Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
498 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 60 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 | #13131107 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13130290 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13129959 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #13124185 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C13×#585 | C4 | 1 | 1 | yes | characteristic, complemented |
| 6 | #11719537 | C22 | 1 | 1 | yes | characteristic |
| 7 | #11719527 | — | 2 | 1 | no | — |
| 8 | C4×#6122 | — | 2 | 1 | no | — |
| 9 | #11719116 | — | 2 | 1 | no | — |
| 10 | #11718907 | C4 | 1 | 2 | yes | complemented |
| 11 | #11718906 | C22 | 1 | 2 | yes | — |
| 12 | #11718903 | — | 2 | 1 | no | — |
| 13 | #11718902 | — | 2 | 1 | no | — |
| 14 | #11718898 | C4 | 1 | 1 | yes | characteristic, complemented |
| 15 | C2×#88077 | — | 2 | 1 | no | — |
| 16 | #11718300 | C22 | 1 | 2 | yes | complemented |
| 17 | #11718299 | C22 | 1 | 2 | yes | complemented |
| 18 | #11718294 | — | 2 | 1 | no | — |
| 19 | #11718293 | — | 2 | 1 | no | — |
| 20 | C13×2−1+4 | — | 4 | 1 | no | — |
| 21 | C13×2−1+4 | C2×C4 | 1 | 2 | yes | — |
| 22 | C13×H(5,𝔽2) | — | 2 | 1 | no | — |
| 23 | C13×H(5,𝔽2) | — | 4 | 1 | no | — |
| 24 | C13×H(5,𝔽2) | — | 4 | 1 | no | — |
| 25 | C2×C13×#41 | — | 2 | 1 | no | — |
| 26 | C2×C13×#41 | — | 4 | 1 | no | — |
| 27 | C2×C13×#41 | — | 4 | 2 | no | — |
| 28 | C2×C13×#41 | C2×C4 | 1 | 1 | yes | characteristic |
| 29 | C2×#6127 | D4 | 1 | 1 | yes | characteristic |
| 30 | C2×#6122 | — | 4 | 1 | no | — |
| 31 | #88237 | — | 4 | 1 | no | — |
| 32 | #88205 | — | 2 | 2 | no | — |
| 33 | #88204 | — | 4 | 2 | no | — |
| 34 | #88203 | — | 2 | 2 | no | — |
| 35 | #88201 | C23 | 1 | 1 | yes | characteristic |
| 36 | #88198 | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | #88196 | — | 4 | 1 | no | — |
| 38 | #88194 | D4 | 1 | 1 | yes | characteristic |
| 39 | #88193 | — | 4 | 1 | no | — |
| 40 | #88190 | D4 | 1 | 1 | yes | characteristic |
| 41 | #88186 | — | 4 | 1 | no | — |
| 42 | C4×C22⋊D13 | — | 4 | 1 | no | — |
| 43 | C2×C4×Dic13 | D4 | 1 | 1 | yes | characteristic |
| 44 | C2×#6099 | — | 2 | 1 | no | — |
| 45 | #88119 | — | 4 | 1 | no | — |
| 46 | #88110 | — | 2 | 2 | no | — |
| 47 | C4×#1057 | — | 4 | 1 | no | — |
| 48 | #88107 | — | 2 | 2 | no | — |
| 49 | #88077 | — | 2 | 2 | no | — |
| 50 | #88077 | — | 2 | 2 | no | — |
