Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1336 conjugacy classes of subgroups.
The subgroup lattice has 498 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #87163 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #83794 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #79180 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #78690 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C3×#1812 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #70658 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #70054 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #68703 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #68698 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #24285 | — | 3 | 1 | no | maximal, Sylow |
| 11 | #5964 | C22 | 1 | 2 | yes | — |
| 12 | C2×C3×#131 | C22 | 1 | 1 | yes | characteristic |
| 13 | #5828 | C22 | 1 | 1 | yes | characteristic |
| 14 | #5753 | — | 2 | 2 | no | — |
| 15 | #5752 | — | 2 | 2 | no | — |
| 16 | #5751 | — | 2 | 4 | no | — |
| 17 | #5748 | — | 2 | 2 | no | — |
| 18 | #5748 | C22 | 1 | 2 | yes | — |
| 19 | C2×#904 | — | 2 | 2 | no | — |
| 20 | C2×#904 | C22 | 1 | 2 | yes | — |
| 21 | C22×D3×C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #5524 | C22 | 1 | 4 | yes | complemented |
| 23 | C3×#427 | C22 | 1 | 2 | yes | complemented |
| 24 | C3×#410 | C22 | 1 | 2 | yes | — |
| 25 | #5234 | C22 | 1 | 1 | yes | characteristic |
| 26 | #5127 | — | 2 | 2 | no | — |
| 27 | #5126 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #5119 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | C8×#67 | — | 2 | 2 | no | — |
| 30 | #5101 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #5006 | C22 | 1 | 4 | yes | complemented |
| 32 | #5005 | C22 | 1 | 4 | yes | complemented |
| 33 | #5002 | C22 | 1 | 4 | yes | complemented |
| 34 | #4887 | — | 2 | 2 | no | — |
| 35 | #4883 | — | 2 | 2 | no | — |
| 36 | #4864 | — | 2 | 4 | no | — |
| 37 | #4742 | — | 2 | 4 | no | — |
| 38 | #4741 | — | 2 | 4 | no | — |
| 39 | C3×H(3,ℤ/4) | C22 | 1 | 2 | yes | complemented |
| 40 | #3584 | — | 3 | 1 | no | — |
| 41 | #3050 | — | 3 | 2 | no | — |
| 42 | #3025 | — | 3 | 2 | no | — |
| 43 | #2929 | — | 3 | 1 | no | — |
| 44 | #2053 | — | 3 | 2 | no | — |
| 45 | #2010 | — | 3 | 2 | no | — |
| 46 | #1976 | — | 3 | 2 | no | — |
| 47 | #1812 | D3 | 1 | 1 | yes | characteristic, complemented |
| 48 | #1794 | — | 3 | 2 | no | — |
| 49 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 50 | #1010 | — | 2 | 4 | no | — |
| 51 | #1009 | — | 2 | 4 | no | — |
| 52 | D3×#41 | — | 4 | 4 | no | — |
| 53 | #1007 | — | 2 | 2 | no | — |
| 54 | #1004 | — | 2 | 2 | no | — |
| 55 | #1004 | — | 2 | 4 | no | — |
| 56 | C2×#235 | — | 2 | 4 | no | — |
