← D3×#135792 #72226185
Subgroups — D3×#135792 #72226185
Order 3072.
2254 conjugacy classes of subgroups.
The subgroup lattice has 658 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#135792 | — | 3 | 1 | no | maximal, Sylow |
| 2 | #72226182 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #72226180 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | D3×#12020 | C2 | 1 | 4 | yes | maximal |
| 5 | D3×#8822 | C2 | 1 | 2 | yes | maximal |
| 6 | #72225823 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C3×#135792 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | D3×C8×M32 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | C4×D3×M32 | C22 | 1 | 2 | yes | — |
| 10 | D3×#1848 | — | 2 | 2 | no | — |
| 11 | D3×#1566 | — | 2 | 2 | no | — |
| 12 | D3×#1566 | C22 | 1 | 4 | yes | — |
| 13 | C2×D3×C82 | C22 | 1 | 1 | yes | characteristic |
| 14 | #10706823 | C22 | 1 | 4 | yes | — |
| 15 | #10706822 | C22 | 1 | 8 | yes | — |
| 16 | #10706821 | — | 2 | 8 | no | — |
| 17 | D3×#1368 | — | 2 | 8 | no | — |
| 18 | C8×#812 | C22 | 1 | 1 | yes | characteristic |
| 19 | #10704165 | C4 | 1 | 2 | yes | — |
| 20 | C3⋊C8×M32 | C22 | 1 | 2 | yes | — |
| 21 | C8×#798 | C4 | 1 | 1 | yes | characteristic |
| 22 | C8×#798 | C4 | 1 | 1 | yes | characteristic |
| 23 | D3×#1311 | C4 | 1 | 2 | yes | — |
| 24 | D3×C8×C16 | C4 | 1 | 1 | yes | characteristic |
| 25 | D3×C8×C16 | C4 | 1 | 1 | yes | characteristic |
| 26 | #10688988 | C22 | 1 | 2 | yes | — |
| 27 | #10688987 | — | 2 | 2 | no | — |
| 28 | #10688987 | C22 | 1 | 4 | yes | — |
| 29 | #10688986 | — | 2 | 2 | no | — |
| 30 | C3×#12020 | C22 | 1 | 4 | yes | — |
| 31 | C3×C8×M32 | C22 | 1 | 1 | yes | characteristic |
| 32 | C3×#8822 | C22 | 1 | 2 | yes | — |
| 33 | C2×#12020 | — | 3 | 4 | no | — |
| 34 | C2×C8×M32 | — | 3 | 1 | no | — |
| 35 | C2×#8822 | — | 3 | 2 | no | — |
| 36 | #135792 | — | 3 | 4 | no | — |
| 37 | #135792 | — | 3 | 1 | no | — |
| 38 | #135792 | — | 3 | 2 | no | — |
| 39 | #135792 | D3 | 1 | 1 | yes | characteristic, direct product factor |
| 40 | C2×D3×M32 | Q8 | 1 | 4 | yes | — |
| 41 | C2×D3×#108 | — | 4 | 4 | no | — |
| 42 | D3×#423 | — | 2 | 4 | no | — |
| 43 | C2×C4×D3×C8 | D4 | 1 | 2 | yes | — |
| 44 | C2×C4×D3×C8 | C23 | 1 | 1 | yes | characteristic |
| 45 | C3×C4×M32 | C23 | 1 | 2 | yes | — |
| 46 | C3×#1848 | — | 2 | 2 | no | — |
| 47 | C3×#1566 | — | 2 | 2 | no | — |
| 48 | C3×#1566 | C23 | 1 | 4 | yes | — |
| 49 | C2×C3×C82 | C23 | 1 | 1 | yes | characteristic |
| 50 | Dic3×M32 | Q8 | 1 | 4 | yes | — |
| 51 | #70693 | — | 4 | 4 | no | — |
| 52 | #70518 | — | 2 | 4 | no | — |
| 53 | #70490 | — | 2 | 4 | no | — |
| 54 | #70490 | — | 2 | 4 | no | — |
| 55 | #69792 | — | 2 | 2 | no | — |
| 56 | C4×#812 | C23 | 1 | 2 | yes | — |
| 57 | #69730 | — | 2 | 2 | no | — |
| 58 | #69730 | C23 | 1 | 4 | yes | — |
| 59 | C2×C8×C3⋊C8 | D4 | 1 | 2 | yes | — |
| 60 | C2×C8×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 61 | #69071 | D4 | 1 | 4 | yes | — |
| 62 | D3×#346 | D4 | 1 | 4 | yes | — |
| 63 | C4×#798 | C2×C4 | 1 | 2 | yes | — |
| 64 | C4×#798 | C2×C4 | 1 | 2 | yes | — |
| 65 | C4×D3×C16 | C2×C4 | 1 | 2 | yes | — |
| 66 | C4×D3×C16 | C2×C4 | 1 | 2 | yes | — |
| 67 | #68529 | — | 2 | 8 | no | — |
| 68 | #68529 | — | 4 | 4 | no | — |
| 69 | D3×#334 | — | 2 | 8 | no | — |
| 70 | D3×#334 | — | 4 | 4 | no | — |
| 71 | D3×C82 | C2×C4 | 1 | 1 | yes | characteristic |
| 72 | D3×C82 | C2×C4 | 1 | 1 | yes | characteristic |
| 73 | D3×C82 | C2×C4 | 1 | 1 | yes | characteristic |
| 74 | D3×C82 | C2×C4 | 1 | 1 | yes | characteristic |
