Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
888 conjugacy classes of subgroups.
The subgroup lattice has 518 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #87163 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×#2117 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72015 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#4518 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#4518 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #71448 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #71442 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #12752 | — | 3 | 1 | no | maximal, Sylow |
| 9 | #5964 | — | 2 | 1 | no | — |
| 10 | C2×C3×#131 | C22 | 1 | 1 | yes | characteristic |
| 11 | #5753 | — | 2 | 1 | no | — |
| 12 | #5753 | C4 | 1 | 2 | yes | complemented |
| 13 | #5752 | — | 2 | 1 | no | — |
| 14 | #5752 | C4 | 1 | 2 | yes | complemented |
| 15 | #5751 | — | 2 | 2 | no | — |
| 16 | #5751 | — | 2 | 2 | no | — |
| 17 | #5748 | — | 2 | 1 | no | — |
| 18 | #5748 | — | 2 | 2 | no | — |
| 19 | C2×#904 | — | 2 | 2 | no | — |
| 20 | C2×#904 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#904 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×C3×M32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C2×C3×M32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #5232 | — | 2 | 1 | no | — |
| 25 | C2×#819 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C2×#817 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C3×#350 | — | 2 | 2 | no | — |
| 28 | #4554 | — | 2 | 1 | no | — |
| 29 | #4518 | — | 2 | 2 | no | — |
| 30 | #4518 | — | 2 | 2 | no | — |
| 31 | #4517 | — | 2 | 1 | no | — |
| 32 | #4516 | — | 2 | 1 | no | — |
| 33 | #4510 | — | 2 | 2 | no | — |
| 34 | #3584 | — | 3 | 1 | no | — |
| 35 | #2148 | — | 3 | 1 | no | — |
| 36 | C2×#360 | — | 3 | 1 | no | — |
| 37 | C2×#360 | — | 3 | 1 | no | — |
| 38 | #2143 | — | 3 | 1 | no | — |
| 39 | #2117 | D3 | 1 | 1 | yes | characteristic, complemented |
| 40 | #1815 | — | 3 | 1 | no | — |
| 41 | C2×C3×#41 | D4 | 1 | 1 | yes | characteristic |
| 42 | #1010 | — | 2 | 2 | no | — |
| 43 | #1010 | — | 2 | 2 | no | — |
| 44 | #1009 | — | 2 | 2 | no | — |
| 45 | #1009 | — | 2 | 2 | no | — |
| 46 | D3×#41 | — | 4 | 2 | no | — |
| 47 | D3×#41 | — | 4 | 2 | no | — |
| 48 | #1007 | — | 4 | 1 | no | — |
| 49 | #1004 | — | 4 | 2 | no | — |
| 50 | #1004 | — | 4 | 1 | no | — |
| 51 | C2×#235 | — | 2 | 4 | no | — |
| 52 | C2×#235 | — | 2 | 1 | no | — |
| 53 | C2×#235 | — | 2 | 1 | no | — |
| 54 | C3×#131 | — | 2 | 1 | no | — |
| 55 | C3×#131 | — | 2 | 1 | no | — |
| 56 | C3×#131 | C2×C4 | 1 | 2 | yes | — |
| 57 | C3×#131 | D4 | 1 | 2 | yes | — |
| 58 | C2×C3×M16 | — | 2 | 1 | no | — |
