Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
2008 conjugacy classes of subgroups.
The subgroup lattice has 554 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13128616 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13127113 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #13126747 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | D4×#6107 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #13126482 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #13125781 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13125727 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #13124901 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #13124129 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #13123903 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C13×#3550 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#88257 | C22 | 1 | 2 | yes | — |
| 13 | C13×#563 | — | 2 | 2 | no | — |
| 14 | C13×#559 | — | 2 | 1 | no | — |
| 15 | Q82×C13 | — | 2 | 1 | no | — |
| 16 | C13×#556 | C22 | 1 | 4 | yes | — |
| 17 | D4×Q8×C13 | C22 | 1 | 4 | yes | — |
| 18 | C13×#542 | — | 2 | 4 | no | — |
| 19 | C13×#536 | C22 | 1 | 4 | yes | — |
| 20 | C13×#533 | C22 | 1 | 2 | yes | — |
| 21 | C13×#532 | C22 | 1 | 1 | yes | characteristic |
| 22 | #11719530 | C22 | 1 | 2 | yes | — |
| 23 | C22×#6107 | C22 | 1 | 4 | yes | — |
| 24 | C2×#88196 | C22 | 1 | 4 | yes | — |
| 25 | D13×C4⋊Q8 | — | 2 | 1 | no | — |
| 26 | #11719421 | — | 2 | 1 | no | — |
| 27 | #11719380 | — | 2 | 2 | no | — |
| 28 | #11719316 | — | 2 | 4 | no | — |
| 29 | #11719256 | C22 | 1 | 4 | yes | — |
| 30 | D4×Dic26 | C22 | 1 | 4 | yes | — |
| 31 | C4×#6127 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×#88123 | C22 | 1 | 1 | yes | characteristic |
| 33 | #11718895 | C22 | 1 | 4 | yes | — |
| 34 | #11718889 | C22 | 1 | 8 | yes | — |
| 35 | #11718755 | C22 | 1 | 2 | yes | — |
| 36 | #11718754 | C22 | 1 | 4 | yes | — |
| 37 | #11718753 | C22 | 1 | 4 | yes | — |
| 38 | #11718751 | C22 | 1 | 2 | yes | — |
| 39 | #11718748 | C22 | 1 | 2 | yes | — |
| 40 | #11718744 | C22 | 1 | 2 | yes | — |
| 41 | #11718713 | C22 | 1 | 8 | yes | — |
| 42 | #11718712 | C22 | 1 | 8 | yes | — |
| 43 | #11718711 | C22 | 1 | 8 | yes | — |
| 44 | #11718711 | C22 | 1 | 8 | yes | — |
| 45 | #11718708 | C22 | 1 | 4 | yes | — |
| 46 | #11718708 | C22 | 1 | 8 | yes | — |
| 47 | #11718706 | C22 | 1 | 4 | yes | — |
| 48 | #11718692 | C22 | 1 | 4 | yes | — |
| 49 | #11718692 | C22 | 1 | 4 | yes | — |
| 50 | C4×#6107 | C22 | 1 | 4 | yes | — |
| 51 | C4×#6106 | C22 | 1 | 4 | yes | — |
| 52 | #11718673 | C22 | 1 | 4 | yes | — |
| 53 | D4×#1055 | C22 | 1 | 4 | yes | — |
| 54 | #11718665 | C22 | 1 | 4 | yes | — |
| 55 | #11718663 | C22 | 1 | 4 | yes | — |
| 56 | #11718657 | C22 | 1 | 8 | yes | — |
| 57 | #11718586 | C22 | 1 | 2 | yes | — |
| 58 | C2×C13×#41 | C23 | 1 | 2 | yes | — |
| 59 | C22×Q8×C13 | C23 | 1 | 4 | yes | — |
