Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1082 conjugacy classes of subgroups.
The subgroup lattice has 612 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13129241 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13126217 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13126214 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13125264 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13113983 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13113954 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13113921 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #13113892 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #13113569 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #13113288 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C13×#1492 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C13×#532 | C22 | 1 | 1 | yes | characteristic |
| 13 | #11719535 | — | 2 | 2 | no | — |
| 14 | C2×#88158 | — | 2 | 2 | no | — |
| 15 | #11719439 | — | 2 | 1 | no | — |
| 16 | #11719422 | — | 2 | 1 | no | — |
| 17 | #11719388 | — | 2 | 2 | no | — |
| 18 | #11719312 | — | 2 | 2 | no | — |
| 19 | #11719312 | — | 2 | 2 | no | — |
| 20 | #11719268 | — | 2 | 1 | no | — |
| 21 | #11719268 | C22 | 1 | 2 | yes | — |
| 22 | D4×D52 | — | 2 | 1 | no | — |
| 23 | D4×D52 | C22 | 1 | 2 | yes | — |
| 24 | #11719182 | C22 | 1 | 1 | yes | characteristic |
| 25 | #11719182 | C22 | 1 | 1 | yes | characteristic |
| 26 | #11719182 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C13×#423 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | C2×C4×C8×C13 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #11718796 | — | 2 | 2 | no | — |
| 30 | #11718745 | — | 2 | 1 | no | — |
| 31 | #11718733 | — | 2 | 1 | no | — |
| 32 | #11718700 | — | 2 | 2 | no | — |
| 33 | #11718676 | C22 | 1 | 2 | yes | complemented |
| 34 | #11718669 | C22 | 1 | 2 | yes | complemented |
| 35 | #11718585 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #11718504 | — | 2 | 1 | no | — |
| 37 | #11718504 | C22 | 1 | 2 | yes | complemented |
| 38 | #11718503 | — | 2 | 1 | no | — |
| 39 | #11718503 | C22 | 1 | 2 | yes | complemented |
| 40 | #11718360 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #11718357 | — | 2 | 2 | no | — |
| 42 | #11718356 | C22 | 1 | 1 | yes | characteristic |
| 43 | #11718354 | C22 | 1 | 1 | yes | characteristic |
| 44 | #11718354 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | C13×D4⋊C8 | C22 | 1 | 2 | yes | complemented |
| 46 | C13×D4⋊C8 | C22 | 1 | 2 | yes | complemented |
| 47 | #11718077 | C22 | 1 | 2 | yes | — |
| 48 | #11718073 | C22 | 1 | 2 | yes | complemented |
| 49 | #11718051 | C22 | 1 | 2 | yes | complemented |
| 50 | #11718051 | C22 | 1 | 2 | yes | complemented |
| 51 | C2×C13×#41 | — | 2 | 1 | no | — |
| 52 | C2×D4×D13 | — | 2 | 2 | no | — |
| 53 | C2×D4×D13 | — | 2 | 2 | no | — |
| 54 | C2×#6127 | — | 2 | 1 | no | — |
| 55 | C2×#6127 | — | 2 | 1 | no | — |
| 56 | C2×#6127 | D4 | 1 | 2 | yes | — |
| 57 | C22×D52 | — | 2 | 2 | no | — |
| 58 | C2×C13×M16 | — | 2 | 1 | no | — |
| 59 | C22×C8×C13 | — | 2 | 1 | no | — |
| 60 | C13×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 61 | C13×#127 | D4 | 1 | 1 | yes | characteristic |
| 62 | C13×#124 | — | 2 | 1 | no | — |
| 63 | C13×#121 | — | 2 | 1 | no | — |
| 64 | C13×#121 | D4 | 1 | 2 | yes | — |