| 57 | C2×#235 | C23 | 1 | 4 | yes | — |
| 58 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 59 | C3×#131 | — | 2 | 2 | no | — |
| 60 | C3×#131 | — | 2 | 2 | no | — |
| 61 | C2×C3×M16 | D4 | 1 | 2 | yes | complemented |
| 62 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 63 | C22×C3×C8 | D4 | 1 | 2 | yes | complemented |
| 64 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 65 | C3×#117 | C23 | 1 | 4 | yes | — |
| 66 | #946 | — | 2 | 1 | no | — |
| 67 | #938 | — | 2 | 1 | no | — |
| 68 | #937 | D4 | 1 | 2 | yes | — |
| 69 | #935 | D4 | 1 | 2 | yes | — |
| 70 | C4×#67 | — | 2 | 2 | no | — |
| 71 | #926 | C23 | 1 | 1 | yes | characteristic |
| 72 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 73 | C22×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 74 | #909 | — | 2 | 8 | no | — |
| 75 | #909 | — | 2 | 4 | no | — |
| 76 | #908 | — | 2 | 8 | no | — |
| 77 | #908 | — | 2 | 4 | no | — |
| 78 | C2×Dic12 | — | 2 | 2 | no | — |
| 79 | C2×Dic12 | D4 | 1 | 2 | yes | complemented |
| 80 | #904 | — | 2 | 4 | no | — |
| 81 | #904 | — | 2 | 4 | no | — |
| 82 | #904 | — | 2 | 2 | no | — |
| 83 | #904 | — | 2 | 4 | no | — |
| 84 | #904 | — | 2 | 2 | no | — |
| 85 | #904 | — | 2 | 2 | no | — |
| 86 | #904 | — | 2 | 2 | no | — |
| 87 | C2×D24 | — | 2 | 2 | no | — |
| 88 | C2×D24 | D4 | 1 | 2 | yes | complemented |
| 89 | C2×#204 | — | 2 | 4 | no | — |
| 90 | C2×#204 | D4 | 1 | 4 | yes | complemented |
| 91 | C2×D3×C8 | — | 2 | 2 | no | — |
| 92 | C2×D3×C8 | — | 2 | 1 | no | — |
| 93 | C2×D3×C8 | — | 2 | 2 | no | — |
| 94 | C2×D3×C8 | — | 2 | 1 | no | — |
| 95 | #897 | — | 2 | 4 | no | — |
| 96 | #895 | — | 2 | 4 | no | — |
| 97 | #886 | — | 2 | 4 | no | — |
| 98 | #882 | — | 2 | 4 | no | — |
| 99 | C4×D12 | — | 4 | 4 | no | — |
| 100 | C3×#107 | — | 2 | 2 | no | — |
| 101 | C3×#106 | — | 2 | 2 | no | — |
| 102 | C3×#99 | — | 2 | 4 | no | — |
| 103 | #830 | — | 2 | 2 | no | — |
| 104 | (C2×D3)⋊C8 | — | 2 | 2 | no | — |
| 105 | #815 | — | 2 | 1 | no | — |
| 106 | Dic3⋊C8 | — | 2 | 2 | no | — |
| 107 | C8×Dic3 | — | 2 | 1 | no | — |
| 108 | #810 | — | 2 | 4 | no | — |
| 109 | #809 | — | 2 | 4 | no | — |
| 110 | #806 | — | 2 | 8 | no | — |
| 111 | #805 | — | 4 | 4 | no | — |
| 112 | #585 | — | 3 | 2 | no | — |
| 113 | #578 | — | 6 | 2 | no | — |
| 114 | #577 | — | 6 | 4 | no | — |
| 115 | #576 | — | 6 | 2 | no | — |
| 116 | #575 | — | 3 | 2 | no | — |
| 117 | #575 | — | 6 | 2 | no | — |
| 118 | C2×#135 | — | 3 | 2 | no | — |
| 119 | C2×#135 | — | 6 | 2 | no | — |
| 120 | C2×#131 | C2×D3 | 1 | 1 | yes | characteristic |
| 121 | C23×C8 | — | 3 | 1 | no | — |
| 122 | #525 | — | 3 | 1 | no | — |
| 123 | #525 | — | 3 | 4 | no | — |
| 124 | #467 | — | 6 | 2 | no | — |
