Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
928 conjugacy classes of subgroups.
The subgroup lattice has 468 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 |
| 2 | C2×C3×#361 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72033 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #71450 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #71437 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #70719 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #70687 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #12750 | — | 3 | 1 | no | maximal, Sylow |
| 9 | C2×#1004 | — | 2 | 1 | no | — |
| 10 | C22×C3×D8 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#932 | — | 2 | 1 | no | — |
| 12 | #5757 | — | 2 | 2 | no | — |
| 13 | #5757 | — | 2 | 2 | no | — |
| 14 | #5757 | — | 2 | 2 | no | — |
| 15 | #5757 | C4 | 1 | 4 | yes | complemented |
| 16 | C2×#912 | — | 2 | 1 | no | — |
| 17 | C2×#911 | — | 2 | 2 | no | — |
| 18 | C2×D3×D8 | — | 2 | 1 | no | — |
| 19 | C2×#904 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#901 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×C3×M32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C2×C3×#108 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #5139 | — | 2 | 1 | no | — |
| 24 | #5106 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C2×#812 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C3×#361 | — | 2 | 2 | no | — |
| 27 | #4562 | — | 2 | 2 | no | — |
| 28 | #4556 | — | 2 | 1 | no | — |
| 29 | #4518 | — | 2 | 2 | no | — |
| 30 | #4508 | — | 2 | 2 | no | — |
| 31 | #4496 | — | 2 | 1 | no | — |
| 32 | #4495 | — | 2 | 1 | no | — |
| 33 | C2×#576 | — | 3 | 1 | no | — |
| 34 | #2148 | — | 3 | 1 | no | — |
| 35 | C2×#361 | D3 | 1 | 1 | yes | characteristic, complemented |
| 36 | #2145 | — | 3 | 1 | no | — |
| 37 | #2140 | — | 3 | 1 | no | — |
| 38 | #2117 | — | 3 | 1 | no | — |
| 39 | #1814 | — | 3 | 1 | no | — |
| 40 | C22×C3×D4 | — | 2 | 1 | no | — |
| 41 | C22×#67 | — | 4 | 2 | no | — |
| 42 | #1004 | — | 2 | 4 | no | — |
| 43 | #1004 | — | 2 | 4 | no | — |
| 44 | #1004 | — | 4 | 2 | no | — |
| 45 | #1004 | — | 4 | 2 | no | — |
| 46 | C2×#237 | — | 2 | 2 | no | — |
| 47 | C2×#237 | — | 4 | 1 | no | — |
| 48 | C2×D3×D4 | — | 2 | 2 | no | — |
| 49 | C2×D3×D4 | — | 4 | 1 | no | — |
| 50 | C2×#235 | — | 2 | 1 | no | — |
| 51 | C2×#235 | D4 | 1 | 1 | yes | characteristic |
| 52 | C2×C3×D8 | — | 2 | 1 | no | — |
| 53 | C2×C3×D8 | — | 2 | 1 | no | — |
| 54 | C2×C3×D8 | — | 2 | 1 | no | — |
| 55 | C2×C3×D8 | C2×C4 | 1 | 2 | yes | — |
| 56 | C2×C3×D8 | D4 | 1 | 2 | yes | — |
| 57 | C2×C3×D8 | D4 | 1 | 2 | yes | — |
| 58 | C2×C3×M16 | — | 2 | 1 | no | — |
| 59 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×#214 | — | 2 | 2 | no | — |
| 61 | #932 | — | 2 | 4 | no | — |
| 62 | #932 | — | 2 | 4 | no | — |