| 75 | D3×C82 | Q8 | 1 | 2 | yes | — |
| 76 | D3×C82 | Q8 | 1 | 2 | yes | — |
| 77 | C3×#1368 | — | 2 | 8 | no | — |
| 78 | C3×#1311 | C2×C4 | 1 | 2 | yes | — |
| 79 | C3×C8×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 80 | C3×C8×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 81 | #67513 | — | 2 | 8 | no | — |
| 82 | #67498 | C2×C4 | 1 | 2 | yes | — |
| 83 | #67498 | C2×C4 | 1 | 2 | yes | — |
| 84 | C16×C3⋊C8 | C2×C4 | 1 | 2 | yes | — |
| 85 | C16×C3⋊C8 | C2×C4 | 1 | 2 | yes | — |
| 86 | #67464 | — | 2 | 16 | no | — |
| 87 | #67437 | C2×C4 | 1 | 2 | yes | — |
| 88 | C8×C3⋊C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 89 | C8×C3⋊C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 90 | C2×C4×M32 | — | 3 | 2 | no | — |
| 91 | C2×#1848 | — | 6 | 2 | no | — |
| 92 | C2×#1566 | — | 3 | 4 | no | — |
| 93 | C2×#1566 | — | 6 | 2 | no | — |
| 94 | C22×C82 | — | 3 | 1 | no | — |
| 95 | #12020 | — | 3 | 4 | no | — |
| 96 | #12020 | — | 3 | 8 | no | — |
| 97 | #12020 | — | 6 | 8 | no | — |
| 98 | #12020 | C2×D3 | 1 | 4 | yes | — |
| 99 | C2×#1368 | — | 6 | 8 | no | — |
| 100 | C8×M32 | — | 3 | 1 | no | — |
| 101 | C8×M32 | — | 3 | 2 | no | — |
| 102 | C8×M32 | — | 3 | 2 | no | — |
| 103 | C8×M32 | — | 3 | 1 | no | — |
| 104 | C8×M32 | — | 3 | 1 | no | — |
| 105 | C8×M32 | C2×D3 | 1 | 1 | yes | characteristic |
| 106 | C2×#1311 | — | 3 | 2 | no | — |
| 107 | C2×C8×C16 | — | 3 | 1 | no | — |
| 108 | C2×C8×C16 | — | 3 | 1 | no | — |
| 109 | #8822 | — | 3 | 2 | no | — |
| 110 | #8822 | — | 3 | 4 | no | — |
| 111 | #8822 | — | 6 | 2 | no | — |
| 112 | #8822 | — | 6 | 2 | no | — |
| 113 | #8822 | C2×D3 | 1 | 2 | yes | — |
| 114 | C2×D3×M16 | — | 4 | 4 | no | — |
| 115 | C22×D3×C8 | SD16 | 1 | 4 | yes | — |
| 116 | C22×D3×C8 | C2×Q8 | 1 | 2 | yes | — |
| 117 | C2×C42×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | C2×C3×M32 | C2×Q8 | 1 | 4 | yes | — |
| 119 | C2×C3×#108 | — | 4 | 4 | no | — |
| 120 | C3×#423 | — | 2 | 4 | no | — |
| 121 | C2×C3×C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 122 | C2×C3×C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 123 | C2×#822 | — | 4 | 8 | no | — |
| 124 | #5118 | — | 4 | 4 | no | — |
| 125 | C2×#819 | — | 4 | 4 | no | — |
| 126 | C2×C8×Dic3 | SD16 | 1 | 4 | yes | — |
| 127 | C2×C8×Dic3 | C2×Q8 | 1 | 2 | yes | — |
| 128 | C2×#812 | C2×Q8 | 1 | 4 | yes | — |
| 129 | #4924 | — | 2 | 4 | no | — |
| 130 | C2×C4×C3⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 131 | C2×C4×C3⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 132 | D3×M32 | — | 2 | 16 | no | — |
| 133 | C2×#798 | C4⋊C4 | 1 | 4 | yes | — |
| 134 | C2×#798 | C4⋊C4 | 1 | 4 | yes | — |
| 135 | C2×D3×C16 | C4⋊C4 | 1 | 4 | yes | — |
| 136 | C2×D3×C16 | C4⋊C4 | 1 | 4 | yes | — |
| 137 | D3×#108 | — | 8 | 16 | no | — |
| 138 | #4837 | — | 4 | 4 | no | — |
| 139 | #4837 | — | 4 | 4 | no | — |
| 140 | D3×C4⋊C8 | — | 4 | 4 | no | — |
| 141 | D3×C4⋊C8 | — | 4 | 4 | no | — |
| 142 | C4×D3×C8 | C4⋊C4 | 1 | 2 | yes | — |
| 143 | C4×D3×C8 | C4⋊C4 | 1 | 2 | yes | — |
| 144 | C4×D3×C8 | C4⋊C4 | 1 | 2 | yes | — |
| 145 | C4×D3×C8 | C4⋊C4 | 1 | 2 | yes | — |
| 146 | C4×D3×C8 | SD16 | 1 | 4 | yes | — |
| 147 | C4×D3×C8 | SD16 | 1 | 4 | yes | — |
| 148 | C4×D3×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 149 | C4×D3×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 150 | C4×D3×C8 | C2×D4 | 1 | 2 | yes | — |
| 151 | C4×D3×C8 | C2×D4 | 1 | 2 | yes | — |
| 152 | C4×D3×C8 | C2×Q8 | 1 | 1 | yes | characteristic |
| 153 | C4×D3×C8 | C2×Q8 | 1 | 1 | yes | characteristic |
