Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1694 conjugacy classes of subgroups.
The subgroup lattice has 610 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13128927 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | Q8×#6131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13127726 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #13127716 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | Q8×#6104 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13127519 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #13127514 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13127484 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #13127479 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #13126014 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #13125998 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #13124910 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | #13124852 | C2 | 1 | 3 | yes | maximal |
| 14 | #13123915 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | Q8×C13×SD16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | Q82×C13 | C22 | 1 | 1 | yes | characteristic |
| 17 | D4×Q8×C13 | C22 | 1 | 1 | yes | characteristic |
| 18 | Q8×C22⋊D13 | — | 2 | 1 | no | — |
| 19 | #11719517 | — | 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 | #11719433 | C22 | 1 | 3 | yes | — |
| 25 | #11719426 | C22 | 1 | 3 | yes | — |
| 26 | #11719344 | — | 2 | 3 | no | — |
| 27 | #11719330 | — | 2 | 3 | no | — |
| 28 | Q8×D52 | — | 2 | 1 | no | — |
| 29 | Q8×D52 | C22 | 1 | 1 | yes | characteristic |
| 30 | C4×#6131 | C22 | 1 | 3 | yes | — |
| 31 | C4×Q8×D13 | — | 2 | 1 | no | — |
| 32 | C4×Q8×D13 | C22 | 1 | 1 | yes | characteristic |
| 33 | #11719275 | C22 | 1 | 3 | yes | — |
| 34 | #11719275 | C22 | 1 | 1 | yes | characteristic |
| 35 | #11719262 | C22 | 1 | 3 | yes | — |
| 36 | #11719247 | 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 | #11718833 | C22 | 1 | 1 | yes | characteristic |
| 43 | #11718827 | C22 | 1 | 3 | yes | — |
| 44 | #11718754 | C22 | 1 | 3 | yes | — |
| 45 | #11718752 | C22 | 1 | 3 | yes | — |
| 46 | #11718748 | C22 | 1 | 3 | yes | — |
| 47 | #11718739 | C22 | 1 | 3 | yes | — |
| 48 | #11718692 | C22 | 1 | 3 | yes | — |
| 49 | C4×#6107 | C22 | 1 | 3 | yes | — |
| 50 | Q8×#1055 | C22 | 1 | 1 | yes | characteristic |
| 51 | C4×#6104 | C22 | 1 | 3 | yes | — |
| 52 | #11718668 | C22 | 1 | 3 | yes | — |
| 53 | #11718532 | C22 | 1 | 3 | yes | — |
| 54 | #11718528 | C22 | 1 | 6 | yes | — |
| 55 | #11718528 | C22 | 1 | 3 | yes | — |
| 56 | #11718519 | C22 | 1 | 6 | yes | — |
| 57 | #11718518 | C22 | 1 | 6 | yes | — |
| 58 | #11718518 | C22 | 1 | 6 | yes | — |
| 59 | #11718513 | C22 | 1 | 6 | yes | — |
| 60 | #11718512 | C22 | 1 | 3 | yes | — |
| 61 | #11718502 | C22 | 1 | 3 | yes | — |
| 62 | #11718494 | C22 | 1 | 3 | yes | — |
| 63 | #11718491 | C22 | 1 | 3 | yes | — |
| 64 | #11718471 | C22 | 1 | 3 | yes | — |
| 65 | #11718460 | C22 | 1 | 3 | yes | — |
| 66 | #11718451 | C22 | 1 | 6 | yes | — |
| 67 | #11718448 | C22 | 1 | 3 | yes | — |
| 68 | #11718440 | C22 | 1 | 3 | yes | — |
| 69 | #11718429 | C22 | 1 | 6 | yes | — |
| 70 | C4×#6095 | C22 | 1 | 3 | yes | — |
| 71 | #11718346 | C22 | 1 | 3 | yes | — |
