Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
416 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 64 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 | C2×#11718228 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#11718226 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13129966 | C2 | 1 | 4 | yes | maximal, direct product factor |
| 4 | C2×#11718376 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C22×Dic52 | — | 2 | 1 | no | — |
| 6 | C22×#6095 | — | 2 | 1 | no | — |
| 7 | C2×#88129 | C22 | 1 | 1 | yes | characteristic |
| 8 | C2×#88123 | C4 | 1 | 1 | yes | characteristic, complemented |
| 9 | C2×#88113 | — | 2 | 1 | no | — |
| 10 | C2×#88107 | — | 2 | 1 | no | — |
| 11 | C2×C13×#97 | C4 | 1 | 1 | yes | characteristic, complemented |
| 12 | #11718376 | — | 2 | 1 | no | — |
| 13 | #11718376 | — | 2 | 1 | no | — |
| 14 | #11718376 | C4 | 1 | 2 | yes | complemented |
| 15 | #11718376 | C22 | 1 | 2 | yes | — |
| 16 | #11718228 | — | 2 | 1 | no | — |
| 17 | #11718228 | C22 | 1 | 2 | yes | — |
| 18 | #11718226 | — | 2 | 1 | no | — |
| 19 | #11718226 | C22 | 1 | 2 | yes | — |
| 20 | C22×D52 | D4 | 1 | 1 | yes | characteristic |
| 21 | C22×Dic26 | — | 2 | 1 | no | — |
| 22 | C22×Dic26 | D4 | 1 | 1 | yes | characteristic |
| 23 | C2×C22⋊#261 | — | 4 | 1 | no | — |
| 24 | C2×#6122 | — | 4 | 1 | no | — |
| 25 | C22×C8×C13 | — | 2 | 1 | no | — |
| 26 | C2×C42×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 27 | C2×#6103 | — | 4 | 1 | no | — |
| 28 | C2×C4⋊Dic13 | — | 4 | 1 | no | — |
| 29 | C2×Dic52 | — | 2 | 2 | no | — |
| 30 | C2×Dic52 | — | 2 | 2 | no | — |
| 31 | C2×Dic52 | — | 4 | 2 | no | — |
| 32 | C2×Dic52 | — | 4 | 2 | no | — |
| 33 | C2×#6095 | — | 2 | 2 | no | — |
| 34 | C2×#6095 | — | 2 | 2 | no | — |
| 35 | C2×#6095 | — | 4 | 2 | no | — |
| 36 | C2×#6095 | — | 4 | 2 | no | — |
| 37 | #88129 | — | 4 | 1 | no | — |
| 38 | #88129 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | #88129 | D4 | 1 | 1 | yes | characteristic |
| 40 | #88129 | D4 | 1 | 1 | yes | characteristic |
| 41 | #88129 | C23 | 1 | 1 | yes | characteristic |
| 42 | #88123 | — | 2 | 1 | no | — |
| 43 | #88123 | — | 4 | 1 | no | — |
| 44 | #88123 | C2×C4 | 1 | 2 | yes | complemented |
| 45 | #88113 | — | 2 | 2 | no | — |
| 46 | #88113 | — | 4 | 1 | no | — |
| 47 | #88107 | — | 2 | 2 | no | — |
| 48 | #88107 | — | 4 | 1 | no | — |
| 49 | C13×#97 | — | 2 | 1 | no | — |
| 50 | C13×#97 | C2×C4 | 1 | 2 | yes | complemented |
| 51 | C2×#1407 | — | 13 | 1 | no | maximal, Sylow |
| 52 | C23×D13 | — | 2 | 1 | no | — |
| 53 | C22×#261 | — | 8 | 1 | no | — |
| 54 | C22×C4×C13 | — | 2 | 1 | no | — |
