Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
468 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 47 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 | #13116819 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #13113888 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13112999 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13112981 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C13×#3292 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C13×#576 | — | 2 | 2 | no | — |
| 7 | #11719422 | C22 | 1 | 1 | yes | characteristic, complemented |
| 8 | C13×#493 | C22 | 1 | 1 | yes | characteristic |
| 9 | C13×#472 | — | 2 | 2 | no | — |
| 10 | C13×#453 | — | 2 | 1 | no | — |
| 11 | C13×#453 | C22 | 1 | 2 | yes | — |
| 12 | C13×#443 | — | 2 | 1 | no | — |
| 13 | #11718905 | — | 2 | 2 | no | — |
| 14 | #11718733 | — | 2 | 1 | no | — |
| 15 | #11718137 | C22 | 1 | 2 | yes | complemented |
| 16 | #11718136 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | #11718067 | — | 2 | 2 | no | — |
| 18 | #11718051 | — | 2 | 1 | no | — |
| 19 | C13×H(5,𝔽2) | — | 2 | 1 | no | — |
| 20 | C13×H(5,𝔽2) | D4 | 1 | 2 | yes | complemented |
| 21 | C2×D4×D13 | — | 4 | 1 | no | — |
| 22 | C13×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 23 | C13×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 24 | C13×AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 25 | C13×AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 26 | C13×#135 | — | 2 | 1 | no | — |
| 27 | C13×#135 | — | 4 | 2 | no | — |
| 28 | C2×C13×D8 | — | 2 | 2 | no | — |
| 29 | C2×C13×D8 | — | 4 | 2 | no | — |
| 30 | C13×#131 | — | 2 | 2 | no | — |
| 31 | C13×#127 | D4 | 1 | 1 | yes | characteristic, complemented |
| 32 | C13×#127 | C23 | 1 | 1 | yes | characteristic |
| 33 | #88192 | — | 4 | 1 | no | — |
| 34 | #88191 | — | 2 | 2 | no | — |
| 35 | #88191 | — | 4 | 2 | no | — |
| 36 | C2×#6104 | — | 4 | 1 | no | — |
| 37 | C4×D52 | — | 2 | 1 | no | — |
| 38 | C13×#108 | — | 2 | 1 | no | — |
| 39 | C13×#104 | — | 2 | 2 | no | — |
| 40 | C13×#100 | — | 2 | 1 | no | — |
| 41 | C13×#100 | D4 | 1 | 2 | yes | complemented |
| 42 | C4×C8×C13 | D4 | 1 | 1 | yes | characteristic, complemented |
| 43 | #88074 | — | 2 | 2 | no | — |
| 44 | #88074 | — | 4 | 2 | no | — |
| 45 | #88072 | — | 4 | 1 | no | — |
| 46 | C4⋊#1055 | — | 2 | 1 | no | — |
| 47 | #13673 | — | 13 | 1 | no | maximal, Sylow |
| 48 | C23×D13 | — | 2 | 2 | no | — |
| 49 | C13×#41 | — | 2 | 2 | no | — |
| 50 | C13×#41 | — | 4 | 2 | no | — |
| 51 | C13×#41 | — | 4 | 2 | no | — |
