← #16727618
Subgroups — #16727618
Order 3328.
1950 conjugacy classes of subgroups.
The subgroup lattice has 440 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13123856 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #13123841 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | #13123812 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #41×#1055 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | Q8×#6099 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×Q8×#1055 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #13123580 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #13123548 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #13123502 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | C4×#88202 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | C13×#3480 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C13×#559 | C4 | 1 | 3 | yes | — |
| 13 | C13×#557 | C4 | 1 | 1 | yes | characteristic |
| 14 | C13×#556 | C4 | 1 | 3 | yes | — |
| 15 | C13×#553 | C4 | 1 | 6 | yes | — |
| 16 | C13×#550 | C4 | 1 | 1 | yes | characteristic |
| 17 | C13×#548 | C4 | 1 | 2 | yes | — |
| 18 | C13×#532 | C22 | 1 | 3 | yes | — |
| 19 | C13×#529 | C22 | 1 | 6 | yes | — |
| 20 | C4×C13×#41 | C22 | 1 | 2 | yes | — |
| 21 | C4×C13×#41 | C22 | 1 | 3 | yes | — |
| 22 | C2×C4×Q8×C13 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#88202 | C22 | 1 | 3 | yes | — |
| 24 | C2×#88202 | C22 | 1 | 3 | yes | — |
| 25 | #11718895 | C22 | 1 | 6 | yes | — |
| 26 | #11718685 | C22 | 1 | 6 | yes | — |
| 27 | Q8×#1055 | C22 | 1 | 3 | yes | — |
| 28 | Q8×#1055 | C22 | 1 | 1 | yes | characteristic |
| 29 | Q8×#1055 | C22 | 1 | 2 | yes | — |
| 30 | Q8×#1055 | C22 | 1 | 1 | yes | characteristic |
| 31 | Q8×#1055 | C22 | 1 | 3 | yes | — |
| 32 | #11718673 | C22 | 1 | 6 | yes | — |
| 33 | #11718673 | C22 | 1 | 6 | yes | — |
| 34 | #11718673 | C22 | 1 | 6 | yes | — |
| 35 | #11718672 | C22 | 1 | 12 | yes | — |
| 36 | D4×#1055 | C22 | 1 | 6 | yes | — |
| 37 | D4×#1055 | C22 | 1 | 6 | yes | — |
| 38 | D4×#1055 | C22 | 1 | 6 | yes | — |
| 39 | #11718661 | C22 | 1 | 12 | yes | — |
| 40 | #11718658 | C22 | 1 | 6 | yes | — |
| 41 | #11718658 | C22 | 1 | 3 | yes | — |
| 42 | #11718658 | C22 | 1 | 1 | yes | characteristic |
| 43 | #11718658 | C22 | 1 | 6 | yes | — |
| 44 | #11718587 | C22 | 1 | 6 | yes | — |
| 45 | #11718586 | C22 | 1 | 6 | yes | — |
| 46 | #11718585 | C22 | 1 | 3 | yes | — |