| 55 | C22×C4×C13 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 56 | C22×Dic13 | — | 2 | 1 | no | — |
| 57 | C22×Dic13 | — | 4 | 1 | no | — |
| 58 | C2×D52 | — | 2 | 1 | no | — |
| 59 | C2×D52 | — | 4 | 1 | no | — |
| 60 | C2×D52 | — | 4 | 1 | no | — |
| 61 | C2×D52 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 62 | C2×D52 | C2×D4 | 1 | 1 | yes | characteristic |
| 63 | C2×Dic26 | — | 2 | 2 | no | — |
| 64 | C2×Dic26 | — | 2 | 1 | no | — |
| 65 | C2×Dic26 | — | 4 | 1 | no | — |
| 66 | C2×Dic26 | — | 4 | 1 | no | — |
| 67 | C2×Dic26 | — | 4 | 1 | no | — |
| 68 | C2×Dic26 | — | 4 | 1 | no | — |
| 69 | C2×Dic26 | — | 4 | 1 | no | — |
| 70 | C2×Dic26 | — | 4 | 1 | no | — |
| 71 | C2×Dic26 | — | 4 | 1 | no | — |
| 72 | C2×Dic26 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 73 | C2×Dic26 | C2×D4 | 1 | 1 | yes | characteristic |
| 74 | C22⋊#261 | — | 4 | 2 | no | — |
| 75 | C22⋊#261 | — | 8 | 1 | no | — |
| 76 | #6122 | — | 4 | 2 | no | — |
| 77 | #6122 | — | 8 | 1 | no | — |
| 78 | C2×#1057 | — | 8 | 1 | no | — |
| 79 | C2×C8×C13 | — | 2 | 2 | no | — |
| 80 | C2×C8×C13 | — | 2 | 2 | no | — |
| 81 | C2×C8×C13 | — | 2 | 2 | no | — |
| 82 | C42×C13 | — | 2 | 1 | no | — |
| 83 | C42×C13 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 84 | C42×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 85 | #6103 | — | 4 | 1 | no | — |
| 86 | #6103 | — | 4 | 1 | no | — |
| 87 | #6103 | — | 4 | 1 | no | — |
| 88 | #6103 | — | 4 | 1 | no | — |
| 89 | C4⋊Dic13 | — | 4 | 2 | no | — |
| 90 | C4⋊Dic13 | — | 4 | 2 | no | — |
| 91 | Dic52 | — | 4 | 4 | no | — |
| 92 | Dic52 | — | 4 | 4 | no | — |
| 93 | #6095 | — | 4 | 4 | no | — |
| 94 | #6095 | — | 4 | 4 | no | — |
| 95 | C2×#497 | — | 13 | 1 | no | — |
| 96 | C2×#355 | — | 13 | 1 | no | — |
| 97 | C2×#354 | — | 13 | 1 | no | — |
| 98 | #1407 | — | 13 | 4 | no | — |
| 99 | C23×C13 | #99 | 1 | 1 | yes | characteristic |
| 100 | C22×D13 | — | 2 | 1 | no | — |
| 101 | C22×D13 | — | 2 | 1 | no | — |
| 102 | C22×D13 | — | 4 | 1 | no | — |
| 103 | C22×D13 | — | 4 | 1 | no | — |
| 104 | C22×D13 | — | 8 | 2 | no | — |
| 105 | C2×#261 | — | 8 | 2 | no | — |
| 106 | C2×#261 | — | 16 | 2 | no | — |
| 107 | C2×C4×C13 | — | 2 | 1 | no | — |
| 108 | C2×C4×C13 | — | 2 | 1 | no | — |
| 109 | C2×C4×C13 | — | 2 | 1 | no | — |
| 110 | C2×C4×C13 | — | 2 | 1 | no | — |
| 111 | C2×C4×C13 | — | 4 | 2 | no | — |
| 112 | C2×C4×C13 | #99 | 1 | 1 | yes | characteristic |
| 113 | C2×C4×C13 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 114 | C2×Dic13 | — | 2 | 1 | no | — |
| 115 | C2×Dic13 | — | 2 | 1 | no | — |
| 116 | C2×Dic13 | — | 4 | 1 | no | — |
| 117 | C2×Dic13 | — | 4 | 1 | no | — |