| 59 | C2×C3×M16 | D4 | 1 | 1 | yes | characteristic |
| 60 | C22×C3×C8 | — | 2 | 1 | no | — |
| 61 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 62 | C2×C4⋊Dic3 | — | 2 | 1 | no | — |
| 63 | C2×#208 | — | 2 | 1 | no | — |
| 64 | #909 | — | 2 | 2 | no | — |
| 65 | #909 | — | 2 | 4 | no | — |
| 66 | #909 | — | 2 | 2 | no | — |
| 67 | #909 | — | 2 | 4 | no | — |
| 68 | #908 | — | 2 | 2 | no | — |
| 69 | #908 | — | 2 | 4 | no | — |
| 70 | #908 | — | 2 | 2 | no | — |
| 71 | #908 | — | 2 | 4 | no | — |
| 72 | C2×Dic12 | — | 2 | 2 | no | — |
| 73 | C2×Dic12 | C2×C4 | 1 | 1 | yes | characteristic |
| 74 | C2×Dic12 | D4 | 1 | 1 | yes | characteristic |
| 75 | #904 | — | 2 | 4 | no | — |
| 76 | #904 | — | 2 | 4 | no | — |
| 77 | #904 | — | 2 | 1 | no | — |
| 78 | #904 | — | 2 | 1 | no | — |
| 79 | #904 | — | 2 | 1 | no | — |
| 80 | #904 | — | 2 | 1 | no | — |
| 81 | #904 | — | 2 | 2 | no | — |
| 82 | #904 | — | 2 | 2 | no | — |
| 83 | #904 | C2×C4 | 1 | 2 | yes | — |
| 84 | #904 | D4 | 1 | 2 | yes | — |
| 85 | #904 | D4 | 1 | 2 | yes | — |
| 86 | #904 | D4 | 1 | 2 | yes | — |
| 87 | C2×D24 | — | 2 | 2 | no | — |
| 88 | C2×D24 | C2×C4 | 1 | 1 | yes | characteristic |
| 89 | C2×D24 | D4 | 1 | 1 | yes | characteristic |
| 90 | C2×#204 | — | 2 | 4 | no | — |
| 91 | C2×#204 | — | 2 | 1 | no | — |
| 92 | C2×#204 | — | 2 | 1 | no | — |
| 93 | C3×M32 | — | 2 | 1 | no | — |
| 94 | C3×M32 | — | 2 | 1 | no | — |
| 95 | C3×M32 | — | 2 | 1 | no | — |
| 96 | C3×M32 | — | 2 | 1 | no | — |
| 97 | C2×C3×C16 | — | 2 | 1 | no | — |
| 98 | C2×C3×C16 | — | 2 | 1 | no | — |
| 99 | #835 | — | 4 | 1 | no | — |
| 100 | #832 | — | 4 | 1 | no | — |
| 101 | #819 | — | 2 | 1 | no | — |
| 102 | #819 | — | 2 | 1 | no | — |
| 103 | #817 | — | 2 | 1 | no | — |
| 104 | #817 | — | 2 | 1 | no | — |
| 105 | #585 | — | 6 | 1 | no | — |
| 106 | #578 | — | 3 | 2 | no | — |
| 107 | #578 | — | 6 | 1 | no | — |
| 108 | #577 | — | 6 | 2 | no | — |
| 109 | #577 | — | 6 | 2 | no | — |
| 110 | #576 | — | 3 | 2 | no | — |
| 111 | #576 | — | 6 | 1 | no | — |
| 112 | #575 | — | 6 | 2 | no | — |
| 113 | #575 | — | 6 | 1 | no | — |
| 114 | C2×#135 | — | 3 | 1 | no | — |
| 115 | C2×#135 | — | 3 | 1 | no | — |
| 116 | C2×#135 | — | 6 | 2 | no | — |
| 117 | C2×#131 | C2×D3 | 1 | 1 | yes | characteristic |
| 118 | C2×M32 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 119 | C2×M32 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 120 | C2×#108 | — | 3 | 1 | no | — |
| 121 | C2×#106 | — | 3 | 1 | no | — |
| 122 | #417 | — | 6 | 1 | no | — |
| 123 | #362 | — | 6 | 1 | no | — |
| 124 | #361 | — | 6 | 1 | no | — |
| 125 | #360 | — | 6 | 2 | no | — |
| 126 | #360 | — | 6 | 2 | no | — |
| 127 | #359 | — | 6 | 2 | no | — |
| 128 | #350 | — | 2 | 2 | no | — |