| 154 | C3×#346 | C2×D4 | 1 | 4 | yes | — |
| 155 | C3×C4×C16 | C22×C4 | 1 | 2 | yes | — |
| 156 | C3×C4×C16 | C22×C4 | 1 | 2 | yes | — |
| 157 | C3×#334 | — | 2 | 8 | no | — |
| 158 | C3×#334 | — | 4 | 4 | no | — |
| 159 | C3×C82 | C22×C4 | 1 | 1 | yes | characteristic |
| 160 | C3×C82 | C22×C4 | 1 | 1 | yes | characteristic |
| 161 | C3×C82 | C2×Q8 | 1 | 2 | yes | — |
| 162 | #4502 | C4⋊C4 | 1 | 4 | yes | — |
| 163 | #4502 | C4⋊C4 | 1 | 4 | yes | — |
| 164 | Dic3×C16 | C4⋊C4 | 1 | 4 | yes | — |
| 165 | Dic3×C16 | C4⋊C4 | 1 | 4 | yes | — |
| 166 | #4480 | — | 4 | 8 | no | — |
| 167 | #4480 | — | 4 | 8 | no | — |
| 168 | #4461 | C2×D4 | 1 | 4 | yes | — |
| 169 | C4×C3⋊C16 | C22×C4 | 1 | 2 | yes | — |
| 170 | C4×C3⋊C16 | C22×C4 | 1 | 2 | yes | — |
| 171 | #4457 | — | 2 | 8 | no | — |
| 172 | #4457 | — | 4 | 4 | no | — |
| 173 | C8×C3⋊C8 | C4⋊C4 | 1 | 2 | yes | — |
| 174 | C8×C3⋊C8 | C4⋊C4 | 1 | 2 | yes | — |
| 175 | C8×C3⋊C8 | C4⋊C4 | 1 | 2 | yes | — |
| 176 | C8×C3⋊C8 | C4⋊C4 | 1 | 2 | yes | — |
| 177 | C8×C3⋊C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 178 | C8×C3⋊C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 179 | C8×C3⋊C8 | C2×Q8 | 1 | 2 | yes | — |
| 180 | C22×M32 | — | 3 | 4 | no | — |
| 181 | C22×#108 | — | 12 | 4 | no | — |
| 182 | C2×#423 | — | 6 | 4 | no | — |
| 183 | C22×C4×C8 | — | 3 | 2 | no | — |
| 184 | C22×C4×C8 | — | 3 | 1 | no | — |
| 185 | C4×M32 | — | 3 | 4 | no | — |
| 186 | C4×M32 | — | 3 | 2 | no | — |
| 187 | C4×M32 | — | 3 | 4 | no | — |
| 188 | C4×M32 | — | 3 | 2 | no | — |
| 189 | C4×M32 | — | 3 | 2 | no | — |
| 190 | C4×M32 | C22×D3 | 1 | 2 | yes | — |
| 191 | C2×#346 | — | 3 | 4 | no | — |
| 192 | C2×C4×C16 | — | 3 | 2 | no | — |
| 193 | C2×C4×C16 | — | 3 | 2 | no | — |
| 194 | #1848 | — | 2 | 2 | no | — |
| 195 | #1848 | — | 6 | 4 | no | — |
| 196 | #1848 | — | 6 | 2 | no | — |
| 197 | #1848 | — | 12 | 4 | no | — |
| 198 | #1566 | — | 2 | 2 | no | — |
| 199 | #1566 | — | 3 | 4 | no | — |
| 200 | #1566 | — | 6 | 8 | no | — |
| 201 | #1566 | — | 6 | 4 | no | — |
| 202 | #1566 | — | 6 | 4 | no | — |
| 203 | #1566 | — | 6 | 2 | no | — |
| 204 | #1566 | — | 12 | 4 | no | — |
| 205 | #1566 | C22×D3 | 1 | 4 | yes | — |
| 206 | C2×#334 | — | 6 | 8 | no | — |
| 207 | C2×#334 | — | 12 | 4 | no | — |
| 208 | C2×C82 | — | 3 | 2 | no | — |
| 209 | C2×C82 | — | 3 | 1 | no | — |
| 210 | C2×C82 | — | 3 | 1 | no | — |
| 211 | C2×C82 | — | 3 | 1 | no | — |
| 212 | C2×C82 | — | 3 | 1 | no | — |
| 213 | C2×C82 | — | 3 | 1 | no | — |
| 214 | C2×C82 | — | 3 | 2 | no | — |
| 215 | C2×C82 | — | 3 | 2 | no | — |
| 216 | C2×C82 | C22×D3 | 1 | 1 | yes | characteristic |
| 217 | #1368 | — | 2 | 8 | no | — |
| 218 | #1368 | — | 6 | 16 | no | — |
| 219 | #1368 | — | 6 | 8 | no | — |
| 220 | #1311 | — | 3 | 2 | no | — |
| 221 | #1311 | — | 3 | 2 | no | — |
| 222 | #1311 | — | 3 | 2 | no | — |
| 223 | #1311 | C4×D3 | 1 | 2 | yes | — |
| 224 | C8×C16 | — | 3 | 2 | no | — |
| 225 | C8×C16 | — | 3 | 2 | no | — |
| 226 | C8×C16 | — | 3 | 1 | no | — |
| 227 | C8×C16 | — | 3 | 1 | no | — |
| 228 | C8×C16 | C4×D3 | 1 | 1 | yes | characteristic |
| 229 | C8×C16 | C4×D3 | 1 | 1 | yes | characteristic |
| 230 | C22×C4×D3 | C4⋊Q8 | 1 | 1 | yes | characteristic |
| 231 | C22×C4×D3 | C2×SD16 | 1 | 2 | yes | — |
| 232 | C2×C3×M16 | — | 4 | 4 | no | — |
| 233 | C22×C3×C8 | C2×SD16 | 1 | 4 | yes | — |
| 234 | C22×C3×C8 | C22×Q8 | 1 | 2 | yes | — |
| 235 | C2×C3×C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 236 | C2×C4×Dic3 | C4⋊Q8 | 1 | 1 | yes | characteristic |