| 65 | C4×D4×C13 | — | 2 | 1 | no | — |
| 66 | C4×D4×C13 | C23 | 1 | 2 | yes | — |
| 67 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 68 | #88201 | — | 2 | 4 | no | — |
| 69 | #88194 | — | 2 | 4 | no | — |
| 70 | #88192 | — | 2 | 2 | no | — |
| 71 | #88192 | — | 2 | 2 | no | — |
| 72 | #88191 | — | 2 | 4 | no | — |
| 73 | #88191 | — | 2 | 4 | no | — |
| 74 | C2×#6104 | — | 2 | 2 | no | — |
| 75 | #88184 | — | 2 | 1 | no | — |
| 76 | #88184 | — | 2 | 1 | no | — |
| 77 | #88184 | — | 2 | 1 | no | — |
| 78 | #88184 | — | 2 | 2 | no | — |
| 79 | #88184 | — | 2 | 1 | no | — |
| 80 | #88184 | — | 2 | 1 | no | — |
| 81 | #88184 | — | 2 | 2 | no | — |
| 82 | #88184 | D4 | 1 | 2 | yes | — |
| 83 | #88180 | — | 2 | 2 | no | — |
| 84 | C2×#6099 | — | 2 | 1 | no | — |
| 85 | C2×Dic52 | — | 2 | 2 | no | — |
| 86 | #88158 | — | 4 | 8 | no | — |
| 87 | C2×D104 | — | 2 | 2 | no | — |
| 88 | C2×D104 | — | 2 | 2 | no | — |
| 89 | C2×#6095 | — | 2 | 2 | no | — |
| 90 | C2×#6095 | — | 2 | 2 | no | — |
| 91 | #88149 | — | 2 | 2 | no | — |
| 92 | #88149 | — | 2 | 2 | no | — |
| 93 | #88146 | — | 2 | 2 | no | — |
| 94 | #88146 | — | 2 | 2 | no | — |
| 95 | #88139 | — | 2 | 4 | no | — |
| 96 | #88139 | — | 2 | 4 | no | — |
| 97 | #88136 | — | 2 | 4 | no | — |
| 98 | #88136 | — | 2 | 4 | no | — |
| 99 | #88129 | — | 2 | 1 | no | — |
| 100 | #88129 | — | 2 | 1 | no | — |
| 101 | #88129 | D4 | 1 | 2 | yes | — |
| 102 | #88128 | D4 | 1 | 1 | yes | characteristic |
| 103 | #88128 | C23 | 1 | 1 | yes | characteristic |
| 104 | #88128 | C23 | 1 | 1 | yes | characteristic |
| 105 | C4×D52 | — | 2 | 1 | no | — |
| 106 | C4×D52 | — | 2 | 1 | no | — |
| 107 | C4×D52 | — | 2 | 1 | no | — |
| 108 | C4×D52 | — | 2 | 1 | no | — |
| 109 | C4×D52 | — | 2 | 1 | no | — |
| 110 | C4×D52 | C23 | 1 | 2 | yes | — |
| 111 | #88123 | D4 | 1 | 1 | yes | characteristic |
| 112 | #88123 | C23 | 1 | 1 | yes | characteristic |
| 113 | #88123 | C23 | 1 | 1 | yes | characteristic |
| 114 | C13×C4⋊C8 | — | 2 | 1 | no | — |
| 115 | C13×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 116 | C4×C8×C13 | — | 2 | 1 | no | — |
| 117 | C4×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 118 | C4×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 119 | #88072 | — | 2 | 2 | no | — |
| 120 | #88061 | — | 2 | 2 | no | — |
| 121 | #88061 | — | 2 | 2 | no | — |
| 122 | #88057 | — | 2 | 2 | no | — |
| 123 | #88049 | — | 2 | 2 | no | — |
| 124 | #88048 | — | 2 | 2 | no | — |
| 125 | C4⋊#1055 | — | 2 | 1 | no | — |
| 126 | C4⋊#1055 | C23 | 1 | 2 | yes | — |
| 127 | #18686 | — | 13 | 1 | no | maximal, Sylow |
| 128 | C23×D13 | — | 2 | 4 | no | — |
| 129 | C13×#41 | — | 8 | 1 | no | — |
| 130 | C13×#41 | — | 8 | 1 | no | — |
| 131 | C2×Q8×C13 | — | 2 | 1 | no | — |
| 132 | C2×D4×C13 | — | 2 | 2 | no | — |
| 133 | C2×D4×C13 | — | 2 | 1 | no | — |
| 134 | C2×D4×C13 | — | 2 | 1 | no | — |
| 135 | C2×D4×C13 | C2×D4 | 1 | 2 | yes | — |
| 136 | C22×C4×C13 | — | 2 | 2 | no | — |
| 137 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 138 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 139 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 140 | C2×C22⋊D13 | — | 2 | 4 | no | — |
| 141 | C2×C22⋊D13 | — | 2 | 4 | no | — |
| 142 | C2×C22⋊D13 | — | 2 | 2 | no | — |
| 143 | C2×C22⋊D13 | — | 2 | 2 | no | — |
| 144 | C2×C22⋊D13 | — | 4 | 1 | no | — |