| 60 | #88257 | — | 4 | 4 | no | — |
| 61 | #88257 | — | 4 | 4 | no | — |
| 62 | C2×Q8×D13 | — | 2 | 2 | no | — |
| 63 | C2×#6129 | — | 2 | 4 | no | — |
| 64 | C2×#6129 | — | 2 | 2 | no | — |
| 65 | C2×#6127 | C23 | 1 | 1 | yes | characteristic |
| 66 | C2×#6127 | C23 | 1 | 4 | yes | — |
| 67 | C22×Dic26 | C23 | 1 | 4 | yes | — |
| 68 | C22×Dic26 | C23 | 1 | 2 | yes | — |
| 69 | C13×C4⋊Q8 | — | 2 | 4 | no | — |
| 70 | C13×C4⋊Q8 | — | 2 | 4 | no | — |
| 71 | C13×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 72 | C13×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 73 | C13×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 74 | C13×#127 | D4 | 1 | 1 | yes | characteristic |
| 75 | C13×#126 | — | 2 | 8 | no | — |
| 76 | C13×#125 | — | 2 | 2 | no | — |
| 77 | C13×#124 | — | 2 | 4 | no | — |
| 78 | C13×#124 | — | 2 | 4 | no | — |
| 79 | C13×#124 | D4 | 1 | 2 | yes | — |
| 80 | C13×#123 | — | 2 | 4 | no | — |
| 81 | C13×#123 | — | 2 | 4 | no | — |
| 82 | C13×C22⋊Q8 | — | 2 | 2 | no | — |
| 83 | C13×C22⋊Q8 | — | 2 | 8 | no | — |
| 84 | C13×C22⋊Q8 | C23 | 1 | 4 | yes | — |
| 85 | C13×C22⋊Q8 | C23 | 1 | 8 | yes | — |
| 86 | C13×#121 | D4 | 1 | 4 | yes | — |
| 87 | C4×Q8×C13 | — | 2 | 4 | no | — |
| 88 | C4×Q8×C13 | — | 2 | 2 | no | — |
| 89 | C4×Q8×C13 | C23 | 1 | 4 | yes | — |
| 90 | C4×D4×C13 | — | 2 | 4 | no | — |
| 91 | C4×D4×C13 | C23 | 1 | 4 | yes | — |
| 92 | C13×#117 | — | 2 | 2 | no | — |
| 93 | C13×#117 | C23 | 1 | 4 | yes | — |
| 94 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 95 | #88198 | — | 2 | 2 | no | — |
| 96 | C2×#6107 | — | 4 | 8 | no | — |
| 97 | C2×#6107 | C23 | 1 | 4 | yes | — |
| 98 | C2×#6107 | C23 | 1 | 8 | yes | — |
| 99 | C2×#6107 | C23 | 1 | 8 | yes | — |
| 100 | #88196 | — | 4 | 8 | no | — |
| 101 | C2×#6106 | C23 | 1 | 4 | yes | — |
| 102 | #88192 | — | 2 | 4 | no | — |
| 103 | #88190 | — | 2 | 2 | no | — |
| 104 | #88189 | — | 2 | 4 | no | — |
| 105 | D4×Dic13 | — | 2 | 4 | no | — |
| 106 | C4×C22⋊D13 | — | 2 | 2 | no | — |
| 107 | #88180 | C23 | 1 | 1 | yes | characteristic |
| 108 | C2×C4⋊Dic13 | — | 2 | 2 | no | — |
| 109 | #88178 | C23 | 1 | 8 | yes | — |
| 110 | C2×#6099 | C23 | 1 | 4 | yes | — |
| 111 | C22×#1055 | C23 | 1 | 4 | yes | — |
| 112 | C4⋊C4×D13 | — | 2 | 4 | no | — |
| 113 | #88142 | — | 2 | 4 | no | — |
| 114 | #88137 | — | 2 | 8 | no | — |
| 115 | #88132 | — | 2 | 8 | no | — |
| 116 | C4×D52 | C23 | 1 | 2 | yes | — |
| 117 | #88126 | — | 2 | 1 | no | — |
| 118 | C42×D13 | — | 2 | 1 | no | — |
| 119 | #88123 | — | 2 | 1 | no | — |
| 120 | #88123 | — | 2 | 1 | no | — |
| 121 | #88123 | C23 | 1 | 4 | yes | — |
| 122 | C4×Dic26 | C23 | 1 | 2 | yes | — |
| 123 | #88075 | C23 | 1 | 4 | yes | — |
| 124 | #88075 | C23 | 1 | 4 | yes | — |
| 125 | C22⋊#1055 | C23 | 1 | 8 | yes | — |
| 126 | C22⋊#1055 | C23 | 1 | 4 | yes | — |
| 127 | #88050 | C23 | 1 | 8 | yes | — |
| 128 | #88050 | C23 | 1 | 8 | yes | — |
