Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1948 conjugacy classes of subgroups.
The subgroup lattice has 632 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13128620 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | Q8×#6131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | Q8×#6106 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13127479 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13127478 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13127192 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #13127190 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #13126703 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #13126698 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #13126154 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #13125981 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #13124865 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | D13×#475 | C2 | 1 | 3 | yes | maximal, complemented |
| 14 | #13123946 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | Q8×C13×SD16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#88254 | — | 2 | 1 | no | — |
| 17 | Q82×C13 | C22 | 1 | 1 | yes | characteristic |
| 18 | D4×Q8×C13 | C22 | 1 | 1 | yes | characteristic |
| 19 | Q8×C22⋊D13 | — | 2 | 1 | no | — |
| 20 | #11719435 | — | 2 | 3 | no | — |
| 21 | #11719435 | C22 | 1 | 3 | yes | — |
| 22 | #11719433 | — | 2 | 3 | no | — |
| 23 | #11719433 | C22 | 1 | 3 | yes | — |
| 24 | #11719431 | C22 | 1 | 3 | yes | — |
| 25 | D13×C4⋊Q8 | C22 | 1 | 3 | yes | — |
| 26 | #11719336 | — | 2 | 3 | no | — |
| 27 | #11719333 | — | 2 | 3 | no | — |
| 28 | Q8×D52 | C22 | 1 | 3 | yes | — |
| 29 | Q8×D52 | C22 | 1 | 1 | yes | characteristic |
| 30 | C4×#6131 | — | 2 | 1 | no | — |
| 31 | C4×#6131 | C22 | 1 | 1 | yes | characteristic |
| 32 | C4×Q8×D13 | C22 | 1 | 3 | yes | — |
| 33 | #11719275 | — | 2 | 1 | no | — |
| 34 | #11719275 | C22 | 1 | 1 | yes | characteristic |
| 35 | #11719256 | C22 | 1 | 3 | yes | — |
| 36 | #11719253 | C22 | 1 | 3 | yes | — |
| 37 | C13×#498 | C22 | 1 | 3 | yes | — |
| 38 | C13×#476 | C22 | 1 | 3 | yes | — |
| 39 | C13×#475 | C22 | 1 | 3 | yes | — |
| 40 | C8×Q8×C13 | C22 | 1 | 1 | yes | characteristic |
| 41 | C4×C13×SD16 | C22 | 1 | 3 | yes | — |
| 42 | #11718831 | C22 | 1 | 3 | yes | — |
| 43 | #11718824 | C22 | 1 | 1 | yes | characteristic |
| 44 | #11718755 | C22 | 1 | 3 | yes | — |
| 45 | #11718754 | C22 | 1 | 3 | yes | — |
| 46 | #11718745 | C22 | 1 | 3 | yes | — |
| 47 | #11718740 | C22 | 1 | 3 | yes | — |
| 48 | C4×#6106 | C22 | 1 | 3 | yes | — |
| 49 | Q8×#1055 | C22 | 1 | 1 | yes | characteristic |
| 50 | #11718681 | C22 | 1 | 3 | yes | — |
| 51 | #11718680 | C22 | 1 | 3 | yes | — |
| 52 | C4×#6105 | C22 | 1 | 3 | yes | — |
| 53 | #11718525 | C22 | 1 | 6 | yes | — |
| 54 | #11718524 | C22 | 1 | 3 | yes | — |
| 55 | #11718523 | C22 | 1 | 6 | yes | — |
| 56 | #11718523 | C22 | 1 | 6 | yes | — |
| 57 | D13×#106 | C22 | 1 | 6 | yes | — |
| 58 | #11718515 | C22 | 1 | 3 | yes | — |
| 59 | #11718515 | C22 | 1 | 6 | yes | — |
| 60 | #11718512 | C22 | 1 | 3 | yes | — |
| 61 | #11718502 | C22 | 1 | 3 | yes | — |
| 62 | #11718495 | C22 | 1 | 3 | yes | — |
| 63 | D13×C4⋊C8 | C22 | 1 | 3 | yes | — |
| 64 | #11718467 | C22 | 1 | 3 | yes | — |
| 65 | D13×#103 | C22 | 1 | 6 | yes | — |
| 66 | #11718452 | C22 | 1 | 3 | yes | — |
| 67 | #11718439 | C22 | 1 | 6 | yes | — |
