Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
332 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 54 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 | #13131136 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13131112 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13129982 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13129981 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13129966 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13129966 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #13125909 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #11719420 | C22 | 1 | 1 | yes | characteristic |
| 9 | #11719402 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | #11719148 | — | 2 | 1 | no | — |
| 11 | D13⋊#99 | — | 2 | 1 | no | — |
| 12 | C13×#490 | C4 | 1 | 1 | yes | characteristic, complemented |
| 13 | #11718737 | C4 | 1 | 1 | yes | characteristic, complemented |
| 14 | #11718729 | C22 | 1 | 1 | yes | characteristic |
| 15 | #11718444 | — | 2 | 1 | no | — |
| 16 | #11718437 | — | 2 | 1 | no | — |
| 17 | #11718428 | — | 2 | 1 | no | — |
| 18 | #11718423 | — | 2 | 1 | no | — |
| 19 | #11718376 | C22 | 1 | 1 | yes | characteristic |
| 20 | #11718370 | C4 | 1 | 1 | yes | characteristic, complemented |
| 21 | #11718295 | — | 2 | 1 | no | — |
| 22 | #11718294 | — | 2 | 1 | no | — |
| 23 | #11718228 | C22 | 1 | 1 | yes | characteristic |
| 24 | #11718228 | C22 | 1 | 1 | yes | characteristic |
| 25 | #11718226 | C22 | 1 | 1 | yes | characteristic |
| 26 | #11718226 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#6129 | D4 | 1 | 1 | yes | characteristic |
| 28 | C2×D4×D13 | D4 | 1 | 1 | yes | characteristic |
| 29 | C2×C22⋊#261 | — | 4 | 1 | no | — |
| 30 | C2×#6122 | — | 4 | 1 | no | — |
| 31 | C13×#127 | C2×C4 | 1 | 1 | yes | characteristic |
| 32 | C13×#125 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 33 | #88194 | D4 | 1 | 1 | yes | characteristic |
| 34 | #88193 | — | 4 | 1 | no | — |
| 35 | #88191 | — | 4 | 1 | no | — |
| 36 | #88190 | D4 | 1 | 1 | yes | characteristic |
| 37 | C2×#6105 | — | 2 | 1 | no | — |
| 38 | C2×#6105 | — | 2 | 1 | no | — |
| 39 | C2×Dic52 | — | 2 | 1 | no | — |
| 40 | C2×#6095 | — | 2 | 1 | no | — |
| 41 | #88152 | — | 4 | 1 | no | — |
| 42 | #88151 | — | 2 | 1 | no | — |
| 43 | #88144 | — | 4 | 1 | no | — |
| 44 | #88141 | — | 2 | 1 | no | — |
| 45 | #88129 | C23 | 1 | 1 | yes | characteristic |
| 46 | #88126 | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | #88123 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 48 | #88121 | — | 4 | 1 | no | — |
| 49 | #88119 | — | 4 | 1 | no | — |
| 50 | #88113 | — | 2 | 1 | no | — |
| 51 | #88113 | — | 2 | 1 | no | — |
| 52 | #88107 | — | 2 | 1 | no | — |
| 53 | #88107 | — | 2 | 1 | no | — |
| 54 | C13×#102 | — | 2 | 1 | no | — |
| 55 | C13×#102 | — | 2 | 1 | no | — |
