Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
340 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 53 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 | #13126226 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13116789 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13116786 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #13116124 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #13112829 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13112786 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C13×#1342 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11719453 | C22 | 1 | 1 | yes | characteristic |
| 9 | #11719327 | — | 2 | 1 | no | — |
| 10 | C13×#470 | C22 | 1 | 1 | yes | characteristic |
| 11 | #11718843 | — | 2 | 1 | no | — |
| 12 | #11718840 | — | 2 | 1 | no | — |
| 13 | C2×#88065 | — | 2 | 1 | no | — |
| 14 | #11718798 | C22 | 1 | 1 | yes | characteristic |
| 15 | #11718793 | — | 2 | 1 | no | — |
| 16 | #11718779 | C22 | 1 | 1 | yes | characteristic |
| 17 | #11718713 | — | 2 | 1 | no | — |
| 18 | #11718570 | — | 2 | 1 | no | — |
| 19 | #11718515 | — | 2 | 1 | no | — |
| 20 | #11718454 | — | 2 | 1 | no | — |
| 21 | #11718452 | — | 2 | 1 | no | — |
| 22 | C13×#349 | C22 | 1 | 1 | yes | characteristic |
| 23 | C13×#338 | C22 | 1 | 1 | yes | characteristic |
| 24 | #11718145 | C22 | 1 | 1 | yes | characteristic |
| 25 | #11718110 | — | 2 | 1 | no | — |
| 26 | #11718080 | — | 2 | 1 | no | — |
| 27 | C2×#6127 | — | 2 | 1 | no | — |
| 28 | C2×C13×Q16 | D4 | 1 | 1 | yes | characteristic |
| 29 | C2×C13×M16 | — | 2 | 1 | no | — |
| 30 | C2×C13×M16 | C23 | 1 | 1 | yes | characteristic |
| 31 | C13×C22⋊Q8 | — | 2 | 1 | no | — |
| 32 | Q8×Dic13 | — | 2 | 1 | no | — |
| 33 | #88198 | — | 2 | 1 | no | — |
| 34 | C2×#6107 | — | 2 | 1 | no | — |
| 35 | #88178 | — | 2 | 1 | no | — |
| 36 | C2×C4×Dic13 | D4 | 1 | 1 | yes | characteristic |
| 37 | C2×#6099 | D4 | 1 | 1 | yes | characteristic |
| 38 | #88163 | — | 4 | 1 | no | — |
| 39 | #88162 | — | 4 | 1 | no | — |
| 40 | C2×Dic52 | D4 | 1 | 1 | yes | characteristic |
| 41 | #88158 | — | 2 | 1 | no | — |
| 42 | #88158 | — | 2 | 1 | no | — |
| 43 | #88143 | — | 4 | 1 | no | — |
| 44 | #88142 | — | 2 | 1 | no | — |
| 45 | #88141 | — | 2 | 1 | no | — |
| 46 | #88141 | — | 4 | 1 | no | — |
| 47 | #88132 | — | 4 | 1 | no | — |
| 48 | #88131 | — | 4 | 1 | no | — |
| 49 | C13×M32 | — | 2 | 1 | no | — |
| 50 | C13×#106 | D4 | 1 | 1 | yes | characteristic |
| 51 | C13×#103 | — | 2 | 1 | no | — |
| 52 | #88075 | — | 2 | 1 | no | — |
| 53 | #88069 | — | 4 | 1 | no | — |
| 54 | #88068 | — | 4 | 1 | no | — |
| 55 | #88065 | — | 4 | 1 | no | — |
| 56 | #88065 | — | 4 | 1 | no | — |
| 57 | #88064 | — | 4 | 1 | no | — |
| 58 | #88063 | — | 4 | 1 | no | — |
| 59 | #88057 | D4 | 1 | 1 | yes | characteristic |
