Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
322 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 322 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 | #13131129 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13131109 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13129983 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #13125237 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #11719182 | C22 | 1 | 1 | yes | characteristic |
| 6 | C2×#88124 | C4 | 1 | 1 | yes | characteristic, complemented |
| 7 | #11719132 | — | 2 | 1 | no | — |
| 8 | #11719116 | — | 2 | 1 | no | — |
| 9 | C4×C13×M16 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | #11718794 | — | 2 | 1 | no | — |
| 11 | #11718794 | — | 2 | 1 | no | — |
| 12 | #11718374 | — | 2 | 1 | no | — |
| 13 | #11718364 | — | 2 | 1 | no | — |
| 14 | #11718358 | C4 | 1 | 2 | yes | complemented |
| 15 | #11718358 | C22 | 1 | 2 | yes | — |
| 16 | #11718228 | C22 | 1 | 2 | yes | — |
| 17 | #11718227 | — | 2 | 1 | no | — |
| 18 | #11718226 | C22 | 1 | 2 | yes | — |
| 19 | #11718225 | — | 2 | 1 | no | — |
| 20 | C2×#6127 | D4 | 1 | 1 | yes | characteristic |
| 21 | C2×#6127 | D4 | 1 | 1 | yes | characteristic |
| 22 | #88237 | — | 4 | 1 | no | — |
| 23 | D13⋊M16 | — | 4 | 1 | no | — |
| 24 | C2×C13×M16 | — | 2 | 1 | no | — |
| 25 | C2×C42×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 26 | #88184 | — | 4 | 1 | no | — |
| 27 | C2×C4⋊Dic13 | — | 2 | 1 | no | — |
| 28 | C2×#6101 | — | 4 | 1 | no | — |
| 29 | #88129 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | #88129 | C23 | 1 | 1 | yes | characteristic |
| 31 | #88128 | D4 | 1 | 1 | yes | characteristic |
| 32 | C4×D52 | — | 4 | 1 | no | — |
| 33 | #88124 | — | 2 | 1 | no | — |
| 34 | #88124 | — | 4 | 1 | no | — |
| 35 | #88124 | C2×C4 | 1 | 2 | yes | — |
| 36 | #88123 | D4 | 1 | 1 | yes | characteristic |
| 37 | #88121 | — | 4 | 1 | no | — |
| 38 | #88119 | — | 4 | 1 | no | — |
| 39 | #88113 | — | 2 | 2 | no | — |
| 40 | #88107 | — | 2 | 2 | no | — |
| 41 | C13×#97 | — | 2 | 1 | no | — |
| 42 | C4×C8×C13 | C2×C4 | 1 | 2 | yes | — |
| 43 | #88061 | — | 2 | 2 | no | — |
| 44 | #88061 | — | 2 | 2 | no | — |
| 45 | #88056 | — | 2 | 2 | no | — |
| 46 | #88056 | — | 2 | 2 | no | — |
| 47 | #13604 | — | 13 | 1 | no | maximal, Sylow |
| 48 | C22×C4×C13 | — | 2 | 1 | no | — |
| 49 | C22×C4×C13 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 50 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 51 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 52 | C22×Dic13 | — | 4 | 1 | no | — |
| 53 | #6127 | — | 4 | 1 | no | — |
| 54 | #6127 | — | 4 | 1 | no | — |
| 55 | #6127 | — | 4 | 1 | no | — |
| 56 | #6127 | — | 4 | 1 | no | — |
| 57 | C2×D52 | — | 4 | 1 | no | — |
| 58 | C2×D52 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 59 | C2×D52 | C2×D4 | 1 | 1 | yes | characteristic |