| 72 | #11718342 | C22 | 1 | 3 | yes | — |
| 73 | C8×Dic26 | C22 | 1 | 3 | yes | — |
| 74 | C22×Q8×C13 | — | 2 | 1 | no | — |
| 75 | C2×#6131 | C23 | 1 | 1 | yes | characteristic |
| 76 | C2×Q8×D13 | — | 2 | 1 | no | — |
| 77 | C2×Q8×D13 | D4 | 1 | 1 | yes | characteristic |
| 78 | C2×C13×SD16 | C23 | 1 | 1 | yes | characteristic |
| 79 | C13×C4⋊Q8 | — | 2 | 3 | no | — |
| 80 | C13×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 81 | C13×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 82 | C13×C22⋊Q8 | — | 2 | 3 | no | — |
| 83 | C4×Q8×C13 | — | 2 | 1 | no | — |
| 84 | C4×Q8×C13 | C23 | 1 | 3 | yes | — |
| 85 | C4×Q8×C13 | C23 | 1 | 1 | yes | characteristic |
| 86 | C4×D4×C13 | C23 | 1 | 3 | yes | — |
| 87 | #88200 | — | 2 | 3 | no | — |
| 88 | #88200 | — | 2 | 3 | no | — |
| 89 | #88200 | — | 2 | 6 | no | — |
| 90 | Q8×Dic13 | — | 2 | 1 | no | — |
| 91 | Q8×Dic13 | — | 2 | 3 | no | — |
| 92 | Q8×Dic13 | — | 2 | 3 | no | — |
| 93 | Q8×Dic13 | — | 2 | 3 | no | — |
| 94 | Q8×Dic13 | D4 | 1 | 1 | yes | characteristic |
| 95 | Q8×Dic13 | C23 | 1 | 3 | yes | — |
| 96 | #88198 | — | 2 | 3 | no | — |
| 97 | C2×#6107 | C23 | 1 | 3 | yes | — |
| 98 | #88192 | C23 | 1 | 1 | yes | characteristic |
| 99 | #88190 | C23 | 1 | 3 | yes | — |
| 100 | C2×#6104 | C23 | 1 | 1 | yes | characteristic |
| 101 | C4×C22⋊D13 | — | 2 | 3 | no | — |
| 102 | #88180 | — | 2 | 3 | no | — |
| 103 | #88180 | — | 2 | 3 | no | — |
| 104 | #88178 | — | 2 | 3 | no | — |
| 105 | C2×#6095 | C23 | 1 | 3 | yes | — |
| 106 | #88151 | — | 2 | 3 | no | — |
| 107 | #88151 | — | 2 | 3 | no | — |
| 108 | #88151 | — | 2 | 3 | no | — |
| 109 | #88151 | C23 | 1 | 3 | yes | — |
| 110 | #88147 | — | 2 | 3 | no | — |
| 111 | #88147 | C23 | 1 | 3 | yes | — |
| 112 | #88146 | — | 2 | 3 | no | — |
| 113 | #88146 | — | 2 | 3 | no | — |
| 114 | #88146 | C23 | 1 | 3 | yes | — |
| 115 | C4⋊C4×D13 | — | 2 | 3 | no | — |
| 116 | C4⋊C4×D13 | D4 | 1 | 3 | yes | — |
| 117 | #88144 | — | 2 | 3 | no | — |
| 118 | #88144 | — | 2 | 6 | no | — |
| 119 | #88144 | — | 2 | 3 | no | — |
| 120 | #88144 | C23 | 1 | 3 | yes | — |
| 121 | #88144 | C23 | 1 | 6 | yes | — |
| 122 | #88143 | — | 2 | 6 | no | — |
| 123 | #88141 | — | 2 | 3 | no | — |
| 124 | #88141 | D4 | 1 | 3 | yes | — |
| 125 | #88141 | C23 | 1 | 6 | yes | — |
| 126 | #88137 | — | 2 | 3 | no | — |
| 127 | #88133 | — | 2 | 6 | no | — |
| 128 | #88133 | — | 2 | 3 | no | — |
| 129 | C4×D52 | — | 2 | 3 | no | — |
| 130 | C4×D52 | C23 | 1 | 3 | yes | — |
| 131 | C42×D13 | — | 2 | 3 | no | — |
| 132 | C42×D13 | C23 | 1 | 3 | yes | — |
| 133 | #88123 | — | 2 | 3 | no | — |
| 134 | #88123 | C23 | 1 | 3 | yes | — |
| 135 | #88123 | C23 | 1 | 3 | yes | — |
| 136 | C4×Dic26 | — | 2 | 3 | no | — |
| 137 | C4×Dic26 | C23 | 1 | 3 | yes | — |
| 138 | C4×Dic26 | C23 | 1 | 3 | yes | — |
| 139 | C13×#106 | C23 | 1 | 3 | yes | — |
| 140 | C13×#106 | C23 | 1 | 6 | yes | — |
| 141 | C13×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 142 | C13×#103 | C23 | 1 | 3 | yes | — |
| 143 | C13×#102 | C23 | 1 | 3 | yes | — |
| 144 | C4×C8×C13 | C23 | 1 | 3 | yes | — |
| 145 | #88075 | C23 | 1 | 1 | yes | characteristic |
| 146 | #88072 | C23 | 1 | 3 | yes | — |
| 147 | #88061 | C23 | 1 | 1 | yes | characteristic |