| 60 | #88056 | — | 2 | 1 | no | — |
| 61 | #88054 | — | 2 | 1 | no | — |
| 62 | #88054 | — | 2 | 1 | no | — |
| 63 | #88052 | — | 2 | 1 | no | — |
| 64 | #88050 | — | 2 | 1 | no | — |
| 65 | #88048 | — | 2 | 1 | no | — |
| 66 | Dic104 | — | 4 | 1 | no | — |
| 67 | #88040 | — | 4 | 1 | no | — |
| 68 | #12174 | — | 13 | 1 | no | maximal, Sylow |
| 69 | C2×Q8×C13 | — | 2 | 1 | no | — |
| 70 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 71 | C2×C22⋊D13 | — | 4 | 1 | no | — |
| 72 | C22×Dic13 | — | 2 | 1 | no | — |
| 73 | #6127 | — | 4 | 1 | no | — |
| 74 | #6127 | — | 4 | 1 | no | — |
| 75 | #6127 | — | 4 | 1 | no | — |
| 76 | #6127 | — | 4 | 1 | no | — |
| 77 | C2×D52 | — | 2 | 1 | no | — |
| 78 | C2×C4×D13 | — | 4 | 1 | no | — |
| 79 | C2×Dic26 | — | 2 | 1 | no | — |
| 80 | C2×Dic26 | — | 2 | 1 | no | — |
| 81 | C2×Dic26 | — | 4 | 1 | no | — |
| 82 | C13×Q16 | — | 4 | 1 | no | — |
| 83 | C13×M16 | — | 4 | 1 | no | — |
| 84 | C13×M16 | — | 4 | 1 | no | — |
| 85 | C13×M16 | — | 4 | 1 | no | — |
| 86 | C2×C8×C13 | — | 4 | 1 | no | — |
| 87 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 88 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 89 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 90 | C13×C4⋊C4 | — | 4 | 1 | no | — |
| 91 | C13×C22⋊C4 | — | 4 | 1 | no | — |
| 92 | C22⋊Dic13 | — | 4 | 1 | no | — |
| 93 | #6107 | — | 8 | 1 | no | — |
| 94 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 95 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 96 | #6101 | — | 4 | 1 | no | — |
| 97 | #6101 | — | 4 | 1 | no | — |
| 98 | #6101 | — | 4 | 1 | no | — |
| 99 | #6101 | — | 4 | 1 | no | — |
| 100 | #6101 | — | 4 | 1 | no | — |
| 101 | C4×Dic13 | — | 2 | 1 | no | — |
| 102 | C4×Dic13 | — | 4 | 1 | no | — |
| 103 | C4×Dic13 | — | 4 | 1 | no | — |
| 104 | C4×Dic13 | D8 | 1 | 1 | yes | characteristic |
| 105 | C4×Dic13 | D8 | 1 | 1 | yes | characteristic |
| 106 | #6099 | — | 4 | 1 | no | — |
| 107 | C2×#1055 | — | 2 | 1 | no | — |
| 108 | Dic52 | — | 2 | 1 | no | — |
| 109 | Dic52 | — | 2 | 1 | no | — |
| 110 | Dic52 | — | 4 | 1 | no | — |
| 111 | D104 | — | 2 | 1 | no | — |
| 112 | D104 | — | 2 | 1 | no | — |
| 113 | #6095 | — | 4 | 1 | no | — |
| 114 | #6095 | — | 4 | 1 | no | — |
| 115 | C13×C16 | — | 4 | 1 | no | — |
| 116 | #6090 | — | 4 | 1 | no | — |
| 117 | #3255 | — | 13 | 1 | no | — |
| 118 | #2191 | — | 13 | 1 | no | — |
| 119 | #2191 | — | 13 | 1 | no | — |
| 120 | #2050 | — | 13 | 1 | no | — |
| 121 | #1342 | — | 13 | 1 | no | — |
| 122 | #1342 | D13 | 1 | 1 | yes | characteristic, complemented |
| 123 | #1327 | — | 13 | 1 | no | — |
| 124 | C23×C13 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 125 | C22×D13 | — | 4 | 1 | no | — |
| 126 | Q8×C13 | — | 4 | 1 | no | — |
| 127 | Q8×C13 | — | 4 | 1 | no | — |