| 68 | #11718438 | C22 | 1 | 3 | yes | — |
| 69 | #11718423 | C22 | 1 | 3 | yes | — |
| 70 | C4×#6095 | C22 | 1 | 3 | yes | — |
| 71 | C8×D52 | C22 | 1 | 3 | yes | — |
| 72 | #11718346 | C22 | 1 | 3 | yes | — |
| 73 | #11718342 | C22 | 1 | 3 | yes | — |
| 74 | C22×Q8×C13 | — | 2 | 1 | no | — |
| 75 | #88254 | — | 4 | 8 | no | — |
| 76 | C2×#6131 | — | 2 | 3 | no | — |
| 77 | C2×#6131 | D4 | 1 | 1 | yes | characteristic |
| 78 | C2×Q8×D13 | — | 2 | 1 | no | — |
| 79 | C2×Q8×D13 | — | 2 | 3 | no | — |
| 80 | C2×Q8×D13 | C23 | 1 | 3 | yes | — |
| 81 | C2×#6127 | — | 2 | 3 | no | — |
| 82 | C2×#6127 | — | 2 | 3 | no | — |
| 83 | C2×C13×SD16 | C23 | 1 | 1 | yes | characteristic |
| 84 | C13×C4⋊Q8 | — | 2 | 3 | no | — |
| 85 | C13×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 86 | C13×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 87 | C13×C22⋊Q8 | — | 2 | 3 | no | — |
| 88 | C4×Q8×C13 | — | 2 | 1 | no | — |
| 89 | C4×Q8×C13 | C23 | 1 | 3 | yes | — |
| 90 | C4×Q8×C13 | C23 | 1 | 1 | yes | characteristic |
| 91 | C4×D4×C13 | C23 | 1 | 3 | yes | — |
| 92 | #88200 | — | 2 | 3 | no | — |
| 93 | #88200 | — | 2 | 6 | no | — |
| 94 | #88200 | — | 2 | 3 | no | — |
| 95 | Q8×Dic13 | — | 2 | 1 | no | — |
| 96 | Q8×Dic13 | — | 2 | 3 | no | — |
| 97 | Q8×Dic13 | D4 | 1 | 1 | yes | characteristic |
| 98 | Q8×Dic13 | C23 | 1 | 1 | yes | characteristic |
| 99 | #88198 | — | 2 | 3 | no | — |
| 100 | C2×#6106 | C23 | 1 | 1 | yes | characteristic |
| 101 | #88194 | C23 | 1 | 1 | yes | characteristic |
| 102 | #88192 | C23 | 1 | 3 | yes | — |
| 103 | C2×#6105 | C23 | 1 | 3 | yes | — |
| 104 | C4×C22⋊D13 | — | 2 | 3 | no | — |
| 105 | #88178 | — | 2 | 3 | no | — |
| 106 | C2×#6095 | C23 | 1 | 3 | yes | — |
| 107 | C2×C8×D13 | C23 | 1 | 6 | yes | — |
| 108 | #88151 | — | 2 | 3 | no | — |
| 109 | #88151 | — | 2 | 6 | no | — |
| 110 | #88151 | C23 | 1 | 6 | yes | — |
| 111 | #88149 | C23 | 1 | 3 | yes | — |
| 112 | #88148 | — | 2 | 6 | no | — |
| 113 | #88147 | — | 2 | 3 | no | — |
| 114 | #88147 | D4 | 1 | 3 | yes | — |
| 115 | #88146 | — | 2 | 3 | no | — |
| 116 | #88146 | D4 | 1 | 3 | yes | — |
| 117 | C4⋊C4×D13 | — | 2 | 3 | no | — |
| 118 | C4⋊C4×D13 | — | 2 | 3 | no | — |
| 119 | C4⋊C4×D13 | C23 | 1 | 6 | yes | — |
| 120 | C4⋊C4×D13 | C23 | 1 | 3 | yes | — |
| 121 | #88144 | — | 2 | 3 | no | — |
| 122 | #88144 | — | 2 | 3 | no | — |
| 123 | #88144 | — | 2 | 3 | no | — |
| 124 | #88142 | — | 2 | 3 | no | — |
| 125 | #88142 | C23 | 1 | 3 | yes | — |
| 126 | #88141 | — | 2 | 3 | no | — |
| 127 | #88141 | C23 | 1 | 3 | yes | — |
| 128 | #88139 | — | 2 | 3 | no | — |
| 129 | #88138 | — | 2 | 3 | no | — |
| 130 | #88137 | — | 2 | 6 | no | — |
| 131 | C4×D52 | — | 2 | 3 | no | — |
| 132 | C4×D52 | C23 | 1 | 3 | yes | — |
| 133 | C4×D52 | C23 | 1 | 3 | yes | — |
| 134 | C42×D13 | — | 2 | 3 | no | — |
| 135 | C42×D13 | C23 | 1 | 3 | yes | — |
| 136 | #88123 | — | 2 | 3 | no | — |
| 137 | #88123 | C23 | 1 | 3 | yes | — |
| 138 | #88123 | C23 | 1 | 3 | yes | — |
| 139 | C4×Dic26 | — | 2 | 3 | no | — |
| 140 | C4×Dic26 | C23 | 1 | 3 | yes | — |
| 141 | C13×#106 | C23 | 1 | 3 | yes | — |
| 142 | C13×#106 | C23 | 1 | 6 | yes | — |
| 143 | C13×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 144 | C13×#103 | C23 | 1 | 3 | yes | — |
| 145 | C13×#102 | C23 | 1 | 3 | yes | — |
| 146 | C4×C8×C13 | C23 | 1 | 3 | yes | — |
| 147 | #88075 | C23 | 1 | 3 | yes | — |
