Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
540 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 73 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 | #13122824 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13114797 | C2 | 1 | 2 | yes | maximal |
| 3 | #13114794 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #13112962 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C13×#1394 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#88254 | C22 | 1 | 1 | yes | characteristic |
| 7 | C2×C13×#101 | C22 | 1 | 2 | yes | — |
| 8 | C13×#391 | C22 | 1 | 1 | yes | characteristic |
| 9 | #11718891 | C22 | 1 | 2 | yes | — |
| 10 | C2×#88076 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#88065 | — | 2 | 2 | no | — |
| 12 | #11718794 | — | 2 | 2 | no | — |
| 13 | #11718647 | — | 2 | 1 | no | — |
| 14 | #11718627 | — | 2 | 1 | no | — |
| 15 | #11718589 | — | 2 | 1 | no | — |
| 16 | C2×#88045 | — | 2 | 1 | no | — |
| 17 | #11718322 | — | 2 | 2 | no | — |
| 18 | #11718316 | — | 2 | 2 | no | — |
| 19 | C22×Q8×C13 | C23 | 1 | 1 | yes | characteristic |
| 20 | #88254 | — | 2 | 2 | no | — |
| 21 | #88254 | — | 2 | 1 | no | — |
| 22 | #88254 | — | 4 | 2 | no | — |
| 23 | #88254 | Q8 | 1 | 2 | yes | — |
| 24 | C2×#6131 | — | 4 | 1 | no | — |
| 25 | C2×Q8×D13 | — | 4 | 1 | no | — |
| 26 | C2×#6127 | — | 2 | 2 | no | — |
| 27 | C2×#6127 | — | 2 | 1 | no | — |
| 28 | C2×C13×M16 | — | 2 | 2 | no | — |
| 29 | C2×C13×C4⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 30 | C2×C42×C13 | D4 | 1 | 1 | yes | characteristic |
| 31 | C2×C4⋊Dic13 | — | 2 | 1 | no | — |
| 32 | C2×C4⋊Dic13 | — | 2 | 1 | no | — |
| 33 | C2×C4⋊Dic13 | — | 2 | 1 | no | — |
| 34 | C2×C4⋊Dic13 | D4 | 1 | 2 | yes | — |
| 35 | C2×#6101 | — | 2 | 2 | no | — |
| 36 | C2×C4×Dic13 | D4 | 1 | 2 | yes | — |
| 37 | C2×#6099 | — | 2 | 1 | no | — |
| 38 | C13×#101 | — | 2 | 2 | no | — |
| 39 | C13×#101 | — | 2 | 2 | no | — |
| 40 | C13×#95 | — | 2 | 2 | no | — |
| 41 | #88076 | — | 2 | 2 | no | — |
| 42 | #88071 | — | 2 | 1 | no | — |
| 43 | #88071 | — | 2 | 2 | no | — |
| 44 | #88071 | — | 2 | 2 | no | — |
| 45 | #88071 | — | 2 | 2 | no | — |
| 46 | #88065 | — | 4 | 4 | no | — |
| 47 | #88061 | — | 4 | 2 | no | — |
| 48 | #88056 | — | 4 | 2 | no | — |
| 49 | #88050 | — | 4 | 1 | no | — |
| 50 | #88049 | — | 4 | 1 | no | — |
| 51 | #88045 | — | 4 | 2 | no | — |
| 52 | #13379 | — | 13 | 1 | no | maximal, Sylow |
| 53 | C2×Q8×C13 | — | 4 | 1 | no | — |
| 54 | C2×Q8×C13 | — | 4 | 1 | no | — |
| 55 | C2×Q8×C13 | C2×Q8 | 1 | 1 | yes | characteristic |
| 56 | C2×Q8×C13 | #41 | 1 | 2 | yes | — |
| 57 | C2×Q8×C13 | #41 | 1 | 1 | yes | characteristic |
| 58 | C22×C4×C13 | — | 2 | 1 | no | — |