| 56 | C13×#97 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 57 | #88060 | — | 2 | 1 | no | — |
| 58 | #88054 | — | 2 | 1 | no | — |
| 59 | #88050 | — | 2 | 1 | no | — |
| 60 | #88049 | — | 2 | 1 | no | — |
| 61 | C4×#1055 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 62 | #13607 | — | 13 | 1 | no | maximal, Sylow |
| 63 | C23×D13 | — | 2 | 1 | no | — |
| 64 | C22×#261 | — | 8 | 1 | no | — |
| 65 | C2×D4×C13 | — | 4 | 1 | no | — |
| 66 | C2×D4×C13 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 67 | C2×D4×C13 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 68 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 69 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 70 | C2×C22⋊D13 | — | 4 | 1 | no | — |
| 71 | C22×Dic13 | — | 2 | 1 | no | — |
| 72 | #6129 | — | 8 | 1 | no | — |
| 73 | D4×D13 | — | 8 | 1 | no | — |
| 74 | C2×D52 | C2×D4 | 1 | 1 | yes | characteristic |
| 75 | C2×C4×D13 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 76 | C2×Dic26 | — | 2 | 1 | no | — |
| 77 | C2×Dic26 | C2×D4 | 1 | 1 | yes | characteristic |
| 78 | C22⋊#261 | — | 4 | 1 | no | — |
| 79 | C22⋊#261 | — | 4 | 1 | no | — |
| 80 | C22⋊#261 | — | 8 | 1 | no | — |
| 81 | #6122 | — | 4 | 1 | no | — |
| 82 | #6122 | — | 4 | 1 | no | — |
| 83 | #6122 | — | 8 | 1 | no | — |
| 84 | C2×#1057 | — | 8 | 1 | no | — |
| 85 | C2×C8×C13 | — | 2 | 1 | no | — |
| 86 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 87 | C13×C4⋊C4 | — | 4 | 1 | no | — |
| 88 | C42×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 89 | C22⋊Dic13 | — | 4 | 1 | no | — |
| 90 | #6105 | — | 8 | 1 | no | — |
| 91 | #6105 | — | 8 | 1 | no | — |
| 92 | #6103 | — | 2 | 1 | no | — |
| 93 | #6103 | — | 4 | 1 | no | — |
| 94 | #6103 | — | 4 | 1 | no | — |
| 95 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 96 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 97 | #6101 | — | 2 | 1 | no | — |
| 98 | #6101 | — | 4 | 1 | no | — |
| 99 | C4×Dic13 | — | 4 | 1 | no | — |
| 100 | C4×Dic13 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 101 | C2×#1055 | — | 2 | 1 | no | — |
| 102 | Dic52 | — | 8 | 1 | no | — |
| 103 | #6095 | — | 8 | 1 | no | — |
| 104 | #3222 | — | 13 | 1 | no | — |
| 105 | #2134 | — | 13 | 1 | no | — |
| 106 | #2127 | — | 13 | 1 | no | — |
| 107 | #1414 | — | 13 | 1 | no | — |
| 108 | #1414 | — | 13 | 1 | no | — |
| 109 | #1407 | — | 13 | 1 | no | — |
| 110 | #1407 | — | 13 | 1 | no | — |
| 111 | C23×C13 | — | 2 | 1 | no | — |
| 112 | C23×C13 | — | 2 | 1 | no | — |
| 113 | C22×D13 | — | 2 | 1 | no | — |
| 114 | C22×D13 | — | 4 | 1 | no | — |
| 115 | C22×D13 | — | 4 | 1 | no | — |
| 116 | C22×D13 | — | 16 | 1 | no | — |
| 117 | C22×D13 | #99 | 1 | 1 | yes | characteristic |
| 118 | C2×#261 | — | 8 | 1 | no | — |
| 119 | C2×#261 | — | 8 | 1 | no | — |
| 120 | C2×#261 | — | 16 | 2 | no | — |
| 121 | D4×C13 | — | 4 | 1 | no | — |
| 122 | D4×C13 | — | 4 | 1 | no | — |