| 148 | #88072 | C23 | 1 | 1 | yes | characteristic |
| 149 | #88061 | C23 | 1 | 1 | yes | characteristic |
| 150 | #88060 | C23 | 1 | 3 | yes | — |
| 151 | #88060 | C23 | 1 | 3 | yes | — |
| 152 | #88057 | C23 | 1 | 3 | yes | — |
| 153 | #88056 | C23 | 1 | 6 | yes | — |
| 154 | #88056 | C23 | 1 | 3 | yes | — |
| 155 | #88054 | C23 | 1 | 3 | yes | — |
| 156 | #88054 | C23 | 1 | 1 | yes | characteristic |
| 157 | #88050 | C23 | 1 | 3 | yes | — |
| 158 | #88050 | C23 | 1 | 6 | yes | — |
| 159 | #88049 | C23 | 1 | 3 | yes | — |
| 160 | #88048 | C23 | 1 | 3 | yes | — |
| 161 | #88048 | C23 | 1 | 6 | yes | — |
| 162 | #88048 | C23 | 1 | 3 | yes | — |
| 163 | C4⋊#1055 | C23 | 1 | 3 | yes | — |
| 164 | C4×#1055 | C23 | 1 | 3 | yes | — |
| 165 | #62099 | — | 13 | 1 | no | maximal, Sylow |
| 166 | C2×Q8×C13 | — | 2 | 3 | no | — |
| 167 | C2×Q8×C13 | — | 2 | 3 | no | — |
| 168 | C2×Q8×C13 | — | 4 | 4 | no | — |
| 169 | C2×Q8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | C2×Q8×C13 | C24 | 1 | 1 | yes | characteristic |
| 171 | C2×D4×C13 | C24 | 1 | 1 | yes | characteristic |
| 172 | C22×C4×C13 | — | 2 | 3 | no | — |
| 173 | C2×C22⋊D13 | — | 2 | 3 | no | — |
| 174 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 175 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 176 | #6131 | — | 4 | 12 | no | — |
| 177 | #6131 | SD16 | 1 | 8 | yes | complemented |
| 178 | Q8×D13 | — | 2 | 6 | no | — |
| 179 | Q8×D13 | — | 4 | 3 | no | — |
| 180 | Q8×D13 | — | 4 | 4 | no | — |
| 181 | Q8×D13 | — | 4 | 12 | no | — |
| 182 | #6127 | — | 4 | 12 | no | — |
| 183 | #6127 | — | 4 | 12 | no | — |
| 184 | C2×D52 | — | 2 | 3 | no | — |
| 185 | C2×D52 | C2×D4 | 1 | 3 | yes | — |
| 186 | C2×D52 | C24 | 1 | 1 | yes | characteristic |
| 187 | C2×C4×D13 | — | 2 | 3 | no | — |
| 188 | C2×C4×D13 | — | 2 | 6 | no | — |
| 189 | C2×C4×D13 | — | 2 | 3 | no | — |
| 190 | C2×C4×D13 | — | 2 | 3 | no | — |
| 191 | C2×C4×D13 | C2×D4 | 1 | 3 | yes | — |
| 192 | C2×C4×D13 | C2×D4 | 1 | 3 | yes | — |
| 193 | C2×C4×D13 | C24 | 1 | 3 | yes | — |
| 194 | C2×Dic26 | — | 2 | 3 | no | — |
| 195 | C2×Dic26 | — | 2 | 3 | no | — |
| 196 | C2×Dic26 | — | 2 | 3 | no | — |
| 197 | C2×Dic26 | C24 | 1 | 3 | yes | — |
| 198 | C13×SD16 | — | 2 | 2 | no | — |
| 199 | C2×C8×C13 | C24 | 1 | 1 | yes | characteristic |
| 200 | C2×C8×C13 | C24 | 1 | 3 | yes | — |
| 201 | C13×C4⋊C4 | — | 2 | 3 | no | — |
| 202 | C13×C4⋊C4 | — | 2 | 3 | no | — |
| 203 | C13×C4⋊C4 | — | 2 | 3 | no | — |
| 204 | C13×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 205 | C13×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 206 | C13×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 207 | C13×C22⋊C4 | — | 2 | 3 | no | — |
| 208 | C42×C13 | — | 2 | 3 | no | — |
| 209 | C42×C13 | C24 | 1 | 3 | yes | — |
| 210 | C22⋊Dic13 | — | 2 | 3 | no | — |
| 211 | #6106 | — | 2 | 2 | no | — |
| 212 | #6105 | — | 4 | 3 | no | — |
| 213 | #6103 | — | 2 | 6 | no | — |
| 214 | #6103 | — | 2 | 3 | no | — |
| 215 | #6103 | — | 2 | 3 | no | — |
| 216 | #6103 | C2×D4 | 1 | 6 | yes | — |
| 217 | C4⋊Dic13 | — | 2 | 3 | no | — |
| 218 | C4⋊Dic13 | — | 2 | 3 | no | — |
| 219 | C4⋊Dic13 | — | 2 | 3 | no | — |
| 220 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 221 | C4⋊Dic13 | — | 2 | 6 | no | — |
| 222 | C4⋊Dic13 | C2×D4 | 1 | 3 | yes | — |
| 223 | C4⋊Dic13 | C24 | 1 | 1 | yes | characteristic |
| 224 | C4⋊Dic13 | C24 | 1 | 3 | yes | — |
| 225 | #6101 | — | 2 | 3 | no | — |
