Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
2144 conjugacy classes of subgroups.
The subgroup lattice has 576 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13129250 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13128609 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13127068 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #13126776 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | D4×#6095 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #13126504 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #13125779 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #13125709 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #13124908 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #13124115 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | C13×#2979 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#88256 | C22 | 1 | 2 | yes | — |
| 13 | C13×#532 | C22 | 1 | 1 | yes | characteristic |
| 14 | #11719535 | C22 | 1 | 2 | yes | — |
| 15 | #11719530 | C22 | 1 | 4 | yes | complemented |
| 16 | C2×#88163 | C22 | 1 | 4 | yes | complemented |
| 17 | C22×#6095 | C22 | 1 | 4 | yes | complemented |
| 18 | #11719430 | — | 2 | 1 | no | — |
| 19 | #11719427 | — | 2 | 1 | no | — |
| 20 | D13×#127 | — | 2 | 1 | no | — |
| 21 | #11719418 | — | 2 | 1 | no | — |
| 22 | #11719379 | — | 2 | 2 | no | — |
| 23 | #11719377 | — | 2 | 2 | no | — |
| 24 | #11719314 | — | 2 | 4 | no | — |
| 25 | #11719308 | — | 2 | 4 | no | — |
| 26 | #11719258 | C22 | 1 | 4 | yes | — |
| 27 | D4×D52 | C22 | 1 | 4 | yes | — |
| 28 | #11719247 | C22 | 1 | 4 | yes | complemented |
| 29 | D4×Dic26 | C22 | 1 | 4 | yes | complemented |
| 30 | C2×#88128 | C22 | 1 | 1 | yes | characteristic |
| 31 | C4×#6127 | C22 | 1 | 1 | yes | characteristic |
| 32 | #11719175 | C22 | 1 | 2 | yes | complemented |
| 33 | C13×#436 | C22 | 1 | 4 | yes | complemented |
| 34 | C8×D4×C13 | C22 | 1 | 4 | yes | complemented |
| 35 | C13×#431 | C22 | 1 | 2 | yes | complemented |
| 36 | C13×#408 | C22 | 1 | 4 | yes | complemented |
| 37 | #11718795 | C22 | 1 | 8 | yes | complemented |
| 38 | #11718792 | C22 | 1 | 4 | yes | complemented |
| 39 | #11718775 | C22 | 1 | 8 | yes | complemented |
| 40 | #11718774 | C22 | 1 | 4 | yes | complemented |
| 41 | #11718512 | C22 | 1 | 2 | yes | complemented |
| 42 | #11718510 | C22 | 1 | 2 | yes | complemented |
| 43 | #11718509 | C22 | 1 | 4 | yes | complemented |
| 44 | #11718509 | C22 | 1 | 4 | yes | complemented |
| 45 | #11718507 | C22 | 1 | 2 | yes | complemented |
| 46 | #11718502 | C22 | 1 | 2 | yes | complemented |
| 47 | #11718399 | C22 | 1 | 8 | yes | complemented |
| 48 | #11718398 | C22 | 1 | 8 | yes | complemented |
| 49 | #11718394 | C22 | 1 | 4 | yes | — |
| 50 | #11718394 | C22 | 1 | 8 | yes | complemented |
| 51 | #11718392 | C22 | 1 | 8 | yes | complemented |
| 52 | #11718392 | C22 | 1 | 8 | yes | complemented |
| 53 | #11718384 | C22 | 1 | 4 | yes | complemented |
| 54 | C4×Dic52 | C22 | 1 | 4 | yes | complemented |
| 55 | #11718355 | C22 | 1 | 4 | yes | complemented |
| 56 | #11718354 | C22 | 1 | 4 | yes | complemented |
| 57 | C4×#6095 | C22 | 1 | 4 | yes | complemented |
| 58 | C2×C13×#41 | C23 | 1 | 2 | yes | — |
| 59 | #88256 | — | 4 | 4 | no | — |