| 59 | C22×C4×C13 | — | 2 | 1 | no | — |
| 60 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 61 | C22×C4×C13 | C2×D4 | 1 | 2 | yes | — |
| 62 | C2×C22⋊D13 | — | 4 | 1 | no | — |
| 63 | C22×Dic13 | — | 2 | 2 | no | — |
| 64 | C22×Dic13 | — | 2 | 2 | no | — |
| 65 | #6131 | — | 4 | 2 | no | — |
| 66 | #6131 | — | 4 | 4 | no | — |
| 67 | #6131 | — | 4 | 2 | no | — |
| 68 | Q8×D13 | — | 4 | 2 | no | — |
| 69 | Q8×D13 | — | 4 | 2 | no | — |
| 70 | Q8×D13 | — | 4 | 4 | no | — |
| 71 | #6127 | — | 2 | 4 | no | — |
| 72 | #6127 | — | 2 | 2 | no | — |
| 73 | #6127 | — | 2 | 4 | no | — |
| 74 | #6127 | — | 2 | 2 | no | — |
| 75 | #6127 | — | 4 | 1 | no | — |
| 76 | #6127 | — | 4 | 2 | no | — |
| 77 | #6127 | — | 4 | 1 | no | — |
| 78 | #6127 | — | 4 | 2 | no | — |
| 79 | C2×D52 | — | 2 | 1 | no | — |
| 80 | C2×D52 | — | 2 | 2 | no | — |
| 81 | C2×C4×D13 | — | 4 | 1 | no | — |
| 82 | C2×C4×D13 | — | 4 | 2 | no | — |
| 83 | C2×Dic26 | — | 2 | 1 | no | — |
| 84 | C2×Dic26 | — | 2 | 2 | no | — |
| 85 | C13×M16 | — | 4 | 2 | no | — |
| 86 | C13×M16 | — | 4 | 2 | no | — |
| 87 | C2×C8×C13 | — | 4 | 2 | no | — |
| 88 | C13×C4⋊C4 | — | 4 | 1 | no | — |
| 89 | C42×C13 | — | 4 | 1 | no | — |
| 90 | C4⋊Dic13 | — | 4 | 2 | no | — |
| 91 | C4⋊Dic13 | — | 4 | 2 | no | — |
| 92 | C4⋊Dic13 | — | 8 | 1 | no | — |
| 93 | C4⋊Dic13 | — | 8 | 1 | no | — |
| 94 | #6101 | — | 4 | 4 | no | — |
| 95 | C4×Dic13 | — | 4 | 2 | no | — |
| 96 | #6099 | — | 4 | 1 | no | — |
| 97 | #6099 | — | 4 | 1 | no | — |
| 98 | C2×#1055 | — | 4 | 1 | no | — |
| 99 | #2809 | — | 13 | 1 | no | — |
| 100 | #1793 | — | 13 | 2 | no | — |
| 101 | #1793 | — | 13 | 1 | no | — |
| 102 | #1394 | — | 13 | 2 | no | — |
| 103 | #1394 | D13 | 1 | 1 | yes | characteristic, complemented |
| 104 | C23×C13 | #120 | 1 | 1 | yes | characteristic |
| 105 | C22×D13 | — | 4 | 1 | no | — |
| 106 | Q8×C13 | — | 4 | 1 | no | — |
| 107 | Q8×C13 | — | 4 | 2 | no | — |
| 108 | Q8×C13 | — | 4 | 1 | no | — |
| 109 | C2×C4×C13 | — | 2 | 1 | no | — |
| 110 | C2×C4×C13 | — | 2 | 1 | no | — |
| 111 | C2×C4×C13 | — | 2 | 2 | no | — |
| 112 | C2×C4×C13 | — | 2 | 2 | no | — |
| 113 | C2×C4×C13 | — | 2 | 2 | no | — |
| 114 | C2×C4×C13 | — | 4 | 1 | no | — |
| 115 | C2×C4×C13 | — | 4 | 1 | no | — |
| 116 | C2×C4×C13 | — | 4 | 2 | no | — |
| 117 | C2×C4×C13 | — | 4 | 1 | no | — |
| 118 | C2×C4×C13 | C22⋊Q8 | 1 | 2 | yes | — |
| 119 | C2×C4×C13 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 120 | C2×C4×C13 | #124 | 1 | 1 | yes | characteristic |
| 121 | C2×C4×C13 | #124 | 1 | 2 | yes | — |
| 122 | C22⋊D13 | — | 4 | 2 | no | — |
| 123 | C22⋊D13 | — | 4 | 2 | no | — |
| 124 | C2×Dic13 | — | 4 | 1 | no | — |
| 125 | C2×Dic13 | — | 4 | 2 | no | — |
| 126 | C2×Dic13 | — | 4 | 2 | no | — |