| 47 | C2×C4⋊#1055 | C22 | 1 | 3 | yes | — |
| 48 | C4×#6099 | C22 | 1 | 6 | yes | — |
| 49 | C4×#6099 | C22 | 1 | 3 | yes | — |
| 50 | C2×C4×#1055 | C22 | 1 | 3 | yes | — |
| 51 | C2×C4×#1055 | C22 | 1 | 6 | yes | — |
| 52 | C2×C13×#41 | C2×C4 | 1 | 2 | yes | — |
| 53 | C2×C13×#41 | C23 | 1 | 3 | yes | — |
| 54 | C22×Q8×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 55 | C13×C4⋊Q8 | C2×C4 | 1 | 3 | yes | — |
| 56 | C13×#127 | C2×C4 | 1 | 3 | yes | — |
| 57 | C13×#126 | C2×C4 | 1 | 12 | yes | — |
| 58 | C13×#125 | C2×C4 | 1 | 6 | yes | — |
| 59 | C13×#124 | C2×C4 | 1 | 6 | yes | — |
| 60 | C13×#124 | C2×C4 | 1 | 6 | yes | — |
| 61 | C13×#123 | C2×C4 | 1 | 12 | yes | — |
| 62 | C13×C22⋊Q8 | C2×C4 | 1 | 6 | yes | — |
| 63 | C13×#121 | C2×C4 | 1 | 6 | yes | — |
| 64 | C13×#121 | C2×C4 | 1 | 6 | yes | — |
| 65 | C13×#121 | C2×C4 | 1 | 6 | yes | — |
| 66 | C4×Q8×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 67 | C4×Q8×C13 | C2×C4 | 1 | 3 | yes | — |
| 68 | C4×Q8×C13 | C2×C4 | 1 | 2 | yes | — |
| 69 | C4×Q8×C13 | C2×C4 | 1 | 3 | yes | — |
| 70 | C4×Q8×C13 | C2×C4 | 1 | 3 | yes | — |
| 71 | C4×Q8×C13 | C23 | 1 | 1 | yes | characteristic |
| 72 | C4×Q8×C13 | C23 | 1 | 3 | yes | — |
| 73 | C4×D4×C13 | C2×C4 | 1 | 6 | yes | — |
| 74 | C4×D4×C13 | C2×C4 | 1 | 3 | yes | — |
| 75 | C4×D4×C13 | C2×C4 | 1 | 6 | yes | — |
| 76 | C4×D4×C13 | C2×C4 | 1 | 6 | yes | — |
| 77 | C4×D4×C13 | C2×C4 | 1 | 3 | yes | — |
| 78 | C4×D4×C13 | C23 | 1 | 6 | yes | — |
| 79 | C4×D4×C13 | C23 | 1 | 6 | yes | — |
| 80 | C13×#117 | C2×C4 | 1 | 6 | yes | — |
| 81 | C13×#117 | C23 | 1 | 1 | yes | characteristic |
| 82 | C13×#117 | C23 | 1 | 6 | yes | — |
| 83 | C2×C13×C4⋊C4 | C2×C4 | 1 | 3 | yes | — |
| 84 | C2×C42×C13 | C23 | 1 | 3 | yes | — |
| 85 | C2×C42×C13 | C23 | 1 | 6 | yes | — |
| 86 | #88202 | — | 2 | 12 | no | — |
| 87 | #88202 | — | 2 | 12 | no | — |
| 88 | C2×#6099 | C23 | 1 | 6 | yes | — |
| 89 | C2×#6099 | C23 | 1 | 6 | yes | — |
| 90 | C2×#6099 | C23 | 1 | 3 | yes | — |
| 91 | C2×#6099 | C23 | 1 | 1 | yes | characteristic |
| 92 | C22×#1055 | C23 | 1 | 6 | yes | — |
| 93 | C22×#1055 | C23 | 1 | 6 | yes | — |
| 94 | C22×#1055 | C23 | 1 | 3 | yes | — |
| 95 | C22×#1055 | C23 | 1 | 1 | yes | characteristic |
| 96 | C22⋊#1055 | C23 | 1 | 12 | yes | — |
| 97 | C22⋊#1055 | C23 | 1 | 12 | yes | — |
| 98 | C4⋊#1055 | C23 | 1 | 6 | yes | — |
| 99 | C4⋊#1055 | C23 | 1 | 6 | yes | — |
| 100 | C4⋊#1055 | C23 | 1 | 3 | yes | — |