| 118 | C2×Dic13 | — | 4 | 2 | no | — |
| 119 | C2×Dic13 | — | 8 | 1 | no | — |
| 120 | C2×Dic13 | — | 8 | 1 | no | — |
| 121 | D52 | — | 4 | 1 | no | — |
| 122 | D52 | — | 4 | 1 | no | — |
| 123 | D52 | — | 8 | 1 | no | — |
| 124 | Dic26 | — | 4 | 1 | no | — |
| 125 | Dic26 | — | 4 | 1 | no | — |
| 126 | Dic26 | — | 4 | 2 | no | — |
| 127 | Dic26 | — | 4 | 2 | no | — |
| 128 | Dic26 | — | 8 | 1 | no | — |
| 129 | Dic26 | — | 8 | 1 | no | — |
| 130 | Dic26 | — | 8 | 1 | no | — |
| 131 | #1057 | — | 8 | 2 | no | — |
| 132 | C8×C13 | — | 2 | 4 | no | — |
| 133 | C22×Q16 | — | 26 | 1 | no | — |
| 134 | C22×SD16 | — | 26 | 1 | no | — |
| 135 | C2×C4⋊Q8 | — | 13 | 1 | no | — |
| 136 | C2×#124 | — | 13 | 1 | no | — |
| 137 | #497 | — | 13 | 2 | no | — |
| 138 | #497 | — | 13 | 2 | no | — |
| 139 | #497 | — | 26 | 1 | no | — |
| 140 | #497 | — | 26 | 1 | no | — |
| 141 | C2×#101 | — | 26 | 1 | no | — |
| 142 | C2×#99 | — | 26 | 1 | no | — |
| 143 | C2×#97 | #261 | 1 | 1 | yes | characteristic, complemented |
| 144 | #355 | — | 13 | 2 | no | — |
| 145 | #355 | — | 26 | 1 | no | — |
| 146 | #354 | — | 13 | 2 | no | — |
| 147 | #354 | — | 26 | 1 | no | — |
| 148 | C22×C13 | — | 2 | 2 | no | — |
| 149 | C22×C13 | #353 | 1 | 1 | yes | characteristic |
| 150 | C22×C13 | #353 | 1 | 1 | yes | characteristic |
| 151 | C22×C13 | C2×#99 | 1 | 1 | yes | characteristic |
| 152 | C2×D13 | — | 4 | 1 | no | — |
| 153 | C2×D13 | — | 4 | 1 | no | — |
| 154 | C2×D13 | — | 8 | 2 | no | — |
| 155 | C2×D13 | — | 8 | 1 | no | — |
| 156 | C2×D13 | — | 8 | 1 | no | — |
| 157 | C2×D13 | — | 16 | 1 | no | — |
| 158 | #261 | — | 16 | 2 | no | — |
| 159 | C4×C13 | — | 2 | 1 | no | — |
| 160 | C4×C13 | — | 2 | 1 | no | — |
| 161 | C4×C13 | — | 4 | 1 | no | — |
| 162 | C4×C13 | — | 4 | 1 | no | — |
| 163 | Dic13 | — | 4 | 1 | no | — |
| 164 | Dic13 | — | 4 | 1 | no | — |
| 165 | Dic13 | — | 8 | 2 | no | — |
| 166 | C22×Q8 | — | 13 | 1 | no | — |
| 167 | C22×Q8 | — | 26 | 1 | no | — |
| 168 | C22×D4 | — | 13 | 1 | no | — |
| 169 | C2×Q16 | — | 26 | 2 | no | — |
| 170 | C2×Q16 | — | 26 | 2 | no | — |
| 171 | C2×Q16 | — | 52 | 2 | no | — |
| 172 | C2×Q16 | — | 52 | 2 | no | — |
| 173 | C2×SD16 | — | 26 | 2 | no | — |
| 174 | C2×SD16 | — | 26 | 2 | no | — |
| 175 | C2×SD16 | — | 52 | 2 | no | — |
| 176 | C2×SD16 | — | 52 | 2 | no | — |
| 177 | C2×M16 | — | 52 | 1 | no | — |
| 178 | C22×C8 | — | 2 | 1 | no | — |
| 179 | C4⋊Q8 | — | 13 | 2 | no | — |
| 180 | C4⋊Q8 | — | 26 | 1 | no | — |
| 181 | C4⋊Q8 | — | 52 | 1 | no | — |
| 182 | #124 | — | 13 | 1 | no | — |
| 183 | #124 | — | 13 | 1 | no | — |
| 184 | #124 | — | 13 | 1 | no | — |