| 125 | #466 | — | 6 | 2 | no | — |
| 126 | #465 | — | 6 | 4 | no | — |
| 127 | #458 | — | 6 | 4 | no | — |
| 128 | B(4,𝔽2) | — | 6 | 4 | no | — |
| 129 | #435 | — | 6 | 2 | no | — |
| 130 | C8×D4 | — | 6 | 2 | no | — |
| 131 | #427 | C2×D3 | 1 | 2 | yes | complemented |
| 132 | #424 | — | 3 | 1 | no | — |
| 133 | #421 | — | 3 | 4 | no | — |
| 134 | #416 | — | 3 | 4 | no | — |
| 135 | #410 | — | 3 | 4 | no | — |
| 136 | #410 | C2×D3 | 1 | 2 | yes | — |
| 137 | #408 | — | 3 | 1 | no | — |
| 138 | #407 | — | 3 | 1 | no | — |
| 139 | #405 | — | 3 | 1 | no | — |
| 140 | H(3,ℤ/4) | C2×D3 | 1 | 2 | yes | complemented |
| 141 | C23×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 142 | C3×#41 | — | 2 | 2 | no | — |
| 143 | C3×#41 | — | 2 | 2 | no | — |
| 144 | C2×C3×Q8 | #41 | 1 | 1 | yes | characteristic |
| 145 | C2×C3×D4 | C2×D4 | 1 | 2 | yes | — |
| 146 | C2×C3×D4 | #41 | 1 | 1 | yes | characteristic |
| 147 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 148 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 149 | C2×#67 | — | 2 | 2 | no | — |
| 150 | C2×#67 | — | 2 | 4 | no | — |
| 151 | C2×#67 | — | 4 | 4 | no | — |
| 152 | C22×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 153 | #239 | — | 4 | 4 | no | — |
| 154 | D3×Q8 | — | 4 | 4 | no | — |
| 155 | #237 | — | 4 | 4 | no | — |
| 156 | #237 | — | 4 | 8 | no | — |
| 157 | D3×D4 | — | 4 | 4 | no | — |
| 158 | D3×D4 | — | 4 | 8 | no | — |
| 159 | #235 | — | 2 | 8 | no | — |
| 160 | #235 | — | 2 | 4 | no | — |
| 161 | #235 | — | 2 | 4 | no | — |
| 162 | #235 | — | 2 | 4 | no | — |
| 163 | #235 | — | 2 | 4 | no | — |
| 164 | #235 | — | 4 | 4 | no | — |
| 165 | #235 | — | 4 | 4 | no | — |
| 166 | C2×D12 | — | 2 | 4 | no | — |
| 167 | C2×D12 | — | 4 | 4 | no | — |
| 168 | C2×D12 | C2×D4 | 1 | 4 | yes | — |
| 169 | C2×C4×D3 | — | 2 | 1 | no | — |
| 170 | C2×C4×D3 | — | 2 | 2 | no | — |
| 171 | C2×C4×D3 | — | 2 | 1 | no | — |
| 172 | C2×C4×D3 | — | 2 | 2 | no | — |
| 173 | C2×C4×D3 | — | 2 | 4 | no | — |
| 174 | C2×C4×D3 | — | 4 | 4 | no | — |
| 175 | C2×Dic6 | — | 2 | 4 | no | — |
| 176 | C2×Dic6 | C2×D4 | 1 | 4 | yes | — |
| 177 | C3×M16 | — | 2 | 2 | no | — |
| 178 | C3×M16 | — | 2 | 4 | no | — |
| 179 | C2×C3×C8 | — | 2 | 2 | no | — |
| 180 | C2×C3×C8 | — | 2 | 2 | no | — |
| 181 | C2×C3×C8 | C2×D4 | 1 | 2 | yes | — |
| 182 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 183 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 184 | C2×C3×C8 | C2×D4 | 1 | 2 | yes | — |
| 185 | C2×C3×C8 | C2×D4 | 1 | 2 | yes | — |
| 186 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 187 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 188 | C3×C42 | — | 2 | 4 | no | — |
| 189 | #217 | — | 2 | 2 | no | — |
| 190 | #217 | C2×D4 | 1 | 2 | yes | — |