| 226 | #6101 | — | 2 | 3 | no | — |
| 227 | #6101 | — | 2 | 3 | no | — |
| 228 | #6101 | — | 2 | 6 | no | — |
| 229 | #6101 | — | 2 | 3 | no | — |
| 230 | C4×Dic13 | — | 2 | 3 | no | — |
| 231 | C4×Dic13 | — | 2 | 1 | no | — |
| 232 | C4×Dic13 | — | 2 | 3 | no | — |
| 233 | C4×Dic13 | C2×D4 | 1 | 3 | yes | — |
| 234 | C4×Dic13 | C2×D4 | 1 | 3 | yes | — |
| 235 | C4×Dic13 | C24 | 1 | 1 | yes | characteristic |
| 236 | C2×#1055 | C24 | 1 | 1 | yes | characteristic |
| 237 | C2×#1055 | C24 | 1 | 3 | yes | — |
| 238 | #6095 | — | 4 | 3 | no | — |
| 239 | C8×D13 | — | 4 | 6 | no | — |
| 240 | #3499 | — | 13 | 1 | no | — |
| 241 | Q8×#41 | — | 13 | 1 | no | — |
| 242 | Q8×SD16 | — | 13 | 1 | no | — |
| 243 | Q8×SD16 | D13 | 1 | 1 | yes | characteristic, complemented |
| 244 | #3359 | — | 13 | 1 | no | — |
| 245 | #3359 | — | 13 | 1 | no | — |
| 246 | #3335 | — | 13 | 3 | no | — |
| 247 | #3335 | — | 13 | 3 | no | — |
| 248 | #3298 | — | 13 | 3 | no | — |
| 249 | #3298 | — | 13 | 3 | no | — |
| 250 | #3246 | — | 13 | 3 | no | — |
| 251 | #3229 | — | 13 | 3 | no | — |
| 252 | #3103 | — | 13 | 3 | no | — |
| 253 | C2×#475 | — | 13 | 3 | no | — |
| 254 | #2988 | — | 13 | 1 | no | — |
| 255 | C23×C13 | — | 2 | 1 | no | — |
| 256 | C22×D13 | — | 2 | 1 | no | — |
| 257 | C22×D13 | C22×D4 | 1 | 3 | yes | — |
| 258 | Q8×C13 | — | 2 | 1 | no | — |
| 259 | Q8×C13 | — | 4 | 6 | no | — |
| 260 | Q8×C13 | — | 8 | 3 | no | — |
| 261 | Q8×C13 | C2×SD16 | 1 | 4 | yes | — |
| 262 | Q8×C13 | 2−1+4 | 1 | 2 | yes | complemented |
| 263 | D4×C13 | — | 2 | 1 | no | — |
| 264 | D4×C13 | — | 2 | 1 | no | — |
| 265 | C2×C4×C13 | — | 2 | 1 | no | — |
| 266 | C2×C4×C13 | — | 2 | 3 | no | — |
| 267 | C2×C4×C13 | — | 2 | 3 | no | — |
| 268 | C2×C4×C13 | — | 4 | 6 | no | — |
| 269 | C2×C4×C13 | C22×D4 | 1 | 3 | yes | — |
| 270 | C2×C4×C13 | C22×D4 | 1 | 3 | yes | — |
| 271 | C2×C4×C13 | C25 | 1 | 1 | yes | characteristic |
| 272 | C22⋊D13 | — | 4 | 2 | no | — |
| 273 | C22⋊D13 | — | 4 | 6 | no | — |
| 274 | C22⋊D13 | — | 4 | 2 | no | — |
| 275 | C2×Dic13 | — | 2 | 1 | no | — |
| 276 | C2×Dic13 | — | 2 | 3 | no | — |
| 277 | C2×Dic13 | — | 2 | 3 | no | — |
| 278 | C2×Dic13 | C22×D4 | 1 | 1 | yes | characteristic |
| 279 | C2×Dic13 | C22×D4 | 1 | 3 | yes | — |
| 280 | C2×Dic13 | C22×D4 | 1 | 1 | yes | characteristic |
| 281 | D52 | — | 2 | 1 | no | — |
| 282 | D52 | — | 2 | 1 | no | — |
| 283 | D52 | — | 4 | 6 | no | — |
| 284 | D52 | C2×SD16 | 1 | 12 | yes | — |
| 285 | C4×D13 | — | 2 | 3 | no | — |
| 286 | C4×D13 | — | 2 | 3 | no | — |
| 287 | C4×D13 | — | 4 | 3 | no | — |
| 288 | C4×D13 | — | 4 | 6 | no | — |
| 289 | C4×D13 | — | 4 | 12 | no | — |
| 290 | C4×D13 | — | 4 | 6 | no | — |
| 291 | C4×D13 | — | 8 | 3 | no | — |
| 292 | C4×D13 | C2×SD16 | 1 | 12 | yes | — |
| 293 | Dic26 | — | 2 | 3 | no | — |
| 294 | Dic26 | — | 2 | 3 | no | — |
| 295 | Dic26 | — | 4 | 6 | no | — |
| 296 | Dic26 | — | 4 | 6 | no | — |
| 297 | Dic26 | — | 4 | 6 | no | — |
| 298 | C8×C13 | — | 2 | 1 | no | — |
| 299 | C8×C13 | — | 2 | 3 | no | — |
| 300 | #1055 | — | 2 | 1 | no | — |
| 301 | #1055 | — | 2 | 3 | no | — |
| 302 | C2×2−1+4 | — | 26 | 1 | no | — |
| 303 | Q82 | C2×D13 | 1 | 1 | yes | characteristic |
| 304 | #557 | — | 13 | 1 | no | — |
| 305 | #557 | — | 26 | 1 | no | — |
| 306 | #554 | — | 13 | 3 | no | — |
| 307 | #554 | — | 26 | 3 | no | — |
| 308 | D4×Q8 | — | 13 | 1 | no | — |