| 60 | C2×C4×D13 | — | 2 | 1 | no | — |
| 61 | C2×C4×D13 | — | 2 | 1 | no | — |
| 62 | C2×Dic26 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 63 | C2×Dic26 | C2×D4 | 1 | 1 | yes | characteristic |
| 64 | C22⋊#261 | — | 4 | 2 | no | — |
| 65 | #6122 | — | 4 | 2 | no | — |
| 66 | C4⋊#261 | — | 8 | 1 | no | — |
| 67 | C4×#261 | — | 8 | 1 | no | — |
| 68 | #6118 | — | 8 | 1 | no | — |
| 69 | D13⋊C8 | — | 8 | 1 | no | — |
| 70 | C13×M16 | — | 4 | 1 | no | — |
| 71 | C13×M16 | — | 4 | 1 | no | — |
| 72 | C2×C8×C13 | — | 2 | 2 | no | — |
| 73 | C42×C13 | — | 2 | 1 | no | — |
| 74 | C42×C13 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 75 | C42×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 76 | #6103 | — | 4 | 1 | no | — |
| 77 | #6103 | — | 4 | 1 | no | — |
| 78 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 79 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 80 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 81 | #6101 | — | 4 | 2 | no | — |
| 82 | #6101 | — | 4 | 2 | no | — |
| 83 | #3142 | — | 13 | 1 | no | — |
| 84 | #2132 | — | 13 | 1 | no | — |
| 85 | #2126 | — | 13 | 1 | no | — |
| 86 | #1414 | — | 13 | 4 | no | — |
| 87 | C23×C13 | #99 | 1 | 1 | yes | characteristic |
| 88 | C22×D13 | — | 2 | 1 | no | — |
| 89 | C22×D13 | — | 2 | 1 | no | — |
| 90 | C2×#261 | — | 8 | 2 | no | — |
| 91 | C2×C4×C13 | — | 2 | 1 | no | — |
| 92 | C2×C4×C13 | — | 2 | 1 | no | — |
| 93 | C2×C4×C13 | — | 2 | 1 | no | — |
| 94 | C2×C4×C13 | — | 2 | 1 | no | — |
| 95 | C2×C4×C13 | — | 8 | 1 | no | — |
| 96 | C2×C4×C13 | #99 | 1 | 1 | yes | characteristic |
| 97 | C2×C4×C13 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 98 | C22⋊D13 | — | 8 | 1 | no | — |
| 99 | C22⋊D13 | — | 8 | 1 | no | — |
| 100 | C2×Dic13 | — | 2 | 1 | no | — |
| 101 | C2×Dic13 | — | 2 | 1 | no | — |
| 102 | C2×Dic13 | — | 4 | 2 | no | — |
| 103 | C2×Dic13 | — | 8 | 2 | no | — |
| 104 | D52 | — | 4 | 1 | no | — |
| 105 | D52 | — | 4 | 1 | no | — |
| 106 | D52 | — | 8 | 2 | no | — |
| 107 | C4×D13 | — | 4 | 1 | no | — |
| 108 | C4×D13 | — | 4 | 1 | no | — |
| 109 | C4×D13 | — | 4 | 1 | no | — |
| 110 | C4×D13 | — | 4 | 1 | no | — |
| 111 | Dic26 | — | 4 | 1 | no | — |
| 112 | Dic26 | — | 4 | 1 | no | — |
| 113 | #1057 | — | 8 | 2 | no | — |
| 114 | C8×C13 | — | 4 | 2 | no | — |
| 115 | #532 | — | 13 | 1 | no | — |
| 116 | C2×#125 | — | 13 | 1 | no | — |
| 117 | #491 | — | 26 | 1 | no | — |
| 118 | #490 | — | 26 | 1 | no | — |
| 119 | #488 | — | 13 | 2 | no | — |
| 120 | #488 | — | 13 | 2 | no | — |
| 121 | #417 | — | 26 | 1 | no | — |
| 122 | #417 | — | 26 | 1 | no | — |
| 123 | #413 | — | 26 | 1 | no | — |
| 124 | #410 | — | 26 | 1 | no | — |
| 125 | C4×M16 | #261 | 1 | 1 | yes | characteristic, complemented |
| 126 | #356 | — | 26 | 1 | no | — |
| 127 | #355 | — | 13 | 2 | no | — |