| 145 | D4×D13 | — | 8 | 2 | no | — |
| 146 | D4×D13 | — | 8 | 2 | no | — |
| 147 | D4×D13 | — | 8 | 4 | no | — |
| 148 | #6127 | — | 4 | 4 | no | — |
| 149 | #6127 | — | 4 | 4 | no | — |
| 150 | #6127 | — | 8 | 1 | no | — |
| 151 | #6127 | — | 8 | 1 | no | — |
| 152 | C2×D52 | — | 2 | 1 | no | — |
| 153 | C2×D52 | — | 2 | 1 | no | — |
| 154 | C2×D52 | — | 2 | 1 | no | — |
| 155 | C2×D52 | — | 2 | 1 | no | — |
| 156 | C2×D52 | — | 2 | 1 | no | — |
| 157 | C2×D52 | — | 2 | 1 | no | — |
| 158 | C2×D52 | — | 2 | 4 | no | — |
| 159 | C2×D52 | — | 2 | 1 | no | — |
| 160 | C2×D52 | — | 8 | 2 | no | — |
| 161 | C2×D52 | — | 8 | 2 | no | — |
| 162 | C2×D52 | C2×D4 | 1 | 2 | yes | — |
| 163 | C2×D52 | C2×D4 | 1 | 2 | yes | — |
| 164 | C2×C4×D13 | — | 2 | 2 | no | — |
| 165 | C2×C4×D13 | — | 2 | 2 | no | — |
| 166 | C2×C4×D13 | — | 4 | 1 | no | — |
| 167 | C2×Dic26 | — | 2 | 1 | no | — |
| 168 | C2×Dic26 | — | 2 | 1 | no | — |
| 169 | C2×Dic26 | C2×D4 | 1 | 2 | yes | — |
| 170 | C13×M16 | — | 8 | 1 | no | — |
| 171 | C2×C8×C13 | — | 2 | 4 | no | — |
| 172 | C2×C8×C13 | — | 2 | 1 | no | — |
| 173 | C2×C8×C13 | — | 2 | 1 | no | — |
| 174 | C2×C8×C13 | — | 2 | 2 | no | — |
| 175 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 176 | C13×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 177 | C13×C22⋊C4 | — | 2 | 2 | no | — |
| 178 | C13×C22⋊C4 | — | 2 | 2 | no | — |
| 179 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 180 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 182 | C42×C13 | C24 | 1 | 1 | yes | characteristic |
| 183 | C22⋊Dic13 | — | 2 | 4 | no | — |
| 184 | #6104 | — | 8 | 2 | no | — |
| 185 | #6103 | — | 2 | 4 | no | — |
| 186 | #6103 | — | 2 | 4 | no | — |
| 187 | #6103 | — | 2 | 2 | no | — |
| 188 | #6103 | — | 2 | 2 | no | — |
| 189 | #6103 | — | 2 | 2 | no | — |
| 190 | #6103 | — | 2 | 2 | no | — |
| 191 | #6103 | — | 4 | 1 | no | — |
| 192 | #6103 | — | 4 | 1 | no | — |
| 193 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 194 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 195 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 196 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 197 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 198 | C4⋊Dic13 | C2×D4 | 1 | 2 | yes | — |
| 199 | C4×Dic13 | — | 2 | 4 | no | — |
| 200 | #6099 | — | 8 | 1 | no | — |
| 201 | C2×#1055 | — | 2 | 2 | no | — |
| 202 | Dic52 | — | 4 | 4 | no | — |
| 203 | D104 | — | 4 | 4 | no | — |
| 204 | D104 | — | 8 | 2 | no | — |
| 205 | #6095 | — | 4 | 4 | no | — |
| 206 | #6095 | — | 4 | 4 | no | — |
| 207 | #3549 | — | 13 | 1 | no | — |
| 208 | #3253 | — | 13 | 1 | no | — |
| 209 | #3253 | — | 13 | 1 | no | — |
| 210 | #3147 | — | 13 | 1 | no | — |
| 211 | #1634 | — | 13 | 2 | no | — |
| 212 | #1629 | — | 13 | 2 | no | — |
| 213 | #1624 | — | 13 | 2 | no | — |
| 214 | #1619 | — | 13 | 2 | no | — |
| 215 | #1560 | — | 13 | 1 | no | — |
| 216 | #1492 | — | 13 | 1 | no | — |
| 217 | #1492 | D13 | 1 | 1 | yes | characteristic, complemented |
| 218 | C23×C13 | — | 2 | 2 | no | — |
| 219 | C23×C13 | #120 | 1 | 1 | yes | characteristic |
| 220 | C22×D13 | — | 2 | 2 | no | — |
| 221 | C22×D13 | — | 2 | 2 | no | — |
| 222 | C22×D13 | — | 4 | 1 | no | — |
| 223 | C22×D13 | — | 8 | 4 | no | — |
| 224 | C22×D13 | — | 8 | 4 | no | — |
| 225 | C22×D13 | — | 8 | 4 | no | — |