| 52 | C2×D4×C13 | — | 2 | 1 | no | — |
| 53 | C2×D4×C13 | — | 4 | 1 | no | — |
| 54 | C2×D4×C13 | — | 4 | 1 | no | — |
| 55 | C2×D4×C13 | — | 4 | 2 | no | — |
| 56 | C2×D4×C13 | — | 4 | 2 | no | — |
| 57 | C2×D4×C13 | — | 4 | 2 | no | — |
| 58 | C2×D4×C13 | — | 8 | 1 | no | — |
| 59 | C2×D4×C13 | C2×D4 | 1 | 2 | yes | — |
| 60 | C2×C22⋊D13 | — | 4 | 2 | no | — |
| 61 | C2×C22⋊D13 | — | 8 | 2 | no | — |
| 62 | D4×D13 | — | 8 | 2 | no | — |
| 63 | D4×D13 | — | 8 | 2 | no | — |
| 64 | C2×D52 | — | 2 | 1 | no | — |
| 65 | C2×C4×D13 | — | 4 | 1 | no | — |
| 66 | C13×Q16 | — | 2 | 1 | no | — |
| 67 | C13×SD16 | — | 2 | 2 | no | — |
| 68 | C13×SD16 | — | 4 | 2 | no | — |
| 69 | C13×SD16 | — | 4 | 2 | no | — |
| 70 | C13×D8 | — | 2 | 1 | no | — |
| 71 | C13×D8 | — | 4 | 2 | no | — |
| 72 | C13×D8 | — | 4 | 2 | no | — |
| 73 | C13×D8 | — | 4 | 2 | no | — |
| 74 | C13×D8 | — | 4 | 2 | no | — |
| 75 | C13×M16 | — | 2 | 2 | no | — |
| 76 | C13×M16 | — | 4 | 2 | no | — |
| 77 | C2×C8×C13 | — | 2 | 1 | no | — |
| 78 | C2×C8×C13 | — | 4 | 2 | no | — |
| 79 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 80 | C22⋊Dic13 | — | 2 | 2 | no | — |
| 81 | C22⋊Dic13 | — | 4 | 2 | no | — |
| 82 | #6104 | — | 8 | 2 | no | — |
| 83 | #6103 | — | 4 | 1 | no | — |
| 84 | #6103 | — | 8 | 2 | no | — |
| 85 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 86 | C2×#1055 | — | 4 | 1 | no | — |
| 87 | #3292 | D13 | 1 | 1 | yes | characteristic, complemented |
| 88 | #2196 | — | 13 | 2 | no | — |
| 89 | #1619 | — | 13 | 1 | no | — |
| 90 | #1408 | — | 13 | 1 | no | — |
| 91 | #1402 | — | 13 | 2 | no | — |
| 92 | C23×C13 | — | 2 | 2 | no | — |
| 93 | C23×C13 | — | 4 | 2 | no | — |
| 94 | C23×C13 | — | 4 | 1 | no | — |
| 95 | C23×C13 | — | 8 | 1 | no | — |
| 96 | C22×D13 | — | 4 | 1 | no | — |
| 97 | C22×D13 | — | 8 | 4 | no | — |
| 98 | C22×D13 | — | 8 | 2 | no | — |
| 99 | Q8×C13 | — | 2 | 2 | no | — |
| 100 | D4×C13 | — | 2 | 2 | no | — |
| 101 | D4×C13 | — | 4 | 2 | no | — |
| 102 | D4×C13 | — | 4 | 2 | no | — |
| 103 | D4×C13 | — | 4 | 2 | no | — |
| 104 | D4×C13 | — | 8 | 1 | no | — |
| 105 | D4×C13 | — | 8 | 1 | no | — |
| 106 | D4×C13 | — | 8 | 1 | no | — |
| 107 | D4×C13 | — | 8 | 1 | no | — |
| 108 | D4×C13 | — | 8 | 2 | no | — |
| 109 | D4×C13 | — | 8 | 2 | no | — |
| 110 | C2×C4×C13 | — | 2 | 1 | no | — |
| 111 | C2×C4×C13 | — | 4 | 2 | no | — |
| 112 | C2×C4×C13 | — | 4 | 2 | no | — |
| 113 | C2×C4×C13 | — | 8 | 1 | no | — |
| 114 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 115 | C22⋊D13 | — | 8 | 4 | no | — |
