Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
442 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 59 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 | #13125701 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13116750 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #13115945 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13112852 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C13×#1315 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11719535 | — | 2 | 1 | no | — |
| 7 | C2×#88203 | — | 2 | 1 | no | — |
| 8 | C22×D104 | C22 | 1 | 1 | yes | characteristic, complemented |
| 9 | C13×#408 | C22 | 1 | 1 | yes | characteristic |
| 10 | #11718796 | — | 2 | 1 | no | — |
| 11 | C2×#88063 | — | 2 | 1 | no | — |
| 12 | #11718776 | C22 | 1 | 2 | yes | — |
| 13 | C2×D208 | — | 2 | 2 | no | — |
| 14 | #11718398 | — | 2 | 2 | no | — |
| 15 | #11718393 | — | 2 | 2 | no | — |
| 16 | C13×C22⋊C16 | C22 | 1 | 2 | yes | complemented |
| 17 | #11718144 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | #11718101 | — | 2 | 2 | no | — |
| 19 | C2×C13×#41 | D4 | 1 | 1 | yes | characteristic |
| 20 | C22×D52 | — | 2 | 1 | no | — |
| 21 | C22×D52 | — | 2 | 1 | no | — |
| 22 | C2×C13×M16 | D4 | 1 | 1 | yes | characteristic |
| 23 | C22×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 24 | #88203 | — | 4 | 2 | no | — |
| 25 | #88203 | — | 4 | 2 | no | — |
| 26 | #88201 | — | 4 | 1 | no | — |
| 27 | C2×#6106 | — | 4 | 1 | no | — |
| 28 | #88194 | — | 4 | 1 | no | — |
| 29 | #88191 | — | 4 | 1 | no | — |
| 30 | #88191 | — | 4 | 1 | no | — |
| 31 | C2×#6104 | — | 4 | 1 | no | — |
| 32 | #88184 | — | 2 | 2 | no | — |
| 33 | #88184 | — | 2 | 2 | no | — |
| 34 | #88180 | — | 2 | 1 | no | — |
| 35 | C2×#6099 | — | 2 | 1 | no | — |
| 36 | C2×D104 | — | 2 | 2 | no | — |
| 37 | C2×D104 | — | 2 | 1 | no | — |
| 38 | C2×D104 | — | 4 | 2 | no | — |
| 39 | C2×D104 | D4 | 1 | 2 | yes | — |
| 40 | C2×C13×C16 | — | 2 | 2 | no | — |
| 41 | C13×C22⋊C8 | — | 2 | 2 | no | — |
| 42 | #88063 | — | 4 | 2 | no | — |
| 43 | #88061 | — | 2 | 2 | no | — |
| 44 | #88061 | — | 2 | 2 | no | — |
| 45 | #88058 | D4 | 1 | 2 | yes | — |
| 46 | #88057 | — | 2 | 1 | no | — |
| 47 | D208 | — | 4 | 4 | no | — |
| 48 | #12108 | — | 13 | 1 | no | maximal, Sylow |
| 49 | C23×D13 | — | 4 | 1 | no | — |
| 50 | C23×D13 | — | 4 | 1 | no | — |
| 51 | C13×#41 | — | 4 | 1 | no | — |
| 52 | C13×#41 | — | 4 | 1 | no | — |
| 53 | C2×Q8×C13 | D8 | 1 | 1 | yes | characteristic |
