Finite Group DatabasebetaFinite Group DatabasebetaOrder 3072.
3038 conjugacy classes of subgroups.
The subgroup lattice has 676 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72225892 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72225890 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72225887 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #72225885 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72225884 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72225882 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #72225817 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #72225815 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C3×#126544 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #72213983 | — | 3 | 1 | no | maximal, Sylow |
| 11 | #10950617 | C22 | 1 | 4 | yes | — |
| 12 | C2×#69091 | — | 2 | 8 | no | — |
| 13 | #10803808 | C22 | 1 | 2 | yes | — |
| 14 | #10803642 | — | 2 | 2 | no | — |
| 15 | #10803642 | C22 | 1 | 2 | yes | — |
| 16 | #10782888 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#68062 | C22 | 1 | 1 | yes | characteristic |
| 18 | #10765754 | — | 2 | 2 | no | — |
| 19 | #10713637 | — | 2 | 8 | no | — |
| 20 | #10713447 | C22 | 1 | 4 | yes | — |
| 21 | #10713435 | C22 | 1 | 4 | yes | — |
| 22 | #10711613 | C22 | 1 | 4 | yes | — |
| 23 | #10709915 | C4 | 1 | 4 | yes | complemented |
| 24 | #10709905 | C4 | 1 | 2 | yes | complemented |
| 25 | #10709899 | C4 | 1 | 2 | yes | complemented |
| 26 | #10695159 | C22 | 1 | 2 | yes | — |
| 27 | #10695092 | — | 2 | 2 | no | — |
| 28 | #10695025 | — | 2 | 2 | no | — |
| 29 | #10695025 | C22 | 1 | 2 | yes | — |
| 30 | #10688988 | C22 | 1 | 1 | yes | characteristic |
| 31 | #10688954 | C22 | 1 | 1 | yes | characteristic |
| 32 | C3×C4×#347 | C22 | 1 | 2 | yes | — |
| 33 | C3×#11404 | C22 | 1 | 2 | yes | — |
| 34 | C3×#11402 | C22 | 1 | 1 | yes | characteristic |
| 35 | C3×C8×M32 | C22 | 1 | 1 | yes | characteristic |
| 36 | C3×#7846 | C22 | 1 | 1 | yes | characteristic |
| 37 | #496124 | — | 3 | 4 | no | — |
| 38 | #491469 | — | 3 | 1 | no | — |
| 39 | #213274 | — | 3 | 1 | no | — |
| 40 | #212918 | — | 3 | 1 | no | — |
| 41 | #141758 | — | 3 | 4 | no | — |
| 42 | #141754 | — | 3 | 1 | no | — |
| 43 | #141751 | — | 3 | 1 | no | — |
| 44 | #135758 | — | 3 | 1 | no | — |
| 45 | #126544 | D3 | 1 | 1 | yes | characteristic, complemented |
| 46 | C2×#4908 | — | 2 | 8 | no | — |
| 47 | C2×#4717 | — | 2 | 4 | no | — |
| 48 | C2×#4711 | — | 2 | 4 | no | — |
| 49 | C2×#4711 | — | 4 | 4 | no | — |
| 50 | #78470 | — | 2 | 2 | no | — |
| 51 | #78467 | C23 | 1 | 2 | yes | — |
| 52 | C2×#4695 | — | 2 | 2 | no | — |
| 53 | C2×#4695 | C23 | 1 | 2 | yes | — |
| 54 | #78458 | — | 2 | 2 | no | — |
| 55 | C4×#874 | — | 2 | 2 | no | — |
| 56 | C2×C3×#347 | D4 | 1 | 8 | yes | — |
| 57 | C3×C4×M32 | C23 | 1 | 2 | yes | — |
| 58 | C3×C4×M32 | C23 | 1 | 2 | yes | — |
| 59 | C3×C4×#97 | D4 | 1 | 2 | yes | — |
| 60 | C3×C4×#97 | C23 | 1 | 1 | yes | characteristic |
| 61 | C2×C3×#322 | D4 | 1 | 2 | yes | — |
| 62 | C2×C3×#322 | C23 | 1 | 1 | yes | characteristic |
| 63 | C2×C3×C82 | C23 | 1 | 1 | yes | characteristic |
| 64 | C2×#4518 | — | 2 | 8 | no | — |
| 65 | C2×#4516 | — | 2 | 8 | no | — |
| 66 | C2×#4513 | — | 2 | 8 | no | — |
| 67 | #69845 | — | 2 | 4 | no | — |
| 68 | #69825 | — | 2 | 4 | no | — |
| 69 | #69825 | — | 4 | 4 | no | — |
| 70 | #69792 | C23 | 1 | 2 | yes | — |
| 71 | #69772 | — | 2 | 2 | no | — |
| 72 | #69772 | — | 2 | 4 | no | — |
| 73 | #69764 | — | 2 | 2 | no | — |
| 74 | #69764 | C23 | 1 | 2 | yes | — |
| 75 | #69735 | — | 2 | 4 | no | — |
| 76 | #69730 | — | 2 | 2 | no | — |
