Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
364 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 61 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 | #13126636 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13117008 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13117007 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13114464 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13112872 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13112813 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C13×#1336 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11719474 | — | 2 | 1 | no | — |
| 9 | #11719457 | — | 2 | 1 | no | — |
| 10 | C13×#443 | C22 | 1 | 1 | yes | characteristic |
| 11 | #11718803 | — | 2 | 1 | no | — |
| 12 | #11718558 | — | 2 | 1 | no | — |
| 13 | #11718483 | — | 2 | 1 | no | — |
| 14 | #11718483 | — | 2 | 1 | no | — |
| 15 | #11718361 | C22 | 1 | 1 | yes | characteristic |
| 16 | #11718356 | C22 | 1 | 1 | yes | characteristic |
| 17 | #11718355 | — | 2 | 1 | no | — |
| 18 | #11718354 | — | 2 | 1 | no | — |
| 19 | #11718341 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C13×#364 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C13×#322 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #11718158 | — | 2 | 1 | no | — |
| 23 | #11718110 | — | 2 | 1 | no | — |
| 24 | #11718105 | — | 2 | 1 | no | — |
| 25 | #11718086 | — | 2 | 1 | no | — |
| 26 | #11718055 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #88256 | — | 2 | 1 | no | — |
| 28 | #88256 | — | 2 | 1 | no | — |
| 29 | C13×#135 | D4 | 1 | 1 | yes | characteristic |
| 30 | C13×#131 | — | 2 | 1 | no | — |
| 31 | #88203 | — | 2 | 1 | no | — |
| 32 | #88203 | — | 2 | 1 | no | — |
| 33 | #88173 | — | 4 | 1 | no | — |
| 34 | #88168 | — | 4 | 1 | no | — |
| 35 | #88168 | — | 4 | 1 | no | — |
| 36 | D8×D13 | — | 4 | 1 | no | — |
| 37 | #88162 | — | 2 | 1 | no | — |
| 38 | #88162 | — | 2 | 1 | no | — |
| 39 | #88162 | — | 4 | 1 | no | — |
| 40 | #88162 | — | 4 | 1 | no | — |
| 41 | #88158 | — | 4 | 1 | no | — |
| 42 | #88158 | D4 | 1 | 1 | yes | characteristic |
| 43 | C2×D104 | — | 2 | 1 | no | — |
| 44 | C2×D104 | — | 2 | 1 | no | — |
| 45 | C2×D104 | — | 4 | 1 | no | — |
| 46 | C2×#6095 | — | 4 | 2 | no | — |
| 47 | #88155 | — | 2 | 1 | no | — |
| 48 | #88128 | D4 | 1 | 1 | yes | characteristic |
| 49 | #88128 | D4 | 1 | 1 | yes | characteristic |
| 50 | #88123 | — | 2 | 1 | no | — |
| 51 | C13×M32 | — | 2 | 1 | no | — |
| 52 | C13×#108 | D4 | 1 | 1 | yes | characteristic |
| 53 | C13×#104 | — | 2 | 1 | no | — |
| 54 | C4×C8×C13 | — | 2 | 1 | no | — |
| 55 | C4×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 56 | #88063 | — | 2 | 1 | no | — |
| 57 | #88063 | — | 2 | 1 | no | — |
| 58 | #88061 | — | 4 | 2 | no | — |
| 59 | #88059 | D4 | 1 | 1 | yes | characteristic |
| 60 | #88057 | — | 2 | 1 | no | — |
| 61 | #88057 | — | 2 | 1 | no | — |
| 62 | #88052 | — | 2 | 1 | no | — |
| 63 | #88045 | — | 2 | 1 | no | — |