| 60 | #88256 | — | 4 | 4 | no | — |
| 61 | C2×#6131 | — | 2 | 2 | no | — |
| 62 | C2×D4×D13 | — | 2 | 4 | no | — |
| 63 | C2×D4×D13 | — | 2 | 2 | no | — |
| 64 | C2×D4×D13 | — | 2 | 4 | no | — |
| 65 | C2×#6127 | C23 | 1 | 1 | yes | characteristic |
| 66 | C2×#6127 | C23 | 1 | 4 | yes | — |
| 67 | C22×D52 | — | 2 | 2 | no | — |
| 68 | C22×D52 | C23 | 1 | 4 | yes | — |
| 69 | C22×D52 | C23 | 1 | 2 | yes | — |
| 70 | C22×Dic26 | C23 | 1 | 4 | yes | — |
| 71 | C2×C13×M16 | C23 | 1 | 4 | yes | — |
| 72 | C22×C8×C13 | C23 | 1 | 4 | yes | — |
| 73 | C13×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 74 | C13×#127 | D4 | 1 | 1 | yes | characteristic |
| 75 | C13×#124 | D4 | 1 | 2 | yes | — |
| 76 | C13×#121 | D4 | 1 | 4 | yes | — |
| 77 | C4×D4×C13 | C23 | 1 | 4 | yes | — |
| 78 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 79 | #88201 | — | 2 | 2 | no | — |
| 80 | #88198 | — | 2 | 4 | no | — |
| 81 | #88194 | — | 2 | 4 | no | — |
| 82 | #88194 | — | 2 | 2 | no | — |
| 83 | #88191 | — | 2 | 4 | no | — |
| 84 | #88190 | — | 2 | 4 | no | — |
| 85 | #88190 | — | 2 | 4 | no | — |
| 86 | #88189 | — | 2 | 4 | no | — |
| 87 | #88189 | — | 2 | 4 | no | — |
| 88 | D4×Dic13 | — | 2 | 4 | no | — |
| 89 | #88184 | C23 | 1 | 8 | yes | — |
| 90 | C4×C22⋊D13 | — | 2 | 2 | no | — |
| 91 | #88180 | — | 2 | 2 | no | — |
| 92 | #88180 | C23 | 1 | 1 | yes | characteristic |
| 93 | #88180 | C23 | 1 | 4 | yes | — |
| 94 | #88178 | — | 2 | 2 | no | — |
| 95 | #88178 | C23 | 1 | 4 | yes | — |
| 96 | #88178 | C23 | 1 | 8 | yes | — |
| 97 | #88163 | — | 4 | 8 | no | — |
| 98 | C2×Dic52 | C23 | 1 | 4 | yes | — |
| 99 | C2×#6095 | — | 4 | 8 | no | — |
| 100 | C2×#6095 | C23 | 1 | 4 | yes | — |
| 101 | C2×#6095 | C23 | 1 | 8 | yes | — |
| 102 | C2×#6095 | C23 | 1 | 8 | yes | — |
| 103 | #88149 | — | 2 | 4 | no | — |
| 104 | #88147 | — | 2 | 4 | no | — |
| 105 | #88142 | — | 2 | 4 | no | — |
| 106 | #88141 | — | 2 | 4 | no | — |
| 107 | #88138 | — | 2 | 8 | no | — |
| 108 | #88136 | — | 2 | 8 | no | — |
| 109 | #88133 | — | 2 | 8 | no | — |
| 110 | #88132 | — | 2 | 8 | no | — |
| 111 | #88128 | — | 2 | 1 | no | — |
| 112 | #88128 | — | 2 | 1 | no | — |
| 113 | #88128 | C23 | 1 | 4 | yes | — |
| 114 | C4×D52 | C23 | 1 | 2 | yes | — |
| 115 | #88126 | — | 2 | 1 | no | — |
| 116 | C42×D13 | — | 2 | 1 | no | — |
| 117 | #88124 | — | 2 | 2 | no | — |
| 118 | #88123 | C23 | 1 | 2 | yes | — |
| 119 | #88123 | C23 | 1 | 2 | yes | — |
| 120 | C4×Dic26 | — | 2 | 2 | no | — |
| 121 | C4×Dic26 | C23 | 1 | 4 | yes | — |
| 122 | C4×Dic26 | C23 | 1 | 2 | yes | — |
| 123 | C13×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 124 | C13×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 125 | C13×C22⋊C8 | C23 | 1 | 4 | yes | — |
| 126 | C13×C22⋊C8 | C23 | 1 | 8 | yes | — |
| 127 | C4×C8×C13 | C23 | 1 | 4 | yes | — |
| 128 | #88061 | C23 | 1 | 4 | yes | — |
| 129 | #88061 | C23 | 1 | 8 | yes | — |
| 130 | #88061 | C23 | 1 | 8 | yes | — |
| 131 | #88058 | C23 | 1 | 4 | yes | — |
| 132 | #88057 | C23 | 1 | 4 | yes | — |
| 133 | #88056 | C23 | 1 | 4 | yes | — |
| 134 | #88056 | C23 | 1 | 4 | yes | — |
| 135 | #88056 | C23 | 1 | 4 | yes | — |
| 136 | #61662 | — | 13 | 1 | no | maximal, Sylow |
| 137 | C23×D13 | — | 2 | 4 | no | — |