| 54 | C2×D4×C13 | — | 2 | 1 | no | — |
| 55 | C2×D4×C13 | D8 | 1 | 1 | yes | characteristic |
| 56 | C22×C4×C13 | — | 2 | 1 | no | — |
| 57 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 58 | C2×C22⋊D13 | — | 4 | 2 | no | — |
| 59 | C2×C22⋊D13 | — | 4 | 2 | no | — |
| 60 | C2×D52 | — | 2 | 2 | no | — |
| 61 | C2×D52 | — | 2 | 2 | no | — |
| 62 | C2×D52 | — | 4 | 1 | no | — |
| 63 | C2×D52 | — | 4 | 1 | no | — |
| 64 | C2×D52 | — | 4 | 1 | no | — |
| 65 | C2×D52 | — | 4 | 1 | no | — |
| 66 | C2×D52 | — | 4 | 1 | no | — |
| 67 | C2×D52 | — | 4 | 1 | no | — |
| 68 | C2×D52 | — | 8 | 1 | no | — |
| 69 | C2×D52 | — | 8 | 1 | no | — |
| 70 | C13×M16 | — | 4 | 1 | no | — |
| 71 | C2×C8×C13 | — | 2 | 1 | no | — |
| 72 | C2×C8×C13 | — | 4 | 1 | no | — |
| 73 | C2×C8×C13 | C2×D4 | 1 | 2 | yes | — |
| 74 | C22⋊Dic13 | — | 4 | 1 | no | — |
| 75 | #6106 | — | 4 | 4 | no | — |
| 76 | #6104 | — | 4 | 4 | no | — |
| 77 | #6103 | — | 4 | 2 | no | — |
| 78 | #6103 | — | 4 | 2 | no | — |
| 79 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 80 | C4×Dic13 | — | 4 | 1 | no | — |
| 81 | #6099 | — | 2 | 2 | no | — |
| 82 | #6099 | — | 4 | 1 | no | — |
| 83 | C2×#1055 | — | 4 | 1 | no | — |
| 84 | D104 | — | 2 | 4 | no | — |
| 85 | D104 | — | 4 | 2 | no | — |
| 86 | D104 | — | 4 | 2 | no | — |
| 87 | D104 | — | 8 | 1 | no | — |
| 88 | C13×C16 | — | 4 | 2 | no | — |
| 89 | #3199 | — | 13 | 1 | no | — |
| 90 | #2184 | — | 13 | 2 | no | — |
| 91 | #2018 | — | 13 | 1 | no | — |
| 92 | #1349 | — | 13 | 2 | no | — |
| 93 | #1315 | D13 | 1 | 1 | yes | characteristic, complemented |
| 94 | C23×C13 | — | 2 | 1 | no | — |
| 95 | C23×C13 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 96 | C22×D13 | — | 4 | 2 | no | — |
| 97 | C22×D13 | — | 4 | 2 | no | — |
| 98 | C22×D13 | — | 8 | 1 | no | — |
| 99 | C22×D13 | — | 8 | 2 | no | — |
| 100 | C22×D13 | — | 8 | 1 | no | — |
| 101 | C22×D13 | — | 16 | 2 | no | — |
| 102 | C22×D13 | — | 16 | 2 | no | — |
| 103 | Q8×C13 | — | 4 | 1 | no | — |
| 104 | D4×C13 | — | 4 | 1 | no | — |
| 105 | D4×C13 | — | 8 | 1 | no | — |
| 106 | C2×C4×C13 | — | 2 | 1 | no | — |
| 107 | C2×C4×C13 | — | 2 | 1 | no | — |
| 108 | C2×C4×C13 | — | 2 | 1 | no | — |
| 109 | C2×C4×C13 | — | 4 | 1 | no | — |
| 110 | C2×C4×C13 | — | 4 | 1 | no | — |
| 111 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 112 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 113 | C22⋊D13 | — | 16 | 2 | no | — |
| 114 | C22⋊D13 | — | 16 | 2 | no | — |
