Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
520 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 95 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 | #13127972 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13124557 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×#11718089 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #13116451 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C13×#1385 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11719453 | — | 2 | 2 | no | — |
| 7 | C2×#88158 | C22 | 1 | 2 | yes | — |
| 8 | C2×#88155 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×C13×M32 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×C13×#108 | C22 | 1 | 2 | yes | — |
| 11 | #11718793 | — | 2 | 2 | no | — |
| 12 | C22×#6090 | C22 | 1 | 1 | yes | characteristic |
| 13 | #11718570 | — | 2 | 2 | no | — |
| 14 | #11718569 | — | 2 | 2 | no | — |
| 15 | #11718565 | — | 2 | 2 | no | — |
| 16 | #11718559 | — | 2 | 4 | no | — |
| 17 | #11718558 | — | 2 | 2 | no | — |
| 18 | #11718557 | — | 2 | 2 | no | — |
| 19 | #11718099 | — | 2 | 2 | no | — |
| 20 | #11718089 | — | 2 | 4 | no | — |
| 21 | C2×#6127 | — | 2 | 2 | no | — |
| 22 | C2×#6127 | D4 | 1 | 1 | yes | characteristic |
| 23 | C2×C13×M16 | — | 2 | 2 | no | — |
| 24 | C22×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 25 | C2×#6099 | D4 | 1 | 1 | yes | characteristic |
| 26 | #88163 | — | 2 | 4 | no | — |
| 27 | #88163 | — | 4 | 2 | no | — |
| 28 | #88162 | — | 2 | 4 | no | — |
| 29 | #88162 | — | 4 | 2 | no | — |
| 30 | C2×Dic52 | D4 | 1 | 2 | yes | — |
| 31 | #88158 | — | 2 | 2 | no | — |
| 32 | #88158 | — | 2 | 2 | no | — |
| 33 | #88158 | — | 2 | 2 | no | — |
| 34 | #88158 | — | 2 | 2 | no | — |
| 35 | #88158 | — | 4 | 4 | no | — |
| 36 | C2×D104 | D4 | 1 | 2 | yes | — |
| 37 | C2×#6095 | — | 2 | 2 | no | — |
| 38 | #88155 | — | 2 | 2 | no | — |
| 39 | #88155 | — | 2 | 2 | no | — |
| 40 | C2×#6094 | — | 2 | 1 | no | — |
| 41 | C2×C8×D13 | — | 2 | 1 | no | — |
| 42 | C13×M32 | — | 2 | 2 | no | — |
| 43 | C2×C13×C16 | D4 | 1 | 2 | yes | — |
| 44 | C13×#108 | — | 2 | 2 | no | — |
| 45 | C13×#108 | D4 | 1 | 4 | yes | — |
| 46 | #88064 | — | 2 | 4 | no | — |
| 47 | #88063 | — | 2 | 4 | no | — |
| 48 | C2×#6090 | — | 2 | 2 | no | — |
| 49 | C2×#6090 | — | 2 | 1 | no | — |
| 50 | Dic104 | — | 2 | 2 | no | — |
| 51 | #88040 | — | 2 | 4 | no | — |
| 52 | D208 | — | 2 | 2 | no | — |
| 53 | #13312 | — | 13 | 1 | no | maximal, Sylow |
| 54 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 55 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 56 | C2×C22⋊D13 | — | 4 | 2 | no | — |
| 57 | #6127 | — | 2 | 2 | no | — |
| 58 | #6127 | — | 2 | 2 | no | — |
| 59 | #6127 | — | 4 | 2 | no | — |
| 60 | #6127 | — | 4 | 2 | no | — |
| 61 | #6127 | — | 4 | 2 | no | — |
| 62 | #6127 | — | 4 | 2 | no | — |
| 63 | C2×D52 | — | 2 | 2 | no | — |
| 64 | C2×D52 | D8 | 1 | 1 | yes | characteristic |