| 128 | #354 | — | 13 | 2 | no | — |
| 129 | #353 | — | 26 | 1 | no | — |
| 130 | C22×C13 | — | 2 | 1 | no | — |
| 131 | C22×C13 | — | 4 | 1 | no | — |
| 132 | C22×C13 | C2×#99 | 1 | 1 | yes | characteristic |
| 133 | C2×D13 | — | 4 | 1 | no | — |
| 134 | C2×D13 | — | 4 | 1 | no | — |
| 135 | C2×D13 | — | 8 | 1 | no | — |
| 136 | C2×D13 | — | 8 | 1 | no | — |
| 137 | #261 | — | 16 | 2 | no | — |
| 138 | C4×C13 | — | 2 | 1 | no | — |
| 139 | C4×C13 | — | 4 | 1 | no | — |
| 140 | C4×C13 | — | 4 | 1 | no | — |
| 141 | C4×C13 | #354 | 1 | 1 | yes | characteristic |
| 142 | C4×C13 | #354 | 1 | 1 | yes | characteristic |
| 143 | Dic13 | — | 4 | 1 | no | — |
| 144 | Dic13 | — | 4 | 1 | no | — |
| 145 | Dic13 | — | 8 | 2 | no | — |
| 146 | C2×#41 | — | 13 | 1 | no | — |
| 147 | C2×#41 | — | 13 | 1 | no | — |
| 148 | C2×M16 | — | 2 | 1 | no | — |
| 149 | C2×M16 | — | 52 | 1 | no | — |
| 150 | C4⋊Q8 | — | 13 | 1 | no | — |
| 151 | #127 | — | 13 | 1 | no | — |
| 152 | #125 | — | 13 | 2 | no | — |
| 153 | #125 | — | 26 | 1 | no | — |
| 154 | #125 | — | 52 | 1 | no | — |
| 155 | #124 | — | 13 | 1 | no | — |
| 156 | #124 | — | 13 | 1 | no | — |
| 157 | #121 | — | 52 | 1 | no | — |
| 158 | C4×D4 | — | 52 | 1 | no | — |
| 159 | #117 | — | 52 | 1 | no | — |
| 160 | C2×C4⋊C4 | — | 26 | 1 | no | — |
| 161 | C2×C4⋊C4 | — | 52 | 1 | no | — |
| 162 | C2×C42 | C2×#261 | 1 | 1 | yes | characteristic |
| 163 | #103 | — | 26 | 2 | no | — |
| 164 | #103 | — | 26 | 2 | no | — |
| 165 | #102 | — | 26 | 2 | no | — |
| 166 | #102 | — | 26 | 2 | no | — |
| 167 | #101 | — | 26 | 2 | no | — |
| 168 | #100 | — | 52 | 1 | no | — |
| 169 | #99 | — | 26 | 2 | no | — |
| 170 | #99 | — | 52 | 1 | no | — |
| 171 | #97 | — | 2 | 1 | no | — |
| 172 | C4×C8 | C2×#261 | 1 | 2 | yes | — |
| 173 | C2×C13 | — | 2 | 1 | no | — |
| 174 | C2×C13 | — | 4 | 1 | no | — |
| 175 | C2×C13 | C2×#354 | 1 | 1 | yes | characteristic |
| 176 | D13 | — | 8 | 1 | no | — |
| 177 | D13 | — | 8 | 1 | no | — |
| 178 | #41 | — | 52 | 1 | no | — |
| 179 | #41 | — | 52 | 1 | no | — |
| 180 | #41 | — | 52 | 1 | no | — |
| 181 | #41 | — | 52 | 1 | no | — |
| 182 | C2×Q8 | — | 13 | 1 | no | — |
| 183 | C2×Q8 | — | 13 | 1 | no | — |
| 184 | C2×D4 | — | 13 | 1 | no | — |
| 185 | C2×D4 | — | 13 | 1 | no | — |
| 186 | C2×D4 | — | 26 | 1 | no | — |
| 187 | C2×D4 | — | 26 | 1 | no | — |
| 188 | C2×D4 | — | 52 | 1 | no | — |
| 189 | C22×C4 | — | 2 | 1 | no | — |
| 190 | C22×C4 | — | 26 | 1 | no | — |
| 191 | C22×C4 | — | 26 | 1 | no | — |
| 192 | C22×C4 | — | 52 | 1 | no | — |
| 193 | C22×C4 | C22⋊#261 | 1 | 1 | yes | characteristic |
| 194 | M16 | — | 4 | 1 | no | — |
| 195 | M16 | — | 4 | 1 | no | — |
| 196 | M16 | — | 52 | 2 | no | — |
| 197 | M16 | — | 104 | 1 | no | — |
| 198 | C2×C8 | — | 2 | 2 | no | — |
| 199 | C2×C8 | — | 104 | 1 | no | — |
| 200 | C4⋊C4 | — | 26 | 2 | no | — |