| 101 | C4⋊#1055 | C23 | 1 | 6 | yes | — |
| 102 | C4⋊#1055 | C23 | 1 | 3 | yes | — |
| 103 | #88043 | C23 | 1 | 2 | yes | — |
| 104 | #88043 | C23 | 1 | 6 | yes | — |
| 105 | #88043 | C23 | 1 | 6 | yes | — |
| 106 | C4×#1055 | C23 | 1 | 2 | yes | — |
| 107 | C4×#1055 | C23 | 1 | 6 | yes | — |
| 108 | C4×#1055 | C23 | 1 | 3 | yes | — |
| 109 | C4×#1055 | C23 | 1 | 3 | yes | — |
| 110 | C4×#1055 | C23 | 1 | 3 | yes | — |
| 111 | C4×#1055 | C23 | 1 | 6 | yes | — |
| 112 | C4×#1055 | C23 | 1 | 3 | yes | — |
| 113 | #60218 | — | 13 | 1 | no | maximal, Sylow |
| 114 | C13×#41 | — | 2 | 8 | no | — |
| 115 | C13×#41 | — | 2 | 6 | no | — |
| 116 | C13×#41 | — | 2 | 6 | no | — |
| 117 | C2×Q8×C13 | — | 2 | 4 | no | — |
| 118 | C2×Q8×C13 | C22×C4 | 1 | 3 | yes | — |
| 119 | C2×Q8×C13 | C22×C4 | 1 | 3 | yes | — |
| 120 | C2×Q8×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 121 | C2×D4×C13 | C22×C4 | 1 | 6 | yes | — |
| 122 | C2×D4×C13 | C22×C4 | 1 | 3 | yes | — |
| 123 | C2×D4×C13 | C22×C4 | 1 | 6 | yes | — |
| 124 | C2×D4×C13 | C22×C4 | 1 | 6 | yes | — |
| 125 | C22×C4×C13 | C22×C4 | 1 | 3 | yes | — |
| 126 | C22×C4×C13 | C22×C4 | 1 | 6 | yes | — |
| 127 | C22×C4×C13 | C22×C4 | 1 | 3 | yes | — |
| 128 | C22×C4×C13 | C22×C4 | 1 | 6 | yes | — |
| 129 | C22×C4×C13 | C24 | 1 | 6 | yes | — |
| 130 | C22×C4×C13 | C24 | 1 | 1 | yes | characteristic |
| 131 | C13×C4⋊C4 | C22×C4 | 1 | 3 | yes | — |
| 132 | C13×C4⋊C4 | C22×C4 | 1 | 3 | yes | — |
| 133 | C13×C4⋊C4 | C22×C4 | 1 | 6 | yes | — |
| 134 | C13×C4⋊C4 | C22×C4 | 1 | 6 | yes | — |
| 135 | C13×C4⋊C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 136 | C13×C4⋊C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 137 | C13×C4⋊C4 | C22×C4 | 1 | 6 | yes | — |
| 138 | C13×C4⋊C4 | C22×C4 | 1 | 6 | yes | — |
| 139 | C13×C4⋊C4 | C22×C4 | 1 | 6 | yes | — |
| 140 | C13×C22⋊C4 | C22×C4 | 1 | 12 | yes | — |
| 141 | C13×C22⋊C4 | C22×C4 | 1 | 2 | yes | — |
| 142 | C13×C22⋊C4 | C22×C4 | 1 | 6 | yes | — |
| 143 | C13×C22⋊C4 | C22×C4 | 1 | 6 | yes | — |
| 144 | C13×C22⋊C4 | C22×C4 | 1 | 12 | yes | — |
| 145 | C42×C13 | C22×C4 | 1 | 6 | yes | — |
| 146 | C42×C13 | C22×C4 | 1 | 6 | yes | — |
| 147 | C42×C13 | C22×C4 | 1 | 3 | yes | — |
| 148 | C42×C13 | C22×C4 | 1 | 3 | yes | — |
| 149 | C42×C13 | C24 | 1 | 2 | yes | — |
| 150 | C42×C13 | C24 | 1 | 3 | yes | — |
| 151 | C42×C13 | C24 | 1 | 3 | yes | — |
| 152 | #6099 | — | 2 | 6 | no | — |
| 153 | #6099 | — | 2 | 12 | no | — |