| 148 | #88060 | C23 | 1 | 3 | yes | — |
| 149 | #88060 | C23 | 1 | 1 | yes | characteristic |
| 150 | #88057 | C23 | 1 | 3 | yes | — |
| 151 | #88056 | C23 | 1 | 6 | yes | — |
| 152 | #88056 | C23 | 1 | 3 | yes | — |
| 153 | #88054 | C23 | 1 | 3 | yes | — |
| 154 | #88054 | C23 | 1 | 3 | yes | — |
| 155 | C8×Dic13 | C23 | 1 | 6 | yes | — |
| 156 | #88050 | C23 | 1 | 6 | yes | — |
| 157 | #88050 | C23 | 1 | 3 | yes | — |
| 158 | #88049 | C23 | 1 | 3 | yes | — |
| 159 | #88047 | C23 | 1 | 6 | yes | — |
| 160 | #88047 | C23 | 1 | 3 | yes | — |
| 161 | #88047 | C23 | 1 | 3 | yes | — |
| 162 | C4⋊#1055 | C23 | 1 | 3 | yes | — |
| 163 | C4×#1055 | C23 | 1 | 3 | yes | — |
| 164 | #61824 | — | 13 | 1 | no | maximal, Sylow |
| 165 | C2×Q8×C13 | — | 2 | 3 | no | — |
| 166 | C2×Q8×C13 | — | 2 | 3 | no | — |
| 167 | C2×Q8×C13 | — | 4 | 4 | no | — |
| 168 | C2×Q8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 169 | C2×Q8×C13 | C24 | 1 | 1 | yes | characteristic |
| 170 | C2×D4×C13 | C24 | 1 | 1 | yes | characteristic |
| 171 | C22×C4×C13 | — | 2 | 3 | no | — |
| 172 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 173 | #6131 | — | 2 | 2 | no | — |
| 174 | #6131 | — | 2 | 2 | no | — |
| 175 | Q8×D13 | — | 2 | 4 | no | — |
| 176 | Q8×D13 | — | 4 | 4 | no | — |
| 177 | C2×D52 | — | 2 | 1 | no | — |
| 178 | C2×D52 | C24 | 1 | 1 | yes | characteristic |
| 179 | C2×C4×D13 | — | 2 | 1 | no | — |
| 180 | C2×C4×D13 | — | 2 | 3 | no | — |
| 181 | C2×C4×D13 | — | 2 | 3 | no | — |
| 182 | C2×C4×D13 | C2×D4 | 1 | 3 | yes | — |
| 183 | C2×C4×D13 | C2×D4 | 1 | 3 | yes | — |
| 184 | C2×C4×D13 | C24 | 1 | 1 | yes | characteristic |
| 185 | C2×Dic26 | — | 2 | 3 | no | — |
| 186 | C2×Dic26 | C2×D4 | 1 | 3 | yes | — |
| 187 | C2×Dic26 | C24 | 1 | 3 | yes | — |
| 188 | C13×SD16 | — | 2 | 2 | no | — |
| 189 | C2×C8×C13 | C24 | 1 | 1 | yes | characteristic |
| 190 | C2×C8×C13 | C24 | 1 | 3 | yes | — |
| 191 | C13×C4⋊C4 | — | 2 | 3 | no | — |
| 192 | C13×C4⋊C4 | — | 2 | 3 | no | — |
| 193 | C13×C4⋊C4 | — | 2 | 3 | no | — |
| 194 | C13×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 195 | C13×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 196 | C13×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 197 | C13×C22⋊C4 | — | 2 | 3 | no | — |
| 198 | C42×C13 | — | 2 | 3 | no | — |
| 199 | C42×C13 | C24 | 1 | 3 | yes | — |
| 200 | C22⋊Dic13 | — | 2 | 3 | no | — |
| 201 | C22⋊Dic13 | — | 2 | 1 | no | — |
| 202 | C22⋊Dic13 | — | 2 | 3 | no | — |
| 203 | #6107 | — | 2 | 6 | no | — |
| 204 | #6104 | — | 2 | 2 | no | — |
| 205 | #6103 | — | 2 | 3 | no | — |
| 206 | #6103 | — | 2 | 3 | no | — |
| 207 | #6103 | — | 2 | 3 | no | — |
| 208 | #6103 | — | 2 | 3 | no | — |
| 209 | C4⋊Dic13 | — | 2 | 3 | no | — |
| 210 | C4⋊Dic13 | — | 2 | 3 | no | — |
| 211 | C4⋊Dic13 | — | 2 | 3 | no | — |
| 212 | C4⋊Dic13 | — | 2 | 3 | no | — |
| 213 | C4⋊Dic13 | — | 2 | 6 | no | — |
| 214 | C4⋊Dic13 | — | 2 | 3 | no | — |
| 215 | C4⋊Dic13 | — | 2 | 3 | no | — |
| 216 | C4⋊Dic13 | C2×D4 | 1 | 3 | yes | — |
| 217 | C4⋊Dic13 | C24 | 1 | 3 | yes | — |
| 218 | C4⋊Dic13 | C24 | 1 | 1 | yes | characteristic |
| 219 | #6101 | — | 2 | 3 | no | — |
| 220 | #6101 | — | 2 | 6 | no | — |
| 221 | #6101 | — | 2 | 6 | no | — |