| 138 | C23×D13 | — | 2 | 2 | no | — |
| 139 | C13×#41 | — | 4 | 2 | no | — |
| 140 | C13×#41 | — | 4 | 2 | no | — |
| 141 | C2×Q8×C13 | C2×D4 | 1 | 2 | yes | — |
| 142 | C2×D4×C13 | C2×D4 | 1 | 4 | yes | — |
| 143 | C2×D4×C13 | C2×D4 | 1 | 2 | yes | — |
| 144 | C2×D4×C13 | C2×D4 | 1 | 4 | yes | — |
| 145 | C22×C4×C13 | C2×D4 | 1 | 2 | yes | — |
| 146 | C22×C4×C13 | C24 | 1 | 1 | yes | characteristic |
| 147 | C22×C4×C13 | C24 | 1 | 4 | yes | — |
| 148 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 149 | C2×C22⋊D13 | — | 2 | 4 | no | — |
| 150 | C2×C22⋊D13 | — | 2 | 8 | no | — |
| 151 | C22×Dic13 | — | 2 | 4 | no | — |
| 152 | #6131 | — | 4 | 8 | no | — |
| 153 | D4×D13 | — | 4 | 8 | no | — |
| 154 | D4×D13 | — | 4 | 16 | no | — |
| 155 | D4×D13 | — | 8 | 8 | no | — |
| 156 | #6127 | — | 2 | 2 | no | — |
| 157 | #6127 | — | 2 | 2 | no | — |
| 158 | #6127 | — | 2 | 8 | no | — |
| 159 | #6127 | — | 4 | 4 | no | — |
| 160 | C2×D52 | — | 2 | 8 | no | — |
| 161 | C2×D52 | — | 2 | 2 | no | — |
| 162 | C2×D52 | — | 2 | 4 | no | — |
| 163 | C2×D52 | — | 2 | 4 | no | — |
| 164 | C2×D52 | — | 2 | 4 | no | — |
| 165 | C2×D52 | — | 4 | 4 | no | — |
| 166 | C2×D52 | — | 4 | 2 | no | — |
| 167 | C2×D52 | — | 4 | 2 | no | — |
| 168 | C2×D52 | — | 8 | 4 | no | — |
| 169 | C2×D52 | C24 | 1 | 4 | yes | — |
| 170 | C2×D52 | C24 | 1 | 1 | yes | characteristic |
| 171 | C2×C4×D13 | — | 2 | 1 | no | — |
| 172 | C2×C4×D13 | — | 2 | 2 | no | — |
| 173 | C2×C4×D13 | — | 2 | 4 | no | — |
| 174 | C2×Dic26 | — | 2 | 2 | no | — |
| 175 | C2×Dic26 | — | 2 | 4 | no | — |
| 176 | C2×Dic26 | — | 4 | 4 | no | — |
| 177 | C2×Dic26 | — | 4 | 4 | no | — |
| 178 | C2×Dic26 | C24 | 1 | 4 | yes | — |
| 179 | C2×Dic26 | C24 | 1 | 1 | yes | characteristic |
| 180 | C13×M16 | — | 4 | 4 | no | — |
| 181 | C2×C8×C13 | — | 4 | 4 | no | — |
| 182 | C2×C8×C13 | C24 | 1 | 4 | yes | — |
| 183 | C2×C8×C13 | C24 | 1 | 4 | yes | — |
| 184 | C13×C4⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 185 | C13×C22⋊C4 | C2×D4 | 1 | 8 | yes | — |
| 186 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 187 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 188 | C42×C13 | C24 | 1 | 2 | yes | — |
| 189 | C22⋊Dic13 | — | 2 | 8 | no | — |
| 190 | C22⋊Dic13 | — | 2 | 4 | no | — |
| 191 | C22⋊Dic13 | — | 2 | 4 | no | — |
| 192 | C22⋊Dic13 | — | 2 | 1 | no | — |
| 193 | #6103 | — | 2 | 2 | no | — |
| 194 | #6103 | — | 2 | 8 | no | — |
| 195 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 196 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 197 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 198 | C4⋊Dic13 | C24 | 1 | 4 | yes | — |
| 199 | C4⋊Dic13 | C24 | 1 | 2 | yes | — |
| 200 | #6101 | — | 2 | 4 | no | — |
| 201 | #6101 | — | 2 | 4 | no | — |
| 202 | #6101 | — | 2 | 2 | no | — |
| 203 | #6101 | — | 2 | 8 | no | — |
| 204 | C4×Dic13 | — | 2 | 4 | no | — |
| 205 | C4×Dic13 | — | 2 | 2 | no | — |
| 206 | C4×Dic13 | — | 2 | 1 | no | — |
| 207 | C4×Dic13 | — | 2 | 4 | no | — |
| 208 | Dic52 | — | 2 | 8 | no | — |
| 209 | #6095 | — | 2 | 8 | no | — |
| 210 | #6095 | — | 4 | 8 | no | — |
| 211 | #6095 | — | 4 | 8 | no | — |
| 212 | #3550 | — | 13 | 1 | no | — |
| 213 | #3498 | — | 13 | 1 | no | — |