| 77 | #69395 | — | 2 | 2 | no | — |
| 78 | #69091 | — | 4 | 32 | no | — |
| 79 | #69081 | — | 2 | 8 | no | — |
| 80 | #69061 | C2×C4 | 1 | 8 | yes | complemented |
| 81 | #69060 | C2×C4 | 1 | 8 | yes | complemented |
| 82 | #68083 | — | 4 | 4 | no | — |
| 83 | #68077 | — | 4 | 4 | no | — |
| 84 | #68065 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 85 | #68062 | — | 2 | 2 | no | — |
| 86 | #68062 | C2×C4 | 1 | 2 | yes | — |
| 87 | #68062 | C2×C4 | 1 | 2 | yes | — |
| 88 | #68062 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 89 | #68060 | C2×C4 | 1 | 2 | yes | complemented |
| 90 | #68058 | — | 2 | 2 | no | — |
| 91 | C3×#1313 | — | 2 | 4 | no | — |
| 92 | C3×#1312 | — | 2 | 2 | no | — |
| 93 | C3×#1311 | C2×C4 | 1 | 2 | yes | complemented |
| 94 | C3×C8×C16 | C2×C4 | 1 | 2 | yes | complemented |
| 95 | #33717 | — | 3 | 4 | no | — |
| 96 | C2×AGL(1,ℤ/16) | — | 6 | 8 | no | — |
| 97 | #21706 | — | 3 | 2 | no | — |
| 98 | #21690 | — | 3 | 2 | no | — |
| 99 | #21690 | — | 6 | 2 | no | — |
| 100 | #19603 | — | 3 | 1 | no | — |
| 101 | C2×#1712 | — | 3 | 1 | no | — |
| 102 | #17962 | — | 6 | 2 | no | — |
| 103 | #13249 | — | 6 | 8 | no | — |
| 104 | #13213 | — | 3 | 4 | no | — |
| 105 | #13210 | — | 3 | 4 | no | — |
| 106 | #12903 | — | 3 | 4 | no | — |
| 107 | C4×#347 | C2×D3 | 1 | 2 | yes | — |
| 108 | #12519 | — | 3 | 4 | no | — |
| 109 | #12517 | — | 3 | 2 | no | — |
| 110 | #12515 | — | 3 | 2 | no | — |
| 111 | #11404 | C2×D3 | 1 | 2 | yes | — |
| 112 | #11402 | C2×D3 | 1 | 1 | yes | characteristic |
| 113 | C8×M32 | C2×D3 | 1 | 1 | yes | characteristic |
| 114 | #9862 | — | 3 | 2 | no | — |
| 115 | #9849 | — | 6 | 2 | no | — |
| 116 | #9837 | — | 3 | 2 | no | — |
| 117 | #9837 | — | 6 | 2 | no | — |
| 118 | #8822 | — | 3 | 1 | no | — |
| 119 | #8813 | — | 3 | 1 | no | — |
| 120 | #7846 | C2×D3 | 1 | 1 | yes | characteristic |
| 121 | C2×#904 | — | 2 | 4 | no | — |
| 122 | C22×D24 | — | 2 | 4 | no | — |
| 123 | C22×D24 | — | 4 | 4 | no | — |
| 124 | C2×#901 | — | 4 | 2 | no | — |
| 125 | #5477 | — | 2 | 2 | no | — |
| 126 | C2×#874 | — | 2 | 2 | no | — |
| 127 | C2×C4×D12 | — | 4 | 4 | no | — |
| 128 | C2×C4×D12 | — | 4 | 2 | no | — |
| 129 | C2×C3×M32 | C2×D4 | 1 | 4 | yes | — |
| 130 | C2×C3×M32 | C2×D4 | 1 | 4 | yes | — |
| 131 | C2×C3×#97 | — | 2 | 4 | no | — |
| 132 | C2×C3×#97 | C2×D4 | 1 | 4 | yes | — |
| 133 | C2×C3×C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 134 | C2×C3×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 135 | C2×C3×C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 136 | C2×C3×C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 137 | C3×C43 | C2×D4 | 1 | 1 | yes | characteristic |
| 138 | #5115 | — | 4 | 4 | no | — |
| 139 | C2×#821 | — | 4 | 8 | no | — |
| 140 | C2×#821 | — | 4 | 4 | no | — |
| 141 | #5110 | — | 4 | 2 | no | — |
| 142 | C2×#819 | — | 2 | 4 | no | — |
| 143 | C2×#817 | — | 2 | 4 | no | — |
| 144 | C2×#817 | — | 4 | 4 | no | — |
| 145 | #4939 | — | 4 | 4 | no | — |
| 146 | #4939 | — | 4 | 2 | no | — |
| 147 | #4935 | — | 2 | 2 | no | — |
| 148 | C2×#805 | — | 4 | 4 | no | — |
| 149 | #4924 | — | 2 | 2 | no | — |
| 150 | #4908 | — | 4 | 16 | no | — |
| 151 | #4908 | — | 4 | 16 | no | — |
| 152 | C2×#800 | — | 2 | 16 | no | — |
| 153 | C2×D48 | — | 2 | 16 | no | — |
| 154 | #4717 | — | 4 | 16 | no | — |
| 155 | #4711 | — | 4 | 16 | no | — |
| 156 | #4711 | — | 8 | 16 | no | — |
| 157 | #4699 | C22×C4 | 1 | 2 | yes | — |
| 158 | #4696 | — | 2 | 4 | no | — |
| 159 | #4695 | — | 2 | 4 | no | — |
| 160 | #4695 | — | 2 | 4 | no | — |
| 161 | #4695 | — | 2 | 2 | no | — |
| 162 | #4695 | — | 2 | 2 | no | — |