| 51 | #88076 | C2×C4 | 1 | 2 | yes | — |
| 52 | #88073 | — | 2 | 1 | no | — |
| 53 | #13568 | — | 13 | 1 | no | maximal, Sylow |
| 54 | C13×#41 | — | 2 | 2 | no | — |
| 55 | C13×#41 | — | 2 | 2 | no | — |
| 56 | C13×#41 | — | 4 | 1 | no | — |
| 57 | C13×#41 | — | 4 | 2 | no | — |
| 58 | C13×#41 | — | 4 | 1 | no | — |
| 59 | C13×#41 | — | 4 | 1 | no | — |
| 60 | C13×#41 | — | 4 | 2 | no | — |
| 61 | C13×#41 | — | 4 | 2 | no | — |
| 62 | C13×#41 | — | 4 | 4 | no | — |
| 63 | C13×#41 | — | 4 | 2 | no | — |
| 64 | C13×#41 | — | 4 | 1 | no | — |
| 65 | C13×#41 | — | 4 | 2 | no | — |
| 66 | C2×Q8×C13 | — | 2 | 1 | no | — |
| 67 | C2×Q8×C13 | — | 4 | 2 | no | — |
| 68 | C2×Q8×C13 | — | 4 | 1 | no | — |
| 69 | C2×Q8×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 70 | C2×D4×C13 | — | 2 | 1 | no | — |
| 71 | C2×D4×C13 | — | 2 | 1 | no | — |
| 72 | C2×D4×C13 | — | 4 | 2 | no | — |
| 73 | C2×D4×C13 | — | 4 | 2 | no | — |
| 74 | C2×D4×C13 | — | 4 | 4 | no | — |
| 75 | C2×D4×C13 | — | 4 | 1 | no | — |
| 76 | C2×D4×C13 | — | 4 | 1 | no | — |
| 77 | C2×D4×C13 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 78 | C22×C4×C13 | — | 2 | 1 | no | — |
| 79 | C22×C4×C13 | — | 4 | 1 | no | — |
| 80 | C22×C4×C13 | — | 4 | 2 | no | — |
| 81 | C22×C4×C13 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 82 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 83 | C2×C22⋊D13 | — | 4 | 1 | no | — |
| 84 | C22×Dic13 | — | 2 | 1 | no | — |
| 85 | #6127 | — | 4 | 1 | no | — |
| 86 | #6127 | — | 4 | 1 | no | — |
| 87 | C2×D52 | C2×D4 | 1 | 1 | yes | characteristic |
| 88 | C2×C4×D13 | — | 2 | 1 | no | — |
| 89 | C2×Dic26 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 90 | C22⋊#261 | — | 4 | 2 | no | — |
| 91 | #6122 | — | 4 | 4 | no | — |
| 92 | C2×#1057 | — | 4 | 2 | no | — |
| 93 | C4⋊#261 | — | 8 | 1 | no | — |
| 94 | C4×#261 | — | 8 | 1 | no | — |
| 95 | C22⋊Dic13 | — | 4 | 1 | no | — |
| 96 | #6107 | — | 4 | 2 | no | — |
| 97 | #6106 | — | 4 | 2 | no | — |
| 98 | #6105 | — | 4 | 2 | no | — |
| 99 | #6104 | — | 4 | 2 | no | — |
| 100 | #6103 | — | 4 | 1 | no | — |
| 101 | #6101 | — | 4 | 1 | no | — |
| 102 | C4×Dic13 | — | 2 | 1 | no | — |
| 103 | C4×Dic13 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 104 | C4×Dic13 | C2×D4 | 1 | 1 | yes | characteristic |
| 105 | #6099 | — | 2 | 2 | no | — |
| 106 | #6099 | — | 4 | 1 | no | — |
| 107 | C2×#1055 | — | 4 | 1 | no | — |
| 108 | #3018 | — | 13 | 1 | no | — |
| 109 | #2126 | — | 13 | 1 | no | — |
