Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
664 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 664 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 | #13121171 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13113776 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #13112838 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #13112768 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C13×#2027 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C13×#544 | C22 | 1 | 1 | yes | characteristic, complemented |
| 7 | C2×#88191 | — | 2 | 1 | no | — |
| 8 | C2×#88136 | — | 2 | 2 | no | — |
| 9 | C13×#418 | — | 2 | 1 | no | — |
| 10 | C13×#390 | C22 | 1 | 1 | yes | characteristic |
| 11 | #11718707 | — | 2 | 2 | no | — |
| 12 | #11718652 | C22 | 1 | 2 | yes | — |
| 13 | #11718622 | — | 2 | 2 | no | — |
| 14 | #11718600 | — | 2 | 1 | no | — |
| 15 | C13×#343 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C13×#339 | — | 2 | 1 | no | — |
| 17 | #11718130 | — | 2 | 2 | no | — |
| 18 | #11718120 | C22 | 1 | 2 | yes | complemented |
| 19 | C24×D13 | — | 2 | 1 | no | — |
| 20 | C22×D4×C13 | D4 | 1 | 1 | yes | characteristic |
| 21 | C22×C22⋊D13 | — | 2 | 2 | no | — |
| 22 | C22×D52 | — | 2 | 1 | no | — |
| 23 | C22×D52 | D4 | 1 | 2 | yes | — |
| 24 | C2×C13×M16 | — | 2 | 1 | no | — |
| 25 | C13×C4⋊Q8 | — | 4 | 1 | no | — |
| 26 | C13×#125 | — | 4 | 1 | no | — |
| 27 | C13×C22⋊Q8 | — | 2 | 2 | no | — |
| 28 | C13×#117 | — | 2 | 1 | no | — |
| 29 | C2×C13×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 30 | C2×C13×C22⋊C4 | — | 2 | 2 | no | — |
| 31 | C2×C42×C13 | D4 | 1 | 1 | yes | characteristic |
| 32 | C2×C22⋊Dic13 | — | 2 | 1 | no | — |
| 33 | C2×#6106 | — | 4 | 2 | no | — |
| 34 | #88191 | — | 4 | 2 | no | — |
| 35 | #88191 | — | 4 | 2 | no | — |
| 36 | C2×#6103 | — | 2 | 2 | no | — |
| 37 | C2×#6103 | — | 2 | 2 | no | — |
| 38 | C2×#6103 | — | 2 | 2 | no | — |
| 39 | C2×C4⋊Dic13 | — | 2 | 1 | no | — |
| 40 | #88136 | — | 4 | 8 | no | — |
| 41 | C13×#102 | — | 4 | 1 | no | — |
| 42 | C13×#102 | — | 4 | 1 | no | — |
| 43 | #88071 | D4 | 1 | 2 | yes | — |
| 44 | C22⋊#1055 | — | 2 | 2 | no | — |
| 45 | #88049 | — | 4 | 2 | no | — |
| 46 | #12208 | — | 13 | 1 | no | maximal, Sylow |
| 47 | C24×C13 | — | 2 | 1 | no | — |
| 48 | C23×D13 | — | 2 | 2 | no | — |
| 49 | C23×D13 | — | 4 | 4 | no | — |
| 50 | C23×D13 | — | 4 | 2 | no | — |
| 51 | C23×D13 | — | 8 | 2 | no | — |
| 52 | C23×D13 | — | 8 | 1 | no | — |
| 53 | C23×D13 | — | 8 | 1 | no | — |
| 54 | C2×Q8×C13 | — | 2 | 2 | no | — |
| 55 | C2×D4×C13 | — | 2 | 1 | no | — |
| 56 | C2×D4×C13 | — | 4 | 1 | no | — |
| 57 | C2×D4×C13 | — | 4 | 1 | no | — |
| 58 | C2×D4×C13 | SD16 | 1 | 2 | yes | complemented |
| 59 | C22×C4×C13 | — | 2 | 1 | no | — |
| 60 | C22×C4×C13 | C2×D4 | 1 | 2 | yes | — |