| 65 | C2×C4×D13 | — | 2 | 1 | no | — |
| 66 | C2×C4×D13 | — | 4 | 2 | no | — |
| 67 | C2×Dic26 | — | 2 | 2 | no | — |
| 68 | C2×Dic26 | D8 | 1 | 1 | yes | characteristic |
| 69 | C13×M16 | — | 2 | 4 | no | — |
| 70 | C13×M16 | — | 4 | 2 | no | — |
| 71 | C2×C8×C13 | — | 4 | 2 | no | — |
| 72 | C2×C8×C13 | C2×D4 | 1 | 2 | yes | — |
| 73 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 74 | C2×C8×C13 | C2×D4 | 1 | 2 | yes | — |
| 75 | C2×C8×C13 | #41 | 1 | 1 | yes | characteristic |
| 76 | #6099 | — | 2 | 2 | no | — |
| 77 | C2×#1055 | — | 2 | 1 | no | — |
| 78 | Dic52 | — | 2 | 2 | no | — |
| 79 | Dic52 | — | 2 | 2 | no | — |
| 80 | Dic52 | — | 4 | 4 | no | — |
| 81 | D104 | — | 2 | 2 | no | — |
| 82 | D104 | — | 2 | 2 | no | — |
| 83 | D104 | — | 4 | 4 | no | — |
| 84 | #6095 | — | 4 | 4 | no | — |
| 85 | #6095 | — | 4 | 4 | no | — |
| 86 | #6095 | — | 4 | 2 | no | — |
| 87 | #6095 | — | 4 | 2 | no | — |
| 88 | #6094 | — | 4 | 2 | no | — |
| 89 | C8×D13 | — | 4 | 1 | no | — |
| 90 | C8×D13 | — | 4 | 1 | no | — |
| 91 | C13×C16 | — | 2 | 2 | no | — |
| 92 | #6090 | — | 4 | 1 | no | — |
| 93 | #3414 | — | 13 | 1 | no | — |
| 94 | #3067 | — | 13 | 2 | no | — |
| 95 | C2×#359 | — | 13 | 2 | no | — |
| 96 | #2113 | — | 13 | 1 | no | — |
| 97 | #1385 | D13 | 1 | 1 | yes | characteristic, complemented |
| 98 | C23×C13 | #135 | 1 | 1 | yes | characteristic |
| 99 | C22×D13 | — | 2 | 1 | no | — |
| 100 | C22×D13 | — | 4 | 2 | no | — |
| 101 | C2×C4×C13 | #120 | 1 | 2 | yes | — |
| 102 | C2×C4×C13 | #121 | 1 | 1 | yes | characteristic |
| 103 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 104 | C2×C4×C13 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 105 | C22⋊D13 | — | 4 | 2 | no | — |
| 106 | C22⋊D13 | — | 8 | 2 | no | — |
| 107 | C22⋊D13 | — | 8 | 2 | no | — |
| 108 | C2×Dic13 | — | 2 | 1 | no | — |
| 109 | C2×Dic13 | — | 4 | 2 | no | — |
| 110 | D52 | — | 2 | 2 | no | — |
| 111 | D52 | — | 4 | 2 | no | — |
| 112 | D52 | — | 4 | 2 | no | — |
| 113 | C4×D13 | — | 4 | 1 | no | — |
| 114 | C4×D13 | — | 4 | 1 | no | — |
| 115 | C4×D13 | — | 8 | 2 | no | — |
| 116 | C4×D13 | — | 8 | 2 | no | — |
| 117 | Dic26 | — | 2 | 2 | no | — |
| 118 | Dic26 | — | 4 | 2 | no | — |
| 119 | Dic26 | — | 4 | 2 | no | — |
| 120 | C8×C13 | — | 4 | 4 | no | — |
| 121 | C8×C13 | #120 | 1 | 1 | yes | characteristic |
| 122 | C8×C13 | #121 | 1 | 2 | yes | — |
| 123 | C8×C13 | #127 | 1 | 1 | yes | characteristic |
| 124 | #1055 | — | 4 | 1 | no | — |
| 125 | #575 | — | 26 | 2 | no | — |
| 126 | C2×#135 | — | 13 | 2 | no | — |
| 127 | C2×#131 | — | 13 | 1 | no | — |
| 128 | #510 | — | 26 | 2 | no | — |
| 129 | #509 | — | 26 | 2 | no | — |
| 130 | #508 | — | 26 | 2 | no | — |
| 131 | C2×M32 | C2×D13 | 1 | 1 | yes | characteristic |
| 132 | C22×C16 | — | 13 | 1 | no | — |
| 133 | #473 | — | 26 | 2 | no | — |
| 134 | #472 | — | 26 | 2 | no | — |
| 135 | #471 | — | 26 | 4 | no | — |
| 136 | C2×#108 | C2×D13 | 1 | 2 | yes | — |