| 309 | D4×Q8 | — | 13 | 3 | no | — |
| 310 | D4×Q8 | — | 26 | 1 | no | — |
| 311 | D4×Q8 | C2×D13 | 1 | 1 | yes | characteristic |
| 312 | #547 | — | 13 | 3 | no | — |
| 313 | #547 | — | 13 | 3 | no | — |
| 314 | #547 | — | 26 | 3 | no | — |
| 315 | #536 | — | 26 | 3 | no | — |
| 316 | #533 | — | 13 | 3 | no | — |
| 317 | #533 | — | 26 | 3 | no | — |
| 318 | #532 | — | 13 | 3 | no | — |
| 319 | C2×C4⋊Q8 | — | 13 | 3 | no | — |
| 320 | C4×#41 | — | 13 | 1 | no | — |
| 321 | C4×#41 | — | 26 | 1 | no | — |
| 322 | C2×C4×Q8 | — | 13 | 3 | no | — |
| 323 | #498 | — | 13 | 3 | no | — |
| 324 | #498 | C2×D13 | 1 | 3 | yes | — |
| 325 | #487 | — | 13 | 3 | no | — |
| 326 | #487 | — | 13 | 3 | no | — |
| 327 | #483 | — | 13 | 6 | no | — |
| 328 | #483 | — | 13 | 6 | no | — |
| 329 | #481 | — | 13 | 3 | no | — |
| 330 | #481 | — | 13 | 3 | no | — |
| 331 | #476 | — | 13 | 3 | no | — |
| 332 | #476 | C2×D13 | 1 | 3 | yes | — |
| 333 | #475 | — | 13 | 3 | no | — |
| 334 | #475 | — | 13 | 3 | no | — |
| 335 | #475 | — | 13 | 6 | no | — |
| 336 | #475 | — | 13 | 3 | no | — |
| 337 | #475 | — | 13 | 3 | no | — |
| 338 | #475 | — | 13 | 3 | no | — |
| 339 | #475 | C2×D13 | 1 | 3 | yes | — |
| 340 | #465 | — | 13 | 6 | no | — |
| 341 | #465 | — | 13 | 6 | no | — |
| 342 | #461 | — | 13 | 3 | no | — |
| 343 | #461 | — | 13 | 3 | no | — |
| 344 | #460 | — | 13 | 1 | no | — |
| 345 | #460 | — | 13 | 3 | no | — |
| 346 | #448 | — | 13 | 3 | no | — |
| 347 | #448 | — | 13 | 3 | no | — |
| 348 | C8×Q8 | — | 13 | 1 | no | — |
| 349 | C8×Q8 | C2×D13 | 1 | 1 | yes | characteristic |
| 350 | C4×SD16 | — | 13 | 3 | no | — |
| 351 | C4×SD16 | — | 13 | 3 | no | — |
| 352 | C4×SD16 | — | 13 | 3 | no | — |
| 353 | C4×SD16 | C2×D13 | 1 | 3 | yes | — |
| 354 | C8×D4 | — | 13 | 3 | no | — |
| 355 | C8×D4 | — | 13 | 3 | no | — |
| 356 | #431 | — | 13 | 3 | no | — |
| 357 | C2×#106 | — | 13 | 6 | no | — |
| 358 | C2×C4⋊C8 | — | 13 | 3 | no | — |
| 359 | C2×#103 | — | 13 | 6 | no | — |
| 360 | C22×C13 | — | 4 | 1 | no | — |
| 361 | C22×C13 | — | 4 | 1 | no | — |
| 362 | C22×C13 | — | 4 | 1 | no | — |
| 363 | C22×C13 | C23×D4 | 1 | 1 | yes | characteristic |
| 364 | C2×D13 | — | 2 | 3 | no | — |
| 365 | C2×D13 | — | 2 | 3 | no | — |
| 366 | C2×D13 | — | 4 | 1 | no | — |
| 367 | C2×D13 | — | 4 | 1 | no | — |
| 368 | C2×D13 | — | 4 | 1 | no | — |
| 369 | C2×D13 | C22×SD16 | 1 | 6 | yes | — |
| 370 | C4×C13 | — | 2 | 3 | no | — |
| 371 | C4×C13 | — | 2 | 2 | no | — |
| 372 | C4×C13 | — | 4 | 3 | no | — |
| 373 | C4×C13 | — | 4 | 3 | no | — |
| 374 | C4×C13 | C22×SD16 | 1 | 6 | yes | — |
| 375 | C4×C13 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 376 | C4×C13 | #585 | 1 | 1 | yes | characteristic |
| 377 | Dic13 | — | 2 | 1 | no | — |
| 378 | Dic13 | — | 2 | 3 | no | — |
| 379 | Dic13 | — | 4 | 1 | no | — |
| 380 | Dic13 | — | 4 | 3 | no | — |
| 381 | Dic13 | — | 4 | 3 | no | — |
| 382 | Dic13 | C22×SD16 | 1 | 2 | yes | — |
| 383 | 2−1+4 | — | 52 | 8 | no | — |
| 384 | C2×#41 | — | 13 | 1 | no | — |
| 385 | C2×#41 | — | 26 | 3 | no | — |
| 386 | C2×#41 | — | 26 | 3 | no | — |
| 387 | C2×#41 | — | 26 | 3 | no | — |
| 388 | C22×Q8 | — | 2 | 1 | no | — |
| 389 | C22×Q8 | — | 13 | 3 | no | — |
| 390 | C22×Q8 | — | 26 | 3 | no | — |
| 391 | C22×Q8 | — | 26 | 1 | no | — |
| 392 | C2×SD16 | — | 13 | 1 | no | — |
| 393 | C2×SD16 | — | 13 | 3 | no | — |
| 394 | C2×SD16 | — | 13 | 3 | no | — |
