Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1908 conjugacy classes of subgroups.
The subgroup lattice has 604 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13123103 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13122977 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #13122966 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #13122962 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #13122953 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #13122908 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #13122879 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13122876 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #13118099 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #13118080 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #13118076 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #13118052 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | C4×#88128 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C4×#88130 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C4×C13×#126 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C22×#6127 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C13×#126 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C4×C22⋊D13 | C22 | 1 | 3 | yes | — |
| 19 | C2×#88130 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#88128 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×C4×D52 | C22 | 1 | 3 | yes | — |
| 22 | C2×C4×D52 | C22 | 1 | 3 | yes | — |
| 23 | C2×C4×D52 | C22 | 1 | 3 | yes | — |
| 24 | C2×#88126 | C22 | 1 | 3 | yes | — |
| 25 | C13×#388 | C22 | 1 | 3 | yes | — |
| 26 | C13×#387 | C22 | 1 | 3 | yes | — |
| 27 | C13×#383 | C22 | 1 | 1 | yes | characteristic |
| 28 | C4×C13×C4⋊C4 | C22 | 1 | 3 | yes | — |
| 29 | C4×C13×C22⋊C4 | C22 | 1 | 3 | yes | — |
| 30 | C43×C13 | C22 | 1 | 1 | yes | characteristic |
| 31 | #11718655 | C22 | 1 | 3 | yes | — |
| 32 | #11718655 | C22 | 1 | 3 | yes | — |
| 33 | #11718654 | C22 | 1 | 3 | yes | — |
| 34 | #11718653 | C22 | 1 | 3 | yes | — |
| 35 | #11718652 | C22 | 1 | 3 | yes | — |
| 36 | #11718652 | C22 | 1 | 3 | yes | — |
| 37 | #11718652 | C22 | 1 | 3 | yes | — |
| 38 | #11718645 | C22 | 1 | 3 | yes | — |
| 39 | #11718622 | C22 | 1 | 3 | yes | — |
| 40 | #11718622 | C22 | 1 | 3 | yes | — |
| 41 | #11718621 | C22 | 1 | 3 | yes | — |
| 42 | #11718621 | C22 | 1 | 3 | yes | — |
| 43 | #11718621 | C22 | 1 | 3 | yes | — |
| 44 | #11718620 | C22 | 1 | 3 | yes | — |
| 45 | #11718620 | C22 | 1 | 3 | yes | — |
| 46 | #11718609 | C22 | 1 | 3 | yes | — |
| 47 | #11718601 | C22 | 1 | 3 | yes | — |
| 48 | #11718600 | C22 | 1 | 3 | yes | — |
| 49 | #11718600 | C22 | 1 | 3 | yes | — |
| 50 | C4×#6103 | C22 | 1 | 3 | yes | — |
| 51 | C4×#6103 | C22 | 1 | 3 | yes | — |
| 52 | C4×#6103 | C22 | 1 | 3 | yes | — |
| 53 | #11718598 | C22 | 1 | 1 | yes | characteristic |
| 54 | #11718596 | C22 | 1 | 1 | yes | characteristic |
| 55 | #11718594 | C22 | 1 | 3 | yes | — |
| 56 | C4×#6101 | C22 | 1 | 3 | yes | — |
| 57 | #11718337 | C22 | 1 | 3 | yes | — |
| 58 | #11718336 | C22 | 1 | 3 | yes | — |
| 59 | #11718336 | C22 | 1 | 3 | yes | — |
| 60 | #11718336 | C22 | 1 | 3 | yes | — |
| 61 | #11718335 | C22 | 1 | 3 | yes | — |
| 62 | #11718334 | C22 | 1 | 3 | yes | — |
| 63 | #11718333 | C22 | 1 | 3 | yes | — |