| 116 | C22⋊D13 | — | 16 | 4 | no | — |
| 117 | C2×Dic13 | — | 4 | 1 | no | — |
| 118 | C2×Dic13 | — | 8 | 2 | no | — |
| 119 | D52 | — | 2 | 2 | no | — |
| 120 | D52 | — | 4 | 1 | no | — |
| 121 | C4×D13 | — | 8 | 1 | no | — |
| 122 | C4×D13 | — | 8 | 1 | no | — |
| 123 | C8×C13 | — | 2 | 1 | no | — |
| 124 | C8×C13 | — | 2 | 1 | no | — |
| 125 | C8×C13 | — | 4 | 2 | no | — |
| 126 | #1055 | — | 8 | 1 | no | — |
| 127 | #576 | — | 2 | 2 | no | — |
| 128 | D42 | — | 13 | 1 | no | — |
| 129 | #493 | C2×D13 | 1 | 1 | yes | characteristic |
| 130 | #472 | — | 2 | 2 | no | — |
| 131 | #459 | — | 26 | 1 | no | — |
| 132 | B(4,𝔽2) | — | 26 | 2 | no | — |
| 133 | #453 | — | 2 | 1 | no | — |
| 134 | #453 | C2×D13 | 1 | 2 | yes | — |
| 135 | #443 | — | 2 | 1 | no | — |
| 136 | #353 | — | 13 | 2 | no | — |
| 137 | AΣL(1,𝔽16) | — | 26 | 2 | no | — |
| 138 | #331 | — | 13 | 1 | no | — |
| 139 | D4⋊C8 | — | 26 | 1 | no | — |
| 140 | C22×C13 | — | 4 | 2 | no | — |
| 141 | C22×C13 | — | 4 | 2 | no | — |
| 142 | C22×C13 | — | 8 | 2 | no | — |
| 143 | C22×C13 | — | 8 | 1 | no | — |
| 144 | C22×C13 | — | 16 | 1 | no | — |
| 145 | C22×C13 | — | 16 | 2 | no | — |
| 146 | C22×C13 | — | 32 | 1 | no | — |
| 147 | C22×C13 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 148 | C2×D13 | — | 4 | 2 | no | — |
| 149 | C2×D13 | — | 8 | 1 | no | — |
| 150 | C2×D13 | — | 8 | 1 | no | — |
| 151 | C2×D13 | — | 8 | 4 | no | — |
| 152 | C2×D13 | — | 16 | 2 | no | — |
| 153 | C4×C13 | — | 2 | 1 | no | — |
| 154 | C4×C13 | — | 2 | 1 | no | — |
| 155 | C4×C13 | — | 2 | 1 | no | — |
| 156 | C4×C13 | — | 4 | 2 | no | — |
| 157 | Dic13 | — | 8 | 1 | no | — |
| 158 | Dic13 | — | 16 | 2 | no | — |
| 159 | H(5,𝔽2) | — | 2 | 1 | no | — |
| 160 | H(5,𝔽2) | C22⋊D13 | 1 | 2 | yes | complemented |
| 161 | C22×D4 | — | 52 | 1 | no | — |
| 162 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 163 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 164 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 165 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 166 | #135 | — | 2 | 1 | no | — |
| 167 | #135 | — | 4 | 2 | no | — |
| 168 | C2×D8 | — | 2 | 2 | no | — |
| 169 | C2×D8 | — | 4 | 2 | no | — |
| 170 | C2×D8 | — | 52 | 1 | no | — |
| 171 | #131 | — | 2 | 2 | no | — |
| 172 | #127 | C22⋊D13 | 1 | 1 | yes | characteristic, complemented |
| 173 | #127 | C22×D13 | 1 | 1 | yes | characteristic |
| 174 | #121 | — | 52 | 1 | no | — |
| 175 | #120 | — | 26 | 2 | no | — |
| 176 | #120 | — | 52 | 2 | no | — |
| 177 | C4×D4 | — | 26 | 1 | no | — |
| 178 | #108 | — | 2 | 1 | no | — |