| 123 | D4×C13 | — | 16 | 1 | no | — |
| 124 | C2×C4×C13 | — | 2 | 1 | no | — |
| 125 | C2×C4×C13 | — | 4 | 1 | no | — |
| 126 | C2×C4×C13 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 127 | C22⋊D13 | — | 8 | 1 | no | — |
| 128 | C22⋊D13 | — | 8 | 1 | no | — |
| 129 | C22⋊D13 | — | 16 | 1 | no | — |
| 130 | C2×Dic13 | — | 2 | 1 | no | — |
| 131 | C2×Dic13 | — | 2 | 1 | no | — |
| 132 | C2×Dic13 | — | 4 | 1 | no | — |
| 133 | C2×Dic13 | — | 4 | 1 | no | — |
| 134 | C2×Dic13 | — | 4 | 1 | no | — |
| 135 | C2×Dic13 | #99 | 1 | 1 | yes | characteristic |
| 136 | D52 | — | 4 | 1 | no | — |
| 137 | C4×D13 | — | 4 | 1 | no | — |
| 138 | Dic26 | — | 4 | 1 | no | — |
| 139 | Dic26 | — | 4 | 1 | no | — |
| 140 | Dic26 | — | 4 | 1 | no | — |
| 141 | #1057 | — | 8 | 1 | no | — |
| 142 | #1057 | — | 8 | 1 | no | — |
| 143 | C8×C13 | — | 4 | 1 | no | — |
| 144 | #1055 | — | 4 | 1 | no | — |
| 145 | #541 | — | 13 | 1 | no | — |
| 146 | #535 | — | 13 | 1 | no | — |
| 147 | #497 | — | 13 | 1 | no | — |
| 148 | #492 | — | 13 | 1 | no | — |
| 149 | #490 | #261 | 1 | 1 | yes | characteristic, complemented |
| 150 | #488 | — | 13 | 1 | no | — |
| 151 | #464 | — | 26 | 1 | no | — |
| 152 | #460 | — | 26 | 1 | no | — |
| 153 | #452 | — | 26 | 1 | no | — |
| 154 | #450 | — | 26 | 1 | no | — |
| 155 | #433 | — | 13 | 1 | no | — |
| 156 | #413 | — | 26 | 1 | no | — |
| 157 | C2×#99 | — | 26 | 1 | no | — |
| 158 | #355 | — | 13 | 1 | no | — |
| 159 | #355 | — | 13 | 1 | no | — |
| 160 | #355 | — | 26 | 1 | no | — |
| 161 | #354 | — | 13 | 1 | no | — |
| 162 | #354 | — | 13 | 1 | no | — |
| 163 | #353 | — | 26 | 1 | no | — |
| 164 | C22×C13 | — | 4 | 1 | no | — |
| 165 | C22×C13 | — | 4 | 1 | no | — |
| 166 | C22×C13 | — | 8 | 1 | no | — |
| 167 | C22×C13 | — | 8 | 1 | no | — |
| 168 | C22×C13 | C2×#99 | 1 | 1 | yes | characteristic |
| 169 | C2×D13 | — | 2 | 1 | no | — |
| 170 | C2×D13 | — | 4 | 1 | no | — |
| 171 | C2×D13 | — | 4 | 1 | no | — |
| 172 | C2×D13 | — | 8 | 2 | no | — |
| 173 | C2×D13 | — | 8 | 1 | no | — |
| 174 | C2×D13 | — | 16 | 1 | no | — |
| 175 | #261 | — | 16 | 1 | no | — |
| 176 | #261 | — | 16 | 1 | no | — |
| 177 | C4×C13 | — | 2 | 1 | no | — |
| 178 | C4×C13 | — | 4 | 1 | no | — |
| 179 | C4×C13 | — | 8 | 1 | no | — |
| 180 | Dic13 | — | 2 | 1 | no | — |
| 181 | Dic13 | — | 4 | 1 | no | — |
| 182 | Dic13 | — | 4 | 1 | no | — |
| 183 | Dic13 | — | 8 | 1 | no | — |
| 184 | C2×#41 | — | 13 | 1 | no | — |
| 185 | C22×D4 | — | 13 | 1 | no | — |
| 186 | C2×Q16 | — | 26 | 1 | no | — |
| 187 | C2×SD16 | — | 26 | 1 | no | — |
| 188 | C2×SD16 | — | 26 | 1 | no | — |
| 189 | C2×SD16 | — | 26 | 1 | no | — |
| 190 | C2×M16 | — | 52 | 1 | no | — |
| 191 | C4⋊Q8 | — | 13 | 1 | no | — |
| 192 | #127 | — | 13 | 1 | no | — |
| 193 | #127 | C2×#261 | 1 | 1 | yes | characteristic |
| 194 | #126 | — | 52 | 1 | no | — |
| 195 | #125 | — | 52 | 1 | no | — |