| 163 | #4695 | — | 2 | 4 | no | — |
| 164 | #4695 | — | 4 | 4 | no | — |
| 165 | #4695 | C22×C4 | 1 | 4 | yes | — |
| 166 | #4695 | C22×C4 | 1 | 2 | yes | — |
| 167 | #4694 | — | 2 | 4 | no | — |
| 168 | #4693 | — | 2 | 2 | no | — |
| 169 | C4×D24 | — | 4 | 4 | no | — |
| 170 | #4688 | — | 4 | 4 | no | — |
| 171 | C8×D12 | — | 4 | 4 | no | — |
| 172 | #4682 | — | 2 | 2 | no | — |
| 173 | C3×#347 | — | 2 | 16 | no | — |
| 174 | C3×#346 | — | 2 | 2 | no | — |
| 175 | C3×#346 | #41 | 1 | 4 | yes | — |
| 176 | C3×C4×C16 | — | 2 | 2 | no | — |
| 177 | C3×C4×C16 | C22×C4 | 1 | 4 | yes | — |
| 178 | C3×#322 | — | 2 | 4 | no | — |
| 179 | C3×#322 | — | 2 | 2 | no | — |
| 180 | C3×C82 | C22×C4 | 1 | 1 | yes | characteristic |
| 181 | C3×C82 | C22×C4 | 1 | 1 | yes | characteristic |
| 182 | C3×C82 | #41 | 1 | 2 | yes | — |
| 183 | #4518 | — | 4 | 16 | no | — |
| 184 | #4516 | — | 4 | 16 | no | — |
| 185 | #4513 | — | 4 | 16 | no | — |
| 186 | #4459 | — | 4 | 8 | no | — |
| 187 | #4457 | — | 4 | 4 | no | — |
| 188 | C2×#509 | — | 6 | 8 | no | — |
| 189 | #3169 | — | 6 | 2 | no | — |
| 190 | #3147 | — | 3 | 2 | no | — |
| 191 | C2×#493 | — | 3 | 2 | no | — |
| 192 | C2×#493 | — | 6 | 2 | no | — |
| 193 | C2×#444 | — | 6 | 4 | no | — |
| 194 | C2×#442 | — | 6 | 4 | no | — |
| 195 | C2×#442 | — | 12 | 4 | no | — |
| 196 | #2931 | — | 6 | 2 | no | — |
| 197 | C4×#127 | — | 6 | 2 | no | — |
| 198 | #2250 | — | 6 | 8 | no | — |
| 199 | #2248 | — | 3 | 8 | no | — |
| 200 | #2246 | — | 3 | 8 | no | — |
| 201 | AGL(1,ℤ/16) | — | 12 | 32 | no | — |
| 202 | C2×#365 | — | 6 | 8 | no | — |
| 203 | C2×#361 | — | 6 | 8 | no | — |
| 204 | C2×#360 | — | 6 | 8 | no | — |
| 205 | C2×#347 | D12 | 1 | 8 | yes | — |
| 206 | C4×M32 | C22×D3 | 1 | 2 | yes | — |
| 207 | C4×M32 | C22×D3 | 1 | 2 | yes | — |
| 208 | #1975 | — | 6 | 4 | no | — |
| 209 | #1972 | — | 6 | 4 | no | — |
| 210 | #1972 | — | 12 | 4 | no | — |
| 211 | #1962 | — | 6 | 2 | no | — |
| 212 | #1957 | — | 6 | 4 | no | — |
| 213 | #1957 | — | 6 | 2 | no | — |
| 214 | #1848 | — | 3 | 2 | no | — |
| 215 | #1844 | — | 3 | 2 | no | — |
| 216 | #1844 | — | 6 | 2 | no | — |
| 217 | C4×#97 | D12 | 1 | 2 | yes | — |
| 218 | C4×#97 | C22×D3 | 1 | 1 | yes | characteristic |
| 219 | #1713 | — | 3 | 1 | no | — |
| 220 | #1712 | — | 3 | 2 | no | — |
| 221 | #1712 | — | 3 | 2 | no | — |
| 222 | #1712 | — | 3 | 1 | no | — |
| 223 | #1712 | — | 6 | 2 | no | — |
| 224 | #1709 | — | 3 | 2 | no | — |
| 225 | #1706 | — | 6 | 2 | no | — |
| 226 | #1594 | — | 12 | 4 | no | — |
| 227 | #1580 | — | 12 | 4 | no | — |
| 228 | #1566 | — | 6 | 2 | no | — |
| 229 | #1492 | — | 6 | 4 | no | — |
| 230 | C2×#322 | D12 | 1 | 2 | yes | — |
| 231 | C2×#322 | C22×D3 | 1 | 1 | yes | characteristic |
| 232 | C2×C82 | C22×D3 | 1 | 1 | yes | characteristic |
| 233 | #1313 | — | 2 | 4 | no | — |
| 234 | #1312 | — | 2 | 2 | no | — |
| 235 | #1311 | C4×D3 | 1 | 2 | yes | complemented |
| 236 | C8×C16 | C4×D3 | 1 | 2 | yes | complemented |
| 237 | C2×#235 | — | 4 | 2 | no | — |
| 238 | C22×D12 | — | 4 | 2 | no | — |
| 239 | C22×D12 | — | 4 | 4 | no | — |
| 240 | C22×C4×D3 | — | 8 | 2 | no | — |
| 241 | C22×C3×C8 | — | 2 | 2 | no | — |
| 242 | C22×C3×C8 | #127 | 1 | 2 | yes | — |
| 243 | C22×C3×C8 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 244 | C22×C3×C8 | C22×D4 | 1 | 2 | yes | — |
| 245 | C2×C3×C42 | — | 2 | 2 | no | — |
| 246 | C2×C3×C42 | #127 | 1 | 2 | yes | — |
| 247 | C2×C3×C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 248 | #930 | — | 4 | 4 | no | — |
| 249 | C2×(C2×D3)⋊C4 | — | 8 | 2 | no | — |
| 250 | C2×(C2×D3)⋊C4 | — | 8 | 4 | no | — |