| 127 | C2×Dic13 | — | 4 | 2 | no | — |
| 128 | C2×Dic13 | — | 4 | 2 | no | — |
| 129 | C2×Dic13 | — | 4 | 2 | no | — |
| 130 | C2×Dic13 | — | 4 | 2 | no | — |
| 131 | D52 | — | 2 | 2 | no | — |
| 132 | D52 | — | 2 | 4 | no | — |
| 133 | D52 | — | 4 | 1 | no | — |
| 134 | D52 | — | 4 | 2 | no | — |
| 135 | C4×D13 | — | 4 | 2 | no | — |
| 136 | C4×D13 | — | 4 | 4 | no | — |
| 137 | C4×D13 | — | 4 | 4 | no | — |
| 138 | C4×D13 | — | 4 | 2 | no | — |
| 139 | Dic26 | — | 2 | 2 | no | — |
| 140 | Dic26 | — | 2 | 4 | no | — |
| 141 | Dic26 | — | 4 | 1 | no | — |
| 142 | Dic26 | — | 4 | 2 | no | — |
| 143 | C8×C13 | — | 8 | 2 | no | — |
| 144 | #1055 | — | 8 | 1 | no | — |
| 145 | C2×2−1+4 | — | 13 | 1 | no | — |
| 146 | C2×#104 | — | 26 | 2 | no | — |
| 147 | C2×#104 | — | 26 | 1 | no | — |
| 148 | #417 | — | 26 | 2 | no | — |
| 149 | #417 | — | 26 | 1 | no | — |
| 150 | C2×#101 | — | 13 | 1 | no | — |
| 151 | C2×#101 | C2×D13 | 1 | 2 | yes | — |
| 152 | #400 | — | 26 | 1 | no | — |
| 153 | #398 | — | 26 | 2 | no | — |
| 154 | #391 | — | 13 | 2 | no | — |
| 155 | #391 | C2×D13 | 1 | 1 | yes | characteristic |
| 156 | #389 | — | 26 | 1 | no | — |
| 157 | #387 | — | 26 | 2 | no | — |
| 158 | C22×C13 | — | 2 | 1 | no | — |
| 159 | C22×C13 | — | 2 | 1 | no | — |
| 160 | C22×C13 | #393 | 1 | 1 | yes | characteristic |
| 161 | C22×C13 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 162 | C22×C13 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 163 | C2×D13 | — | 4 | 2 | no | — |
| 164 | C2×D13 | — | 8 | 1 | no | — |
| 165 | C2×D13 | — | 8 | 1 | no | — |
| 166 | C4×C13 | — | 2 | 1 | no | — |
| 167 | C4×C13 | — | 2 | 2 | no | — |
| 168 | C4×C13 | — | 2 | 2 | no | — |
| 169 | C4×C13 | — | 2 | 1 | no | — |
| 170 | C4×C13 | — | 4 | 2 | no | — |
| 171 | C4×C13 | — | 8 | 1 | no | — |
| 172 | Dic13 | — | 4 | 2 | no | — |
| 173 | Dic13 | — | 8 | 2 | no | — |
| 174 | Dic13 | — | 8 | 2 | no | — |
| 175 | 2−1+4 | — | 13 | 2 | no | — |
| 176 | 2−1+4 | — | 26 | 2 | no | — |
| 177 | 2−1+4 | — | 26 | 1 | no | — |
| 178 | 2−1+4 | — | 52 | 2 | no | — |
| 179 | C2×#41 | — | 26 | 1 | no | — |
| 180 | C2×#41 | — | 26 | 2 | no | — |
| 181 | C2×#41 | — | 52 | 1 | no | — |
| 182 | C22×Q8 | — | 52 | 1 | no | — |
| 183 | C22×Q8 | C22×D13 | 1 | 1 | yes | characteristic |
| 184 | C2×M16 | — | 2 | 2 | no | — |
| 185 | C2×M16 | — | 26 | 1 | no | — |
| 186 | C2×C4⋊C4 | — | 13 | 2 | no | — |
| 187 | C2×C4⋊C4 | — | 26 | 2 | no | — |
| 188 | C2×C4⋊C4 | — | 26 | 1 | no | — |
| 189 | C2×C4⋊C4 | — | 26 | 1 | no | — |
| 190 | C2×C4⋊C4 | — | 26 | 1 | no | — |
| 191 | C2×C4⋊C4 | D52 | 1 | 1 | yes | characteristic |
| 192 | C2×C42 | — | 13 | 2 | no | — |
| 193 | C2×C42 | D52 | 1 | 1 | yes | characteristic |