| 191 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 192 | (C2×D3)⋊C4 | — | 4 | 4 | no | — |
| 193 | (C2×D3)⋊C4 | — | 4 | 4 | no | — |
| 194 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 195 | C4⋊Dic3 | — | 4 | 4 | no | — |
| 196 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 197 | C4×Dic3 | — | 2 | 1 | no | — |
| 198 | #208 | — | 2 | 2 | no | — |
| 199 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 200 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 201 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 202 | Dic12 | — | 2 | 4 | no | — |
| 203 | Dic12 | — | 2 | 2 | no | — |
| 204 | Dic12 | — | 2 | 2 | no | — |
| 205 | D24 | — | 2 | 4 | no | — |
| 206 | D24 | — | 2 | 2 | no | — |
| 207 | D24 | — | 2 | 2 | no | — |
| 208 | #204 | — | 2 | 8 | no | — |
| 209 | #204 | — | 2 | 4 | no | — |
| 210 | #204 | — | 2 | 4 | no | — |
| 211 | D3×C8 | — | 4 | 1 | no | — |
| 212 | D3×C8 | — | 4 | 2 | no | — |
| 213 | D3×C8 | — | 4 | 1 | no | — |
| 214 | 2−1+4 | — | 6 | 4 | no | — |
| 215 | 2−1+4 | — | 6 | 2 | no | — |
| 216 | H(5,𝔽2) | — | 6 | 4 | no | — |
| 217 | H(5,𝔽2) | — | 6 | 4 | no | — |
| 218 | H(5,𝔽2) | — | 6 | 2 | no | — |
| 219 | C2×#41 | — | 3 | 4 | no | — |
| 220 | C2×#41 | — | 6 | 4 | no | — |
| 221 | C2×#41 | — | 12 | 4 | no | — |
| 222 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 223 | C23×C4 | — | 3 | 1 | no | — |
| 224 | #137 | — | 6 | 4 | no | — |
| 225 | #137 | — | 6 | 8 | no | — |
| 226 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 227 | AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 228 | #135 | — | 6 | 4 | no | — |
| 229 | #135 | — | 6 | 4 | no | — |
| 230 | #135 | — | 6 | 2 | no | — |
| 231 | #135 | — | 6 | 2 | no | — |
| 232 | #135 | — | 6 | 4 | no | — |
| 233 | #135 | — | 6 | 2 | no | — |
| 234 | #135 | — | 6 | 2 | no | — |
| 235 | C2×Q16 | — | 3 | 2 | no | — |
| 236 | C2×Q16 | — | 6 | 2 | no | — |
| 237 | C2×SD16 | — | 3 | 4 | no | — |
| 238 | C2×SD16 | — | 6 | 4 | no | — |
| 239 | C2×D8 | — | 3 | 2 | no | — |
| 240 | C2×D8 | — | 6 | 2 | no | — |
| 241 | #131 | — | 2 | 2 | no | — |
| 242 | #131 | — | 2 | 2 | no | — |
| 243 | C2×M16 | — | 3 | 1 | no | — |
| 244 | C2×M16 | D12 | 1 | 2 | yes | complemented |
| 245 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 246 | C22×C8 | — | 3 | 1 | no | — |
| 247 | C22×C8 | — | 6 | 1 | no | — |
| 248 | C22×C8 | — | 6 | 1 | no | — |
| 249 | C22×C8 | — | 6 | 2 | no | — |
| 250 | C22×C8 | — | 6 | 2 | no | — |
| 251 | C22×C8 | D12 | 1 | 2 | yes | complemented |
| 252 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 253 | #123 | — | 3 | 2 | no | — |
| 254 | #123 | — | 6 | 4 | no | — |
| 255 | C22⋊Q8 | — | 6 | 1 | no | — |
| 256 | C22⋊Q8 | — | 6 | 4 | no | — |