| 110 | #1525 | — | 13 | 1 | no | — |
| 111 | #1404 | — | 13 | 4 | no | — |
| 112 | C23×C13 | — | 2 | 1 | no | — |
| 113 | C23×C13 | — | 4 | 1 | no | — |
| 114 | C23×C13 | — | 4 | 2 | no | — |
| 115 | C23×C13 | #99 | 1 | 1 | yes | characteristic |
| 116 | C22×D13 | — | 2 | 1 | no | — |
| 117 | C2×#261 | — | 8 | 2 | no | — |
| 118 | Q8×C13 | — | 2 | 2 | no | — |
| 119 | Q8×C13 | — | 4 | 1 | no | — |
| 120 | Q8×C13 | — | 4 | 1 | no | — |
| 121 | Q8×C13 | — | 4 | 2 | no | — |
| 122 | D4×C13 | — | 2 | 2 | no | — |
| 123 | D4×C13 | — | 4 | 1 | no | — |
| 124 | D4×C13 | — | 4 | 2 | no | — |
| 125 | D4×C13 | — | 4 | 2 | no | — |
| 126 | D4×C13 | — | 4 | 4 | no | — |
| 127 | D4×C13 | — | 4 | 2 | no | — |
| 128 | D4×C13 | — | 4 | 2 | no | — |
| 129 | D4×C13 | — | 4 | 1 | no | — |
| 130 | C2×C4×C13 | — | 2 | 1 | no | — |
| 131 | C2×C4×C13 | — | 2 | 1 | no | — |
| 132 | C2×C4×C13 | — | 2 | 1 | no | — |
| 133 | C2×C4×C13 | — | 4 | 2 | no | — |
| 134 | C2×C4×C13 | — | 4 | 1 | no | — |
| 135 | C2×C4×C13 | — | 4 | 4 | no | — |
| 136 | C2×C4×C13 | — | 4 | 2 | no | — |
| 137 | C2×C4×C13 | — | 4 | 1 | no | — |
| 138 | C2×C4×C13 | — | 4 | 1 | no | — |
| 139 | C2×C4×C13 | — | 4 | 2 | no | — |
| 140 | C2×C4×C13 | #99 | 1 | 1 | yes | characteristic |
| 141 | C2×C4×C13 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 142 | C22⋊D13 | — | 8 | 2 | no | — |
| 143 | C22⋊D13 | — | 8 | 1 | no | — |
| 144 | C2×Dic13 | — | 2 | 1 | no | — |
| 145 | C2×Dic13 | — | 2 | 1 | no | — |
| 146 | C2×Dic13 | — | 2 | 1 | no | — |
| 147 | C2×Dic13 | — | 4 | 2 | no | — |
| 148 | D52 | — | 4 | 1 | no | — |
| 149 | C4×D13 | — | 4 | 1 | no | — |
| 150 | C4×D13 | — | 4 | 1 | no | — |
| 151 | Dic26 | — | 4 | 1 | no | — |
| 152 | #1057 | — | 4 | 4 | no | — |
| 153 | #1055 | — | 4 | 2 | no | — |
| 154 | #585 | #261 | 1 | 1 | yes | characteristic, complemented |
| 155 | #575 | — | 26 | 1 | no | — |
| 156 | #532 | — | 13 | 1 | no | — |
| 157 | #456 | — | 13 | 2 | no | — |
| 158 | #455 | — | 26 | 1 | no | — |
| 159 | #454 | — | 13 | 2 | no | — |
| 160 | #453 | — | 26 | 1 | no | — |
| 161 | C2×#104 | — | 26 | 1 | no | — |
| 162 | #413 | — | 13 | 1 | no | — |
| 163 | #410 | — | 26 | 1 | no | — |
| 164 | C4×M16 | — | 26 | 1 | no | — |
| 165 | #354 | — | 13 | 2 | no | — |
| 166 | #353 | — | 26 | 1 | no | — |
| 167 | #329 | — | 13 | 2 | no | — |
| 168 | #329 | — | 26 | 1 | no | — |
| 169 | C22×C13 | — | 2 | 1 | no | — |
| 170 | C22×C13 | — | 4 | 1 | no | — |
| 171 | C22×C13 | — | 4 | 2 | no | — |