| 115 | C2×Dic13 | — | 4 | 2 | no | — |
| 116 | D52 | — | 4 | 2 | no | — |
| 117 | D52 | — | 4 | 2 | no | — |
| 118 | D52 | — | 4 | 2 | no | — |
| 119 | D52 | — | 4 | 2 | no | — |
| 120 | D52 | — | 8 | 1 | no | — |
| 121 | D52 | — | 8 | 2 | no | — |
| 122 | D52 | — | 8 | 1 | no | — |
| 123 | C8×C13 | — | 2 | 2 | no | — |
| 124 | C8×C13 | — | 4 | 1 | no | — |
| 125 | #1055 | — | 4 | 2 | no | — |
| 126 | C2×AGL(1,ℤ/8) | — | 26 | 1 | no | — |
| 127 | C22×D8 | — | 13 | 1 | no | — |
| 128 | #535 | — | 26 | 1 | no | — |
| 129 | C2×D16 | — | 26 | 2 | no | — |
| 130 | #482 | — | 26 | 2 | no | — |
| 131 | #469 | — | 26 | 1 | no | — |
| 132 | #466 | — | 13 | 2 | no | — |
| 133 | #447 | — | 26 | 2 | no | — |
| 134 | C2×#100 | — | 26 | 1 | no | — |
| 135 | #408 | C2×D13 | 1 | 1 | yes | characteristic |
| 136 | #357 | — | 26 | 2 | no | — |
| 137 | C22⋊C16 | C2×D13 | 1 | 2 | yes | complemented |
| 138 | #341 | — | 13 | 1 | no | — |
| 139 | C22×C13 | — | 2 | 1 | no | — |
| 140 | C22×C13 | — | 2 | 2 | no | — |
| 141 | C22×C13 | — | 4 | 1 | no | — |
| 142 | C22×C13 | — | 4 | 2 | no | — |
| 143 | C22×C13 | #447 | 1 | 1 | yes | characteristic |
| 144 | C2×D13 | — | 8 | 2 | no | — |
| 145 | C2×D13 | — | 8 | 2 | no | — |
| 146 | C2×D13 | — | 8 | 2 | no | — |
| 147 | C2×D13 | — | 8 | 2 | no | — |
| 148 | C2×D13 | — | 16 | 2 | no | — |
| 149 | C2×D13 | — | 16 | 4 | no | — |
| 150 | C2×D13 | — | 16 | 2 | no | — |
| 151 | C2×D13 | — | 16 | 2 | no | — |
| 152 | C4×C13 | — | 2 | 1 | no | — |
| 153 | C4×C13 | — | 4 | 1 | no | — |
| 154 | C4×C13 | #453 | 1 | 1 | yes | characteristic |
| 155 | C4×C13 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 156 | Dic13 | — | 8 | 2 | no | — |
| 157 | C2×#41 | D52 | 1 | 1 | yes | characteristic |
| 158 | C22×D4 | — | 26 | 1 | no | — |
| 159 | C22×D4 | — | 26 | 1 | no | — |
| 160 | AGL(1,ℤ/8) | — | 52 | 2 | no | — |
| 161 | AGL(1,ℤ/8) | — | 52 | 2 | no | — |
| 162 | C2×SD16 | — | 52 | 1 | no | — |
| 163 | C2×D8 | — | 13 | 2 | no | — |
| 164 | C2×D8 | — | 26 | 1 | no | — |
| 165 | C2×D8 | — | 26 | 2 | no | — |
| 166 | C2×D8 | — | 52 | 2 | no | — |
| 167 | C2×D8 | — | 52 | 1 | no | — |
| 168 | C2×M16 | — | 26 | 1 | no | — |
| 169 | C2×M16 | D52 | 1 | 1 | yes | characteristic |
| 170 | C22×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 171 | #127 | — | 52 | 1 | no | — |
| 172 | #124 | — | 52 | 1 | no | — |
| 173 | #121 | — | 26 | 2 | no | — |
| 174 | #121 | — | 26 | 2 | no | — |
| 175 | #120 | — | 52 | 1 | no | — |