| 179 | C4⋊C8 | — | 26 | 1 | no | — |
| 180 | #104 | — | 2 | 2 | no | — |
| 181 | #102 | — | 52 | 1 | no | — |
| 182 | #100 | — | 2 | 1 | no | — |
| 183 | #100 | C22⋊D13 | 1 | 2 | yes | complemented |
| 184 | #99 | — | 26 | 2 | no | — |
| 185 | #99 | — | 52 | 2 | no | — |
| 186 | C4×C8 | C22⋊D13 | 1 | 1 | yes | characteristic, complemented |
| 187 | C2×C13 | — | 2 | 1 | no | — |
| 188 | C2×C13 | — | 8 | 2 | no | — |
| 189 | C2×C13 | — | 8 | 2 | no | — |
| 190 | C2×C13 | — | 16 | 1 | no | — |
| 191 | C2×C13 | #2196 | 1 | 1 | yes | characteristic |
| 192 | D13 | — | 8 | 2 | no | — |
| 193 | C24 | — | 26 | 2 | no | — |
| 194 | #41 | — | 2 | 2 | no | — |
| 195 | #41 | — | 4 | 2 | no | — |
| 196 | #41 | — | 4 | 2 | no | — |
| 197 | C2×D4 | — | 2 | 1 | no | — |
| 198 | C2×D4 | — | 4 | 1 | no | — |
| 199 | C2×D4 | — | 4 | 1 | no | — |
| 200 | C2×D4 | — | 4 | 2 | no | — |
| 201 | C2×D4 | — | 4 | 2 | no | — |
| 202 | C2×D4 | — | 4 | 2 | no | — |
| 203 | C2×D4 | — | 8 | 1 | no | — |
| 204 | C2×D4 | — | 26 | 1 | no | — |
| 205 | C2×D4 | — | 52 | 2 | no | — |
| 206 | C2×D4 | — | 104 | 2 | no | — |
| 207 | C2×D4 | — | 104 | 2 | no | — |
| 208 | C2×D4 | — | 104 | 2 | no | — |
| 209 | C2×D4 | C2×C22⋊D13 | 1 | 2 | yes | — |
| 210 | C22×C4 | — | 52 | 1 | no | — |
| 211 | Q16 | — | 2 | 1 | no | — |
| 212 | SD16 | — | 2 | 2 | no | — |
| 213 | SD16 | — | 4 | 2 | no | — |
| 214 | SD16 | — | 4 | 2 | no | — |
| 215 | D8 | — | 2 | 1 | no | — |
| 216 | D8 | — | 4 | 2 | no | — |
| 217 | D8 | — | 4 | 2 | no | — |
| 218 | D8 | — | 4 | 2 | no | — |
| 219 | D8 | — | 4 | 2 | no | — |
| 220 | D8 | — | 104 | 2 | no | — |
| 221 | M16 | — | 2 | 2 | no | — |
| 222 | M16 | — | 4 | 2 | no | — |
| 223 | C2×C8 | — | 2 | 1 | no | — |
| 224 | C2×C8 | — | 4 | 2 | no | — |
| 225 | C2×C8 | — | 52 | 1 | no | — |
| 226 | C4⋊C4 | — | 26 | 1 | no | — |
| 227 | C22⋊C4 | — | 26 | 2 | no | — |
| 228 | C22⋊C4 | — | 52 | 1 | no | — |
| 229 | C22⋊C4 | — | 52 | 2 | no | — |
| 230 | C22⋊C4 | — | 104 | 2 | no | — |
| 231 | C42 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 232 | C13 | #13673 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 233 | C23 | — | 2 | 2 | no | — |
| 234 | C23 | — | 4 | 2 | no | — |
| 235 | C23 | — | 4 | 1 | no | — |
| 236 | C23 | — | 8 | 1 | no | — |
| 237 | C23 | — | 52 | 1 | no | — |
| 238 | C23 | — | 104 | 2 | no | — |
| 239 | C23 | — | 104 | 4 | no | — |
| 240 | Q8 | — | 2 | 2 | no | — |
| 241 | D4 | — | 2 | 2 | no | — |
| 242 | D4 | — | 4 | 2 | no | — |
| 243 | D4 | — | 4 | 2 | no | — |
| 244 | D4 | — | 4 | 2 | no | — |