| 64 | #12366 | — | 13 | 1 | no | maximal, Sylow |
| 65 | C13×#41 | — | 2 | 1 | no | — |
| 66 | #6131 | — | 4 | 1 | no | — |
| 67 | #6131 | — | 4 | 1 | no | — |
| 68 | D4×D13 | — | 4 | 1 | no | — |
| 69 | D4×D13 | — | 4 | 1 | no | — |
| 70 | D4×D13 | — | 8 | 1 | no | — |
| 71 | D4×D13 | — | 8 | 1 | no | — |
| 72 | #6127 | — | 2 | 1 | no | — |
| 73 | #6127 | — | 4 | 1 | no | — |
| 74 | #6127 | — | 4 | 1 | no | — |
| 75 | C2×D52 | — | 2 | 1 | no | — |
| 76 | C2×D52 | — | 2 | 1 | no | — |
| 77 | C2×D52 | — | 4 | 1 | no | — |
| 78 | C2×D52 | — | 4 | 1 | no | — |
| 79 | C2×D52 | — | 4 | 1 | no | — |
| 80 | C2×D52 | — | 4 | 1 | no | — |
| 81 | C2×Dic26 | — | 4 | 1 | no | — |
| 82 | C13×Q16 | SD16 | 1 | 1 | yes | characteristic, complemented |
| 83 | C13×SD16 | — | 2 | 1 | no | — |
| 84 | C13×D8 | SD16 | 1 | 1 | yes | characteristic, complemented |
| 85 | C13×M16 | — | 2 | 1 | no | — |
| 86 | C13×M16 | — | 4 | 1 | no | — |
| 87 | C2×C8×C13 | — | 2 | 2 | no | — |
| 88 | C2×C8×C13 | — | 4 | 1 | no | — |
| 89 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 90 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 92 | #6106 | — | 4 | 1 | no | — |
| 93 | #6106 | — | 4 | 1 | no | — |
| 94 | #6104 | — | 4 | 1 | no | — |
| 95 | #6104 | — | 4 | 1 | no | — |
| 96 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 97 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 98 | #6099 | — | 2 | 1 | no | — |
| 99 | Dic52 | SD16 | 1 | 1 | yes | characteristic, complemented |
| 100 | D104 | — | 4 | 1 | no | — |
| 101 | D104 | — | 4 | 1 | no | — |
| 102 | D104 | — | 4 | 1 | no | — |
| 103 | D104 | — | 4 | 1 | no | — |
| 104 | D104 | — | 4 | 1 | no | — |
| 105 | D104 | — | 4 | 1 | no | — |
| 106 | D104 | SD16 | 1 | 1 | yes | characteristic, complemented |
| 107 | #6095 | — | 2 | 1 | no | — |
| 108 | #6095 | — | 4 | 1 | no | — |
| 109 | #6095 | — | 4 | 1 | no | — |
| 110 | #6095 | — | 8 | 4 | no | — |
| 111 | #6094 | — | 4 | 1 | no | — |
| 112 | C8×D13 | — | 4 | 1 | no | — |
| 113 | C13×C16 | — | 4 | 1 | no | — |
| 114 | #6090 | — | 4 | 1 | no | — |
| 115 | #3292 | — | 13 | 1 | no | — |
| 116 | #2230 | — | 13 | 1 | no | — |
| 117 | #2230 | — | 13 | 1 | no | — |
| 118 | #1715 | — | 13 | 1 | no | — |
| 119 | #1357 | — | 13 | 1 | no | — |
| 120 | #1336 | — | 13 | 1 | no | — |
| 121 | #1336 | D13 | 1 | 1 | yes | characteristic, complemented |
| 122 | C22×D13 | — | 4 | 1 | no | — |
| 123 | C22×D13 | — | 4 | 1 | no | — |
| 124 | C22×D13 | — | 8 | 1 | no | — |
| 125 | C22×D13 | — | 8 | 1 | no | — |
| 126 | Q8×C13 | — | 2 | 1 | no | — |
| 127 | D4×C13 | — | 2 | 1 | no | — |
| 128 | D4×C13 | — | 4 | 1 | no | — |
| 129 | C2×C4×C13 | — | 2 | 1 | no | — |
| 130 | C2×C4×C13 | — | 4 | 1 | no | — |
| 131 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 132 | C22⋊D13 | — | 4 | 1 | no | — |
| 133 | C22⋊D13 | — | 8 | 1 | no | — |
| 134 | C22⋊D13 | — | 8 | 1 | no | — |
| 135 | C2×Dic13 | — | 8 | 1 | no | — |
| 136 | D52 | — | 2 | 1 | no | — |
| 137 | D52 | — | 4 | 1 | no | — |