| 129 | #343 | — | 6 | 1 | no | — |
| 130 | C3×#41 | — | 2 | 1 | no | — |
| 131 | C3×#41 | — | 2 | 1 | no | — |
| 132 | C3×#41 | C22⋊C4 | 1 | 2 | yes | — |
| 133 | C3×#41 | SD16 | 1 | 2 | yes | — |
| 134 | C2×C3×Q8 | D8 | 1 | 1 | yes | characteristic |
| 135 | C2×C3×D4 | — | 2 | 1 | no | — |
| 136 | C2×C3×D4 | D8 | 1 | 1 | yes | characteristic |
| 137 | C22×C3×C4 | — | 2 | 1 | no | — |
| 138 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 139 | C2×#67 | — | 4 | 4 | no | — |
| 140 | C2×#67 | — | 4 | 1 | no | — |
| 141 | C2×#67 | — | 4 | 1 | no | — |
| 142 | C22×Dic3 | — | 4 | 1 | no | — |
| 143 | #239 | — | 4 | 2 | no | — |
| 144 | #239 | — | 4 | 2 | no | — |
| 145 | D3×Q8 | — | 4 | 2 | no | — |
| 146 | D3×Q8 | — | 4 | 2 | no | — |
| 147 | #237 | — | 4 | 4 | no | — |
| 148 | #237 | — | 4 | 4 | no | — |
| 149 | #237 | — | 4 | 2 | no | — |
| 150 | #237 | — | 4 | 2 | no | — |
| 151 | D3×D4 | — | 4 | 4 | no | — |
| 152 | D3×D4 | — | 4 | 4 | no | — |
| 153 | D3×D4 | — | 4 | 2 | no | — |
| 154 | D3×D4 | — | 4 | 2 | no | — |
| 155 | #235 | — | 2 | 4 | no | — |
| 156 | #235 | — | 2 | 4 | no | — |
| 157 | #235 | — | 2 | 2 | no | — |
| 158 | #235 | — | 2 | 2 | no | — |
| 159 | #235 | — | 2 | 2 | no | — |
| 160 | #235 | — | 2 | 2 | no | — |
| 161 | #235 | — | 4 | 4 | no | — |
| 162 | #235 | — | 4 | 4 | no | — |
| 163 | #235 | — | 4 | 1 | no | — |
| 164 | #235 | — | 4 | 1 | no | — |
| 165 | #235 | — | 4 | 1 | no | — |
| 166 | #235 | — | 4 | 1 | no | — |
| 167 | C2×D12 | — | 2 | 4 | no | — |
| 168 | C2×D12 | — | 2 | 1 | no | — |
| 169 | C2×D12 | — | 2 | 1 | no | — |
| 170 | C2×C4×D3 | — | 4 | 4 | no | — |
| 171 | C2×C4×D3 | — | 4 | 1 | no | — |
| 172 | C2×C4×D3 | — | 4 | 1 | no | — |
| 173 | C2×Dic6 | — | 2 | 4 | no | — |
| 174 | C2×Dic6 | — | 2 | 1 | no | — |
| 175 | C2×Dic6 | — | 2 | 1 | no | — |
| 176 | C3×M16 | — | 2 | 1 | no | — |
| 177 | C3×M16 | — | 2 | 2 | no | — |
| 178 | C3×M16 | — | 2 | 2 | no | — |
| 179 | C3×M16 | C22⋊C4 | 1 | 2 | yes | — |
| 180 | C2×C3×C8 | — | 2 | 1 | no | — |
| 181 | C2×C3×C8 | — | 2 | 2 | no | — |
| 182 | C2×C3×C8 | — | 2 | 2 | no | — |
| 183 | C2×C3×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 184 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 185 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 186 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 187 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 188 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 189 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 190 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 191 | #208 | — | 4 | 1 | no | — |
| 192 | #208 | — | 4 | 1 | no | — |
| 193 | C2×C3⋊C8 | — | 4 | 1 | no | — |
| 194 | Dic12 | — | 2 | 4 | no | — |