| 61 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 62 | C2×C22⋊D13 | — | 4 | 4 | no | — |
| 63 | C2×C22⋊D13 | — | 4 | 4 | no | — |
| 64 | C2×C22⋊D13 | — | 8 | 2 | no | — |
| 65 | C22×Dic13 | — | 2 | 2 | no | — |
| 66 | C2×D52 | — | 2 | 4 | no | — |
| 67 | C2×D52 | — | 4 | 2 | no | — |
| 68 | C2×D52 | — | 4 | 4 | no | — |
| 69 | C2×D52 | — | 8 | 1 | no | — |
| 70 | C2×D52 | — | 8 | 1 | no | — |
| 71 | C13×M16 | — | 4 | 1 | no | — |
| 72 | C13×M16 | — | 4 | 1 | no | — |
| 73 | C2×C8×C13 | — | 4 | 1 | no | — |
| 74 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 75 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 76 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 77 | C13×C4⋊C4 | — | 4 | 1 | no | — |
| 78 | C13×C4⋊C4 | — | 4 | 2 | no | — |
| 79 | C13×C22⋊C4 | — | 4 | 4 | no | — |
| 80 | C13×C22⋊C4 | — | 4 | 1 | no | — |
| 81 | C42×C13 | — | 4 | 1 | no | — |
| 82 | C42×C13 | — | 4 | 1 | no | — |
| 83 | C22⋊Dic13 | — | 4 | 2 | no | — |
| 84 | #6106 | — | 8 | 4 | no | — |
| 85 | #6103 | — | 4 | 4 | no | — |
| 86 | #6103 | — | 4 | 4 | no | — |
| 87 | #6103 | — | 4 | 2 | no | — |
| 88 | #6103 | — | 4 | 2 | no | — |
| 89 | C4⋊Dic13 | — | 8 | 1 | no | — |
| 90 | C2×#1055 | — | 4 | 2 | no | — |
| 91 | #2679 | — | 13 | 1 | no | — |
| 92 | #2027 | D13 | 1 | 1 | yes | characteristic, complemented |
| 93 | #1599 | — | 13 | 2 | no | — |
| 94 | #1345 | — | 13 | 2 | no | — |
| 95 | #1318 | — | 13 | 1 | no | — |
| 96 | C23×C13 | — | 2 | 2 | no | — |
| 97 | C23×C13 | — | 4 | 2 | no | — |
| 98 | C23×C13 | — | 4 | 2 | no | — |
| 99 | C23×C13 | — | 4 | 1 | no | — |
| 100 | C23×C13 | — | 4 | 1 | no | — |
| 101 | C23×C13 | #120 | 1 | 1 | yes | characteristic |
| 102 | C22×D13 | — | 2 | 4 | no | — |
| 103 | C22×D13 | — | 4 | 2 | no | — |
| 104 | C22×D13 | — | 4 | 2 | no | — |
| 105 | C22×D13 | — | 4 | 2 | no | — |
| 106 | C22×D13 | — | 4 | 2 | no | — |
| 107 | C22×D13 | — | 4 | 2 | no | — |
| 108 | C22×D13 | — | 4 | 2 | no | — |
| 109 | C22×D13 | — | 8 | 4 | no | — |
| 110 | C22×D13 | — | 8 | 8 | no | — |
| 111 | C22×D13 | — | 8 | 8 | no | — |
| 112 | C22×D13 | — | 8 | 4 | no | — |
| 113 | C22×D13 | — | 8 | 4 | no | — |
| 114 | Q8×C13 | — | 8 | 2 | no | — |
| 115 | D4×C13 | — | 4 | 2 | no | — |
| 116 | D4×C13 | — | 8 | 1 | no | — |
| 117 | C2×C4×C13 | — | 2 | 1 | no | — |
| 118 | C2×C4×C13 | — | 2 | 1 | no | — |
| 119 | C2×C4×C13 | — | 2 | 2 | no | — |
| 120 | C2×C4×C13 | — | 2 | 2 | no | — |
| 121 | C2×C4×C13 | — | 4 | 1 | no | — |
| 122 | C2×C4×C13 | — | 4 | 1 | no | — |
| 123 | C2×C4×C13 | — | 4 | 2 | no | — |
| 124 | C2×C4×C13 | — | 4 | 1 | no | — |
| 125 | C2×C4×C13 | — | 4 | 1 | no | — |
| 126 | C2×C4×C13 | C2×SD16 | 1 | 1 | yes | characteristic |
| 127 | C2×C4×C13 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 128 | C22⋊D13 | — | 8 | 8 | no | — |
| 129 | C2×Dic13 | — | 4 | 2 | no | — |