| 214 | #3324 | — | 13 | 4 | no | — |
| 215 | #3304 | — | 13 | 4 | no | — |
| 216 | D4×SD16 | — | 13 | 4 | no | — |
| 217 | #3278 | — | 13 | 4 | no | — |
| 218 | #3208 | — | 13 | 2 | no | — |
| 219 | #3200 | — | 13 | 4 | no | — |
| 220 | #3107 | — | 13 | 2 | no | — |
| 221 | #3009 | — | 13 | 4 | no | — |
| 222 | #2979 | D13 | 1 | 1 | yes | characteristic, complemented |
| 223 | C23×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 224 | C23×C13 | C22×D4 | 1 | 4 | yes | — |
| 225 | C22×D13 | — | 2 | 1 | no | — |
| 226 | C22×D13 | — | 2 | 4 | no | — |
| 227 | C22×D13 | — | 4 | 8 | no | — |
| 228 | C22×D13 | — | 4 | 4 | no | — |
| 229 | C22×D13 | — | 8 | 4 | no | — |
| 230 | C22×D13 | — | 8 | 8 | no | — |
| 231 | Q8×C13 | — | 4 | 2 | no | — |
| 232 | D4×C13 | — | 2 | 8 | no | — |
| 233 | D4×C13 | — | 4 | 4 | no | — |
| 234 | D4×C13 | — | 4 | 2 | no | — |
| 235 | C2×C4×C13 | — | 2 | 4 | no | — |
| 236 | C2×C4×C13 | — | 2 | 4 | no | — |
| 237 | C2×C4×C13 | — | 2 | 4 | no | — |
| 238 | C2×C4×C13 | — | 2 | 1 | no | — |
| 239 | C2×C4×C13 | — | 2 | 1 | no | — |
| 240 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 241 | C2×C4×C13 | C22×D4 | 1 | 4 | yes | — |
| 242 | C2×C4×C13 | C22×D4 | 1 | 2 | yes | — |
| 243 | C2×C4×C13 | C22×D4 | 1 | 2 | yes | — |
| 244 | C2×C4×C13 | C25 | 1 | 1 | yes | characteristic |
| 245 | C22⋊D13 | — | 2 | 4 | no | — |
| 246 | C22⋊D13 | — | 4 | 8 | no | — |
| 247 | C22⋊D13 | — | 8 | 8 | no | — |
| 248 | C2×Dic13 | — | 2 | 1 | no | — |
| 249 | C2×Dic13 | — | 2 | 4 | no | — |
| 250 | C2×Dic13 | — | 2 | 2 | no | — |
| 251 | C2×Dic13 | — | 2 | 4 | no | — |
| 252 | C2×Dic13 | — | 8 | 4 | no | — |
| 253 | D52 | — | 2 | 1 | no | — |
| 254 | D52 | — | 2 | 4 | no | — |
| 255 | D52 | — | 2 | 4 | no | — |
| 256 | D52 | — | 4 | 8 | no | — |
| 257 | D52 | — | 4 | 4 | no | — |
| 258 | D52 | — | 4 | 8 | no | — |
| 259 | D52 | — | 8 | 4 | no | — |
| 260 | D52 | H(5,𝔽2) | 1 | 2 | yes | — |
| 261 | C4×D13 | — | 2 | 4 | no | — |
| 262 | C4×D13 | — | 4 | 8 | no | — |
| 263 | C4×D13 | — | 4 | 4 | no | — |
| 264 | Dic26 | — | 2 | 1 | no | — |
| 265 | Dic26 | — | 2 | 4 | no | — |
| 266 | Dic26 | — | 2 | 4 | no | — |
| 267 | Dic26 | — | 4 | 4 | no | — |
| 268 | Dic26 | — | 8 | 4 | no | — |
| 269 | Dic26 | H(5,𝔽2) | 1 | 2 | yes | — |
| 270 | C8×C13 | — | 2 | 4 | no | — |
| 271 | C8×C13 | — | 2 | 4 | no | — |
| 272 | C2×H(5,𝔽2) | — | 13 | 2 | no | — |
| 273 | C2×#137 | — | 13 | 4 | no | — |
| 274 | C22×SD16 | — | 13 | 4 | no | — |
| 275 | #563 | — | 26 | 2 | no | — |
| 276 | #559 | — | 26 | 1 | no | — |
| 277 | Q82 | — | 26 | 1 | no | — |
| 278 | #556 | — | 13 | 4 | no | — |
| 279 | #550 | — | 13 | 4 | no | — |
| 280 | D4×Q8 | — | 13 | 4 | no | — |
| 281 | D42 | — | 13 | 4 | no | — |
| 282 | D42 | — | 26 | 4 | no | — |
| 283 | #542 | — | 26 | 4 | no | — |
| 284 | #536 | — | 13 | 4 | no | — |
| 285 | #535 | — | 13 | 2 | no | — |
| 286 | #535 | — | 26 | 2 | no | — |
| 287 | #533 | — | 13 | 2 | no | — |
| 288 | #532 | — | 26 | 1 | no | — |
| 289 | #532 | C2×D13 | 1 | 1 | yes | characteristic |
| 290 | C2×#127 | — | 13 | 1 | no | — |
| 291 | C2×#127 | — | 26 | 1 | no | — |
| 292 | C4×#41 | — | 13 | 1 | no | — |
| 293 | #492 | — | 13 | 4 | no | — |
| 294 | #486 | — | 13 | 4 | no | — |
| 295 | #485 | — | 13 | 4 | no | — |