| 63 | C2×#213 | — | 2 | 2 | no | — |
| 64 | #926 | — | 2 | 1 | no | — |
| 65 | C2×#208 | D4 | 1 | 1 | yes | characteristic |
| 66 | #912 | — | 2 | 4 | no | — |
| 67 | #912 | — | 2 | 4 | no | — |
| 68 | #911 | — | 2 | 8 | no | — |
| 69 | #911 | — | 2 | 8 | no | — |
| 70 | D3×D8 | — | 2 | 4 | no | — |
| 71 | D3×D8 | — | 2 | 4 | no | — |
| 72 | C2×Dic12 | D4 | 1 | 1 | yes | characteristic |
| 73 | #904 | — | 2 | 1 | no | — |
| 74 | #904 | — | 2 | 1 | no | — |
| 75 | #904 | C2×C4 | 1 | 2 | yes | — |
| 76 | #904 | D4 | 1 | 2 | yes | — |
| 77 | C2×D24 | D4 | 1 | 1 | yes | characteristic |
| 78 | C2×#204 | — | 2 | 1 | no | — |
| 79 | #901 | — | 2 | 1 | no | — |
| 80 | #901 | — | 2 | 1 | no | — |
| 81 | #901 | C2×C4 | 1 | 2 | yes | — |
| 82 | #901 | D4 | 1 | 2 | yes | — |
| 83 | C2×ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 84 | C2×D3×C8 | — | 2 | 1 | no | — |
| 85 | C3×M32 | — | 2 | 1 | no | — |
| 86 | C3×M32 | — | 2 | 1 | no | — |
| 87 | C2×C3×C16 | — | 2 | 1 | no | — |
| 88 | C3×#108 | — | 2 | 1 | no | — |
| 89 | C3×#108 | — | 2 | 1 | no | — |
| 90 | #825 | — | 4 | 2 | no | — |
| 91 | #818 | — | 2 | 1 | no | — |
| 92 | #817 | — | 2 | 1 | no | — |
| 93 | #812 | — | 2 | 1 | no | — |
| 94 | #812 | — | 2 | 1 | no | — |
| 95 | C2×C3⋊C16 | — | 2 | 1 | no | — |
| 96 | C2×H(5,𝔽2) | — | 6 | 1 | no | — |
| 97 | #576 | — | 3 | 4 | no | — |
| 98 | #576 | — | 6 | 2 | no | — |
| 99 | #576 | — | 6 | 2 | no | — |
| 100 | #576 | — | 6 | 2 | no | — |
| 101 | C2×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 102 | C2×AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 103 | C2×#135 | — | 3 | 1 | no | — |
| 104 | C2×#135 | — | 6 | 1 | no | — |
| 105 | C22×D8 | — | 6 | 1 | no | — |
| 106 | C22×D8 | C2×D3 | 1 | 1 | yes | characteristic |
| 107 | C2×#131 | — | 3 | 1 | no | — |
| 108 | C2×M32 | — | 3 | 1 | no | — |
| 109 | C2×M32 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 110 | C2×#108 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 111 | #427 | — | 3 | 1 | no | — |
| 112 | #421 | — | 6 | 1 | no | — |
| 113 | #362 | — | 6 | 1 | no | — |
| 114 | #361 | — | 2 | 2 | no | — |
| 115 | #361 | — | 6 | 1 | no | — |
| 116 | #360 | — | 6 | 2 | no | — |
| 117 | #357 | — | 6 | 2 | no | — |
| 118 | #350 | — | 6 | 2 | no | — |
| 119 | #344 | — | 6 | 1 | no | — |
| 120 | C24×C3 | — | 4 | 1 | no | — |
| 121 | C23×D3 | — | 4 | 2 | no | — |
| 122 | C2×C3×D4 | — | 2 | 2 | no | — |
| 123 | C2×C3×D4 | — | 2 | 2 | no | — |
| 124 | C2×C3×D4 | — | 2 | 2 | no | — |
| 125 | C2×C3×D4 | — | 4 | 1 | no | — |
| 126 | C2×C3×D4 | — | 4 | 1 | no | — |
| 127 | C2×C3×D4 | — | 4 | 1 | no | — |
| 128 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | C2×#67 | — | 2 | 1 | no | — |
| 130 | C2×#67 | — | 4 | 2 | no | — |
| 131 | C2×#67 | — | 4 | 8 | no | — |
| 132 | C2×#67 | — | 4 | 8 | no | — |
