Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
6338 conjugacy classes of subgroups.
The subgroup lattice has 382 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13129331 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | #13129330 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #13129329 | C2 | 1 | 12 | yes | maximal, complemented |
| 4 | #13129328 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | D13×#564 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | D13×#557 | C2 | 1 | 12 | yes | maximal, complemented |
| 7 | D13×#541 | C2 | 1 | 12 | yes | maximal |
| 8 | D13×#533 | C2 | 1 | 3 | yes | maximal |
| 9 | C13×#3556 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C13×#564 | C22 | 1 | 4 | yes | complemented |
| 11 | C13×#557 | C22 | 1 | 12 | yes | complemented |
| 12 | C13×#541 | C22 | 1 | 12 | yes | — |
| 13 | C13×#533 | C22 | 1 | 3 | yes | — |
| 14 | #11719436 | C22 | 1 | 12 | yes | — |
| 15 | #11719433 | C22 | 1 | 6 | yes | — |
| 16 | D13×C4⋊Q8 | C22 | 1 | 12 | yes | — |
| 17 | D13×C4⋊Q8 | C22 | 1 | 6 | yes | — |
| 18 | #11719426 | C22 | 1 | 24 | yes | complemented |
| 19 | #11719426 | C22 | 1 | 12 | yes | complemented |
| 20 | D13×#126 | C22 | 1 | 16 | yes | — |
| 21 | #11719406 | C22 | 1 | 48 | yes | — |
| 22 | #11719402 | C22 | 1 | 12 | yes | — |
| 23 | #11719401 | C22 | 1 | 48 | yes | — |
| 24 | #11719393 | C22 | 1 | 6 | yes | — |
| 25 | D13×#125 | C22 | 1 | 48 | yes | — |
| 26 | D13×#125 | C22 | 1 | 12 | yes | — |
| 27 | D13×#125 | C22 | 1 | 6 | yes | — |
| 28 | C13⋊#564 | C22 | 1 | 48 | yes | complemented |
| 29 | C13⋊#564 | C22 | 1 | 12 | yes | complemented |
| 30 | #11719390 | C22 | 1 | 24 | yes | complemented |
| 31 | #11719390 | C22 | 1 | 48 | yes | complemented |
| 32 | D13×C22⋊Q8 | C22 | 1 | 12 | yes | — |
| 33 | #11719330 | C22 | 1 | 24 | yes | — |
| 34 | #11719327 | C22 | 1 | 12 | yes | — |
| 35 | #11719288 | C22 | 1 | 24 | yes | — |
| 36 | #11719283 | C22 | 1 | 12 | yes | — |
| 37 | C4×Q8×D13 | C22 | 1 | 24 | yes | — |
| 38 | C4×Q8×D13 | C22 | 1 | 12 | yes | — |
| 39 | #11719275 | C22 | 1 | 12 | yes | complemented |
| 40 | #11719274 | C22 | 1 | 24 | yes | complemented |
| 41 | #11719272 | C22 | 1 | 24 | yes | complemented |
| 42 | #11719272 | C22 | 1 | 12 | yes | complemented |
| 43 | D13×#117 | C22 | 1 | 6 | yes | — |
| 44 | #11719223 | C22 | 1 | 12 | yes | — |
| 45 | #11719222 | C22 | 1 | 6 | yes | — |
| 46 | C2×C42×D13 | C22 | 1 | 1 | yes | characteristic |
| 47 | #11719175 | C22 | 1 | 3 | yes | — |
| 48 | C2×Q8×D13 | C23 | 1 | 12 | yes | — |