| 128 | C2×C4×C13 | — | 2 | 1 | no | — |
| 129 | C2×C4×C13 | — | 2 | 1 | no | — |
| 130 | C2×C4×C13 | — | 4 | 1 | no | — |
| 131 | C2×C4×C13 | — | 4 | 1 | no | — |
| 132 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 133 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 134 | C22⋊D13 | — | 8 | 1 | no | — |
| 135 | C22⋊D13 | — | 8 | 1 | no | — |
| 136 | C2×Dic13 | — | 2 | 1 | no | — |
| 137 | C2×Dic13 | — | 2 | 1 | no | — |
| 138 | C2×Dic13 | — | 4 | 2 | no | — |
| 139 | C2×Dic13 | — | 4 | 1 | no | — |
| 140 | C2×Dic13 | — | 4 | 1 | no | — |
| 141 | C2×Dic13 | — | 4 | 1 | no | — |
| 142 | D52 | — | 4 | 1 | no | — |
| 143 | D52 | — | 4 | 1 | no | — |
| 144 | C4×D13 | — | 8 | 1 | no | — |
| 145 | C4×D13 | — | 8 | 1 | no | — |
| 146 | Dic26 | — | 4 | 1 | no | — |
| 147 | Dic26 | — | 4 | 1 | no | — |
| 148 | Dic26 | — | 4 | 1 | no | — |
| 149 | Dic26 | — | 4 | 1 | no | — |
| 150 | Dic26 | — | 8 | 2 | no | — |
| 151 | C8×C13 | — | 2 | 1 | no | — |
| 152 | C8×C13 | — | 2 | 1 | no | — |
| 153 | C8×C13 | — | 8 | 1 | no | — |
| 154 | #1055 | — | 4 | 1 | no | — |
| 155 | #575 | — | 13 | 1 | no | — |
| 156 | #533 | — | 26 | 1 | no | — |
| 157 | #510 | — | 26 | 1 | no | — |
| 158 | #510 | — | 26 | 1 | no | — |
| 159 | #475 | — | 26 | 1 | no | — |
| 160 | #475 | — | 26 | 1 | no | — |
| 161 | #470 | — | 13 | 1 | no | — |
| 162 | #470 | — | 26 | 1 | no | — |
| 163 | #470 | C2×D13 | 1 | 1 | yes | characteristic |
| 164 | #462 | — | 26 | 1 | no | — |
| 165 | #462 | — | 26 | 1 | no | — |
| 166 | #423 | — | 13 | 1 | no | — |
| 167 | C2×#104 | — | 26 | 1 | no | — |
| 168 | #413 | — | 26 | 1 | no | — |
| 169 | #360 | — | 26 | 1 | no | — |
| 170 | #360 | — | 26 | 1 | no | — |
| 171 | #349 | — | 13 | 1 | no | — |
| 172 | #349 | C2×D13 | 1 | 1 | yes | characteristic |
| 173 | #338 | C2×D13 | 1 | 1 | yes | characteristic |
| 174 | C22×C13 | — | 2 | 1 | no | — |
| 175 | C22×C13 | — | 4 | 1 | no | — |
| 176 | C22×C13 | #447 | 1 | 1 | yes | characteristic |
| 177 | C2×D13 | — | 8 | 1 | no | — |
| 178 | C2×D13 | — | 16 | 1 | no | — |
| 179 | C4×C13 | — | 2 | 1 | no | — |
| 180 | C4×C13 | — | 8 | 1 | no | — |
| 181 | C4×C13 | — | 8 | 1 | no | — |
| 182 | C4×C13 | #454 | 1 | 1 | yes | characteristic |
| 183 | C4×C13 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 184 | Dic13 | — | 2 | 2 | no | — |
| 185 | Dic13 | — | 4 | 1 | no | — |
| 186 | Dic13 | — | 8 | 1 | no | — |
| 187 | Dic13 | — | 8 | 1 | no | — |
| 188 | Dic13 | — | 8 | 1 | no | — |
| 189 | C2×#41 | — | 26 | 1 | no | — |
| 190 | #137 | — | 52 | 1 | no | — |
| 191 | AGL(1,ℤ/8) | — | 52 | 1 | no | — |
| 192 | #135 | — | 26 | 1 | no | — |
| 193 | #135 | — | 26 | 1 | no | — |
| 194 | C2×Q16 | — | 13 | 1 | no | — |
| 195 | C2×Q16 | — | 26 | 1 | no | — |
| 196 | C2×Q16 | D52 | 1 | 1 | yes | characteristic |
| 197 | C2×M16 | — | 2 | 1 | no | — |