| 133 | C2×#67 | — | 4 | 2 | no | — |
| 134 | C2×#67 | — | 4 | 1 | no | — |
| 135 | C22×Dic3 | — | 4 | 2 | no | — |
| 136 | #237 | — | 2 | 8 | no | — |
| 137 | #237 | — | 4 | 4 | no | — |
| 138 | #237 | — | 4 | 4 | no | — |
| 139 | #237 | — | 4 | 4 | no | — |
| 140 | D3×D4 | — | 2 | 8 | no | — |
| 141 | D3×D4 | — | 4 | 4 | no | — |
| 142 | D3×D4 | — | 4 | 4 | no | — |
| 143 | D3×D4 | — | 4 | 4 | no | — |
| 144 | #235 | — | 2 | 1 | no | — |
| 145 | #235 | — | 2 | 1 | no | — |
| 146 | #235 | — | 2 | 2 | no | — |
| 147 | #235 | — | 2 | 2 | no | — |
| 148 | #235 | — | 4 | 1 | no | — |
| 149 | #235 | — | 4 | 1 | no | — |
| 150 | #235 | C22⋊C4 | 1 | 2 | yes | — |
| 151 | #235 | D8 | 1 | 2 | yes | — |
| 152 | C2×D12 | — | 2 | 1 | no | — |
| 153 | C2×D12 | SD16 | 1 | 1 | yes | characteristic |
| 154 | C2×C4×D3 | — | 2 | 1 | no | — |
| 155 | C2×C4×D3 | — | 4 | 1 | no | — |
| 156 | C2×Dic6 | — | 2 | 1 | no | — |
| 157 | C2×Dic6 | SD16 | 1 | 1 | yes | characteristic |
| 158 | C3×D8 | — | 2 | 2 | no | — |
| 159 | C3×D8 | — | 2 | 2 | no | — |
| 160 | C3×D8 | — | 2 | 2 | no | — |
| 161 | C3×D8 | C22⋊C4 | 1 | 4 | yes | — |
| 162 | C3×M16 | — | 4 | 1 | no | — |
| 163 | C3×M16 | — | 4 | 1 | no | — |
| 164 | C2×C3×C8 | — | 4 | 1 | no | — |
| 165 | C2×C3×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 166 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 168 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 169 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 171 | #217 | — | 4 | 1 | no | — |
| 172 | #214 | — | 2 | 8 | no | — |
| 173 | #213 | — | 2 | 8 | no | — |
| 174 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 175 | C4×Dic3 | — | 4 | 1 | no | — |
| 176 | #208 | — | 2 | 1 | no | — |
| 177 | #208 | C22⋊C4 | 1 | 2 | yes | — |
| 178 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 179 | Dic12 | — | 2 | 1 | no | — |
| 180 | Dic12 | C22⋊C4 | 1 | 2 | yes | — |
| 181 | D24 | — | 2 | 1 | no | — |
| 182 | D24 | C22⋊C4 | 1 | 2 | yes | — |
| 183 | #204 | — | 2 | 2 | no | — |
| 184 | #204 | — | 2 | 2 | no | — |
| 185 | ΓL(1,𝔽25) | — | 2 | 2 | no | — |
| 186 | ΓL(1,𝔽25) | — | 2 | 2 | no | — |
| 187 | D3×C8 | — | 2 | 2 | no | — |
| 188 | D3×C8 | — | 2 | 2 | no | — |
| 189 | C3×C16 | — | 4 | 1 | no | — |
| 190 | C3⋊C16 | — | 4 | 1 | no | — |
| 191 | H(5,𝔽2) | — | 6 | 4 | no | — |
| 192 | H(5,𝔽2) | — | 6 | 4 | no | — |
| 193 | H(5,𝔽2) | — | 12 | 2 | no | — |
| 194 | H(5,𝔽2) | — | 12 | 2 | no | — |
| 195 | C2×#41 | — | 3 | 1 | no | — |
| 196 | C2×#41 | — | 6 | 2 | no | — |
| 197 | C2×#41 | — | 6 | 1 | no | — |
| 198 | C2×#41 | — | 12 | 1 | no | — |
| 199 | C22×D4 | — | 2 | 1 | no | — |
| 200 | C22×D4 | — | 6 | 2 | no | — |
| 201 | C22×D4 | — | 12 | 1 | no | — |
| 202 | C22×D4 | — | 12 | 2 | no | — |
