Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1130 conjugacy classes of subgroups.
The subgroup lattice has 578 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#5757 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#5147 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #82009 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #79256 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×C3×#361 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #71438 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #70690 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #69259 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #69258 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #33539 | — | 3 | 1 | no | maximal, Sylow |
| 11 | C2×#1004 | — | 2 | 1 | no | — |
| 12 | C22×C3×D8 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#932 | — | 2 | 1 | no | — |
| 14 | #5757 | — | 2 | 2 | no | — |
| 15 | #5757 | — | 2 | 2 | no | — |
| 16 | #5757 | — | 2 | 2 | no | — |
| 17 | #5757 | C22 | 1 | 4 | yes | — |
| 18 | C2×#912 | — | 2 | 1 | no | — |
| 19 | C2×#911 | — | 2 | 2 | no | — |
| 20 | C2×D3×D8 | — | 2 | 1 | no | — |
| 21 | #5748 | — | 2 | 1 | no | — |
| 22 | C2×#904 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#904 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | C2×#901 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×C3×M32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C2×C3×#108 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C2×#827 | C22 | 1 | 2 | yes | complemented |
| 28 | #5147 | — | 2 | 2 | no | — |
| 29 | #5147 | — | 2 | 2 | no | — |
| 30 | C2×#826 | C22 | 1 | 2 | yes | complemented |
| 31 | #5132 | — | 2 | 1 | no | — |
| 32 | C2×#812 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #4909 | — | 2 | 1 | no | — |
| 34 | #4909 | C22 | 1 | 2 | yes | complemented |
| 35 | #4908 | — | 2 | 1 | no | — |
| 36 | #4908 | C22 | 1 | 2 | yes | complemented |
| 37 | #4904 | — | 2 | 2 | no | — |
| 38 | #4898 | — | 2 | 2 | no | — |
| 39 | #4897 | C22 | 1 | 2 | yes | complemented |
| 40 | #4896 | C22 | 1 | 2 | yes | complemented |
| 41 | C3×#361 | C22 | 1 | 4 | yes | complemented |
| 42 | #4515 | C22 | 1 | 4 | yes | complemented |
| 43 | #4497 | C22 | 1 | 4 | yes | complemented |
| 44 | C2×#576 | — | 3 | 1 | no | — |
| 45 | #3414 | — | 3 | 1 | no | — |
| 46 | C2×#509 | — | 3 | 1 | no | — |
| 47 | #3067 | — | 3 | 1 | no | — |
| 48 | #2194 | — | 3 | 4 | no | — |
| 49 | #2192 | — | 3 | 4 | no | — |
| 50 | C2×#361 | D3 | 1 | 1 | yes | characteristic, complemented |
| 51 | #2143 | — | 3 | 1 | no | — |
| 52 | #2117 | — | 3 | 1 | no | — |
| 53 | C22×C3×D4 | — | 2 | 1 | no | — |
| 54 | C22×#67 | — | 4 | 2 | no | — |
| 55 | #1004 | — | 2 | 4 | no | — |
| 56 | #1004 | — | 2 | 4 | no | — |
| 57 | #1004 | — | 4 | 2 | no | — |
| 58 | #1004 | — | 4 | 2 | no | — |
| 59 | C2×#237 | — | 2 | 2 | no | — |
| 60 | C2×#237 | — | 4 | 1 | no | — |
| 61 | C2×D3×D4 | — | 2 | 2 | no | — |
| 62 | C2×D3×D4 | — | 4 | 1 | no | — |
| 63 | C2×#235 | — | 2 | 1 | no | — |
| 64 | C2×#235 | — | 2 | 1 | no | — |
| 65 | C2×#235 | D4 | 1 | 1 | yes | characteristic |