| 49 | C22×C4×D13 | C23 | 1 | 3 | yes | — |
| 50 | C13×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 51 | C13×C4⋊Q8 | C23 | 1 | 12 | yes | — |
| 52 | C13×#126 | C23 | 1 | 16 | yes | — |
| 53 | C13×#125 | C23 | 1 | 6 | yes | — |
| 54 | C13×#125 | C23 | 1 | 12 | yes | — |
| 55 | C13×#125 | C23 | 1 | 48 | yes | — |
| 56 | C13×C22⋊Q8 | C23 | 1 | 12 | yes | — |
| 57 | C4×Q8×C13 | C23 | 1 | 24 | yes | — |
| 58 | C4×Q8×C13 | C23 | 1 | 12 | yes | — |
| 59 | C13×#117 | C23 | 1 | 6 | yes | — |
| 60 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 61 | #88200 | C23 | 1 | 12 | yes | — |
| 62 | Q8×Dic13 | C23 | 1 | 12 | yes | — |
| 63 | Q8×Dic13 | C23 | 1 | 24 | yes | — |
| 64 | #88198 | C23 | 1 | 12 | yes | — |
| 65 | #88198 | C23 | 1 | 24 | yes | — |
| 66 | #88180 | C23 | 1 | 6 | yes | — |
| 67 | #88178 | C23 | 1 | 12 | yes | — |
| 68 | C2×C4×Dic13 | C23 | 1 | 3 | yes | — |
| 69 | #88152 | C23 | 1 | 48 | yes | — |
| 70 | #88151 | C23 | 1 | 12 | yes | — |
| 71 | #88150 | C23 | 1 | 24 | yes | — |
| 72 | #88146 | C23 | 1 | 12 | yes | — |
| 73 | C4⋊C4×D13 | C23 | 1 | 12 | yes | — |
| 74 | C4⋊C4×D13 | C23 | 1 | 12 | yes | — |
| 75 | C4⋊C4×D13 | C23 | 1 | 48 | yes | — |
| 76 | C4⋊C4×D13 | C23 | 1 | 24 | yes | — |
| 77 | #88144 | C23 | 1 | 24 | yes | — |
| 78 | #88144 | C23 | 1 | 48 | yes | — |
| 79 | #88144 | C23 | 1 | 12 | yes | — |
| 80 | #88144 | C23 | 1 | 48 | yes | — |
| 81 | #88143 | C23 | 1 | 48 | yes | — |
| 82 | #88143 | C23 | 1 | 48 | yes | — |
| 83 | #88143 | C23 | 1 | 48 | yes | — |
| 84 | #88143 | C23 | 1 | 48 | yes | — |
| 85 | #88143 | C23 | 1 | 48 | yes | — |
| 86 | #88143 | C23 | 1 | 24 | yes | — |
| 87 | #88142 | C23 | 1 | 12 | yes | — |
| 88 | #88142 | C23 | 1 | 12 | yes | — |
| 89 | #88142 | C23 | 1 | 48 | yes | — |
| 90 | #88141 | C23 | 1 | 24 | yes | — |
| 91 | #88141 | C23 | 1 | 48 | yes | — |
| 92 | #88141 | C23 | 1 | 12 | yes | — |
| 93 | #88141 | C23 | 1 | 24 | yes | — |
| 94 | C22⋊C4×D13 | C23 | 1 | 12 | yes | — |
| 95 | #88133 | C23 | 1 | 48 | yes | — |
| 96 | #88132 | C23 | 1 | 24 | yes | — |
| 97 | #88131 | C23 | 1 | 12 | yes | — |
| 98 | #88130 | C23 | 1 | 16 | yes | — |
| 99 | #88126 | C23 | 1 | 12 | yes | — |
| 100 | C42×D13 | C23 | 1 | 3 | yes | — |
| 101 | C42×D13 | C23 | 1 | 12 | yes | — |
| 102 | C42×D13 | C23 | 1 | 3 | yes | — |
| 103 | C42×D13 | C23 | 1 | 1 | yes | characteristic |
| 104 | C42×D13 | C23 | 1 | 1 | yes | characteristic |
| 105 | C42×D13 | C23 | 1 | 16 | yes | — |
| 106 | #88124 | C23 | 1 | 6 | yes | — |
| 107 | #88124 | C23 | 1 | 12 | yes | — |