| 64 | #11718333 | C22 | 1 | 3 | yes | — |
| 65 | #11718333 | C22 | 1 | 3 | yes | — |
| 66 | #11718333 | C22 | 1 | 3 | yes | — |
| 67 | #11718332 | C22 | 1 | 3 | yes | — |
| 68 | #11718332 | C22 | 1 | 3 | yes | — |
| 69 | #11718322 | C22 | 1 | 3 | yes | — |
| 70 | #11718321 | C22 | 1 | 3 | yes | — |
| 71 | #11718318 | C22 | 1 | 3 | yes | — |
| 72 | #11718317 | C22 | 1 | 3 | yes | — |
| 73 | C23×C4×C13 | C23 | 1 | 1 | yes | characteristic |
| 74 | C22×C22⋊D13 | C23 | 1 | 3 | yes | — |
| 75 | C22×C22⋊D13 | C23 | 1 | 1 | yes | characteristic |
| 76 | C22×C22⋊D13 | C23 | 1 | 1 | yes | characteristic |
| 77 | C2×#6127 | — | 4 | 6 | no | — |
| 78 | C22×D52 | C23 | 1 | 3 | yes | — |
| 79 | C22×D52 | C23 | 1 | 3 | yes | — |
| 80 | C22×D52 | C23 | 1 | 3 | yes | — |
| 81 | C22×D52 | C23 | 1 | 1 | yes | characteristic |
| 82 | C22×C4×D13 | C23 | 1 | 3 | yes | — |
| 83 | C22×C4×D13 | C23 | 1 | 1 | yes | characteristic |
| 84 | C22×C4×D13 | C23 | 1 | 1 | yes | characteristic |
| 85 | C22×Dic26 | C23 | 1 | 1 | yes | characteristic |
| 86 | C13×#126 | — | 2 | 4 | no | — |
| 87 | C2×C13×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 88 | C2×C13×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 89 | C2×C13×C22⋊C4 | C23 | 1 | 3 | yes | — |
| 90 | C2×C13×C22⋊C4 | C23 | 1 | 3 | yes | — |
| 91 | C2×C42×C13 | C23 | 1 | 3 | yes | — |
| 92 | C2×C42×C13 | C23 | 1 | 3 | yes | — |
| 93 | C2×C42×C13 | C23 | 1 | 3 | yes | — |
| 94 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×C22⋊Dic13 | C23 | 1 | 3 | yes | — |
| 96 | C4×C22⋊D13 | — | 4 | 6 | no | — |
| 97 | C2×#6103 | C23 | 1 | 3 | yes | — |
| 98 | C2×#6103 | C23 | 1 | 3 | yes | — |
| 99 | C2×#6103 | C23 | 1 | 3 | yes | — |
| 100 | C2×#6103 | C23 | 1 | 3 | yes | — |
| 101 | C2×#6103 | C23 | 1 | 3 | yes | — |
| 102 | C2×#6103 | C23 | 1 | 3 | yes | — |
| 103 | C2×#6103 | C23 | 1 | 3 | yes | — |
| 104 | C2×#6103 | C23 | 1 | 3 | yes | — |
| 105 | C2×#6103 | C23 | 1 | 3 | yes | — |
| 106 | C2×#6103 | C23 | 1 | 3 | yes | — |
| 107 | C2×#6103 | C23 | 1 | 3 | yes | — |
| 108 | C2×#6103 | C23 | 1 | 3 | yes | — |
| 109 | C2×#6103 | C23 | 1 | 3 | yes | — |
| 110 | C2×#6103 | C23 | 1 | 3 | yes | — |
| 111 | C2×#6103 | C23 | 1 | 3 | yes | — |
| 112 | C2×C4⋊Dic13 | C23 | 1 | 3 | yes | — |
| 113 | C2×C4⋊Dic13 | C23 | 1 | 3 | yes | — |
| 114 | C2×C4⋊Dic13 | C23 | 1 | 3 | yes | — |
| 115 | C2×#6101 | C23 | 1 | 3 | yes | — |
| 116 | C2×#6101 | C23 | 1 | 3 | yes | — |
| 117 | C2×#6101 | C23 | 1 | 3 | yes | — |
| 118 | C2×#6101 | C23 | 1 | 3 | yes | — |
| 119 | C2×#6101 | C23 | 1 | 3 | yes | — |
| 120 | C2×C4×Dic13 | C23 | 1 | 3 | yes | — |
| 121 | #88130 | — | 2 | 4 | no | — |
| 122 | #88128 | — | 2 | 4 | no | — |
| 123 | C4×D52 | — | 4 | 6 | no | — |
| 124 | C4×D52 | — | 4 | 6 | no | — |
| 125 | C4×D52 | — | 4 | 6 | no | — |
| 126 | #88126 | — | 4 | 6 | no | — |
| 127 | C13×#95 | C23 | 1 | 3 | yes | — |
| 128 | C13×#95 | C23 | 1 | 3 | yes | — |
| 129 | C13×#95 | C23 | 1 | 3 | yes | — |
| 130 | C13×#95 | C23 | 1 | 3 | yes | — |
| 131 | #88071 | C23 | 1 | 3 | yes | — |
| 132 | #88071 | C23 | 1 | 3 | yes | — |
| 133 | #88071 | C23 | 1 | 3 | yes | — |
| 134 | #88071 | C23 | 1 | 3 | yes | — |
| 135 | #88071 | C23 | 1 | 3 | yes | — |
| 136 | #88071 | C23 | 1 | 3 | yes | — |
| 137 | #88071 | C23 | 1 | 3 | yes | — |