| 66 | C2×C3×D8 | — | 2 | 1 | no | — |
| 67 | C2×C3×D8 | — | 2 | 1 | no | — |
| 68 | C2×C3×D8 | — | 2 | 1 | no | — |
| 69 | C2×C3×D8 | D4 | 1 | 2 | yes | — |
| 70 | C2×C3×D8 | D4 | 1 | 2 | yes | — |
| 71 | C2×C3×D8 | C23 | 1 | 2 | yes | — |
| 72 | C2×C3×M16 | — | 2 | 1 | no | — |
| 73 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×#214 | — | 2 | 2 | no | — |
| 75 | #932 | — | 2 | 4 | no | — |
| 76 | #932 | — | 2 | 4 | no | — |
| 77 | C2×#213 | — | 2 | 2 | no | — |
| 78 | C2×#208 | D4 | 1 | 1 | yes | characteristic |
| 79 | #912 | — | 2 | 4 | no | — |
| 80 | #912 | — | 2 | 4 | no | — |
| 81 | #911 | — | 2 | 8 | no | — |
| 82 | #911 | — | 2 | 8 | no | — |
| 83 | D3×D8 | — | 2 | 4 | no | — |
| 84 | D3×D8 | — | 2 | 4 | no | — |
| 85 | #909 | — | 2 | 2 | no | — |
| 86 | #909 | — | 4 | 1 | no | — |
| 87 | #908 | — | 2 | 2 | no | — |
| 88 | #908 | — | 4 | 1 | no | — |
| 89 | C2×Dic12 | D4 | 1 | 1 | yes | characteristic |
| 90 | C2×Dic12 | C23 | 1 | 1 | yes | characteristic, complemented |
| 91 | #904 | — | 2 | 1 | no | — |
| 92 | #904 | — | 2 | 1 | no | — |
| 93 | #904 | — | 2 | 1 | no | — |
| 94 | #904 | — | 2 | 1 | no | — |
| 95 | #904 | — | 2 | 1 | no | — |
| 96 | #904 | — | 2 | 1 | no | — |
| 97 | #904 | — | 4 | 2 | no | — |
| 98 | #904 | D4 | 1 | 2 | yes | — |
| 99 | #904 | C23 | 1 | 2 | yes | — |
| 100 | C2×D24 | D4 | 1 | 1 | yes | characteristic |
| 101 | C2×D24 | C23 | 1 | 1 | yes | characteristic, complemented |
| 102 | C2×#204 | — | 2 | 1 | no | — |
| 103 | C2×#204 | — | 2 | 1 | no | — |
| 104 | #901 | — | 2 | 1 | no | — |
| 105 | #901 | — | 2 | 1 | no | — |
| 106 | #901 | D4 | 1 | 2 | yes | — |
| 107 | #901 | C23 | 1 | 2 | yes | — |
| 108 | C2×ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 109 | C2×D3×C8 | — | 2 | 1 | no | — |
| 110 | C3×M32 | — | 2 | 1 | no | — |
| 111 | C3×M32 | C23 | 1 | 2 | yes | complemented |
| 112 | C2×C3×C16 | — | 2 | 1 | no | — |
| 113 | C3×#108 | — | 2 | 1 | no | — |
| 114 | C3×#108 | C23 | 1 | 2 | yes | complemented |
| 115 | #827 | — | 2 | 4 | no | — |
| 116 | #826 | — | 2 | 4 | no | — |
| 117 | #824 | — | 2 | 2 | no | — |
| 118 | #823 | — | 2 | 2 | no | — |
| 119 | #812 | — | 2 | 1 | no | — |
| 120 | #812 | — | 2 | 1 | no | — |
| 121 | C2×C3⋊C16 | C23 | 1 | 2 | yes | complemented |
| 122 | Dic24 | — | 2 | 2 | no | — |
| 123 | #800 | — | 2 | 2 | no | — |
| 124 | #800 | — | 2 | 2 | no | — |
| 125 | D48 | — | 2 | 2 | no | — |
| 126 | C2×H(5,𝔽2) | — | 6 | 1 | no | — |
| 127 | #576 | — | 3 | 4 | no | — |
| 128 | #576 | — | 6 | 2 | no | — |
| 129 | #576 | — | 6 | 2 | no | — |
| 130 | #576 | — | 6 | 2 | no | — |
| 131 | #575 | — | 6 | 1 | no | — |
| 132 | C2×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 133 | C2×AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 134 | C2×#135 | — | 3 | 1 | no | — |
| 135 | C2×#135 | — | 3 | 1 | no | — |
| 136 | C2×#135 | — | 6 | 1 | no | — |
| 137 | C22×D8 | — | 6 | 1 | no | — |
| 138 | C22×D8 | C2×D3 | 1 | 1 | yes | characteristic |
| 139 | C2×#131 | — | 3 | 1 | no | — |
| 140 | #510 | — | 3 | 2 | no | — |
| 141 | #510 | — | 6 | 1 | no | — |
| 142 | #509 | — | 3 | 2 | no | — |