| 198 | C2×M16 | — | 13 | 1 | no | — |
| 199 | C2×M16 | C22×D13 | 1 | 1 | yes | characteristic |
| 200 | C4⋊Q8 | — | 26 | 1 | no | — |
| 201 | C4⋊Q8 | — | 26 | 1 | no | — |
| 202 | #125 | — | 52 | 1 | no | — |
| 203 | C22⋊Q8 | — | 2 | 1 | no | — |
| 204 | C22⋊Q8 | — | 26 | 1 | no | — |
| 205 | C22⋊Q8 | — | 52 | 1 | no | — |
| 206 | C4×Q8 | — | 26 | 1 | no | — |
| 207 | C4×Q8 | — | 26 | 1 | no | — |
| 208 | C4×Q8 | — | 52 | 1 | no | — |
| 209 | #117 | — | 52 | 1 | no | — |
| 210 | C2×C42 | — | 13 | 1 | no | — |
| 211 | Q32 | — | 52 | 1 | no | — |
| 212 | Q32 | — | 52 | 1 | no | — |
| 213 | SD32 | — | 52 | 1 | no | — |
| 214 | SD32 | — | 52 | 1 | no | — |
| 215 | M32 | — | 2 | 1 | no | — |
| 216 | M32 | — | 26 | 1 | no | — |
| 217 | #106 | — | 13 | 1 | no | — |
| 218 | #106 | — | 26 | 1 | no | — |
| 219 | #106 | D52 | 1 | 1 | yes | characteristic |
| 220 | C4⋊C8 | — | 26 | 1 | no | — |
| 221 | C4⋊C8 | — | 26 | 1 | no | — |
| 222 | #104 | — | 52 | 1 | no | — |
| 223 | #104 | — | 52 | 1 | no | — |
| 224 | #103 | — | 2 | 1 | no | — |
| 225 | #103 | — | 26 | 1 | no | — |
| 226 | #103 | — | 26 | 1 | no | — |
| 227 | #103 | — | 26 | 1 | no | — |
| 228 | #101 | — | 52 | 1 | no | — |
| 229 | #100 | — | 52 | 1 | no | — |
| 230 | C2×C13 | — | 2 | 1 | no | — |
| 231 | C2×C13 | — | 4 | 1 | no | — |
| 232 | C2×C13 | #1598 | 1 | 1 | yes | characteristic |
| 233 | D13 | — | 16 | 1 | no | — |
| 234 | #41 | — | 52 | 1 | no | — |
| 235 | #41 | — | 52 | 1 | no | — |
| 236 | #41 | — | 52 | 1 | no | — |
| 237 | #41 | — | 52 | 1 | no | — |
| 238 | C2×Q8 | — | 2 | 1 | no | — |
| 239 | C2×Q8 | — | 26 | 1 | no | — |
| 240 | C2×Q8 | — | 26 | 1 | no | — |
| 241 | C2×Q8 | — | 52 | 1 | no | — |
| 242 | C2×D4 | — | 26 | 1 | no | — |
| 243 | C2×D4 | — | 52 | 1 | no | — |
| 244 | C22×C4 | — | 26 | 1 | no | — |
| 245 | C22×C4 | — | 52 | 1 | no | — |
| 246 | C22×C4 | D4×D13 | 1 | 1 | yes | characteristic |
| 247 | Q16 | — | 4 | 1 | no | — |
| 248 | Q16 | — | 26 | 1 | no | — |
| 249 | Q16 | — | 26 | 1 | no | — |
| 250 | Q16 | — | 52 | 1 | no | — |
| 251 | Q16 | — | 104 | 1 | no | — |
| 252 | SD16 | — | 52 | 1 | no | — |
| 253 | SD16 | — | 52 | 1 | no | — |
| 254 | D8 | — | 26 | 1 | no | — |
| 255 | D8 | — | 26 | 1 | no | — |
| 256 | M16 | — | 4 | 1 | no | — |
| 257 | M16 | — | 4 | 1 | no | — |
| 258 | M16 | — | 4 | 1 | no | — |
| 259 | M16 | — | 52 | 1 | no | — |
| 260 | C2×C8 | — | 4 | 1 | no | — |
| 261 | C2×C8 | — | 26 | 1 | no | — |
| 262 | C2×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 263 | C2×C8 | D4×D13 | 1 | 1 | yes | characteristic |
| 264 | C4⋊C4 | — | 2 | 1 | no | — |
| 265 | C4⋊C4 | — | 4 | 1 | no | — |
| 266 | C4⋊C4 | — | 26 | 1 | no | — |
| 267 | C4⋊C4 | — | 52 | 1 | no | — |
| 268 | C4⋊C4 | — | 52 | 1 | no | — |
| 269 | C4⋊C4 | — | 52 | 1 | no | — |
| 270 | C4⋊C4 | — | 52 | 1 | no | — |