| 138 | #88071 | C23 | 1 | 3 | yes | — |
| 139 | #36696 | — | 13 | 1 | no | maximal, Sylow |
| 140 | C24×C13 | C24 | 1 | 1 | yes | characteristic |
| 141 | C23×D13 | C24 | 1 | 1 | yes | characteristic |
| 142 | C23×D13 | C24 | 1 | 3 | yes | — |
| 143 | C23×D13 | C24 | 1 | 1 | yes | characteristic |
| 144 | C22×C4×C13 | — | 2 | 6 | no | — |
| 145 | C22×C4×C13 | C24 | 1 | 3 | yes | — |
| 146 | C22×C4×C13 | C24 | 1 | 3 | yes | — |
| 147 | C22×C4×C13 | C24 | 1 | 3 | yes | — |
| 148 | C22×C4×C13 | C24 | 1 | 1 | yes | characteristic |
| 149 | C22×C4×C13 | C24 | 1 | 3 | yes | — |
| 150 | C22×C4×C13 | C24 | 1 | 1 | yes | characteristic |
| 151 | C2×C22⋊D13 | — | 4 | 3 | no | — |
| 152 | C2×C22⋊D13 | — | 4 | 3 | no | — |
| 153 | C2×C22⋊D13 | — | 4 | 3 | no | — |
| 154 | C2×C22⋊D13 | — | 4 | 3 | no | — |
| 155 | C2×C22⋊D13 | — | 4 | 3 | no | — |
| 156 | C22×Dic13 | C24 | 1 | 3 | yes | — |
| 157 | C22×Dic13 | C24 | 1 | 1 | yes | characteristic |
| 158 | C22×Dic13 | C24 | 1 | 1 | yes | characteristic |
| 159 | C22×Dic13 | C24 | 1 | 3 | yes | — |
| 160 | C22×Dic13 | C24 | 1 | 3 | yes | — |
| 161 | #6127 | — | 4 | 16 | no | — |
| 162 | C2×D52 | — | 2 | 6 | no | — |
| 163 | C2×D52 | — | 2 | 6 | no | — |
| 164 | C2×D52 | — | 4 | 3 | no | — |
| 165 | C2×D52 | — | 4 | 3 | no | — |
| 166 | C2×D52 | — | 4 | 3 | no | — |
| 167 | C2×D52 | — | 4 | 3 | no | — |
| 168 | C2×D52 | — | 4 | 3 | no | — |
| 169 | C2×D52 | — | 4 | 3 | no | — |
| 170 | C2×D52 | — | 4 | 3 | no | — |
| 171 | C2×D52 | — | 4 | 3 | no | — |
| 172 | C2×C4×D13 | — | 2 | 6 | no | — |
| 173 | C2×C4×D13 | — | 2 | 6 | no | — |
| 174 | C2×C4×D13 | — | 2 | 6 | no | — |
| 175 | C2×C4×D13 | — | 2 | 6 | no | — |
| 176 | C2×C4×D13 | — | 2 | 6 | no | — |
| 177 | C2×Dic26 | — | 4 | 3 | no | — |
| 178 | C13×C4⋊C4 | — | 2 | 6 | no | — |
| 179 | C13×C4⋊C4 | — | 4 | 3 | no | — |
| 180 | C13×C22⋊C4 | — | 2 | 6 | no | — |
| 181 | C13×C22⋊C4 | — | 4 | 3 | no | — |
| 182 | C42×C13 | — | 2 | 6 | no | — |
| 183 | C42×C13 | — | 2 | 6 | no | — |
| 184 | C42×C13 | — | 4 | 3 | no | — |
| 185 | C42×C13 | #41 | 1 | 4 | yes | complemented |
| 186 | C22⋊Dic13 | — | 4 | 3 | no | — |
| 187 | #6103 | — | 2 | 6 | no | — |
| 188 | #6103 | — | 4 | 3 | no | — |
| 189 | #6103 | — | 4 | 3 | no | — |
| 190 | #6103 | — | 4 | 3 | no | — |
| 191 | #6103 | — | 4 | 3 | no | — |
| 192 | #6103 | — | 4 | 3 | no | — |
| 193 | #6103 | — | 4 | 3 | no | — |
| 194 | #6103 | — | 4 | 3 | no | — |
| 195 | #6103 | — | 4 | 3 | no | — |
| 196 | #6103 | — | 4 | 3 | no | — |
| 197 | #6103 | — | 4 | 3 | no | — |
| 198 | #6103 | — | 4 | 3 | no | — |
| 199 | #6103 | — | 4 | 3 | no | — |
| 200 | #6103 | — | 4 | 3 | no | — |
| 201 | #6103 | — | 4 | 3 | no | — |
| 202 | C4⋊Dic13 | — | 4 | 3 | no | — |
| 203 | C4⋊Dic13 | — | 4 | 3 | no | — |
| 204 | C4⋊Dic13 | — | 4 | 3 | no | — |
| 205 | #6101 | — | 2 | 6 | no | — |
| 206 | #6101 | — | 4 | 3 | no | — |
| 207 | #6101 | — | 4 | 3 | no | — |
| 208 | #6101 | — | 4 | 3 | no | — |
| 209 | #6101 | — | 4 | 3 | no | — |
| 210 | C4×Dic13 | — | 2 | 6 | no | — |
| 211 | #2843 | — | 13 | 1 | no | — |
| 212 | #2830 | — | 13 | 3 | no | — |
| 213 | #2829 | — | 13 | 3 | no | — |
| 214 | #2829 | — | 13 | 3 | no | — |
| 215 | #2828 | — | 13 | 3 | no | — |
| 216 | #2823 | — | 13 | 1 | no | — |
| 217 | #2818 | — | 13 | 1 | no | — |