| 138 | D52 | — | 4 | 1 | no | — |
| 139 | D52 | — | 4 | 1 | no | — |
| 140 | D52 | — | 4 | 1 | no | — |
| 141 | D52 | — | 8 | 2 | no | — |
| 142 | D52 | — | 8 | 2 | no | — |
| 143 | D52 | — | 8 | 1 | no | — |
| 144 | D52 | — | 8 | 1 | no | — |
| 145 | C4×D13 | — | 4 | 1 | no | — |
| 146 | C4×D13 | — | 8 | 1 | no | — |
| 147 | C4×D13 | — | 8 | 1 | no | — |
| 148 | Dic26 | — | 2 | 1 | no | — |
| 149 | Dic26 | — | 8 | 2 | no | — |
| 150 | C8×C13 | — | 4 | 2 | no | — |
| 151 | C8×C13 | — | 4 | 1 | no | — |
| 152 | C8×C13 | C2×SD16 | 1 | 1 | yes | characteristic |
| 153 | C8×C13 | C2×SD16 | 1 | 1 | yes | characteristic |
| 154 | C8×C13 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 155 | C8×C13 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 156 | #1055 | — | 4 | 1 | no | — |
| 157 | #576 | — | 26 | 1 | no | — |
| 158 | #576 | — | 26 | 1 | no | — |
| 159 | #498 | — | 13 | 1 | no | — |
| 160 | #493 | — | 13 | 1 | no | — |
| 161 | #492 | — | 26 | 1 | no | — |
| 162 | #486 | — | 26 | 1 | no | — |
| 163 | #472 | — | 26 | 1 | no | — |
| 164 | #472 | — | 26 | 1 | no | — |
| 165 | #453 | — | 26 | 1 | no | — |
| 166 | #453 | — | 26 | 1 | no | — |
| 167 | #443 | — | 13 | 1 | no | — |
| 168 | #443 | C2×D13 | 1 | 1 | yes | characteristic |
| 169 | #365 | — | 26 | 1 | no | — |
| 170 | #365 | — | 26 | 1 | no | — |
| 171 | #364 | — | 13 | 1 | no | — |
| 172 | #364 | C2×D13 | 1 | 1 | yes | characteristic, complemented |
| 173 | #360 | — | 26 | 1 | no | — |
| 174 | #360 | — | 26 | 1 | no | — |
| 175 | #322 | C2×D13 | 1 | 1 | yes | characteristic, complemented |
| 176 | C22×C13 | — | 4 | 1 | no | — |
| 177 | C22×C13 | #453 | 1 | 1 | yes | characteristic |
| 178 | C2×D13 | — | 4 | 1 | no | — |
| 179 | C2×D13 | — | 8 | 1 | no | — |
| 180 | C2×D13 | — | 8 | 1 | no | — |
| 181 | C2×D13 | — | 16 | 1 | no | — |
| 182 | C2×D13 | — | 16 | 1 | no | — |
| 183 | C2×D13 | — | 32 | 1 | no | — |
| 184 | C2×D13 | — | 32 | 1 | no | — |
| 185 | C4×C13 | — | 2 | 2 | no | — |
| 186 | C4×C13 | — | 4 | 1 | no | — |
| 187 | C4×C13 | #450 | 1 | 1 | yes | characteristic |
| 188 | C4×C13 | #450 | 1 | 1 | yes | characteristic |
| 189 | Dic13 | — | 4 | 1 | no | — |
| 190 | Dic13 | — | 16 | 1 | no | — |
| 191 | H(5,𝔽2) | — | 26 | 1 | no | — |
| 192 | H(5,𝔽2) | — | 26 | 1 | no | — |
| 193 | AGL(1,ℤ/8) | — | 26 | 1 | no | — |
| 194 | AGL(1,ℤ/8) | — | 26 | 1 | no | — |
| 195 | AGL(1,ℤ/8) | — | 26 | 1 | no | — |
| 196 | AGL(1,ℤ/8) | — | 26 | 1 | no | — |
| 197 | AGL(1,ℤ/8) | — | 52 | 1 | no | — |
| 198 | AGL(1,ℤ/8) | — | 52 | 1 | no | — |
| 199 | AGL(1,ℤ/8) | — | 52 | 1 | no | — |
| 200 | AGL(1,ℤ/8) | — | 52 | 1 | no | — |
| 201 | #135 | — | 13 | 1 | no | — |
| 202 | #135 | — | 52 | 1 | no | — |
| 203 | #135 | — | 52 | 1 | no | — |
| 204 | #135 | D52 | 1 | 1 | yes | characteristic |
| 205 | C2×SD16 | — | 52 | 2 | no | — |
| 206 | C2×D8 | — | 26 | 1 | no | — |
| 207 | C2×D8 | — | 26 | 1 | no | — |
| 208 | C2×D8 | — | 52 | 1 | no | — |
| 209 | C2×D8 | — | 52 | 1 | no | — |
| 210 | #131 | — | 2 | 1 | no | — |