| 129 | #88050 | C23 | 1 | 4 | yes | — |
| 130 | #88049 | C23 | 1 | 4 | yes | — |
| 131 | #88048 | C23 | 1 | 4 | yes | — |
| 132 | #88047 | C23 | 1 | 4 | yes | — |
| 133 | C4⋊#1055 | C23 | 1 | 2 | yes | — |
| 134 | C4⋊#1055 | C23 | 1 | 2 | yes | — |
| 135 | C4×#1055 | C23 | 1 | 4 | yes | — |
| 136 | #61665 | — | 13 | 1 | no | maximal, Sylow |
| 137 | C13×#41 | — | 4 | 2 | no | — |
| 138 | C13×#41 | — | 4 | 2 | no | — |
| 139 | C2×Q8×C13 | — | 2 | 2 | no | — |
| 140 | C2×Q8×C13 | — | 2 | 4 | no | — |
| 141 | C2×Q8×C13 | — | 4 | 4 | no | — |
| 142 | C2×Q8×C13 | — | 4 | 4 | no | — |
| 143 | C2×Q8×C13 | C2×D4 | 1 | 2 | yes | — |
| 144 | C2×Q8×C13 | C24 | 1 | 4 | yes | — |
| 145 | C2×D4×C13 | C2×D4 | 1 | 4 | yes | — |
| 146 | C2×D4×C13 | C2×D4 | 1 | 4 | yes | — |
| 147 | C2×D4×C13 | C2×D4 | 1 | 2 | yes | — |
| 148 | C22×C4×C13 | — | 2 | 4 | no | — |
| 149 | C22×C4×C13 | C2×D4 | 1 | 2 | yes | — |
| 150 | C22×C4×C13 | C24 | 1 | 1 | yes | characteristic |
| 151 | C22×C4×C13 | C24 | 1 | 4 | yes | — |
| 152 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 153 | C2×C22⋊D13 | — | 2 | 4 | no | — |
| 154 | C22×Dic13 | — | 2 | 4 | no | — |
| 155 | C22×Dic13 | — | 2 | 2 | no | — |
| 156 | Q8×D13 | — | 4 | 8 | no | — |
| 157 | #6129 | — | 4 | 8 | no | — |
| 158 | #6129 | — | 4 | 16 | no | — |
| 159 | #6127 | — | 2 | 2 | no | — |
| 160 | #6127 | — | 2 | 8 | no | — |
| 161 | #6127 | — | 2 | 2 | no | — |
| 162 | #6127 | — | 4 | 4 | no | — |
| 163 | C2×D52 | C24 | 1 | 1 | yes | characteristic |
| 164 | C2×C4×D13 | — | 2 | 1 | no | — |
| 165 | C2×C4×D13 | — | 2 | 2 | no | — |
| 166 | C2×C4×D13 | — | 2 | 4 | no | — |
| 167 | C2×Dic26 | — | 2 | 8 | no | — |
| 168 | C2×Dic26 | — | 2 | 2 | no | — |
| 169 | C2×Dic26 | — | 2 | 4 | no | — |
| 170 | C2×Dic26 | — | 4 | 4 | no | — |
| 171 | C2×Dic26 | — | 4 | 2 | no | — |
| 172 | C2×Dic26 | — | 4 | 2 | no | — |
| 173 | C2×Dic26 | C24 | 1 | 4 | yes | — |
| 174 | C2×Dic26 | C24 | 1 | 1 | yes | characteristic |
| 175 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 176 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 177 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 178 | C13×C4⋊C4 | — | 2 | 8 | no | — |
| 179 | C13×C4⋊C4 | — | 2 | 4 | no | — |
| 180 | C13×C4⋊C4 | — | 2 | 4 | no | — |
| 181 | C13×C4⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 182 | C13×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 183 | C13×C22⋊C4 | — | 2 | 4 | no | — |
| 184 | C13×C22⋊C4 | — | 2 | 4 | no | — |
| 185 | C13×C22⋊C4 | — | 2 | 8 | no | — |
| 186 | C13×C22⋊C4 | C2×D4 | 1 | 8 | yes | — |
| 187 | C42×C13 | — | 2 | 4 | no | — |
| 188 | C42×C13 | — | 2 | 4 | no | — |
| 189 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 190 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | C42×C13 | C24 | 1 | 2 | yes | — |
| 192 | C22⋊Dic13 | — | 2 | 8 | no | — |
| 193 | C22⋊Dic13 | — | 2 | 1 | no | — |
| 194 | #6107 | — | 2 | 8 | no | — |
| 195 | #6107 | — | 4 | 8 | no | — |