| 222 | #6101 | — | 2 | 3 | no | — |
| 223 | #6101 | C2×D4 | 1 | 6 | yes | — |
| 224 | C4×Dic13 | — | 2 | 3 | no | — |
| 225 | C4×Dic13 | — | 2 | 3 | no | — |
| 226 | C4×Dic13 | — | 2 | 3 | no | — |
| 227 | C4×Dic13 | — | 2 | 6 | no | — |
| 228 | C4×Dic13 | C2×D4 | 1 | 3 | yes | — |
| 229 | C4×Dic13 | C2×D4 | 1 | 3 | yes | — |
| 230 | C4×Dic13 | C24 | 1 | 3 | yes | — |
| 231 | C2×#1055 | C24 | 1 | 3 | yes | — |
| 232 | C2×#1055 | C24 | 1 | 1 | yes | characteristic |
| 233 | #6095 | — | 2 | 6 | no | — |
| 234 | #3523 | — | 13 | 1 | no | — |
| 235 | Q8×#41 | — | 13 | 1 | no | — |
| 236 | #3383 | — | 13 | 3 | no | — |
| 237 | #3381 | — | 13 | 3 | no | — |
| 238 | Q8×SD16 | D13 | 1 | 1 | yes | characteristic, complemented |
| 239 | Q8×D8 | — | 13 | 1 | no | — |
| 240 | #3364 | — | 13 | 3 | no | — |
| 241 | #3363 | — | 13 | 1 | no | — |
| 242 | #3360 | — | 13 | 3 | no | — |
| 243 | #3359 | — | 13 | 1 | no | — |
| 244 | #3233 | — | 13 | 3 | no | — |
| 245 | #3231 | — | 13 | 3 | no | — |
| 246 | #3107 | — | 13 | 3 | no | — |
| 247 | #3102 | — | 13 | 3 | no | — |
| 248 | #2982 | — | 13 | 1 | no | — |
| 249 | C23×C13 | — | 2 | 1 | no | — |
| 250 | C22×D13 | — | 2 | 1 | no | — |
| 251 | C22×D13 | C22×D4 | 1 | 1 | yes | characteristic |
| 252 | Q8×C13 | — | 2 | 1 | no | — |
| 253 | Q8×C13 | — | 4 | 6 | no | — |
| 254 | Q8×C13 | — | 8 | 3 | no | — |
| 255 | Q8×C13 | #135 | 1 | 4 | yes | — |
| 256 | Q8×C13 | 2−1+4 | 1 | 2 | yes | — |
| 257 | D4×C13 | — | 2 | 1 | no | — |
| 258 | D4×C13 | — | 2 | 1 | no | — |
| 259 | C2×C4×C13 | — | 2 | 1 | no | — |
| 260 | C2×C4×C13 | — | 2 | 3 | no | — |
| 261 | C2×C4×C13 | — | 2 | 3 | no | — |
| 262 | C2×C4×C13 | — | 4 | 6 | no | — |
| 263 | C2×C4×C13 | C22×D4 | 1 | 3 | yes | — |
| 264 | C2×C4×C13 | C22×D4 | 1 | 3 | yes | — |
| 265 | C2×C4×C13 | C25 | 1 | 1 | yes | characteristic |
| 266 | C22⋊D13 | — | 4 | 2 | no | — |
| 267 | C2×Dic13 | — | 2 | 1 | no | — |
| 268 | C2×Dic13 | — | 2 | 3 | no | — |
| 269 | C2×Dic13 | — | 2 | 3 | no | — |
| 270 | C2×Dic13 | C22×D4 | 1 | 1 | yes | characteristic |
| 271 | C2×Dic13 | C22×D4 | 1 | 3 | yes | — |
| 272 | C2×Dic13 | C22×D4 | 1 | 3 | yes | — |
| 273 | D52 | — | 2 | 4 | no | — |
| 274 | D52 | — | 2 | 1 | no | — |
| 275 | D52 | 2−1+4 | 1 | 2 | yes | — |
| 276 | C4×D13 | — | 2 | 4 | no | — |
| 277 | C4×D13 | — | 2 | 6 | no | — |
| 278 | C4×D13 | — | 2 | 1 | no | — |
| 279 | C4×D13 | — | 2 | 1 | no | — |
| 280 | C4×D13 | — | 4 | 3 | no | — |
| 281 | C4×D13 | — | 4 | 6 | no | — |
| 282 | C4×D13 | — | 8 | 3 | no | — |
| 283 | Dic26 | — | 2 | 6 | no | — |
| 284 | Dic26 | — | 2 | 3 | no | — |
| 285 | Dic26 | — | 2 | 3 | no | — |
| 286 | Dic26 | — | 4 | 6 | no | — |
| 287 | C8×C13 | — | 2 | 3 | no | — |
| 288 | C8×C13 | — | 2 | 1 | no | — |
| 289 | #1055 | — | 2 | 1 | no | — |
| 290 | #1055 | — | 2 | 3 | no | — |
| 291 | Q82 | C2×D13 | 1 | 1 | yes | characteristic |
| 292 | #557 | — | 13 | 3 | no | — |
| 293 | #557 | — | 13 | 3 | no | — |
| 294 | #557 | — | 13 | 1 | no | — |
| 295 | #556 | — | 13 | 3 | no | — |
| 296 | #554 | — | 13 | 3 | no | — |
| 297 | #554 | — | 26 | 3 | no | — |
| 298 | #552 | — | 26 | 3 | no | — |
| 299 | D4×Q8 | — | 13 | 1 | no | — |
| 300 | D4×Q8 | — | 26 | 1 | no | — |
| 301 | D4×Q8 | — | 26 | 1 | no | — |