| 143 | #509 | — | 6 | 1 | no | — |
| 144 | #509 | — | 6 | 2 | no | — |
| 145 | #509 | — | 6 | 2 | no | — |
| 146 | #508 | — | 6 | 2 | no | — |
| 147 | C2×SD32 | — | 3 | 2 | no | — |
| 148 | C2×D16 | — | 3 | 2 | no | — |
| 149 | C2×M32 | — | 3 | 1 | no | — |
| 150 | C2×M32 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 151 | #473 | — | 3 | 2 | no | — |
| 152 | #472 | — | 3 | 2 | no | — |
| 153 | #471 | — | 6 | 2 | no | — |
| 154 | C2×#108 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 155 | #413 | — | 6 | 1 | no | — |
| 156 | #361 | C2×D3 | 1 | 4 | yes | complemented |
| 157 | #359 | — | 3 | 4 | no | — |
| 158 | #350 | — | 3 | 4 | no | — |
| 159 | C24×C3 | — | 4 | 1 | no | — |
| 160 | C23×D3 | — | 4 | 2 | no | — |
| 161 | C2×C3×D4 | — | 2 | 2 | no | — |
| 162 | C2×C3×D4 | — | 2 | 2 | no | — |
| 163 | C2×C3×D4 | — | 2 | 2 | no | — |
| 164 | C2×C3×D4 | — | 4 | 1 | no | — |
| 165 | C2×C3×D4 | — | 4 | 1 | no | — |
| 166 | C2×C3×D4 | — | 4 | 1 | no | — |
| 167 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 168 | C2×#67 | — | 2 | 1 | no | — |
| 169 | C2×#67 | — | 4 | 2 | no | — |
| 170 | C2×#67 | — | 4 | 8 | no | — |
| 171 | C2×#67 | — | 4 | 8 | no | — |
| 172 | C2×#67 | — | 4 | 2 | no | — |
| 173 | C2×#67 | — | 4 | 1 | no | — |
| 174 | C2×#67 | — | 4 | 1 | no | — |
| 175 | C22×Dic3 | — | 4 | 2 | no | — |
| 176 | #237 | — | 2 | 8 | no | — |
| 177 | #237 | — | 4 | 4 | no | — |
| 178 | #237 | — | 4 | 4 | no | — |
| 179 | #237 | — | 4 | 4 | no | — |
| 180 | D3×D4 | — | 2 | 8 | no | — |
| 181 | D3×D4 | — | 4 | 4 | no | — |
| 182 | D3×D4 | — | 4 | 4 | no | — |
| 183 | D3×D4 | — | 4 | 4 | no | — |
| 184 | #235 | — | 2 | 1 | no | — |
| 185 | #235 | — | 2 | 1 | no | — |
| 186 | #235 | — | 2 | 2 | no | — |
| 187 | #235 | — | 2 | 2 | no | — |
| 188 | #235 | — | 4 | 1 | no | — |
| 189 | #235 | — | 4 | 1 | no | — |
| 190 | #235 | — | 4 | 1 | no | — |
| 191 | #235 | — | 4 | 1 | no | — |
| 192 | #235 | — | 4 | 1 | no | — |
| 193 | #235 | — | 4 | 1 | no | — |
| 194 | #235 | D8 | 1 | 2 | yes | — |
| 195 | #235 | C2×D4 | 1 | 2 | yes | — |
| 196 | C2×D12 | — | 2 | 1 | no | — |
| 197 | C2×D12 | — | 2 | 1 | no | — |
| 198 | C2×D12 | D8 | 1 | 1 | yes | characteristic |
| 199 | C2×C4×D3 | — | 2 | 1 | no | — |
| 200 | C2×C4×D3 | — | 4 | 1 | no | — |
| 201 | C2×C4×D3 | — | 4 | 1 | no | — |
| 202 | C2×Dic6 | — | 2 | 1 | no | — |
| 203 | C2×Dic6 | — | 2 | 1 | no | — |
| 204 | C2×Dic6 | D8 | 1 | 1 | yes | characteristic |
| 205 | C3×D8 | — | 2 | 2 | no | — |
| 206 | C3×D8 | — | 2 | 2 | no | — |
| 207 | C3×D8 | — | 2 | 2 | no | — |
| 208 | C3×D8 | C2×D4 | 1 | 4 | yes | — |
| 209 | C3×M16 | — | 2 | 2 | no | — |
| 210 | C3×M16 | — | 4 | 1 | no | — |
| 211 | C2×C3×C8 | — | 4 | 1 | no | — |
| 212 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 213 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 214 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 215 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 216 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 217 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 218 | #214 | — | 2 | 8 | no | — |