| 196 | #6107 | — | 4 | 8 | no | — |
| 197 | #6106 | — | 2 | 8 | no | — |
| 198 | #6103 | — | 2 | 2 | no | — |
| 199 | C4⋊Dic13 | — | 2 | 4 | no | — |
| 200 | C4⋊Dic13 | — | 2 | 4 | no | — |
| 201 | C4⋊Dic13 | C24 | 1 | 2 | yes | — |
| 202 | #6101 | — | 2 | 2 | no | — |
| 203 | #6101 | — | 2 | 8 | no | — |
| 204 | C4×Dic13 | — | 2 | 2 | no | — |
| 205 | C4×Dic13 | — | 2 | 1 | no | — |
| 206 | #6099 | — | 4 | 4 | no | — |
| 207 | C2×#1055 | — | 4 | 4 | no | — |
| 208 | C2×#1055 | C24 | 1 | 4 | yes | — |
| 209 | C2×#1055 | C24 | 1 | 4 | yes | — |
| 210 | #3550 | D13 | 1 | 1 | yes | characteristic, complemented |
| 211 | #3499 | — | 13 | 1 | no | — |
| 212 | #3328 | — | 13 | 4 | no | — |
| 213 | #3302 | — | 13 | 4 | no | — |
| 214 | D4×Q16 | — | 13 | 4 | no | — |
| 215 | #3276 | — | 13 | 4 | no | — |
| 216 | #3209 | — | 13 | 2 | no | — |
| 217 | #3202 | — | 13 | 4 | no | — |
| 218 | #3107 | — | 13 | 2 | no | — |
| 219 | #3011 | — | 13 | 4 | no | — |
| 220 | #2979 | — | 13 | 1 | no | — |
| 221 | C23×C13 | C22×D4 | 1 | 4 | yes | — |
| 222 | C23×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 223 | C22×D13 | — | 2 | 1 | no | — |
| 224 | Q8×C13 | — | 2 | 4 | no | — |
| 225 | Q8×C13 | — | 2 | 4 | no | — |
| 226 | Q8×C13 | — | 4 | 2 | no | — |
| 227 | Q8×C13 | — | 4 | 4 | no | — |
| 228 | Q8×C13 | — | 8 | 4 | no | — |
| 229 | D4×C13 | — | 2 | 8 | no | — |
| 230 | D4×C13 | — | 4 | 2 | no | — |
| 231 | D4×C13 | — | 4 | 4 | no | — |
| 232 | C2×C4×C13 | — | 2 | 4 | no | — |
| 233 | C2×C4×C13 | — | 2 | 4 | no | — |
| 234 | C2×C4×C13 | — | 2 | 4 | no | — |
| 235 | C2×C4×C13 | — | 2 | 1 | no | — |
| 236 | C2×C4×C13 | — | 2 | 1 | no | — |
| 237 | C2×C4×C13 | — | 2 | 4 | no | — |
| 238 | C2×C4×C13 | — | 2 | 4 | no | — |
| 239 | C2×C4×C13 | — | 8 | 4 | 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 | C2×Dic13 | — | 2 | 1 | no | — |
| 248 | C2×Dic13 | — | 2 | 2 | no | — |
| 249 | C2×Dic13 | — | 2 | 4 | no | — |
| 250 | C2×Dic13 | — | 4 | 8 | no | — |
| 251 | C2×Dic13 | — | 4 | 4 | no | — |
| 252 | D52 | — | 2 | 1 | no | — |
| 253 | D52 | H(5,𝔽2) | 1 | 2 | yes | — |
| 254 | C4×D13 | — | 2 | 4 | no | — |
| 255 | C4×D13 | — | 4 | 8 | no | — |
| 256 | C4×D13 | — | 4 | 4 | no | — |
| 257 | Dic26 | — | 2 | 1 | no | — |
| 258 | Dic26 | — | 2 | 4 | no | — |
| 259 | Dic26 | — | 2 | 4 | no | — |
| 260 | Dic26 | — | 4 | 8 | no | — |
| 261 | Dic26 | — | 4 | 4 | no | — |
| 262 | Dic26 | H(5,𝔽2) | 1 | 2 | yes | — |
| 263 | #1055 | — | 2 | 4 | no | — |
| 264 | #1055 | — | 2 | 4 | no | — |
| 265 | C2×2−1+4 | — | 13 | 2 | no | — |
| 266 | C2×#137 | — | 13 | 4 | no | — |
| 267 | C22×Q16 | — | 13 | 4 | no | — |
| 268 | #563 | — | 2 | 2 | no | — |
| 269 | #559 | — | 2 | 1 | no | — |
| 270 | Q82 | — | 2 | 1 | no | — |
| 271 | #556 | C2×D13 | 1 | 4 | yes | — |
| 272 | D4×Q8 | — | 13 | 4 | no | — |
| 273 | D4×Q8 | C2×D13 | 1 | 4 | yes | — |
| 274 | #547 | — | 13 | 4 | no | — |