| 195 | Dic12 | — | 2 | 1 | no | — |
| 196 | Dic12 | — | 2 | 1 | no | — |
| 197 | Dic12 | C22⋊C4 | 1 | 2 | yes | — |
| 198 | Dic12 | C22⋊C4 | 1 | 2 | yes | — |
| 199 | D24 | — | 2 | 4 | no | — |
| 200 | D24 | — | 2 | 1 | no | — |
| 201 | D24 | — | 2 | 1 | no | — |
| 202 | D24 | C22⋊C4 | 1 | 2 | yes | — |
| 203 | D24 | C22⋊C4 | 1 | 2 | yes | — |
| 204 | #204 | — | 2 | 4 | no | — |
| 205 | #204 | — | 2 | 4 | no | — |
| 206 | #204 | — | 2 | 2 | no | — |
| 207 | #204 | — | 2 | 2 | no | — |
| 208 | #204 | — | 2 | 2 | no | — |
| 209 | #204 | — | 2 | 2 | no | — |
| 210 | C3×C16 | — | 4 | 1 | no | — |
| 211 | C3×C16 | — | 4 | 1 | no | — |
| 212 | 2−1+4 | — | 6 | 2 | no | — |
| 213 | 2−1+4 | — | 6 | 2 | no | — |
| 214 | 2−1+4 | — | 12 | 1 | no | — |
| 215 | H(5,𝔽2) | — | 6 | 2 | no | — |
| 216 | H(5,𝔽2) | — | 6 | 2 | no | — |
| 217 | H(5,𝔽2) | — | 12 | 2 | no | — |
| 218 | H(5,𝔽2) | — | 12 | 1 | no | — |
| 219 | C2×#41 | — | 6 | 4 | no | — |
| 220 | C2×#41 | — | 6 | 1 | no | — |
| 221 | C2×#41 | — | 6 | 1 | no | — |
| 222 | C2×#41 | — | 12 | 2 | no | — |
| 223 | C2×#41 | — | 12 | 2 | no | — |
| 224 | C2×#41 | D12 | 1 | 1 | yes | characteristic |
| 225 | #137 | — | 6 | 4 | no | — |
| 226 | #137 | — | 6 | 2 | no | — |
| 227 | #137 | — | 6 | 4 | no | — |
| 228 | #137 | — | 6 | 2 | no | — |
| 229 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 230 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 231 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 232 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 233 | #135 | — | 3 | 2 | no | — |
| 234 | #135 | — | 3 | 2 | no | — |
| 235 | #135 | — | 3 | 2 | no | — |
| 236 | #135 | — | 3 | 2 | no | — |
| 237 | #135 | — | 6 | 2 | no | — |
| 238 | #135 | — | 6 | 2 | no | — |
| 239 | #135 | — | 6 | 4 | no | — |
| 240 | #135 | — | 6 | 4 | no | — |
| 241 | #135 | — | 6 | 1 | no | — |
| 242 | #135 | — | 6 | 1 | no | — |
| 243 | #135 | — | 6 | 1 | no | — |
| 244 | #135 | — | 6 | 1 | no | — |
| 245 | C2×Q16 | — | 3 | 1 | no | — |
| 246 | C2×Q16 | — | 3 | 1 | no | — |
| 247 | C2×Q16 | — | 6 | 2 | no | — |
| 248 | C2×SD16 | — | 6 | 4 | no | — |
| 249 | C2×SD16 | — | 6 | 1 | no | — |
| 250 | C2×SD16 | — | 6 | 1 | no | — |
| 251 | C2×D8 | — | 3 | 1 | no | — |
| 252 | C2×D8 | — | 3 | 1 | no | — |
| 253 | C2×D8 | — | 6 | 2 | no | — |
| 254 | #131 | — | 2 | 1 | no | — |
| 255 | #131 | — | 2 | 1 | no | — |
| 256 | #131 | C4×D3 | 1 | 2 | yes | — |
| 257 | #131 | #67 | 1 | 2 | yes | — |
| 258 | C2×M16 | — | 2 | 1 | no | — |
| 259 | C2×M16 | — | 6 | 1 | no | — |
| 260 | C2×M16 | D12 | 1 | 1 | yes | characteristic |
| 261 | C22×C8 | — | 2 | 1 | no | — |
| 262 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 263 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 264 | M32 | — | 2 | 1 | no | — |
