Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1098 conjugacy classes of subgroups.
The subgroup lattice has 532 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#5766 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C22×#828 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#4908 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#4897 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×C3×#362 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#4515 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×#4497 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #69268 | C2 | 1 | 8 | yes | maximal, direct product factor |
| 9 | C2×#2193 | — | 3 | 1 | no | maximal, Sylow |
| 10 | C2×#1007 | — | 2 | 1 | no | — |
| 11 | C22×C3×Q16 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#942 | — | 2 | 1 | no | — |
| 13 | #5766 | — | 2 | 2 | no | — |
| 14 | #5766 | — | 2 | 2 | no | — |
| 15 | #5766 | — | 2 | 2 | no | — |
| 16 | #5766 | C22 | 1 | 4 | yes | complemented |
| 17 | C2×#919 | — | 2 | 1 | no | — |
| 18 | C2×#918 | — | 2 | 2 | no | — |
| 19 | C2×D3×Q16 | — | 2 | 1 | no | — |
| 20 | C2×#908 | — | 2 | 1 | no | — |
| 21 | C2×#904 | C22 | 1 | 1 | yes | characteristic |
| 22 | C22×D24 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#901 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×C3×M32 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×C3×#108 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#828 | — | 2 | 2 | no | — |
| 27 | C2×#828 | — | 2 | 2 | no | — |
| 28 | C2×#828 | C22 | 1 | 4 | yes | complemented |
| 29 | C2×#823 | — | 2 | 1 | no | — |
| 30 | C22×C3⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 31 | #4908 | — | 2 | 2 | no | — |
| 32 | #4908 | C22 | 1 | 4 | yes | complemented |
| 33 | C2×#800 | — | 2 | 1 | no | — |
| 34 | C2×D48 | — | 2 | 1 | no | — |
| 35 | #4897 | — | 2 | 2 | no | — |
| 36 | #4897 | C22 | 1 | 4 | yes | complemented |
| 37 | C3×#362 | C22 | 1 | 4 | yes | complemented |
| 38 | #4515 | C22 | 1 | 4 | yes | complemented |
| 39 | #4497 | C22 | 1 | 4 | yes | complemented |
| 40 | C2×#578 | — | 3 | 1 | no | — |
| 41 | C2×#509 | — | 3 | 1 | no | — |
| 42 | C22×SD32 | — | 3 | 1 | no | — |
| 43 | C2×#472 | — | 3 | 1 | no | — |
| 44 | #2193 | — | 3 | 8 | no | — |
| 45 | C2×#362 | D3 | 1 | 1 | yes | characteristic, complemented |
| 46 | C2×#359 | — | 3 | 1 | no | — |
| 47 | C2×#350 | — | 3 | 1 | no | — |
| 48 | C22×C3×Q8 | — | 2 | 1 | no | — |
| 49 | #1007 | — | 2 | 4 | no | — |
| 50 | #1007 | — | 2 | 4 | no | — |
| 51 | #1007 | — | 4 | 2 | no | — |
| 52 | #1007 | — | 4 | 2 | no | — |
| 53 | C2×#239 | — | 2 | 2 | no | — |
| 54 | C2×#239 | — | 4 | 1 | no | — |