| 245 | D4 | — | 8 | 1 | no | — |
| 246 | D4 | — | 8 | 1 | no | — |
| 247 | D4 | — | 8 | 1 | no | — |
| 248 | D4 | — | 8 | 1 | no | — |
| 249 | D4 | — | 8 | 2 | no | — |
| 250 | D4 | — | 8 | 2 | no | — |
| 251 | D4 | — | 26 | 2 | no | — |
| 252 | D4 | — | 52 | 1 | no | — |
| 253 | D4 | — | 104 | 4 | no | — |
| 254 | D4 | — | 208 | 4 | no | — |
| 255 | C2×C4 | — | 2 | 1 | no | — |
| 256 | C2×C4 | — | 4 | 2 | no | — |
| 257 | C2×C4 | — | 4 | 2 | no | — |
| 258 | C2×C4 | — | 8 | 1 | no | — |
| 259 | C2×C4 | — | 52 | 1 | no | — |
| 260 | C2×C4 | — | 104 | 1 | no | — |
| 261 | C2×C4 | — | 104 | 1 | no | — |
| 262 | C2×C4 | — | 104 | 2 | no | — |
| 263 | C2×C4 | #88207 | 1 | 1 | yes | characteristic |
| 264 | C8 | — | 2 | 1 | no | — |
| 265 | C8 | — | 2 | 1 | no | — |
| 266 | C8 | — | 4 | 2 | no | — |
| 267 | C8 | — | 104 | 1 | no | — |
| 268 | C22 | — | 4 | 2 | no | — |
| 269 | C22 | — | 4 | 2 | no | — |
| 270 | C22 | — | 8 | 2 | no | — |
| 271 | C22 | — | 8 | 1 | no | — |
| 272 | C22 | — | 16 | 1 | no | — |
| 273 | C22 | — | 16 | 2 | no | — |
| 274 | C22 | — | 32 | 1 | no | — |
| 275 | C22 | — | 52 | 2 | no | — |
| 276 | C22 | — | 104 | 1 | no | — |
| 277 | C22 | — | 104 | 4 | no | — |
| 278 | C22 | — | 104 | 1 | no | — |
| 279 | C22 | — | 208 | 2 | no | — |
| 280 | C22 | #11718905 | 1 | 1 | yes | characteristic |
| 281 | C4 | — | 2 | 1 | no | — |
| 282 | C4 | — | 2 | 1 | no | — |
| 283 | C4 | — | 2 | 1 | no | — |
| 284 | C4 | — | 4 | 2 | no | — |
| 285 | C4 | — | 104 | 1 | no | — |
| 286 | C4 | — | 208 | 2 | no | — |
| 287 | C2 | — | 2 | 1 | no | — |
| 288 | C2 | — | 8 | 2 | no | — |
| 289 | C2 | — | 8 | 2 | no | — |
| 290 | C2 | — | 16 | 1 | no | — |
| 291 | C2 | — | 104 | 2 | no | — |
| 292 | C2 | #13116820 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13116819 | C2 | semidirect |
| 2. #13113888 | C2 | semidirect |
| 3. #13112999 | C2 | semidirect |
| 4. #13112981 | C2 | semidirect |
| 5. C13×#3292 | C2 | semidirect |
| 7. #11719422 | C22 | semidirect |
| 15. #11718137 | C22 | semidirect |
| 16. #11718136 | C22 | semidirect |
| 20. C13×H(5,𝔽2) | D4 | semidirect |
| 31. C13×#127 | D4 | semidirect |
| 41. C13×#100 | D4 | semidirect |
| 42. C4×C8×C13 | D4 | semidirect |
| 87. #3292 | D13 | semidirect |
| 160. H(5,𝔽2) | C22⋊D13 | semidirect |
| 172. #127 | C22⋊D13 | semidirect |
| 183. #100 | C22⋊D13 | semidirect |
| 186. C4×C8 | C22⋊D13 | semidirect |
| 232. C13 | #13673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13116819 | 2 |
| #13113888 | 2 |
| #13112999 | 2 |
| #13112981 | 2 |
| C13×#3292 | 2 |
| #13673 | 13 |