| 218 | #2818 | — | 13 | 1 | no | — |
| 219 | #2395 | — | 13 | 3 | no | — |
| 220 | #2392 | — | 13 | 3 | no | — |
| 221 | #2392 | — | 13 | 3 | no | — |
| 222 | #2388 | — | 13 | 3 | no | — |
| 223 | C4×#127 | — | 13 | 1 | no | — |
| 224 | C4×#126 | — | 13 | 1 | no | — |
| 225 | C4×#126 | D13 | 1 | 1 | yes | characteristic, complemented |
| 226 | C23×C13 | — | 2 | 1 | no | — |
| 227 | C23×C13 | — | 2 | 3 | no | — |
| 228 | C23×C13 | — | 2 | 3 | no | — |
| 229 | C23×C13 | C25 | 1 | 1 | yes | characteristic |
| 230 | C22×D13 | — | 2 | 1 | no | — |
| 231 | C22×D13 | — | 2 | 3 | no | — |
| 232 | C22×D13 | — | 2 | 1 | no | — |
| 233 | C22×D13 | — | 2 | 3 | no | — |
| 234 | C22×D13 | — | 2 | 3 | no | — |
| 235 | C22×D13 | — | 2 | 3 | no | — |
| 236 | C22×D13 | — | 2 | 3 | no | — |
| 237 | C22×D13 | — | 2 | 3 | no | — |
| 238 | C22×D13 | — | 2 | 3 | no | — |
| 239 | C22×D13 | — | 2 | 3 | no | — |
| 240 | C22×D13 | — | 2 | 3 | no | — |
| 241 | C22×D13 | — | 2 | 3 | no | — |
| 242 | C22×D13 | — | 2 | 3 | no | — |
| 243 | C2×C4×C13 | — | 2 | 3 | no | — |
| 244 | C2×C4×C13 | — | 2 | 3 | no | — |
| 245 | C2×C4×C13 | — | 2 | 3 | no | — |
| 246 | C2×C4×C13 | — | 2 | 3 | no | — |
| 247 | C2×C4×C13 | — | 2 | 3 | no | — |
| 248 | C2×C4×C13 | — | 2 | 3 | no | — |
| 249 | C2×C4×C13 | — | 2 | 3 | no | — |
| 250 | C2×C4×C13 | — | 2 | 3 | no | — |
| 251 | C2×C4×C13 | — | 2 | 3 | no | — |
| 252 | C2×C4×C13 | — | 2 | 3 | no | — |
| 253 | C2×C4×C13 | — | 2 | 3 | no | — |
| 254 | C2×C4×C13 | — | 2 | 3 | no | — |
| 255 | C2×C4×C13 | — | 4 | 4 | no | — |
| 256 | C2×C4×C13 | C2×#41 | 1 | 6 | yes | — |
| 257 | C2×C4×C13 | H(5,𝔽2) | 1 | 6 | yes | — |
| 258 | C22⋊D13 | — | 4 | 4 | no | — |
| 259 | C22⋊D13 | — | 4 | 4 | no | — |
| 260 | C22⋊D13 | — | 4 | 12 | no | — |
| 261 | C2×Dic13 | — | 2 | 3 | no | — |
| 262 | C2×Dic13 | — | 2 | 3 | no | — |
| 263 | C2×Dic13 | — | 2 | 3 | no | — |
| 264 | C2×Dic13 | — | 2 | 3 | no | — |
| 265 | C2×Dic13 | — | 2 | 3 | no | — |
| 266 | C2×Dic13 | — | 2 | 3 | no | — |
| 267 | C2×Dic13 | — | 2 | 3 | no | — |
| 268 | C2×Dic13 | — | 2 | 3 | no | — |
| 269 | C2×Dic13 | — | 2 | 3 | no | — |
| 270 | C2×Dic13 | — | 2 | 3 | no | — |
| 271 | C2×Dic13 | — | 2 | 3 | no | — |
| 272 | D52 | — | 4 | 12 | no | — |
| 273 | D52 | — | 4 | 12 | no | — |
| 274 | D52 | — | 4 | 12 | no | — |
| 275 | D52 | — | 4 | 4 | no | — |
| 276 | C4×D13 | — | 4 | 12 | no | — |
| 277 | C4×D13 | — | 4 | 4 | no | — |
| 278 | C4×D13 | — | 4 | 4 | no | — |
| 279 | Dic26 | — | 4 | 4 | no | — |
| 280 | C22×#41 | — | 13 | 1 | no | — |
| 281 | C2×#127 | — | 13 | 1 | no | — |
| 282 | C2×#126 | — | 13 | 1 | no | — |
| 283 | C2×#126 | C2×D13 | 1 | 1 | yes | characteristic |
| 284 | C2×C4×D4 | — | 13 | 3 | no | — |
| 285 | C2×C4×D4 | — | 13 | 3 | no | — |
| 286 | C2×C4×D4 | — | 13 | 3 | no | — |
| 287 | C2×C4×D4 | — | 13 | 3 | no | — |
| 288 | C2×#117 | — | 13 | 3 | no | — |
| 289 | #400 | — | 13 | 3 | no | — |
| 290 | #399 | — | 13 | 3 | no | — |
| 291 | #398 | — | 13 | 3 | no | — |
| 292 | #398 | — | 13 | 3 | no | — |
| 293 | #398 | — | 13 | 3 | no | — |
| 294 | #397 | — | 13 | 3 | no | — |
| 295 | #397 | — | 13 | 3 | no | — |
| 296 | #397 | — | 13 | 3 | no | — |
| 297 | #397 | — | 13 | 3 | no | — |
| 298 | #397 | — | 13 | 3 | no | — |
| 299 | #396 | — | 13 | 3 | no | — |
| 300 | #396 | — | 13 | 3 | no | — |