| 237 | C2×C4×Dic3 | C2×SD16 | 1 | 2 | yes | — |
| 238 | C2×#208 | — | 4 | 4 | no | — |
| 239 | C22×C3⋊C8 | C4⋊Q8 | 1 | 2 | yes | — |
| 240 | C22×C3⋊C8 | C2×SD16 | 1 | 4 | yes | — |
| 241 | D3×M16 | — | 8 | 16 | no | — |
| 242 | C2×ΓL(1,𝔽25) | — | 8 | 4 | no | — |
| 243 | C2×D3×C8 | — | 2 | 16 | no | — |
| 244 | C2×D3×C8 | — | 2 | 8 | no | — |
| 245 | C2×D3×C8 | — | 8 | 4 | no | — |
| 246 | C2×D3×C8 | #106 | 1 | 4 | yes | — |
| 247 | C2×D3×C8 | #106 | 1 | 4 | yes | — |
| 248 | C2×D3×C8 | #106 | 1 | 4 | yes | — |
| 249 | C2×D3×C8 | #106 | 1 | 4 | yes | — |
| 250 | C2×D3×C8 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 251 | C2×D3×C8 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 252 | C2×D3×C8 | C4⋊Q8 | 1 | 2 | yes | — |
| 253 | C2×D3×C8 | C4⋊Q8 | 1 | 2 | yes | — |
| 254 | C42×D3 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 255 | C42×D3 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 256 | C42×D3 | #127 | 1 | 1 | yes | characteristic |
| 257 | C42×D3 | #127 | 1 | 1 | yes | characteristic |
| 258 | C42×D3 | C2×SD16 | 1 | 2 | yes | — |
| 259 | C42×D3 | C2×SD16 | 1 | 2 | yes | — |
| 260 | C3×M32 | — | 2 | 8 | no | — |
| 261 | C2×C3×C16 | C2×C4⋊C4 | 1 | 4 | yes | — |
| 262 | C2×C3×C16 | C2×C4⋊C4 | 1 | 4 | yes | — |
| 263 | C3×#108 | — | 8 | 8 | no | — |
| 264 | C3×C4⋊C8 | — | 4 | 4 | no | — |
| 265 | C3×C4⋊C8 | — | 4 | 4 | no | — |
| 266 | C3×C4×C8 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 267 | C3×C4×C8 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 268 | C3×C4×C8 | C2×SD16 | 1 | 4 | yes | — |
| 269 | C3×C4×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 270 | C3×C4×C8 | C22×D4 | 1 | 2 | yes | — |
| 271 | C3×C4×C8 | C22×Q8 | 1 | 1 | yes | characteristic |
| 272 | #822 | — | 8 | 16 | no | — |
| 273 | #819 | — | 8 | 8 | no | — |
| 274 | Dic3⋊C8 | — | 8 | 4 | no | — |
| 275 | Dic3⋊C8 | — | 8 | 4 | no | — |
| 276 | C8×Dic3 | #106 | 1 | 4 | yes | — |
| 277 | C8×Dic3 | #106 | 1 | 4 | yes | — |
| 278 | C8×Dic3 | #106 | 1 | 4 | yes | — |
| 279 | C8×Dic3 | #106 | 1 | 4 | yes | — |
| 280 | C8×Dic3 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 281 | C8×Dic3 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 282 | C8×Dic3 | C4⋊Q8 | 1 | 2 | yes | — |
| 283 | C8×Dic3 | C4⋊Q8 | 1 | 2 | yes | — |
| 284 | #812 | — | 2 | 8 | no | — |
| 285 | C2×C3⋊C16 | C2×C4⋊C4 | 1 | 4 | yes | — |
| 286 | C2×C3⋊C16 | C2×C4⋊C4 | 1 | 4 | yes | — |
| 287 | C4⋊(C3⋊C8) | — | 4 | 4 | no | — |
| 288 | C4⋊(C3⋊C8) | — | 4 | 4 | no | — |
| 289 | C4×C3⋊C8 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 290 | C4×C3⋊C8 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 291 | C4×C3⋊C8 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 292 | C4×C3⋊C8 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 293 | C4×C3⋊C8 | #127 | 1 | 2 | yes | — |
| 294 | C4×C3⋊C8 | C2×SD16 | 1 | 4 | yes | — |
| 295 | #798 | — | 2 | 8 | no | — |
| 296 | #798 | — | 2 | 8 | no | — |
| 297 | D3×C16 | — | 2 | 8 | no | — |
| 298 | D3×C16 | #108 | 1 | 16 | yes | complemented |
| 299 | C22×M16 | — | 12 | 4 | no | — |
| 300 | C23×C8 | — | 3 | 4 | no | — |
| 301 | C23×C8 | — | 3 | 2 | no | — |
| 302 | C22×C42 | — | 3 | 1 | no | — |
| 303 | C2×M32 | — | 3 | 4 | no | — |
| 304 | C2×M32 | — | 3 | 4 | no | — |
| 305 | C2×M32 | — | 3 | 4 | no | — |
| 306 | C2×M32 | — | 6 | 16 | no | — |
| 307 | C2×M32 | D3×Q8 | 1 | 4 | yes | — |
| 308 | C22×C16 | — | 3 | 4 | no | — |
| 309 | C22×C16 | — | 3 | 4 | no | — |
| 310 | C2×#108 | — | 4 | 4 | no | — |
| 311 | C2×#108 | — | 12 | 8 | no | — |