| 194 | #104 | — | 52 | 2 | no | — |
| 195 | #104 | — | 52 | 4 | no | — |
| 196 | #103 | — | 52 | 1 | no | — |
| 197 | #103 | — | 52 | 2 | no | — |
| 198 | #102 | — | 52 | 1 | no | — |
| 199 | #102 | — | 52 | 2 | no | — |
| 200 | #101 | — | 2 | 2 | no | — |
| 201 | #101 | — | 2 | 2 | no | — |
| 202 | #101 | — | 26 | 2 | no | — |
| 203 | #95 | — | 2 | 2 | no | — |
| 204 | #95 | — | 26 | 1 | no | — |
| 205 | #95 | — | 26 | 2 | no | — |
| 206 | #95 | — | 26 | 2 | no | — |
| 207 | #95 | — | 26 | 2 | no | — |
| 208 | C2×C13 | — | 2 | 1 | no | — |
| 209 | C2×C13 | — | 2 | 1 | no | — |
| 210 | C2×C13 | #2029 | 1 | 1 | yes | characteristic |
| 211 | C2×C13 | #2203 | 1 | 1 | yes | characteristic |
| 212 | C2×C13 | #2204 | 1 | 1 | yes | characteristic |
| 213 | D13 | — | 8 | 2 | no | — |
| 214 | #41 | — | 26 | 2 | no | — |
| 215 | #41 | — | 26 | 4 | no | — |
| 216 | #41 | — | 26 | 4 | no | — |
| 217 | #41 | — | 26 | 2 | no | — |
| 218 | #41 | — | 52 | 1 | no | — |
| 219 | #41 | — | 52 | 2 | no | — |
| 220 | #41 | — | 52 | 2 | no | — |
| 221 | #41 | — | 52 | 4 | no | — |
| 222 | #41 | — | 52 | 2 | no | — |
| 223 | #41 | — | 52 | 1 | no | — |
| 224 | #41 | — | 52 | 2 | no | — |
| 225 | C2×Q8 | — | 4 | 1 | no | — |
| 226 | C2×Q8 | — | 4 | 1 | no | — |
| 227 | C2×Q8 | — | 26 | 1 | no | — |
| 228 | C2×Q8 | — | 26 | 2 | no | — |
| 229 | C2×Q8 | — | 52 | 2 | no | — |
| 230 | C2×Q8 | — | 52 | 4 | no | — |
| 231 | C2×Q8 | — | 52 | 2 | no | — |
| 232 | C2×Q8 | #6127 | 1 | 2 | yes | — |
| 233 | C2×Q8 | #6129 | 1 | 1 | yes | characteristic |
| 234 | C2×Q8 | Q8×D13 | 1 | 1 | yes | characteristic |
| 235 | C2×D4 | — | 26 | 1 | no | — |
| 236 | C2×D4 | — | 26 | 2 | no | — |
| 237 | C2×D4 | — | 52 | 1 | no | — |
| 238 | C22×C4 | — | 2 | 1 | no | — |
| 239 | C22×C4 | — | 2 | 1 | no | — |
| 240 | C22×C4 | — | 26 | 2 | no | — |
| 241 | C22×C4 | — | 26 | 2 | no | — |
| 242 | C22×C4 | — | 52 | 1 | no | — |
| 243 | C22×C4 | — | 52 | 2 | no | — |
| 244 | C22×C4 | C2×D52 | 1 | 1 | yes | characteristic |
| 245 | C22×C4 | D4×D13 | 1 | 2 | yes | — |
| 246 | M16 | — | 4 | 2 | no | — |
| 247 | M16 | — | 4 | 2 | no | — |
| 248 | M16 | — | 52 | 1 | no | — |
| 249 | M16 | — | 52 | 1 | no | — |
| 250 | C2×C8 | — | 4 | 2 | no | — |
| 251 | C2×C8 | — | 52 | 1 | no | — |
| 252 | C4⋊C4 | — | 4 | 1 | no | — |
| 253 | C4⋊C4 | — | 52 | 2 | no | — |
| 254 | C4⋊C4 | — | 52 | 4 | no | — |
| 255 | C4⋊C4 | — | 52 | 2 | no | — |
| 256 | C4⋊C4 | — | 104 | 1 | no | — |
| 257 | C4⋊C4 | — | 104 | 1 | no | — |
| 258 | C42 | — | 4 | 1 | no | — |
| 259 | C42 | — | 52 | 2 | no | — |
| 260 | C13 | #13379 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 261 | C23 | — | 52 | 1 | no | — |
| 262 | C23 | #88136 | 1 | 1 | yes | characteristic |