| 203 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 204 | AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 205 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 206 | AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 207 | #135 | — | 3 | 2 | no | — |
| 208 | #135 | — | 3 | 2 | no | — |
| 209 | #135 | — | 6 | 4 | no | — |
| 210 | #135 | — | 6 | 4 | no | — |
| 211 | #135 | — | 6 | 1 | no | — |
| 212 | #135 | — | 6 | 1 | no | — |
| 213 | C2×Q16 | — | 3 | 1 | no | — |
| 214 | C2×SD16 | — | 6 | 2 | no | — |
| 215 | C2×SD16 | — | 6 | 1 | no | — |
| 216 | C2×D8 | — | 2 | 1 | no | — |
| 217 | C2×D8 | — | 2 | 1 | no | — |
| 218 | C2×D8 | — | 2 | 1 | no | — |
| 219 | C2×D8 | — | 3 | 1 | no | — |
| 220 | C2×D8 | — | 6 | 4 | no | — |
| 221 | C2×D8 | — | 6 | 4 | no | — |
| 222 | C2×D8 | — | 6 | 2 | no | — |
| 223 | C2×D8 | C4×D3 | 1 | 2 | yes | — |
| 224 | C2×D8 | D12 | 1 | 2 | yes | — |
| 225 | C2×D8 | #67 | 1 | 2 | yes | — |
| 226 | #131 | — | 3 | 2 | no | — |
| 227 | #131 | — | 3 | 2 | no | — |
| 228 | #131 | — | 6 | 1 | no | — |
| 229 | #131 | — | 6 | 1 | no | — |
| 230 | C2×M16 | — | 2 | 1 | no | — |
| 231 | C2×M16 | — | 3 | 1 | no | — |
| 232 | C2×M16 | — | 6 | 1 | no | — |
| 233 | C22×C8 | — | 6 | 1 | no | — |
| 234 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 235 | #117 | — | 6 | 1 | no | — |
| 236 | M32 | — | 2 | 1 | no | — |
| 237 | M32 | — | 2 | 1 | no | — |
| 238 | M32 | — | 6 | 1 | no | — |
| 239 | M32 | — | 6 | 1 | no | — |
| 240 | C2×C16 | — | 2 | 1 | no | — |
| 241 | C2×C16 | — | 6 | 1 | no | — |
| 242 | #108 | — | 2 | 1 | no | — |
| 243 | #108 | — | 2 | 1 | no | — |
| 244 | #107 | — | 6 | 1 | no | — |
| 245 | #106 | — | 6 | 1 | no | — |
| 246 | #104 | — | 12 | 2 | no | — |
| 247 | C23×C3 | — | 4 | 2 | no | — |
| 248 | C23×C3 | — | 4 | 2 | no | — |
| 249 | C23×C3 | — | 4 | 2 | no | — |
| 250 | C23×C3 | — | 16 | 2 | no | — |
| 251 | C23×C3 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 252 | C22×D3 | — | 2 | 1 | no | — |
| 253 | C22×D3 | — | 4 | 8 | no | — |
| 254 | C22×D3 | — | 4 | 1 | no | — |
| 255 | C22×D3 | — | 16 | 4 | no | — |
| 256 | C3×D4 | — | 2 | 4 | no | — |
| 257 | C3×D4 | — | 4 | 2 | no | — |
| 258 | C3×D4 | — | 4 | 2 | no | — |
| 259 | C3×D4 | — | 4 | 2 | no | — |
| 260 | C2×C3×C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 261 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 262 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 263 | C2×C3×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 264 | C2×C3×C4 | C2×SD16 | 1 | 1 | yes | characteristic |
| 265 | C2×C3×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 266 | #67 | — | 2 | 2 | no | — |
| 267 | #67 | — | 2 | 2 | no | — |
| 268 | #67 | — | 4 | 8 | no | — |
| 269 | #67 | — | 4 | 8 | no | — |
| 270 | #67 | — | 4 | 2 | no | — |
| 271 | #67 | — | 4 | 2 | no | — |
| 272 | C2×Dic3 | — | 2 | 1 | no | — |