| 275 | #547 | — | 26 | 4 | no | — |
| 276 | #542 | — | 2 | 4 | no | — |
| 277 | #536 | — | 13 | 2 | no | — |
| 278 | #536 | — | 26 | 2 | no | — |
| 279 | #536 | C2×D13 | 1 | 4 | yes | — |
| 280 | #533 | C2×D13 | 1 | 2 | yes | — |
| 281 | #532 | — | 26 | 1 | no | — |
| 282 | #532 | C2×D13 | 1 | 1 | yes | characteristic |
| 283 | C2×C4⋊Q8 | — | 13 | 1 | no | — |
| 284 | C2×C4⋊Q8 | — | 26 | 1 | no | — |
| 285 | C4×#41 | — | 13 | 1 | no | — |
| 286 | #494 | — | 13 | 4 | no | — |
| 287 | #487 | — | 13 | 4 | no | — |
| 288 | #485 | — | 13 | 4 | no | — |
| 289 | #485 | — | 13 | 8 | no | — |
| 290 | #475 | — | 13 | 2 | no | — |
| 291 | #474 | — | 13 | 2 | no | — |
| 292 | #470 | — | 13 | 8 | no | — |
| 293 | #467 | — | 13 | 8 | no | — |
| 294 | #462 | — | 13 | 2 | no | — |
| 295 | #462 | — | 13 | 4 | no | — |
| 296 | #462 | — | 13 | 4 | no | — |
| 297 | #461 | — | 13 | 2 | no | — |
| 298 | #452 | — | 13 | 4 | no | — |
| 299 | #452 | — | 13 | 8 | no | — |
| 300 | #451 | — | 13 | 8 | no | — |
| 301 | #451 | — | 13 | 8 | no | — |
| 302 | #451 | — | 13 | 8 | no | — |
| 303 | C4×Q16 | — | 13 | 4 | no | — |
| 304 | C4×SD16 | — | 13 | 4 | no | — |
| 305 | #436 | — | 13 | 4 | no | — |
| 306 | C8×D4 | — | 13 | 4 | no | — |
| 307 | #431 | — | 13 | 2 | no | — |
| 308 | #419 | — | 13 | 4 | no | — |
| 309 | #416 | — | 13 | 4 | no | — |
| 310 | #408 | — | 13 | 4 | no | — |
| 311 | C22×C13 | — | 2 | 1 | no | — |
| 312 | C22×C13 | — | 2 | 4 | no | — |
| 313 | C22×C13 | — | 2 | 2 | no | — |
| 314 | C22×C13 | — | 2 | 8 | no | — |
| 315 | C22×C13 | C23×D4 | 1 | 1 | yes | characteristic |
| 316 | C2×D13 | — | 2 | 2 | no | — |
| 317 | C2×D13 | — | 4 | 2 | no | — |
| 318 | C4×C13 | — | 2 | 1 | no | — |
| 319 | C4×C13 | — | 2 | 4 | no | — |
| 320 | C4×C13 | — | 2 | 2 | no | — |
| 321 | C4×C13 | — | 4 | 4 | no | — |
| 322 | C4×C13 | — | 4 | 4 | no | — |
| 323 | C4×C13 | #578 | 1 | 4 | yes | — |
| 324 | C4×C13 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 325 | C4×C13 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 326 | Dic13 | — | 2 | 2 | no | — |
| 327 | Dic13 | — | 4 | 4 | no | — |
| 328 | Dic13 | — | 4 | 2 | no | — |
| 329 | 2−1+4 | — | 52 | 4 | no | — |
| 330 | 2−1+4 | — | 52 | 4 | no | — |
| 331 | C2×#41 | — | 13 | 1 | no | — |
| 332 | C2×#41 | — | 13 | 4 | no | — |
| 333 | C2×#41 | — | 26 | 2 | no | — |
| 334 | C2×#41 | — | 26 | 4 | no | — |
| 335 | C2×#41 | C22×D13 | 1 | 2 | yes | — |
| 336 | C22×Q8 | — | 13 | 4 | no | — |
| 337 | C22×Q8 | — | 13 | 2 | no | — |
| 338 | C22×Q8 | — | 26 | 2 | no | — |
| 339 | C22×Q8 | C22×D13 | 1 | 4 | yes | — |
| 340 | #137 | — | 52 | 8 | no | — |
| 341 | C2×Q16 | — | 13 | 4 | no | — |
| 342 | C2×Q16 | — | 13 | 8 | no | — |
| 343 | C2×Q16 | — | 13 | 8 | no | — |
| 344 | C2×Q16 | — | 52 | 8 | no | — |
| 345 | C2×SD16 | — | 13 | 4 | no | — |
| 346 | C2×M16 | — | 13 | 4 | no | — |
| 347 | C22×C8 | — | 13 | 4 | no | — |
| 348 | C4⋊Q8 | — | 2 | 4 | no | — |