| 312 | C2×#108 | — | 12 | 4 | no | — |
| 313 | C2×#108 | — | 24 | 16 | no | — |
| 314 | #423 | — | 2 | 4 | no | — |
| 315 | #423 | — | 6 | 4 | no | — |
| 316 | #423 | — | 12 | 4 | no | — |
| 317 | #423 | — | 12 | 4 | no | — |
| 318 | #423 | — | 12 | 4 | no | — |
| 319 | C2×C4⋊C8 | — | 12 | 4 | no | — |
| 320 | C2×C4⋊C8 | — | 12 | 4 | no | — |
| 321 | C2×C4×C8 | — | 3 | 4 | no | — |
| 322 | C2×C4×C8 | — | 3 | 2 | no | — |
| 323 | C2×C4×C8 | — | 3 | 1 | no | — |
| 324 | C2×C4×C8 | — | 3 | 2 | no | — |
| 325 | C2×C4×C8 | — | 3 | 2 | no | — |
| 326 | C2×C4×C8 | — | 3 | 2 | no | — |
| 327 | C2×C4×C8 | — | 3 | 2 | no | — |
| 328 | C2×C4×C8 | — | 3 | 2 | no | — |
| 329 | C2×C4×C8 | — | 3 | 4 | no | — |
| 330 | C2×C4×C8 | — | 3 | 4 | no | — |
| 331 | C2×C4×C8 | — | 3 | 1 | no | — |
| 332 | C2×C4×C8 | — | 3 | 1 | no | — |
| 333 | C2×C4×C8 | — | 3 | 2 | no | — |
| 334 | C2×C4×C8 | — | 3 | 2 | no | — |
| 335 | C2×C4×C8 | — | 3 | 1 | no | — |
| 336 | C2×C4×C8 | — | 3 | 1 | no | — |
| 337 | C2×C4×C8 | D3×D4 | 1 | 2 | yes | — |
| 338 | C2×C4×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 339 | #346 | — | 3 | 4 | no | — |
| 340 | #346 | — | 3 | 4 | no | — |
| 341 | #346 | — | 3 | 4 | no | — |
| 342 | #346 | D3×D4 | 1 | 4 | yes | — |
| 343 | C4×C16 | — | 3 | 4 | no | — |
| 344 | C4×C16 | — | 3 | 4 | no | — |
| 345 | C4×C16 | — | 3 | 2 | no | — |
| 346 | C4×C16 | — | 3 | 2 | no | — |
| 347 | C4×C16 | C2×C4×D3 | 1 | 2 | yes | — |
| 348 | C4×C16 | C2×C4×D3 | 1 | 2 | yes | — |
| 349 | #334 | — | 2 | 8 | no | — |
| 350 | #334 | — | 4 | 4 | no | — |
| 351 | #334 | — | 6 | 8 | no | — |
| 352 | #334 | — | 12 | 8 | no | — |
| 353 | #334 | — | 12 | 8 | no | — |
| 354 | #334 | — | 12 | 4 | no | — |
| 355 | C82 | — | 3 | 2 | no | — |
| 356 | C82 | — | 3 | 2 | no | — |
| 357 | C82 | — | 3 | 2 | no | — |
| 358 | C82 | — | 3 | 2 | no | — |
| 359 | C82 | — | 3 | 1 | no | — |
| 360 | C82 | — | 3 | 1 | no | — |
| 361 | C82 | — | 3 | 2 | no | — |
| 362 | C82 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 363 | C82 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 364 | C82 | D3×Q8 | 1 | 2 | yes | — |
| 365 | C23×D3 | #498 | 1 | 1 | yes | characteristic |
| 366 | C22×C3×C4 | C2×C4⋊Q8 | 1 | 1 | yes | characteristic |
| 367 | C22×C3×C4 | C22×SD16 | 1 | 2 | yes | — |
| 368 | C22×Dic3 | #498 | 1 | 2 | yes | — |
| 369 | C22×Dic3 | #498 | 1 | 1 | yes | characteristic |
| 370 | C2×C4×D3 | — | 2 | 4 | no | — |
| 371 | C2×C4×D3 | — | 2 | 8 | no | — |
| 372 | C2×C4×D3 | #384 | 1 | 1 | yes | characteristic |
| 373 | C2×C4×D3 | #384 | 1 | 1 | yes | characteristic |
| 374 | C2×C4×D3 | C2×#106 | 1 | 2 | yes | — |
| 375 | C2×C4×D3 | C2×#106 | 1 | 2 | yes | — |
| 376 | C2×C4×D3 | #492 | 1 | 2 | yes | — |
| 377 | C2×C4×D3 | #492 | 1 | 2 | yes | — |
| 378 | C2×C4×D3 | #498 | 1 | 1 | yes | characteristic |
| 379 | C2×C4×D3 | #498 | 1 | 1 | yes | characteristic |
| 380 | C3×M16 | — | 8 | 8 | no | — |
| 381 | C2×C3×C8 | — | 2 | 4 | no | — |
| 382 | C2×C3×C8 | — | 2 | 8 | no | — |
| 383 | C2×C3×C8 | — | 8 | 4 | no | — |
| 384 | C2×C3×C8 | C2×#106 | 1 | 4 | yes | — |
| 385 | C2×C3×C8 | C2×#106 | 1 | 4 | yes | — |
| 386 | C2×C3×C8 | C22×C4⋊C4 | 1 | 2 | yes | — |
| 387 | C2×C3×C8 | C2×C4⋊Q8 | 1 | 2 | yes | — |
| 388 | C3×C42 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 389 | C3×C42 | C2×#127 | 1 | 1 | yes | characteristic |
| 390 | C3×C42 | C22×SD16 | 1 | 2 | yes | — |
| 391 | C4×Dic3 | #384 | 1 | 1 | yes | characteristic |
| 392 | C4×Dic3 | #384 | 1 | 1 | yes | characteristic |
| 393 | C4×Dic3 | C2×#106 | 1 | 2 | yes | — |