| 257 | #121 | — | 6 | 1 | no | — |
| 258 | #121 | — | 6 | 4 | no | — |
| 259 | #120 | — | 3 | 2 | no | — |
| 260 | #120 | — | 6 | 4 | no | — |
| 261 | C4×D4 | — | 6 | 2 | no | — |
| 262 | C4×D4 | — | 12 | 4 | no | — |
| 263 | #117 | — | 3 | 1 | no | — |
| 264 | #117 | C22×D3 | 1 | 4 | yes | — |
| 265 | #107 | — | 2 | 2 | no | — |
| 266 | #106 | — | 2 | 2 | no | — |
| 267 | C4⋊C8 | — | 6 | 2 | no | — |
| 268 | #104 | — | 12 | 4 | no | — |
| 269 | #103 | — | 6 | 4 | no | — |
| 270 | #102 | — | 6 | 4 | no | — |
| 271 | #99 | — | 2 | 4 | no | — |
| 272 | #99 | — | 6 | 8 | no | — |
| 273 | C22⋊C8 | — | 6 | 2 | no | — |
| 274 | C22⋊C8 | — | 6 | 2 | no | — |
| 275 | #97 | — | 6 | 1 | no | — |
| 276 | C4×C8 | — | 6 | 1 | no | — |
| 277 | C23×C3 | #121 | 1 | 2 | yes | — |
| 278 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 279 | C22×D3 | — | 2 | 1 | no | — |
| 280 | C22×D3 | — | 2 | 2 | no | — |
| 281 | C22×D3 | — | 2 | 4 | no | — |
| 282 | C22×D3 | — | 4 | 2 | no | — |
| 283 | C22×D3 | — | 4 | 4 | no | — |
| 284 | C3×Q8 | — | 2 | 2 | no | — |
| 285 | C3×D4 | — | 2 | 4 | no | — |
| 286 | C3×D4 | — | 2 | 2 | no | — |
| 287 | C2×C3×C4 | — | 2 | 2 | no | — |
| 288 | C2×C3×C4 | — | 2 | 2 | no | — |
| 289 | C2×C3×C4 | — | 4 | 4 | no | — |
| 290 | C2×C3×C4 | #121 | 1 | 2 | yes | — |
| 291 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 292 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 293 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 294 | C2×C3×C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 295 | #67 | — | 4 | 4 | no | — |
| 296 | #67 | — | 4 | 8 | no | — |
| 297 | #67 | — | 4 | 4 | no | — |
| 298 | #67 | — | 4 | 4 | no | — |
| 299 | C2×Dic3 | — | 2 | 2 | no | — |
| 300 | C2×Dic3 | — | 2 | 1 | no | — |
| 301 | C2×Dic3 | — | 2 | 2 | no | — |
| 302 | C2×Dic3 | — | 2 | 4 | no | — |
| 303 | C2×Dic3 | — | 4 | 4 | no | — |
| 304 | D12 | — | 2 | 4 | no | — |
| 305 | D12 | — | 2 | 4 | no | — |
| 306 | D12 | — | 4 | 4 | no | — |
| 307 | D12 | — | 8 | 8 | no | — |
| 308 | C4×D3 | — | 4 | 8 | no | — |
| 309 | C4×D3 | — | 4 | 1 | no | — |
| 310 | C4×D3 | — | 4 | 1 | no | — |
| 311 | C4×D3 | — | 4 | 4 | no | — |
| 312 | C4×D3 | — | 4 | 2 | no | — |
| 313 | C4×D3 | — | 4 | 4 | no | — |
| 314 | Dic6 | — | 2 | 4 | no | — |
| 315 | Dic6 | — | 2 | 4 | no | — |
| 316 | Dic6 | — | 4 | 4 | no | — |
| 317 | C3×C8 | — | 2 | 2 | no | — |
| 318 | C3×C8 | #120 | 1 | 1 | yes | characteristic |
| 319 | C3×C8 | #120 | 1 | 2 | yes | — |
| 320 | C3×C8 | #120 | 1 | 1 | yes | characteristic |
| 321 | C3⋊C8 | — | 4 | 1 | no | — |
| 322 | C3⋊C8 | — | 4 | 1 | no | — |
| 323 | C24 | — | 3 | 1 | no | — |
| 324 | #41 | — | 2 | 2 | no | — |
| 325 | #41 | — | 2 | 2 | no | — |