| 226 | Q8×C13 | — | 8 | 1 | no | — |
| 227 | D4×C13 | — | 2 | 2 | no | — |
| 228 | D4×C13 | — | 2 | 2 | no | — |
| 229 | D4×C13 | — | 4 | 2 | no | — |
| 230 | D4×C13 | — | 8 | 1 | no | — |
| 231 | D4×C13 | — | 8 | 2 | no | — |
| 232 | C2×C4×C13 | — | 2 | 1 | no | — |
| 233 | C2×C4×C13 | — | 2 | 1 | no | — |
| 234 | C2×C4×C13 | — | 2 | 1 | no | — |
| 235 | C2×C4×C13 | — | 2 | 1 | no | — |
| 236 | C2×C4×C13 | — | 2 | 2 | no | — |
| 237 | C2×C4×C13 | — | 2 | 2 | no | — |
| 238 | C2×C4×C13 | — | 4 | 2 | no | — |
| 239 | C2×C4×C13 | — | 4 | 2 | no | — |
| 240 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 241 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 242 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 243 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 244 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 245 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 246 | C22⋊D13 | — | 8 | 2 | no | — |
| 247 | C22⋊D13 | — | 8 | 2 | no | — |
| 248 | C22⋊D13 | — | 8 | 4 | no | — |
| 249 | C22⋊D13 | — | 8 | 4 | no | — |
| 250 | C22⋊D13 | — | 8 | 2 | no | — |
| 251 | C2×Dic13 | — | 2 | 2 | no | — |
| 252 | C2×Dic13 | — | 2 | 2 | no | — |
| 253 | C2×Dic13 | — | 4 | 1 | no | — |
| 254 | D52 | — | 2 | 2 | no | — |
| 255 | D52 | — | 2 | 2 | no | — |
| 256 | D52 | — | 4 | 2 | no | — |
| 257 | D52 | — | 4 | 2 | no | — |
| 258 | D52 | — | 4 | 1 | no | — |
| 259 | D52 | — | 4 | 1 | no | — |
| 260 | D52 | — | 4 | 1 | no | — |
| 261 | D52 | — | 4 | 1 | no | — |
| 262 | D52 | — | 4 | 1 | no | — |
| 263 | D52 | — | 4 | 1 | no | — |
| 264 | D52 | — | 4 | 1 | no | — |
| 265 | D52 | — | 4 | 1 | no | — |
| 266 | D52 | — | 4 | 2 | no | — |
| 267 | D52 | — | 8 | 1 | no | — |
| 268 | D52 | — | 8 | 4 | no | — |
| 269 | C4×D13 | — | 4 | 2 | no | — |
| 270 | C4×D13 | — | 4 | 2 | no | — |
| 271 | C4×D13 | — | 4 | 4 | no | — |
| 272 | C4×D13 | — | 8 | 2 | no | — |
| 273 | Dic26 | — | 4 | 2 | no | — |
| 274 | Dic26 | — | 4 | 2 | no | — |
| 275 | Dic26 | — | 8 | 1 | no | — |
| 276 | C8×C13 | — | 2 | 2 | no | — |
| 277 | C8×C13 | — | 2 | 2 | no | — |
| 278 | C8×C13 | — | 4 | 2 | no | — |
| 279 | #1055 | — | 4 | 2 | no | — |
| 280 | C2×#135 | — | 26 | 2 | no | — |
| 281 | H(3,𝔽4) | — | 26 | 2 | no | — |
| 282 | #555 | — | 13 | 2 | no | — |
| 283 | #555 | — | 26 | 1 | no | — |
| 284 | #555 | — | 26 | 1 | no | — |
| 285 | D42 | — | 13 | 2 | no | — |
| 286 | D42 | — | 26 | 1 | no | — |
| 287 | D42 | — | 26 | 1 | no | — |
| 288 | #535 | — | 26 | 2 | no | — |
| 289 | #535 | — | 26 | 2 | no | — |
| 290 | #535 | — | 26 | 2 | no | — |
| 291 | #532 | — | 13 | 1 | no | — |
| 292 | #532 | — | 13 | 1 | no | — |
| 293 | #532 | — | 13 | 1 | no | — |
| 294 | #532 | C2×D13 | 1 | 1 | yes | characteristic |
| 295 | #495 | — | 26 | 2 | no | — |
| 296 | #494 | — | 13 | 1 | no | — |
| 297 | #493 | — | 13 | 1 | no | — |
| 298 | #492 | — | 13 | 1 | no | — |
| 299 | #492 | — | 13 | 1 | no | — |
| 300 | #476 | — | 13 | 2 | no | — |
| 301 | #476 | — | 13 | 2 | no | — |
| 302 | #476 | — | 26 | 1 | no | — |
| 303 | #476 | — | 26 | 1 | no | — |
| 304 | #469 | — | 26 | 2 | no | — |
| 305 | #469 | — | 26 | 2 | no | — |
| 306 | #459 | — | 13 | 2 | no | — |
| 307 | #459 | — | 13 | 2 | no | — |
| 308 | #459 | — | 26 | 1 | no | — |
| 309 | #459 | — | 26 | 1 | no | — |
| 310 | #423 | — | 13 | 1 | no | — |