| 108 | #88124 | C23 | 1 | 48 | yes | — |
| 109 | #88123 | C23 | 1 | 6 | yes | — |
| 110 | #88123 | C23 | 1 | 12 | yes | — |
| 111 | C4×Dic26 | C23 | 1 | 12 | yes | — |
| 112 | C4×Dic26 | C23 | 1 | 24 | yes | — |
| 113 | C4×Dic26 | C23 | 1 | 24 | yes | — |
| 114 | C4×Dic26 | C23 | 1 | 48 | yes | — |
| 115 | C2×#3556 | — | 13 | 1 | no | maximal, Sylow |
| 116 | C23×D13 | C24 | 1 | 1 | yes | characteristic |
| 117 | C2×Q8×C13 | C24 | 1 | 12 | yes | — |
| 118 | C22×C4×C13 | C24 | 1 | 3 | yes | — |
| 119 | C22×Dic13 | C24 | 1 | 3 | yes | — |
| 120 | Q8×D13 | — | 2 | 48 | no | — |
| 121 | C2×C4×D13 | — | 2 | 12 | no | — |
| 122 | C2×C4×D13 | C24 | 1 | 24 | yes | — |
| 123 | C2×C4×D13 | C24 | 1 | 3 | yes | — |
| 124 | C2×C4×D13 | C24 | 1 | 3 | yes | — |
| 125 | C2×C4×D13 | C24 | 1 | 3 | yes | — |
| 126 | C2×C4×D13 | C24 | 1 | 3 | yes | — |
| 127 | C2×Dic26 | C24 | 1 | 12 | yes | — |
| 128 | C2×Dic26 | C24 | 1 | 24 | yes | — |
| 129 | C13×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 130 | C13×C4⋊C4 | C24 | 1 | 48 | yes | — |
| 131 | C13×C4⋊C4 | C24 | 1 | 24 | yes | — |
| 132 | C13×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 133 | C13×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 134 | C42×C13 | C24 | 1 | 3 | yes | — |
| 135 | C42×C13 | C24 | 1 | 12 | yes | — |
| 136 | C42×C13 | C24 | 1 | 16 | yes | — |
| 137 | C42×C13 | C24 | 1 | 1 | yes | characteristic |
| 138 | C22⋊Dic13 | C24 | 1 | 12 | yes | — |
| 139 | #6103 | C24 | 1 | 24 | yes | — |
| 140 | C4⋊Dic13 | C24 | 1 | 12 | yes | — |
| 141 | C4⋊Dic13 | C24 | 1 | 48 | yes | — |
| 142 | C4⋊Dic13 | C24 | 1 | 24 | yes | — |
| 143 | C4⋊Dic13 | C24 | 1 | 12 | yes | — |
| 144 | #6101 | C24 | 1 | 24 | yes | — |
| 145 | #6101 | C24 | 1 | 24 | yes | — |
| 146 | #6101 | C24 | 1 | 48 | yes | — |
| 147 | #6101 | C24 | 1 | 48 | yes | — |
| 148 | #6101 | C24 | 1 | 24 | yes | — |
| 149 | #6101 | C24 | 1 | 24 | yes | — |
| 150 | C4×Dic13 | C24 | 1 | 6 | yes | — |
| 151 | C4×Dic13 | C24 | 1 | 12 | yes | — |
| 152 | C4×Dic13 | C24 | 1 | 24 | yes | — |
| 153 | C4×Dic13 | C24 | 1 | 48 | yes | — |
| 154 | C4×Dic13 | C24 | 1 | 3 | yes | — |
| 155 | C4×Dic13 | C24 | 1 | 3 | yes | — |
| 156 | #3556 | — | 13 | 4 | no | — |
| 157 | #3556 | — | 13 | 12 | no | — |
| 158 | #3556 | — | 13 | 12 | no | — |
| 159 | #3556 | — | 13 | 3 | no | — |
| 160 | #3556 | D13 | 1 | 1 | yes | characteristic, direct product factor |
| 161 | C2×#564 | — | 13 | 4 | no | — |
| 162 | C2×#557 | — | 13 | 12 | no | — |
| 163 | C2×#541 | — | 13 | 12 | no | — |