| 137 | #413 | — | 26 | 2 | no | — |
| 138 | #359 | — | 26 | 4 | no | — |
| 139 | C22⋊C16 | — | 26 | 2 | no | — |
| 140 | C22×C13 | — | 4 | 1 | no | — |
| 141 | C22×C13 | #449 | 1 | 2 | yes | — |
| 142 | C22×C13 | #466 | 1 | 1 | yes | characteristic |
| 143 | C2×D13 | — | 4 | 2 | no | — |
| 144 | C2×D13 | — | 4 | 1 | no | — |
| 145 | C2×D13 | — | 8 | 2 | no | — |
| 146 | C2×D13 | — | 16 | 2 | no | — |
| 147 | C4×C13 | #392 | 1 | 1 | yes | characteristic |
| 148 | C4×C13 | #447 | 1 | 2 | yes | — |
| 149 | C4×C13 | #469 | 1 | 1 | yes | characteristic |
| 150 | Dic13 | — | 4 | 1 | no | — |
| 151 | Dic13 | — | 8 | 2 | no | — |
| 152 | C2×#41 | — | 13 | 1 | no | — |
| 153 | C2×#41 | — | 26 | 2 | no | — |
| 154 | #137 | — | 26 | 4 | no | — |
| 155 | #137 | — | 52 | 2 | no | — |
| 156 | AGL(1,ℤ/8) | — | 26 | 4 | no | — |
| 157 | AGL(1,ℤ/8) | — | 52 | 2 | no | — |
| 158 | #135 | — | 26 | 2 | no | — |
| 159 | #135 | — | 26 | 2 | no | — |
| 160 | #135 | — | 26 | 2 | no | — |
| 161 | #135 | — | 26 | 2 | no | — |
| 162 | #135 | — | 52 | 4 | no | — |
| 163 | C2×Q16 | — | 13 | 2 | no | — |
| 164 | C2×SD16 | — | 26 | 2 | no | — |
| 165 | C2×D8 | — | 13 | 2 | no | — |
| 166 | #131 | — | 26 | 2 | no | — |
| 167 | #131 | — | 26 | 2 | no | — |
| 168 | C2×M16 | — | 2 | 2 | no | — |
| 169 | C2×M16 | — | 13 | 1 | no | — |
| 170 | C2×M16 | — | 26 | 1 | no | — |
| 171 | C22×C8 | — | 26 | 1 | no | — |
| 172 | C22×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 173 | Q32 | — | 26 | 2 | no | — |
| 174 | SD32 | — | 26 | 4 | no | — |
| 175 | D16 | — | 26 | 2 | no | — |
| 176 | M32 | — | 2 | 2 | no | — |
| 177 | C2×C16 | — | 26 | 1 | no | — |
| 178 | C2×C16 | — | 26 | 2 | no | — |
| 179 | C2×C16 | D52 | 1 | 2 | yes | — |
| 180 | #108 | — | 2 | 2 | no | — |
| 181 | #108 | D52 | 1 | 4 | yes | — |
| 182 | #101 | — | 26 | 4 | no | — |
| 183 | #100 | — | 26 | 4 | no | — |
| 184 | C2×C13 | — | 2 | 1 | no | — |
| 185 | C2×C13 | — | 2 | 2 | no | — |
| 186 | C2×C13 | #1999 | 1 | 1 | yes | characteristic |
| 187 | D13 | — | 8 | 1 | no | — |
| 188 | D13 | — | 16 | 2 | no | — |
| 189 | #41 | — | 26 | 2 | no | — |
| 190 | #41 | — | 26 | 2 | no | — |
| 191 | #41 | — | 52 | 2 | no | — |
| 192 | #41 | — | 52 | 2 | no | — |
| 193 | #41 | — | 52 | 2 | no | — |
| 194 | #41 | — | 52 | 2 | no | — |
| 195 | C2×Q8 | — | 13 | 1 | no | — |
| 196 | C2×Q8 | — | 26 | 2 | no | — |
| 197 | C2×D4 | — | 13 | 1 | no | — |
| 198 | C2×D4 | — | 26 | 1 | no | — |
| 199 | C2×D4 | — | 26 | 2 | no | — |
| 200 | C2×D4 | — | 52 | 2 | no | — |
| 201 | C22×C4 | — | 26 | 1 | no | — |
| 202 | C22×C4 | — | 52 | 2 | no | — |
| 203 | C22×C4 | D4×D13 | 1 | 1 | yes | characteristic |
| 204 | Q16 | — | 26 | 2 | no | — |
| 205 | Q16 | — | 26 | 2 | no | — |
| 206 | Q16 | — | 52 | 4 | no | — |
| 207 | SD16 | — | 52 | 4 | no | — |
| 208 | SD16 | — | 52 | 4 | no | — |
| 209 | SD16 | — | 52 | 2 | no | — |
| 210 | SD16 | — | 52 | 2 | no | — |