| 302 | D4×Q8 | C2×D13 | 1 | 1 | yes | characteristic |
| 303 | #541 | — | 26 | 3 | no | — |
| 304 | #533 | — | 13 | 3 | no | — |
| 305 | #533 | — | 13 | 3 | no | — |
| 306 | #533 | — | 26 | 3 | no | — |
| 307 | #529 | — | 13 | 3 | no | — |
| 308 | #519 | — | 26 | 1 | no | — |
| 309 | C4×#41 | — | 13 | 3 | no | — |
| 310 | C2×C4×Q8 | — | 13 | 1 | no | — |
| 311 | C2×C4×Q8 | — | 26 | 1 | no | — |
| 312 | #500 | — | 13 | 3 | no | — |
| 313 | #499 | — | 13 | 6 | no | — |
| 314 | #498 | C2×D13 | 1 | 3 | yes | — |
| 315 | #488 | — | 13 | 6 | no | — |
| 316 | #487 | — | 13 | 3 | no | — |
| 317 | #487 | — | 13 | 3 | no | — |
| 318 | #485 | — | 13 | 3 | no | — |
| 319 | #485 | — | 13 | 6 | no | — |
| 320 | #482 | — | 13 | 3 | no | — |
| 321 | #479 | — | 13 | 6 | no | — |
| 322 | #479 | — | 13 | 6 | no | — |
| 323 | #479 | — | 13 | 3 | no | — |
| 324 | #478 | — | 13 | 3 | no | — |
| 325 | #477 | — | 13 | 3 | no | — |
| 326 | #476 | C2×D13 | 1 | 3 | yes | — |
| 327 | #475 | — | 13 | 3 | no | — |
| 328 | #475 | C2×D13 | 1 | 3 | yes | — |
| 329 | #474 | — | 13 | 3 | no | — |
| 330 | #474 | — | 13 | 3 | no | — |
| 331 | #464 | — | 13 | 3 | no | — |
| 332 | #463 | — | 13 | 3 | no | — |
| 333 | #462 | — | 13 | 3 | no | — |
| 334 | #461 | — | 13 | 3 | no | — |
| 335 | #452 | — | 13 | 3 | no | — |
| 336 | #449 | — | 13 | 1 | no | — |
| 337 | C8×Q8 | — | 13 | 1 | no | — |
| 338 | C8×Q8 | — | 13 | 3 | no | — |
| 339 | C8×Q8 | — | 13 | 3 | no | — |
| 340 | C8×Q8 | C2×D13 | 1 | 1 | yes | characteristic |
| 341 | C4×Q16 | — | 13 | 3 | no | — |
| 342 | C4×Q16 | — | 13 | 6 | no | — |
| 343 | C4×SD16 | — | 13 | 6 | no | — |
| 344 | C4×SD16 | — | 13 | 3 | no | — |
| 345 | C4×SD16 | C2×D13 | 1 | 3 | yes | — |
| 346 | C4×D8 | — | 13 | 3 | no | — |
| 347 | #431 | — | 13 | 3 | no | — |
| 348 | #431 | — | 13 | 3 | no | — |
| 349 | C22×C13 | — | 4 | 1 | no | — |
| 350 | C22×C13 | — | 4 | 1 | no | — |
| 351 | C22×C13 | — | 4 | 1 | no | — |
| 352 | C22×C13 | C23×D4 | 1 | 1 | yes | characteristic |
| 353 | C2×D13 | — | 2 | 1 | no | — |
| 354 | C2×D13 | — | 2 | 1 | no | — |
| 355 | C2×D13 | — | 2 | 2 | no | — |
| 356 | C2×D13 | — | 2 | 1 | no | — |
| 357 | C2×D13 | — | 4 | 1 | no | — |
| 358 | C2×D13 | — | 4 | 1 | no | — |
| 359 | C4×C13 | — | 2 | 3 | no | — |
| 360 | C4×C13 | — | 2 | 2 | no | — |
| 361 | C4×C13 | — | 4 | 3 | no | — |
| 362 | C4×C13 | — | 4 | 3 | no | — |
| 363 | C4×C13 | C2×#135 | 1 | 6 | yes | — |
| 364 | C4×C13 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 365 | C4×C13 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 366 | Dic13 | — | 2 | 3 | no | — |
| 367 | Dic13 | — | 2 | 1 | no | — |
| 368 | Dic13 | — | 2 | 3 | no | — |
| 369 | Dic13 | — | 4 | 1 | no | — |
| 370 | Dic13 | — | 4 | 3 | no | — |
| 371 | Dic13 | — | 4 | 3 | no | — |
| 372 | C2×#41 | — | 13 | 1 | no | — |
| 373 | C22×Q8 | — | 2 | 1 | no | — |
| 374 | C22×Q8 | — | 13 | 1 | no | — |
| 375 | C22×Q8 | — | 26 | 1 | no | — |
| 376 | C2×Q16 | — | 13 | 3 | no | — |
| 377 | C2×SD16 | — | 13 | 3 | no | — |
| 378 | C2×SD16 | C22×D13 | 1 | 1 | yes | characteristic |
| 379 | C2×D8 | — | 13 | 1 | no | — |
| 380 | C4⋊Q8 | — | 2 | 3 | no | — |
| 381 | C4⋊Q8 | — | 13 | 3 | no | — |
| 382 | C4⋊Q8 | — | 13 | 3 | no | — |