| 296 | #482 | — | 13 | 8 | no | — |
| 297 | #475 | — | 13 | 2 | no | — |
| 298 | #474 | — | 13 | 2 | no | — |
| 299 | #468 | — | 13 | 8 | no | — |
| 300 | #465 | — | 13 | 8 | no | — |
| 301 | #462 | — | 13 | 2 | no | — |
| 302 | #461 | — | 13 | 2 | no | — |
| 303 | #460 | — | 13 | 4 | no | — |
| 304 | #460 | — | 13 | 4 | no | — |
| 305 | #452 | — | 13 | 4 | no | — |
| 306 | #452 | — | 13 | 8 | no | — |
| 307 | #450 | — | 13 | 8 | no | — |
| 308 | #450 | — | 13 | 8 | no | — |
| 309 | #448 | — | 13 | 8 | no | — |
| 310 | C4×Q16 | — | 13 | 4 | no | — |
| 311 | C4×SD16 | — | 13 | 4 | no | — |
| 312 | #436 | C2×D13 | 1 | 4 | yes | complemented |
| 313 | C8×D4 | C2×D13 | 1 | 4 | yes | complemented |
| 314 | #431 | C2×D13 | 1 | 2 | yes | complemented |
| 315 | #418 | — | 13 | 4 | no | — |
| 316 | #416 | — | 13 | 4 | no | — |
| 317 | #408 | C2×D13 | 1 | 4 | yes | complemented |
| 318 | C22×C13 | — | 2 | 4 | no | — |
| 319 | C22×C13 | — | 2 | 1 | no | — |
| 320 | C22×C13 | — | 2 | 8 | no | — |
| 321 | C22×C13 | — | 2 | 2 | no | — |
| 322 | C22×C13 | C23×D4 | 1 | 1 | yes | characteristic |
| 323 | C2×D13 | — | 2 | 2 | no | — |
| 324 | C2×D13 | — | 4 | 2 | no | — |
| 325 | C2×D13 | — | 4 | 4 | no | — |
| 326 | C2×D13 | — | 4 | 8 | no | — |
| 327 | C2×D13 | — | 16 | 8 | no | — |
| 328 | C2×D13 | — | 16 | 4 | no | — |
| 329 | C4×C13 | — | 2 | 4 | no | — |
| 330 | C4×C13 | — | 2 | 1 | no | — |
| 331 | C4×C13 | — | 2 | 2 | no | — |
| 332 | C4×C13 | #577 | 1 | 4 | yes | — |
| 333 | C4×C13 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 334 | C4×C13 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 335 | Dic13 | — | 2 | 2 | no | — |
| 336 | Dic13 | — | 4 | 4 | no | — |
| 337 | Dic13 | — | 4 | 4 | no | — |
| 338 | Dic13 | — | 4 | 2 | no | — |
| 339 | H(5,𝔽2) | — | 52 | 4 | no | — |
| 340 | H(5,𝔽2) | — | 52 | 4 | no | — |
| 341 | C2×#41 | — | 13 | 1 | no | — |
| 342 | C2×#41 | — | 13 | 4 | no | — |
| 343 | C2×#41 | — | 26 | 2 | no | — |
| 344 | C2×#41 | C22×D13 | 1 | 2 | yes | — |
| 345 | C22×Q8 | — | 13 | 4 | no | — |
| 346 | C22×D4 | — | 13 | 4 | no | — |
| 347 | C22×D4 | — | 13 | 2 | no | — |
| 348 | C22×D4 | — | 26 | 2 | no | — |
| 349 | C22×D4 | — | 26 | 4 | no | — |
| 350 | C22×D4 | — | 26 | 4 | no | — |
| 351 | C22×D4 | — | 26 | 2 | no | — |
| 352 | #137 | — | 52 | 8 | no | — |
| 353 | C2×Q16 | — | 13 | 4 | no | — |
| 354 | C2×SD16 | — | 13 | 4 | no | — |
| 355 | C2×SD16 | — | 13 | 8 | no | — |
| 356 | C2×SD16 | — | 13 | 8 | no | — |
| 357 | C2×SD16 | — | 52 | 8 | no | — |
| 358 | C2×M16 | C22×D13 | 1 | 4 | yes | — |
| 359 | C22×C8 | C22×D13 | 1 | 4 | yes | — |
| 360 | C4⋊Q8 | — | 13 | 2 | no | — |
| 361 | C4⋊Q8 | — | 13 | 2 | no | — |
| 362 | C4⋊Q8 | — | 26 | 4 | no | — |
| 363 | C4⋊Q8 | — | 26 | 4 | no | — |
| 364 | C4⋊Q8 | D52 | 1 | 1 | yes | characteristic |
| 365 | #127 | — | 13 | 4 | no | — |
| 366 | #127 | — | 26 | 2 | no | — |
| 367 | #127 | — | 26 | 4 | no | — |
| 368 | #127 | — | 26 | 1 | no | — |
| 369 | #127 | — | 26 | 1 | no | — |
| 370 | #127 | D52 | 1 | 1 | yes | characteristic |
| 371 | #126 | — | 26 | 8 | no | — |
| 372 | #125 | — | 26 | 2 | no | — |
| 373 | #124 | — | 26 | 2 | no | — |
| 374 | #124 | — | 26 | 4 | no | — |
| 375 | #124 | — | 26 | 4 | no | — |