| 326 | #41 | — | 6 | 8 | no | — |
| 327 | #41 | — | 6 | 4 | no | — |
| 328 | #41 | — | 6 | 4 | no | — |
| 329 | #41 | — | 6 | 4 | no | — |
| 330 | #41 | — | 6 | 4 | no | — |
| 331 | #41 | — | 12 | 4 | no | — |
| 332 | #41 | — | 12 | 8 | no | — |
| 333 | #41 | — | 12 | 4 | no | — |
| 334 | #41 | — | 12 | 4 | no | — |
| 335 | #41 | — | 12 | 4 | no | — |
| 336 | C2×Q8 | — | 3 | 4 | no | — |
| 337 | C2×Q8 | — | 6 | 4 | no | — |
| 338 | C2×Q8 | — | 12 | 4 | no | — |
| 339 | C2×Q8 | #239 | 1 | 1 | yes | characteristic |
| 340 | C2×D4 | — | 3 | 4 | no | — |
| 341 | C2×D4 | — | 6 | 4 | no | — |
| 342 | C2×D4 | — | 6 | 2 | no | — |
| 343 | C2×D4 | — | 6 | 4 | no | — |
| 344 | C2×D4 | — | 12 | 4 | no | — |
| 345 | C2×D4 | — | 12 | 4 | no | — |
| 346 | C2×D4 | — | 12 | 8 | no | — |
| 347 | C2×D4 | — | 12 | 4 | no | — |
| 348 | C2×D4 | D3×D4 | 1 | 2 | yes | — |
| 349 | C2×D4 | #239 | 1 | 1 | yes | characteristic |
| 350 | C22×C4 | — | 3 | 1 | no | — |
| 351 | C22×C4 | — | 6 | 1 | no | — |
| 352 | C22×C4 | — | 6 | 2 | no | — |
| 353 | C22×C4 | — | 6 | 1 | no | — |
| 354 | C22×C4 | — | 6 | 2 | no | — |
| 355 | C22×C4 | — | 6 | 4 | no | — |
| 356 | C22×C4 | — | 12 | 4 | no | — |
| 357 | C22×C4 | C2×D12 | 1 | 2 | yes | — |
| 358 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 359 | Q16 | — | 6 | 4 | no | — |
| 360 | Q16 | — | 6 | 2 | no | — |
| 361 | Q16 | — | 6 | 2 | no | — |
| 362 | SD16 | — | 6 | 8 | no | — |
| 363 | SD16 | — | 6 | 4 | no | — |
| 364 | SD16 | — | 6 | 4 | no | — |
| 365 | D8 | — | 6 | 4 | no | — |
| 366 | D8 | — | 6 | 2 | no | — |
| 367 | D8 | — | 6 | 2 | no | — |
| 368 | M16 | — | 2 | 2 | no | — |
| 369 | M16 | — | 2 | 4 | no | — |
| 370 | M16 | — | 6 | 2 | no | — |
| 371 | C2×C8 | — | 2 | 2 | no | — |
| 372 | C2×C8 | — | 2 | 2 | no | — |
| 373 | C2×C8 | — | 6 | 1 | no | — |
| 374 | C2×C8 | — | 6 | 1 | no | — |
| 375 | C2×C8 | — | 6 | 2 | no | — |
| 376 | C2×C8 | — | 12 | 1 | no | — |
| 377 | C2×C8 | — | 12 | 1 | no | — |
| 378 | C2×C8 | — | 12 | 2 | no | — |
| 379 | C2×C8 | C2×D12 | 1 | 2 | yes | — |
| 380 | C2×C8 | C2×D12 | 1 | 1 | yes | characteristic |
| 381 | C2×C8 | C2×D12 | 1 | 1 | yes | characteristic |
| 382 | C2×C8 | D3×D4 | 1 | 2 | yes | — |
| 383 | C2×C8 | D3×D4 | 1 | 2 | yes | — |
| 384 | C4⋊C4 | — | 2 | 4 | no | — |
| 385 | C4⋊C4 | — | 6 | 2 | no | — |
| 386 | C4⋊C4 | — | 6 | 1 | no | — |
| 387 | C4⋊C4 | — | 12 | 4 | no | — |
| 388 | C22⋊C4 | — | 2 | 4 | no | — |
| 389 | C22⋊C4 | — | 3 | 2 | no | — |
| 390 | C22⋊C4 | — | 6 | 2 | no | — |
| 391 | C22⋊C4 | — | 6 | 2 | no | — |
| 392 | C22⋊C4 | — | 12 | 4 | no | — |
| 393 | C22⋊C4 | — | 12 | 4 | no | — |
| 394 | C42 | — | 2 | 4 | no | — |
| 395 | C42 | — | 6 | 1 | no | — |
| 396 | C22×C3 | — | 2 | 2 | no | — |