| 251 | C2×C4⋊Dic3 | — | 4 | 2 | no | — |
| 252 | C2×C4⋊Dic3 | — | 4 | 4 | no | — |
| 253 | C2×#208 | — | 4 | 2 | no | — |
| 254 | C2×Dic12 | — | 2 | 4 | no | — |
| 255 | #904 | — | 4 | 8 | no | — |
| 256 | #904 | — | 4 | 8 | no | — |
| 257 | C2×D24 | — | 2 | 4 | no | — |
| 258 | C2×D24 | — | 2 | 8 | no | — |
| 259 | C2×D24 | — | 4 | 8 | no | — |
| 260 | C2×D24 | — | 4 | 8 | no | — |
| 261 | C2×D24 | — | 4 | 4 | no | — |
| 262 | C2×D24 | — | 4 | 4 | no | — |
| 263 | C2×D24 | — | 4 | 8 | no | — |
| 264 | C2×D24 | — | 4 | 8 | no | — |
| 265 | C2×D24 | — | 8 | 8 | no | — |
| 266 | C2×D24 | — | 8 | 8 | no | — |
| 267 | C2×#204 | — | 4 | 4 | no | — |
| 268 | #901 | — | 8 | 8 | no | — |
| 269 | C2×ΓL(1,𝔽25) | — | 8 | 2 | no | — |
| 270 | C2×D3×C8 | — | 8 | 2 | no | — |
| 271 | #875 | — | 4 | 2 | no | — |
| 272 | #874 | — | 2 | 2 | no | — |
| 273 | #874 | — | 2 | 4 | no | — |
| 274 | #874 | — | 4 | 2 | no | — |
| 275 | #874 | — | 4 | 4 | no | — |
| 276 | C4×D12 | — | 4 | 4 | no | — |
| 277 | C4×D12 | — | 8 | 8 | no | — |
| 278 | C4×D12 | — | 8 | 16 | no | — |
| 279 | #869 | — | 2 | 2 | no | — |
| 280 | C3×M32 | — | 2 | 8 | no | — |
| 281 | C3×M32 | AGL(1,ℤ/8) | 1 | 16 | yes | — |
| 282 | C2×C3×C16 | — | 2 | 4 | no | — |
| 283 | C2×C3×C16 | C4×D4 | 1 | 8 | yes | — |
| 284 | C3×#97 | — | 2 | 8 | no | — |
| 285 | C3×#97 | — | 4 | 8 | no | — |
| 286 | C3×C4×C8 | — | 2 | 2 | no | — |
| 287 | C3×C4×C8 | — | 2 | 2 | no | — |
| 288 | C3×C4×C8 | — | 2 | 2 | no | — |
| 289 | C3×C4×C8 | C4×D4 | 1 | 2 | yes | — |
| 290 | C3×C4×C8 | C4×D4 | 1 | 2 | yes | — |
| 291 | C3×C4×C8 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 292 | C3×C4×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 293 | C3×C4×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 294 | C3×C4×C8 | C2×#41 | 1 | 2 | yes | — |
| 295 | #821 | — | 4 | 8 | no | — |
| 296 | #821 | — | 8 | 8 | no | — |
| 297 | #821 | — | 8 | 16 | no | — |
| 298 | (C2×D3)⋊C8 | — | 8 | 4 | no | — |
| 299 | #819 | — | 4 | 8 | no | — |
| 300 | #818 | — | 4 | 4 | no | — |
| 301 | #817 | — | 4 | 8 | no | — |
| 302 | #817 | — | 8 | 8 | no | — |
| 303 | #805 | — | 8 | 8 | no | — |
| 304 | C4⋊(C3⋊C8) | — | 4 | 4 | no | — |
| 305 | #800 | — | 4 | 32 | no | — |
| 306 | D48 | — | 4 | 32 | no | — |
| 307 | C2×#135 | — | 6 | 4 | no | — |
| 308 | C22×D8 | — | 6 | 4 | no | — |
| 309 | C22×D8 | — | 12 | 4 | no | — |
| 310 | C2×#131 | — | 12 | 2 | no | — |
| 311 | #532 | — | 6 | 2 | no | — |
| 312 | C2×#127 | — | 6 | 2 | no | — |
| 313 | C2×C4×D4 | — | 12 | 4 | no | — |
| 314 | C2×C4×D4 | — | 12 | 2 | no | — |
| 315 | #509 | — | 12 | 16 | no | — |
| 316 | #509 | — | 12 | 16 | no | — |
| 317 | C2×SD32 | — | 6 | 16 | no | — |
| 318 | C2×D16 | — | 6 | 16 | no | — |
| 319 | C2×M32 | C2×D12 | 1 | 4 | yes | — |
| 320 | C2×M32 | C2×D12 | 1 | 4 | yes | — |
| 321 | #500 | — | 6 | 2 | no | — |
| 322 | #495 | — | 6 | 4 | no | — |
| 323 | #494 | — | 3 | 2 | no | — |
| 324 | #493 | — | 3 | 4 | no | — |
| 325 | #493 | — | 3 | 2 | no | — |
| 326 | #493 | — | 6 | 4 | no | — |
| 327 | #493 | — | 6 | 4 | no | — |
| 328 | #493 | — | 6 | 2 | no | — |
| 329 | #493 | — | 6 | 2 | no | — |
| 330 | #493 | — | 6 | 4 | no | — |
| 331 | #493 | — | 12 | 4 | no | — |
| 332 | #492 | — | 6 | 2 | no | — |
| 333 | #486 | — | 6 | 4 | no | — |
| 334 | #466 | — | 12 | 4 | no | — |
| 335 | #444 | — | 12 | 16 | no | — |
| 336 | #442 | — | 12 | 16 | no | — |
| 337 | #442 | — | 24 | 16 | no | — |
| 338 | C4×D8 | — | 12 | 4 | no | — |
| 339 | #436 | — | 12 | 4 | no | — |
| 340 | C8×D4 | — | 12 | 4 | no | — |
| 341 | C2×#108 | — | 6 | 4 | no | — |
| 342 | C2×#106 | — | 6 | 4 | no | — |