| 383 | C4⋊Q8 | — | 26 | 3 | no | — |
| 384 | C4⋊Q8 | — | 26 | 3 | no | — |
| 385 | C4⋊Q8 | C22×D13 | 1 | 3 | yes | — |
| 386 | C4⋊Q8 | C22×D13 | 1 | 3 | yes | — |
| 387 | #126 | — | 26 | 3 | no | — |
| 388 | #126 | — | 26 | 6 | no | — |
| 389 | #125 | — | 13 | 3 | no | — |
| 390 | #125 | — | 13 | 6 | no | — |
| 391 | #125 | — | 26 | 3 | no | — |
| 392 | #125 | — | 26 | 6 | no | — |
| 393 | #125 | — | 26 | 6 | no | — |
| 394 | #125 | — | 26 | 3 | no | — |
| 395 | #124 | — | 13 | 3 | no | — |
| 396 | #123 | — | 26 | 3 | no | — |
| 397 | C22⋊Q8 | — | 2 | 3 | no | — |
| 398 | C22⋊Q8 | — | 13 | 3 | no | — |
| 399 | C22⋊Q8 | — | 26 | 3 | no | — |
| 400 | C22⋊Q8 | — | 26 | 3 | no | — |
| 401 | C22⋊Q8 | — | 26 | 6 | no | — |
| 402 | C22⋊Q8 | — | 26 | 3 | no | — |
| 403 | C22⋊Q8 | — | 26 | 3 | no | — |
| 404 | C22⋊Q8 | — | 26 | 3 | no | — |
| 405 | C22⋊Q8 | — | 26 | 3 | no | — |
| 406 | #121 | — | 13 | 1 | no | — |
| 407 | C4×Q8 | — | 2 | 1 | no | — |
| 408 | C4×Q8 | — | 13 | 1 | no | — |
| 409 | C4×Q8 | — | 13 | 3 | no | — |
| 410 | C4×Q8 | — | 13 | 3 | no | — |
| 411 | C4×Q8 | — | 13 | 3 | no | — |
| 412 | C4×Q8 | — | 13 | 6 | no | — |
| 413 | C4×Q8 | — | 13 | 3 | no | — |
| 414 | C4×Q8 | — | 26 | 3 | no | — |
| 415 | C4×Q8 | — | 26 | 3 | no | — |
| 416 | C4×Q8 | — | 26 | 3 | no | — |
| 417 | C4×Q8 | — | 26 | 3 | no | — |
| 418 | C4×Q8 | — | 26 | 3 | no | — |
| 419 | C4×Q8 | — | 26 | 1 | no | — |
| 420 | C4×Q8 | C22×D13 | 1 | 3 | yes | — |
| 421 | C4×Q8 | C22×D13 | 1 | 1 | yes | characteristic |
| 422 | C4×D4 | — | 13 | 3 | no | — |
| 423 | C4×D4 | — | 13 | 3 | no | — |
| 424 | C4×D4 | — | 26 | 3 | no | — |
| 425 | C4×D4 | — | 26 | 3 | no | — |
| 426 | C4×D4 | — | 26 | 3 | no | — |
| 427 | C4×D4 | C22×D13 | 1 | 3 | yes | — |
| 428 | #117 | — | 13 | 3 | no | — |
| 429 | #117 | — | 26 | 3 | no | — |
| 430 | #117 | — | 26 | 3 | no | — |
| 431 | #117 | — | 26 | 3 | no | — |
| 432 | #117 | — | 26 | 3 | no | — |
| 433 | C2×C4⋊C4 | — | 13 | 3 | no | — |
| 434 | C2×C4⋊C4 | — | 26 | 3 | no | — |
| 435 | C2×C42 | — | 13 | 3 | no | — |
| 436 | C2×C42 | — | 26 | 3 | no | — |
| 437 | #107 | — | 13 | 3 | no | — |
| 438 | #107 | — | 13 | 6 | no | — |
| 439 | #107 | — | 13 | 3 | no | — |
| 440 | #106 | — | 13 | 3 | no | — |
| 441 | #106 | C22×D13 | 1 | 6 | yes | — |
| 442 | #106 | C22×D13 | 1 | 3 | yes | — |
| 443 | C4⋊C8 | — | 13 | 3 | no | — |
| 444 | C4⋊C8 | — | 13 | 3 | no | — |
| 445 | C4⋊C8 | — | 13 | 3 | no | — |
| 446 | C4⋊C8 | C22×D13 | 1 | 3 | yes | — |
| 447 | #103 | — | 13 | 1 | no | — |
| 448 | #103 | — | 13 | 3 | no | — |
| 449 | #103 | — | 13 | 6 | no | — |
| 450 | #103 | — | 13 | 6 | no | — |
| 451 | #103 | — | 13 | 3 | no | — |
| 452 | #103 | C22×D13 | 1 | 3 | yes | — |
| 453 | #102 | — | 13 | 3 | no | — |
| 454 | #102 | — | 13 | 1 | no | — |
| 455 | #102 | — | 13 | 3 | no | — |
| 456 | #102 | C22×D13 | 1 | 3 | yes | — |
| 457 | C22⋊C8 | — | 13 | 1 | no | — |
| 458 | C22⋊C8 | — | 13 | 3 | no | — |
| 459 | C4×C8 | — | 13 | 6 | no | — |
| 460 | C4×C8 | — | 13 | 3 | no | — |
| 461 | C4×C8 | C22×D13 | 1 | 3 | yes | — |
| 462 | C2×C13 | — | 8 | 1 | no | — |
| 463 | C2×C13 | #3486 | 1 | 1 | yes | characteristic |
| 464 | C2×C13 | C22×#135 | 1 | 1 | yes | characteristic |
| 465 | C2×C13 | #3586 | 1 | 1 | yes | characteristic |