| 185 | #124 | — | 13 | 1 | no | — |
| 186 | #124 | — | 52 | 1 | no | — |
| 187 | C2×C4⋊C4 | — | 52 | 1 | no | — |
| 188 | C2×C22⋊C4 | — | 52 | 1 | no | — |
| 189 | C2×C22⋊C4 | — | 52 | 1 | no | — |
| 190 | C2×C42 | C2×#261 | 1 | 1 | yes | characteristic |
| 191 | #101 | — | 26 | 2 | no | — |
| 192 | #101 | — | 52 | 1 | no | — |
| 193 | #99 | — | 26 | 2 | no | — |
| 194 | #99 | — | 52 | 1 | no | — |
| 195 | #97 | — | 2 | 1 | no | — |
| 196 | #97 | C2×#261 | 1 | 2 | yes | complemented |
| 197 | C2×C13 | — | 2 | 1 | no | — |
| 198 | C2×C13 | — | 2 | 1 | no | — |
| 199 | C2×C13 | #1407 | 1 | 2 | yes | complemented |
| 200 | C2×C13 | C2×#353 | 1 | 1 | yes | characteristic |
| 201 | D13 | — | 8 | 1 | no | — |
| 202 | D13 | — | 8 | 1 | no | — |
| 203 | C24 | — | 26 | 1 | no | — |
| 204 | C2×Q8 | — | 13 | 1 | no | — |
| 205 | C2×Q8 | — | 13 | 1 | no | — |
| 206 | C2×Q8 | — | 26 | 1 | no | — |
| 207 | C2×Q8 | — | 26 | 2 | no | — |
| 208 | C2×Q8 | — | 52 | 1 | no | — |
| 209 | C2×Q8 | — | 52 | 1 | no | — |
| 210 | C2×Q8 | — | 52 | 1 | no | — |
| 211 | C2×Q8 | — | 52 | 1 | no | — |
| 212 | C2×Q8 | — | 52 | 1 | no | — |
| 213 | C2×Q8 | — | 52 | 1 | no | — |
| 214 | C2×Q8 | — | 52 | 1 | no | — |
| 215 | C2×D4 | — | 13 | 1 | no | — |
| 216 | C2×D4 | — | 13 | 1 | no | — |
| 217 | C2×D4 | — | 26 | 1 | no | — |
| 218 | C2×D4 | — | 52 | 1 | no | — |
| 219 | C2×D4 | — | 52 | 1 | no | — |
| 220 | C22×C4 | — | 2 | 1 | no | — |
| 221 | C22×C4 | — | 26 | 1 | no | — |
| 222 | C22×C4 | — | 52 | 1 | no | — |
| 223 | C22×C4 | — | 104 | 1 | no | — |
| 224 | C22×C4 | C22⋊#261 | 1 | 1 | yes | characteristic |
| 225 | Q16 | — | 52 | 4 | no | — |
| 226 | Q16 | — | 52 | 4 | no | — |
| 227 | SD16 | — | 52 | 4 | no | — |
| 228 | SD16 | — | 52 | 4 | no | — |
| 229 | M16 | — | 52 | 2 | no | — |
| 230 | M16 | — | 104 | 1 | no | — |
| 231 | C2×C8 | — | 2 | 2 | no | — |
| 232 | C2×C8 | — | 2 | 2 | no | — |
| 233 | C2×C8 | — | 2 | 2 | no | — |
| 234 | C2×C8 | — | 104 | 1 | no | — |
| 235 | C4⋊C4 | — | 52 | 2 | no | — |
| 236 | C4⋊C4 | — | 52 | 2 | no | — |
| 237 | C22⋊C4 | — | 52 | 1 | no | — |
| 238 | C22⋊C4 | — | 52 | 1 | no | — |
| 239 | C22⋊C4 | — | 52 | 1 | no | — |
| 240 | C22⋊C4 | — | 52 | 1 | no | — |
| 241 | C22⋊C4 | — | 52 | 2 | no | — |
| 242 | C22⋊C4 | — | 104 | 1 | no | — |
| 243 | C42 | — | 2 | 1 | no | — |
| 244 | C42 | C22⋊#261 | 1 | 1 | yes | characteristic |
| 245 | C42 | C22×#261 | 1 | 1 | yes | characteristic |
| 246 | C13 | C2×#1407 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 247 | C23 | — | 26 | 1 | no | — |
| 248 | C23 | — | 26 | 1 | no | — |
| 249 | C23 | — | 52 | 1 | no | — |
| 250 | C23 | — | 52 | 1 | no | — |
| 251 | C23 | — | 104 | 2 | no | — |