| 311 | #423 | C2×D13 | 1 | 1 | yes | characteristic, complemented |
| 312 | C2×C4×C8 | C2×D13 | 1 | 1 | yes | characteristic, complemented |
| 313 | #333 | — | 13 | 2 | no | — |
| 314 | #331 | — | 13 | 2 | no | — |
| 315 | D4⋊C8 | — | 13 | 2 | no | — |
| 316 | D4⋊C8 | — | 13 | 2 | no | — |
| 317 | D4⋊C8 | C2×D13 | 1 | 2 | yes | complemented |
| 318 | D4⋊C8 | C2×D13 | 1 | 2 | yes | complemented |
| 319 | C22×C13 | — | 2 | 1 | no | — |
| 320 | C22×C13 | — | 2 | 1 | no | — |
| 321 | C22×C13 | — | 2 | 1 | no | — |
| 322 | C22×C13 | — | 4 | 2 | no | — |
| 323 | C22×C13 | — | 4 | 2 | no | — |
| 324 | C22×C13 | — | 4 | 2 | no | — |
| 325 | C22×C13 | C2×#120 | 1 | 1 | yes | characteristic |
| 326 | C2×D13 | — | 4 | 2 | no | — |
| 327 | C2×D13 | — | 4 | 2 | no | — |
| 328 | C2×D13 | — | 4 | 2 | no | — |
| 329 | C2×D13 | — | 4 | 2 | no | — |
| 330 | C2×D13 | — | 4 | 2 | no | — |
| 331 | C2×D13 | — | 4 | 2 | no | — |
| 332 | C2×D13 | — | 8 | 1 | no | — |
| 333 | C2×D13 | — | 8 | 1 | no | — |
| 334 | C2×D13 | — | 8 | 1 | no | — |
| 335 | C2×D13 | — | 16 | 8 | no | — |
| 336 | C4×C13 | — | 2 | 1 | no | — |
| 337 | C4×C13 | — | 2 | 1 | no | — |
| 338 | C4×C13 | — | 2 | 1 | no | — |
| 339 | C4×C13 | — | 4 | 2 | no | — |
| 340 | C4×C13 | #453 | 1 | 2 | yes | — |
| 341 | C4×C13 | #576 | 1 | 1 | yes | characteristic |
| 342 | C4×C13 | #576 | 1 | 1 | yes | characteristic |
| 343 | C4×C13 | #577 | 1 | 1 | yes | characteristic |
| 344 | C4×C13 | #577 | 1 | 1 | yes | characteristic |
| 345 | Dic13 | — | 4 | 2 | no | — |
| 346 | Dic13 | — | 4 | 2 | no | — |
| 347 | Dic13 | — | 8 | 1 | no | — |
| 348 | C2×#41 | — | 2 | 1 | no | — |
| 349 | C2×#41 | — | 13 | 2 | no | — |
| 350 | C2×#41 | — | 26 | 1 | no | — |
| 351 | C2×#41 | — | 26 | 1 | no | — |
| 352 | C22×D4 | — | 26 | 2 | no | — |
| 353 | C22×D4 | — | 26 | 2 | no | — |
| 354 | C22×D4 | — | 26 | 2 | no | — |
| 355 | #135 | — | 52 | 8 | no | — |
| 356 | C2×Q16 | — | 26 | 2 | no | — |
| 357 | C2×SD16 | — | 26 | 2 | no | — |
| 358 | C2×SD16 | — | 26 | 2 | no | — |
| 359 | C2×D8 | — | 26 | 2 | no | — |
| 360 | C2×D8 | — | 26 | 2 | no | — |
| 361 | C2×D8 | — | 26 | 2 | no | — |
| 362 | C2×M16 | — | 2 | 1 | no | — |
| 363 | C2×M16 | — | 26 | 1 | no | — |
| 364 | C22×C8 | — | 2 | 1 | no | — |
| 365 | C4⋊Q8 | — | 13 | 1 | no | — |
| 366 | C4⋊Q8 | — | 13 | 1 | no | — |
| 367 | C4⋊Q8 | — | 13 | 1 | no | — |
| 368 | C4⋊Q8 | D52 | 1 | 1 | yes | characteristic |
| 369 | #127 | — | 13 | 1 | no | — |
| 370 | #127 | — | 13 | 1 | no | — |
| 371 | #127 | — | 13 | 1 | no | — |
| 372 | #127 | — | 26 | 4 | no | — |
| 373 | #127 | D52 | 1 | 1 | yes | characteristic |
| 374 | #124 | — | 2 | 1 | no | — |
| 375 | #124 | — | 13 | 2 | no | — |
| 376 | #124 | — | 26 | 4 | no | — |
| 377 | #124 | — | 26 | 4 | no | — |
| 378 | #124 | — | 26 | 4 | no | — |
| 379 | #124 | — | 26 | 1 | no | — |
| 380 | #124 | — | 26 | 1 | no | — |
| 381 | #121 | — | 2 | 1 | no | — |
| 382 | #121 | — | 13 | 2 | no | — |
| 383 | #121 | — | 26 | 2 | no | — |
| 384 | #121 | — | 26 | 2 | no | — |
| 385 | #121 | — | 26 | 2 | no | — |
| 386 | #121 | — | 26 | 2 | no | — |
| 387 | #121 | — | 26 | 2 | no | — |
| 388 | #121 | — | 26 | 1 | no | — |
| 389 | #121 | — | 26 | 1 | no | — |
| 390 | #121 | — | 26 | 1 | no | — |
| 391 | #121 | — | 26 | 2 | no | — |
| 392 | #121 | — | 26 | 1 | no | — |
| 393 | #121 | — | 26 | 1 | no | — |