| 349 | C4⋊Q8 | — | 2 | 4 | no | — |
| 350 | C4⋊Q8 | — | 13 | 4 | no | — |
| 351 | C4⋊Q8 | — | 26 | 2 | no | — |
| 352 | C4⋊Q8 | — | 26 | 4 | no | — |
| 353 | C4⋊Q8 | — | 26 | 1 | no | — |
| 354 | C4⋊Q8 | — | 26 | 1 | no | — |
| 355 | C4⋊Q8 | C22⋊D13 | 1 | 1 | yes | characteristic |
| 356 | C4⋊Q8 | C22×D13 | 1 | 2 | yes | — |
| 357 | C4⋊Q8 | C22×D13 | 1 | 2 | yes | — |
| 358 | #127 | C22⋊D13 | 1 | 1 | yes | characteristic |
| 359 | #126 | — | 2 | 8 | no | — |
| 360 | #125 | — | 2 | 2 | no | — |
| 361 | #124 | — | 2 | 4 | no | — |
| 362 | #124 | — | 2 | 4 | no | — |
| 363 | #124 | — | 26 | 2 | no | — |
| 364 | #124 | C22⋊D13 | 1 | 2 | yes | — |
| 365 | #123 | — | 2 | 4 | no | — |
| 366 | #123 | — | 2 | 4 | no | — |
| 367 | #123 | — | 26 | 4 | no | — |
| 368 | #123 | — | 26 | 8 | no | — |
| 369 | C22⋊Q8 | — | 2 | 2 | no | — |
| 370 | C22⋊Q8 | — | 2 | 8 | no | — |
| 371 | C22⋊Q8 | — | 13 | 8 | no | — |
| 372 | C22⋊Q8 | — | 26 | 8 | no | — |
| 373 | C22⋊Q8 | C22×D13 | 1 | 4 | yes | — |
| 374 | C22⋊Q8 | C22×D13 | 1 | 8 | yes | — |
| 375 | #121 | — | 26 | 4 | no | — |
| 376 | #121 | C22⋊D13 | 1 | 4 | yes | — |
| 377 | C4×Q8 | — | 2 | 4 | no | — |
| 378 | C4×Q8 | — | 2 | 2 | no | — |
| 379 | C4×Q8 | — | 13 | 2 | no | — |
| 380 | C4×Q8 | C22×D13 | 1 | 4 | yes | — |
| 381 | C4×D4 | — | 2 | 4 | no | — |
| 382 | C4×D4 | — | 13 | 2 | no | — |
| 383 | C4×D4 | — | 26 | 4 | no | — |
| 384 | C4×D4 | — | 26 | 2 | no | — |
| 385 | C4×D4 | C22×D13 | 1 | 4 | yes | — |
| 386 | #117 | — | 2 | 2 | no | — |
| 387 | #117 | — | 13 | 1 | no | — |
| 388 | #117 | — | 26 | 1 | no | — |
| 389 | #117 | C22×D13 | 1 | 4 | yes | — |
| 390 | C2×C4⋊C4 | — | 26 | 2 | no | — |
| 391 | C2×C4⋊C4 | — | 26 | 4 | no | — |
| 392 | C2×C42 | — | 26 | 1 | no | — |
| 393 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 394 | #107 | — | 13 | 4 | no | — |
| 395 | #106 | — | 13 | 4 | no | — |
| 396 | C4⋊C8 | — | 13 | 2 | no | — |
| 397 | C4⋊C8 | — | 13 | 2 | no | — |
| 398 | #103 | — | 13 | 4 | no | — |
| 399 | #103 | — | 13 | 4 | no | — |
| 400 | #103 | — | 13 | 8 | no | — |
| 401 | #103 | — | 13 | 4 | no | — |
| 402 | #103 | — | 13 | 8 | no | — |
| 403 | #102 | — | 13 | 4 | no | — |
| 404 | C22⋊C8 | — | 13 | 4 | no | — |
| 405 | C22⋊C8 | — | 13 | 8 | no | — |
| 406 | C4×C8 | — | 13 | 4 | no | — |
| 407 | C2×C13 | — | 4 | 1 | no | — |
| 408 | C2×C13 | — | 4 | 4 | no | — |
| 409 | C2×C13 | #3484 | 1 | 1 | yes | characteristic |
| 410 | C2×C13 | C2×#578 | 1 | 2 | yes | — |
| 411 | D13 | — | 4 | 2 | no | — |
| 412 | #41 | — | 4 | 2 | no | — |
| 413 | #41 | — | 4 | 2 | no | — |
| 414 | #41 | — | 26 | 2 | no | — |
| 415 | #41 | — | 26 | 2 | no | — |
| 416 | #41 | — | 26 | 8 | no | — |
| 417 | #41 | — | 52 | 4 | no | — |
| 418 | #41 | — | 52 | 8 | no | — |
| 419 | #41 | — | 52 | 16 | no | — |
| 420 | C2×Q8 | — | 2 | 2 | no | — |
| 421 | C2×Q8 | — | 2 | 4 | no | — |
| 422 | C2×Q8 | — | 4 | 4 | no | — |
| 423 | C2×Q8 | — | 4 | 4 | no | — |