| 273 | C2×Dic3 | — | 4 | 8 | no | — |
| 274 | C2×Dic3 | — | 4 | 1 | no | — |
| 275 | C2×Dic3 | — | 8 | 1 | no | — |
| 276 | D12 | — | 2 | 2 | no | — |
| 277 | D12 | — | 2 | 1 | no | — |
| 278 | D12 | — | 4 | 1 | no | — |
| 279 | D12 | #102 | 1 | 2 | yes | — |
| 280 | C4×D3 | — | 2 | 2 | no | — |
| 281 | C4×D3 | — | 2 | 2 | no | — |
| 282 | C4×D3 | — | 4 | 2 | no | — |
| 283 | C4×D3 | — | 4 | 2 | no | — |
| 284 | Dic6 | — | 2 | 1 | no | — |
| 285 | Dic6 | — | 2 | 2 | no | — |
| 286 | Dic6 | — | 4 | 1 | no | — |
| 287 | Dic6 | #102 | 1 | 2 | yes | — |
| 288 | C3×C8 | — | 8 | 1 | no | — |
| 289 | C3×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 290 | C3×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 291 | C3×C8 | #120 | 1 | 1 | yes | characteristic |
| 292 | C3×C8 | #120 | 1 | 1 | yes | characteristic |
| 293 | C3⋊C8 | — | 2 | 2 | no | — |
| 294 | C24 | — | 4 | 1 | no | — |
| 295 | C24 | — | 12 | 2 | no | — |
| 296 | #41 | — | 3 | 2 | no | — |
| 297 | #41 | — | 3 | 2 | no | — |
| 298 | #41 | — | 6 | 1 | no | — |
| 299 | #41 | — | 6 | 1 | no | — |
| 300 | #41 | — | 6 | 8 | no | — |
| 301 | #41 | — | 6 | 2 | no | — |
| 302 | #41 | — | 6 | 2 | no | — |
| 303 | #41 | — | 12 | 4 | no | — |
| 304 | #41 | — | 12 | 4 | no | — |
| 305 | #41 | — | 12 | 4 | no | — |
| 306 | #41 | — | 12 | 1 | no | — |
| 307 | #41 | — | 12 | 1 | no | — |
| 308 | C2×Q8 | — | 3 | 1 | no | — |
| 309 | C2×Q8 | — | 6 | 1 | no | — |
| 310 | C2×D4 | — | 2 | 2 | no | — |
| 311 | C2×D4 | — | 2 | 2 | no | — |
| 312 | C2×D4 | — | 2 | 2 | no | — |
| 313 | C2×D4 | — | 3 | 1 | no | — |
| 314 | C2×D4 | — | 4 | 1 | no | — |
| 315 | C2×D4 | — | 4 | 1 | no | — |
| 316 | C2×D4 | — | 4 | 1 | no | — |
| 317 | C2×D4 | — | 6 | 8 | no | — |
| 318 | C2×D4 | — | 6 | 1 | no | — |
| 319 | C2×D4 | — | 6 | 1 | no | — |
| 320 | C2×D4 | — | 12 | 4 | no | — |
| 321 | C2×D4 | — | 12 | 2 | no | — |
| 322 | C2×D4 | — | 12 | 4 | no | — |
| 323 | C2×D4 | — | 12 | 4 | no | — |
| 324 | C2×D4 | — | 12 | 8 | no | — |
| 325 | C2×D4 | — | 12 | 8 | no | — |
| 326 | C2×D4 | — | 12 | 2 | no | — |
| 327 | C2×D4 | — | 12 | 1 | no | — |
| 328 | C22×C4 | — | 6 | 1 | no | — |
| 329 | C22×C4 | — | 12 | 2 | no | — |
| 330 | C22×C4 | — | 12 | 1 | no | — |
| 331 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 332 | Q16 | — | 3 | 2 | no | — |
| 333 | Q16 | — | 6 | 1 | no | — |
| 334 | SD16 | — | 6 | 8 | no | — |
| 335 | SD16 | — | 6 | 2 | no | — |
| 336 | SD16 | — | 6 | 2 | no | — |
| 337 | D8 | — | 2 | 2 | no | — |
| 338 | D8 | — | 2 | 2 | no | — |
| 339 | D8 | — | 2 | 2 | no | — |
| 340 | D8 | — | 3 | 2 | no | — |
| 341 | D8 | — | 6 | 8 | no | — |
| 342 | D8 | — | 6 | 1 | no | — |
| 343 | D8 | (C2×D3)⋊C4 | 1 | 4 | yes | — |
| 344 | M16 | — | 3 | 2 | no | — |
| 345 | M16 | — | 4 | 1 | no | — |
| 346 | M16 | — | 4 | 1 | no | — |
| 347 | M16 | — | 6 | 1 | no | — |