| 252 | C23 | #88107 | 1 | 1 | yes | characteristic |
| 253 | Q8 | — | 52 | 1 | no | — |
| 254 | Q8 | — | 52 | 1 | no | — |
| 255 | Q8 | — | 52 | 2 | no | — |
| 256 | Q8 | — | 52 | 2 | no | — |
| 257 | Q8 | — | 104 | 1 | no | — |
| 258 | Q8 | — | 104 | 1 | no | — |
| 259 | Q8 | — | 104 | 1 | no | — |
| 260 | D4 | — | 52 | 1 | no | — |
| 261 | D4 | — | 52 | 1 | no | — |
| 262 | D4 | — | 104 | 1 | no | — |
| 263 | C2×C4 | — | 2 | 1 | no | — |
| 264 | C2×C4 | — | 2 | 1 | no | — |
| 265 | C2×C4 | — | 2 | 1 | no | — |
| 266 | C2×C4 | — | 2 | 1 | no | — |
| 267 | C2×C4 | — | 4 | 2 | no | — |
| 268 | C2×C4 | — | 26 | 1 | no | — |
| 269 | C2×C4 | — | 26 | 1 | no | — |
| 270 | C2×C4 | — | 52 | 1 | no | — |
| 271 | C2×C4 | — | 52 | 1 | no | — |
| 272 | C2×C4 | — | 52 | 2 | no | — |
| 273 | C2×C4 | — | 104 | 1 | no | — |
| 274 | C2×C4 | — | 104 | 1 | no | — |
| 275 | C2×C4 | — | 104 | 2 | no | — |
| 276 | C2×C4 | — | 208 | 2 | no | — |
| 277 | C2×C4 | #88107 | 1 | 1 | yes | characteristic |
| 278 | C2×C4 | C2×C22⋊#261 | 1 | 1 | yes | characteristic |
| 279 | C8 | — | 2 | 4 | no | — |
| 280 | C8 | — | 104 | 2 | no | — |
| 281 | C22 | — | 2 | 2 | no | — |
| 282 | C22 | — | 52 | 1 | no | — |
| 283 | C22 | — | 52 | 1 | no | — |
| 284 | C22 | — | 104 | 1 | no | — |
| 285 | C22 | — | 104 | 1 | no | — |
| 286 | C22 | — | 104 | 2 | no | — |
| 287 | C22 | — | 208 | 1 | no | — |
| 288 | C22 | #11718225 | 1 | 1 | yes | characteristic |
| 289 | C22 | #11718225 | 1 | 1 | yes | characteristic |
| 290 | C22 | C2×#88107 | 1 | 1 | yes | characteristic |
| 291 | C4 | — | 2 | 1 | no | — |
| 292 | C4 | — | 2 | 1 | no | — |
| 293 | C4 | — | 4 | 1 | no | — |
| 294 | C4 | — | 4 | 1 | no | — |
| 295 | C4 | — | 52 | 1 | no | — |
| 296 | C4 | — | 52 | 1 | no | — |
| 297 | C4 | — | 104 | 2 | no | — |
| 298 | C4 | — | 208 | 2 | no | — |
| 299 | C2 | — | 2 | 1 | no | — |
| 300 | C2 | — | 2 | 1 | no | — |
| 301 | C2 | — | 104 | 1 | no | — |
| 302 | C2 | — | 104 | 1 | no | — |
| 303 | C2 | #13129966 | 1 | 2 | yes | direct product factor |
| 304 | C2 | C2×#11718225 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #13129966 | C2 | direct (N × H) |
| 8. C2×#88123 | C4 | semidirect |
| 11. C2×C13×#97 | C4 | semidirect |
| 14. #11718376 | C4 | semidirect |
| 44. #88123 | C2×C4 | semidirect |
| 50. C13×#97 | C2×C4 | semidirect |
| 143. C2×#97 | #261 | semidirect |
| 196. #97 | C2×#261 | semidirect |
| 199. C2×C13 | #1407 | semidirect |
| 246. C13 | C2×#1407 | semidirect |
| 303. C2 | #13129966 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11718228 | 2 |
| C2×#11718226 | 2 |
| #13129966 | 2 |
| C2×#11718376 | 2 |
| C2×#1407 | 13 |