| 376 | #124 | D52 | 1 | 2 | yes | — |
| 377 | #123 | — | 26 | 4 | no | — |
| 378 | #123 | — | 26 | 4 | no | — |
| 379 | C22⋊Q8 | — | 13 | 4 | no | — |
| 380 | C22⋊Q8 | — | 13 | 8 | no | — |
| 381 | C22⋊Q8 | — | 26 | 2 | no | — |
| 382 | C22⋊Q8 | — | 26 | 8 | no | — |
| 383 | #121 | — | 13 | 8 | no | — |
| 384 | #121 | — | 26 | 4 | no | — |
| 385 | #121 | — | 26 | 8 | no | — |
| 386 | #121 | D52 | 1 | 4 | yes | — |
| 387 | #120 | — | 26 | 4 | no | — |
| 388 | #120 | — | 26 | 8 | no | — |
| 389 | C4×Q8 | — | 13 | 2 | no | — |
| 390 | C4×Q8 | — | 13 | 4 | no | — |
| 391 | C4×Q8 | — | 26 | 4 | no | — |
| 392 | C4×Q8 | — | 26 | 2 | no | — |
| 393 | C4×D4 | — | 13 | 2 | no | — |
| 394 | C4×D4 | — | 26 | 4 | no | — |
| 395 | C4×D4 | — | 26 | 2 | no | — |
| 396 | C4×D4 | — | 26 | 4 | no | — |
| 397 | C4×D4 | C22×D13 | 1 | 4 | yes | — |
| 398 | #117 | — | 13 | 1 | no | — |
| 399 | #117 | — | 13 | 4 | no | — |
| 400 | #117 | — | 26 | 2 | no | — |
| 401 | #117 | — | 26 | 1 | no | — |
| 402 | C2×C42 | — | 26 | 1 | no | — |
| 403 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 404 | #107 | — | 13 | 4 | no | — |
| 405 | #106 | — | 13 | 4 | no | — |
| 406 | C4⋊C8 | C22×D13 | 1 | 2 | yes | — |
| 407 | C4⋊C8 | C22×D13 | 1 | 2 | yes | — |
| 408 | #103 | — | 13 | 4 | no | — |
| 409 | #103 | — | 13 | 4 | no | — |
| 410 | #103 | — | 13 | 4 | no | — |
| 411 | #102 | — | 13 | 8 | no | — |
| 412 | #102 | — | 13 | 4 | no | — |
| 413 | #102 | — | 13 | 8 | no | — |
| 414 | C22⋊C8 | C22×D13 | 1 | 4 | yes | — |
| 415 | C22⋊C8 | C22×D13 | 1 | 8 | yes | — |
| 416 | C4×C8 | C22×D13 | 1 | 4 | yes | — |
| 417 | C2×C13 | — | 4 | 1 | no | — |
| 418 | C2×C13 | — | 4 | 4 | no | — |
| 419 | C2×C13 | #3484 | 1 | 1 | yes | characteristic |
| 420 | C2×C13 | C2×#577 | 1 | 2 | yes | — |
| 421 | D13 | — | 4 | 2 | no | — |
| 422 | D13 | — | 8 | 4 | no | — |
| 423 | C24 | — | 26 | 4 | no | — |
| 424 | C24 | — | 26 | 2 | no | — |
| 425 | #41 | — | 4 | 2 | no | — |
| 426 | #41 | — | 4 | 2 | no | — |
| 427 | #41 | — | 26 | 2 | no | — |
| 428 | #41 | — | 26 | 2 | no | — |
| 429 | #41 | — | 26 | 8 | no | — |
| 430 | #41 | — | 52 | 4 | no | — |
| 431 | #41 | — | 52 | 8 | no | — |
| 432 | C2×Q8 | — | 13 | 1 | no | — |
| 433 | C2×Q8 | — | 13 | 4 | no | — |
| 434 | C2×Q8 | — | 26 | 2 | no | — |
| 435 | C2×Q8 | — | 26 | 4 | no | — |
| 436 | C2×Q8 | — | 52 | 4 | no | — |
| 437 | C2×Q8 | — | 52 | 4 | no | — |
| 438 | C2×Q8 | C2×D52 | 1 | 2 | yes | — |
| 439 | C2×D4 | — | 13 | 1 | no | — |
| 440 | C2×D4 | — | 13 | 4 | no | — |
| 441 | C2×D4 | — | 26 | 8 | no | — |
| 442 | C2×D4 | — | 26 | 1 | no | — |
| 443 | C2×D4 | — | 26 | 4 | no | — |
| 444 | C2×D4 | — | 26 | 8 | no | — |
| 445 | C2×D4 | — | 26 | 4 | no | — |
| 446 | C2×D4 | — | 26 | 4 | no | — |
| 447 | C2×D4 | — | 26 | 2 | no | — |
| 448 | C2×D4 | — | 26 | 4 | no | — |
| 449 | C2×D4 | — | 52 | 4 | no | — |
| 450 | C2×D4 | — | 52 | 2 | no | — |
| 451 | C2×D4 | — | 52 | 2 | no | — |
| 452 | C2×D4 | — | 52 | 8 | no | — |
| 453 | C2×D4 | — | 52 | 16 | no | — |
| 454 | C2×D4 | — | 104 | 4 | no | — |
| 455 | C2×D4 | — | 104 | 8 | no | — |
| 456 | C2×D4 | C2×D52 | 1 | 4 | yes | — |
| 457 | C2×D4 | C2×D52 | 1 | 4 | yes | — |
| 458 | C2×D4 | C2×D52 | 1 | 2 | yes | — |
| 459 | C22×C4 | — | 26 | 1 | no | — |