| 164 | C2×#533 | — | 13 | 3 | no | — |
| 165 | C23×C13 | C25 | 1 | 1 | yes | characteristic |
| 166 | C22×D13 | — | 2 | 6 | no | — |
| 167 | C22×D13 | C25 | 1 | 1 | yes | characteristic |
| 168 | C22×D13 | C25 | 1 | 1 | yes | characteristic |
| 169 | Q8×C13 | — | 2 | 24 | no | — |
| 170 | C2×C4×C13 | — | 2 | 6 | no | — |
| 171 | C2×C4×C13 | C25 | 1 | 24 | yes | — |
| 172 | C2×C4×C13 | C25 | 1 | 3 | yes | — |
| 173 | C2×C4×C13 | C25 | 1 | 3 | yes | — |
| 174 | C2×Dic13 | — | 2 | 6 | no | — |
| 175 | C2×Dic13 | C25 | 1 | 24 | yes | — |
| 176 | C2×Dic13 | C25 | 1 | 3 | yes | — |
| 177 | C2×Dic13 | C25 | 1 | 3 | yes | — |
| 178 | C4×D13 | — | 2 | 6 | no | — |
| 179 | C4×D13 | — | 2 | 48 | no | — |
| 180 | C4×D13 | — | 2 | 6 | no | — |
| 181 | C4×D13 | — | 2 | 6 | no | — |
| 182 | C4×D13 | 2−1+4 | 1 | 12 | yes | — |
| 183 | Dic26 | — | 2 | 24 | no | — |
| 184 | Dic26 | — | 2 | 48 | no | — |
| 185 | #564 | — | 13 | 48 | no | — |
| 186 | #564 | — | 13 | 12 | no | — |
| 187 | #564 | C2×D13 | 1 | 4 | yes | complemented |
| 188 | #557 | — | 13 | 24 | no | — |
| 189 | #557 | — | 13 | 12 | no | — |
| 190 | #557 | — | 13 | 48 | no | — |
| 191 | #557 | — | 13 | 24 | no | — |
| 192 | #557 | — | 13 | 24 | no | — |
| 193 | #557 | — | 13 | 12 | no | — |
| 194 | #557 | — | 13 | 24 | no | — |
| 195 | #557 | — | 13 | 12 | no | — |
| 196 | #557 | C2×D13 | 1 | 12 | yes | complemented |
| 197 | #541 | — | 13 | 12 | no | — |
| 198 | #541 | — | 13 | 48 | no | — |
| 199 | #541 | — | 13 | 48 | no | — |
| 200 | #541 | — | 13 | 12 | no | — |
| 201 | #541 | — | 13 | 24 | no | — |
| 202 | #541 | — | 13 | 24 | no | — |
| 203 | #541 | — | 13 | 12 | no | — |
| 204 | #541 | C2×D13 | 1 | 12 | yes | — |
| 205 | #533 | — | 13 | 6 | no | — |
| 206 | #533 | — | 13 | 6 | no | — |
| 207 | #533 | — | 13 | 12 | no | — |
| 208 | #533 | — | 13 | 12 | no | — |
| 209 | #533 | — | 13 | 6 | no | — |
| 210 | #533 | — | 13 | 3 | no | — |
| 211 | #533 | C2×D13 | 1 | 3 | yes | — |
| 212 | C2×C4⋊Q8 | — | 13 | 6 | no | — |
| 213 | C2×C4⋊Q8 | — | 13 | 12 | no | — |
| 214 | C2×#126 | — | 13 | 16 | no | — |
| 215 | C2×#125 | — | 13 | 6 | no | — |
| 216 | C2×#125 | — | 13 | 12 | no | — |
| 217 | C2×#125 | — | 13 | 48 | no | — |
| 218 | C2×C22⋊Q8 | — | 13 | 12 | no | — |
| 219 | C2×C4×Q8 | — | 13 | 12 | no | — |
| 220 | C2×C4×Q8 | — | 13 | 24 | no | — |
| 221 | C2×#117 | — | 13 | 6 | no | — |
| 222 | C22×C42 | — | 13 | 1 | no | — |
| 223 | C22×C13 | — | 2 | 3 | no | — |
| 224 | C22×C13 | C26 | 1 | 1 | yes | characteristic |
| 225 | C2×D13 | — | 2 | 3 | no | — |