| 130 | C2×Dic13 | — | 4 | 2 | no | — |
| 131 | C2×Dic13 | — | 4 | 2 | no | — |
| 132 | D52 | — | 4 | 4 | no | — |
| 133 | D52 | — | 8 | 4 | no | — |
| 134 | D52 | — | 8 | 2 | no | — |
| 135 | C8×C13 | — | 8 | 1 | no | — |
| 136 | #1055 | — | 8 | 2 | no | — |
| 137 | #544 | C2×D13 | 1 | 1 | yes | characteristic, complemented |
| 138 | C2×#120 | — | 26 | 2 | no | — |
| 139 | C2×#120 | — | 26 | 1 | no | — |
| 140 | #450 | — | 26 | 2 | no | — |
| 141 | #418 | — | 2 | 1 | no | — |
| 142 | #394 | — | 13 | 2 | no | — |
| 143 | #394 | — | 26 | 2 | no | — |
| 144 | #390 | — | 26 | 1 | no | — |
| 145 | #390 | C2×D13 | 1 | 1 | yes | characteristic |
| 146 | #343 | C2×D13 | 1 | 1 | yes | characteristic, complemented |
| 147 | #339 | — | 2 | 1 | no | — |
| 148 | #328 | — | 26 | 2 | no | — |
| 149 | #324 | — | 13 | 2 | no | — |
| 150 | C22×C13 | — | 2 | 1 | no | — |
| 151 | C22×C13 | — | 2 | 1 | no | — |
| 152 | C22×C13 | — | 4 | 4 | no | — |
| 153 | C22×C13 | — | 4 | 2 | no | — |
| 154 | C22×C13 | — | 8 | 2 | no | — |
| 155 | C22×C13 | — | 8 | 1 | no | — |
| 156 | C22×C13 | — | 8 | 1 | no | — |
| 157 | C22×C13 | #450 | 1 | 1 | yes | characteristic |
| 158 | C22×C13 | #455 | 1 | 1 | yes | characteristic |
| 159 | C22×C13 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 160 | C2×D13 | — | 4 | 4 | no | — |
| 161 | C2×D13 | — | 4 | 4 | no | — |
| 162 | C2×D13 | — | 4 | 4 | no | — |
| 163 | C2×D13 | — | 8 | 2 | no | — |
| 164 | C2×D13 | — | 8 | 2 | no | — |
| 165 | C2×D13 | — | 8 | 16 | no | — |
| 166 | C2×D13 | — | 8 | 2 | no | — |
| 167 | C2×D13 | — | 8 | 2 | no | — |
| 168 | C4×C13 | — | 2 | 1 | no | — |
| 169 | C4×C13 | — | 2 | 1 | no | — |
| 170 | C4×C13 | — | 4 | 2 | no | — |
| 171 | C4×C13 | — | 4 | 2 | no | — |
| 172 | C4×C13 | — | 8 | 1 | no | — |
| 173 | C4×C13 | — | 8 | 1 | no | — |
| 174 | Dic13 | — | 8 | 2 | no | — |
| 175 | C25 | — | 26 | 1 | no | — |
| 176 | C22×D4 | — | 13 | 2 | no | — |
| 177 | C22×D4 | — | 26 | 1 | no | — |
| 178 | C22×D4 | — | 26 | 2 | no | — |
| 179 | C22×D4 | C22⋊D13 | 1 | 1 | yes | characteristic |
| 180 | C2×SD16 | — | 52 | 2 | no | — |
| 181 | C2×M16 | — | 2 | 1 | no | — |
| 182 | C4⋊Q8 | — | 4 | 1 | no | — |
| 183 | #125 | — | 4 | 1 | no | — |
| 184 | C22⋊Q8 | — | 2 | 2 | no | — |
| 185 | #120 | — | 52 | 8 | no | — |
| 186 | #120 | — | 52 | 2 | no | — |
| 187 | #120 | — | 52 | 2 | no | — |
| 188 | #117 | — | 2 | 1 | no | — |
| 189 | C2×C4⋊C4 | — | 26 | 1 | no | — |
| 190 | C2×C4⋊C4 | C22×D13 | 1 | 1 | yes | characteristic |
| 191 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 192 | C2×C22⋊C4 | — | 26 | 2 | no | — |
| 193 | C2×C22⋊C4 | — | 26 | 1 | no | — |
| 194 | C2×C22⋊C4 | — | 26 | 2 | no | — |
| 195 | C2×C22⋊C4 | — | 26 | 2 | no | — |
| 196 | C2×C42 | C22⋊D13 | 1 | 1 | yes | characteristic |
| 197 | #102 | — | 4 | 1 | no | — |