| 265 | M32 | — | 2 | 1 | no | — |
| 266 | M32 | — | 2 | 1 | no | — |
| 267 | M32 | — | 2 | 1 | no | — |
| 268 | C2×C16 | — | 2 | 1 | no | — |
| 269 | C2×C16 | — | 2 | 1 | no | — |
| 270 | #108 | — | 6 | 1 | no | — |
| 271 | #108 | — | 6 | 1 | no | — |
| 272 | #106 | — | 6 | 1 | no | — |
| 273 | #106 | — | 6 | 1 | no | — |
| 274 | #103 | — | 12 | 1 | no | — |
| 275 | #102 | — | 12 | 1 | no | — |
| 276 | C23×C3 | — | 2 | 1 | no | — |
| 277 | C23×C3 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 278 | C22×D3 | — | 4 | 4 | no | — |
| 279 | C22×D3 | — | 4 | 1 | no | — |
| 280 | C22×D3 | — | 4 | 1 | no | — |
| 281 | C3×Q8 | — | 2 | 1 | no | — |
| 282 | C3×Q8 | #102 | 1 | 2 | yes | — |
| 283 | C3×D4 | — | 2 | 2 | no | — |
| 284 | C3×D4 | — | 2 | 2 | no | — |
| 285 | C3×D4 | — | 2 | 1 | no | — |
| 286 | C3×D4 | #102 | 1 | 2 | yes | — |
| 287 | C2×C3×C4 | — | 2 | 1 | no | — |
| 288 | C2×C3×C4 | — | 2 | 2 | no | — |
| 289 | C2×C3×C4 | — | 2 | 2 | no | — |
| 290 | C2×C3×C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 291 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 292 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 293 | C2×C3×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 294 | C2×C3×C4 | C2×SD16 | 1 | 1 | yes | characteristic |
| 295 | C2×C3×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 296 | #67 | — | 4 | 4 | no | — |
| 297 | #67 | — | 4 | 4 | no | — |
| 298 | #67 | — | 4 | 2 | no | — |
| 299 | #67 | — | 4 | 2 | no | — |
| 300 | #67 | — | 4 | 2 | no | — |
| 301 | #67 | — | 4 | 2 | no | — |
| 302 | C2×Dic3 | — | 4 | 4 | no | — |
| 303 | C2×Dic3 | — | 4 | 1 | no | — |
| 304 | C2×Dic3 | — | 4 | 1 | no | — |
| 305 | C2×Dic3 | — | 8 | 1 | no | — |
| 306 | C2×Dic3 | — | 16 | 1 | no | — |
| 307 | D12 | — | 2 | 2 | no | — |
| 308 | D12 | — | 2 | 2 | no | — |
| 309 | D12 | — | 4 | 4 | no | — |
| 310 | D12 | — | 4 | 1 | no | — |
| 311 | D12 | — | 4 | 1 | no | — |
| 312 | C4×D3 | — | 4 | 4 | no | — |
| 313 | C4×D3 | — | 4 | 4 | no | — |
| 314 | C4×D3 | — | 4 | 2 | no | — |
| 315 | C4×D3 | — | 4 | 2 | no | — |
| 316 | C4×D3 | — | 4 | 2 | no | — |
| 317 | C4×D3 | — | 4 | 2 | no | — |
| 318 | Dic6 | — | 2 | 2 | no | — |
| 319 | Dic6 | — | 2 | 2 | no | — |
| 320 | Dic6 | — | 4 | 4 | no | — |
| 321 | Dic6 | — | 4 | 1 | no | — |
| 322 | Dic6 | — | 4 | 1 | no | — |
| 323 | C3×C8 | — | 2 | 2 | no | — |
| 324 | C3×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 325 | C3×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 326 | C3×C8 | #120 | 1 | 1 | yes | characteristic |
| 327 | C3×C8 | #120 | 1 | 1 | yes | characteristic |
| 328 | C3⋊C8 | — | 8 | 1 | no | — |
| 329 | #41 | — | 2 | 1 | no | — |
| 330 | #41 | — | 2 | 1 | no | — |