| 219 | #213 | — | 2 | 8 | no | — |
| 220 | #208 | — | 2 | 1 | no | — |
| 221 | #208 | C2×D4 | 1 | 2 | yes | — |
| 222 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 223 | Dic12 | — | 2 | 1 | no | — |
| 224 | Dic12 | — | 2 | 1 | no | — |
| 225 | Dic12 | — | 2 | 1 | no | — |
| 226 | Dic12 | — | 4 | 2 | no | — |
| 227 | Dic12 | C2×D4 | 1 | 2 | yes | — |
| 228 | D24 | — | 2 | 1 | no | — |
| 229 | D24 | — | 2 | 1 | no | — |
| 230 | D24 | — | 2 | 1 | no | — |
| 231 | D24 | — | 4 | 2 | no | — |
| 232 | D24 | C2×D4 | 1 | 2 | yes | — |
| 233 | #204 | — | 2 | 2 | no | — |
| 234 | #204 | — | 2 | 2 | no | — |
| 235 | #204 | — | 4 | 2 | no | — |
| 236 | #204 | — | 4 | 2 | no | — |
| 237 | #204 | — | 4 | 1 | no | — |
| 238 | #204 | — | 4 | 1 | no | — |
| 239 | ΓL(1,𝔽25) | — | 2 | 2 | no | — |
| 240 | ΓL(1,𝔽25) | — | 2 | 2 | no | — |
| 241 | D3×C8 | — | 2 | 2 | no | — |
| 242 | D3×C8 | — | 2 | 2 | no | — |
| 243 | C3×C16 | — | 2 | 2 | no | — |
| 244 | C3⋊C16 | — | 2 | 2 | no | — |
| 245 | H(5,𝔽2) | — | 6 | 4 | no | — |
| 246 | H(5,𝔽2) | — | 6 | 4 | no | — |
| 247 | H(5,𝔽2) | — | 12 | 2 | no | — |
| 248 | H(5,𝔽2) | — | 12 | 2 | no | — |
| 249 | C2×#41 | — | 3 | 1 | no | — |
| 250 | C2×#41 | — | 6 | 2 | no | — |
| 251 | C2×#41 | — | 6 | 1 | no | — |
| 252 | C2×#41 | — | 6 | 1 | no | — |
| 253 | C2×#41 | — | 12 | 1 | no | — |
| 254 | C22×D4 | — | 2 | 1 | no | — |
| 255 | C22×D4 | — | 6 | 2 | no | — |
| 256 | C22×D4 | — | 12 | 1 | no | — |
| 257 | C22×D4 | — | 12 | 2 | no | — |
| 258 | #137 | — | 6 | 2 | no | — |
| 259 | #137 | — | 12 | 1 | no | — |
| 260 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 261 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 262 | AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 263 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 264 | AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 265 | AGL(1,ℤ/8) | — | 12 | 1 | no | — |
| 266 | #135 | — | 3 | 2 | no | — |
| 267 | #135 | — | 3 | 2 | no | — |
| 268 | #135 | — | 6 | 4 | no | — |
| 269 | #135 | — | 6 | 4 | no | — |
| 270 | #135 | — | 6 | 1 | no | — |
| 271 | #135 | — | 6 | 1 | no | — |
| 272 | #135 | — | 6 | 1 | no | — |
| 273 | #135 | — | 6 | 1 | no | — |
| 274 | #135 | — | 6 | 1 | no | — |
| 275 | #135 | — | 6 | 1 | no | — |
| 276 | #135 | — | 12 | 2 | no | — |
| 277 | C2×Q16 | — | 3 | 1 | no | — |
| 278 | C2×Q16 | — | 3 | 1 | no | — |
| 279 | C2×SD16 | — | 6 | 2 | no | — |
| 280 | C2×SD16 | — | 6 | 1 | no | — |
| 281 | C2×SD16 | — | 6 | 1 | no | — |
| 282 | C2×D8 | — | 2 | 1 | no | — |
| 283 | C2×D8 | — | 2 | 1 | no | — |
| 284 | C2×D8 | — | 2 | 1 | no | — |
| 285 | C2×D8 | — | 3 | 1 | no | — |
| 286 | C2×D8 | — | 3 | 1 | no | — |
| 287 | C2×D8 | — | 6 | 4 | no | — |
| 288 | C2×D8 | — | 6 | 4 | no | — |
| 289 | C2×D8 | — | 6 | 2 | no | — |
| 290 | C2×D8 | D12 | 1 | 2 | yes | — |
| 291 | C2×D8 | D12 | 1 | 2 | yes | — |
| 292 | C2×D8 | C22×D3 | 1 | 2 | yes | — |
| 293 | #131 | — | 3 | 2 | no | — |
| 294 | #131 | — | 3 | 2 | no | — |
| 295 | #131 | — | 6 | 1 | no | — |
| 296 | #131 | — | 6 | 1 | no | — |
| 297 | C2×M16 | — | 2 | 1 | no | — |
| 298 | C2×M16 | — | 3 | 1 | no | — |