| 394 | #121 | D52 | 1 | 2 | yes | — |
| 395 | #120 | — | 26 | 4 | no | — |
| 396 | #120 | — | 26 | 4 | no | — |
| 397 | #120 | — | 26 | 4 | no | — |
| 398 | #120 | — | 26 | 4 | no | — |
| 399 | C4×D4 | — | 2 | 1 | no | — |
| 400 | C4×D4 | — | 13 | 2 | no | — |
| 401 | C4×D4 | — | 26 | 1 | no | — |
| 402 | C4×D4 | — | 26 | 1 | no | — |
| 403 | C4×D4 | — | 26 | 1 | no | — |
| 404 | C4×D4 | — | 26 | 1 | no | — |
| 405 | C4×D4 | — | 26 | 1 | no | — |
| 406 | C4×D4 | C22×D13 | 1 | 2 | yes | — |
| 407 | #117 | — | 26 | 2 | no | — |
| 408 | #117 | — | 26 | 2 | no | — |
| 409 | #117 | — | 26 | 2 | no | — |
| 410 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 411 | #106 | — | 26 | 2 | no | — |
| 412 | #106 | — | 26 | 2 | no | — |
| 413 | C4⋊C8 | — | 2 | 1 | no | — |
| 414 | C4⋊C8 | — | 13 | 2 | no | — |
| 415 | C4⋊C8 | — | 26 | 1 | no | — |
| 416 | C4⋊C8 | C22×D13 | 1 | 2 | yes | — |
| 417 | #102 | — | 26 | 2 | no | — |
| 418 | #102 | — | 26 | 2 | no | — |
| 419 | #102 | — | 26 | 2 | no | — |
| 420 | #102 | — | 26 | 2 | no | — |
| 421 | C4×C8 | — | 2 | 1 | no | — |
| 422 | C4×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 423 | C4×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 424 | C2×C13 | — | 4 | 1 | no | — |
| 425 | C2×C13 | — | 8 | 2 | no | — |
| 426 | C2×C13 | #3012 | 1 | 1 | yes | characteristic |
| 427 | C2×C13 | #3012 | 1 | 1 | yes | characteristic |
| 428 | C2×C13 | C2×#453 | 1 | 1 | yes | characteristic |
| 429 | D13 | — | 8 | 2 | no | — |
| 430 | D13 | — | 8 | 2 | no | — |
| 431 | D13 | — | 16 | 1 | no | — |
| 432 | C24 | — | 26 | 4 | no | — |
| 433 | #41 | — | 8 | 1 | no | — |
| 434 | #41 | — | 8 | 1 | no | — |
| 435 | #41 | — | 52 | 4 | no | — |
| 436 | #41 | — | 52 | 4 | no | — |
| 437 | #41 | — | 104 | 1 | no | — |
| 438 | #41 | — | 104 | 1 | no | — |
| 439 | C2×Q8 | — | 2 | 1 | no | — |
| 440 | C2×Q8 | — | 13 | 2 | no | — |
| 441 | C2×Q8 | — | 26 | 1 | no | — |
| 442 | C2×Q8 | — | 26 | 1 | no | — |
| 443 | C2×D4 | — | 2 | 2 | no | — |
| 444 | C2×D4 | — | 2 | 1 | no | — |
| 445 | C2×D4 | — | 2 | 1 | no | — |
| 446 | C2×D4 | — | 13 | 2 | no | — |
| 447 | C2×D4 | — | 13 | 2 | no | — |
| 448 | C2×D4 | — | 26 | 4 | no | — |
| 449 | C2×D4 | — | 26 | 4 | no | — |
| 450 | C2×D4 | — | 26 | 4 | no | — |
| 451 | C2×D4 | — | 26 | 2 | no | — |
| 452 | C2×D4 | — | 26 | 2 | no | — |
| 453 | C2×D4 | — | 26 | 1 | no | — |
| 454 | C2×D4 | — | 26 | 1 | no | — |
| 455 | C2×D4 | — | 26 | 1 | no | — |
| 456 | C2×D4 | — | 26 | 1 | no | — |
| 457 | C2×D4 | — | 26 | 1 | no | — |
| 458 | C2×D4 | — | 26 | 1 | no | — |
| 459 | C2×D4 | — | 26 | 1 | no | — |
| 460 | C2×D4 | — | 52 | 1 | no | — |
| 461 | C2×D4 | — | 104 | 2 | no | — |
| 462 | C2×D4 | — | 104 | 2 | no | — |
| 463 | C2×D4 | — | 104 | 2 | no | — |
| 464 | C2×D4 | — | 104 | 2 | no | — |
| 465 | C2×D4 | — | 104 | 4 | no | — |
| 466 | C2×D4 | C2×D52 | 1 | 2 | yes | — |
| 467 | C22×C4 | — | 2 | 2 | no | — |
| 468 | C22×C4 | — | 26 | 2 | no | — |
| 469 | C22×C4 | — | 26 | 2 | no | — |
| 470 | C22×C4 | — | 52 | 1 | no | — |
| 471 | C22×C4 | C2×D52 | 1 | 1 | yes | characteristic |
| 472 | C22×C4 | D4×D13 | 1 | 1 | yes | characteristic |
| 473 | C22×C4 | D4×D13 | 1 | 1 | yes | characteristic |
| 474 | Q16 | — | 52 | 4 | no | — |
| 475 | SD16 | — | 52 | 4 | no | — |
| 476 | SD16 | — | 52 | 4 | no | — |
| 477 | D8 | — | 52 | 4 | no | — |