| 211 | D8 | — | 26 | 2 | no | — |
| 212 | D8 | — | 26 | 2 | no | — |
| 213 | D8 | — | 52 | 4 | no | — |
| 214 | M16 | — | 2 | 4 | no | — |
| 215 | M16 | — | 4 | 2 | no | — |
| 216 | M16 | — | 26 | 2 | no | — |
| 217 | M16 | — | 52 | 2 | no | — |
| 218 | C2×C8 | — | 4 | 2 | no | — |
| 219 | C2×C8 | — | 26 | 1 | no | — |
| 220 | C2×C8 | — | 52 | 1 | no | — |
| 221 | C2×C8 | — | 52 | 1 | no | — |
| 222 | C2×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 223 | C2×C8 | C2×D52 | 1 | 2 | yes | — |
| 224 | C2×C8 | D4×D13 | 1 | 2 | yes | — |
| 225 | C2×C8 | #6131 | 1 | 1 | yes | characteristic |
| 226 | C16 | — | 2 | 2 | no | — |
| 227 | C16 | — | 52 | 1 | no | — |
| 228 | C13 | #13312 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 229 | C23 | — | 26 | 1 | no | — |
| 230 | C23 | — | 52 | 2 | no | — |
| 231 | C23 | #88173 | 1 | 1 | yes | characteristic |
| 232 | Q8 | — | 26 | 2 | no | — |
| 233 | Q8 | — | 52 | 2 | no | — |
| 234 | Q8 | — | 52 | 2 | no | — |
| 235 | D4 | — | 26 | 2 | no | — |
| 236 | D4 | — | 52 | 2 | no | — |
| 237 | D4 | — | 52 | 2 | no | — |
| 238 | D4 | — | 52 | 2 | no | — |
| 239 | D4 | — | 104 | 2 | no | — |
| 240 | D4 | — | 104 | 2 | no | — |
| 241 | C2×C4 | — | 26 | 1 | no | — |
| 242 | C2×C4 | — | 52 | 1 | no | — |
| 243 | C2×C4 | — | 52 | 1 | no | — |
| 244 | C2×C4 | — | 52 | 2 | no | — |
| 245 | C2×C4 | — | 104 | 2 | no | — |
| 246 | C2×C4 | — | 104 | 2 | no | — |
| 247 | C2×C4 | #88136 | 1 | 2 | yes | — |
| 248 | C2×C4 | #88149 | 1 | 1 | yes | characteristic |
| 249 | C2×C4 | D8×D13 | 1 | 1 | yes | characteristic |
| 250 | C2×C4 | #88168 | 1 | 2 | yes | — |
| 251 | C8 | — | 4 | 4 | no | — |
| 252 | C8 | — | 52 | 1 | no | — |
| 253 | C8 | #88128 | 1 | 1 | yes | characteristic |
| 254 | C8 | #88136 | 1 | 1 | yes | characteristic |
| 255 | C8 | #88149 | 1 | 2 | yes | — |
| 256 | C22 | — | 4 | 1 | no | — |
| 257 | C22 | — | 52 | 2 | no | — |
| 258 | C22 | — | 52 | 1 | no | — |
| 259 | C22 | — | 104 | 2 | no | — |
| 260 | C22 | — | 208 | 2 | no | — |
| 261 | C22 | #11718472 | 1 | 2 | yes | — |
| 262 | C22 | #11718544 | 1 | 1 | yes | characteristic |
| 263 | C4 | — | 52 | 1 | no | — |
| 264 | C4 | — | 104 | 2 | no | — |
| 265 | C4 | #11718332 | 1 | 1 | yes | characteristic |
| 266 | C4 | #11718434 | 1 | 2 | yes | — |
| 267 | C4 | #11718526 | 1 | 1 | yes | characteristic |
| 268 | C2 | — | 2 | 1 | no | — |
| 269 | C2 | — | 2 | 2 | no | — |
| 270 | C2 | — | 104 | 1 | no | — |
| 271 | C2 | — | 208 | 2 | no | — |
| 272 | C2 | #13115835 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13127972 | C2 | semidirect |
| 2. #13124557 | C2 | semidirect |
| 3. C2×#11718089 | C2 | semidirect |
| 4. #13116451 | C2 | semidirect |
| 5. C13×#1385 | C2 | semidirect |
| 97. #1385 | D13 | semidirect |
| 228. C13 | #13312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13127972 | 2 |
| #13124557 | 2 |
| C2×#11718089 | 2 |
| #13116451 | 2 |
| C13×#1385 | 2 |
| #13312 | 13 |