| 299 | C2×M16 | — | 6 | 1 | no | — |
| 300 | C22×C8 | — | 6 | 1 | no | — |
| 301 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 302 | Q32 | — | 6 | 2 | no | — |
| 303 | SD32 | — | 6 | 2 | no | — |
| 304 | SD32 | — | 6 | 2 | no | — |
| 305 | SD32 | — | 6 | 4 | no | — |
| 306 | D16 | — | 6 | 2 | no | — |
| 307 | D16 | — | 6 | 4 | no | — |
| 308 | M32 | — | 2 | 1 | no | — |
| 309 | M32 | — | 6 | 1 | no | — |
| 310 | M32 | — | 6 | 1 | no | — |
| 311 | M32 | C22×D3 | 1 | 2 | yes | complemented |
| 312 | C2×C16 | — | 2 | 1 | no | — |
| 313 | C2×C16 | — | 3 | 2 | no | — |
| 314 | #108 | — | 2 | 1 | no | — |
| 315 | #108 | C22×D3 | 1 | 2 | yes | complemented |
| 316 | #101 | — | 6 | 2 | no | — |
| 317 | #100 | — | 6 | 2 | no | — |
| 318 | C23×C3 | — | 4 | 2 | no | — |
| 319 | C23×C3 | — | 4 | 2 | no | — |
| 320 | C23×C3 | — | 4 | 2 | no | — |
| 321 | C23×C3 | — | 16 | 2 | no | — |
| 322 | C23×C3 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 323 | C22×D3 | — | 2 | 1 | no | — |
| 324 | C22×D3 | — | 4 | 8 | no | — |
| 325 | C22×D3 | — | 4 | 1 | no | — |
| 326 | C22×D3 | — | 4 | 1 | no | — |
| 327 | C22×D3 | — | 16 | 4 | no | — |
| 328 | C3×D4 | — | 2 | 4 | no | — |
| 329 | C3×D4 | — | 4 | 2 | no | — |
| 330 | C3×D4 | — | 4 | 2 | no | — |
| 331 | C3×D4 | — | 4 | 2 | no | — |
| 332 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 333 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 334 | C2×C3×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 335 | C2×C3×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 336 | C2×C3×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 337 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 338 | #67 | — | 2 | 2 | no | — |
| 339 | #67 | — | 2 | 2 | no | — |
| 340 | #67 | — | 4 | 8 | no | — |
| 341 | #67 | — | 4 | 8 | no | — |
| 342 | #67 | — | 4 | 2 | no | — |
| 343 | #67 | — | 4 | 2 | no | — |
| 344 | #67 | — | 8 | 1 | no | — |
| 345 | #67 | — | 8 | 1 | no | — |
| 346 | C2×Dic3 | — | 2 | 1 | no | — |
| 347 | C2×Dic3 | — | 4 | 8 | no | — |
| 348 | C2×Dic3 | — | 4 | 1 | no | — |
| 349 | C2×Dic3 | — | 4 | 1 | no | — |
| 350 | D12 | — | 2 | 2 | no | — |
| 351 | D12 | — | 2 | 1 | no | — |
| 352 | D12 | — | 4 | 1 | no | — |
| 353 | D12 | — | 4 | 1 | no | — |
| 354 | D12 | — | 4 | 1 | no | — |
| 355 | D12 | C2×D8 | 1 | 2 | yes | — |
| 356 | C4×D3 | — | 2 | 2 | no | — |
| 357 | C4×D3 | — | 2 | 2 | no | — |
| 358 | C4×D3 | — | 4 | 2 | no | — |
| 359 | C4×D3 | — | 4 | 2 | no | — |
| 360 | C4×D3 | — | 8 | 1 | no | — |
| 361 | C4×D3 | — | 8 | 1 | no | — |
| 362 | Dic6 | — | 2 | 1 | no | — |
| 363 | Dic6 | — | 2 | 2 | no | — |
| 364 | Dic6 | — | 4 | 1 | no | — |
| 365 | Dic6 | — | 4 | 1 | no | — |
| 366 | Dic6 | — | 4 | 1 | no | — |
| 367 | Dic6 | C2×D8 | 1 | 2 | yes | — |
| 368 | C3×C8 | — | 4 | 2 | no | — |
| 369 | C3×C8 | #120 | 1 | 1 | yes | characteristic |
| 370 | C3×C8 | #120 | 1 | 1 | yes | characteristic |
| 371 | C3×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 372 | C3×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 373 | C3⋊C8 | — | 2 | 2 | no | — |
| 374 | C24 | — | 4 | 1 | no | — |