| 394 | C4×Dic3 | C2×#106 | 1 | 2 | yes | — |
| 395 | C4×Dic3 | #492 | 1 | 2 | yes | — |
| 396 | C4×Dic3 | #492 | 1 | 2 | yes | — |
| 397 | C4×Dic3 | #498 | 1 | 2 | yes | — |
| 398 | #208 | — | 8 | 8 | no | — |
| 399 | C2×C3⋊C8 | — | 2 | 4 | no | — |
| 400 | C2×C3⋊C8 | — | 2 | 8 | no | — |
| 401 | C2×C3⋊C8 | — | 8 | 4 | no | — |
| 402 | C2×C3⋊C8 | #384 | 1 | 2 | yes | — |
| 403 | C2×C3⋊C8 | #384 | 1 | 2 | yes | — |
| 404 | C2×C3⋊C8 | C2×#106 | 1 | 4 | yes | — |
| 405 | C2×C3⋊C8 | C2×#106 | 1 | 4 | yes | — |
| 406 | ΓL(1,𝔽25) | — | 16 | 8 | no | — |
| 407 | D3×C8 | — | 2 | 4 | no | — |
| 408 | D3×C8 | — | 2 | 8 | no | — |
| 409 | D3×C8 | — | 2 | 4 | no | — |
| 410 | D3×C8 | — | 2 | 8 | no | — |
| 411 | D3×C8 | — | 2 | 4 | no | — |
| 412 | D3×C8 | — | 2 | 8 | no | — |
| 413 | D3×C8 | — | 16 | 8 | no | — |
| 414 | D3×C8 | #365 | 1 | 16 | yes | — |
| 415 | D3×C8 | C2×#108 | 1 | 8 | yes | — |
| 416 | C3×C16 | — | 2 | 4 | no | — |
| 417 | C3×C16 | C2×#108 | 1 | 8 | yes | complemented |
| 418 | C3⋊C16 | — | 2 | 4 | no | — |
| 419 | C3⋊C16 | C2×#108 | 1 | 8 | yes | complemented |
| 420 | C23×C4 | — | 3 | 1 | no | — |
| 421 | C23×C4 | — | 3 | 2 | no | — |
| 422 | C2×M16 | — | 4 | 4 | no | — |
| 423 | C2×M16 | — | 12 | 4 | no | — |
| 424 | C2×M16 | — | 24 | 4 | no | — |
| 425 | C2×M16 | — | 24 | 16 | no | — |
| 426 | C22×C8 | — | 3 | 2 | no | — |
| 427 | C22×C8 | — | 3 | 4 | no | — |
| 428 | C22×C8 | — | 3 | 2 | no | — |
| 429 | C22×C8 | — | 3 | 4 | no | — |
| 430 | C22×C8 | — | 3 | 2 | no | — |
| 431 | C22×C8 | — | 3 | 2 | no | — |
| 432 | C22×C8 | — | 3 | 2 | no | — |
| 433 | C22×C8 | — | 3 | 4 | no | — |
| 434 | C22×C8 | — | 3 | 4 | no | — |
| 435 | C22×C8 | — | 3 | 4 | no | — |
| 436 | C22×C8 | — | 6 | 16 | no | — |
| 437 | C22×C8 | — | 6 | 8 | no | — |
| 438 | C22×C8 | — | 24 | 4 | no | — |
| 439 | C22×C8 | D3×SD16 | 1 | 4 | yes | — |
| 440 | C22×C8 | C2×D3×Q8 | 1 | 2 | yes | — |
| 441 | C2×C42 | — | 3 | 1 | no | — |
| 442 | C2×C42 | — | 3 | 2 | no | — |
| 443 | C2×C42 | — | 3 | 1 | no | — |
| 444 | C2×C42 | — | 3 | 1 | no | — |
| 445 | C2×C42 | — | 3 | 1 | no | — |
| 446 | C2×C42 | — | 3 | 1 | no | — |
| 447 | C2×C42 | — | 3 | 2 | no | — |
| 448 | C2×C42 | — | 3 | 2 | no | — |
| 449 | C2×C42 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 450 | M32 | — | 2 | 8 | no | — |
| 451 | M32 | — | 6 | 8 | no | — |
| 452 | M32 | — | 6 | 8 | no | — |
| 453 | M32 | — | 6 | 8 | no | — |
| 454 | C2×C16 | — | 3 | 4 | no | — |
| 455 | C2×C16 | — | 3 | 16 | no | — |
| 456 | C2×C16 | — | 3 | 4 | no | — |
| 457 | C2×C16 | — | 6 | 8 | no | — |
| 458 | C2×C16 | D3×C4⋊C4 | 1 | 4 | yes | — |
| 459 | C2×C16 | D3×C4⋊C4 | 1 | 4 | yes | — |
| 460 | #108 | — | 8 | 8 | no | — |
| 461 | #108 | — | 24 | 8 | no | — |
| 462 | #108 | — | 24 | 16 | no | — |
| 463 | C4⋊C8 | — | 4 | 4 | no | — |
| 464 | C4⋊C8 | — | 4 | 4 | no | — |
| 465 | C4⋊C8 | — | 12 | 4 | no | — |
| 466 | C4⋊C8 | — | 12 | 4 | no | — |
| 467 | C4⋊C8 | — | 24 | 4 | no | — |
| 468 | C4⋊C8 | — | 24 | 4 | no | — |
| 469 | C4×C8 | — | 3 | 2 | no | — |
| 470 | C4×C8 | — | 3 | 2 | no | — |
| 471 | C4×C8 | — | 3 | 2 | no | — |
| 472 | C4×C8 | — | 3 | 2 | no | — |
| 473 | C4×C8 | — | 3 | 4 | no | — |
| 474 | C4×C8 | — | 3 | 4 | no | — |
| 475 | C4×C8 | — | 3 | 4 | no | — |
| 476 | C4×C8 | — | 3 | 4 | no | — |
| 477 | C4×C8 | — | 3 | 2 | no | — |
| 478 | C4×C8 | — | 3 | 2 | no | — |
| 479 | C4×C8 | — | 3 | 1 | no | — |
| 480 | C4×C8 | — | 3 | 2 | no | — |
| 481 | C4×C8 | — | 3 | 1 | no | — |
| 482 | C4×C8 | — | 3 | 4 | no | — |