| 348 | M16 | — | 6 | 2 | no | — |
| 349 | M16 | — | 6 | 2 | no | — |
| 350 | C2×C8 | — | 4 | 1 | no | — |
| 351 | C2×C8 | — | 6 | 1 | no | — |
| 352 | C2×C8 | — | 6 | 2 | no | — |
| 353 | C2×C8 | — | 6 | 2 | no | — |
| 354 | C2×C8 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 355 | C2×C8 | C2×D12 | 1 | 1 | yes | characteristic |
| 356 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 357 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 358 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 359 | C2×C8 | C2×#67 | 1 | 1 | yes | characteristic |
| 360 | C4⋊C4 | — | 12 | 1 | no | — |
| 361 | C22⋊C4 | — | 12 | 1 | no | — |
| 362 | C42 | — | 12 | 1 | no | — |
| 363 | C16 | — | 4 | 1 | no | — |
| 364 | C16 | — | 12 | 1 | no | — |
| 365 | C22×C3 | — | 4 | 1 | no | — |
| 366 | C22×C3 | — | 4 | 4 | no | — |
| 367 | C22×C3 | — | 8 | 4 | no | — |
| 368 | C22×C3 | — | 16 | 2 | no | — |
| 369 | C22×C3 | — | 16 | 2 | no | — |
| 370 | C22×C3 | #418 | 1 | 1 | yes | characteristic |
| 371 | C22×C3 | #447 | 1 | 1 | yes | characteristic |
| 372 | C22×C3 | #450 | 1 | 1 | yes | characteristic |
| 373 | C2×D3 | — | 2 | 2 | no | — |
| 374 | C2×D3 | — | 4 | 2 | no | — |
| 375 | C2×D3 | — | 4 | 2 | no | — |
| 376 | C2×D3 | — | 8 | 2 | no | — |
| 377 | C2×D3 | — | 16 | 8 | no | — |
| 378 | C3×C4 | #379 | 1 | 1 | yes | characteristic |
| 379 | C3×C4 | C2×#102 | 1 | 1 | yes | characteristic |
| 380 | C3×C4 | #447 | 1 | 1 | yes | characteristic |
| 381 | C3×C4 | #450 | 1 | 1 | yes | characteristic |
| 382 | Dic3 | — | 2 | 2 | no | — |
| 383 | Dic3 | — | 4 | 2 | no | — |
| 384 | Dic3 | — | 16 | 1 | no | — |
| 385 | C23 | — | 4 | 2 | no | — |
| 386 | C23 | — | 4 | 2 | no | — |
| 387 | C23 | — | 4 | 2 | no | — |
| 388 | C23 | — | 6 | 1 | no | — |
| 389 | C23 | — | 12 | 8 | no | — |
| 390 | C23 | — | 12 | 1 | no | — |
| 391 | C23 | — | 16 | 2 | no | — |
| 392 | C23 | — | 48 | 4 | no | — |
| 393 | C23 | #914 | 1 | 1 | yes | characteristic |
| 394 | Q8 | — | 3 | 2 | no | — |
| 395 | Q8 | — | 6 | 1 | no | — |
| 396 | Q8 | — | 6 | 2 | no | — |
| 397 | Q8 | — | 12 | 1 | no | — |
| 398 | D4 | — | 2 | 4 | no | — |
| 399 | D4 | — | 3 | 2 | no | — |
| 400 | D4 | — | 4 | 2 | no | — |
| 401 | D4 | — | 4 | 2 | no | — |
| 402 | D4 | — | 4 | 2 | no | — |
| 403 | D4 | — | 6 | 2 | no | — |
| 404 | D4 | — | 6 | 2 | no | — |
| 405 | D4 | — | 6 | 2 | no | — |
| 406 | D4 | — | 6 | 1 | no | — |
| 407 | D4 | — | 12 | 8 | no | — |
| 408 | D4 | — | 12 | 8 | no | — |
| 409 | D4 | — | 12 | 2 | no | — |
| 410 | D4 | — | 12 | 2 | no | — |
| 411 | D4 | — | 12 | 1 | no | — |
| 412 | C2×C4 | — | 6 | 1 | no | — |
| 413 | C2×C4 | — | 6 | 2 | no | — |
| 414 | C2×C4 | — | 6 | 2 | no | — |
| 415 | C2×C4 | — | 12 | 8 | no | — |
| 416 | C2×C4 | — | 12 | 1 | no | — |
| 417 | C2×C4 | — | 12 | 2 | no | — |