| 397 | C22×C3 | — | 4 | 1 | no | — |
| 398 | C22×C3 | — | 4 | 2 | no | — |
| 399 | C22×C3 | C2×#121 | 1 | 1 | yes | characteristic |
| 400 | C22×C3 | D42 | 1 | 2 | yes | — |
| 401 | C2×D3 | — | 2 | 4 | no | — |
| 402 | C2×D3 | — | 2 | 2 | no | — |
| 403 | C2×D3 | — | 4 | 1 | no | — |
| 404 | C2×D3 | — | 4 | 2 | no | — |
| 405 | C2×D3 | — | 4 | 1 | no | — |
| 406 | C2×D3 | — | 4 | 4 | no | — |
| 407 | C2×D3 | — | 8 | 4 | no | — |
| 408 | C2×D3 | — | 16 | 4 | no | — |
| 409 | C3×C4 | — | 2 | 2 | no | — |
| 410 | C3×C4 | — | 8 | 4 | no | — |
| 411 | C3×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 412 | C3×C4 | #535 | 1 | 1 | yes | characteristic |
| 413 | C3×C4 | #546 | 1 | 2 | yes | — |
| 414 | Dic3 | — | 4 | 2 | no | — |
| 415 | Dic3 | — | 4 | 4 | no | — |
| 416 | Dic3 | — | 4 | 1 | no | — |
| 417 | C23 | — | 6 | 1 | no | — |
| 418 | C23 | — | 6 | 2 | no | — |
| 419 | C23 | — | 6 | 4 | no | — |
| 420 | C23 | — | 12 | 4 | no | — |
| 421 | C23 | — | 12 | 2 | no | — |
| 422 | C23 | #895 | 1 | 2 | yes | — |
| 423 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 424 | Q8 | — | 2 | 2 | no | — |
| 425 | Q8 | — | 6 | 4 | no | — |
| 426 | Q8 | — | 6 | 4 | no | — |
| 427 | Q8 | — | 12 | 4 | no | — |
| 428 | D4 | — | 2 | 4 | no | — |
| 429 | D4 | — | 2 | 2 | no | — |
| 430 | D4 | — | 6 | 4 | no | — |
| 431 | D4 | — | 6 | 4 | no | — |
| 432 | D4 | — | 12 | 4 | no | — |
| 433 | D4 | — | 12 | 8 | no | — |
| 434 | D4 | — | 12 | 4 | no | — |
| 435 | D4 | — | 12 | 4 | no | — |
| 436 | D4 | — | 12 | 4 | no | — |
| 437 | D4 | — | 24 | 8 | no | — |
| 438 | C2×C4 | — | 2 | 2 | no | — |
| 439 | C2×C4 | — | 2 | 2 | no | — |
| 440 | C2×C4 | — | 4 | 4 | no | — |
| 441 | C2×C4 | — | 6 | 2 | no | — |
| 442 | C2×C4 | — | 6 | 1 | no | — |
| 443 | C2×C4 | — | 6 | 2 | no | — |
| 444 | C2×C4 | — | 6 | 4 | no | — |
| 445 | C2×C4 | — | 12 | 8 | no | — |
| 446 | C2×C4 | — | 12 | 4 | no | — |
| 447 | C2×C4 | — | 12 | 1 | no | — |
| 448 | C2×C4 | — | 12 | 1 | no | — |
| 449 | C2×C4 | — | 12 | 4 | no | — |
| 450 | C2×C4 | — | 12 | 2 | no | — |
| 451 | C2×C4 | — | 12 | 4 | no | — |
| 452 | C2×C4 | #895 | 1 | 2 | yes | — |
| 453 | C2×C4 | C22×D12 | 1 | 1 | yes | characteristic |
| 454 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 455 | C2×C4 | C2×#239 | 1 | 1 | yes | characteristic |
| 456 | C2×C4 | #1009 | 1 | 2 | yes | — |
| 457 | C8 | — | 2 | 2 | no | — |
| 458 | C8 | — | 12 | 1 | no | — |
| 459 | C8 | — | 12 | 1 | no | — |
| 460 | C8 | #882 | 1 | 1 | yes | characteristic |
| 461 | C8 | #882 | 1 | 1 | yes | characteristic |
| 462 | C8 | #882 | 1 | 2 | yes | — |
| 463 | C2×C3 | — | 2 | 1 | no | — |
| 464 | C2×C3 | — | 2 | 2 | no | — |
| 465 | C2×C3 | — | 4 | 2 | no | — |
| 466 | C2×C3 | #2408 | 1 | 1 | yes | characteristic |