| 154 | #6099 | — | 2 | 12 | no | — |
| 155 | #6099 | #41 | 1 | 4 | yes | complemented |
| 156 | C2×#1055 | — | 2 | 6 | no | — |
| 157 | C2×#1055 | — | 2 | 12 | no | — |
| 158 | C2×#1055 | — | 2 | 12 | no | — |
| 159 | C2×#1055 | #41 | 1 | 4 | yes | complemented |
| 160 | C2×#1055 | C24 | 1 | 3 | yes | — |
| 161 | C2×#1055 | C24 | 1 | 6 | yes | — |
| 162 | C2×#1055 | C24 | 1 | 3 | yes | — |
| 163 | C2×#1055 | C24 | 1 | 1 | yes | characteristic |
| 164 | C2×#1055 | C24 | 1 | 2 | yes | — |
| 165 | C2×#1055 | C24 | 1 | 1 | yes | characteristic |
| 166 | #3480 | D13 | 1 | 1 | yes | characteristic |
| 167 | #2971 | — | 13 | 2 | no | — |
| 168 | #2969 | — | 13 | 6 | no | — |
| 169 | #2966 | — | 13 | 6 | no | — |
| 170 | C8×#41 | — | 13 | 2 | no | — |
| 171 | Q8×M16 | — | 13 | 1 | no | — |
| 172 | C2×C8×Q8 | — | 13 | 1 | no | — |
| 173 | #2935 | — | 13 | 3 | no | — |
| 174 | #2931 | — | 13 | 3 | no | — |
| 175 | #2925 | — | 13 | 3 | no | — |
| 176 | C4×#131 | — | 13 | 3 | no | — |
| 177 | C23×C13 | C23×C4 | 1 | 6 | yes | — |
| 178 | C23×C13 | C23×C4 | 1 | 1 | yes | characteristic |
| 179 | Q8×C13 | — | 2 | 6 | no | — |
| 180 | Q8×C13 | — | 2 | 6 | no | — |
| 181 | Q8×C13 | #131 | 1 | 4 | yes | complemented |
| 182 | D4×C13 | — | 2 | 12 | no | — |
| 183 | D4×C13 | — | 2 | 6 | no | — |
| 184 | D4×C13 | — | 2 | 12 | no | — |
| 185 | D4×C13 | — | 4 | 6 | no | — |
| 186 | C2×C4×C13 | — | 2 | 6 | no | — |
| 187 | C2×C4×C13 | — | 2 | 12 | no | — |
| 188 | C2×C4×C13 | — | 2 | 6 | no | — |
| 189 | C2×C4×C13 | — | 2 | 6 | no | — |
| 190 | C2×C4×C13 | — | 4 | 6 | no | — |
| 191 | C2×C4×C13 | — | 4 | 3 | no | — |
| 192 | C2×C4×C13 | C23×C4 | 1 | 2 | yes | — |
| 193 | C2×C4×C13 | C23×C4 | 1 | 3 | yes | — |
| 194 | C2×C4×C13 | C23×C4 | 1 | 2 | yes | — |
| 195 | C2×C4×C13 | C23×C4 | 1 | 6 | yes | — |
| 196 | C2×C4×C13 | C23×C4 | 1 | 3 | yes | — |
| 197 | C2×C4×C13 | C23×C4 | 1 | 3 | yes | — |
| 198 | C2×C4×C13 | C23×C4 | 1 | 1 | yes | characteristic |
| 199 | C2×C4×C13 | C23×C4 | 1 | 3 | yes | — |
| 200 | C2×C4×C13 | C2×#41 | 1 | 2 | yes | — |
| 201 | C2×C4×C13 | C2×#41 | 1 | 2 | yes | — |
| 202 | C2×C4×C13 | C25 | 1 | 1 | yes | characteristic |
| 203 | #1055 | — | 2 | 3 | no | — |
| 204 | #1055 | — | 2 | 3 | no | — |
| 205 | #1055 | — | 2 | 6 | no | — |
| 206 | #1055 | C2×#41 | 1 | 2 | yes | — |
| 207 | #1055 | C2×#41 | 1 | 4 | yes | — |
| 208 | #1055 | C2×#41 | 1 | 2 | yes | — |
| 209 | C2×#131 | — | 13 | 3 | no | — |