| 226 | C2×D13 | — | 4 | 4 | no | — |
| 227 | C2×D13 | C2×2−1+4 | 1 | 6 | yes | — |
| 228 | C4×C13 | — | 2 | 24 | no | — |
| 229 | C4×C13 | — | 2 | 3 | no | — |
| 230 | C4×C13 | C2×2−1+4 | 1 | 6 | yes | — |
| 231 | Dic13 | — | 2 | 24 | no | — |
| 232 | Dic13 | — | 2 | 3 | no | — |
| 233 | Dic13 | C2×2−1+4 | 1 | 6 | yes | — |
| 234 | C22×Q8 | — | 13 | 12 | no | — |
| 235 | C23×C4 | — | 13 | 3 | no | — |
| 236 | C4⋊Q8 | — | 13 | 12 | no | — |
| 237 | C4⋊Q8 | — | 13 | 24 | no | — |
| 238 | C4⋊Q8 | — | 13 | 12 | no | — |
| 239 | C4⋊Q8 | — | 13 | 12 | no | — |
| 240 | C4⋊Q8 | — | 13 | 48 | no | — |
| 241 | C4⋊Q8 | — | 13 | 6 | no | — |
| 242 | C4⋊Q8 | — | 13 | 12 | no | — |
| 243 | C4⋊Q8 | C22×D13 | 1 | 6 | yes | — |
| 244 | C4⋊Q8 | C22×D13 | 1 | 12 | yes | — |
| 245 | #126 | — | 13 | 48 | no | — |
| 246 | #126 | — | 13 | 48 | no | — |
| 247 | #126 | — | 13 | 16 | no | — |
| 248 | #126 | C22×D13 | 1 | 16 | yes | — |
| 249 | #125 | — | 13 | 24 | no | — |
| 250 | #125 | — | 13 | 12 | no | — |
| 251 | #125 | — | 13 | 48 | no | — |
| 252 | #125 | — | 13 | 24 | no | — |
| 253 | #125 | — | 13 | 48 | no | — |
| 254 | #125 | — | 13 | 48 | no | — |
| 255 | #125 | — | 13 | 48 | no | — |
| 256 | #125 | — | 13 | 48 | no | — |
| 257 | #125 | — | 13 | 48 | no | — |
| 258 | #125 | — | 13 | 48 | no | — |
| 259 | #125 | — | 13 | 6 | no | — |
| 260 | #125 | — | 13 | 12 | no | — |
| 261 | #125 | — | 13 | 48 | no | — |
| 262 | #125 | C22×D13 | 1 | 6 | yes | — |
| 263 | #125 | C22×D13 | 1 | 12 | yes | — |
| 264 | #125 | C22×D13 | 1 | 48 | yes | — |
| 265 | C22⋊Q8 | — | 13 | 12 | no | — |
| 266 | C22⋊Q8 | — | 13 | 12 | no | — |
| 267 | C22⋊Q8 | — | 13 | 24 | no | — |
| 268 | C22⋊Q8 | — | 13 | 12 | no | — |
| 269 | C22⋊Q8 | — | 13 | 24 | no | — |
| 270 | C22⋊Q8 | C22×D13 | 1 | 12 | yes | — |
| 271 | C4×Q8 | — | 13 | 12 | no | — |
| 272 | C4×Q8 | — | 13 | 24 | no | — |
| 273 | C4×Q8 | — | 13 | 24 | no | — |
| 274 | C4×Q8 | — | 13 | 12 | no | — |
| 275 | C4×Q8 | — | 13 | 48 | no | — |
| 276 | C4×Q8 | — | 13 | 24 | no | — |
| 277 | C4×Q8 | — | 13 | 24 | no | — |
| 278 | C4×Q8 | — | 13 | 12 | no | — |
| 279 | C4×Q8 | — | 13 | 48 | no | — |
| 280 | C4×Q8 | — | 13 | 24 | no | — |
| 281 | C4×Q8 | C22×D13 | 1 | 12 | yes | — |
| 282 | C4×Q8 | C22×D13 | 1 | 24 | yes | — |
| 283 | #117 | — | 13 | 6 | no | — |
| 284 | #117 | — | 13 | 12 | no | — |
| 285 | #117 | — | 13 | 12 | no | — |
| 286 | #117 | — | 13 | 12 | no | — |
| 287 | #117 | C22×D13 | 1 | 6 | yes | — |
| 288 | C2×C4⋊C4 | — | 13 | 12 | no | — |
| 289 | C2×C4⋊C4 | — | 13 | 12 | no | — |