| 460 | C22×C4 | — | 26 | 4 | no | — |
| 461 | C22×C4 | — | 26 | 2 | no | — |
| 462 | C22×C4 | — | 26 | 4 | no | — |
| 463 | C22×C4 | C2×D52 | 1 | 2 | yes | — |
| 464 | C22×C4 | C23×D13 | 1 | 1 | yes | characteristic |
| 465 | C22×C4 | C23×D13 | 1 | 4 | yes | — |
| 466 | Q16 | — | 26 | 8 | no | — |
| 467 | SD16 | — | 26 | 8 | no | — |
| 468 | SD16 | — | 52 | 8 | no | — |
| 469 | SD16 | — | 52 | 8 | no | — |
| 470 | M16 | — | 4 | 4 | no | — |
| 471 | C2×C8 | — | 4 | 4 | no | — |
| 472 | C2×C8 | C23×D13 | 1 | 4 | yes | — |
| 473 | C2×C8 | C23×D13 | 1 | 4 | yes | — |
| 474 | C4⋊C4 | — | 13 | 4 | no | — |
| 475 | C4⋊C4 | — | 13 | 2 | no | — |
| 476 | C4⋊C4 | — | 26 | 2 | no | — |
| 477 | C4⋊C4 | — | 26 | 2 | no | — |
| 478 | C4⋊C4 | — | 26 | 2 | no | — |
| 479 | C4⋊C4 | — | 26 | 2 | no | — |
| 480 | C4⋊C4 | — | 26 | 4 | no | — |
| 481 | C4⋊C4 | — | 26 | 8 | no | — |
| 482 | C4⋊C4 | — | 26 | 4 | no | — |
| 483 | C4⋊C4 | C2×D52 | 1 | 4 | yes | — |
| 484 | C22⋊C4 | — | 26 | 1 | no | — |
| 485 | C22⋊C4 | — | 26 | 4 | no | — |
| 486 | C22⋊C4 | — | 26 | 4 | no | — |
| 487 | C22⋊C4 | — | 26 | 8 | no | — |
| 488 | C22⋊C4 | — | 26 | 2 | no | — |
| 489 | C22⋊C4 | — | 26 | 8 | no | — |
| 490 | C22⋊C4 | C2×D52 | 1 | 8 | yes | — |
| 491 | C42 | — | 26 | 1 | no | — |
| 492 | C42 | — | 26 | 2 | no | — |
| 493 | C42 | — | 26 | 4 | no | — |
| 494 | C42 | — | 26 | 4 | no | — |
| 495 | C42 | C2×D52 | 1 | 1 | yes | characteristic |
| 496 | C42 | C2×D52 | 1 | 1 | yes | characteristic |
| 497 | C42 | C23×D13 | 1 | 2 | yes | — |
| 498 | C13 | #61662 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 499 | C23 | — | 26 | 1 | no | — |
| 500 | C23 | — | 26 | 4 | no | — |
| 501 | C23 | — | 52 | 8 | no | — |
| 502 | C23 | — | 52 | 4 | no | — |
| 503 | C23 | — | 104 | 4 | no | — |
| 504 | C23 | — | 104 | 8 | no | — |
| 505 | C23 | C22×D52 | 1 | 1 | yes | characteristic |
| 506 | C23 | C22×D52 | 1 | 4 | yes | — |
| 507 | Q8 | — | 4 | 2 | no | — |
| 508 | Q8 | — | 13 | 2 | no | — |
| 509 | Q8 | — | 26 | 1 | no | — |
| 510 | Q8 | — | 26 | 4 | no | — |
| 511 | Q8 | — | 26 | 4 | no | — |
| 512 | Q8 | — | 52 | 4 | no | — |
| 513 | Q8 | — | 104 | 4 | no | — |
| 514 | D4 | — | 2 | 8 | no | — |
| 515 | D4 | — | 4 | 2 | no | — |
| 516 | D4 | — | 4 | 4 | no | — |
| 517 | D4 | — | 13 | 2 | no | — |
| 518 | D4 | — | 26 | 4 | no | — |
| 519 | D4 | — | 26 | 1 | no | — |
| 520 | D4 | — | 26 | 4 | no | — |
| 521 | D4 | — | 26 | 4 | no | — |
| 522 | D4 | — | 52 | 8 | no | — |
| 523 | D4 | — | 52 | 4 | no | — |
| 524 | D4 | — | 52 | 8 | no | — |
| 525 | D4 | — | 52 | 8 | no | — |
| 526 | D4 | — | 104 | 4 | no | — |
| 527 | D4 | — | 104 | 8 | no | — |
| 528 | C2×C4 | — | 2 | 4 | no | — |
| 529 | C2×C4 | — | 2 | 4 | no | — |
| 530 | C2×C4 | — | 2 | 4 | no | — |
| 531 | C2×C4 | — | 2 | 1 | no | — |
| 532 | C2×C4 | — | 2 | 1 | no | — |
| 533 | C2×C4 | — | 26 | 4 | no | — |
| 534 | C2×C4 | — | 26 | 1 | no | — |
| 535 | C2×C4 | — | 26 | 4 | no | — |
| 536 | C2×C4 | — | 26 | 2 | no | — |
| 537 | C2×C4 | — | 26 | 4 | no | — |
| 538 | C2×C4 | — | 52 | 8 | no | — |
| 539 | C2×C4 | — | 52 | 4 | no | — |
| 540 | C2×C4 | — | 104 | 4 | no | — |
| 541 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 542 | C2×C4 | C22×D52 | 1 | 4 | yes | — |