| 210 | C2×#131 | — | 13 | 3 | no | — |
| 211 | #559 | Dic13 | 1 | 3 | yes | — |
| 212 | #557 | Dic13 | 1 | 1 | yes | characteristic |
| 213 | #556 | Dic13 | 1 | 3 | yes | — |
| 214 | #553 | Dic13 | 1 | 6 | yes | — |
| 215 | #550 | Dic13 | 1 | 1 | yes | characteristic |
| 216 | #548 | Dic13 | 1 | 2 | yes | — |
| 217 | #532 | C2×D13 | 1 | 3 | yes | — |
| 218 | #529 | C2×D13 | 1 | 6 | yes | — |
| 219 | C4×#41 | C2×D13 | 1 | 2 | yes | — |
| 220 | C4×#41 | C2×D13 | 1 | 3 | yes | — |
| 221 | C2×C4×Q8 | C2×D13 | 1 | 1 | yes | characteristic |
| 222 | #446 | — | 13 | 6 | no | — |
| 223 | C8×Q8 | — | 13 | 1 | no | — |
| 224 | C8×Q8 | — | 13 | 3 | no | — |
| 225 | C8×Q8 | — | 13 | 3 | no | — |
| 226 | C8×Q8 | — | 13 | 1 | no | — |
| 227 | C8×Q8 | — | 13 | 2 | no | — |
| 228 | #436 | — | 13 | 6 | no | — |
| 229 | #436 | — | 13 | 6 | no | — |
| 230 | #436 | — | 13 | 6 | no | — |
| 231 | #435 | — | 13 | 12 | no | — |
| 232 | C8×D4 | — | 13 | 6 | no | — |
| 233 | C8×D4 | — | 13 | 6 | no | — |
| 234 | C8×D4 | — | 13 | 6 | no | — |
| 235 | #433 | — | 13 | 12 | no | — |
| 236 | #432 | — | 13 | 6 | no | — |
| 237 | #431 | — | 13 | 6 | no | — |
| 238 | #423 | — | 13 | 3 | no | — |
| 239 | C2×C4⋊C8 | — | 13 | 3 | no | — |
| 240 | #408 | — | 13 | 6 | no | — |
| 241 | #405 | — | 13 | 1 | no | — |
| 242 | #405 | — | 13 | 3 | no | — |
| 243 | #405 | — | 13 | 6 | no | — |
| 244 | #405 | — | 13 | 6 | no | — |
| 245 | C4×M16 | — | 13 | 3 | no | — |
| 246 | C4×M16 | — | 13 | 6 | no | — |
| 247 | C2×C4×C8 | — | 13 | 3 | no | — |
| 248 | C2×C4×C8 | — | 13 | 6 | no | — |
| 249 | C22×C13 | — | 2 | 1 | no | — |
| 250 | C22×C13 | — | 2 | 1 | no | — |
| 251 | C22×C13 | — | 2 | 6 | no | — |
| 252 | C22×C13 | — | 2 | 6 | no | — |
| 253 | C22×C13 | — | 2 | 6 | no | — |
| 254 | C22×C13 | C4×#41 | 1 | 2 | yes | — |
| 255 | C22×C13 | C24×C4 | 1 | 1 | yes | characteristic |
| 256 | C4×C13 | — | 2 | 6 | no | — |
| 257 | C4×C13 | — | 2 | 2 | no | — |
| 258 | C4×C13 | — | 2 | 3 | no | — |
| 259 | C4×C13 | — | 2 | 2 | no | — |
| 260 | C4×C13 | — | 2 | 3 | no | — |
| 261 | C4×C13 | — | 2 | 3 | no | — |
| 262 | C4×C13 | C4×#41 | 1 | 2 | yes | — |
| 263 | C4×C13 | C2×#131 | 1 | 6 | yes | — |
| 264 | C4×C13 | C22×#41 | 1 | 1 | yes | characteristic |
| 265 | C4×C13 | C22×#41 | 1 | 1 | yes | characteristic |
| 266 | C2×#41 | C2×Dic13 | 1 | 2 | yes | — |
| 267 | C2×#41 | C22×D13 | 1 | 3 | yes | — |
| 268 | C22×Q8 | C2×Dic13 | 1 | 1 | yes | characteristic |