| 172 | C22×C13 | — | 4 | 1 | no | — |
| 173 | C22×C13 | — | 8 | 1 | no | — |
| 174 | C22×C13 | — | 16 | 1 | no | — |
| 175 | C22×C13 | — | 16 | 2 | no | — |
| 176 | C22×C13 | C2×#99 | 1 | 1 | yes | characteristic |
| 177 | C2×D13 | — | 4 | 1 | no | — |
| 178 | C2×D13 | — | 8 | 1 | no | — |
| 179 | #261 | — | 16 | 2 | no | — |
| 180 | C4×C13 | — | 2 | 1 | no | — |
| 181 | C4×C13 | — | 4 | 1 | no | — |
| 182 | C4×C13 | — | 4 | 2 | no | — |
| 183 | C4×C13 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 184 | C4×C13 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 185 | Dic13 | — | 2 | 2 | no | — |
| 186 | Dic13 | — | 4 | 1 | no | — |
| 187 | Dic13 | — | 4 | 1 | no | — |
| 188 | 2−1+4 | — | 4 | 1 | no | — |
| 189 | 2−1+4 | C2×#261 | 1 | 2 | yes | — |
| 190 | H(5,𝔽2) | — | 2 | 1 | no | — |
| 191 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 192 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 193 | C2×#41 | — | 2 | 1 | no | — |
| 194 | C2×#41 | — | 4 | 1 | no | — |
| 195 | C2×#41 | — | 4 | 2 | no | — |
| 196 | C2×#41 | — | 13 | 1 | no | — |
| 197 | C2×#41 | C2×#261 | 1 | 1 | yes | characteristic |
| 198 | #137 | — | 26 | 2 | no | — |
| 199 | #137 | — | 52 | 1 | no | — |
| 200 | AGL(1,ℤ/8) | — | 26 | 2 | no | — |
| 201 | AGL(1,ℤ/8) | — | 52 | 1 | no | — |
| 202 | #135 | — | 52 | 2 | no | — |
| 203 | C2×M16 | — | 26 | 1 | no | — |
| 204 | C2×M16 | — | 52 | 1 | no | — |
| 205 | C4⋊Q8 | — | 13 | 1 | no | — |
| 206 | #127 | — | 13 | 1 | no | — |
| 207 | #124 | — | 13 | 1 | no | — |
| 208 | #124 | — | 13 | 1 | no | — |
| 209 | #121 | — | 52 | 1 | no | — |
| 210 | C4×D4 | — | 52 | 1 | no | — |
| 211 | #117 | — | 52 | 1 | no | — |
| 212 | C2×C42 | — | 13 | 1 | no | — |
| 213 | #104 | — | 26 | 2 | no | — |
| 214 | #104 | — | 26 | 2 | no | — |
| 215 | #101 | — | 13 | 2 | no | — |
| 216 | #100 | — | 26 | 1 | no | — |
| 217 | #99 | — | 26 | 2 | no | — |
| 218 | #99 | — | 52 | 1 | no | — |
| 219 | #97 | — | 26 | 2 | no | — |
| 220 | C4×C8 | — | 52 | 1 | no | — |
| 221 | C2×C13 | — | 2 | 1 | no | — |
| 222 | C2×C13 | — | 4 | 1 | no | — |
| 223 | C2×C13 | — | 8 | 1 | no | — |
| 224 | C2×C13 | — | 8 | 2 | no | — |
| 225 | C2×C13 | C2×AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 226 | D13 | — | 8 | 1 | no | — |
| 227 | #41 | — | 2 | 2 | no | — |
| 228 | #41 | — | 2 | 2 | no | — |
| 229 | #41 | — | 4 | 1 | no | — |
| 230 | #41 | — | 4 | 2 | no | — |
| 231 | #41 | — | 4 | 1 | no | — |
| 232 | #41 | — | 4 | 1 | no | — |