| 331 | #41 | — | 6 | 4 | no | — |
| 332 | #41 | — | 6 | 4 | no | — |
| 333 | #41 | — | 6 | 2 | no | — |
| 334 | #41 | — | 6 | 2 | no | — |
| 335 | #41 | — | 6 | 2 | no | — |
| 336 | #41 | — | 6 | 2 | no | — |
| 337 | #41 | — | 12 | 4 | no | — |
| 338 | #41 | — | 12 | 4 | no | — |
| 339 | #41 | — | 12 | 4 | no | — |
| 340 | #41 | — | 12 | 4 | no | — |
| 341 | #41 | — | 12 | 2 | no | — |
| 342 | #41 | — | 12 | 2 | no | — |
| 343 | #41 | — | 12 | 2 | no | — |
| 344 | #41 | — | 12 | 2 | no | — |
| 345 | #41 | — | 12 | 1 | no | — |
| 346 | #41 | — | 12 | 1 | no | — |
| 347 | #41 | — | 12 | 1 | no | — |
| 348 | #41 | — | 12 | 1 | no | — |
| 349 | #41 | #204 | 1 | 2 | yes | — |
| 350 | #41 | (C2×D3)⋊C4 | 1 | 2 | yes | — |
| 351 | C2×Q8 | — | 6 | 4 | no | — |
| 352 | C2×Q8 | — | 6 | 1 | no | — |
| 353 | C2×Q8 | — | 6 | 1 | no | — |
| 354 | C2×Q8 | — | 12 | 2 | no | — |
| 355 | C2×Q8 | — | 12 | 2 | no | — |
| 356 | C2×Q8 | D24 | 1 | 1 | yes | characteristic |
| 357 | C2×D4 | — | 2 | 1 | no | — |
| 358 | C2×D4 | — | 6 | 4 | no | — |
| 359 | C2×D4 | — | 6 | 1 | no | — |
| 360 | C2×D4 | — | 6 | 1 | no | — |
| 361 | C2×D4 | — | 12 | 4 | no | — |
| 362 | C2×D4 | — | 12 | 4 | no | — |
| 363 | C2×D4 | — | 12 | 2 | no | — |
| 364 | C2×D4 | — | 12 | 4 | no | — |
| 365 | C2×D4 | — | 12 | 1 | no | — |
| 366 | C2×D4 | — | 12 | 1 | no | — |
| 367 | C2×D4 | — | 12 | 2 | no | — |
| 368 | C2×D4 | D24 | 1 | 1 | yes | characteristic |
| 369 | C22×C4 | — | 2 | 1 | no | — |
| 370 | C22×C4 | — | 12 | 4 | no | — |
| 371 | C22×C4 | — | 12 | 1 | no | — |
| 372 | C22×C4 | — | 12 | 1 | no | — |
| 373 | C22×C4 | — | 12 | 1 | no | — |
| 374 | C22×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 375 | Q16 | — | 3 | 2 | no | — |
| 376 | Q16 | — | 3 | 2 | no | — |
| 377 | Q16 | — | 6 | 4 | no | — |
| 378 | Q16 | — | 6 | 1 | no | — |
| 379 | Q16 | — | 6 | 1 | no | — |
| 380 | SD16 | — | 6 | 4 | no | — |
| 381 | SD16 | — | 6 | 4 | no | — |
| 382 | SD16 | — | 6 | 2 | no | — |
| 383 | SD16 | — | 6 | 2 | no | — |
| 384 | SD16 | — | 6 | 2 | no | — |
| 385 | SD16 | — | 6 | 2 | no | — |
| 386 | D8 | — | 3 | 2 | no | — |
| 387 | D8 | — | 3 | 2 | no | — |
| 388 | D8 | — | 6 | 4 | no | — |
| 389 | D8 | — | 6 | 1 | no | — |
| 390 | D8 | — | 6 | 1 | no | — |
| 391 | M16 | — | 2 | 1 | no | — |
| 392 | M16 | — | 2 | 2 | no | — |
| 393 | M16 | — | 2 | 2 | no | — |
| 394 | M16 | — | 12 | 1 | no | — |
| 395 | M16 | — | 12 | 1 | no | — |
| 396 | M16 | (C2×D3)⋊C4 | 1 | 2 | yes | — |
| 397 | C2×C8 | — | 2 | 1 | no | — |
| 398 | C2×C8 | — | 2 | 2 | no | — |
| 399 | C2×C8 | — | 2 | 2 | no | — |
| 400 | C2×C8 | — | 12 | 1 | no | — |