| 290 | C2×C4⋊C4 | — | 13 | 24 | no | — |
| 291 | C2×C4⋊C4 | — | 13 | 48 | no | — |
| 292 | C2×C22⋊C4 | — | 13 | 12 | no | — |
| 293 | C2×C42 | — | 13 | 3 | no | — |
| 294 | C2×C42 | — | 13 | 12 | no | — |
| 295 | C2×C42 | — | 13 | 3 | no | — |
| 296 | C2×C42 | — | 13 | 16 | no | — |
| 297 | C2×C42 | — | 13 | 1 | no | — |
| 298 | C2×C42 | — | 13 | 1 | no | — |
| 299 | C2×C42 | — | 13 | 3 | no | — |
| 300 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 301 | C2×C13 | — | 4 | 1 | no | — |
| 302 | C2×C13 | C22×2−1+4 | 1 | 3 | yes | — |
| 303 | D13 | — | 4 | 1 | no | — |
| 304 | D13 | #3556 | 1 | 4 | yes | direct product factor |
| 305 | C24 | — | 13 | 1 | no | — |
| 306 | C2×Q8 | — | 13 | 24 | no | — |
| 307 | C2×Q8 | — | 13 | 12 | no | — |
| 308 | C2×Q8 | — | 26 | 48 | no | — |
| 309 | C2×Q8 | C23×D13 | 1 | 12 | yes | — |
| 310 | C22×C4 | — | 13 | 3 | no | — |
| 311 | C22×C4 | — | 13 | 3 | no | — |
| 312 | C22×C4 | — | 13 | 24 | no | — |
| 313 | C22×C4 | — | 13 | 3 | no | — |
| 314 | C22×C4 | — | 13 | 3 | no | — |
| 315 | C22×C4 | — | 13 | 3 | no | — |
| 316 | C22×C4 | — | 26 | 12 | no | — |
| 317 | C22×C4 | C23×D13 | 1 | 3 | yes | — |
| 318 | C4⋊C4 | — | 13 | 24 | no | — |
| 319 | C4⋊C4 | — | 13 | 12 | no | — |
| 320 | C4⋊C4 | — | 13 | 24 | no | — |
| 321 | C4⋊C4 | — | 13 | 12 | no | — |
| 322 | C4⋊C4 | — | 13 | 24 | no | — |
| 323 | C4⋊C4 | — | 13 | 24 | no | — |
| 324 | C4⋊C4 | — | 13 | 24 | no | — |
| 325 | C4⋊C4 | — | 13 | 48 | no | — |
| 326 | C4⋊C4 | — | 13 | 48 | no | — |
| 327 | C4⋊C4 | — | 13 | 48 | no | — |
| 328 | C4⋊C4 | C23×D13 | 1 | 12 | yes | — |
| 329 | C4⋊C4 | C23×D13 | 1 | 12 | yes | — |
| 330 | C4⋊C4 | C23×D13 | 1 | 24 | yes | — |
| 331 | C4⋊C4 | C23×D13 | 1 | 48 | yes | — |
| 332 | C22⋊C4 | — | 13 | 12 | no | — |
| 333 | C22⋊C4 | — | 13 | 24 | no | — |
| 334 | C22⋊C4 | C23×D13 | 1 | 12 | yes | — |
| 335 | C42 | — | 13 | 3 | no | — |
| 336 | C42 | — | 13 | 6 | no | — |
| 337 | C42 | — | 13 | 3 | no | — |
| 338 | C42 | — | 13 | 24 | no | — |
| 339 | C42 | — | 13 | 12 | no | — |
| 340 | C42 | — | 13 | 48 | no | — |
| 341 | C42 | C23×D13 | 1 | 3 | yes | — |
| 342 | C42 | C23×D13 | 1 | 1 | yes | characteristic |
| 343 | C42 | C23×D13 | 1 | 12 | yes | — |
| 344 | C42 | C23×D13 | 1 | 16 | yes | — |
| 345 | C13 | C2×#3556 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 346 | C23 | — | 13 | 1 | no | — |
| 347 | C23 | — | 13 | 1 | no | — |
| 348 | C23 | — | 26 | 6 | no | — |
| 349 | C23 | C24×D13 | 1 | 1 | yes | characteristic |
| 350 | Q8 | — | 2 | 24 | no | — |