| 233 | #41 | — | 4 | 2 | no | — |
| 234 | #41 | — | 4 | 2 | no | — |
| 235 | #41 | — | 4 | 4 | no | — |
| 236 | #41 | — | 4 | 2 | no | — |
| 237 | #41 | — | 4 | 1 | no | — |
| 238 | #41 | — | 4 | 2 | no | — |
| 239 | #41 | — | 52 | 1 | no | — |
| 240 | #41 | — | 52 | 1 | no | — |
| 241 | C2×Q8 | — | 2 | 1 | no | — |
| 242 | C2×Q8 | — | 4 | 2 | no | — |
| 243 | C2×Q8 | — | 4 | 1 | no | — |
| 244 | C2×Q8 | — | 13 | 1 | no | — |
| 245 | C2×Q8 | C22×#261 | 1 | 1 | yes | characteristic |
| 246 | C2×D4 | — | 2 | 1 | no | — |
| 247 | C2×D4 | — | 2 | 1 | no | — |
| 248 | C2×D4 | — | 4 | 2 | no | — |
| 249 | C2×D4 | — | 4 | 2 | no | — |
| 250 | C2×D4 | — | 4 | 4 | no | — |
| 251 | C2×D4 | — | 4 | 1 | no | — |
| 252 | C2×D4 | — | 4 | 1 | no | — |
| 253 | C2×D4 | — | 13 | 1 | no | — |
| 254 | C2×D4 | — | 26 | 1 | no | — |
| 255 | C2×D4 | — | 52 | 1 | no | — |
| 256 | C2×D4 | C22⋊#261 | 1 | 1 | yes | characteristic |
| 257 | C22×C4 | — | 2 | 1 | no | — |
| 258 | C22×C4 | — | 4 | 1 | no | — |
| 259 | C22×C4 | — | 4 | 2 | no | — |
| 260 | C22×C4 | — | 26 | 1 | no | — |
| 261 | C22×C4 | — | 26 | 1 | no | — |
| 262 | C22×C4 | C22⋊#261 | 1 | 1 | yes | characteristic |
| 263 | Q16 | — | 52 | 2 | no | — |
| 264 | SD16 | — | 52 | 2 | no | — |
| 265 | SD16 | — | 52 | 2 | no | — |
| 266 | D8 | — | 52 | 2 | no | — |
| 267 | M16 | — | 26 | 2 | no | — |
| 268 | M16 | — | 52 | 1 | no | — |
| 269 | M16 | — | 52 | 4 | no | — |
| 270 | C2×C8 | — | 52 | 1 | no | — |
| 271 | C2×C8 | — | 52 | 2 | no | — |
| 272 | C4⋊C4 | — | 52 | 1 | no | — |
| 273 | C4⋊C4 | — | 104 | 1 | no | — |
| 274 | C22⋊C4 | — | 52 | 1 | no | — |
| 275 | C22⋊C4 | — | 52 | 1 | no | — |
| 276 | C22⋊C4 | — | 52 | 2 | no | — |
| 277 | C42 | — | 13 | 1 | no | — |
| 278 | C42 | — | 13 | 1 | no | — |
| 279 | C42 | — | 26 | 1 | no | — |
| 280 | C42 | — | 104 | 1 | no | — |
| 281 | C13 | #13568 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 282 | C23 | — | 2 | 1 | no | — |
| 283 | C23 | — | 4 | 1 | no | — |
| 284 | C23 | — | 4 | 2 | no | — |
| 285 | C23 | — | 26 | 1 | no | — |
| 286 | C23 | #88119 | 1 | 1 | yes | characteristic |
| 287 | Q8 | — | 2 | 2 | no | — |
| 288 | Q8 | — | 4 | 1 | no | — |
| 289 | Q8 | — | 4 | 2 | no | — |
| 290 | Q8 | — | 4 | 1 | no | — |
| 291 | Q8 | — | 52 | 1 | no | — |
| 292 | D4 | — | 2 | 2 | no | — |
| 293 | D4 | — | 4 | 1 | no | — |
| 294 | D4 | — | 4 | 2 | no | — |
| 295 | D4 | — | 4 | 2 | no | — |
| 296 | D4 | — | 4 | 2 | no | — |