| 395 | C2×SD16 | C22×D13 | 1 | 1 | yes | characteristic |
| 396 | C22×C8 | — | 13 | 6 | no | — |
| 397 | C4⋊Q8 | — | 2 | 3 | no | — |
| 398 | C4⋊Q8 | — | 13 | 3 | no | — |
| 399 | C4⋊Q8 | — | 13 | 3 | no | — |
| 400 | C4⋊Q8 | — | 13 | 3 | no | — |
| 401 | C4⋊Q8 | — | 26 | 3 | no | — |
| 402 | C4⋊Q8 | — | 26 | 3 | no | — |
| 403 | C4⋊Q8 | — | 26 | 3 | no | — |
| 404 | C4⋊Q8 | C22×D13 | 1 | 3 | yes | — |
| 405 | C4⋊Q8 | C22×D13 | 1 | 3 | yes | — |
| 406 | #127 | — | 13 | 1 | no | — |
| 407 | #125 | — | 26 | 3 | no | — |
| 408 | #125 | — | 26 | 3 | no | — |
| 409 | #125 | — | 26 | 3 | no | — |
| 410 | #124 | — | 26 | 3 | no | — |
| 411 | #123 | — | 26 | 6 | no | — |
| 412 | #123 | — | 26 | 6 | no | — |
| 413 | C22⋊Q8 | — | 2 | 3 | no | — |
| 414 | C22⋊Q8 | — | 13 | 6 | no | — |
| 415 | C22⋊Q8 | — | 26 | 6 | no | — |
| 416 | C22⋊Q8 | — | 26 | 6 | no | — |
| 417 | C22⋊Q8 | — | 26 | 3 | no | — |
| 418 | C22⋊Q8 | — | 26 | 3 | no | — |
| 419 | C22⋊Q8 | — | 26 | 3 | no | — |
| 420 | C22⋊Q8 | — | 26 | 3 | no | — |
| 421 | #121 | — | 13 | 3 | no | — |
| 422 | #121 | — | 13 | 3 | no | — |
| 423 | #121 | — | 26 | 3 | no | — |
| 424 | C4×Q8 | — | 2 | 1 | no | — |
| 425 | C4×Q8 | — | 13 | 1 | no | — |
| 426 | C4×Q8 | — | 13 | 1 | no | — |
| 427 | C4×Q8 | — | 13 | 3 | no | — |
| 428 | C4×Q8 | — | 13 | 3 | no | — |
| 429 | C4×Q8 | — | 26 | 3 | no | — |
| 430 | C4×Q8 | — | 26 | 3 | no | — |
| 431 | C4×Q8 | — | 26 | 3 | no | — |
| 432 | C4×Q8 | — | 26 | 1 | no | — |
| 433 | C4×Q8 | C22×D13 | 1 | 3 | yes | — |
| 434 | C4×Q8 | C22×D13 | 1 | 1 | yes | characteristic |
| 435 | C4×D4 | — | 13 | 3 | no | — |
| 436 | C4×D4 | — | 13 | 3 | no | — |
| 437 | C4×D4 | — | 13 | 3 | no | — |
| 438 | C4×D4 | — | 26 | 3 | no | — |
| 439 | C4×D4 | — | 26 | 3 | no | — |
| 440 | C4×D4 | — | 26 | 3 | no | — |
| 441 | C4×D4 | C22×D13 | 1 | 3 | yes | — |
| 442 | #117 | — | 13 | 3 | no | — |
| 443 | #117 | — | 26 | 3 | no | — |
| 444 | C2×C4⋊C4 | — | 13 | 3 | no | — |
| 445 | C2×C4⋊C4 | — | 13 | 6 | no | — |
| 446 | C2×C4⋊C4 | — | 26 | 3 | no | — |
| 447 | C2×C4⋊C4 | — | 26 | 3 | no | — |
| 448 | C2×C42 | — | 13 | 3 | no | — |
| 449 | C2×C42 | — | 26 | 3 | no | — |
| 450 | #106 | — | 13 | 3 | no | — |
| 451 | #106 | — | 13 | 3 | no | — |
| 452 | #106 | — | 13 | 6 | no | — |
| 453 | #106 | — | 13 | 3 | no | — |
| 454 | #106 | C22×D13 | 1 | 6 | yes | — |
| 455 | #106 | C22×D13 | 1 | 3 | yes | — |
| 456 | C4⋊C8 | — | 13 | 3 | no | — |
| 457 | C4⋊C8 | — | 13 | 1 | no | — |
| 458 | C4⋊C8 | — | 13 | 3 | no | — |
| 459 | C4⋊C8 | C22×D13 | 1 | 3 | yes | — |
| 460 | #103 | — | 13 | 3 | no | — |
| 461 | #103 | — | 13 | 6 | no | — |
| 462 | #103 | — | 13 | 3 | no | — |
| 463 | #103 | — | 13 | 6 | no | — |
| 464 | #103 | — | 13 | 3 | no | — |
| 465 | #103 | C22×D13 | 1 | 3 | yes | — |
| 466 | #102 | — | 13 | 1 | no | — |
| 467 | #102 | — | 13 | 1 | no | — |
| 468 | #102 | — | 13 | 3 | no | — |
| 469 | #102 | C22×D13 | 1 | 3 | yes | — |
| 470 | C22⋊C8 | — | 13 | 3 | no | — |
| 471 | C22⋊C8 | — | 13 | 3 | no | — |
| 472 | C4×C8 | — | 13 | 3 | no | — |
| 473 | C4×C8 | C22×D13 | 1 | 3 | yes | — |
| 474 | C2×C13 | — | 8 | 1 | no | — |
| 475 | C2×C13 | #3489 | 1 | 1 | yes | characteristic |
| 476 | C2×C13 | C23×SD16 | 1 | 1 | yes | characteristic |
| 477 | C2×C13 | #3586 | 1 | 1 | yes | characteristic |
| 478 | D13 | — | 2 | 6 | no | — |
| 479 | D13 | — | 8 | 1 | no | — |
| 480 | #41 | — | 13 | 8 | no | — |
| 481 | #41 | — | 52 | 12 | no | — |