| 351 | Q8 | — | 26 | 48 | no | — |
| 352 | Q8 | — | 26 | 24 | no | — |
| 353 | C2×C4 | — | 2 | 6 | no | — |
| 354 | C2×C4 | — | 13 | 3 | no | — |
| 355 | C2×C4 | — | 13 | 12 | no | — |
| 356 | C2×C4 | — | 13 | 24 | no | — |
| 357 | C2×C4 | — | 13 | 3 | no | — |
| 358 | C2×C4 | — | 26 | 6 | no | — |
| 359 | C2×C4 | — | 26 | 6 | no | — |
| 360 | C2×C4 | — | 26 | 48 | no | — |
| 361 | C2×C4 | — | 26 | 6 | no | — |
| 362 | C2×C4 | — | 26 | 6 | no | — |
| 363 | C2×C4 | C24×D13 | 1 | 24 | yes | — |
| 364 | C2×C4 | C24×D13 | 1 | 3 | yes | — |
| 365 | C2×C4 | C24×D13 | 1 | 3 | yes | — |
| 366 | C22 | — | 2 | 3 | no | — |
| 367 | C22 | — | 13 | 6 | no | — |
| 368 | C22 | — | 26 | 3 | no | — |
| 369 | C22 | — | 52 | 4 | no | — |
| 370 | C22 | C25×D13 | 1 | 1 | yes | characteristic |
| 371 | C4 | — | 2 | 3 | no | — |
| 372 | C4 | — | 2 | 24 | no | — |
| 373 | C4 | — | 13 | 6 | no | — |
| 374 | C4 | — | 26 | 3 | no | — |
| 375 | C4 | — | 26 | 24 | no | — |
| 376 | C4 | D13×2−1+4 | 1 | 6 | yes | — |
| 377 | C2 | — | 4 | 1 | no | — |
| 378 | C2 | — | 13 | 4 | no | — |
| 379 | C2 | — | 52 | 1 | no | — |
| 380 | C2 | C2×D13×2−1+4 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D13 |
| commutator, socle, cosocle | C22×C13 | C26 |
| Fitting | C13×#3556 | C2 |
| prime radical | C23×D13 | C24 |
| hypercenter | #3556 | D13 |
| hypocenter | C13 | C2×#3556 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ #3556 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13129331 | C2 | semidirect |
| 2. #13129330 | C2 | semidirect |
| 3. #13129329 | C2 | semidirect |
| 4. #13129328 | C2 | semidirect |
| 5. D13×#564 | C2 | semidirect |
| 6. D13×#557 | C2 | semidirect |
| 9. C13×#3556 | C2 | semidirect |
| 10. C13×#564 | C22 | semidirect |
| 11. C13×#557 | C22 | semidirect |
| 18. #11719426 | C22 | semidirect |
| 19. #11719426 | C22 | semidirect |
| 28. C13⋊#564 | C22 | semidirect |
| 29. C13⋊#564 | C22 | semidirect |
| 30. #11719390 | C22 | semidirect |
| 31. #11719390 | C22 | semidirect |
| 39. #11719275 | C22 | semidirect |
| 40. #11719274 | C22 | semidirect |
| 41. #11719272 | C22 | semidirect |
| 42. #11719272 | C22 | semidirect |
| 160. #3556 | D13 | direct (N × H) |
| 187. #564 | C2×D13 | semidirect |
| 196. #557 | C2×D13 | semidirect |
| 304. D13 | #3556 | direct (N × H) |
| 345. C13 | C2×#3556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13129331 | 2 |
| #13129330 | 2 |
| #13129329 | 2 |
| #13129328 | 2 |
| D13×#564 | 2 |
| D13×#557 | 2 |
| D13×#541 | 2 |
| D13×#533 | 2 |
| C13×#3556 | 2 |
| C2×#3556 | 13 |