| 297 | D4 | — | 4 | 4 | no | — |
| 298 | D4 | — | 4 | 2 | no | — |
| 299 | D4 | — | 4 | 1 | no | — |
| 300 | D4 | — | 52 | 1 | no | — |
| 301 | D4 | — | 104 | 2 | no | — |
| 302 | D4 | — | 104 | 1 | no | — |
| 303 | C2×C4 | — | 2 | 1 | no | — |
| 304 | C2×C4 | — | 2 | 1 | no | — |
| 305 | C2×C4 | — | 2 | 1 | no | — |
| 306 | C2×C4 | — | 4 | 2 | no | — |
| 307 | C2×C4 | — | 4 | 1 | no | — |
| 308 | C2×C4 | — | 4 | 4 | no | — |
| 309 | C2×C4 | — | 4 | 2 | no | — |
| 310 | C2×C4 | — | 4 | 1 | no | — |
| 311 | C2×C4 | — | 4 | 1 | no | — |
| 312 | C2×C4 | — | 4 | 2 | no | — |
| 313 | C2×C4 | — | 26 | 1 | no | — |
| 314 | C2×C4 | — | 26 | 1 | no | — |
| 315 | C2×C4 | — | 26 | 1 | no | — |
| 316 | C2×C4 | — | 52 | 2 | no | — |
| 317 | C2×C4 | — | 52 | 1 | no | — |
| 318 | C2×C4 | — | 52 | 1 | no | — |
| 319 | C2×C4 | — | 104 | 2 | no | — |
| 320 | C2×C4 | #88119 | 1 | 1 | yes | characteristic |
| 321 | C2×C4 | C2×C22⋊#261 | 1 | 1 | yes | characteristic |
| 322 | C8 | — | 52 | 2 | no | — |
| 323 | C8 | — | 52 | 4 | no | — |
| 324 | C22 | — | 2 | 1 | no | — |
| 325 | C22 | — | 4 | 1 | no | — |
| 326 | C22 | — | 4 | 2 | no | — |
| 327 | C22 | — | 4 | 1 | no | — |
| 328 | C22 | — | 8 | 1 | no | — |
| 329 | C22 | — | 16 | 1 | no | — |
| 330 | C22 | — | 16 | 2 | no | — |
| 331 | C22 | — | 52 | 1 | no | — |
| 332 | C22 | — | 104 | 1 | no | — |
| 333 | C22 | C2×#88119 | 1 | 1 | yes | characteristic |
| 334 | C4 | — | 2 | 1 | no | — |
| 335 | C4 | — | 4 | 1 | no | — |
| 336 | C4 | — | 4 | 2 | no | — |
| 337 | C4 | — | 26 | 2 | no | — |
| 338 | C4 | — | 52 | 1 | no | — |
| 339 | C4 | — | 52 | 1 | no | — |
| 340 | C4 | — | 208 | 2 | no | — |
| 341 | C4 | #11718306 | 1 | 1 | yes | characteristic |
| 342 | C4 | #11718306 | 1 | 1 | yes | characteristic |
| 343 | C2 | — | 2 | 1 | no | — |
| 344 | C2 | — | 4 | 1 | no | — |
| 345 | C2 | — | 8 | 1 | no | — |
| 346 | C2 | — | 8 | 2 | no | — |
| 347 | C2 | — | 104 | 1 | no | — |
| 348 | C2 | C2×#11718306 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13131107 | C2 | semidirect |
| 2. #13130290 | C2 | semidirect |
| 3. #13129959 | C2 | semidirect |
| 5. C13×#585 | C4 | semidirect |
| 10. #11718907 | C4 | semidirect |
| 14. #11718898 | C4 | semidirect |
| 16. #11718300 | C22 | semidirect |
| 17. #11718299 | C22 | semidirect |
| 154. #585 | #261 | semidirect |
| 281. C13 | #13568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13131107 | 2 |
| #13130290 | 2 |
| #13129959 | 2 |
| #13124185 | 2 |
| #13568 | 13 |