| 401 | C2×C8 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 402 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 403 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 404 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 405 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 406 | C2×C8 | C2×#67 | 1 | 1 | yes | characteristic |
| 407 | C4⋊C4 | — | 12 | 1 | no | — |
| 408 | C4⋊C4 | — | 12 | 1 | no | — |
| 409 | C16 | — | 4 | 1 | no | — |
| 410 | C16 | — | 4 | 1 | no | — |
| 411 | C22×C3 | — | 2 | 2 | no | — |
| 412 | C22×C3 | — | 4 | 1 | no | — |
| 413 | C22×C3 | — | 8 | 1 | no | — |
| 414 | C22×C3 | #418 | 1 | 1 | yes | characteristic |
| 415 | C22×C3 | #447 | 1 | 1 | yes | characteristic |
| 416 | C22×C3 | #450 | 1 | 1 | yes | characteristic |
| 417 | C2×D3 | — | 4 | 2 | no | — |
| 418 | C2×D3 | — | 4 | 2 | no | — |
| 419 | C2×D3 | — | 16 | 1 | no | — |
| 420 | C2×D3 | — | 16 | 1 | no | — |
| 421 | C2×D3 | — | 16 | 4 | no | — |
| 422 | C3×C4 | — | 2 | 2 | no | — |
| 423 | C3×C4 | #379 | 1 | 1 | yes | characteristic |
| 424 | C3×C4 | C2×#102 | 1 | 1 | yes | characteristic |
| 425 | C3×C4 | #447 | 1 | 1 | yes | characteristic |
| 426 | C3×C4 | #450 | 1 | 1 | yes | characteristic |
| 427 | Dic3 | — | 4 | 2 | no | — |
| 428 | Dic3 | — | 4 | 2 | no | — |
| 429 | Dic3 | — | 16 | 1 | no | — |
| 430 | C23 | — | 2 | 1 | no | — |
| 431 | C23 | — | 12 | 4 | no | — |
| 432 | C23 | — | 12 | 1 | no | — |
| 433 | C23 | — | 12 | 1 | no | — |
| 434 | C23 | #908 | 1 | 1 | yes | characteristic |
| 435 | Q8 | — | 2 | 1 | no | — |
| 436 | Q8 | — | 6 | 2 | no | — |
| 437 | Q8 | — | 6 | 2 | no | — |
| 438 | Q8 | — | 12 | 4 | no | — |
| 439 | Q8 | — | 12 | 1 | no | — |
| 440 | Q8 | — | 12 | 1 | no | — |
| 441 | Q8 | #821 | 1 | 2 | yes | — |
| 442 | D4 | — | 2 | 2 | no | — |
| 443 | D4 | — | 2 | 2 | no | — |
| 444 | D4 | — | 2 | 1 | no | — |
| 445 | D4 | — | 6 | 2 | no | — |
| 446 | D4 | — | 6 | 2 | no | — |
| 447 | D4 | — | 12 | 4 | no | — |
| 448 | D4 | — | 12 | 4 | no | — |
| 449 | D4 | — | 12 | 4 | no | — |
| 450 | D4 | — | 12 | 2 | no | — |
| 451 | D4 | — | 12 | 2 | no | — |
| 452 | D4 | — | 12 | 2 | no | — |
| 453 | D4 | — | 12 | 2 | no | — |
| 454 | D4 | — | 12 | 1 | no | — |
| 455 | D4 | — | 12 | 1 | no | — |
| 456 | D4 | #821 | 1 | 2 | yes | — |
| 457 | C2×C4 | — | 2 | 1 | no | — |
| 458 | C2×C4 | — | 2 | 2 | no | — |
| 459 | C2×C4 | — | 2 | 2 | no | — |
| 460 | C2×C4 | — | 12 | 4 | no | — |
| 461 | C2×C4 | — | 12 | 4 | no | — |
| 462 | C2×C4 | — | 12 | 4 | no | — |
| 463 | C2×C4 | — | 12 | 1 | no | — |
| 464 | C2×C4 | — | 12 | 1 | no | — |
| 465 | C2×C4 | — | 12 | 2 | no | — |
| 466 | C2×C4 | — | 12 | 2 | no | — |
| 467 | C2×C4 | — | 12 | 2 | no | — |
| 468 | C2×C4 | — | 12 | 2 | no | — |
| 469 | C2×C4 | — | 24 | 1 | no | — |
| 470 | C2×C4 | — | 48 | 1 | no | — |