| 198 | #102 | — | 4 | 1 | no | — |
| 199 | #102 | — | 52 | 2 | no | — |
| 200 | C22⋊C8 | — | 26 | 2 | no | — |
| 201 | #95 | — | 13 | 2 | no | — |
| 202 | C2×C13 | — | 2 | 1 | no | — |
| 203 | C2×C13 | — | 2 | 1 | no | — |
| 204 | C2×C13 | — | 8 | 2 | no | — |
| 205 | C2×C13 | #1601 | 1 | 1 | yes | characteristic |
| 206 | C2×C13 | #2196 | 1 | 1 | yes | characteristic |
| 207 | C2×C13 | #2202 | 1 | 1 | yes | characteristic |
| 208 | D13 | — | 8 | 4 | no | — |
| 209 | C24 | — | 2 | 1 | no | — |
| 210 | C24 | — | 26 | 2 | no | — |
| 211 | C24 | — | 52 | 2 | no | — |
| 212 | C24 | — | 52 | 4 | no | — |
| 213 | C24 | — | 104 | 2 | no | — |
| 214 | C24 | — | 104 | 1 | no | — |
| 215 | C24 | — | 104 | 1 | no | — |
| 216 | C2×Q8 | — | 2 | 2 | no | — |
| 217 | C2×D4 | — | 2 | 1 | no | — |
| 218 | C2×D4 | — | 4 | 1 | no | — |
| 219 | C2×D4 | — | 4 | 1 | no | — |
| 220 | C2×D4 | — | 26 | 4 | no | — |
| 221 | C2×D4 | — | 52 | 2 | no | — |
| 222 | C2×D4 | — | 52 | 4 | no | — |
| 223 | C2×D4 | — | 52 | 4 | no | — |
| 224 | C2×D4 | — | 52 | 4 | no | — |
| 225 | C2×D4 | — | 104 | 1 | no | — |
| 226 | C2×D4 | — | 104 | 1 | no | — |
| 227 | C2×D4 | — | 104 | 2 | no | — |
| 228 | C2×D4 | #6106 | 1 | 2 | yes | complemented |
| 229 | C22×C4 | — | 2 | 1 | no | — |
| 230 | C22×C4 | — | 26 | 2 | no | — |
| 231 | C22×C4 | D4×D13 | 1 | 2 | yes | — |
| 232 | C22×C4 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 233 | SD16 | — | 104 | 4 | no | — |
| 234 | M16 | — | 4 | 1 | no | — |
| 235 | M16 | — | 4 | 1 | no | — |
| 236 | C2×C8 | — | 4 | 1 | no | — |
| 237 | C2×C8 | — | 52 | 2 | no | — |
| 238 | C4⋊C4 | — | 2 | 1 | no | — |
| 239 | C4⋊C4 | — | 2 | 1 | no | — |
| 240 | C4⋊C4 | — | 2 | 2 | no | — |
| 241 | C4⋊C4 | — | 4 | 1 | no | — |
| 242 | C4⋊C4 | — | 4 | 2 | no | — |
| 243 | C4⋊C4 | — | 104 | 1 | no | — |
| 244 | C22⋊C4 | — | 4 | 4 | no | — |
| 245 | C22⋊C4 | — | 4 | 1 | no | — |
| 246 | C22⋊C4 | — | 52 | 4 | no | — |
| 247 | C22⋊C4 | — | 52 | 4 | no | — |
| 248 | C22⋊C4 | — | 52 | 2 | no | — |
| 249 | C22⋊C4 | — | 52 | 2 | no | — |
| 250 | C22⋊C4 | — | 52 | 2 | no | — |
| 251 | C42 | — | 4 | 1 | no | — |
| 252 | C42 | — | 4 | 1 | no | — |
| 253 | C13 | #12208 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 254 | C23 | — | 2 | 2 | no | — |
| 255 | C23 | — | 4 | 2 | no | — |
| 256 | C23 | — | 4 | 2 | no | — |
| 257 | C23 | — | 4 | 1 | no | — |
| 258 | C23 | — | 4 | 1 | no | — |
| 259 | C23 | — | 26 | 4 | no | — |
| 260 | C23 | — | 52 | 2 | no | — |
| 261 | C23 | — | 52 | 2 | no | — |
| 262 | C23 | — | 52 | 2 | no | — |
| 263 | C23 | — | 52 | 2 | no | — |
| 264 | C23 | — | 52 | 2 | no | — |
| 265 | C23 | — | 52 | 2 | no | — |
| 266 | C23 | — | 104 | 8 | no | — |
| 267 | C23 | — | 104 | 4 | no | — |
| 268 | C23 | — | 104 | 4 | no | — |
| 269 | C23 | — | 104 | 8 | no | — |