| 424 | C2×Q8 | — | 13 | 1 | no | — |
| 425 | C2×Q8 | — | 13 | 4 | no | — |
| 426 | C2×Q8 | — | 26 | 8 | no | — |
| 427 | C2×Q8 | — | 26 | 4 | no | — |
| 428 | C2×Q8 | — | 26 | 2 | no | — |
| 429 | C2×Q8 | — | 52 | 4 | no | — |
| 430 | C2×Q8 | — | 52 | 2 | no | — |
| 431 | C2×Q8 | — | 52 | 2 | no | — |
| 432 | C2×Q8 | — | 52 | 8 | no | — |
| 433 | C2×Q8 | C2×C22⋊D13 | 1 | 2 | yes | — |
| 434 | C2×Q8 | C23×D13 | 1 | 4 | yes | — |
| 435 | C2×D4 | — | 13 | 1 | no | — |
| 436 | C2×D4 | — | 26 | 1 | no | — |
| 437 | C2×D4 | — | 26 | 4 | no | — |
| 438 | C2×D4 | C2×C22⋊D13 | 1 | 4 | yes | — |
| 439 | C2×D4 | C2×C22⋊D13 | 1 | 4 | yes | — |
| 440 | C2×D4 | C2×C22⋊D13 | 1 | 2 | yes | — |
| 441 | C22×C4 | — | 2 | 4 | no | — |
| 442 | C22×C4 | — | 26 | 1 | no | — |
| 443 | C22×C4 | — | 26 | 2 | no | — |
| 444 | C22×C4 | — | 26 | 4 | no | — |
| 445 | C22×C4 | — | 26 | 2 | no | — |
| 446 | C22×C4 | — | 26 | 4 | no | — |
| 447 | C22×C4 | C2×C22⋊D13 | 1 | 2 | yes | — |
| 448 | C22×C4 | C23×D13 | 1 | 1 | yes | characteristic |
| 449 | C22×C4 | C23×D13 | 1 | 4 | yes | — |
| 450 | Q16 | — | 26 | 8 | no | — |
| 451 | Q16 | — | 52 | 8 | no | — |
| 452 | Q16 | — | 52 | 8 | no | — |
| 453 | SD16 | — | 26 | 8 | no | — |
| 454 | M16 | — | 52 | 4 | no | — |
| 455 | C2×C8 | — | 13 | 4 | no | — |
| 456 | C2×C8 | — | 13 | 4 | no | — |
| 457 | C2×C8 | — | 52 | 4 | no | — |
| 458 | C4⋊C4 | — | 2 | 2 | no | — |
| 459 | C4⋊C4 | — | 2 | 2 | no | — |
| 460 | C4⋊C4 | — | 2 | 2 | no | — |
| 461 | C4⋊C4 | — | 2 | 8 | no | — |
| 462 | C4⋊C4 | — | 2 | 4 | no | — |
| 463 | C4⋊C4 | — | 2 | 4 | no | — |
| 464 | C4⋊C4 | — | 13 | 2 | no | — |
| 465 | C4⋊C4 | — | 26 | 4 | no | — |
| 466 | C4⋊C4 | — | 26 | 8 | no | — |
| 467 | C4⋊C4 | — | 26 | 4 | no | — |
| 468 | C4⋊C4 | — | 26 | 2 | no | — |
| 469 | C4⋊C4 | C2×C22⋊D13 | 1 | 4 | yes | — |
| 470 | C4⋊C4 | C23×D13 | 1 | 4 | yes | — |
| 471 | C22⋊C4 | — | 2 | 4 | no | — |
| 472 | C22⋊C4 | — | 2 | 4 | no | — |
| 473 | C22⋊C4 | — | 2 | 8 | no | — |
| 474 | C22⋊C4 | — | 26 | 1 | no | — |
| 475 | C22⋊C4 | — | 26 | 8 | no | — |
| 476 | C22⋊C4 | — | 26 | 2 | no | — |
| 477 | C22⋊C4 | C2×C22⋊D13 | 1 | 8 | yes | — |
| 478 | C42 | — | 2 | 4 | no | — |
| 479 | C42 | — | 2 | 4 | no | — |
| 480 | C42 | — | 26 | 1 | no | — |
| 481 | C42 | — | 26 | 2 | no | — |
| 482 | C42 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 483 | C42 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 484 | C42 | C23×D13 | 1 | 2 | yes | — |
| 485 | C13 | #61665 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 486 | C23 | — | 26 | 1 | no | — |
| 487 | C23 | C22×C22⋊D13 | 1 | 1 | yes | characteristic |
| 488 | C23 | C22×C22⋊D13 | 1 | 4 | yes | — |
| 489 | Q8 | — | 2 | 4 | no | — |
| 490 | Q8 | — | 2 | 4 | no | — |
| 491 | Q8 | — | 4 | 2 | no | — |
| 492 | Q8 | — | 4 | 4 | no | — |
| 493 | Q8 | — | 8 | 4 | no | — |
| 494 | Q8 | — | 13 | 2 | no | — |
| 495 | Q8 | — | 26 | 1 | no | — |