| 176 | #120 | — | 52 | 1 | no | — |
| 177 | #117 | — | 26 | 1 | no | — |
| 178 | D16 | — | 52 | 4 | no | — |
| 179 | C2×C16 | — | 2 | 2 | no | — |
| 180 | #107 | — | 13 | 2 | no | — |
| 181 | #106 | — | 26 | 1 | no | — |
| 182 | #102 | — | 26 | 2 | no | — |
| 183 | #102 | — | 26 | 2 | no | — |
| 184 | #100 | — | 52 | 2 | no | — |
| 185 | C22⋊C8 | — | 2 | 2 | no | — |
| 186 | C2×C13 | — | 4 | 1 | no | — |
| 187 | C2×C13 | — | 8 | 1 | no | — |
| 188 | C2×C13 | #1595 | 1 | 1 | yes | characteristic |
| 189 | C2×C13 | #2192 | 1 | 2 | yes | — |
| 190 | D13 | — | 16 | 2 | no | — |
| 191 | D13 | — | 16 | 2 | no | — |
| 192 | C24 | — | 52 | 1 | no | — |
| 193 | C24 | — | 52 | 1 | no | — |
| 194 | #41 | — | 4 | 1 | no | — |
| 195 | #41 | — | 4 | 1 | no | — |
| 196 | C2×Q8 | D104 | 1 | 1 | yes | characteristic |
| 197 | C2×D4 | — | 2 | 1 | no | — |
| 198 | C2×D4 | — | 26 | 2 | no | — |
| 199 | C2×D4 | — | 26 | 2 | no | — |
| 200 | C2×D4 | — | 52 | 1 | no | — |
| 201 | C2×D4 | — | 52 | 1 | no | — |
| 202 | C2×D4 | — | 52 | 1 | no | — |
| 203 | C2×D4 | — | 52 | 1 | no | — |
| 204 | C2×D4 | — | 52 | 2 | no | — |
| 205 | C2×D4 | — | 52 | 2 | no | — |
| 206 | C2×D4 | — | 52 | 1 | no | — |
| 207 | C2×D4 | — | 52 | 1 | no | — |
| 208 | C2×D4 | — | 104 | 1 | no | — |
| 209 | C2×D4 | — | 104 | 1 | no | — |
| 210 | C2×D4 | D104 | 1 | 1 | yes | characteristic |
| 211 | C22×C4 | — | 2 | 1 | no | — |
| 212 | C22×C4 | C2×D52 | 1 | 1 | yes | characteristic |
| 213 | SD16 | — | 52 | 4 | no | — |
| 214 | D8 | — | 26 | 4 | no | — |
| 215 | D8 | — | 52 | 2 | no | — |
| 216 | D8 | — | 52 | 2 | no | — |
| 217 | D8 | — | 52 | 4 | no | — |
| 218 | D8 | — | 104 | 1 | no | — |
| 219 | M16 | — | 4 | 1 | no | — |
| 220 | M16 | — | 26 | 2 | no | — |
| 221 | M16 | — | 52 | 1 | no | — |
| 222 | C2×C8 | — | 2 | 1 | no | — |
| 223 | C2×C8 | — | 4 | 1 | no | — |
| 224 | C2×C8 | — | 52 | 1 | no | — |
| 225 | C2×C8 | D4×D13 | 1 | 2 | yes | — |
| 226 | C4⋊C4 | — | 26 | 2 | no | — |
| 227 | C22⋊C4 | — | 52 | 2 | no | — |
| 228 | C22⋊C4 | — | 52 | 1 | no | — |
| 229 | C22⋊C4 | — | 52 | 2 | no | — |
| 230 | C42 | — | 52 | 1 | no | — |
| 231 | C16 | — | 4 | 2 | no | — |
| 232 | C13 | #12108 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 233 | C23 | — | 2 | 1 | no | — |
| 234 | C23 | — | 52 | 2 | no | — |
| 235 | C23 | — | 52 | 2 | no | — |
| 236 | C23 | — | 104 | 1 | no | — |
| 237 | C23 | — | 104 | 2 | no | — |
| 238 | C23 | — | 104 | 1 | no | — |