| 269 | #131 | — | 26 | 12 | no | — |
| 270 | #131 | — | 26 | 12 | no | — |
| 271 | C2×M16 | — | 13 | 1 | no | — |
| 272 | C2×M16 | — | 13 | 3 | no | — |
| 273 | C2×M16 | — | 13 | 6 | no | — |
| 274 | C2×M16 | — | 13 | 6 | no | — |
| 275 | C22×C8 | — | 13 | 1 | no | — |
| 276 | C22×C8 | — | 13 | 3 | no | — |
| 277 | C22×C8 | — | 13 | 6 | no | — |
| 278 | C22×C8 | — | 13 | 6 | no | — |
| 279 | C4⋊Q8 | C2×Dic13 | 1 | 3 | yes | — |
| 280 | #127 | C2×Dic13 | 1 | 3 | yes | — |
| 281 | #126 | C2×Dic13 | 1 | 12 | yes | — |
| 282 | #125 | C2×Dic13 | 1 | 6 | yes | — |
| 283 | #124 | C2×Dic13 | 1 | 6 | yes | — |
| 284 | #124 | C2×Dic13 | 1 | 6 | yes | — |
| 285 | #123 | C2×Dic13 | 1 | 12 | yes | — |
| 286 | C22⋊Q8 | C2×Dic13 | 1 | 6 | yes | — |
| 287 | #121 | C2×Dic13 | 1 | 6 | yes | — |
| 288 | #121 | C2×Dic13 | 1 | 6 | yes | — |
| 289 | #121 | C2×Dic13 | 1 | 6 | yes | — |
| 290 | C4×Q8 | C2×Dic13 | 1 | 1 | yes | characteristic |
| 291 | C4×Q8 | C2×Dic13 | 1 | 3 | yes | — |
| 292 | C4×Q8 | C2×Dic13 | 1 | 2 | yes | — |
| 293 | C4×Q8 | C2×Dic13 | 1 | 3 | yes | — |
| 294 | C4×Q8 | C2×Dic13 | 1 | 3 | yes | — |
| 295 | C4×Q8 | C22×D13 | 1 | 1 | yes | characteristic |
| 296 | C4×Q8 | C22×D13 | 1 | 3 | yes | — |
| 297 | C4×D4 | C2×Dic13 | 1 | 6 | yes | — |
| 298 | C4×D4 | C2×Dic13 | 1 | 3 | yes | — |
| 299 | C4×D4 | C2×Dic13 | 1 | 6 | yes | — |
| 300 | C4×D4 | C2×Dic13 | 1 | 6 | yes | — |
| 301 | C4×D4 | C2×Dic13 | 1 | 3 | yes | — |
| 302 | C4×D4 | C22×D13 | 1 | 6 | yes | — |
| 303 | C4×D4 | C22×D13 | 1 | 6 | yes | — |
| 304 | #117 | C2×Dic13 | 1 | 6 | yes | — |
| 305 | #117 | C22×D13 | 1 | 1 | yes | characteristic |
| 306 | #117 | C22×D13 | 1 | 6 | yes | — |
| 307 | C2×C4⋊C4 | C2×Dic13 | 1 | 3 | yes | — |
| 308 | C2×C42 | C22×D13 | 1 | 3 | yes | — |
| 309 | C2×C42 | C22×D13 | 1 | 6 | yes | — |
| 310 | C4⋊C8 | — | 13 | 3 | no | — |
| 311 | C4⋊C8 | — | 13 | 3 | no | — |
| 312 | C4⋊C8 | — | 13 | 6 | no | — |
| 313 | C4⋊C8 | — | 13 | 6 | no | — |
| 314 | C4⋊C8 | — | 13 | 6 | no | — |
| 315 | C22⋊C8 | — | 13 | 12 | no | — |
| 316 | C22⋊C8 | — | 13 | 12 | no | — |
| 317 | #97 | — | 13 | 2 | no | — |
| 318 | #97 | — | 13 | 6 | no | — |
| 319 | #97 | — | 13 | 6 | no | — |
| 320 | C4×C8 | — | 13 | 2 | no | — |
| 321 | C4×C8 | — | 13 | 3 | no | — |
| 322 | C4×C8 | — | 13 | 6 | no | — |
| 323 | C4×C8 | — | 13 | 3 | no | — |
| 324 | C4×C8 | — | 13 | 6 | no | — |
| 325 | C4×C8 | — | 13 | 3 | no | — |