| 211 | #131 | — | 26 | 1 | no | — |
| 212 | C4⋊Q8 | — | 26 | 1 | no | — |
| 213 | #127 | — | 13 | 1 | no | — |
| 214 | #127 | — | 13 | 1 | no | — |
| 215 | M32 | — | 2 | 1 | no | — |
| 216 | M32 | — | 26 | 1 | no | — |
| 217 | #108 | — | 13 | 1 | no | — |
| 218 | #108 | D52 | 1 | 1 | yes | characteristic |
| 219 | #106 | — | 26 | 1 | no | — |
| 220 | #106 | — | 26 | 1 | no | — |
| 221 | #104 | — | 2 | 1 | no | — |
| 222 | #104 | — | 26 | 1 | no | — |
| 223 | #102 | — | 52 | 2 | no | — |
| 224 | #100 | — | 26 | 1 | no | — |
| 225 | #100 | — | 26 | 1 | no | — |
| 226 | C4×C8 | — | 2 | 1 | no | — |
| 227 | C4×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 228 | C2×C13 | — | 2 | 1 | no | — |
| 229 | C2×C13 | — | 8 | 1 | no | — |
| 230 | C2×C13 | #1629 | 1 | 1 | yes | characteristic |
| 231 | D13 | — | 8 | 1 | no | — |
| 232 | D13 | — | 16 | 1 | no | — |
| 233 | D13 | — | 16 | 1 | no | — |
| 234 | #41 | — | 2 | 1 | no | — |
| 235 | #41 | — | 26 | 1 | no | — |
| 236 | #41 | — | 52 | 1 | no | — |
| 237 | #41 | — | 52 | 1 | no | — |
| 238 | #41 | — | 52 | 1 | no | — |
| 239 | #41 | — | 52 | 1 | no | — |
| 240 | C2×Q8 | — | 52 | 1 | no | — |
| 241 | C2×D4 | — | 26 | 1 | no | — |
| 242 | C2×D4 | — | 26 | 1 | no | — |
| 243 | C2×D4 | — | 52 | 1 | no | — |
| 244 | C2×D4 | — | 52 | 1 | no | — |
| 245 | C2×D4 | — | 52 | 1 | no | — |
| 246 | C2×D4 | — | 52 | 1 | no | — |
| 247 | C2×D4 | — | 52 | 1 | no | — |
| 248 | C2×D4 | — | 52 | 1 | no | — |
| 249 | C2×D4 | — | 104 | 1 | no | — |
| 250 | C2×D4 | — | 104 | 1 | no | — |
| 251 | Q16 | — | 13 | 1 | no | — |
| 252 | Q16 | #6095 | 1 | 1 | yes | characteristic, complemented |
| 253 | SD16 | — | 2 | 1 | no | — |
| 254 | SD16 | — | 26 | 1 | no | — |
| 255 | SD16 | — | 52 | 1 | no | — |
| 256 | SD16 | — | 52 | 1 | no | — |
| 257 | SD16 | — | 52 | 1 | no | — |
| 258 | SD16 | — | 52 | 1 | no | — |
| 259 | SD16 | — | 104 | 4 | no | — |
| 260 | D8 | — | 13 | 1 | no | — |
| 261 | D8 | — | 52 | 1 | no | — |
| 262 | D8 | — | 52 | 1 | no | — |
| 263 | D8 | — | 52 | 1 | no | — |
| 264 | D8 | — | 52 | 1 | no | — |
| 265 | D8 | — | 52 | 1 | no | — |
| 266 | D8 | — | 52 | 1 | no | — |
| 267 | D8 | — | 52 | 1 | no | — |
| 268 | D8 | — | 52 | 1 | no | — |
| 269 | D8 | #6095 | 1 | 1 | yes | characteristic, complemented |
| 270 | M16 | — | 2 | 1 | no | — |
| 271 | M16 | — | 4 | 1 | no | — |
| 272 | M16 | — | 26 | 1 | no | — |
| 273 | M16 | — | 52 | 1 | no | — |
| 274 | C2×C8 | — | 2 | 2 | no | — |
| 275 | C2×C8 | — | 4 | 1 | no | — |
| 276 | C2×C8 | — | 52 | 1 | no | — |
| 277 | C2×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 278 | C2×C8 | D4×D13 | 1 | 1 | yes | characteristic |
| 279 | C4⋊C4 | — | 52 | 1 | no | — |
| 280 | C4⋊C4 | — | 52 | 1 | no | — |
| 281 | C42 | D4×D13 | 1 | 1 | yes | characteristic |
| 282 | C16 | — | 4 | 1 | no | — |
| 283 | C16 | — | 52 | 1 | no | — |
| 284 | C13 | #12366 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 285 | C23 | — | 52 | 1 | no | — |
| 286 | C23 | — | 52 | 1 | no | — |