| 483 | C4×C8 | D3×C4⋊C4 | 1 | 2 | yes | — |
| 484 | C4×C8 | D3×C4⋊C4 | 1 | 2 | yes | — |
| 485 | C4×C8 | D3×SD16 | 1 | 4 | yes | — |
| 486 | C4×C8 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 487 | C4×C8 | C2×D3×D4 | 1 | 2 | yes | — |
| 488 | C4×C8 | C2×D3×Q8 | 1 | 1 | yes | characteristic |
| 489 | C23×C3 | C2×#498 | 1 | 1 | yes | characteristic |
| 490 | C22×D3 | — | 2 | 4 | no | — |
| 491 | C22×D3 | — | 2 | 2 | no | — |
| 492 | C22×D3 | #1844 | 1 | 1 | yes | characteristic |
| 493 | C22×D3 | #1844 | 1 | 1 | yes | characteristic |
| 494 | C2×C3×C4 | — | 2 | 2 | no | — |
| 495 | C2×C3×C4 | — | 2 | 4 | no | — |
| 496 | C2×C3×C4 | C2×#384 | 1 | 1 | yes | characteristic |
| 497 | C2×C3×C4 | C22×#106 | 1 | 2 | yes | — |
| 498 | C2×C3×C4 | C2×#492 | 1 | 2 | yes | — |
| 499 | C2×C3×C4 | C2×#498 | 1 | 1 | yes | characteristic |
| 500 | C2×Dic3 | — | 2 | 4 | no | — |
| 501 | C2×Dic3 | — | 2 | 2 | no | — |
| 502 | C2×Dic3 | #1844 | 1 | 2 | yes | — |
| 503 | C2×Dic3 | #1844 | 1 | 1 | yes | characteristic |
| 504 | C2×Dic3 | #1844 | 1 | 2 | yes | — |
| 505 | C2×Dic3 | #1844 | 1 | 1 | yes | characteristic |
| 506 | C4×D3 | — | 2 | 4 | no | — |
| 507 | C4×D3 | — | 2 | 2 | no | — |
| 508 | C4×D3 | — | 2 | 2 | no | — |
| 509 | C4×D3 | — | 2 | 4 | no | — |
| 510 | C4×D3 | — | 2 | 4 | no | — |
| 511 | C4×D3 | — | 2 | 2 | no | — |
| 512 | C4×D3 | #1848 | 1 | 4 | yes | — |
| 513 | C4×D3 | C2×#365 | 1 | 8 | yes | — |
| 514 | C3×C8 | — | 2 | 2 | no | — |
| 515 | C3×C8 | — | 2 | 4 | no | — |
| 516 | C3×C8 | — | 16 | 4 | no | — |
| 517 | C3×C8 | C2×#365 | 1 | 8 | yes | — |
| 518 | C3×C8 | C22×#108 | 1 | 4 | yes | — |
| 519 | C3⋊C8 | — | 2 | 2 | no | — |
| 520 | C3⋊C8 | — | 2 | 4 | no | — |
| 521 | C3⋊C8 | — | 16 | 4 | no | — |
| 522 | C3⋊C8 | #1848 | 1 | 4 | yes | — |
| 523 | C3⋊C8 | C2×#365 | 1 | 8 | yes | — |
| 524 | C24 | — | 3 | 1 | no | — |
| 525 | C22×C4 | — | 3 | 2 | no | — |
| 526 | C22×C4 | — | 3 | 1 | no | — |
| 527 | C22×C4 | — | 3 | 2 | no | — |
| 528 | C22×C4 | — | 3 | 1 | no | — |
| 529 | C22×C4 | — | 3 | 2 | no | — |
| 530 | C22×C4 | — | 3 | 2 | no | — |
| 531 | C22×C4 | — | 3 | 2 | no | — |
| 532 | C22×C4 | — | 3 | 1 | no | — |
| 533 | C22×C4 | — | 3 | 1 | no | — |
| 534 | C22×C4 | — | 3 | 1 | no | — |
| 535 | C22×C4 | — | 6 | 8 | no | — |
| 536 | C22×C4 | — | 6 | 4 | no | — |
| 537 | C22×C4 | D3×C4⋊Q8 | 1 | 1 | yes | characteristic |
| 538 | C22×C4 | C2×D3×SD16 | 1 | 2 | yes | — |
| 539 | M16 | — | 8 | 8 | no | — |
| 540 | M16 | — | 24 | 8 | no | — |
| 541 | M16 | — | 48 | 8 | no | — |
| 542 | C2×C8 | — | 2 | 4 | no | — |
| 543 | C2×C8 | — | 2 | 8 | no | — |
| 544 | C2×C8 | — | 3 | 4 | no | — |
| 545 | C2×C8 | — | 3 | 2 | no | — |
| 546 | C2×C8 | — | 3 | 8 | no | — |
| 547 | C2×C8 | — | 3 | 16 | no | — |
| 548 | C2×C8 | — | 3 | 4 | no | — |
| 549 | C2×C8 | — | 3 | 2 | no | — |
| 550 | C2×C8 | — | 6 | 8 | no | — |
| 551 | C2×C8 | — | 6 | 4 | no | — |
| 552 | C2×C8 | — | 6 | 8 | no | — |
| 553 | C2×C8 | — | 6 | 4 | no | — |
| 554 | C2×C8 | — | 6 | 8 | no | — |
| 555 | C2×C8 | — | 6 | 4 | no | — |
| 556 | C2×C8 | — | 6 | 4 | no | — |
| 557 | C2×C8 | — | 6 | 8 | no | — |
| 558 | C2×C8 | — | 8 | 4 | no | — |
| 559 | C2×C8 | — | 24 | 4 | no | — |
| 560 | C2×C8 | — | 48 | 8 | no | — |
| 561 | C2×C8 | D3×#106 | 1 | 4 | yes | — |
| 562 | C2×C8 | D3×#106 | 1 | 4 | yes | — |
| 563 | C2×C8 | C2×D3×C4⋊C4 | 1 | 2 | yes | — |
| 564 | C2×C8 | D3×C4⋊Q8 | 1 | 2 | yes | — |
| 565 | C42 | — | 3 | 2 | no | — |
| 566 | C42 | — | 3 | 2 | no | — |
| 567 | C42 | — | 3 | 2 | no | — |
| 568 | C42 | — | 3 | 2 | no | — |