| 478 | D8 | — | 104 | 2 | no | — |
| 479 | D8 | — | 104 | 2 | no | — |
| 480 | M16 | — | 8 | 1 | no | — |
| 481 | M16 | — | 104 | 1 | no | — |
| 482 | C2×C8 | — | 2 | 4 | no | — |
| 483 | C2×C8 | — | 2 | 1 | no | — |
| 484 | C2×C8 | — | 2 | 1 | no | — |
| 485 | C2×C8 | — | 2 | 2 | no | — |
| 486 | C2×C8 | — | 26 | 2 | no | — |
| 487 | C4⋊C4 | — | 2 | 1 | no | — |
| 488 | C4⋊C4 | — | 13 | 2 | no | — |
| 489 | C4⋊C4 | — | 26 | 1 | no | — |
| 490 | C4⋊C4 | — | 26 | 1 | no | — |
| 491 | C4⋊C4 | — | 26 | 1 | no | — |
| 492 | C4⋊C4 | — | 26 | 1 | no | — |
| 493 | C4⋊C4 | — | 26 | 1 | no | — |
| 494 | C4⋊C4 | C2×D52 | 1 | 2 | yes | — |
| 495 | C22⋊C4 | — | 2 | 2 | no | — |
| 496 | C22⋊C4 | — | 2 | 2 | no | — |
| 497 | C22⋊C4 | — | 26 | 4 | no | — |
| 498 | C22⋊C4 | — | 26 | 4 | no | — |
| 499 | C22⋊C4 | — | 26 | 4 | no | — |
| 500 | C22⋊C4 | — | 26 | 2 | no | — |
| 501 | C22⋊C4 | — | 26 | 2 | no | — |
| 502 | C22⋊C4 | — | 26 | 2 | no | — |
| 503 | C22⋊C4 | — | 26 | 2 | no | — |
| 504 | C22⋊C4 | — | 52 | 1 | no | — |
| 505 | C22⋊C4 | — | 52 | 1 | no | — |
| 506 | C42 | — | 26 | 4 | no | — |
| 507 | C42 | C2×D52 | 1 | 1 | yes | characteristic |
| 508 | C42 | D4×D13 | 1 | 1 | yes | characteristic |
| 509 | C42 | D4×D13 | 1 | 1 | yes | characteristic |
| 510 | C42 | C23×D13 | 1 | 1 | yes | characteristic |
| 511 | C13 | #18686 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 512 | C23 | — | 2 | 2 | no | — |
| 513 | C23 | — | 26 | 2 | no | — |
| 514 | C23 | — | 26 | 2 | no | — |
| 515 | C23 | — | 52 | 1 | no | — |
| 516 | C23 | — | 104 | 4 | no | — |
| 517 | C23 | — | 104 | 4 | no | — |
| 518 | C23 | — | 104 | 4 | no | — |
| 519 | C23 | #88136 | 1 | 1 | yes | characteristic |
| 520 | Q8 | — | 8 | 1 | no | — |
| 521 | Q8 | — | 52 | 2 | no | — |
| 522 | Q8 | — | 52 | 2 | no | — |
| 523 | Q8 | — | 104 | 1 | no | — |
| 524 | D4 | — | 2 | 2 | no | — |
| 525 | D4 | — | 2 | 2 | no | — |
| 526 | D4 | — | 4 | 2 | no | — |
| 527 | D4 | — | 8 | 1 | no | — |
| 528 | D4 | — | 8 | 2 | no | — |
| 529 | D4 | — | 26 | 2 | no | — |
| 530 | D4 | — | 26 | 2 | no | — |
| 531 | D4 | — | 52 | 2 | no | — |
| 532 | D4 | — | 52 | 2 | no | — |
| 533 | D4 | — | 52 | 1 | no | — |
| 534 | D4 | — | 52 | 1 | no | — |
| 535 | D4 | — | 52 | 1 | no | — |
| 536 | D4 | — | 52 | 1 | no | — |
| 537 | D4 | — | 52 | 1 | no | — |
| 538 | D4 | — | 52 | 1 | no | — |
| 539 | D4 | — | 52 | 1 | no | — |
| 540 | D4 | — | 52 | 1 | no | — |
| 541 | D4 | — | 52 | 2 | no | — |
| 542 | D4 | — | 104 | 1 | no | — |
| 543 | D4 | — | 104 | 4 | no | — |
| 544 | D4 | — | 104 | 2 | no | — |
| 545 | D4 | — | 104 | 2 | no | — |
| 546 | D4 | — | 104 | 4 | no | — |
| 547 | D4 | — | 104 | 4 | no | — |
| 548 | D4 | — | 104 | 2 | no | — |
| 549 | C2×C4 | — | 2 | 1 | no | — |
| 550 | C2×C4 | — | 2 | 1 | no | — |
| 551 | C2×C4 | — | 2 | 1 | no | — |
| 552 | C2×C4 | — | 2 | 1 | no | — |
| 553 | C2×C4 | — | 2 | 2 | no | — |
| 554 | C2×C4 | — | 2 | 2 | no | — |
| 555 | C2×C4 | — | 4 | 2 | no | — |
| 556 | C2×C4 | — | 4 | 2 | no | — |
| 557 | C2×C4 | — | 26 | 2 | no | — |
| 558 | C2×C4 | — | 26 | 2 | no | — |
| 559 | C2×C4 | — | 52 | 2 | no | — |
| 560 | C2×C4 | — | 52 | 2 | no | — |
| 561 | C2×C4 | — | 52 | 4 | no | — |
| 562 | C2×C4 | — | 52 | 1 | no | — |
| 563 | C2×C4 | — | 104 | 2 | no | — |
| 564 | C2×C4 | #88136 | 1 | 1 | yes | characteristic |