| 301 | #396 | — | 13 | 3 | no | — |
| 302 | #396 | — | 13 | 3 | no | — |
| 303 | #395 | — | 13 | 3 | no | — |
| 304 | #394 | — | 13 | 3 | no | — |
| 305 | #394 | — | 13 | 3 | no | — |
| 306 | #394 | — | 13 | 3 | no | — |
| 307 | #394 | — | 13 | 3 | no | — |
| 308 | #394 | — | 13 | 3 | no | — |
| 309 | #394 | — | 13 | 3 | no | — |
| 310 | #394 | — | 13 | 3 | no | — |
| 311 | #394 | — | 13 | 3 | no | — |
| 312 | #394 | — | 13 | 3 | no | — |
| 313 | #394 | — | 13 | 3 | no | — |
| 314 | #394 | — | 13 | 3 | no | — |
| 315 | #393 | — | 13 | 3 | no | — |
| 316 | #392 | — | 13 | 3 | no | — |
| 317 | #392 | — | 13 | 3 | no | — |
| 318 | #392 | — | 13 | 3 | no | — |
| 319 | #392 | — | 13 | 3 | no | — |
| 320 | #392 | — | 13 | 3 | no | — |
| 321 | #390 | — | 13 | 3 | no | — |
| 322 | #390 | — | 13 | 3 | no | — |
| 323 | #388 | — | 13 | 3 | no | — |
| 324 | #388 | C2×D13 | 1 | 3 | yes | — |
| 325 | #387 | — | 13 | 3 | no | — |
| 326 | #387 | C2×D13 | 1 | 3 | yes | — |
| 327 | #384 | — | 13 | 1 | no | — |
| 328 | #383 | — | 13 | 1 | no | — |
| 329 | #383 | C2×D13 | 1 | 1 | yes | characteristic |
| 330 | C4×C4⋊C4 | — | 13 | 3 | no | — |
| 331 | C4×C4⋊C4 | C2×D13 | 1 | 3 | yes | — |
| 332 | C4×C22⋊C4 | — | 13 | 3 | no | — |
| 333 | C4×C22⋊C4 | — | 13 | 3 | no | — |
| 334 | C4×C22⋊C4 | — | 13 | 3 | no | — |
| 335 | C4×C22⋊C4 | C2×D13 | 1 | 3 | yes | — |
| 336 | C43 | C2×D13 | 1 | 1 | yes | characteristic |
| 337 | C22×C13 | — | 4 | 3 | no | — |
| 338 | C22×C13 | — | 4 | 1 | no | — |
| 339 | C22×C13 | — | 4 | 3 | no | — |
| 340 | C22×C13 | C22×#41 | 1 | 1 | yes | characteristic |
| 341 | C22×C13 | C2×H(5,𝔽2) | 1 | 3 | yes | — |
| 342 | C22×C13 | #585 | 1 | 3 | yes | — |
| 343 | C2×D13 | — | 4 | 3 | no | — |
| 344 | C2×D13 | — | 4 | 3 | no | — |
| 345 | C2×D13 | — | 4 | 3 | no | — |
| 346 | C2×D13 | — | 4 | 3 | no | — |
| 347 | C2×D13 | — | 4 | 3 | no | — |
| 348 | C2×D13 | — | 4 | 1 | no | — |
| 349 | C2×D13 | — | 4 | 1 | no | — |
| 350 | C2×D13 | — | 4 | 3 | no | — |
| 351 | C2×D13 | — | 4 | 3 | no | — |
| 352 | C2×D13 | — | 4 | 3 | no | — |
| 353 | C2×D13 | — | 4 | 3 | no | — |
| 354 | C2×D13 | — | 4 | 3 | no | — |
| 355 | C2×D13 | — | 4 | 3 | no | — |
| 356 | C4×C13 | — | 2 | 6 | no | — |
| 357 | C4×C13 | — | 4 | 3 | no | — |
| 358 | C4×C13 | — | 4 | 1 | no | — |
| 359 | C4×C13 | — | 4 | 3 | no | — |
| 360 | C4×C13 | — | 4 | 3 | no | — |
| 361 | C4×C13 | #560 | 1 | 4 | yes | — |
| 362 | Dic13 | — | 4 | 3 | no | — |
| 363 | Dic13 | — | 4 | 1 | no | — |
| 364 | Dic13 | — | 4 | 1 | no | — |
| 365 | Dic13 | — | 4 | 3 | no | — |
| 366 | Dic13 | — | 4 | 3 | no | — |
| 367 | C2×#41 | — | 52 | 6 | no | — |
| 368 | C22×Q8 | — | 13 | 1 | no | — |
| 369 | C22×D4 | — | 13 | 3 | no | — |
| 370 | C22×D4 | — | 13 | 1 | no | — |
| 371 | C22×D4 | — | 13 | 1 | no | — |
| 372 | C22×D4 | — | 13 | 3 | no | — |
| 373 | C22×D4 | — | 13 | 3 | no | — |
| 374 | C22×D4 | — | 13 | 3 | no | — |
| 375 | C22×D4 | — | 13 | 1 | no | — |
| 376 | C23×C4 | — | 13 | 3 | no | — |
| 377 | C23×C4 | — | 13 | 1 | no | — |
| 378 | C23×C4 | — | 13 | 1 | no | — |
| 379 | C23×C4 | C22×D13 | 1 | 1 | yes | characteristic |
| 380 | #127 | — | 26 | 4 | no | — |
| 381 | #126 | — | 2 | 4 | no | — |
| 382 | #126 | — | 26 | 4 | no | — |
| 383 | C4×D4 | — | 52 | 6 | no | — |