| 271 | C4⋊C4 | — | 52 | 1 | no | — |
| 272 | C4⋊C4 | — | 52 | 1 | no | — |
| 273 | C22⋊C4 | — | 4 | 1 | no | — |
| 274 | C22⋊C4 | — | 52 | 1 | no | — |
| 275 | C42 | — | 13 | 1 | no | — |
| 276 | C42 | — | 13 | 1 | no | — |
| 277 | C42 | — | 26 | 1 | no | — |
| 278 | C42 | — | 52 | 1 | no | — |
| 279 | C42 | — | 52 | 1 | no | — |
| 280 | C16 | — | 4 | 1 | no | — |
| 281 | C16 | — | 52 | 1 | no | — |
| 282 | C13 | #12174 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 283 | C23 | — | 52 | 1 | no | — |
| 284 | C23 | #88168 | 1 | 1 | yes | characteristic |
| 285 | Q8 | — | 4 | 1 | no | — |
| 286 | Q8 | — | 4 | 1 | no | — |
| 287 | Q8 | — | 52 | 1 | no | — |
| 288 | Q8 | — | 52 | 1 | no | — |
| 289 | Q8 | — | 52 | 1 | no | — |
| 290 | Q8 | — | 52 | 1 | no | — |
| 291 | Q8 | — | 104 | 2 | no | — |
| 292 | D4 | — | 52 | 1 | no | — |
| 293 | D4 | — | 52 | 1 | no | — |
| 294 | D4 | — | 104 | 1 | no | — |
| 295 | D4 | — | 104 | 1 | no | — |
| 296 | C2×C4 | — | 2 | 1 | no | — |
| 297 | C2×C4 | — | 2 | 1 | no | — |
| 298 | C2×C4 | — | 4 | 1 | no | — |
| 299 | C2×C4 | — | 4 | 1 | no | — |
| 300 | C2×C4 | — | 26 | 1 | no | — |
| 301 | C2×C4 | — | 26 | 1 | no | — |
| 302 | C2×C4 | — | 52 | 2 | no | — |
| 303 | C2×C4 | — | 52 | 1 | no | — |
| 304 | C2×C4 | — | 52 | 1 | no | — |
| 305 | C2×C4 | — | 52 | 1 | no | — |
| 306 | C2×C4 | — | 104 | 1 | no | — |
| 307 | C2×C4 | — | 104 | 1 | no | — |
| 308 | C2×C4 | #88136 | 1 | 1 | yes | characteristic |
| 309 | C2×C4 | D8×D13 | 1 | 1 | yes | characteristic |
| 310 | C8 | — | 2 | 1 | no | — |
| 311 | C8 | — | 2 | 1 | no | — |
| 312 | C8 | — | 8 | 1 | no | — |
| 313 | C8 | — | 52 | 1 | no | — |
| 314 | C22 | — | 2 | 1 | no | — |
| 315 | C22 | — | 4 | 1 | no | — |
| 316 | C22 | — | 104 | 1 | no | — |
| 317 | C22 | — | 208 | 1 | no | — |
| 318 | C22 | #11718434 | 1 | 1 | yes | characteristic |
| 319 | C4 | — | 2 | 1 | no | — |
| 320 | C4 | — | 8 | 1 | no | — |
| 321 | C4 | — | 8 | 1 | no | — |
| 322 | C4 | — | 26 | 2 | no | — |
| 323 | C4 | — | 52 | 1 | no | — |
| 324 | C4 | — | 104 | 1 | no | — |
| 325 | C4 | — | 104 | 1 | no | — |
| 326 | C4 | — | 104 | 1 | no | — |
| 327 | C4 | #11718402 | 1 | 1 | yes | characteristic |
| 328 | C4 | #11718488 | 1 | 1 | yes | characteristic |
| 329 | C2 | — | 2 | 1 | no | — |
| 330 | C2 | — | 4 | 1 | no | — |
| 331 | C2 | — | 208 | 1 | no | — |
| 332 | C2 | #13113772 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13126226 | C2 | semidirect |
| 5. #13112829 | C2 | semidirect |
| 6. #13112786 | C2 | semidirect |
| 7. C13×#1342 | C2 | semidirect |
| 122. #1342 | D13 | semidirect |
| 282. C13 | #12174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13126226 | 2 |
| #13116789 | 2 |
| #13116786 | 2 |
| #13116124 | 2 |
| #13112829 | 2 |
| #13112786 | 2 |
| C13×#1342 | 2 |
| #12174 | 13 |