| 326 | C4×C8 | — | 13 | 3 | no | — |
| 327 | C2×C13 | — | 2 | 2 | no | — |
| 328 | C2×C13 | — | 4 | 6 | no | — |
| 329 | C2×C13 | C2×C4×#41 | 1 | 1 | yes | characteristic |
| 330 | C2×C13 | C22×#131 | 1 | 1 | yes | characteristic |
| 331 | C2×C13 | #3573 | 1 | 1 | yes | characteristic |
| 332 | #41 | — | 2 | 8 | no | — |
| 333 | #41 | — | 2 | 6 | no | — |
| 334 | #41 | — | 2 | 6 | no | — |
| 335 | C2×Q8 | — | 2 | 4 | no | — |
| 336 | C2×Q8 | C22×Dic13 | 1 | 3 | yes | — |
| 337 | C2×Q8 | C22×Dic13 | 1 | 3 | yes | — |
| 338 | C2×Q8 | C22×Dic13 | 1 | 1 | yes | characteristic |
| 339 | C2×D4 | C22×Dic13 | 1 | 6 | yes | — |
| 340 | C2×D4 | C22×Dic13 | 1 | 3 | yes | — |
| 341 | C2×D4 | C22×Dic13 | 1 | 6 | yes | — |
| 342 | C2×D4 | C22×Dic13 | 1 | 6 | yes | — |
| 343 | C22×C4 | C22×Dic13 | 1 | 3 | yes | — |
| 344 | C22×C4 | C22×Dic13 | 1 | 6 | yes | — |
| 345 | C22×C4 | C22×Dic13 | 1 | 3 | yes | — |
| 346 | C22×C4 | C22×Dic13 | 1 | 6 | yes | — |
| 347 | C22×C4 | C23×D13 | 1 | 6 | yes | — |
| 348 | C22×C4 | C23×D13 | 1 | 1 | yes | characteristic |
| 349 | M16 | — | 13 | 4 | no | — |
| 350 | M16 | — | 26 | 12 | no | — |
| 351 | M16 | — | 26 | 12 | no | — |
| 352 | M16 | — | 26 | 6 | no | — |
| 353 | C2×C8 | — | 13 | 4 | no | — |
| 354 | C2×C8 | — | 13 | 1 | no | — |
| 355 | C2×C8 | — | 13 | 1 | no | — |
| 356 | C2×C8 | — | 13 | 2 | no | — |
| 357 | C2×C8 | — | 13 | 3 | no | — |
| 358 | C2×C8 | — | 13 | 6 | no | — |
| 359 | C2×C8 | — | 13 | 3 | no | — |
| 360 | C2×C8 | — | 26 | 12 | no | — |
| 361 | C2×C8 | — | 26 | 12 | no | — |
| 362 | C2×C8 | — | 26 | 6 | no | — |
| 363 | C4⋊C4 | C22×Dic13 | 1 | 3 | yes | — |
| 364 | C4⋊C4 | C22×Dic13 | 1 | 3 | yes | — |
| 365 | C4⋊C4 | C22×Dic13 | 1 | 6 | yes | — |
| 366 | C4⋊C4 | C22×Dic13 | 1 | 6 | yes | — |
| 367 | C4⋊C4 | C22×Dic13 | 1 | 1 | yes | characteristic |
| 368 | C4⋊C4 | C22×Dic13 | 1 | 1 | yes | characteristic |
| 369 | C4⋊C4 | C22×Dic13 | 1 | 6 | yes | — |
| 370 | C4⋊C4 | C22×Dic13 | 1 | 6 | yes | — |
| 371 | C4⋊C4 | C22×Dic13 | 1 | 6 | yes | — |
| 372 | C22⋊C4 | C22×Dic13 | 1 | 12 | yes | — |
| 373 | C22⋊C4 | C22×Dic13 | 1 | 2 | yes | — |
| 374 | C22⋊C4 | C22×Dic13 | 1 | 6 | yes | — |
| 375 | C22⋊C4 | C22×Dic13 | 1 | 6 | yes | — |
| 376 | C22⋊C4 | C22×Dic13 | 1 | 12 | yes | — |
| 377 | C42 | C22×Dic13 | 1 | 6 | yes | — |
| 378 | C42 | C22×Dic13 | 1 | 6 | yes | — |
| 379 | C42 | C22×Dic13 | 1 | 3 | yes | — |
| 380 | C42 | C22×Dic13 | 1 | 3 | yes | — |