| 471 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 472 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 473 | C2×C4 | C2×#204 | 1 | 1 | yes | characteristic |
| 474 | C2×C4 | C2×D24 | 1 | 1 | yes | characteristic |
| 475 | C2×C4 | #908 | 1 | 1 | yes | characteristic |
| 476 | C2×C4 | C2×(C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 477 | C8 | — | 2 | 2 | no | — |
| 478 | C8 | — | 24 | 1 | no | — |
| 479 | C8 | D3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 480 | C8 | D3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 481 | C8 | #937 | 1 | 1 | yes | characteristic |
| 482 | C8 | #937 | 1 | 1 | yes | characteristic |
| 483 | C2×C3 | — | 2 | 1 | no | — |
| 484 | C2×C3 | — | 2 | 1 | no | — |
| 485 | C2×C3 | — | 2 | 1 | no | — |
| 486 | C2×C3 | — | 4 | 2 | no | — |
| 487 | C2×C3 | #1786 | 1 | 1 | yes | characteristic |
| 488 | D3 | — | 8 | 2 | no | — |
| 489 | D3 | — | 8 | 2 | no | — |
| 490 | C22 | — | 2 | 2 | no | — |
| 491 | C22 | — | 4 | 1 | no | — |
| 492 | C22 | — | 8 | 1 | no | — |
| 493 | C22 | — | 12 | 2 | no | — |
| 494 | C22 | — | 12 | 2 | no | — |
| 495 | C22 | — | 48 | 1 | no | — |
| 496 | C22 | — | 48 | 1 | no | — |
| 497 | C22 | — | 48 | 4 | no | — |
| 498 | C22 | #4731 | 1 | 1 | yes | characteristic |
| 499 | C22 | #4732 | 1 | 1 | yes | characteristic |
| 500 | C22 | #5131 | 1 | 1 | yes | characteristic |
| 501 | C4 | — | 2 | 2 | no | — |
| 502 | C4 | — | 12 | 2 | no | — |
| 503 | C4 | — | 12 | 2 | no | — |
| 504 | C4 | — | 48 | 1 | no | — |
| 505 | C4 | #4731 | 1 | 1 | yes | characteristic |
| 506 | C4 | #4732 | 1 | 1 | yes | characteristic |
| 507 | C4 | #4955 | 1 | 1 | yes | characteristic |
| 508 | C4 | C2×#821 | 1 | 1 | yes | characteristic |
| 509 | C3 | #12752 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 510 | C2 | — | 2 | 1 | no | — |
| 511 | C2 | — | 2 | 1 | no | — |
| 512 | C2 | — | 2 | 1 | no | — |
| 513 | C2 | — | 4 | 2 | no | — |
| 514 | C2 | — | 24 | 2 | no | — |
| 515 | C2 | — | 24 | 2 | no | — |
| 516 | C2 | #69959 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#2117 | C2 | semidirect |
| 3. #72015 | C2 | semidirect |
| 4. C2×#4518 | C2 | semidirect |
| 5. C2×#4518 | C2 | semidirect |
| 6. #71448 | C2 | semidirect |
| 7. #71442 | C2 | semidirect |
| 12. #5753 | C4 | semidirect |
| 14. #5752 | C4 | semidirect |
| 22. C2×C3×M32 | C22 | semidirect |
| 23. C2×C3×M32 | C22 | semidirect |
| 25. C2×#819 | C22 | semidirect |
| 26. C2×#817 | C22 | semidirect |
| 39. #2117 | D3 | semidirect |
| 118. C2×M32 | C2×D3 | semidirect |
| 119. C2×M32 | C2×D3 | semidirect |
| 509. C3 | #12752 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #87163 | 2 |
| C3×#2117 | 2 |
| #72015 | 2 |
| C2×#4518 | 2 |
| #71448 | 2 |
| #71442 | 2 |
| #12752 | 3 |