| 482 | #41 | — | 52 | 12 | no | — |
| 483 | #41 | — | 52 | 12 | no | — |
| 484 | C2×Q8 | — | 2 | 3 | no | — |
| 485 | C2×Q8 | — | 2 | 3 | no | — |
| 486 | C2×Q8 | — | 4 | 4 | no | — |
| 487 | C2×Q8 | — | 13 | 3 | no | — |
| 488 | C2×Q8 | — | 26 | 3 | no | — |
| 489 | C2×Q8 | — | 26 | 3 | no | — |
| 490 | C2×Q8 | — | 26 | 3 | no | — |
| 491 | C2×Q8 | — | 26 | 6 | no | — |
| 492 | C2×Q8 | — | 52 | 12 | no | — |
| 493 | C2×Q8 | — | 52 | 3 | no | — |
| 494 | C2×Q8 | — | 52 | 4 | no | — |
| 495 | C2×Q8 | D4×D13 | 1 | 1 | yes | characteristic |
| 496 | C2×Q8 | C23×D13 | 1 | 1 | yes | characteristic |
| 497 | C2×D4 | — | 13 | 3 | no | — |
| 498 | C2×D4 | — | 13 | 1 | no | — |
| 499 | C2×D4 | — | 26 | 3 | no | — |
| 500 | C2×D4 | — | 26 | 1 | no | — |
| 501 | C2×D4 | — | 26 | 1 | no | — |
| 502 | C2×D4 | — | 26 | 3 | no | — |
| 503 | C2×D4 | C23×D13 | 1 | 1 | yes | characteristic |
| 504 | C22×C4 | — | 2 | 3 | no | — |
| 505 | C22×C4 | — | 13 | 3 | no | — |
| 506 | C22×C4 | — | 13 | 3 | no | — |
| 507 | C22×C4 | — | 13 | 3 | no | — |
| 508 | C22×C4 | — | 26 | 3 | no | — |
| 509 | C22×C4 | — | 26 | 6 | no | — |
| 510 | C22×C4 | — | 26 | 3 | no | — |
| 511 | C22×C4 | — | 26 | 3 | no | — |
| 512 | SD16 | — | 2 | 2 | no | — |
| 513 | SD16 | — | 26 | 2 | no | — |
| 514 | SD16 | — | 52 | 3 | no | — |
| 515 | SD16 | — | 52 | 3 | no | — |
| 516 | C2×C8 | — | 13 | 1 | no | — |
| 517 | C2×C8 | — | 13 | 3 | no | — |
| 518 | C2×C8 | — | 52 | 6 | no | — |
| 519 | C2×C8 | C23×D13 | 1 | 1 | yes | characteristic |
| 520 | C2×C8 | C23×D13 | 1 | 3 | yes | — |
| 521 | C4⋊C4 | — | 2 | 3 | no | — |
| 522 | C4⋊C4 | — | 2 | 3 | no | — |
| 523 | C4⋊C4 | — | 2 | 3 | no | — |
| 524 | C4⋊C4 | — | 13 | 3 | no | — |
| 525 | C4⋊C4 | — | 13 | 1 | no | — |
| 526 | C4⋊C4 | — | 13 | 3 | no | — |
| 527 | C4⋊C4 | — | 26 | 3 | no | — |
| 528 | C4⋊C4 | — | 26 | 6 | no | — |
| 529 | C4⋊C4 | — | 26 | 1 | no | — |
| 530 | C4⋊C4 | — | 26 | 3 | no | — |
| 531 | C4⋊C4 | — | 26 | 3 | no | — |
| 532 | C4⋊C4 | — | 26 | 6 | no | — |
| 533 | C4⋊C4 | — | 26 | 3 | no | — |
| 534 | C4⋊C4 | — | 26 | 3 | no | — |
| 535 | C4⋊C4 | — | 26 | 3 | no | — |
| 536 | C4⋊C4 | — | 26 | 3 | no | — |
| 537 | C4⋊C4 | D4×D13 | 1 | 3 | yes | — |
| 538 | C4⋊C4 | C23×D13 | 1 | 3 | yes | — |
| 539 | C4⋊C4 | C23×D13 | 1 | 3 | yes | — |
| 540 | C22⋊C4 | — | 2 | 3 | no | — |
| 541 | C22⋊C4 | — | 13 | 6 | no | — |
| 542 | C22⋊C4 | — | 26 | 3 | no | — |
| 543 | C22⋊C4 | — | 26 | 6 | no | — |
| 544 | C22⋊C4 | — | 26 | 3 | no | — |
| 545 | C22⋊C4 | — | 26 | 3 | no | — |
| 546 | C42 | — | 2 | 3 | no | — |
| 547 | C42 | — | 13 | 3 | no | — |
| 548 | C42 | — | 13 | 3 | no | — |
| 549 | C42 | — | 13 | 1 | no | — |
| 550 | C42 | — | 26 | 1 | no | — |
| 551 | C42 | — | 26 | 3 | no | — |
| 552 | C42 | — | 26 | 3 | no | — |
| 553 | C42 | C23×D13 | 1 | 3 | yes | — |
| 554 | C13 | #62099 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 555 | C23 | — | 2 | 1 | no | — |
| 556 | C23 | — | 13 | 3 | no | — |
| 557 | C23 | — | 26 | 1 | no | — |
| 558 | Q8 | — | 2 | 1 | no | — |
| 559 | Q8 | — | 4 | 6 | no | — |
| 560 | Q8 | — | 8 | 3 | no | — |
| 561 | Q8 | — | 26 | 3 | no | — |
| 562 | Q8 | — | 26 | 3 | no | — |
| 563 | Q8 | — | 52 | 6 | no | — |
| 564 | Q8 | — | 52 | 6 | no | — |
| 565 | Q8 | — | 52 | 6 | no | — |
| 566 | Q8 | SD16×D13 | 1 | 4 | yes | — |
| 567 | Q8 | #88254 | 1 | 2 | yes | complemented |
| 568 | D4 | — | 2 | 1 | no | — |