| 343 | C2×#106 | — | 12 | 4 | no | — |
| 344 | #423 | — | 6 | 2 | no | — |
| 345 | C2×#104 | — | 12 | 4 | no | — |
| 346 | C2×#102 | — | 12 | 8 | no | — |
| 347 | C2×#102 | — | 12 | 4 | no | — |
| 348 | #408 | — | 12 | 2 | no | — |
| 349 | C2×#97 | — | 2 | 4 | no | — |
| 350 | C2×#97 | C2×D12 | 1 | 4 | yes | — |
| 351 | C2×C4×C8 | C2×D12 | 1 | 2 | yes | — |
| 352 | C2×C4×C8 | C2×D12 | 1 | 1 | yes | characteristic |
| 353 | C2×C4×C8 | C2×D12 | 1 | 2 | yes | — |
| 354 | C2×C4×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 355 | #390 | — | 12 | 4 | no | — |
| 356 | #390 | — | 12 | 2 | no | — |
| 357 | #384 | — | 6 | 2 | no | — |
| 358 | C43 | C2×D12 | 1 | 1 | yes | characteristic |
| 359 | #365 | — | 12 | 16 | no | — |
| 360 | #361 | — | 12 | 16 | no | — |
| 361 | #360 | — | 12 | 16 | no | — |
| 362 | #347 | — | 2 | 16 | no | — |
| 363 | #346 | — | 2 | 2 | no | — |
| 364 | #346 | #235 | 1 | 4 | yes | — |
| 365 | C4×C16 | — | 2 | 2 | no | — |
| 366 | C4×C16 | C2×C4×D3 | 1 | 4 | yes | — |
| 367 | #334 | — | 12 | 4 | no | — |
| 368 | D4⋊C8 | — | 12 | 8 | no | — |
| 369 | #322 | — | 2 | 4 | no | — |
| 370 | #322 | — | 2 | 2 | no | — |
| 371 | C82 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 372 | C82 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 373 | C82 | #235 | 1 | 2 | yes | — |
| 374 | C23×D3 | — | 8 | 2 | no | — |
| 375 | C22×C3×C4 | — | 2 | 2 | no | — |
| 376 | C22×C3×C4 | C2×#127 | 1 | 1 | yes | characteristic |
| 377 | C22×C3×C4 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 378 | C2×#67 | — | 8 | 2 | no | — |
| 379 | C22×Dic3 | — | 8 | 2 | no | — |
| 380 | #235 | — | 8 | 4 | no | — |
| 381 | #235 | — | 8 | 4 | no | — |
| 382 | C2×D12 | — | 4 | 4 | no | — |
| 383 | C2×D12 | — | 4 | 2 | no | — |
| 384 | C2×D12 | — | 4 | 4 | no | — |
| 385 | C2×D12 | — | 4 | 8 | no | — |
| 386 | C2×D12 | — | 8 | 8 | no | — |
| 387 | C2×D12 | — | 8 | 8 | no | — |
| 388 | C2×D12 | — | 8 | 4 | no | — |
| 389 | C2×D12 | — | 8 | 4 | no | — |
| 390 | C2×D12 | — | 8 | 2 | no | — |
| 391 | C2×D12 | — | 8 | 4 | no | — |
| 392 | C2×C4×D3 | — | 8 | 2 | no | — |
| 393 | C2×C4×D3 | — | 16 | 8 | no | — |
| 394 | C2×C4×D3 | — | 16 | 4 | no | — |
| 395 | C2×Dic6 | — | 4 | 2 | no | — |
| 396 | C2×C3×C8 | — | 2 | 8 | no | — |
| 397 | C2×C3×C8 | — | 2 | 2 | no | — |
| 398 | C2×C3×C8 | — | 2 | 4 | no | — |
| 399 | C2×C3×C8 | — | 4 | 4 | no | — |
| 400 | C2×C3×C8 | — | 4 | 2 | no | — |
| 401 | C2×C3×C8 | #442 | 1 | 4 | yes | — |
| 402 | C2×C3×C8 | #442 | 1 | 4 | yes | — |
| 403 | C2×C3×C8 | C2×C4×D4 | 1 | 2 | yes | — |
| 404 | C2×C3×C8 | #532 | 1 | 2 | yes | — |
| 405 | C2×C3×C8 | C2×AGL(1,ℤ/8) | 1 | 8 | yes | — |
| 406 | C3×C42 | — | 2 | 4 | no | — |
| 407 | C3×C42 | — | 4 | 4 | no | — |
| 408 | C3×C42 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 409 | C3×C42 | #532 | 1 | 1 | yes | characteristic |
| 410 | C3×C42 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 411 | (C2×D3)⋊C4 | — | 8 | 4 | no | — |
| 412 | (C2×D3)⋊C4 | — | 16 | 8 | no | — |
| 413 | (C2×D3)⋊C4 | — | 16 | 4 | no | — |
| 414 | C4⋊Dic3 | — | 4 | 4 | no | — |
| 415 | C4⋊Dic3 | — | 8 | 8 | no | — |
| 416 | C4⋊Dic3 | — | 8 | 4 | no | — |
| 417 | #208 | — | 8 | 4 | no | — |
| 418 | C2×C3⋊C8 | — | 8 | 2 | no | — |
| 419 | Dic12 | — | 4 | 8 | no | — |
| 420 | D24 | — | 4 | 8 | no | — |
| 421 | D24 | — | 4 | 16 | no | — |
| 422 | D24 | — | 8 | 16 | no | — |
| 423 | D24 | — | 8 | 8 | no | — |
| 424 | D24 | — | 8 | 8 | no | — |
| 425 | D24 | — | 8 | 16 | no | — |
| 426 | #204 | — | 8 | 8 | no | — |
| 427 | ΓL(1,𝔽25) | — | 16 | 4 | no | — |
| 428 | D3×C8 | — | 16 | 4 | no | — |
| 429 | C3×C16 | — | 4 | 4 | no | — |
| 430 | C3×C16 | #442 | 1 | 16 | yes | complemented |
| 431 | C2×#41 | — | 12 | 2 | no | — |
| 432 | C22×D4 | — | 12 | 2 | no | — |
| 433 | C22×D4 | — | 12 | 4 | no | — |
| 434 | C23×C4 | — | 24 | 2 | no | — |
| 435 | #135 | — | 12 | 8 | no | — |
| 436 | #135 | — | 12 | 8 | no | — |
| 437 | C2×Q16 | — | 6 | 4 | no | — |
| 438 | C2×SD16 | — | 12 | 4 | no | — |
| 439 | C2×D8 | — | 6 | 8 | no | — |
| 440 | C2×D8 | — | 6 | 4 | no | — |
| 441 | C2×D8 | — | 12 | 4 | no | — |
| 442 | C2×D8 | — | 12 | 8 | no | — |
| 443 | C2×D8 | — | 12 | 8 | no | — |
| 444 | C2×D8 | — | 12 | 4 | no | — |
| 445 | C2×D8 | — | 12 | 8 | no | — |
| 446 | C2×D8 | — | 12 | 8 | no | — |
| 447 | C2×D8 | — | 24 | 8 | no | — |
| 448 | C2×D8 | — | 24 | 8 | no | — |
| 449 | #131 | — | 24 | 8 | no | — |
| 450 | C2×M16 | — | 12 | 2 | no | — |
| 451 | C2×M16 | — | 24 | 2 | no | — |
| 452 | C22×C8 | — | 2 | 2 | no | — |
| 453 | C22×C8 | — | 24 | 2 | no | — |
| 454 | C22×C8 | #874 | 1 | 2 | yes | — |
| 455 | C22×C8 | #908 | 1 | 4 | yes | — |
| 456 | C22×C8 | C22×D12 | 1 | 2 | yes | — |
| 457 | C4⋊Q8 | — | 6 | 2 | no | — |
| 458 | #127 | — | 6 | 4 | no | — |
| 459 | #127 | — | 6 | 2 | no | — |
| 460 | #127 | — | 12 | 2 | no | — |
| 461 | #127 | — | 12 | 4 | no | — |
| 462 | #124 | — | 12 | 2 | no | — |
| 463 | #121 | — | 12 | 4 | no | — |
| 464 | C4×D4 | — | 12 | 4 | no | — |
| 465 | C4×D4 | — | 24 | 8 | no | — |
| 466 | C4×D4 | — | 24 | 16 | no | — |
| 467 | C2×C4⋊C4 | — | 12 | 2 | no | — |
| 468 | C2×C4⋊C4 | — | 12 | 4 | no | — |
| 469 | C2×C22⋊C4 | — | 24 | 4 | no | — |
| 470 | C2×C22⋊C4 | — | 24 | 2 | no | — |
| 471 | C2×C42 | — | 2 | 2 | no | — |
| 472 | C2×C42 | #874 | 1 | 2 | yes | — |
| 473 | C2×C42 | C22×D12 | 1 | 1 | yes | characteristic |
| 474 | SD32 | — | 12 | 32 | no | — |
| 475 | D16 | — | 12 | 32 | no | — |
| 476 | M32 | — | 2 | 8 | no | — |
| 477 | M32 | #908 | 1 | 16 | yes | — |
| 478 | C2×C16 | — | 2 | 4 | no | — |
| 479 | C2×C16 | C4×D12 | 1 | 8 | yes | — |
| 480 | #108 | — | 12 | 8 | no | — |
| 481 | #107 | — | 12 | 4 | no | — |
| 482 | #106 | — | 12 | 8 | no | — |
| 483 | #106 | — | 24 | 8 | no | — |
| 484 | C4⋊C8 | — | 12 | 4 | no | — |
| 485 | #104 | — | 24 | 8 | no | — |
| 486 | #102 | — | 12 | 8 | no | — |
| 487 | #102 | — | 24 | 8 | no | — |
| 488 | #102 | — | 24 | 16 | no | — |
| 489 | C22⋊C8 | — | 24 | 4 | no | — |
| 490 | #97 | — | 2 | 8 | no | — |
| 491 | #97 | — | 4 | 8 | no | — |
| 492 | C4×C8 | — | 2 | 2 | no | — |
| 493 | C4×C8 | — | 2 | 2 | no | — |
| 494 | C4×C8 | — | 2 | 2 | no | — |
| 495 | C4×C8 | C4×D12 | 1 | 2 | yes | — |
| 496 | C4×C8 | C4×D12 | 1 | 2 | yes | — |
| 497 | C4×C8 | #908 | 1 | 4 | yes | — |
| 498 | C4×C8 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 499 | C4×C8 | C2×#235 | 1 | 1 | yes | characteristic |
| 500 | C4×C8 | C2×#235 | 1 | 2 | yes | — |
| 501 | C23×C3 | #3151 | 1 | 1 | yes | characteristic |
| 502 | C22×D3 | — | 8 | 2 | no | — |
| 503 | C22×D3 | — | 8 | 4 | no | — |
| 504 | C22×D3 | — | 16 | 4 | no | — |
| 505 | C22×D3 | — | 16 | 4 | no | — |
| 506 | C22×D3 | — | 16 | 2 | no | — |
| 507 | C22×D3 | — | 16 | 2 | no | — |
| 508 | C2×C3×C4 | — | 2 | 4 | no | — |
| 509 | C2×C3×C4 | — | 4 | 4 | no | — |
| 510 | C2×C3×C4 | — | 4 | 2 | no | — |
| 511 | C2×C3×C4 | C4×#127 | 1 | 1 | yes | characteristic |
| 512 | C2×C3×C4 | C2×#442 | 1 | 2 | yes | — |
| 513 | C2×C3×C4 | #3151 | 1 | 1 | yes | characteristic |
| 514 | C2×C3×C4 | #3151 | 1 | 4 | yes | — |
| 515 | C2×C3×C4 | #3184 | 1 | 2 | yes | — |
| 516 | #67 | — | 16 | 4 | no | — |
| 517 | C2×Dic3 | — | 8 | 2 | no | — |
| 518 | C2×Dic3 | — | 16 | 4 | no | — |
| 519 | C2×Dic3 | — | 16 | 2 | no | — |
| 520 | D12 | — | 8 | 4 | no | — |
| 521 | D12 | — | 8 | 8 | no | — |
| 522 | D12 | — | 8 | 16 | no | — |
| 523 | D12 | — | 8 | 8 | no | — |
| 524 | D12 | — | 16 | 8 | no | — |
| 525 | D12 | — | 16 | 4 | no | — |
| 526 | C4×D3 | — | 16 | 2 | no | — |
| 527 | C4×D3 | — | 16 | 2 | no | — |
| 528 | C4×D3 | — | 32 | 8 | no | — |
| 529 | Dic6 | — | 8 | 4 | no | — |
| 530 | C3×C8 | — | 2 | 4 | no | — |
| 531 | C3×C8 | — | 4 | 2 | no | — |
| 532 | C3×C8 | — | 8 | 2 | no | — |
| 533 | C3×C8 | AGL(1,ℤ/16) | 1 | 8 | yes | complemented |
| 534 | C3×C8 | C2×#442 | 1 | 4 | yes | — |
| 535 | C3×C8 | #3184 | 1 | 4 | yes | — |
| 536 | C3⋊C8 | — | 16 | 2 | no | — |
| 537 | C24 | — | 24 | 2 | no | — |
| 538 | #41 | — | 24 | 4 | no | — |
| 539 | #41 | — | 24 | 4 | no | — |
| 540 | C2×Q8 | — | 12 | 2 | no | — |
| 541 | C2×D4 | — | 12 | 2 | no | — |
| 542 | C2×D4 | — | 12 | 4 | no | — |
| 543 | C2×D4 | — | 12 | 4 | no | — |
| 544 | C2×D4 | — | 12 | 8 | no | — |
| 545 | C2×D4 | — | 24 | 8 | no | — |
| 546 | C2×D4 | — | 24 | 8 | no | — |
| 547 | C2×D4 | — | 24 | 2 | no | — |
| 548 | C2×D4 | — | 24 | 4 | no | — |
| 549 | C2×D4 | — | 24 | 4 | no | — |
| 550 | C2×D4 | — | 24 | 2 | no | — |
| 551 | C2×D4 | — | 24 | 4 | no | — |
| 552 | C22×C4 | — | 2 | 2 | no | — |
| 553 | C22×C4 | — | 24 | 2 | no | — |
| 554 | C22×C4 | — | 24 | 2 | no | — |
| 555 | C22×C4 | — | 48 | 8 | no | — |
| 556 | C22×C4 | — | 48 | 4 | no | — |
| 557 | C22×C4 | C2×#874 | 1 | 1 | yes | characteristic |
| 558 | C22×C4 | C2×#908 | 1 | 2 | yes | — |
| 559 | Q16 | — | 12 | 8 | no | — |
| 560 | SD16 | — | 24 | 8 | no | — |
| 561 | D8 | — | 12 | 8 | no | — |
| 562 | D8 | — | 12 | 16 | no | — |
| 563 | D8 | — | 24 | 16 | no | — |
| 564 | D8 | — | 24 | 8 | no | — |
| 565 | D8 | — | 24 | 16 | no | — |
| 566 | D8 | — | 24 | 8 | no | — |
| 567 | M16 | — | 24 | 4 | no | — |
| 568 | M16 | — | 48 | 4 | no | — |
| 569 | C2×C8 | — | 2 | 8 | no | — |
| 570 | C2×C8 | — | 2 | 2 | no | — |
| 571 | C2×C8 | — | 2 | 4 | no | — |
| 572 | C2×C8 | — | 4 | 4 | no | — |
| 573 | C2×C8 | — | 4 | 2 | no | — |
| 574 | C2×C8 | — | 24 | 2 | no | — |
| 575 | C2×C8 | — | 48 | 4 | no | — |
| 576 | C2×C8 | #4711 | 1 | 4 | yes | — |
| 577 | C2×C8 | #4711 | 1 | 4 | yes | — |
| 578 | C2×C8 | C2×C4×D12 | 1 | 2 | yes | — |
| 579 | C2×C8 | #5477 | 1 | 2 | yes | — |
| 580 | C2×C8 | C2×#908 | 1 | 8 | yes | — |
| 581 | C4⋊C4 | — | 12 | 4 | no | — |
| 582 | C4⋊C4 | — | 24 | 8 | no | — |
| 583 | C4⋊C4 | — | 24 | 4 | no | — |
| 584 | C22⋊C4 | — | 24 | 4 | no | — |
| 585 | C22⋊C4 | — | 48 | 8 | no | — |
| 586 | C22⋊C4 | — | 48 | 4 | no | — |
| 587 | C42 | — | 2 | 4 | no | — |
| 588 | C42 | — | 4 | 4 | no | — |
| 589 | C42 | C2×C4×D12 | 1 | 1 | yes | characteristic |
| 590 | C42 | #5477 | 1 | 1 | yes | characteristic |
| 591 | C42 | C2×#908 | 1 | 2 | yes | — |
| 592 | C16 | — | 4 | 4 | no | — |
| 593 | C16 | #4711 | 1 | 16 | yes | complemented |
| 594 | C22×C3 | — | 2 | 2 | no | — |
| 595 | C22×C3 | #19745 | 1 | 2 | yes | — |
| 596 | C22×C3 | #21690 | 1 | 1 | yes | characteristic |
| 597 | C2×D3 | — | 16 | 2 | no | — |
| 598 | C2×D3 | — | 16 | 4 | no | — |
| 599 | C2×D3 | — | 16 | 8 | no | — |
| 600 | C2×D3 | — | 16 | 4 | no | — |
| 601 | C2×D3 | — | 32 | 2 | no | — |
| 602 | C2×D3 | — | 32 | 4 | no | — |
| 603 | C2×D3 | — | 32 | 2 | no | — |
| 604 | C3×C4 | — | 2 | 2 | no | — |
| 605 | C3×C4 | — | 8 | 2 | no | — |
| 606 | C3×C4 | #19745 | 1 | 2 | yes | — |
| 607 | C3×C4 | #21690 | 1 | 2 | yes | — |
| 608 | C3×C4 | C2×AGL(1,ℤ/16) | 1 | 4 | yes | — |
| 609 | Dic3 | — | 16 | 2 | no | — |
| 610 | Dic3 | — | 32 | 2 | no | — |
| 611 | C23 | — | 24 | 2 | no | — |
| 612 | C23 | — | 24 | 4 | no | — |
| 613 | C23 | — | 48 | 4 | no | — |
| 614 | C23 | — | 48 | 4 | no | — |
| 615 | C23 | — | 48 | 2 | no | — |
| 616 | C23 | — | 48 | 2 | no | — |
| 617 | C23 | #78530 | 1 | 1 | yes | characteristic |
| 618 | Q8 | — | 24 | 4 | no | — |
| 619 | D4 | — | 24 | 16 | no | — |
| 620 | D4 | — | 24 | 8 | no | — |
| 621 | D4 | — | 24 | 8 | no | — |
| 622 | D4 | — | 24 | 4 | no | — |
| 623 | D4 | — | 48 | 8 | no | — |
| 624 | D4 | — | 48 | 4 | no | — |
| 625 | D4 | — | 48 | 4 | no | — |
| 626 | C2×C4 | — | 2 | 4 | no | — |
| 627 | C2×C4 | — | 4 | 4 | no | — |
| 628 | C2×C4 | — | 4 | 2 | no | — |
| 629 | C2×C4 | — | 24 | 2 | no | — |
| 630 | C2×C4 | — | 48 | 2 | no | — |
| 631 | C2×C4 | — | 48 | 2 | no | — |
| 632 | C2×C4 | — | 48 | 4 | no | — |
| 633 | C2×C4 | — | 48 | 2 | no | — |
| 634 | C2×C4 | — | 96 | 8 | no | — |
| 635 | C2×C4 | C4×#874 | 1 | 1 | yes | characteristic |
| 636 | C2×C4 | C2×#4711 | 1 | 2 | yes | — |
| 637 | C2×C4 | #78530 | 1 | 1 | yes | characteristic |
| 638 | C2×C4 | #78530 | 1 | 4 | yes | — |
| 639 | C2×C4 | #78535 | 1 | 2 | yes | — |
| 640 | C8 | — | 2 | 4 | no | — |
| 641 | C8 | — | 4 | 2 | no | — |
| 642 | C8 | — | 8 | 2 | no | — |
| 643 | C8 | — | 48 | 2 | no | — |
| 644 | C8 | #69091 | 1 | 8 | yes | complemented |
| 645 | C8 | C2×#4711 | 1 | 4 | yes | — |
| 646 | C8 | #78535 | 1 | 4 | yes | — |
| 647 | C2×C3 | — | 2 | 2 | no | — |
| 648 | C2×C3 | #212918 | 1 | 1 | yes | characteristic |
| 649 | C2×C3 | #496124 | 1 | 2 | yes | — |
| 650 | D3 | — | 32 | 2 | no | — |
| 651 | D3 | — | 32 | 4 | no | — |
| 652 | C22 | — | 2 | 2 | no | — |
| 653 | C22 | — | 48 | 8 | no | — |
| 654 | C22 | — | 48 | 4 | no | — |
| 655 | C22 | — | 48 | 2 | no | — |
| 656 | C22 | — | 48 | 4 | no | — |
| 657 | C22 | — | 96 | 2 | no | — |
| 658 | C22 | — | 96 | 4 | no | — |
| 659 | C22 | — | 96 | 2 | no | — |
| 660 | C22 | #10784428 | 1 | 2 | yes | — |
| 661 | C22 | #10803642 | 1 | 1 | yes | characteristic |
| 662 | C4 | — | 2 | 2 | no | — |
| 663 | C4 | — | 8 | 2 | no | — |
| 664 | C4 | — | 48 | 2 | no | — |
| 665 | C4 | — | 96 | 2 | no | — |
| 666 | C4 | #10784428 | 1 | 2 | yes | — |
| 667 | C4 | #10803642 | 1 | 2 | yes | — |
| 668 | C4 | C2×#69091 | 1 | 4 | yes | — |
| 669 | C3 | #72213983 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 670 | C2 | — | 2 | 2 | no | — |
| 671 | C2 | — | 96 | 4 | no | — |
| 672 | C2 | — | 96 | 2 | no | — |
| 673 | C2 | #72225882 | 1 | 2 | yes | — |
| 674 | C2 | #72225884 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72225892 | C2 | semidirect |
| 2. #72225890 | C2 | semidirect |
| 3. #72225887 | C2 | semidirect |
| 4. #72225885 | C2 | semidirect |
| 5. #72225884 | C2 | semidirect |
| 6. #72225882 | C2 | semidirect |
| 8. #72225815 | C2 | semidirect |
| 9. C3×#126544 | C2 | semidirect |
| 23. #10709915 | C4 | semidirect |
| 24. #10709905 | C4 | semidirect |
| 25. #10709899 | C4 | semidirect |
| 45. #126544 | D3 | semidirect |
| 80. #69061 | C2×C4 | semidirect |
| 81. #69060 | C2×C4 | semidirect |
| 84. #68065 | C2×C4 | semidirect |
| 88. #68062 | C2×C4 | semidirect |
| 89. #68060 | C2×C4 | semidirect |
| 93. C3×#1311 | C2×C4 | semidirect |
| 94. C3×C8×C16 | C2×C4 | semidirect |
| 235. #1311 | C4×D3 | semidirect |
| 236. C8×C16 | C4×D3 | semidirect |
| 430. C3×C16 | #442 | semidirect |
| 533. C3×C8 | AGL(1,ℤ/16) | semidirect |
| 593. C16 | #4711 | semidirect |
| 644. C8 | #69091 | semidirect |
| 669. C3 | #72213983 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72225892 | 2 |
| #72225890 | 2 |
| #72225887 | 2 |
| #72225885 | 2 |
| #72225884 | 2 |
| #72225882 | 2 |
| #72225817 | 2 |
| #72225815 | 2 |
| C3×#126544 | 2 |
| #72213983 | 3 |