| 418 | C2×C4 | — | 12 | 2 | no | — |
| 419 | C2×C4 | — | 24 | 1 | no | — |
| 420 | C2×C4 | D3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 421 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 422 | C2×C4 | D3×D8 | 1 | 1 | yes | characteristic |
| 423 | C2×C4 | #911 | 1 | 1 | yes | characteristic |
| 424 | C2×C4 | D3×SD16 | 1 | 1 | yes | characteristic |
| 425 | C2×C4 | #937 | 1 | 1 | yes | characteristic |
| 426 | C8 | — | 6 | 2 | no | — |
| 427 | C8 | — | 8 | 1 | no | — |
| 428 | C8 | D3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 429 | C8 | #882 | 1 | 1 | yes | characteristic |
| 430 | C8 | C2×(C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 431 | C8 | #937 | 1 | 1 | yes | characteristic |
| 432 | C2×C3 | — | 2 | 1 | no | — |
| 433 | C2×C3 | — | 2 | 1 | no | — |
| 434 | C2×C3 | — | 2 | 1 | no | — |
| 435 | C2×C3 | — | 8 | 4 | no | — |
| 436 | C2×C3 | #1786 | 1 | 1 | yes | characteristic |
| 437 | D3 | — | 4 | 2 | no | — |
| 438 | D3 | — | 8 | 2 | no | — |
| 439 | C22 | — | 4 | 1 | no | — |
| 440 | C22 | — | 4 | 4 | no | — |
| 441 | C22 | — | 6 | 2 | no | — |
| 442 | C22 | — | 8 | 4 | no | — |
| 443 | C22 | — | 12 | 2 | no | — |
| 444 | C22 | — | 12 | 2 | no | — |
| 445 | C22 | — | 16 | 2 | no | — |
| 446 | C22 | — | 16 | 2 | no | — |
| 447 | C22 | — | 24 | 2 | no | — |
| 448 | C22 | — | 48 | 8 | no | — |
| 449 | C22 | #4770 | 1 | 1 | yes | characteristic |
| 450 | C22 | #4773 | 1 | 1 | yes | characteristic |
| 451 | C22 | #5169 | 1 | 1 | yes | characteristic |
| 452 | C4 | — | 6 | 2 | no | — |
| 453 | C4 | — | 12 | 2 | no | — |
| 454 | C4 | — | 48 | 1 | no | — |
| 455 | C4 | D3×#102 | 1 | 1 | yes | characteristic |
| 456 | C4 | #4776 | 1 | 1 | yes | characteristic |
| 457 | C4 | #4955 | 1 | 1 | yes | characteristic |
| 458 | C4 | #5156 | 1 | 1 | yes | characteristic |
| 459 | C3 | #12750 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 460 | C2 | — | 2 | 1 | no | — |
| 461 | C2 | — | 2 | 1 | no | — |
| 462 | C2 | — | 2 | 1 | no | — |
| 463 | C2 | — | 8 | 4 | no | — |
| 464 | C2 | — | 12 | 2 | no | — |
| 465 | C2 | — | 24 | 2 | no | — |
| 466 | C2 | #70198 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×#361 | C2 | semidirect |
| 3. #72033 | C2 | semidirect |
| 4. #71450 | C2 | semidirect |
| 5. #71437 | C2 | semidirect |
| 6. #70719 | C2 | semidirect |
| 7. #70687 | C2 | semidirect |
| 15. #5757 | C4 | semidirect |
| 21. C2×C3×M32 | C22 | semidirect |
| 22. C2×C3×#108 | C22 | semidirect |
| 24. #5106 | C22 | semidirect |
| 25. C2×#812 | C22 | semidirect |
| 35. C2×#361 | D3 | semidirect |
| 109. C2×M32 | C2×D3 | semidirect |
| 110. C2×#108 | C2×D3 | semidirect |
| 459. C3 | #12750 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5757 | 2 |
| C2×C3×#361 | 2 |
| #72033 | 2 |
| #71450 | 2 |
| #71437 | 2 |
| #70719 | 2 |
| #70687 | 2 |
| #12750 | 3 |