| 569 | C42 | — | 3 | 1 | no | — |
| 570 | C42 | — | 3 | 1 | no | — |
| 571 | C42 | — | 3 | 2 | no | — |
| 572 | C42 | C2×D3×C4⋊C4 | 1 | 1 | yes | characteristic |
| 573 | C42 | D3×#127 | 1 | 1 | yes | characteristic |
| 574 | C42 | C2×D3×SD16 | 1 | 2 | yes | — |
| 575 | C16 | — | 2 | 4 | no | — |
| 576 | C16 | — | 3 | 8 | no | — |
| 577 | C16 | — | 6 | 4 | no | — |
| 578 | C16 | D3×#108 | 1 | 8 | yes | complemented |
| 579 | C22×C3 | — | 2 | 2 | no | — |
| 580 | C22×C3 | — | 2 | 1 | no | — |
| 581 | C22×C3 | C2×#1844 | 1 | 1 | yes | characteristic |
| 582 | C2×D3 | — | 2 | 2 | no | — |
| 583 | C2×D3 | — | 2 | 1 | no | — |
| 584 | C2×D3 | — | 4 | 4 | no | — |
| 585 | C2×D3 | #8822 | 1 | 2 | yes | — |
| 586 | C2×D3 | #12903 | 1 | 4 | yes | — |
| 587 | C3×C4 | — | 2 | 2 | no | — |
| 588 | C3×C4 | — | 2 | 1 | no | — |
| 589 | C3×C4 | C2×#1848 | 1 | 2 | yes | — |
| 590 | C3×C4 | C22×#365 | 1 | 4 | yes | — |
| 591 | Dic3 | — | 2 | 2 | no | — |
| 592 | Dic3 | — | 2 | 1 | no | — |
| 593 | Dic3 | #8822 | 1 | 2 | yes | — |
| 594 | Dic3 | #12903 | 1 | 4 | yes | — |
| 595 | C23 | — | 3 | 1 | no | — |
| 596 | C23 | — | 3 | 1 | no | — |
| 597 | C23 | — | 6 | 4 | no | — |
| 598 | C23 | — | 6 | 2 | no | — |
| 599 | C23 | D3×#498 | 1 | 1 | yes | characteristic |
| 600 | C2×C4 | — | 2 | 4 | no | — |
| 601 | C2×C4 | — | 2 | 2 | no | — |
| 602 | C2×C4 | — | 3 | 2 | no | — |
| 603 | C2×C4 | — | 3 | 1 | no | — |
| 604 | C2×C4 | — | 3 | 8 | no | — |
| 605 | C2×C4 | — | 3 | 4 | no | — |
| 606 | C2×C4 | — | 3 | 2 | no | — |
| 607 | C2×C4 | — | 3 | 1 | no | — |
| 608 | C2×C4 | — | 6 | 4 | no | — |
| 609 | C2×C4 | — | 6 | 2 | no | — |
| 610 | C2×C4 | — | 6 | 4 | no | — |
| 611 | C2×C4 | — | 6 | 2 | no | — |
| 612 | C2×C4 | — | 6 | 4 | no | — |
| 613 | C2×C4 | — | 6 | 2 | no | — |
| 614 | C2×C4 | — | 6 | 4 | no | — |
| 615 | C2×C4 | — | 6 | 2 | no | — |
| 616 | C2×C4 | D3×#384 | 1 | 1 | yes | characteristic |
| 617 | C2×C4 | C2×D3×#106 | 1 | 2 | yes | — |
| 618 | C2×C4 | D3×#492 | 1 | 2 | yes | — |
| 619 | C2×C4 | D3×#498 | 1 | 1 | yes | characteristic |
| 620 | C8 | — | 2 | 4 | no | — |
| 621 | C8 | — | 2 | 2 | no | — |
| 622 | C8 | — | 3 | 8 | no | — |
| 623 | C8 | — | 3 | 4 | no | — |
| 624 | C8 | — | 6 | 4 | no | — |
| 625 | C8 | — | 6 | 2 | no | — |
| 626 | C8 | — | 16 | 4 | no | — |
| 627 | C8 | — | 48 | 4 | no | — |
| 628 | C8 | D3×#365 | 1 | 8 | yes | — |
| 629 | C8 | C2×D3×#108 | 1 | 4 | yes | — |
| 630 | C2×C3 | — | 4 | 1 | no | — |
| 631 | C2×C3 | C2×#8822 | 1 | 1 | yes | characteristic |
| 632 | C2×C3 | C2×#12903 | 1 | 2 | yes | — |
| 633 | D3 | — | 4 | 1 | no | — |
| 634 | D3 | #135792 | 1 | 4 | yes | direct product factor |
| 635 | C22 | — | 2 | 2 | no | — |
| 636 | C22 | — | 2 | 1 | no | — |
| 637 | C22 | — | 3 | 4 | no | — |
| 638 | C22 | — | 3 | 2 | no | — |
| 639 | C22 | — | 6 | 2 | no | — |
| 640 | C22 | — | 6 | 1 | no | — |
| 641 | C22 | — | 12 | 4 | no | — |
| 642 | C22 | D3×#1844 | 1 | 1 | yes | characteristic |
| 643 | C4 | — | 2 | 2 | no | — |
| 644 | C4 | — | 2 | 1 | no | — |
| 645 | C4 | — | 3 | 4 | no | — |
| 646 | C4 | — | 3 | 2 | no | — |
| 647 | C4 | — | 6 | 2 | no | — |
| 648 | C4 | — | 6 | 1 | no | — |
| 649 | C4 | D3×#1848 | 1 | 2 | yes | — |
| 650 | C4 | C2×D3×#365 | 1 | 4 | yes | — |
| 651 | C3 | C2×#135792 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 652 | C2 | — | 3 | 4 | no | — |
| 653 | C2 | — | 4 | 1 | no | — |
| 654 | C2 | — | 12 | 1 | no | — |
| 655 | C2 | D3×#12903 | 1 | 2 | yes | — |
| 656 | C2 | D3×#8822 | 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