| 196 | #125 | C2×#261 | 1 | 1 | yes | characteristic, complemented |
| 197 | #124 | — | 13 | 1 | no | — |
| 198 | #124 | — | 13 | 1 | no | — |
| 199 | C22⋊Q8 | — | 26 | 1 | no | — |
| 200 | #121 | — | 52 | 1 | no | — |
| 201 | #120 | — | 52 | 1 | no | — |
| 202 | C4×Q8 | — | 26 | 1 | no | — |
| 203 | #117 | — | 13 | 1 | no | — |
| 204 | C2×C22⋊C4 | — | 52 | 1 | no | — |
| 205 | C4⋊C8 | — | 26 | 1 | no | — |
| 206 | #103 | — | 26 | 1 | no | — |
| 207 | #102 | — | 2 | 1 | no | — |
| 208 | #102 | — | 2 | 1 | no | — |
| 209 | #102 | — | 26 | 1 | no | — |
| 210 | #101 | — | 26 | 1 | no | — |
| 211 | #101 | — | 26 | 1 | no | — |
| 212 | #100 | — | 52 | 1 | no | — |
| 213 | #99 | — | 26 | 1 | no | — |
| 214 | #99 | — | 26 | 1 | no | — |
| 215 | #99 | — | 52 | 1 | no | — |
| 216 | C22⋊C8 | — | 26 | 1 | no | — |
| 217 | #97 | C2×#261 | 1 | 1 | yes | characteristic, complemented |
| 218 | C4×C8 | — | 13 | 1 | no | — |
| 219 | C2×C13 | — | 2 | 1 | no | — |
| 220 | C2×C13 | — | 8 | 1 | no | — |
| 221 | C2×C13 | — | 8 | 1 | no | — |
| 222 | C2×C13 | #2127 | 1 | 1 | yes | characteristic |
| 223 | D13 | — | 4 | 1 | no | — |
| 224 | D13 | — | 8 | 1 | no | — |
| 225 | C24 | — | 26 | 1 | no | — |
| 226 | #41 | — | 104 | 1 | no | — |
| 227 | C2×Q8 | — | 13 | 1 | no | — |
| 228 | C2×Q8 | — | 26 | 1 | no | — |
| 229 | C2×D4 | — | 4 | 1 | no | — |
| 230 | C2×D4 | — | 13 | 1 | no | — |
| 231 | C2×D4 | — | 26 | 1 | no | — |
| 232 | C2×D4 | — | 26 | 1 | no | — |
| 233 | C2×D4 | — | 52 | 1 | no | — |
| 234 | C2×D4 | — | 104 | 1 | no | — |
| 235 | C2×D4 | C22⋊#261 | 1 | 1 | yes | characteristic |
| 236 | C2×D4 | C22⋊#261 | 1 | 1 | yes | characteristic |
| 237 | C22×C4 | — | 13 | 1 | no | — |
| 238 | C22×C4 | — | 26 | 1 | no | — |
| 239 | C22×C4 | — | 104 | 1 | no | — |
| 240 | Q16 | — | 104 | 1 | no | — |
| 241 | SD16 | — | 104 | 1 | no | — |
| 242 | SD16 | — | 104 | 1 | no | — |
| 243 | SD16 | — | 104 | 1 | no | — |
| 244 | M16 | — | 52 | 1 | no | — |
| 245 | M16 | — | 52 | 1 | no | — |
| 246 | M16 | — | 104 | 1 | no | — |
| 247 | C2×C8 | — | 2 | 1 | no | — |
| 248 | C2×C8 | — | 26 | 1 | no | — |
| 249 | C2×C8 | — | 104 | 1 | no | — |
| 250 | C4⋊C4 | — | 2 | 1 | no | — |
| 251 | C4⋊C4 | — | 4 | 1 | no | — |
| 252 | C4⋊C4 | — | 26 | 1 | no | — |
| 253 | C4⋊C4 | — | 52 | 1 | no | — |
| 254 | C4⋊C4 | — | 52 | 1 | no | — |
| 255 | C4⋊C4 | — | 52 | 1 | no | — |
| 256 | C22⋊C4 | — | 26 | 1 | no | — |
| 257 | C22⋊C4 | — | 52 | 1 | no | — |
| 258 | C22⋊C4 | — | 52 | 1 | no | — |
| 259 | C22⋊C4 | — | 52 | 1 | no | — |
| 260 | C22⋊C4 | — | 52 | 1 | no | — |
| 261 | C22⋊C4 | — | 52 | 1 | no | — |
| 262 | C22⋊C4 | — | 104 | 1 | no | — |
| 263 | C42 | — | 13 | 1 | no | — |
| 264 | C42 | — | 52 | 1 | no | — |
| 265 | C42 | C22×#261 | 1 | 1 | yes | characteristic |
| 266 | C13 | #13607 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 267 | C23 | — | 2 | 1 | no | — |
| 268 | C23 | — | 2 | 1 | no | — |