| 375 | C24 | — | 12 | 2 | no | — |
| 376 | #41 | — | 3 | 2 | no | — |
| 377 | #41 | — | 3 | 2 | no | — |
| 378 | #41 | — | 6 | 1 | no | — |
| 379 | #41 | — | 6 | 1 | no | — |
| 380 | #41 | — | 6 | 8 | no | — |
| 381 | #41 | — | 6 | 2 | no | — |
| 382 | #41 | — | 6 | 2 | no | — |
| 383 | #41 | — | 12 | 4 | no | — |
| 384 | #41 | — | 12 | 4 | no | — |
| 385 | #41 | — | 12 | 4 | no | — |
| 386 | #41 | — | 12 | 1 | no | — |
| 387 | #41 | — | 12 | 1 | no | — |
| 388 | #41 | — | 12 | 1 | no | — |
| 389 | #41 | — | 12 | 1 | no | — |
| 390 | #41 | — | 12 | 1 | no | — |
| 391 | #41 | — | 12 | 1 | no | — |
| 392 | C2×Q8 | — | 3 | 1 | no | — |
| 393 | C2×Q8 | — | 6 | 1 | no | — |
| 394 | C2×Q8 | — | 6 | 1 | no | — |
| 395 | C2×D4 | — | 2 | 2 | no | — |
| 396 | C2×D4 | — | 2 | 2 | no | — |
| 397 | C2×D4 | — | 2 | 2 | no | — |
| 398 | C2×D4 | — | 3 | 1 | no | — |
| 399 | C2×D4 | — | 4 | 1 | no | — |
| 400 | C2×D4 | — | 4 | 1 | no | — |
| 401 | C2×D4 | — | 4 | 1 | no | — |
| 402 | C2×D4 | — | 6 | 8 | no | — |
| 403 | C2×D4 | — | 6 | 1 | no | — |
| 404 | C2×D4 | — | 6 | 1 | no | — |
| 405 | C2×D4 | — | 6 | 1 | no | — |
| 406 | C2×D4 | — | 12 | 4 | no | — |
| 407 | C2×D4 | — | 12 | 2 | no | — |
| 408 | C2×D4 | — | 12 | 4 | no | — |
| 409 | C2×D4 | — | 12 | 4 | no | — |
| 410 | C2×D4 | — | 12 | 8 | no | — |
| 411 | C2×D4 | — | 12 | 8 | no | — |
| 412 | C2×D4 | — | 12 | 2 | no | — |
| 413 | C2×D4 | — | 12 | 1 | no | — |
| 414 | C2×D4 | — | 12 | 1 | no | — |
| 415 | C22×C4 | — | 6 | 1 | no | — |
| 416 | C22×C4 | — | 12 | 2 | no | — |
| 417 | C22×C4 | — | 12 | 1 | no | — |
| 418 | C22×C4 | — | 12 | 1 | no | — |
| 419 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 420 | Q16 | — | 3 | 2 | no | — |
| 421 | Q16 | — | 6 | 1 | no | — |
| 422 | Q16 | — | 6 | 1 | no | — |
| 423 | Q16 | — | 6 | 1 | no | — |
| 424 | Q16 | — | 12 | 2 | no | — |
| 425 | SD16 | — | 6 | 8 | no | — |
| 426 | SD16 | — | 6 | 2 | no | — |
| 427 | SD16 | — | 6 | 2 | no | — |
| 428 | SD16 | — | 12 | 2 | no | — |
| 429 | SD16 | — | 12 | 2 | no | — |
| 430 | SD16 | — | 12 | 1 | no | — |
| 431 | SD16 | — | 12 | 1 | no | — |
| 432 | D8 | — | 2 | 2 | no | — |
| 433 | D8 | — | 2 | 2 | no | — |
| 434 | D8 | — | 2 | 2 | no | — |
| 435 | D8 | — | 3 | 2 | no | — |
| 436 | D8 | — | 6 | 8 | no | — |
| 437 | D8 | — | 6 | 1 | no | — |
| 438 | D8 | — | 6 | 1 | no | — |
| 439 | D8 | — | 6 | 1 | no | — |
| 440 | D8 | — | 12 | 2 | no | — |
| 441 | D8 | C2×D12 | 1 | 4 | yes | — |
| 442 | M16 | — | 2 | 2 | no | — |
| 443 | M16 | — | 3 | 2 | no | — |
| 444 | M16 | — | 4 | 1 | no | — |
| 445 | M16 | — | 6 | 1 | no | — |
| 446 | M16 | — | 6 | 2 | no | — |
| 447 | M16 | — | 6 | 2 | no | — |
| 448 | C2×C8 | — | 4 | 1 | no | — |
| 449 | C2×C8 | — | 6 | 1 | no | — |
| 450 | C2×C8 | — | 6 | 2 | no | — |
| 451 | C2×C8 | — | 6 | 2 | no | — |
| 452 | C2×C8 | C2×D12 | 1 | 1 | yes | characteristic |
| 453 | C2×C8 | C2×D12 | 1 | 1 | yes | characteristic |
| 454 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 455 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 456 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 457 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 458 | C16 | — | 2 | 2 | no | — |