| 287 | C23 | — | 104 | 1 | no | — |
| 288 | C23 | — | 104 | 1 | no | — |
| 289 | Q8 | — | 2 | 1 | no | — |
| 290 | Q8 | — | 26 | 1 | no | — |
| 291 | Q8 | — | 104 | 2 | no | — |
| 292 | D4 | — | 2 | 1 | no | — |
| 293 | D4 | — | 4 | 1 | no | — |
| 294 | D4 | — | 26 | 1 | no | — |
| 295 | D4 | — | 52 | 1 | no | — |
| 296 | D4 | — | 52 | 1 | no | — |
| 297 | D4 | — | 52 | 1 | no | — |
| 298 | D4 | — | 52 | 1 | no | — |
| 299 | D4 | — | 52 | 1 | no | — |
| 300 | D4 | — | 104 | 2 | no | — |
| 301 | D4 | — | 104 | 2 | no | — |
| 302 | D4 | — | 104 | 1 | no | — |
| 303 | D4 | — | 104 | 1 | no | — |
| 304 | D4 | — | 104 | 1 | no | — |
| 305 | D4 | — | 104 | 1 | no | — |
| 306 | C2×C4 | — | 2 | 1 | no | — |
| 307 | C2×C4 | — | 4 | 1 | no | — |
| 308 | C2×C4 | — | 52 | 1 | no | — |
| 309 | C2×C4 | — | 104 | 1 | no | — |
| 310 | C2×C4 | — | 104 | 1 | no | — |
| 311 | C2×C4 | — | 104 | 1 | no | — |
| 312 | C2×C4 | #88136 | 1 | 1 | yes | characteristic |
| 313 | C8 | — | 4 | 2 | no | — |
| 314 | C8 | — | 4 | 1 | no | — |
| 315 | C8 | — | 52 | 1 | no | — |
| 316 | C8 | C2×#6095 | 1 | 1 | yes | characteristic |
| 317 | C8 | #88162 | 1 | 1 | yes | characteristic |
| 318 | C8 | #88165 | 1 | 1 | yes | characteristic |
| 319 | C8 | SD16×D13 | 1 | 1 | yes | characteristic |
| 320 | C22 | — | 4 | 1 | no | — |
| 321 | C22 | — | 52 | 1 | no | — |
| 322 | C22 | — | 104 | 1 | no | — |
| 323 | C22 | — | 104 | 1 | no | — |
| 324 | C22 | — | 416 | 1 | no | — |
| 325 | C22 | — | 416 | 1 | no | — |
| 326 | C22 | — | 208 | 1 | no | — |
| 327 | C22 | — | 208 | 1 | no | — |
| 328 | C22 | #11718483 | 1 | 1 | yes | characteristic |
| 329 | C4 | — | 2 | 2 | no | — |
| 330 | C4 | — | 4 | 1 | no | — |
| 331 | C4 | — | 52 | 1 | no | — |
| 332 | C4 | — | 208 | 1 | no | — |
| 333 | C4 | #11718392 | 1 | 1 | yes | characteristic |
| 334 | C4 | #11718437 | 1 | 1 | yes | characteristic |
| 335 | C2 | — | 2 | 1 | no | — |
| 336 | C2 | — | 8 | 1 | no | — |
| 337 | C2 | — | 104 | 1 | no | — |
| 338 | C2 | — | 208 | 1 | no | — |
| 339 | C2 | — | 208 | 1 | no | — |
| 340 | C2 | #13113954 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13117008 | C2 | semidirect |
| 3. #13117007 | C2 | semidirect |
| 4. #13114464 | C2 | semidirect |
| 5. #13112872 | C2 | semidirect |
| 6. #13112813 | C2 | semidirect |
| 7. C13×#1336 | C2 | semidirect |
| 19. #11718341 | C22 | semidirect |
| 20. C13×#364 | C22 | semidirect |
| 21. C13×#322 | C22 | semidirect |
| 26. #11718055 | C22 | semidirect |
| 82. C13×Q16 | SD16 | semidirect |
| 84. C13×D8 | SD16 | semidirect |
| 99. Dic52 | SD16 | semidirect |
| 106. D104 | SD16 | semidirect |
| 121. #1336 | D13 | semidirect |
| 172. #364 | C2×D13 | semidirect |
| 175. #322 | C2×D13 | semidirect |
| 252. Q16 | #6095 | semidirect |
| 269. D8 | #6095 | semidirect |
| 284. C13 | #12366 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13126636 | 2 |
| #13117008 | 2 |
| #13117007 | 2 |
| #13114464 | 2 |
| #13112872 | 2 |
| #13112813 | 2 |
| C13×#1336 | 2 |
| #12366 | 13 |