| 269 | C23 | — | 13 | 1 | no | — |
| 270 | C23 | — | 26 | 1 | no | — |
| 271 | C23 | — | 52 | 1 | no | — |
| 272 | C23 | — | 52 | 1 | no | — |
| 273 | C23 | — | 208 | 1 | no | — |
| 274 | Q8 | — | 52 | 1 | no | — |
| 275 | Q8 | — | 52 | 1 | no | — |
| 276 | Q8 | — | 52 | 1 | no | — |
| 277 | D4 | — | 4 | 1 | no | — |
| 278 | D4 | — | 4 | 1 | no | — |
| 279 | D4 | — | 16 | 1 | no | — |
| 280 | D4 | — | 52 | 1 | no | — |
| 281 | D4 | — | 104 | 1 | no | — |
| 282 | D4 | — | 104 | 1 | no | — |
| 283 | D4 | — | 208 | 1 | no | — |
| 284 | C2×C4 | — | 2 | 1 | no | — |
| 285 | C2×C4 | — | 4 | 1 | no | — |
| 286 | C2×C4 | — | 13 | 1 | no | — |
| 287 | C2×C4 | — | 26 | 1 | no | — |
| 288 | C2×C4 | — | 26 | 1 | no | — |
| 289 | C2×C4 | — | 52 | 1 | no | — |
| 290 | C2×C4 | — | 52 | 1 | no | — |
| 291 | C2×C4 | — | 52 | 1 | no | — |
| 292 | C2×C4 | — | 52 | 1 | no | — |
| 293 | C2×C4 | — | 104 | 1 | no | — |
| 294 | C2×C4 | — | 104 | 1 | no | — |
| 295 | C2×C4 | — | 208 | 2 | no | — |
| 296 | C2×C4 | C2×C22⋊#261 | 1 | 1 | yes | characteristic |
| 297 | C8 | — | 4 | 1 | no | — |
| 298 | C8 | — | 52 | 1 | no | — |
| 299 | C8 | — | 104 | 1 | no | — |
| 300 | C8 | — | 104 | 1 | no | — |
| 301 | C22 | — | 4 | 1 | no | — |
| 302 | C22 | — | 4 | 1 | no | — |
| 303 | C22 | — | 8 | 1 | no | — |
| 304 | C22 | — | 8 | 1 | no | — |
| 305 | C22 | — | 26 | 1 | no | — |
| 306 | C22 | — | 52 | 1 | no | — |
| 307 | C22 | — | 52 | 1 | no | — |
| 308 | C22 | — | 104 | 1 | no | — |
| 309 | C22 | — | 104 | 2 | no | — |
| 310 | C22 | — | 208 | 1 | no | — |
| 311 | C22 | D13⋊#99 | 1 | 1 | yes | characteristic |
| 312 | C4 | — | 2 | 1 | no | — |
| 313 | C4 | — | 4 | 1 | no | — |
| 314 | C4 | — | 8 | 1 | no | — |
| 315 | C4 | — | 26 | 1 | no | — |
| 316 | C4 | — | 52 | 1 | no | — |
| 317 | C4 | — | 52 | 1 | no | — |
| 318 | C4 | — | 104 | 1 | no | — |
| 319 | C4 | — | 208 | 1 | no | — |
| 320 | C4 | — | 208 | 1 | no | — |
| 321 | C2 | — | 2 | 1 | no | — |
| 322 | C2 | — | 8 | 1 | no | — |
| 323 | C2 | — | 8 | 1 | no | — |
| 324 | C2 | — | 52 | 1 | no | — |
| 325 | C2 | — | 104 | 1 | no | — |
| 326 | C2 | #13131114 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #13129982 | C2 | semidirect |
| 4. #13129981 | C2 | semidirect |
| 5. #13129966 | C2 | semidirect |
| 6. #13129966 | C2 | semidirect |
| 9. #11719402 | C4 | semidirect |
| 12. C13×#490 | C4 | semidirect |
| 13. #11718737 | C4 | semidirect |
| 20. #11718370 | C4 | semidirect |
| 32. C13×#125 | C2×C4 | semidirect |
| 47. #88123 | C2×C4 | semidirect |
| 56. C13×#97 | C2×C4 | semidirect |
| 61. C4×#1055 | C2×C4 | semidirect |
| 149. #490 | #261 | semidirect |
| 196. #125 | C2×#261 | semidirect |
| 217. #97 | C2×#261 | semidirect |
| 266. C13 | #13607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13131136 | 2 |
| #13131112 | 2 |
| #13129982 | 2 |
| #13129981 | 2 |
| #13129966 | 2 |
| #13125909 | 2 |
| #13607 | 13 |