| 569 | D4 | — | 2 | 1 | no | — |
| 570 | D4 | — | 13 | 12 | no | — |
| 571 | D4 | — | 26 | 1 | no | — |
| 572 | D4 | — | 26 | 1 | no | — |
| 573 | D4 | — | 52 | 6 | no | — |
| 574 | D4 | — | 52 | 2 | no | — |
| 575 | D4 | — | 52 | 2 | no | — |
| 576 | D4 | — | 52 | 6 | no | — |
| 577 | C2×C4 | — | 2 | 1 | no | — |
| 578 | C2×C4 | — | 2 | 3 | no | — |
| 579 | C2×C4 | — | 2 | 3 | no | — |
| 580 | C2×C4 | — | 4 | 6 | no | — |
| 581 | C2×C4 | — | 13 | 1 | no | — |
| 582 | C2×C4 | — | 13 | 12 | no | — |
| 583 | C2×C4 | — | 13 | 1 | no | — |
| 584 | C2×C4 | — | 13 | 3 | no | — |
| 585 | C2×C4 | — | 26 | 3 | no | — |
| 586 | C2×C4 | — | 26 | 3 | no | — |
| 587 | C2×C4 | — | 26 | 1 | no | — |
| 588 | C2×C4 | — | 26 | 3 | no | — |
| 589 | C2×C4 | — | 26 | 3 | no | — |
| 590 | C2×C4 | — | 52 | 3 | no | — |
| 591 | C2×C4 | — | 52 | 6 | no | — |
| 592 | C2×C4 | — | 52 | 12 | no | — |
| 593 | C2×C4 | — | 52 | 6 | no | — |
| 594 | C2×C4 | — | 104 | 3 | no | — |
| 595 | C2×C4 | C2×D4×D13 | 1 | 3 | yes | — |
| 596 | C2×C4 | C2×D4×D13 | 1 | 3 | yes | — |
| 597 | C2×C4 | C24×D13 | 1 | 1 | yes | characteristic |
| 598 | C8 | — | 2 | 1 | no | — |
| 599 | C8 | — | 2 | 3 | no | — |
| 600 | C8 | — | 26 | 1 | no | — |
| 601 | C8 | — | 26 | 3 | no | — |
| 602 | C22 | — | 4 | 1 | no | — |
| 603 | C22 | — | 4 | 1 | no | — |
| 604 | C22 | — | 4 | 1 | no | — |
| 605 | C22 | — | 13 | 6 | no | — |
| 606 | C22 | — | 26 | 3 | no | — |
| 607 | C22 | — | 26 | 3 | no | — |
| 608 | C22 | — | 52 | 1 | no | — |
| 609 | C22 | — | 52 | 1 | no | — |
| 610 | C22 | — | 52 | 1 | no | — |
| 611 | C22 | C22×D4×D13 | 1 | 1 | yes | characteristic |
| 612 | C4 | — | 2 | 2 | no | — |
| 613 | C4 | — | 2 | 3 | no | — |
| 614 | C4 | — | 4 | 3 | no | — |
| 615 | C4 | — | 4 | 3 | no | — |
| 616 | C4 | — | 13 | 2 | no | — |
| 617 | C4 | — | 26 | 3 | no | — |
| 618 | C4 | — | 26 | 1 | no | — |
| 619 | C4 | — | 52 | 3 | no | — |
| 620 | C4 | — | 52 | 3 | no | — |
| 621 | C4 | — | 52 | 1 | no | — |
| 622 | C4 | C2×SD16×D13 | 1 | 6 | yes | — |
| 623 | C4 | C2×#88254 | 1 | 1 | yes | characteristic |
| 624 | C4 | #11719652 | 1 | 1 | yes | characteristic |
| 625 | C2 | — | 8 | 1 | no | — |
| 626 | C2 | — | 26 | 6 | no | — |
| 627 | C2 | — | 104 | 1 | no | — |
| 628 | C2 | #13128513 | 1 | 1 | yes | characteristic |
| 629 | C2 | C22×SD16×D13 | 1 | 1 | yes | characteristic |
| 630 | C2 | #13129618 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q8×#6131 | C2 | semidirect |
| 3. Q8×#6106 | C2 | semidirect |
| 4. #13127479 | C2 | semidirect |
| 5. #13127478 | C2 | semidirect |
| 6. #13127192 | C2 | semidirect |
| 7. #13127190 | C2 | semidirect |
| 8. #13126703 | C2 | semidirect |
| 9. #13126698 | C2 | semidirect |
| 10. #13126154 | C2 | semidirect |
| 11. #13125981 | C2 | semidirect |
| 12. #13124865 | C2 | semidirect |
| 13. D13×#475 | C2 | semidirect |
| 14. #13123946 | C2 | semidirect |
| 15. Q8×C13×SD16 | C2 | semidirect |
| 177. #6131 | SD16 | semidirect |
| 243. Q8×SD16 | D13 | semidirect |
| 262. Q8×C13 | 2−1+4 | semidirect |
| 554. C13 | #62099 | semidirect |
| 567. Q8 | #88254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13128620 | 2 |
| Q8×#6131 | 2 |
| Q8×#6106 | 2 |
| #13127479 | 2 |
| #13127478 | 2 |
| #13127192 | 2 |
| #13127190 | 2 |
| #13126703 | 2 |
| #13126698 | 2 |
| #13126154 | 2 |
| #13125981 | 2 |
| #13124865 | 2 |
| D13×#475 | 2 |
| #13123946 | 2 |
| Q8×C13×SD16 | 2 |
| #62099 | 13 |