| 263 | Q8 | — | 4 | 2 | no | — |
| 264 | Q8 | — | 4 | 1 | no | — |
| 265 | Q8 | — | 4 | 1 | no | — |
| 266 | Q8 | — | 26 | 4 | no | — |
| 267 | Q8 | — | 26 | 2 | no | — |
| 268 | Q8 | — | 52 | 2 | no | — |
| 269 | Q8 | — | 52 | 1 | no | — |
| 270 | D4 | — | 26 | 4 | no | — |
| 271 | D4 | — | 26 | 2 | no | — |
| 272 | D4 | — | 52 | 2 | no | — |
| 273 | D4 | — | 52 | 1 | no | — |
| 274 | D4 | — | 52 | 2 | no | — |
| 275 | D4 | — | 52 | 2 | no | — |
| 276 | C2×C4 | — | 2 | 1 | no | — |
| 277 | C2×C4 | — | 2 | 2 | no | — |
| 278 | C2×C4 | — | 2 | 1 | no | — |
| 279 | C2×C4 | — | 2 | 2 | no | — |
| 280 | C2×C4 | — | 2 | 2 | no | — |
| 281 | C2×C4 | — | 4 | 1 | no | — |
| 282 | C2×C4 | — | 4 | 1 | no | — |
| 283 | C2×C4 | — | 4 | 2 | no | — |
| 284 | C2×C4 | — | 4 | 1 | no | — |
| 285 | C2×C4 | — | 52 | 4 | no | — |
| 286 | C2×C4 | — | 52 | 2 | no | — |
| 287 | C2×C4 | — | 52 | 4 | no | — |
| 288 | C2×C4 | — | 52 | 2 | no | — |
| 289 | C2×C4 | — | 52 | 1 | no | — |
| 290 | C2×C4 | — | 52 | 2 | no | — |
| 291 | C2×C4 | — | 52 | 2 | no | — |
| 292 | C2×C4 | — | 52 | 2 | no | — |
| 293 | C2×C4 | — | 52 | 2 | no | — |
| 294 | C2×C4 | — | 52 | 2 | no | — |
| 295 | C2×C4 | — | 52 | 2 | no | — |
| 296 | C2×C4 | #88129 | 1 | 1 | yes | characteristic |
| 297 | C2×C4 | #88139 | 1 | 2 | yes | — |
| 298 | C2×C4 | #88150 | 1 | 2 | yes | — |
| 299 | C2×C4 | #88151 | 1 | 1 | yes | characteristic |
| 300 | C8 | — | 8 | 2 | no | — |
| 301 | C8 | — | 104 | 1 | no | — |
| 302 | C22 | — | 2 | 1 | no | — |
| 303 | C22 | — | 2 | 1 | no | — |
| 304 | C22 | — | 52 | 2 | no | — |
| 305 | C22 | — | 104 | 1 | no | — |
| 306 | C22 | — | 104 | 1 | no | — |
| 307 | C22 | #11718334 | 1 | 1 | yes | characteristic |
| 308 | C22 | #11718402 | 1 | 1 | yes | characteristic |
| 309 | C22 | #11718402 | 1 | 1 | yes | characteristic |
| 310 | C4 | — | 2 | 2 | no | — |
| 311 | C4 | — | 2 | 1 | no | — |
| 312 | C4 | — | 2 | 2 | no | — |
| 313 | C4 | — | 2 | 1 | no | — |
| 314 | C4 | — | 4 | 2 | no | — |
| 315 | C4 | — | 8 | 1 | no | — |
| 316 | C4 | — | 52 | 2 | no | — |
| 317 | C4 | — | 104 | 2 | no | — |
| 318 | C4 | — | 104 | 2 | no | — |
| 319 | C2 | — | 2 | 1 | no | — |
| 320 | C2 | — | 2 | 1 | no | — |
| 321 | C2 | — | 104 | 2 | no | — |
| 322 | C2 | #13116001 | 1 | 1 | yes | characteristic |
| 323 | C2 | #13116859 | 1 | 1 | yes | characteristic |
| 324 | C2 | #13116864 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13122824 | C2 | semidirect |
| 4. #13112962 | C2 | semidirect |
| 5. C13×#1394 | C2 | semidirect |
| 103. #1394 | D13 | semidirect |
| 260. C13 | #13379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13122824 | 2 |
| #13114797 | 2 |
| #13114794 | 2 |
| #13112962 | 2 |
| C13×#1394 | 2 |
| #13379 | 13 |