| 384 | C4×D4 | — | 52 | 6 | no | — |
| 385 | C4×D4 | — | 52 | 6 | no | — |
| 386 | C4×D4 | — | 52 | 6 | no | — |
| 387 | #117 | — | 52 | 6 | no | — |
| 388 | C2×C4⋊C4 | — | 13 | 3 | no | — |
| 389 | C2×C4⋊C4 | — | 13 | 3 | no | — |
| 390 | C2×C4⋊C4 | — | 13 | 3 | no | — |
| 391 | C2×C4⋊C4 | — | 13 | 3 | no | — |
| 392 | C2×C4⋊C4 | — | 13 | 3 | no | — |
| 393 | C2×C4⋊C4 | — | 13 | 3 | no | — |
| 394 | C2×C4⋊C4 | — | 13 | 3 | no | — |
| 395 | C2×C4⋊C4 | — | 13 | 3 | no | — |
| 396 | C2×C4⋊C4 | C22×D13 | 1 | 3 | yes | — |
| 397 | C2×C4⋊C4 | C22×D13 | 1 | 3 | yes | — |
| 398 | C2×C22⋊C4 | — | 13 | 3 | no | — |
| 399 | C2×C22⋊C4 | — | 13 | 3 | no | — |
| 400 | C2×C22⋊C4 | — | 13 | 3 | no | — |
| 401 | C2×C22⋊C4 | — | 13 | 3 | no | — |
| 402 | C2×C22⋊C4 | — | 13 | 3 | no | — |
| 403 | C2×C22⋊C4 | — | 13 | 3 | no | — |
| 404 | C2×C22⋊C4 | — | 13 | 3 | no | — |
| 405 | C2×C22⋊C4 | — | 13 | 3 | no | — |
| 406 | C2×C22⋊C4 | — | 13 | 3 | no | — |
| 407 | C2×C22⋊C4 | — | 13 | 3 | no | — |
| 408 | C2×C22⋊C4 | — | 13 | 3 | no | — |
| 409 | C2×C22⋊C4 | — | 13 | 3 | no | — |
| 410 | C2×C22⋊C4 | — | 13 | 3 | no | — |
| 411 | C2×C22⋊C4 | — | 13 | 3 | no | — |
| 412 | C2×C22⋊C4 | — | 13 | 3 | no | — |
| 413 | C2×C22⋊C4 | — | 13 | 3 | no | — |
| 414 | C2×C22⋊C4 | C22×D13 | 1 | 3 | yes | — |
| 415 | C2×C22⋊C4 | C22×D13 | 1 | 3 | yes | — |
| 416 | C2×C42 | — | 13 | 3 | no | — |
| 417 | C2×C42 | C22×D13 | 1 | 3 | yes | — |
| 418 | C2×C42 | C22×D13 | 1 | 3 | yes | — |
| 419 | C2×C42 | C22×D13 | 1 | 3 | yes | — |
| 420 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 421 | #95 | — | 13 | 3 | no | — |
| 422 | #95 | — | 13 | 3 | no | — |
| 423 | #95 | — | 13 | 3 | no | — |
| 424 | #95 | — | 13 | 3 | no | — |
| 425 | #95 | — | 13 | 3 | no | — |
| 426 | #95 | — | 13 | 3 | no | — |
| 427 | #95 | — | 13 | 3 | no | — |
| 428 | #95 | — | 13 | 3 | no | — |
| 429 | #95 | C22×D13 | 1 | 3 | yes | — |
| 430 | #95 | C22×D13 | 1 | 3 | yes | — |
| 431 | #95 | C22×D13 | 1 | 3 | yes | — |
| 432 | #95 | C22×D13 | 1 | 3 | yes | — |
| 433 | C2×C13 | — | 8 | 1 | no | — |
| 434 | C2×C13 | #3460 | 1 | 3 | yes | — |
| 435 | C2×C13 | C2×#560 | 1 | 1 | yes | characteristic |
| 436 | C2×C13 | #3529 | 1 | 3 | yes | — |
| 437 | D13 | — | 8 | 1 | no | — |
| 438 | D13 | — | 8 | 3 | no | — |
| 439 | D13 | — | 8 | 1 | no | — |
| 440 | C24 | — | 13 | 1 | no | — |
| 441 | C24 | — | 13 | 3 | no | — |
| 442 | C24 | — | 13 | 1 | no | — |
| 443 | C24 | C23×D13 | 1 | 1 | yes | characteristic |
| 444 | #41 | — | 52 | 16 | no | — |
| 445 | C2×Q8 | — | 52 | 3 | no | — |
| 446 | C2×D4 | — | 26 | 6 | no | — |
| 447 | C2×D4 | — | 26 | 6 | no | — |
| 448 | C2×D4 | — | 52 | 3 | no | — |
| 449 | C2×D4 | — | 52 | 3 | no | — |
| 450 | C2×D4 | — | 52 | 3 | no | — |
| 451 | C2×D4 | — | 52 | 3 | no | — |
| 452 | C2×D4 | — | 52 | 3 | no | — |
| 453 | C2×D4 | — | 52 | 3 | no | — |
| 454 | C2×D4 | — | 52 | 3 | no | — |
| 455 | C2×D4 | — | 52 | 3 | no | — |
| 456 | C2×D4 | — | 52 | 3 | no | — |
| 457 | C2×D4 | — | 52 | 3 | no | — |
| 458 | C2×D4 | — | 52 | 3 | no | — |
| 459 | C2×D4 | — | 52 | 3 | no | — |
| 460 | C2×D4 | — | 52 | 3 | no | — |
| 461 | C22×C4 | — | 2 | 6 | no | — |
| 462 | C22×C4 | — | 13 | 3 | no | — |
| 463 | C22×C4 | — | 13 | 1 | no | — |
| 464 | C22×C4 | — | 13 | 1 | no | — |
| 465 | C22×C4 | — | 13 | 3 | no | — |