| 270 | C23 | — | 104 | 4 | no | — |
| 271 | C23 | #88191 | 1 | 1 | yes | characteristic |
| 272 | Q8 | — | 8 | 2 | no | — |
| 273 | D4 | — | 4 | 2 | no | — |
| 274 | D4 | — | 8 | 1 | no | — |
| 275 | D4 | — | 52 | 4 | no | — |
| 276 | D4 | — | 104 | 4 | no | — |
| 277 | D4 | — | 104 | 2 | no | — |
| 278 | D4 | — | 104 | 8 | no | — |
| 279 | C2×C4 | — | 2 | 1 | no | — |
| 280 | C2×C4 | — | 2 | 1 | no | — |
| 281 | C2×C4 | — | 2 | 2 | no | — |
| 282 | C2×C4 | — | 2 | 2 | no | — |
| 283 | C2×C4 | — | 4 | 1 | no | — |
| 284 | C2×C4 | — | 4 | 1 | no | — |
| 285 | C2×C4 | — | 4 | 2 | no | — |
| 286 | C2×C4 | — | 4 | 1 | no | — |
| 287 | C2×C4 | — | 4 | 1 | no | — |
| 288 | C2×C4 | — | 52 | 2 | no | — |
| 289 | C2×C4 | — | 52 | 2 | no | — |
| 290 | C2×C4 | — | 52 | 2 | no | — |
| 291 | C2×C4 | C2×#6106 | 1 | 1 | yes | characteristic |
| 292 | C2×C4 | #88203 | 1 | 1 | yes | characteristic |
| 293 | C8 | — | 8 | 1 | no | — |
| 294 | C8 | — | 104 | 2 | no | — |
| 295 | C22 | — | 2 | 1 | no | — |
| 296 | C22 | — | 2 | 1 | no | — |
| 297 | C22 | — | 4 | 4 | no | — |
| 298 | C22 | — | 4 | 2 | no | — |
| 299 | C22 | — | 8 | 2 | no | — |
| 300 | C22 | — | 8 | 1 | no | — |
| 301 | C22 | — | 8 | 1 | no | — |
| 302 | C22 | — | 52 | 4 | no | — |
| 303 | C22 | — | 52 | 4 | no | — |
| 304 | C22 | — | 52 | 4 | no | — |
| 305 | C22 | — | 104 | 2 | no | — |
| 306 | C22 | — | 104 | 2 | no | — |
| 307 | C22 | — | 104 | 16 | no | — |
| 308 | C22 | — | 104 | 2 | no | — |
| 309 | C22 | — | 104 | 2 | no | — |
| 310 | C22 | #11718693 | 1 | 1 | yes | characteristic |
| 311 | C22 | #11718707 | 1 | 1 | yes | characteristic |
| 312 | C22 | #11718722 | 1 | 1 | yes | characteristic |
| 313 | C4 | — | 2 | 1 | no | — |
| 314 | C4 | — | 2 | 1 | no | — |
| 315 | C4 | — | 4 | 2 | no | — |
| 316 | C4 | — | 4 | 2 | no | — |
| 317 | C4 | — | 8 | 1 | no | — |
| 318 | C4 | — | 8 | 1 | no | — |
| 319 | C4 | — | 104 | 2 | no | — |
| 320 | C2 | — | 2 | 1 | no | — |
| 321 | C2 | — | 2 | 1 | no | — |
| 322 | C2 | — | 8 | 2 | no | — |
| 323 | C2 | — | 104 | 4 | no | — |
| 324 | C2 | #13113787 | 1 | 1 | yes | characteristic |
| 325 | C2 | #13116819 | 1 | 1 | yes | characteristic |
| 326 | C2 | #13116852 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13113776 | C2 | semidirect |
| 3. #13112838 | C2 | semidirect |
| 4. #13112768 | C2 | semidirect |
| 5. C13×#2027 | C2 | semidirect |
| 6. C13×#544 | C22 | semidirect |
| 15. C13×#343 | C22 | semidirect |
| 18. #11718120 | C22 | semidirect |
| 58. C2×D4×C13 | SD16 | semidirect |
| 92. #2027 | D13 | semidirect |
| 137. #544 | C2×D13 | semidirect |
| 146. #343 | C2×D13 | semidirect |
| 228. C2×D4 | #6106 | semidirect |
| 253. C13 | #12208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13121171 | 2 |
| #13113776 | 2 |
| #13112838 | 2 |
| #13112768 | 2 |
| C13×#2027 | 2 |
| #12208 | 13 |