| 467 | D3 | — | 4 | 2 | no | — |
| 468 | D3 | — | 8 | 4 | no | — |
| 469 | C22 | — | 2 | 2 | no | — |
| 470 | C22 | — | 4 | 1 | no | — |
| 471 | C22 | — | 4 | 2 | no | — |
| 472 | C22 | — | 6 | 2 | no | — |
| 473 | C22 | — | 6 | 4 | no | — |
| 474 | C22 | — | 12 | 2 | no | — |
| 475 | C22 | — | 12 | 1 | no | — |
| 476 | C22 | — | 12 | 1 | no | — |
| 477 | C22 | — | 12 | 4 | no | — |
| 478 | C22 | — | 24 | 4 | no | — |
| 479 | C22 | — | 48 | 4 | no | — |
| 480 | C22 | C2×#895 | 1 | 1 | yes | characteristic |
| 481 | C22 | #5609 | 1 | 2 | yes | — |
| 482 | C4 | — | 2 | 2 | no | — |
| 483 | C4 | — | 8 | 4 | no | — |
| 484 | C4 | — | 12 | 2 | no | — |
| 485 | C4 | — | 12 | 1 | no | — |
| 486 | C4 | — | 12 | 4 | no | — |
| 487 | C4 | C2×#882 | 1 | 1 | yes | characteristic |
| 488 | C4 | #5525 | 1 | 1 | yes | characteristic |
| 489 | C4 | #5630 | 1 | 2 | yes | — |
| 490 | C3 | #24285 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 491 | C2 | — | 2 | 2 | no | — |
| 492 | C2 | — | 2 | 1 | no | — |
| 493 | C2 | — | 4 | 2 | no | — |
| 494 | C2 | — | 12 | 2 | no | — |
| 495 | C2 | — | 24 | 4 | no | — |
| 496 | C2 | #74016 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #5525 |
| commutator, cosocle | C22×C3×C4 | C24 |
| Frattini | C22×C4 | C23×D3 |
| Fitting | C3×#1812 | C2 |
| socle | C2×C3 | #2408 |
| hypercenter | #1812 | D3 |
| hypocenter | C3 | #24285 |
| LCS | G ▷ C22×C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #1812 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #87163 | C2 | semidirect |
| 2. #83794 | C2 | semidirect |
| 3. #79180 | C2 | semidirect |
| 4. #78690 | C2 | semidirect |
| 5. C3×#1812 | C2 | semidirect |
| 6. #70658 | C2 | semidirect |
| 7. #70054 | C2 | semidirect |
| 8. #68703 | C2 | semidirect |
| 9. #68698 | C2 | semidirect |
| 21. C22×D3×C8 | C22 | semidirect |
| 22. #5524 | C22 | semidirect |
| 23. C3×#427 | C22 | semidirect |
| 27. #5126 | C22 | semidirect |
| 28. #5119 | C22 | semidirect |
| 30. #5101 | C22 | semidirect |
| 31. #5006 | C22 | semidirect |
| 32. #5005 | C22 | semidirect |
| 33. #5002 | C22 | semidirect |
| 39. C3×H(3,ℤ/4) | C22 | semidirect |
| 47. #1812 | D3 | semidirect |
| 61. C2×C3×M16 | D4 | semidirect |
| 63. C22×C3×C8 | D4 | semidirect |
| 79. C2×Dic12 | D4 | semidirect |
| 88. C2×D24 | D4 | semidirect |
| 90. C2×#204 | D4 | semidirect |
| 131. #427 | C2×D3 | semidirect |
| 140. H(3,ℤ/4) | C2×D3 | semidirect |
| 244. C2×M16 | D12 | semidirect |
| 251. C22×C8 | D12 | semidirect |
| 490. C3 | #24285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #87163 | 2 |
| #83794 | 2 |
| #79180 | 2 |
| #78690 | 2 |
| C3×#1812 | 2 |
| #70658 | 2 |
| #70054 | 2 |
| #68703 | 2 |
| #68698 | 2 |
| #24285 | 3 |