
| 258 | C22×C4 | C2×D52 | 1 | 1 | yes | characteristic |
| 259 | C22×C4 | D4×D13 | 1 | 2 | yes | — |
| 260 | SD16 | — | 52 | 8 | no | — |
| 261 | M16 | — | 52 | 2 | no | — |
| 262 | C2×C8 | — | 2 | 4 | no | — |
| 263 | C2×C8 | — | 26 | 2 | no | — |
| 264 | C4⋊C4 | — | 13 | 4 | no | — |
| 265 | C4⋊C4 | — | 26 | 2 | no | — |
| 266 | C4⋊C4 | — | 26 | 2 | no | — |
| 267 | C4⋊C4 | — | 26 | 2 | no | — |
| 268 | C4⋊C4 | — | 52 | 2 | no | — |
| 269 | C22⋊C4 | — | 26 | 8 | no | — |
| 270 | C22⋊C4 | — | 26 | 4 | no | — |
| 271 | C22⋊C4 | — | 26 | 4 | no | — |
| 272 | C22⋊C4 | — | 52 | 1 | no | — |
| 273 | C42 | — | 52 | 1 | no | — |
| 274 | C42 | C2×D52 | 1 | 1 | yes | characteristic |
| 275 | C42 | D4×D13 | 1 | 2 | yes | — |
| 276 | C42 | C23×D13 | 1 | 1 | yes | characteristic |
| 277 | C13 | #18529 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 278 | C23 | — | 2 | 4 | no | — |
| 279 | C23 | — | 4 | 8 | no | — |
| 280 | C23 | — | 4 | 4 | no | — |
| 281 | C23 | — | 26 | 8 | no | — |
| 282 | C23 | — | 26 | 4 | no | — |
| 283 | C23 | — | 52 | 4 | no | — |
| 284 | C23 | — | 52 | 32 | no | — |
| 285 | C23 | — | 52 | 4 | no | — |
| 286 | C23 | — | 104 | 8 | no | — |
| 287 | C23 | — | 104 | 32 | no | — |
| 288 | C23 | #88136 | 1 | 1 | yes | characteristic |
| 289 | Q8 | — | 52 | 4 | no | — |
| 290 | D4 | — | 4 | 4 | no | — |
| 291 | D4 | — | 4 | 8 | no | — |
| 292 | D4 | — | 4 | 8 | no | — |
| 293 | D4 | — | 8 | 2 | no | — |
| 294 | D4 | — | 13 | 8 | no | — |
| 295 | D4 | — | 26 | 8 | no | — |
| 296 | D4 | — | 26 | 4 | no | — |
| 297 | D4 | — | 52 | 32 | no | — |
| 298 | C2×C4 | — | 2 | 2 | no | — |
| 299 | C2×C4 | — | 2 | 4 | no | — |
| 300 | C2×C4 | — | 26 | 4 | no | — |
| 301 | C2×C4 | — | 52 | 8 | no | — |
| 302 | C2×C4 | — | 52 | 4 | no | — |
| 303 | C2×C4 | — | 52 | 8 | no | — |
| 304 | C2×C4 | — | 52 | 2 | no | — |
| 305 | C2×C4 | #88136 | 1 | 1 | yes | characteristic |
| 306 | C2×C4 | #88136 | 1 | 2 | yes | — |
| 307 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 308 | C2×C4 | C2×D4×D13 | 1 | 2 | yes | — |
| 309 | C8 | — | 4 | 4 | no | — |
| 310 | C8 | — | 52 | 2 | no | — |
| 311 | C22 | — | 2 | 2 | no | — |
| 312 | C22 | — | 4 | 4 | no | — |
| 313 | C22 | — | 4 | 8 | no | — |
| 314 | C22 | — | 8 | 8 | no | — |
| 315 | C22 | — | 26 | 8 | no | — |
| 316 | C22 | — | 52 | 16 | no | — |
| 317 | C22 | — | 52 | 4 | no | — |
| 318 | C22 | — | 52 | 4 | no | — |
| 319 | C22 | — | 104 | 32 | no | — |
| 320 | C22 | #11718407 | 1 | 2 | yes | — |
| 321 | C22 | C2×#88136 | 1 | 1 | yes | characteristic |
| 322 | C4 | — | 2 | 1 | no | — |
| 323 | C4 | — | 2 | 1 | no | — |
| 324 | C4 | — | 2 | 2 | no | — |
| 325 | C4 | — | 52 | 4 | no | — |
| 326 | C4 | — | 104 | 2 | no | — |
| 327 | C4 | D13×AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 328 | C2 | — | 2 | 2 | no | — |
| 329 | C2 | — | 8 | 4 | no | — |
| 330 | C2 | — | 52 | 8 | no | — |
| 331 | C2 | #13124065 | 1 | 2 | yes | — |
| 332 | C2 | C2×#11718407 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13125210 | C2 | semidirect |
| 3. #13124936 | C2 | semidirect |
| 4. #13114016 | C2 | semidirect |
| 5. #13113278 | C2 | semidirect |
| 6. C13×#1555 | C2 | semidirect |
| 15. #11719175 | C22 | semidirect |
| 16. C13×#432 | C22 | semidirect |
| 19. #11718731 | C22 | semidirect |
| 20. C4×#6099 | C22 | semidirect |
| 21. #11718507 | C22 | semidirect |
| 22. #11718502 | C22 | semidirect |
| 26. C13×#331 | C22 | semidirect |
| 27. #11718075 | C22 | semidirect |
| 57. #88123 | C23 | semidirect |
| 59. C13×C4⋊C8 | C23 | semidirect |
| 67. C4×#1055 | C23 | semidirect |
| 116. #1555 | D13 | semidirect |
| 167. #432 | C2×D13 | semidirect |
| 170. #331 | C2×D13 | semidirect |
| 221. C4⋊C8 | C22×D13 | semidirect |
| 277. C13 | #18529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11719422 | 2 |
| #13125210 | 2 |
| #13124936 | 2 |
| #13114016 | 2 |
| #13113278 | 2 |
| C13×#1555 | 2 |
| #18529 | 13 |