| 466 | D13 | — | 4 | 1 | no | — |
| 467 | D13 | — | 4 | 2 | no | — |
| 468 | #41 | — | 26 | 2 | no | — |
| 469 | #41 | — | 26 | 2 | no | — |
| 470 | C2×Q8 | — | 2 | 3 | no | — |
| 471 | C2×Q8 | — | 2 | 3 | no | — |
| 472 | C2×Q8 | — | 4 | 4 | no | — |
| 473 | C2×Q8 | — | 13 | 3 | no | — |
| 474 | C2×Q8 | — | 13 | 3 | no | — |
| 475 | C2×Q8 | — | 26 | 4 | no | — |
| 476 | C2×Q8 | — | 26 | 3 | no | — |
| 477 | C2×Q8 | — | 52 | 4 | no | — |
| 478 | C2×Q8 | D4×D13 | 1 | 1 | yes | characteristic |
| 479 | C2×Q8 | C23×D13 | 1 | 1 | yes | characteristic |
| 480 | C2×D4 | — | 13 | 1 | no | — |
| 481 | C2×D4 | — | 26 | 1 | no | — |
| 482 | C2×D4 | — | 26 | 1 | no | — |
| 483 | C2×D4 | C23×D13 | 1 | 1 | yes | characteristic |
| 484 | C22×C4 | — | 2 | 3 | no | — |
| 485 | C22×C4 | — | 13 | 3 | no | — |
| 486 | C22×C4 | — | 13 | 1 | no | — |
| 487 | C22×C4 | — | 13 | 3 | no | — |
| 488 | C22×C4 | — | 26 | 1 | no | — |
| 489 | C22×C4 | — | 26 | 3 | no | — |
| 490 | C22×C4 | — | 26 | 3 | no | — |
| 491 | Q16 | — | 26 | 6 | no | — |
| 492 | SD16 | — | 2 | 2 | no | — |
| 493 | SD16 | — | 26 | 6 | no | — |
| 494 | D8 | — | 26 | 2 | no | — |
| 495 | C2×C8 | — | 13 | 3 | no | — |
| 496 | C2×C8 | — | 13 | 1 | no | — |
| 497 | C2×C8 | C23×D13 | 1 | 3 | yes | — |
| 498 | C2×C8 | C23×D13 | 1 | 1 | yes | characteristic |
| 499 | C4⋊C4 | — | 2 | 3 | no | — |
| 500 | C4⋊C4 | — | 2 | 3 | no | — |
| 501 | C4⋊C4 | — | 2 | 3 | no | — |
| 502 | C4⋊C4 | — | 13 | 3 | no | — |
| 503 | C4⋊C4 | — | 13 | 6 | no | — |
| 504 | C4⋊C4 | — | 13 | 3 | no | — |
| 505 | C4⋊C4 | — | 13 | 1 | no | — |
| 506 | C4⋊C4 | — | 26 | 6 | no | — |
| 507 | C4⋊C4 | — | 26 | 3 | no | — |
| 508 | C4⋊C4 | — | 26 | 3 | no | — |
| 509 | C4⋊C4 | — | 26 | 3 | no | — |
| 510 | C4⋊C4 | — | 26 | 3 | no | — |
| 511 | C4⋊C4 | — | 26 | 6 | no | — |
| 512 | C4⋊C4 | — | 26 | 6 | no | — |
| 513 | C4⋊C4 | — | 26 | 3 | no | — |
| 514 | C4⋊C4 | — | 26 | 3 | no | — |
| 515 | C4⋊C4 | — | 26 | 3 | no | — |
| 516 | C4⋊C4 | — | 26 | 3 | no | — |
| 517 | C4⋊C4 | D4×D13 | 1 | 3 | yes | — |
| 518 | C4⋊C4 | C23×D13 | 1 | 3 | yes | — |
| 519 | C4⋊C4 | C23×D13 | 1 | 3 | yes | — |
| 520 | C22⋊C4 | — | 2 | 3 | no | — |
| 521 | C22⋊C4 | — | 26 | 3 | no | — |
| 522 | C22⋊C4 | — | 26 | 3 | no | — |
| 523 | C22⋊C4 | — | 26 | 3 | no | — |
| 524 | C22⋊C4 | — | 26 | 1 | no | — |
| 525 | C22⋊C4 | — | 26 | 3 | no | — |
| 526 | C22⋊C4 | — | 26 | 3 | no | — |
| 527 | C22⋊C4 | — | 26 | 3 | no | — |
| 528 | C42 | — | 2 | 3 | no | — |
| 529 | C42 | — | 13 | 3 | no | — |
| 530 | C42 | — | 13 | 3 | no | — |
| 531 | C42 | — | 13 | 3 | no | — |
| 532 | C42 | — | 26 | 3 | no | — |
| 533 | C42 | — | 26 | 3 | no | — |
| 534 | C42 | — | 26 | 6 | no | — |
| 535 | C42 | — | 26 | 3 | no | — |
| 536 | C42 | C23×D13 | 1 | 3 | yes | — |
| 537 | C13 | #61824 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 538 | C23 | — | 2 | 1 | no | — |
| 539 | C23 | — | 13 | 1 | no | — |
| 540 | C23 | — | 26 | 1 | no | — |
| 541 | Q8 | — | 2 | 1 | no | — |
| 542 | Q8 | — | 4 | 6 | no | — |
| 543 | Q8 | — | 8 | 3 | no | — |
| 544 | Q8 | — | 26 | 6 | no | — |
| 545 | Q8 | — | 26 | 3 | no | — |
| 546 | Q8 | — | 26 | 3 | no | — |
| 547 | Q8 | — | 52 | 6 | no | — |
| 548 | Q8 | #88170 | 1 | 4 | yes | — |