| 466 | C22×C4 | — | 13 | 3 | no | — |
| 467 | C22×C4 | — | 26 | 6 | no | — |
| 468 | C22×C4 | — | 26 | 6 | no | — |
| 469 | C22×C4 | — | 26 | 6 | no | — |
| 470 | C22×C4 | — | 26 | 6 | no | — |
| 471 | C22×C4 | — | 26 | 6 | no | — |
| 472 | C22×C4 | C23×D13 | 1 | 3 | yes | — |
| 473 | C22×C4 | C23×D13 | 1 | 3 | yes | — |
| 474 | C22×C4 | C23×D13 | 1 | 3 | yes | — |
| 475 | C22×C4 | C23×D13 | 1 | 1 | yes | characteristic |
| 476 | C22×C4 | C23×D13 | 1 | 3 | yes | — |
| 477 | C22×C4 | C23×D13 | 1 | 1 | yes | characteristic |
| 478 | C4⋊C4 | — | 2 | 6 | no | — |
| 479 | C4⋊C4 | — | 4 | 3 | no | — |
| 480 | C4⋊C4 | — | 26 | 6 | no | — |
| 481 | C4⋊C4 | — | 52 | 3 | no | — |
| 482 | C4⋊C4 | — | 52 | 3 | no | — |
| 483 | C4⋊C4 | — | 52 | 3 | no | — |
| 484 | C4⋊C4 | — | 52 | 3 | no | — |
| 485 | C4⋊C4 | — | 52 | 3 | no | — |
| 486 | C4⋊C4 | — | 52 | 3 | no | — |
| 487 | C4⋊C4 | — | 52 | 3 | no | — |
| 488 | C22⋊C4 | — | 2 | 6 | no | — |
| 489 | C22⋊C4 | — | 4 | 3 | no | — |
| 490 | C22⋊C4 | — | 26 | 6 | no | — |
| 491 | C22⋊C4 | — | 52 | 3 | no | — |
| 492 | C22⋊C4 | — | 52 | 3 | no | — |
| 493 | C22⋊C4 | — | 52 | 3 | no | — |
| 494 | C22⋊C4 | — | 52 | 3 | no | — |
| 495 | C22⋊C4 | — | 52 | 3 | no | — |
| 496 | C22⋊C4 | — | 52 | 3 | no | — |
| 497 | C22⋊C4 | — | 52 | 3 | no | — |
| 498 | C22⋊C4 | — | 52 | 3 | no | — |
| 499 | C22⋊C4 | — | 52 | 3 | no | — |
| 500 | C22⋊C4 | — | 52 | 3 | no | — |
| 501 | C22⋊C4 | — | 52 | 3 | no | — |
| 502 | C22⋊C4 | — | 52 | 3 | no | — |
| 503 | C22⋊C4 | — | 52 | 3 | no | — |
| 504 | C22⋊C4 | — | 52 | 3 | no | — |
| 505 | C22⋊C4 | — | 52 | 3 | no | — |
| 506 | C42 | — | 2 | 6 | no | — |
| 507 | C42 | — | 2 | 6 | no | — |
| 508 | C42 | — | 4 | 3 | no | — |
| 509 | C42 | — | 26 | 6 | no | — |
| 510 | C42 | #6127 | 1 | 4 | yes | complemented |
| 511 | C13 | #36696 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 512 | C23 | — | 2 | 1 | no | — |
| 513 | C23 | — | 2 | 3 | no | — |
| 514 | C23 | — | 2 | 3 | no | — |
| 515 | C23 | — | 26 | 1 | no | — |
| 516 | C23 | — | 26 | 3 | no | — |
| 517 | C23 | — | 26 | 1 | no | — |
| 518 | C23 | — | 26 | 3 | no | — |
| 519 | C23 | — | 26 | 3 | no | — |
| 520 | C23 | — | 26 | 3 | no | — |
| 521 | C23 | — | 26 | 3 | no | — |
| 522 | C23 | — | 26 | 3 | no | — |
| 523 | C23 | — | 26 | 3 | no | — |
| 524 | C23 | — | 26 | 3 | no | — |
| 525 | C23 | — | 26 | 3 | no | — |
| 526 | C23 | — | 26 | 3 | no | — |
| 527 | C23 | — | 26 | 3 | no | — |
| 528 | C23 | C24×D13 | 1 | 1 | yes | characteristic |
| 529 | Q8 | — | 52 | 4 | no | — |
| 530 | D4 | — | 52 | 12 | no | — |
| 531 | D4 | — | 52 | 12 | no | — |
| 532 | D4 | — | 52 | 12 | no | — |
| 533 | D4 | — | 52 | 4 | no | — |
| 534 | D4 | — | 52 | 12 | no | — |
| 535 | D4 | — | 52 | 4 | no | — |
| 536 | D4 | — | 52 | 4 | no | — |
| 537 | C2×C4 | — | 2 | 3 | no | — |
| 538 | C2×C4 | — | 2 | 3 | no | — |
| 539 | C2×C4 | — | 2 | 3 | no | — |
| 540 | C2×C4 | — | 2 | 3 | no | — |
| 541 | C2×C4 | — | 2 | 3 | no | — |
| 542 | C2×C4 | — | 2 | 3 | no | — |
| 543 | C2×C4 | — | 2 | 3 | no | — |
| 544 | C2×C4 | — | 2 | 3 | no | — |
| 545 | C2×C4 | — | 2 | 3 | no | — |
| 546 | C2×C4 | — | 2 | 3 | no | — |
| 547 | C2×C4 | — | 2 | 3 | no | — |
| 548 | C2×C4 | — | 2 | 3 | no | — |
| 549 | C2×C4 | — | 4 | 4 | no | — |
| 550 | C2×C4 | — | 26 | 3 | no | — |