| 565 | C2×C4 | #88136 | 1 | 1 | yes | characteristic |
| 566 | C2×C4 | #88136 | 1 | 1 | yes | characteristic |
| 567 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 568 | C2×C4 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 569 | C2×C4 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 570 | C8 | — | 2 | 2 | no | — |
| 571 | C8 | — | 2 | 2 | no | — |
| 572 | C8 | — | 4 | 2 | no | — |
| 573 | C8 | — | 52 | 2 | no | — |
| 574 | C22 | — | 2 | 1 | no | — |
| 575 | C22 | — | 2 | 1 | no | — |
| 576 | C22 | — | 2 | 1 | no | — |
| 577 | C22 | — | 4 | 2 | no | — |
| 578 | C22 | — | 4 | 2 | no | — |
| 579 | C22 | — | 4 | 2 | no | — |
| 580 | C22 | — | 52 | 2 | no | — |
| 581 | C22 | — | 52 | 2 | no | — |
| 582 | C22 | — | 52 | 2 | no | — |
| 583 | C22 | — | 52 | 2 | no | — |
| 584 | C22 | — | 52 | 2 | no | — |
| 585 | C22 | — | 52 | 2 | no | — |
| 586 | C22 | — | 104 | 1 | no | — |
| 587 | C22 | — | 104 | 1 | no | — |
| 588 | C22 | — | 104 | 1 | no | — |
| 589 | C22 | — | 208 | 8 | no | — |
| 590 | C22 | C2×#88136 | 1 | 1 | yes | characteristic |
| 591 | C4 | — | 2 | 1 | no | — |
| 592 | C4 | — | 2 | 1 | no | — |
| 593 | C4 | — | 2 | 1 | no | — |
| 594 | C4 | — | 4 | 2 | no | — |
| 595 | C4 | — | 52 | 2 | no | — |
| 596 | C4 | — | 52 | 2 | no | — |
| 597 | C4 | — | 104 | 1 | no | — |
| 598 | C4 | #11718483 | 1 | 2 | yes | — |
| 599 | C4 | #11719456 | 1 | 1 | yes | characteristic |
| 600 | C4 | #11719457 | 1 | 1 | yes | characteristic |
| 601 | C4 | #11719462 | 1 | 1 | yes | characteristic |
| 602 | C4 | #11719467 | 1 | 1 | yes | characteristic |
| 603 | C2 | — | 4 | 1 | no | — |
| 604 | C2 | — | 8 | 2 | no | — |
| 605 | C2 | — | 104 | 2 | no | — |
| 606 | C2 | — | 104 | 2 | no | — |
| 607 | C2 | — | 208 | 1 | no | — |
| 608 | C2 | #13124143 | 1 | 1 | yes | characteristic |
| 609 | C2 | #13124145 | 1 | 1 | yes | characteristic |
| 610 | C2 | C2×#11718483 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13129241 | C2 | semidirect |
| 2. #13126217 | C2 | semidirect |
| 3. #13126214 | C2 | semidirect |
| 4. #13125264 | C2 | semidirect |
| 5. #13113983 | C2 | semidirect |
| 6. #13113954 | C2 | semidirect |
| 7. #13113921 | C2 | semidirect |
| 8. #13113892 | C2 | semidirect |
| 9. #13113569 | C2 | semidirect |
| 10. #13113288 | C2 | semidirect |
| 11. C13×#1492 | C2 | semidirect |
| 26. #11719182 | C22 | semidirect |
| 27. C13×#423 | C22 | semidirect |
| 28. C2×C4×C8×C13 | C22 | semidirect |
| 33. #11718676 | C22 | semidirect |
| 34. #11718669 | C22 | semidirect |
| 35. #11718585 | C22 | semidirect |
| 37. #11718504 | C22 | semidirect |
| 39. #11718503 | C22 | semidirect |
| 40. #11718360 | C22 | semidirect |
| 44. #11718354 | C22 | semidirect |
| 45. C13×D4⋊C8 | C22 | semidirect |
| 46. C13×D4⋊C8 | C22 | semidirect |
| 48. #11718073 | C22 | semidirect |
| 49. #11718051 | C22 | semidirect |
| 50. #11718051 | C22 | semidirect |
| 217. #1492 | D13 | semidirect |
| 311. #423 | C2×D13 | semidirect |
| 312. C2×C4×C8 | C2×D13 | semidirect |
| 317. D4⋊C8 | C2×D13 | semidirect |
| 318. D4⋊C8 | C2×D13 | semidirect |
| 511. C13 | #18686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13129241 | 2 |
| #13126217 | 2 |
| #13126214 | 2 |
| #13125264 | 2 |
| #13113983 | 2 |
| #13113954 | 2 |
| #13113921 | 2 |
| #13113892 | 2 |
| #13113569 | 2 |
| #13113288 | 2 |
| C13×#1492 | 2 |
| #18686 | 13 |