| 239 | C23 | — | 208 | 2 | no | — |
| 240 | C23 | — | 208 | 2 | no | — |
| 241 | C23 | #88162 | 1 | 1 | yes | characteristic |
| 242 | Q8 | — | 4 | 1 | no | — |
| 243 | D4 | — | 4 | 1 | no | — |
| 244 | D4 | — | 8 | 1 | no | — |
| 245 | D4 | — | 52 | 2 | no | — |
| 246 | D4 | — | 52 | 2 | no | — |
| 247 | D4 | — | 52 | 2 | no | — |
| 248 | D4 | — | 52 | 2 | no | — |
| 249 | D4 | — | 104 | 1 | no | — |
| 250 | D4 | — | 104 | 2 | no | — |
| 251 | D4 | — | 104 | 1 | no | — |
| 252 | D4 | — | 208 | 2 | no | — |
| 253 | D4 | — | 208 | 2 | no | — |
| 254 | C2×C4 | — | 2 | 1 | no | — |
| 255 | C2×C4 | — | 2 | 1 | no | — |
| 256 | C2×C4 | — | 2 | 1 | no | — |
| 257 | C2×C4 | — | 4 | 1 | no | — |
| 258 | C2×C4 | — | 4 | 1 | no | — |
| 259 | C2×C4 | — | 52 | 2 | no | — |
| 260 | C2×C4 | #88136 | 1 | 1 | yes | characteristic |
| 261 | C2×C4 | C2×D104 | 1 | 1 | yes | characteristic |
| 262 | C8 | — | 2 | 2 | no | — |
| 263 | C8 | — | 4 | 1 | no | — |
| 264 | C8 | — | 52 | 2 | no | — |
| 265 | C22 | — | 2 | 2 | no | — |
| 266 | C22 | — | 2 | 1 | no | — |
| 267 | C22 | — | 4 | 2 | no | — |
| 268 | C22 | — | 4 | 1 | no | — |
| 269 | C22 | — | 104 | 2 | no | — |
| 270 | C22 | — | 104 | 2 | no | — |
| 271 | C22 | — | 104 | 2 | no | — |
| 272 | C22 | — | 104 | 2 | no | — |
| 273 | C22 | — | 208 | 2 | no | — |
| 274 | C22 | — | 208 | 2 | no | — |
| 275 | C22 | — | 208 | 4 | no | — |
| 276 | C22 | — | 208 | 2 | no | — |
| 277 | C22 | #11718393 | 1 | 1 | yes | characteristic |
| 278 | C4 | — | 2 | 1 | no | — |
| 279 | C4 | — | 4 | 1 | no | — |
| 280 | C4 | — | 104 | 2 | no | — |
| 281 | C4 | #11718402 | 1 | 1 | yes | characteristic |
| 282 | C4 | #11718408 | 1 | 1 | yes | characteristic |
| 283 | C2 | — | 4 | 1 | no | — |
| 284 | C2 | — | 8 | 1 | no | — |
| 285 | C2 | — | 208 | 2 | no | — |
| 286 | C2 | — | 208 | 2 | no | — |
| 287 | C2 | #13113756 | 1 | 1 | yes | characteristic |
| 288 | C2 | #13116795 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13125701 | C2 | semidirect |
| 2. #13116750 | C2 | semidirect |
| 3. #13115945 | C2 | semidirect |
| 4. #13112852 | C2 | semidirect |
| 5. C13×#1315 | C2 | semidirect |
| 8. C22×D104 | C22 | semidirect |
| 16. C13×C22⋊C16 | C22 | semidirect |
| 17. #11718144 | C22 | semidirect |
| 93. #1315 | D13 | semidirect |
| 137. C22⋊C16 | C2×D13 | semidirect |
| 232. C13 | #12108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13125701 | 2 |
| #13116750 | 2 |
| #13115945 | 2 |
| #13112852 | 2 |
| C13×#1315 | 2 |
| #12108 | 13 |