| 549 | Q8 | #88254 | 1 | 2 | yes | — |
| 550 | D4 | — | 2 | 1 | no | — |
| 551 | D4 | — | 2 | 1 | no | — |
| 552 | D4 | — | 13 | 2 | no | — |
| 553 | D4 | — | 26 | 4 | no | — |
| 554 | D4 | — | 26 | 1 | no | — |
| 555 | D4 | — | 52 | 2 | no | — |
| 556 | C2×C4 | — | 2 | 1 | no | — |
| 557 | C2×C4 | — | 2 | 3 | no | — |
| 558 | C2×C4 | — | 2 | 3 | no | — |
| 559 | C2×C4 | — | 4 | 6 | no | — |
| 560 | C2×C4 | — | 13 | 1 | no | — |
| 561 | C2×C4 | — | 13 | 3 | no | — |
| 562 | C2×C4 | — | 13 | 3 | no | — |
| 563 | C2×C4 | — | 26 | 4 | no | — |
| 564 | C2×C4 | — | 26 | 6 | no | — |
| 565 | C2×C4 | — | 26 | 1 | no | — |
| 566 | C2×C4 | — | 26 | 1 | no | — |
| 567 | C2×C4 | — | 26 | 3 | no | — |
| 568 | C2×C4 | — | 26 | 1 | no | — |
| 569 | C2×C4 | — | 26 | 3 | no | — |
| 570 | C2×C4 | — | 52 | 3 | no | — |
| 571 | C2×C4 | — | 52 | 6 | no | — |
| 572 | C2×C4 | — | 104 | 3 | no | — |
| 573 | C2×C4 | C2×D4×D13 | 1 | 3 | yes | — |
| 574 | C2×C4 | C2×D4×D13 | 1 | 3 | yes | — |
| 575 | C2×C4 | C24×D13 | 1 | 1 | yes | characteristic |
| 576 | C8 | — | 2 | 1 | no | — |
| 577 | C8 | — | 2 | 3 | no | — |
| 578 | C8 | — | 26 | 3 | no | — |
| 579 | C8 | — | 26 | 1 | no | — |
| 580 | C22 | — | 4 | 1 | no | — |
| 581 | C22 | — | 4 | 1 | no | — |
| 582 | C22 | — | 4 | 1 | no | — |
| 583 | C22 | — | 26 | 2 | no | — |
| 584 | C22 | — | 26 | 1 | no | — |
| 585 | C22 | — | 26 | 1 | no | — |
| 586 | C22 | — | 26 | 1 | no | — |
| 587 | C22 | — | 52 | 1 | no | — |
| 588 | C22 | — | 52 | 1 | no | — |
| 589 | C22 | C22×D4×D13 | 1 | 1 | yes | characteristic |
| 590 | C4 | — | 2 | 2 | no | — |
| 591 | C4 | — | 2 | 3 | no | — |
| 592 | C4 | — | 4 | 3 | no | — |
| 593 | C4 | — | 4 | 3 | no | — |
| 594 | C4 | — | 26 | 1 | no | — |
| 595 | C4 | — | 26 | 3 | no | — |
| 596 | C4 | — | 26 | 3 | no | — |
| 597 | C4 | — | 52 | 3 | no | — |
| 598 | C4 | — | 52 | 3 | no | — |
| 599 | C4 | — | 52 | 1 | no | — |
| 600 | C4 | C2×#88170 | 1 | 6 | yes | — |
| 601 | C4 | C2×#88254 | 1 | 1 | yes | characteristic |
| 602 | C4 | D13×2−1+4 | 1 | 1 | yes | characteristic |
| 603 | C2 | — | 8 | 1 | no | — |
| 604 | C2 | — | 52 | 1 | no | — |
| 605 | C2 | — | 52 | 2 | no | — |
| 606 | C2 | #13128486 | 1 | 1 | yes | characteristic |
| 607 | C2 | C22×#88170 | 1 | 1 | yes | characteristic |
| 608 | C2 | #13129618 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13128927 | C2 | semidirect |
| 2. Q8×#6131 | C2 | semidirect |
| 3. #13127726 | C2 | semidirect |
| 4. #13127716 | C2 | semidirect |
| 5. Q8×#6104 | C2 | semidirect |
| 6. #13127519 | C2 | semidirect |
| 7. #13127514 | C2 | semidirect |
| 8. #13127484 | C2 | semidirect |
| 9. #13127479 | C2 | semidirect |
| 10. #13126014 | C2 | semidirect |
| 11. #13125998 | C2 | semidirect |
| 12. #13124910 | C2 | semidirect |
| 14. #13123915 | C2 | semidirect |
| 15. Q8×C13×SD16 | C2 | semidirect |
| 238. Q8×SD16 | D13 | semidirect |
| 537. C13 | #61824 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13128927 | 2 |
| Q8×#6131 | 2 |
| #13127726 | 2 |
| #13127716 | 2 |
| Q8×#6104 | 2 |
| #13127519 | 2 |
| #13127514 | 2 |
| #13127484 | 2 |
| #13127479 | 2 |
| #13126014 | 2 |
| #13125998 | 2 |
| #13124910 | 2 |
| #13124852 | 2 |
| #13123915 | 2 |
| Q8×C13×SD16 | 2 |
| #61824 | 13 |