| 459 | C16 | — | 6 | 2 | no | — |
| 460 | C22×C3 | — | 4 | 1 | no | — |
| 461 | C22×C3 | — | 4 | 4 | no | — |
| 462 | C22×C3 | — | 8 | 4 | no | — |
| 463 | C22×C3 | — | 16 | 2 | no | — |
| 464 | C22×C3 | — | 16 | 2 | no | — |
| 465 | C22×C3 | #447 | 1 | 1 | yes | characteristic |
| 466 | C22×C3 | #447 | 1 | 1 | yes | characteristic |
| 467 | C22×C3 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 468 | C2×D3 | — | 2 | 2 | no | — |
| 469 | C2×D3 | — | 4 | 2 | no | — |
| 470 | C2×D3 | — | 4 | 2 | no | — |
| 471 | C2×D3 | — | 8 | 2 | no | — |
| 472 | C2×D3 | — | 8 | 1 | no | — |
| 473 | C2×D3 | — | 16 | 8 | no | — |
| 474 | C2×D3 | — | 16 | 1 | no | — |
| 475 | C3×C4 | #447 | 1 | 1 | yes | characteristic |
| 476 | C3×C4 | #447 | 1 | 1 | yes | characteristic |
| 477 | C3×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 478 | C3×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 479 | Dic3 | — | 2 | 2 | no | — |
| 480 | Dic3 | — | 4 | 2 | no | — |
| 481 | Dic3 | — | 8 | 1 | no | — |
| 482 | C23 | — | 4 | 2 | no | — |
| 483 | C23 | — | 4 | 2 | no | — |
| 484 | C23 | — | 4 | 2 | no | — |
| 485 | C23 | — | 6 | 1 | no | — |
| 486 | C23 | — | 12 | 8 | no | — |
| 487 | C23 | — | 12 | 1 | no | — |
| 488 | C23 | — | 12 | 1 | no | — |
| 489 | C23 | — | 16 | 2 | no | — |
| 490 | C23 | — | 48 | 4 | no | — |
| 491 | C23 | #914 | 1 | 1 | yes | characteristic |
| 492 | Q8 | — | 3 | 2 | no | — |
| 493 | Q8 | — | 6 | 1 | no | — |
| 494 | Q8 | — | 6 | 2 | no | — |
| 495 | Q8 | — | 12 | 1 | no | — |
| 496 | Q8 | — | 12 | 1 | no | — |
| 497 | Q8 | — | 12 | 1 | no | — |
| 498 | D4 | — | 2 | 4 | no | — |
| 499 | D4 | — | 3 | 2 | no | — |
| 500 | D4 | — | 4 | 2 | no | — |
| 501 | D4 | — | 4 | 2 | no | — |
| 502 | D4 | — | 4 | 2 | no | — |
| 503 | D4 | — | 6 | 2 | no | — |
| 504 | D4 | — | 6 | 2 | no | — |
| 505 | D4 | — | 6 | 2 | no | — |
| 506 | D4 | — | 6 | 1 | no | — |
| 507 | D4 | — | 12 | 8 | no | — |
| 508 | D4 | — | 12 | 8 | no | — |
| 509 | D4 | — | 12 | 2 | no | — |
| 510 | D4 | — | 12 | 2 | no | — |
| 511 | D4 | — | 12 | 1 | no | — |
| 512 | D4 | — | 12 | 1 | no | — |
| 513 | D4 | — | 12 | 1 | no | — |
| 514 | D4 | — | 24 | 1 | no | — |
| 515 | D4 | — | 24 | 1 | no | — |
| 516 | C2×C4 | — | 6 | 1 | no | — |
| 517 | C2×C4 | — | 6 | 2 | no | — |
| 518 | C2×C4 | — | 6 | 2 | no | — |
| 519 | C2×C4 | — | 12 | 8 | no | — |
| 520 | C2×C4 | — | 12 | 1 | no | — |
| 521 | C2×C4 | — | 12 | 2 | no | — |
| 522 | C2×C4 | — | 12 | 2 | no | — |
| 523 | C2×C4 | — | 12 | 1 | no | — |
| 524 | C2×C4 | — | 24 | 1 | no | — |
| 525 | C2×C4 | — | 24 | 1 | no | — |
| 526 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 527 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 528 | C2×C4 | D3×D8 | 1 | 1 | yes | characteristic |
| 529 | C2×C4 | D3×D8 | 1 | 1 | yes | characteristic |
| 530 | C2×C4 | #914 | 1 | 1 | yes | characteristic |
| 531 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 532 | C8 | — | 4 | 2 | no | — |
| 533 | C8 | — | 6 | 2 | no | — |
| 534 | C8 | #882 | 1 | 1 | yes | characteristic |