| 381 | C42 | C23×D13 | 1 | 2 | yes | — |
| 382 | C42 | C23×D13 | 1 | 3 | yes | — |
| 383 | C42 | C23×D13 | 1 | 3 | yes | — |
| 384 | C13 | #60218 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 385 | C23 | C23×Dic13 | 1 | 6 | yes | — |
| 386 | C23 | C23×Dic13 | 1 | 1 | yes | characteristic |
| 387 | Q8 | — | 2 | 6 | no | — |
| 388 | Q8 | — | 2 | 6 | no | — |
| 389 | Q8 | #88202 | 1 | 4 | yes | complemented |
| 390 | D4 | — | 2 | 12 | no | — |
| 391 | D4 | — | 2 | 12 | no | — |
| 392 | D4 | — | 2 | 6 | no | — |
| 393 | D4 | — | 4 | 6 | no | — |
| 394 | C2×C4 | — | 2 | 6 | no | — |
| 395 | C2×C4 | — | 2 | 12 | no | — |
| 396 | C2×C4 | — | 2 | 6 | no | — |
| 397 | C2×C4 | — | 2 | 6 | no | — |
| 398 | C2×C4 | — | 4 | 6 | no | — |
| 399 | C2×C4 | — | 4 | 3 | no | — |
| 400 | C2×C4 | #41×D13 | 1 | 2 | yes | — |
| 401 | C2×C4 | #41×D13 | 1 | 2 | yes | — |
| 402 | C2×C4 | C23×Dic13 | 1 | 2 | yes | — |
| 403 | C2×C4 | C23×Dic13 | 1 | 3 | yes | — |
| 404 | C2×C4 | C23×Dic13 | 1 | 2 | yes | — |
| 405 | C2×C4 | C23×Dic13 | 1 | 6 | yes | — |
| 406 | C2×C4 | C23×Dic13 | 1 | 3 | yes | — |
| 407 | C2×C4 | C23×Dic13 | 1 | 3 | yes | — |
| 408 | C2×C4 | C23×Dic13 | 1 | 3 | yes | — |
| 409 | C2×C4 | C23×Dic13 | 1 | 1 | yes | characteristic |
| 410 | C2×C4 | C24×D13 | 1 | 1 | yes | characteristic |
| 411 | C8 | — | 13 | 2 | no | — |
| 412 | C8 | — | 13 | 2 | no | — |
| 413 | C8 | — | 13 | 4 | no | — |
| 414 | C8 | — | 26 | 3 | no | — |
| 415 | C8 | — | 26 | 6 | no | — |
| 416 | C8 | — | 26 | 3 | no | — |
| 417 | C22 | — | 2 | 1 | no | — |
| 418 | C22 | — | 2 | 1 | no | — |
| 419 | C22 | — | 2 | 6 | no | — |
| 420 | C22 | — | 2 | 6 | no | — |
| 421 | C22 | — | 2 | 6 | no | — |
| 422 | C22 | #41×Dic13 | 1 | 2 | yes | — |
| 423 | C22 | C24×Dic13 | 1 | 1 | yes | characteristic |
| 424 | C4 | — | 2 | 2 | no | — |
| 425 | C4 | — | 2 | 3 | no | — |
| 426 | C4 | — | 2 | 2 | no | — |
| 427 | C4 | — | 2 | 3 | no | — |
| 428 | C4 | — | 2 | 3 | no | — |
| 429 | C4 | — | 2 | 6 | no | — |
| 430 | C4 | C2×#88202 | 1 | 6 | yes | — |
| 431 | C4 | #41×Dic13 | 1 | 2 | yes | — |
| 432 | C4 | C2×#41×D13 | 1 | 1 | yes | characteristic |
| 433 | C4 | C2×#41×D13 | 1 | 1 | yes | characteristic |
| 434 | C2 | — | 2 | 2 | no | — |
| 435 | C2 | — | 4 | 6 | no | — |
| 436 | C2 | C2×#41×Dic13 | 1 | 1 | yes | characteristic |
| 437 | C2 | C22×#88202 | 1 | 1 | yes | characteristic |
| 438 | C2 | #13129548 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta