Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1380 conjugacy classes of subgroups.
The subgroup lattice has 560 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×D3×D8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#4914 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #80758 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#2187 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72035 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #71485 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #71085 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #69191 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #69190 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #69108 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #69106 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #33517 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C22×D3×D4 | — | 2 | 1 | no | — |
| 14 | C22×C3×D8 | C22 | 1 | 1 | yes | characteristic |
| 15 | C22×#213 | — | 2 | 1 | no | — |
| 16 | C2×#919 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C2×D3×D8 | — | 2 | 8 | no | — |
| 18 | C2×D3×D8 | — | 2 | 1 | no | — |
| 19 | C2×D3×D8 | — | 2 | 1 | no | — |
| 20 | C2×D3×D8 | C22 | 1 | 2 | yes | — |
| 21 | C2×D3×D8 | C22 | 1 | 2 | yes | — |
| 22 | C22×D24 | C22 | 1 | 1 | yes | characteristic |
| 23 | C22×D3×C8 | C22 | 1 | 1 | yes | characteristic |
| 24 | #5627 | — | 2 | 1 | no | — |
| 25 | C2×C3×SD32 | C22 | 1 | 2 | yes | complemented |
| 26 | C3×#467 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #5188 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | C2×#828 | C22 | 1 | 2 | yes | complemented |
| 29 | C2×#826 | C22 | 1 | 2 | yes | complemented |
| 30 | #5115 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #5048 | — | 2 | 1 | no | — |
| 32 | #4914 | — | 2 | 8 | no | — |
| 33 | C2×D48 | C22 | 1 | 2 | yes | complemented |
| 34 | C2×#798 | C22 | 1 | 2 | yes | complemented |
| 35 | #4883 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #4880 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #4807 | — | 2 | 1 | no | — |
| 38 | #4804 | — | 2 | 1 | no | — |
| 39 | C3×#357 | C22 | 1 | 2 | yes | complemented |
| 40 | C3×C22⋊C16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #4562 | C22 | 1 | 2 | yes | complemented |
| 42 | #4549 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | #4509 | C22 | 1 | 2 | yes | complemented |
| 44 | (C2×D3)⋊C16 | C22 | 1 | 2 | yes | complemented |
| 45 | #4491 | C22 | 1 | 2 | yes | complemented |
| 46 | C23×D8 | — | 3 | 1 | no | — |
| 47 | C2×#509 | — | 3 | 2 | no | — |
| 48 | #3050 | — | 3 | 1 | no | — |
| 49 | #2187 | — | 3 | 2 | no | — |
| 50 | #2187 | — | 3 | 1 | no | — |
| 51 | #2187 | D3 | 1 | 1 | yes | characteristic, complemented |
| 52 | #2184 | — | 3 | 2 | no | — |
| 53 | #2184 | — | 3 | 1 | no | — |
| 54 | #2184 | — | 3 | 1 | no | — |
| 55 | #2140 | — | 3 | 2 | no | — |
| 56 | #2112 | — | 3 | 1 | no | — |
| 57 | C24×D3 | — | 4 | 1 | no | — |
| 58 | C22×C3×D4 | — | 2 | 1 | no | — |
| 59 | C22×#67 | — | 4 | 1 | no | — |
| 60 | C2×#239 | — | 2 | 1 | no | — |
| 61 | C2×D3×D4 | — | 2 | 8 | no | — |
| 62 | C2×D3×D4 | — | 2 | 2 | no | — |
| 63 | C2×D3×D4 | — | 2 | 2 | no | — |
| 64 | C2×D3×D4 | — | 4 | 4 | no | — |
| 65 | C2×D3×D4 | — | 4 | 1 | no | — |
| 66 | C2×D3×D4 | — | 4 | 1 | no | — |
| 67 | C22×D12 | — | 2 | 1 | no | — |
| 68 | C22×C4×D3 | D4 | 1 | 1 | yes | characteristic |
| 69 | C2×C3×Q16 | C23 | 1 | 1 | yes | characteristic, complemented |
| 70 | C2×C3×D8 | — | 2 | 4 | no | — |
| 71 | C2×C3×D8 | — | 2 | 1 | no | — |
| 72 | C2×C3×D8 | C23 | 1 | 2 | yes | — |
| 73 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 74 | C3×C22⋊Q8 | — | 2 | 1 | no | — |
| 75 | #946 | — | 2 | 1 | no | — |
| 76 | C2×#215 | — | 2 | 1 | no | — |
| 77 | C2×#213 | — | 2 | 8 | no | — |
| 78 | C2×#213 | — | 2 | 2 | no | — |
| 79 | C2×#213 | — | 2 | 2 | no | — |
| 80 | #930 | — | 2 | 1 | no | — |
| 81 | C22×C3⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 82 | #919 | — | 2 | 4 | no | — |
| 83 | D3×D8 | — | 2 | 8 | no | — |
| 84 | D3×D8 | — | 2 | 8 | no | — |
| 85 | D3×D8 | — | 2 | 4 | no | — |
| 86 | D3×D8 | — | 2 | 4 | no | — |
| 87 | D3×D8 | — | 2 | 4 | no | — |
| 88 | D3×D8 | D4 | 1 | 8 | yes | complemented |
| 89 | C2×D24 | — | 2 | 1 | no | — |
| 90 | C2×D24 | — | 2 | 4 | no | — |
| 91 | C2×D24 | C23 | 1 | 2 | yes | — |
| 92 | C2×D24 | C23 | 1 | 1 | yes | characteristic, complemented |
| 93 | C2×D3×C8 | — | 2 | 4 | no | — |
| 94 | C2×D3×C8 | D4 | 1 | 1 | yes | characteristic |
| 95 | C2×D3×C8 | D4 | 1 | 1 | yes | characteristic |
| 96 | C2×D3×C8 | C23 | 1 | 1 | yes | characteristic |
| 97 | C2×D3×C8 | C23 | 1 | 1 | yes | characteristic |
| 98 | #895 | — | 2 | 1 | no | — |
| 99 | #894 | — | 4 | 1 | no | — |
| 100 | #893 | — | 4 | 1 | no | — |
| 101 | #892 | — | 2 | 1 | no | — |
| 102 | #882 | — | 4 | 1 | no | — |
| 103 | #67⋊C4 | — | 4 | 1 | no | — |
| 104 | C3×SD32 | — | 2 | 4 | no | — |
| 105 | C2×C3×C16 | C23 | 1 | 2 | yes | complemented |
| 106 | C3×#107 | C23 | 1 | 1 | yes | characteristic, complemented |
| 107 | C3×#103 | — | 2 | 1 | no | — |
| 108 | #835 | — | 2 | 1 | no | — |
| 109 | #828 | — | 2 | 4 | no | — |
| 110 | #826 | — | 2 | 4 | no | — |
| 111 | #821 | — | 2 | 1 | no | — |
| 112 | #818 | C23 | 1 | 1 | yes | characteristic, complemented |
| 113 | C2×C3⋊C16 | C23 | 1 | 2 | yes | complemented |
| 114 | #809 | — | 2 | 1 | no | — |
| 115 | #808 | — | 2 | 1 | no | — |
| 116 | D48 | — | 2 | 4 | no | — |
| 117 | #798 | — | 2 | 4 | no | — |
| 118 | C23×D4 | — | 6 | 1 | no | — |
| 119 | C2×#135 | — | 3 | 1 | no | — |
| 120 | C22×D8 | — | 3 | 2 | no | — |
| 121 | C22×D8 | — | 3 | 2 | no | — |
| 122 | C22×D8 | — | 3 | 1 | no | — |
| 123 | C22×D8 | — | 6 | 1 | no | — |
| 124 | C22×D8 | — | 6 | 1 | no | — |
| 125 | C22×D8 | — | 6 | 1 | no | — |
| 126 | C22×D8 | — | 6 | 8 | no | — |
| 127 | C22×D8 | C2×D3 | 1 | 1 | yes | characteristic |
| 128 | C23×C8 | — | 3 | 1 | no | — |
| 129 | #525 | — | 6 | 1 | no | — |
| 130 | #509 | — | 6 | 8 | no | — |
| 131 | C2×SD32 | — | 3 | 2 | no | — |
| 132 | C2×SD32 | C2×D3 | 1 | 2 | yes | complemented |
| 133 | C2×D16 | — | 3 | 2 | no | — |
| 134 | C2×D16 | — | 3 | 2 | no | — |
| 135 | C2×M32 | — | 3 | 2 | no | — |
| 136 | #467 | — | 3 | 1 | no | — |
| 137 | #467 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 138 | #466 | — | 3 | 1 | no | — |
| 139 | #466 | — | 3 | 1 | no | — |
| 140 | #465 | — | 6 | 1 | no | — |
| 141 | #465 | — | 6 | 1 | no | — |
| 142 | #427 | — | 3 | 1 | no | — |
| 143 | #416 | — | 6 | 1 | no | — |
| 144 | #357 | — | 3 | 2 | no | — |
| 145 | #357 | — | 3 | 2 | no | — |
| 146 | #357 | — | 3 | 2 | no | — |
| 147 | #357 | C2×D3 | 1 | 2 | yes | complemented |
| 148 | C22⋊C16 | — | 3 | 1 | no | — |
| 149 | C22⋊C16 | — | 3 | 2 | no | — |
| 150 | C22⋊C16 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 151 | C24×C3 | — | 4 | 1 | no | — |
| 152 | C23×D3 | — | 4 | 8 | no | — |
| 153 | C23×D3 | — | 4 | 1 | no | — |
| 154 | C23×D3 | — | 4 | 2 | no | — |
| 155 | C23×D3 | — | 4 | 2 | no | — |
| 156 | C23×D3 | — | 8 | 4 | no | — |
| 157 | C23×D3 | — | 8 | 4 | no | — |
| 158 | C23×D3 | D8 | 1 | 1 | yes | characteristic |
| 159 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 160 | C2×C3×D4 | — | 2 | 4 | no | — |
| 161 | C2×C3×D4 | — | 2 | 2 | no | — |
| 162 | C2×C3×D4 | — | 4 | 2 | no | — |
| 163 | C2×C3×D4 | — | 4 | 1 | no | — |
| 164 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 165 | C2×#67 | — | 4 | 8 | no | — |
| 166 | C2×#67 | — | 4 | 1 | no | — |
| 167 | C2×#67 | — | 4 | 2 | no | — |
| 168 | C2×#67 | — | 4 | 2 | no | — |
| 169 | C22×Dic3 | D8 | 1 | 1 | yes | characteristic |
| 170 | #239 | — | 4 | 2 | no | — |
| 171 | #239 | — | 4 | 2 | no | — |
| 172 | D3×D4 | — | 2 | 8 | no | — |
| 173 | D3×D4 | — | 2 | 8 | no | — |
| 174 | D3×D4 | — | 4 | 8 | no | — |
| 175 | D3×D4 | — | 4 | 4 | no | — |
| 176 | D3×D4 | — | 4 | 8 | no | — |
| 177 | D3×D4 | — | 4 | 4 | no | — |
| 178 | C2×D12 | — | 2 | 4 | no | — |
| 179 | C2×D12 | — | 2 | 2 | no | — |
| 180 | C2×D12 | — | 2 | 1 | no | — |
| 181 | C2×D12 | — | 4 | 2 | no | — |
| 182 | C2×D12 | — | 4 | 1 | no | — |
| 183 | C2×D12 | — | 4 | 1 | no | — |
| 184 | C2×D12 | — | 4 | 1 | no | — |
| 185 | C2×C4×D3 | — | 2 | 2 | no | — |
| 186 | C2×C4×D3 | — | 2 | 2 | no | — |
| 187 | C2×C4×D3 | — | 4 | 1 | no | — |
| 188 | C2×C4×D3 | D8 | 1 | 1 | yes | characteristic |
| 189 | C2×C4×D3 | D8 | 1 | 1 | yes | characteristic |
| 190 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C3×Q16 | — | 2 | 2 | no | — |
| 193 | C3×D8 | — | 2 | 4 | no | — |
| 194 | C3×D8 | — | 2 | 2 | no | — |
| 195 | C3×D8 | C2×D4 | 1 | 4 | yes | — |
| 196 | C2×C3×C8 | — | 2 | 2 | no | — |
| 197 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 198 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 199 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 200 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 201 | C3×C22⋊C4 | — | 4 | 1 | no | — |
| 202 | #215 | — | 4 | 2 | no | — |
| 203 | #213 | — | 2 | 8 | no | — |
| 204 | #213 | — | 2 | 8 | no | — |
| 205 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 206 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 207 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 208 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 209 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 210 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 211 | C4×Dic3 | — | 4 | 1 | no | — |
| 212 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 213 | C2×C3⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 214 | C2×C3⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 215 | D24 | — | 2 | 4 | no | — |
| 216 | D24 | — | 2 | 2 | no | — |
| 217 | D24 | — | 2 | 2 | no | — |
| 218 | D24 | C2×D4 | 1 | 4 | yes | — |
| 219 | D3×C8 | — | 2 | 2 | no | — |
| 220 | D3×C8 | — | 2 | 2 | no | — |
| 221 | D3×C8 | — | 2 | 2 | no | — |
| 222 | D3×C8 | C2×D4 | 1 | 4 | yes | — |
| 223 | C3×C16 | — | 2 | 2 | no | — |
| 224 | C3⋊C16 | — | 2 | 2 | no | — |
| 225 | C25 | — | 12 | 1 | no | — |
| 226 | C2×#41 | — | 6 | 1 | no | — |
| 227 | C22×D4 | — | 2 | 1 | no | — |
| 228 | C22×D4 | — | 6 | 2 | no | — |
| 229 | C22×D4 | — | 6 | 2 | no | — |
| 230 | C22×D4 | — | 6 | 8 | no | — |
| 231 | C22×D4 | — | 6 | 1 | no | — |
| 232 | C22×D4 | — | 12 | 1 | no | — |
| 233 | C22×D4 | — | 12 | 1 | no | — |
| 234 | C22×D4 | — | 12 | 1 | no | — |
| 235 | C22×D4 | — | 12 | 4 | no | — |
| 236 | C23×C4 | — | 3 | 1 | no | — |
| 237 | #135 | — | 6 | 4 | no | — |
| 238 | C2×Q16 | C22×D3 | 1 | 1 | yes | characteristic, complemented |
| 239 | C2×SD16 | — | 6 | 1 | no | — |
| 240 | C2×D8 | — | 2 | 4 | no | — |
| 241 | C2×D8 | — | 2 | 1 | no | — |
| 242 | C2×D8 | — | 3 | 8 | no | — |
| 243 | C2×D8 | — | 3 | 2 | no | — |
| 244 | C2×D8 | — | 3 | 1 | no | — |
| 245 | C2×D8 | — | 6 | 4 | no | — |
| 246 | C2×D8 | — | 6 | 4 | no | — |
| 247 | C2×D8 | — | 6 | 2 | no | — |
| 248 | C2×D8 | — | 6 | 2 | no | — |
| 249 | C2×D8 | — | 6 | 4 | no | — |
| 250 | C2×D8 | — | 6 | 8 | no | — |
| 251 | C2×D8 | — | 6 | 8 | no | — |
| 252 | C2×D8 | — | 6 | 8 | no | — |
| 253 | C2×D8 | — | 6 | 4 | no | — |
| 254 | C2×D8 | — | 6 | 1 | no | — |
| 255 | C2×D8 | C22×D3 | 1 | 2 | yes | — |
| 256 | C22×C8 | — | 3 | 1 | no | — |
| 257 | C22×C8 | — | 3 | 1 | no | — |
| 258 | C22×C8 | — | 3 | 1 | no | — |
| 259 | C22×C8 | — | 3 | 1 | no | — |
| 260 | C22×C8 | — | 3 | 1 | no | — |
| 261 | C22×C8 | — | 6 | 4 | no | — |
| 262 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 263 | #123 | — | 12 | 1 | no | — |
| 264 | C22⋊Q8 | — | 2 | 1 | no | — |
| 265 | C22⋊Q8 | — | 6 | 1 | no | — |
| 266 | #121 | — | 6 | 1 | no | — |
| 267 | #121 | — | 6 | 1 | no | — |
| 268 | #120 | — | 12 | 1 | no | — |
| 269 | C4×D4 | — | 12 | 1 | no | — |
| 270 | C4×D4 | — | 12 | 1 | no | — |
| 271 | #117 | — | 6 | 1 | no | — |
| 272 | SD32 | — | 2 | 4 | no | — |
| 273 | SD32 | — | 6 | 4 | no | — |
| 274 | D16 | — | 6 | 4 | no | — |
| 275 | D16 | — | 6 | 4 | no | — |
| 276 | M32 | — | 6 | 4 | no | — |
| 277 | C2×C16 | — | 3 | 2 | no | — |
| 278 | C2×C16 | C22×D3 | 1 | 2 | yes | complemented |
| 279 | #107 | — | 3 | 1 | no | — |
| 280 | #107 | C22×D3 | 1 | 1 | yes | characteristic, complemented |
| 281 | #106 | — | 6 | 1 | no | — |
| 282 | #103 | — | 2 | 1 | no | — |
| 283 | #103 | — | 6 | 1 | no | — |
| 284 | #102 | — | 6 | 1 | no | — |
| 285 | #102 | — | 6 | 1 | no | — |
| 286 | C23×C3 | — | 4 | 4 | no | — |
| 287 | C23×C3 | — | 4 | 2 | no | — |
| 288 | C23×C3 | — | 8 | 2 | no | — |
| 289 | C23×C3 | — | 8 | 2 | no | — |
| 290 | C23×C3 | C2×D8 | 1 | 1 | yes | characteristic |
| 291 | C22×D3 | — | 2 | 2 | no | — |
| 292 | C22×D3 | — | 2 | 2 | no | — |
| 293 | C22×D3 | — | 2 | 2 | no | — |
| 294 | C22×D3 | — | 4 | 8 | no | — |
| 295 | C22×D3 | — | 4 | 4 | no | — |
| 296 | C22×D3 | — | 4 | 2 | no | — |
| 297 | C22×D3 | — | 4 | 8 | no | — |
| 298 | C22×D3 | — | 4 | 1 | no | — |
| 299 | C22×D3 | — | 8 | 32 | no | — |
| 300 | C22×D3 | — | 8 | 4 | no | — |
| 301 | C22×D3 | — | 8 | 4 | no | — |
| 302 | C22×D3 | — | 8 | 4 | no | — |
| 303 | C22×D3 | — | 8 | 2 | no | — |
| 304 | C22×D3 | — | 8 | 2 | no | — |
| 305 | C22×D3 | — | 8 | 4 | no | — |
| 306 | C22×D3 | C2×D8 | 1 | 1 | yes | characteristic |
| 307 | C22×D3 | C2×D8 | 1 | 1 | yes | characteristic |
| 308 | C3×Q8 | — | 4 | 1 | no | — |
| 309 | C3×Q8 | — | 4 | 1 | no | — |
| 310 | C3×D4 | — | 2 | 4 | no | — |
| 311 | C3×D4 | — | 4 | 4 | no | — |
| 312 | C3×D4 | — | 4 | 2 | no | — |
| 313 | C2×C3×C4 | — | 2 | 1 | no | — |
| 314 | C2×C3×C4 | — | 2 | 1 | no | — |
| 315 | C2×C3×C4 | — | 4 | 1 | no | — |
| 316 | C2×C3×C4 | — | 4 | 1 | no | — |
| 317 | C2×C3×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 318 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 319 | #67 | — | 4 | 8 | no | — |
| 320 | #67 | — | 4 | 8 | no | — |
| 321 | #67 | — | 8 | 2 | no | — |
| 322 | C2×Dic3 | — | 2 | 2 | no | — |
| 323 | C2×Dic3 | — | 4 | 1 | no | — |
| 324 | C2×Dic3 | C2×D8 | 1 | 1 | yes | characteristic |
| 325 | C2×Dic3 | C2×D8 | 1 | 1 | yes | characteristic |
| 326 | D12 | — | 2 | 4 | no | — |
| 327 | D12 | — | 4 | 4 | no | — |
| 328 | D12 | — | 4 | 1 | no | — |
| 329 | D12 | — | 4 | 2 | no | — |
| 330 | D12 | — | 4 | 1 | no | — |
| 331 | D12 | — | 8 | 2 | no | — |
| 332 | D12 | — | 8 | 2 | no | — |
| 333 | C4×D3 | — | 2 | 2 | no | — |
| 334 | C4×D3 | — | 2 | 1 | no | — |
| 335 | C4×D3 | — | 2 | 1 | no | — |
| 336 | C4×D3 | — | 2 | 2 | no | — |
| 337 | C4×D3 | — | 8 | 2 | no | — |
| 338 | C4×D3 | #120 | 1 | 2 | yes | — |
| 339 | C4×D3 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 340 | C3×C8 | — | 2 | 1 | no | — |
| 341 | C3×C8 | C22×D4 | 1 | 2 | yes | — |
| 342 | C3⋊C8 | — | 2 | 1 | no | — |
| 343 | C3⋊C8 | #120 | 1 | 2 | yes | — |
| 344 | C24 | — | 3 | 1 | no | — |
| 345 | C24 | — | 4 | 1 | no | — |
| 346 | C24 | — | 12 | 2 | no | — |
| 347 | C24 | — | 12 | 2 | no | — |
| 348 | C24 | — | 12 | 8 | no | — |
| 349 | C24 | — | 12 | 1 | no | — |
| 350 | C24 | — | 24 | 4 | no | — |
| 351 | C24 | — | 24 | 4 | no | — |
| 352 | #41 | — | 12 | 2 | no | — |
| 353 | #41 | — | 12 | 2 | no | — |
| 354 | C2×Q8 | — | 2 | 1 | no | — |
| 355 | C2×D4 | — | 2 | 4 | no | — |
| 356 | C2×D4 | — | 2 | 2 | no | — |
| 357 | C2×D4 | — | 4 | 2 | no | — |
| 358 | C2×D4 | — | 4 | 1 | no | — |
| 359 | C2×D4 | — | 6 | 4 | no | — |
| 360 | C2×D4 | — | 6 | 8 | no | — |
| 361 | C2×D4 | — | 6 | 8 | no | — |
| 362 | C2×D4 | — | 6 | 2 | no | — |
| 363 | C2×D4 | — | 6 | 1 | no | — |
| 364 | C2×D4 | — | 12 | 2 | no | — |
| 365 | C2×D4 | — | 12 | 4 | no | — |
| 366 | C2×D4 | — | 12 | 2 | no | — |
| 367 | C2×D4 | — | 12 | 2 | no | — |
| 368 | C2×D4 | — | 12 | 1 | no | — |
| 369 | C2×D4 | — | 12 | 1 | no | — |
| 370 | C2×D4 | — | 12 | 8 | no | — |
| 371 | C2×D4 | — | 12 | 8 | no | — |
| 372 | C2×D4 | — | 12 | 4 | no | — |
| 373 | C2×D4 | — | 12 | 8 | no | — |
| 374 | C2×D4 | — | 12 | 1 | no | — |
| 375 | C2×D4 | — | 12 | 1 | no | — |
| 376 | C22×C4 | — | 3 | 1 | no | — |
| 377 | C22×C4 | — | 3 | 1 | no | — |
| 378 | C22×C4 | — | 3 | 1 | no | — |
| 379 | C22×C4 | — | 3 | 1 | no | — |
| 380 | C22×C4 | — | 3 | 1 | no | — |
| 381 | C22×C4 | — | 6 | 2 | no | — |
| 382 | C22×C4 | — | 6 | 2 | no | — |
| 383 | C22×C4 | — | 12 | 1 | no | — |
| 384 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 385 | Q16 | — | 2 | 2 | no | — |
| 386 | SD16 | — | 12 | 2 | no | — |
| 387 | D8 | — | 2 | 4 | no | — |
| 388 | D8 | — | 2 | 2 | no | — |
| 389 | D8 | — | 3 | 4 | no | — |
| 390 | D8 | — | 6 | 4 | no | — |
| 391 | D8 | — | 6 | 8 | no | — |
| 392 | D8 | — | 6 | 8 | no | — |
| 393 | D8 | — | 6 | 2 | no | — |
| 394 | D8 | — | 6 | 2 | no | — |
| 395 | D8 | D3×D4 | 1 | 4 | yes | — |
| 396 | C2×C8 | — | 2 | 2 | no | — |
| 397 | C2×C8 | — | 3 | 1 | no | — |
| 398 | C2×C8 | — | 3 | 4 | no | — |
| 399 | C2×C8 | — | 3 | 1 | no | — |
| 400 | C2×C8 | — | 6 | 2 | no | — |
| 401 | C2×C8 | — | 6 | 2 | no | — |
| 402 | C2×C8 | — | 6 | 2 | no | — |
| 403 | C2×C8 | — | 6 | 2 | no | — |
| 404 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 405 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 406 | C4⋊C4 | — | 2 | 1 | no | — |
| 407 | C4⋊C4 | — | 4 | 1 | no | — |
| 408 | C4⋊C4 | — | 6 | 1 | no | — |
| 409 | C4⋊C4 | — | 12 | 1 | no | — |
| 410 | C22⋊C4 | — | 4 | 1 | no | — |
| 411 | C22⋊C4 | — | 12 | 1 | no | — |
| 412 | C22⋊C4 | — | 12 | 1 | no | — |
| 413 | C22⋊C4 | — | 12 | 1 | no | — |
| 414 | C22⋊C4 | — | 12 | 1 | no | — |
| 415 | C42 | — | 12 | 1 | no | — |
| 416 | C16 | — | 2 | 2 | no | — |
| 417 | C16 | — | 6 | 2 | no | — |
| 418 | C22×C3 | — | 2 | 1 | no | — |
| 419 | C22×C3 | — | 2 | 1 | no | — |
| 420 | C22×C3 | — | 4 | 4 | no | — |
| 421 | C22×C3 | — | 8 | 8 | no | — |
| 422 | C22×C3 | — | 8 | 2 | no | — |
| 423 | C22×C3 | — | 8 | 2 | no | — |
| 424 | C22×C3 | #509 | 1 | 2 | yes | complemented |
| 425 | C22×C3 | C22×D8 | 1 | 1 | yes | characteristic |
| 426 | C2×D3 | — | 2 | 8 | no | — |
| 427 | C2×D3 | — | 2 | 1 | no | — |
| 428 | C2×D3 | — | 2 | 1 | no | — |
| 429 | C2×D3 | — | 2 | 1 | no | — |
| 430 | C2×D3 | — | 2 | 1 | no | — |
| 431 | C2×D3 | — | 4 | 4 | no | — |
| 432 | C2×D3 | — | 8 | 16 | no | — |
| 433 | C2×D3 | — | 8 | 16 | no | — |
| 434 | C2×D3 | — | 8 | 8 | no | — |
| 435 | C2×D3 | — | 8 | 2 | no | — |
| 436 | C2×D3 | — | 8 | 2 | no | — |
| 437 | C2×D3 | — | 8 | 1 | no | — |
| 438 | C2×D3 | — | 8 | 1 | no | — |
| 439 | C2×D3 | — | 8 | 1 | no | — |
| 440 | C2×D3 | #447 | 1 | 2 | yes | — |
| 441 | C2×D3 | #509 | 1 | 2 | yes | complemented |
| 442 | C3×C4 | — | 2 | 1 | no | — |
| 443 | C3×C4 | — | 8 | 1 | no | — |
| 444 | C3×C4 | — | 8 | 1 | no | — |
| 445 | C3×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 446 | C3×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 447 | Dic3 | — | 2 | 1 | no | — |
| 448 | Dic3 | — | 8 | 1 | no | — |
| 449 | Dic3 | #447 | 1 | 2 | yes | — |
| 450 | C23 | — | 3 | 1 | no | — |
| 451 | C23 | — | 3 | 1 | no | — |
| 452 | C23 | — | 4 | 4 | no | — |
| 453 | C23 | — | 4 | 2 | no | — |
| 454 | C23 | — | 6 | 2 | no | — |
| 455 | C23 | — | 6 | 2 | no | — |
| 456 | C23 | — | 6 | 2 | no | — |
| 457 | C23 | — | 8 | 2 | no | — |
| 458 | C23 | — | 8 | 2 | no | — |
| 459 | C23 | — | 12 | 4 | no | — |
| 460 | C23 | — | 12 | 8 | no | — |
| 461 | C23 | — | 12 | 8 | no | — |
| 462 | C23 | — | 12 | 2 | no | — |
| 463 | C23 | — | 12 | 1 | no | — |
| 464 | C23 | — | 24 | 2 | no | — |
| 465 | C23 | — | 24 | 4 | no | — |
| 466 | C23 | — | 24 | 32 | no | — |
| 467 | C23 | — | 24 | 4 | no | — |
| 468 | C23 | — | 24 | 4 | no | — |
| 469 | C23 | — | 24 | 4 | no | — |
| 470 | C23 | — | 24 | 2 | no | — |
| 471 | C23 | D3×D8 | 1 | 1 | yes | characteristic |
| 472 | Q8 | — | 4 | 1 | no | — |
| 473 | Q8 | — | 4 | 1 | no | — |
| 474 | D4 | — | 2 | 4 | no | — |
| 475 | D4 | — | 4 | 4 | no | — |
| 476 | D4 | — | 4 | 2 | no | — |
| 477 | D4 | — | 6 | 4 | no | — |
| 478 | D4 | — | 12 | 4 | no | — |
| 479 | D4 | — | 12 | 8 | no | — |
| 480 | D4 | — | 12 | 8 | no | — |
| 481 | D4 | — | 12 | 2 | no | — |
| 482 | D4 | — | 12 | 1 | no | — |
| 483 | D4 | — | 12 | 1 | no | — |
| 484 | D4 | — | 24 | 2 | no | — |
| 485 | D4 | — | 24 | 2 | no | — |
| 486 | D4 | — | 24 | 2 | no | — |
| 487 | C2×C4 | — | 2 | 1 | no | — |
| 488 | C2×C4 | — | 2 | 1 | no | — |
| 489 | C2×C4 | — | 3 | 1 | no | — |
| 490 | C2×C4 | — | 3 | 2 | no | — |
| 491 | C2×C4 | — | 3 | 2 | no | — |
| 492 | C2×C4 | — | 3 | 1 | no | — |
| 493 | C2×C4 | — | 4 | 1 | no | — |
| 494 | C2×C4 | — | 4 | 1 | no | — |
| 495 | C2×C4 | — | 6 | 2 | no | — |
| 496 | C2×C4 | — | 6 | 2 | no | — |
| 497 | C2×C4 | — | 6 | 2 | no | — |
| 498 | C2×C4 | — | 6 | 1 | no | — |
| 499 | C2×C4 | — | 6 | 1 | no | — |
| 500 | C2×C4 | — | 12 | 1 | no | — |
| 501 | C2×C4 | — | 24 | 2 | no | — |
| 502 | C2×C4 | D3×D8 | 1 | 1 | yes | characteristic |
| 503 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 504 | C8 | — | 2 | 1 | no | — |
| 505 | C8 | — | 3 | 2 | no | — |
| 506 | C8 | — | 6 | 1 | no | — |
| 507 | C8 | C2×D3×D4 | 1 | 2 | yes | — |
| 508 | C2×C3 | — | 2 | 2 | no | — |
| 509 | C2×C3 | — | 8 | 4 | no | — |
| 510 | C2×C3 | C2×#447 | 1 | 1 | yes | characteristic |
| 511 | C2×C3 | C2×#509 | 1 | 1 | yes | characteristic |
| 512 | C2×C3 | C2×#509 | 1 | 1 | yes | characteristic |
| 513 | D3 | — | 2 | 2 | no | — |
| 514 | D3 | — | 2 | 2 | no | — |
| 515 | D3 | — | 8 | 4 | no | — |
| 516 | D3 | — | 16 | 1 | no | — |
| 517 | C22 | — | 2 | 1 | no | — |
| 518 | C22 | — | 2 | 1 | no | — |
| 519 | C22 | — | 3 | 2 | no | — |
| 520 | C22 | — | 3 | 2 | no | — |
| 521 | C22 | — | 4 | 4 | no | — |
| 522 | C22 | — | 6 | 8 | no | — |
| 523 | C22 | — | 6 | 1 | no | — |
| 524 | C22 | — | 6 | 1 | no | — |
| 525 | C22 | — | 6 | 1 | no | — |
| 526 | C22 | — | 6 | 1 | no | — |
| 527 | C22 | — | 8 | 8 | no | — |
| 528 | C22 | — | 8 | 2 | no | — |
| 529 | C22 | — | 8 | 2 | no | — |
| 530 | C22 | — | 12 | 4 | no | — |
| 531 | C22 | — | 24 | 8 | no | — |
| 532 | C22 | — | 24 | 16 | no | — |
| 533 | C22 | — | 24 | 16 | no | — |
| 534 | C22 | — | 24 | 2 | no | — |
| 535 | C22 | — | 24 | 2 | no | — |
| 536 | C22 | — | 24 | 1 | no | — |
| 537 | C22 | — | 24 | 1 | no | — |
| 538 | C22 | — | 24 | 1 | no | — |
| 539 | C22 | #4914 | 1 | 2 | yes | complemented |
| 540 | C22 | C2×D3×D8 | 1 | 1 | yes | characteristic |
| 541 | C4 | — | 2 | 1 | no | — |
| 542 | C4 | — | 3 | 2 | no | — |
| 543 | C4 | — | 6 | 1 | no | — |
| 544 | C4 | — | 8 | 1 | no | — |
| 545 | C4 | — | 8 | 1 | no | — |
| 546 | C4 | — | 24 | 1 | no | — |
| 547 | C4 | D3×#120 | 1 | 1 | yes | characteristic |
| 548 | C4 | D3×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 549 | C3 | #33517 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 550 | C2 | — | 2 | 2 | no | — |
| 551 | C2 | — | 6 | 2 | no | — |
| 552 | C2 | — | 6 | 2 | no | — |
| 553 | C2 | — | 8 | 4 | no | — |
| 554 | C2 | — | 24 | 4 | no | — |
| 555 | C2 | — | 48 | 1 | no | — |
| 556 | C2 | D3×#447 | 1 | 1 | yes | characteristic |
| 557 | C2 | C2×#4914 | 1 | 1 | yes | characteristic |
| 558 | C2 | D3×#509 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D3×D8 | C2 | semidirect |
| 2. C2×#4914 | C2 | semidirect |
| 3. #80758 | C2 | semidirect |
| 4. C3×#2187 | C2 | semidirect |
| 5. #72035 | C2 | semidirect |
| 6. #71485 | C2 | semidirect |
| 7. #71085 | C2 | semidirect |
| 8. #69191 | C2 | semidirect |
| 9. #69190 | C2 | semidirect |
| 10. #69108 | C2 | semidirect |
| 11. #69106 | C2 | semidirect |
| 16. C2×#919 | C22 | semidirect |
| 25. C2×C3×SD32 | C22 | semidirect |
| 26. C3×#467 | C22 | semidirect |
| 27. #5188 | C22 | semidirect |
| 28. C2×#828 | C22 | semidirect |
| 29. C2×#826 | C22 | semidirect |
| 30. #5115 | C22 | semidirect |
| 33. C2×D48 | C22 | semidirect |
| 34. C2×#798 | C22 | semidirect |
| 35. #4883 | C22 | semidirect |
| 36. #4880 | C22 | semidirect |
| 39. C3×#357 | C22 | semidirect |
| 40. C3×C22⋊C16 | C22 | semidirect |
| 41. #4562 | C22 | semidirect |
| 42. #4549 | C22 | semidirect |
| 43. #4509 | C22 | semidirect |
| 44. (C2×D3)⋊C16 | C22 | semidirect |
| 45. #4491 | C22 | semidirect |
| 51. #2187 | D3 | semidirect |
| 69. C2×C3×Q16 | C23 | semidirect |
| 88. D3×D8 | D4 | semidirect |
| 92. C2×D24 | C23 | semidirect |
| 105. C2×C3×C16 | C23 | semidirect |
| 106. C3×#107 | C23 | semidirect |
| 112. #818 | C23 | semidirect |
| 113. C2×C3⋊C16 | C23 | semidirect |
| 132. C2×SD32 | C2×D3 | semidirect |
| 137. #467 | C2×D3 | semidirect |
| 147. #357 | C2×D3 | semidirect |
| 150. C22⋊C16 | C2×D3 | semidirect |
| 238. C2×Q16 | C22×D3 | semidirect |
| 278. C2×C16 | C22×D3 | semidirect |
| 280. #107 | C22×D3 | semidirect |
| 424. C22×C3 | #509 | semidirect |
| 441. C2×D3 | #509 | semidirect |
| 539. C22 | #4914 | semidirect |
| 549. C3 | #33517 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×D8 | 2 |
| C2×#4914 | 2 |
| #80758 | 2 |
| C3×#2187 | 2 |
| #72035 | 2 |
| #71485 | 2 |
| #71085 | 2 |
| #69191 | 2 |
| #69190 | 2 |
| #69108 | 2 |
| #69106 | 2 |
| #33517 | 3 |