| 543 | C2×C4 | C22×D52 | 1 | 2 | yes | — |
| 544 | C2×C4 | C22×D52 | 1 | 2 | yes | — |
| 545 | C2×C4 | C24×D13 | 1 | 1 | yes | characteristic |
| 546 | C8 | — | 2 | 4 | no | — |
| 547 | C8 | — | 2 | 4 | no | — |
| 548 | C22 | — | 2 | 4 | no | — |
| 549 | C22 | — | 2 | 1 | no | — |
| 550 | C22 | — | 2 | 2 | no | — |
| 551 | C22 | — | 2 | 8 | no | — |
| 552 | C22 | — | 26 | 2 | no | — |
| 553 | C22 | — | 52 | 2 | no | — |
| 554 | C22 | — | 52 | 4 | no | — |
| 555 | C22 | — | 52 | 8 | no | — |
| 556 | C22 | — | 208 | 8 | no | — |
| 557 | C22 | — | 208 | 4 | no | — |
| 558 | C22 | C23×D52 | 1 | 1 | yes | characteristic |
| 559 | C4 | — | 2 | 1 | no | — |
| 560 | C4 | — | 2 | 4 | no | — |
| 561 | C4 | — | 2 | 2 | no | — |
| 562 | C4 | — | 26 | 2 | no | — |
| 563 | C4 | — | 52 | 4 | no | — |
| 564 | C4 | — | 52 | 2 | no | — |
| 565 | C4 | — | 52 | 4 | no | — |
| 566 | C4 | #11719456 | 1 | 4 | yes | — |
| 567 | C4 | D13×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 568 | C4 | D13×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 569 | C2 | — | 4 | 1 | no | — |
| 570 | C2 | — | 4 | 4 | no | — |
| 571 | C2 | — | 52 | 2 | no | — |
| 572 | C2 | — | 104 | 4 | no | — |
| 573 | C2 | #13128472 | 1 | 1 | yes | characteristic |
| 574 | C2 | C2×#11719456 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13129250 | C2 | semidirect |
| 3. #13127068 | C2 | semidirect |
| 4. #13126776 | C2 | semidirect |
| 5. D4×#6095 | C2 | semidirect |
| 6. #13126504 | C2 | semidirect |
| 7. #13125779 | C2 | semidirect |
| 8. #13125709 | C2 | semidirect |
| 9. #13124908 | C2 | semidirect |
| 10. #13124115 | C2 | semidirect |
| 11. C13×#2979 | C2 | semidirect |
| 15. #11719530 | C22 | semidirect |
| 16. C2×#88163 | C22 | semidirect |
| 17. C22×#6095 | C22 | semidirect |
| 28. #11719247 | C22 | semidirect |
| 29. D4×Dic26 | C22 | semidirect |
| 32. #11719175 | C22 | semidirect |
| 33. C13×#436 | C22 | semidirect |
| 34. C8×D4×C13 | C22 | semidirect |
| 35. C13×#431 | C22 | semidirect |
| 36. C13×#408 | C22 | semidirect |
| 37. #11718795 | C22 | semidirect |
| 38. #11718792 | C22 | semidirect |
| 39. #11718775 | C22 | semidirect |
| 40. #11718774 | C22 | semidirect |
| 41. #11718512 | C22 | semidirect |
| 42. #11718510 | C22 | semidirect |
| 43. #11718509 | C22 | semidirect |
| 44. #11718509 | C22 | semidirect |
| 45. #11718507 | C22 | semidirect |
| 46. #11718502 | C22 | semidirect |
| 47. #11718399 | C22 | semidirect |
| 48. #11718398 | C22 | semidirect |
| 50. #11718394 | C22 | semidirect |
| 51. #11718392 | C22 | semidirect |
| 52. #11718392 | C22 | semidirect |
| 53. #11718384 | C22 | semidirect |
| 54. C4×Dic52 | C22 | semidirect |
| 55. #11718355 | C22 | semidirect |
| 56. #11718354 | C22 | semidirect |
| 57. C4×#6095 | C22 | semidirect |
| 222. #2979 | D13 | semidirect |
| 312. #436 | C2×D13 | semidirect |
| 313. C8×D4 | C2×D13 | semidirect |
| 314. #431 | C2×D13 | semidirect |
| 317. #408 | C2×D13 | semidirect |
| 498. C13 | #61662 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13129250 | 2 |
| #13128609 | 2 |
| #13127068 | 2 |
| #13126776 | 2 |
| D4×#6095 | 2 |
| #13126504 | 2 |
| #13125779 | 2 |
| #13125709 | 2 |
| #13124908 | 2 |
| #13124115 | 2 |
| C13×#2979 | 2 |
| #61662 | 13 |