| 551 | C2×C4 | — | 26 | 3 | no | — |
| 552 | C2×C4 | — | 26 | 3 | no | — |
| 553 | C2×C4 | — | 26 | 3 | no | — |
| 554 | C2×C4 | — | 26 | 3 | no | — |
| 555 | C2×C4 | — | 26 | 3 | no | — |
| 556 | C2×C4 | — | 26 | 3 | no | — |
| 557 | C2×C4 | — | 26 | 3 | no | — |
| 558 | C2×C4 | — | 26 | 3 | no | — |
| 559 | C2×C4 | — | 26 | 3 | no | — |
| 560 | C2×C4 | — | 26 | 3 | no | — |
| 561 | C2×C4 | — | 52 | 12 | no | — |
| 562 | C2×C4 | — | 52 | 4 | no | — |
| 563 | C2×C4 | — | 52 | 4 | no | — |
| 564 | C2×C4 | C2×#6127 | 1 | 6 | yes | — |
| 565 | C2×C4 | #88256 | 1 | 6 | yes | — |
| 566 | C22 | — | 4 | 3 | no | — |
| 567 | C22 | — | 4 | 3 | no | — |
| 568 | C22 | — | 4 | 1 | no | — |
| 569 | C22 | — | 52 | 3 | no | — |
| 570 | C22 | — | 52 | 3 | no | — |
| 571 | C22 | — | 52 | 3 | no | — |
| 572 | C22 | — | 52 | 3 | no | — |
| 573 | C22 | — | 52 | 3 | no | — |
| 574 | C22 | — | 52 | 3 | no | — |
| 575 | C22 | — | 52 | 3 | no | — |
| 576 | C22 | — | 52 | 3 | no | — |
| 577 | C22 | — | 52 | 3 | no | — |
| 578 | C22 | — | 52 | 3 | no | — |
| 579 | C22 | — | 52 | 1 | no | — |
| 580 | C22 | — | 52 | 1 | no | — |
| 581 | C22 | — | 52 | 3 | no | — |
| 582 | C22 | C22×#6127 | 1 | 1 | yes | characteristic |
| 583 | C22 | C2×#88256 | 1 | 3 | yes | — |
| 584 | C22 | #11719648 | 1 | 3 | yes | — |
| 585 | C4 | — | 2 | 6 | no | — |
| 586 | C4 | — | 4 | 3 | no | — |
| 587 | C4 | — | 4 | 3 | no | — |
| 588 | C4 | — | 4 | 3 | no | — |
| 589 | C4 | — | 4 | 1 | no | — |
| 590 | C4 | — | 52 | 3 | no | — |
| 591 | C4 | — | 52 | 3 | no | — |
| 592 | C4 | — | 52 | 3 | no | — |
| 593 | C4 | — | 52 | 1 | no | — |
| 594 | C4 | — | 52 | 1 | no | — |
| 595 | C4 | #11719416 | 1 | 4 | yes | — |
| 596 | C2 | — | 8 | 1 | no | — |
| 597 | C2 | — | 104 | 1 | no | — |
| 598 | C2 | — | 104 | 3 | no | — |
| 599 | C2 | — | 104 | 1 | no | — |
| 600 | C2 | #13128252 | 1 | 3 | yes | — |
| 601 | C2 | C2×#11719416 | 1 | 1 | yes | characteristic |
| 602 | C2 | #13128975 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C23×D13 |
| commutator, socle, cosocle | C23×C13 | C25 |
| Frattini | C23 | C24×D13 |
| Fitting | C4×C13×#126 | C2 |
| hypercenter | C4×#126 | D13 |
| hypocenter | C13 | #36696 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C22×C4 ◁ C4×#126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13123103 | C2 | semidirect |
| 2. #13122977 | C2 | semidirect |
| 3. #13122966 | C2 | semidirect |
| 4. #13122962 | C2 | semidirect |
| 5. #13122953 | C2 | semidirect |
| 6. #13122908 | C2 | semidirect |
| 7. #13122879 | C2 | semidirect |
| 8. #13122876 | C2 | semidirect |
| 9. #13118099 | C2 | semidirect |
| 10. #13118080 | C2 | semidirect |
| 11. #13118076 | C2 | semidirect |
| 12. #13118052 | C2 | semidirect |
| 13. C4×#88128 | C2 | semidirect |
| 14. C4×#88130 | C2 | semidirect |
| 15. C4×C13×#126 | C2 | semidirect |
| 185. C42×C13 | #41 | semidirect |
| 225. C4×#126 | D13 | semidirect |
| 510. C42 | #6127 | semidirect |
| 511. C13 | #36696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13123103 | 2 |
| #13122977 | 2 |
| #13122966 | 2 |
| #13122962 | 2 |
| #13122953 | 2 |
| #13122908 | 2 |
| #13122879 | 2 |
| #13122876 | 2 |
| #13118099 | 2 |
| #13118080 | 2 |
| #13118076 | 2 |
| #13118052 | 2 |
| C4×#88128 | 2 |
| C4×#88130 | 2 |
| C4×C13×#126 | 2 |
| #36696 | 13 |