| 496 | Q8 | — | 26 | 4 | no | — |
| 497 | Q8 | — | 26 | 4 | no | — |
| 498 | Q8 | — | 52 | 8 | no | — |
| 499 | Q8 | — | 52 | 4 | no | — |
| 500 | D4 | — | 2 | 8 | no | — |
| 501 | D4 | — | 4 | 2 | no | — |
| 502 | D4 | — | 4 | 4 | no | — |
| 503 | D4 | — | 13 | 2 | no | — |
| 504 | D4 | — | 26 | 4 | no | — |
| 505 | D4 | — | 26 | 1 | no | — |
| 506 | D4 | — | 52 | 8 | no | — |
| 507 | C2×C4 | — | 2 | 4 | no | — |
| 508 | C2×C4 | — | 2 | 4 | no | — |
| 509 | C2×C4 | — | 2 | 4 | no | — |
| 510 | C2×C4 | — | 2 | 1 | no | — |
| 511 | C2×C4 | — | 2 | 1 | no | — |
| 512 | C2×C4 | — | 2 | 4 | no | — |
| 513 | C2×C4 | — | 2 | 4 | no | — |
| 514 | C2×C4 | — | 8 | 4 | no | — |
| 515 | C2×C4 | — | 26 | 4 | no | — |
| 516 | C2×C4 | — | 26 | 1 | no | — |
| 517 | C2×C4 | — | 26 | 2 | no | — |
| 518 | C2×C4 | — | 26 | 4 | no | — |
| 519 | C2×C4 | — | 52 | 8 | no | — |
| 520 | C2×C4 | — | 52 | 8 | no | — |
| 521 | C2×C4 | — | 52 | 4 | no | — |
| 522 | C2×C4 | — | 52 | 4 | no | — |
| 523 | C2×C4 | C22×C22⋊D13 | 1 | 4 | yes | — |
| 524 | C2×C4 | C22×C22⋊D13 | 1 | 1 | yes | characteristic |
| 525 | C2×C4 | C22×C22⋊D13 | 1 | 2 | yes | — |
| 526 | C2×C4 | C22×C22⋊D13 | 1 | 2 | yes | — |
| 527 | C2×C4 | C24×D13 | 1 | 1 | yes | characteristic |
| 528 | C8 | — | 26 | 4 | no | — |
| 529 | C8 | — | 26 | 4 | no | — |
| 530 | C22 | — | 2 | 4 | no | — |
| 531 | C22 | — | 2 | 1 | no | — |
| 532 | C22 | — | 2 | 2 | no | — |
| 533 | C22 | — | 2 | 8 | no | — |
| 534 | C22 | — | 26 | 2 | no | — |
| 535 | C22 | — | 52 | 2 | no | — |
| 536 | C22 | C23×C22⋊D13 | 1 | 1 | yes | characteristic |
| 537 | C4 | — | 2 | 1 | no | — |
| 538 | C4 | — | 2 | 4 | no | — |
| 539 | C4 | — | 2 | 2 | no | — |
| 540 | C4 | — | 4 | 4 | no | — |
| 541 | C4 | — | 4 | 4 | no | — |
| 542 | C4 | — | 26 | 2 | no | — |
| 543 | C4 | — | 52 | 4 | no | — |
| 544 | C4 | — | 52 | 2 | no | — |
| 545 | C4 | #11719543 | 1 | 4 | yes | — |
| 546 | C4 | D13×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 547 | C4 | D13×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 548 | C2 | — | 4 | 4 | no | — |
| 549 | C2 | — | 4 | 1 | no | — |
| 550 | C2 | — | 52 | 2 | no | — |
| 551 | C2 | #13128467 | 1 | 1 | yes | characteristic |
| 552 | C2 | C2×#11719543 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13127113 | C2 | semidirect |
| 3. #13126747 | C2 | semidirect |
| 4. D4×#6107 | C2 | semidirect |
| 5. #13126482 | C2 | semidirect |
| 6. #13125781 | C2 | semidirect |
| 7. #13125727 | C2 | semidirect |
| 8. #13124901 | C2 | semidirect |
| 9. #13124129 | C2 | semidirect |
| 10. #13123903 | C2 | semidirect |
| 11. C13×#3550 | C2 | semidirect |
| 210. #3550 | D13 | semidirect |
| 485. C13 | #61665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13128616 | 2 |
| #13127113 | 2 |
| #13126747 | 2 |
| D4×#6107 | 2 |
| #13126482 | 2 |
| #13125781 | 2 |
| #13125727 | 2 |
| #13124901 | 2 |
| #13124129 | 2 |
| #13123903 | 2 |
| C13×#3550 | 2 |
| #61665 | 13 |