| 535 | C8 | #882 | 1 | 1 | yes | characteristic |
| 536 | C8 | C22×D12 | 1 | 1 | yes | characteristic |
| 537 | C8 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 538 | C2×C3 | — | 2 | 1 | no | — |
| 539 | C2×C3 | — | 2 | 1 | no | — |
| 540 | C2×C3 | — | 2 | 1 | no | — |
| 541 | C2×C3 | — | 8 | 4 | no | — |
| 542 | C2×C3 | C2×#447 | 1 | 1 | yes | characteristic |
| 543 | D3 | — | 4 | 2 | no | — |
| 544 | D3 | — | 8 | 2 | no | — |
| 545 | D3 | — | 16 | 1 | no | — |
| 546 | C22 | — | 4 | 1 | no | — |
| 547 | C22 | — | 4 | 4 | no | — |
| 548 | C22 | — | 6 | 2 | no | — |
| 549 | C22 | — | 8 | 4 | no | — |
| 550 | C22 | — | 12 | 2 | no | — |
| 551 | C22 | — | 12 | 2 | no | — |
| 552 | C22 | — | 16 | 2 | no | — |
| 553 | C22 | — | 16 | 2 | no | — |
| 554 | C22 | — | 24 | 2 | no | — |
| 555 | C22 | — | 24 | 1 | no | — |
| 556 | C22 | — | 48 | 1 | no | — |
| 557 | C22 | — | 48 | 8 | no | — |
| 558 | C22 | #4773 | 1 | 1 | yes | characteristic |
| 559 | C22 | #4773 | 1 | 1 | yes | characteristic |
| 560 | C22 | C2×#914 | 1 | 1 | yes | characteristic |
| 561 | C4 | — | 6 | 2 | no | — |
| 562 | C4 | — | 12 | 2 | no | — |
| 563 | C4 | — | 24 | 1 | no | — |
| 564 | C4 | #4773 | 1 | 1 | yes | characteristic |
| 565 | C4 | #4773 | 1 | 1 | yes | characteristic |
| 566 | C4 | C2×#882 | 1 | 1 | yes | characteristic |
| 567 | C4 | C2×D3×D8 | 1 | 1 | yes | characteristic |
| 568 | C3 | #33539 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 569 | C2 | — | 2 | 1 | no | — |
| 570 | C2 | — | 2 | 1 | no | — |
| 571 | C2 | — | 2 | 1 | no | — |
| 572 | C2 | — | 8 | 4 | no | — |
| 573 | C2 | — | 12 | 2 | no | — |
| 574 | C2 | — | 24 | 2 | no | — |
| 575 | C2 | — | 48 | 1 | no | — |
| 576 | C2 | C2×#4773 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#5757 | C2 | semidirect |
| 2. C2×#5147 | C2 | semidirect |
| 3. #82009 | C2 | semidirect |
| 4. #79256 | C2 | semidirect |
| 5. C2×C3×#361 | C2 | semidirect |
| 6. #71438 | C2 | semidirect |
| 7. #70690 | C2 | semidirect |
| 8. #69259 | C2 | semidirect |
| 9. #69258 | C2 | semidirect |
| 23. C2×#904 | C22 | semidirect |
| 25. C2×C3×M32 | C22 | semidirect |
| 26. C2×C3×#108 | C22 | semidirect |
| 27. C2×#827 | C22 | semidirect |
| 30. C2×#826 | C22 | semidirect |
| 32. C2×#812 | C22 | semidirect |
| 34. #4909 | C22 | semidirect |
| 36. #4908 | C22 | semidirect |
| 39. #4897 | C22 | semidirect |
| 40. #4896 | C22 | semidirect |
| 41. C3×#361 | C22 | semidirect |
| 42. #4515 | C22 | semidirect |
| 43. #4497 | C22 | semidirect |
| 50. C2×#361 | D3 | semidirect |
| 90. C2×Dic12 | C23 | semidirect |
| 101. C2×D24 | C23 | semidirect |
| 111. C3×M32 | C23 | semidirect |
| 114. C3×#108 | C23 | semidirect |
| 121. C2×C3⋊C16 | C23 | semidirect |
| 150. C2×M32 | C2×D3 | semidirect |
| 154. C2×#108 | C2×D3 | semidirect |
| 156. #361 | C2×D3 | semidirect |
| 311. M32 | C22×D3 | semidirect |
| 315. #108 | C22×D3 | semidirect |
| 568. C3 | #33539 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5757 | 2 |
| C2×#5147 | 2 |
| #82009 | 2 |
| #79256 | 2 |
| C2×C3×#361 | 2 |
| #71438 | 2 |
| #70690 | 2 |
| #69259 | 2 |
| #69258 | 2 |
| #33539 | 3 |