| 201 | C4⋊C4 | — | 52 | 1 | no | — |
| 202 | C4⋊C4 | — | 52 | 2 | no | — |
| 203 | C4⋊C4 | — | 52 | 2 | no | — |
| 204 | C4⋊C4 | — | 52 | 1 | no | — |
| 205 | C4⋊C4 | — | 104 | 1 | no | — |
| 206 | C22⋊C4 | — | 52 | 1 | no | — |
| 207 | C22⋊C4 | — | 52 | 1 | no | — |
| 208 | C22⋊C4 | — | 52 | 2 | no | — |
| 209 | C42 | — | 2 | 1 | no | — |
| 210 | C42 | — | 104 | 1 | no | — |
| 211 | C42 | C22⋊#261 | 1 | 1 | yes | characteristic |
| 212 | C42 | C22×#261 | 1 | 1 | yes | characteristic |
| 213 | C13 | #13604 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 214 | C23 | — | 26 | 1 | no | — |
| 215 | C23 | — | 26 | 1 | no | — |
| 216 | C23 | #88107 | 1 | 1 | yes | characteristic |
| 217 | Q8 | — | 52 | 1 | no | — |
| 218 | Q8 | — | 52 | 1 | no | — |
| 219 | D4 | — | 52 | 1 | no | — |
| 220 | D4 | — | 52 | 1 | no | — |
| 221 | D4 | — | 104 | 2 | no | — |
| 222 | D4 | — | 104 | 1 | no | — |
| 223 | D4 | — | 104 | 1 | no | — |
| 224 | C2×C4 | — | 2 | 1 | no | — |
| 225 | C2×C4 | — | 2 | 1 | no | — |
| 226 | C2×C4 | — | 2 | 1 | no | — |
| 227 | C2×C4 | — | 2 | 1 | no | — |
| 228 | C2×C4 | — | 8 | 1 | no | — |
| 229 | C2×C4 | — | 26 | 1 | no | — |
| 230 | C2×C4 | — | 26 | 1 | no | — |
| 231 | C2×C4 | — | 52 | 1 | no | — |
| 232 | C2×C4 | — | 52 | 1 | no | — |
| 233 | C2×C4 | — | 52 | 1 | no | — |
| 234 | C2×C4 | — | 52 | 1 | no | — |
| 235 | C2×C4 | — | 52 | 2 | no | — |
| 236 | C2×C4 | — | 104 | 2 | no | — |
| 237 | C2×C4 | — | 104 | 2 | no | — |
| 238 | C2×C4 | #88107 | 1 | 1 | yes | characteristic |
| 239 | C2×C4 | C2×C22⋊#261 | 1 | 1 | yes | characteristic |
| 240 | C8 | — | 4 | 2 | no | — |
| 241 | C8 | — | 104 | 2 | no | — |
| 242 | C22 | — | 2 | 1 | no | — |
| 243 | C22 | — | 4 | 1 | no | — |
| 244 | C22 | — | 52 | 1 | no | — |
| 245 | C22 | — | 52 | 1 | no | — |
| 246 | C22 | — | 104 | 1 | no | — |
| 247 | C22 | — | 104 | 1 | no | — |
| 248 | C22 | C2×#88107 | 1 | 1 | yes | characteristic |
| 249 | C4 | — | 2 | 1 | no | — |
| 250 | C4 | — | 4 | 1 | no | — |
| 251 | C4 | — | 4 | 1 | no | — |
| 252 | C4 | — | 52 | 1 | no | — |
| 253 | C4 | — | 52 | 1 | no | — |
| 254 | C4 | — | 104 | 2 | no | — |
| 255 | C4 | — | 208 | 2 | no | — |
| 256 | C4 | #11718226 | 1 | 1 | yes | characteristic |
| 257 | C4 | #11718226 | 1 | 1 | yes | characteristic |
| 258 | C2 | — | 2 | 1 | no | — |
| 259 | C2 | — | 4 | 1 | no | — |
| 260 | C2 | — | 104 | 1 | no | — |
| 261 | C2 | — | 104 | 1 | no | — |
| 262 | C2 | C2×#11718226 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #13129983 | C2 | semidirect |
| 6. C2×#88124 | C4 | semidirect |
| 9. C4×C13×M16 | C4 | semidirect |
| 14. #11718358 | C4 | semidirect |
| 125. C4×M16 | #261 | semidirect |
| 213. C13 | #13604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13131129 | 2 |
| #13131109 | 2 |
| #13129983 | 2 |
| #13125237 | 2 |
| #13604 | 13 |