| 55 | C2×D3×Q8 | — | 2 | 2 | no | — |
| 56 | C2×D3×Q8 | — | 4 | 1 | no | — |
| 57 | C2×#235 | — | 2 | 1 | no | — |
| 58 | C2×#235 | — | 4 | 2 | no | — |
| 59 | C2×#235 | D4 | 1 | 1 | yes | characteristic |
| 60 | C22×D12 | — | 2 | 1 | no | — |
| 61 | C2×C3×Q16 | — | 2 | 1 | no | — |
| 62 | C2×C3×Q16 | — | 2 | 1 | no | — |
| 63 | C2×C3×Q16 | — | 2 | 1 | no | — |
| 64 | C2×C3×Q16 | D4 | 1 | 2 | yes | — |
| 65 | C2×C3×Q16 | D4 | 1 | 2 | yes | — |
| 66 | C2×C3×Q16 | C23 | 1 | 2 | yes | — |
| 67 | C2×C3×M16 | — | 2 | 1 | no | — |
| 68 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×#216 | — | 2 | 2 | no | — |
| 70 | #942 | — | 2 | 4 | no | — |
| 71 | #942 | — | 2 | 4 | no | — |
| 72 | C2×#215 | — | 2 | 2 | no | — |
| 73 | C2×#208 | D4 | 1 | 1 | yes | characteristic |
| 74 | #919 | — | 2 | 4 | no | — |
| 75 | #919 | — | 2 | 4 | no | — |
| 76 | #918 | — | 2 | 8 | no | — |
| 77 | #918 | — | 2 | 8 | no | — |
| 78 | D3×Q16 | — | 2 | 4 | no | — |
| 79 | D3×Q16 | — | 2 | 4 | no | — |
| 80 | #908 | — | 2 | 4 | no | — |
| 81 | #908 | — | 4 | 2 | no | — |
| 82 | C2×Dic12 | D4 | 1 | 1 | yes | characteristic |
| 83 | #904 | — | 2 | 1 | no | — |
| 84 | #904 | — | 2 | 1 | no | — |
| 85 | #904 | D4 | 1 | 2 | yes | — |
| 86 | #904 | C23 | 1 | 2 | yes | — |
| 87 | C2×D24 | — | 2 | 1 | no | — |
| 88 | C2×D24 | — | 2 | 1 | no | — |
| 89 | C2×D24 | — | 2 | 1 | no | — |
| 90 | C2×D24 | — | 2 | 1 | no | — |
| 91 | C2×D24 | — | 2 | 1 | no | — |
| 92 | C2×D24 | — | 4 | 1 | no | — |
| 93 | C2×D24 | D4 | 1 | 1 | yes | characteristic |
| 94 | C2×D24 | C23 | 1 | 2 | yes | — |
| 95 | C2×#204 | — | 2 | 1 | no | — |
| 96 | C2×#204 | — | 4 | 1 | no | — |
| 97 | #901 | — | 2 | 1 | no | — |
| 98 | #901 | — | 2 | 1 | no | — |
| 99 | #901 | D4 | 1 | 2 | yes | — |
| 100 | #901 | C23 | 1 | 2 | yes | — |
| 101 | C2×ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 102 | C2×D3×C8 | — | 2 | 1 | no | — |
| 103 | C3×M32 | — | 2 | 1 | no | — |
| 104 | C3×M32 | C23 | 1 | 2 | yes | — |
| 105 | C2×C3×C16 | — | 2 | 1 | no | — |
| 106 | C3×#108 | — | 2 | 1 | no | — |
| 107 | C3×#108 | C23 | 1 | 2 | yes | — |
| 108 | #828 | — | 2 | 8 | no | — |
| 109 | #823 | — | 2 | 4 | no | — |
| 110 | C2×C3⋊C16 | — | 2 | 1 | no | — |
| 111 | C2×C3⋊C16 | — | 2 | 1 | no | — |
| 112 | C2×C3⋊C16 | C23 | 1 | 2 | yes | — |
| 113 | #800 | — | 2 | 4 | no | — |
| 114 | D48 | — | 2 | 4 | no | — |
| 115 | C2×2−1+4 | — | 6 | 1 | no | — |
| 116 | #578 | — | 3 | 4 | no | — |
| 117 | #578 | — | 6 | 2 | no | — |
| 118 | #578 | — | 6 | 2 | no | — |
| 119 | #578 | — | 6 | 2 | no | — |
| 120 | C2×#137 | — | 6 | 1 | no | — |
| 121 | C2×#137 | — | 6 | 2 | no | — |
| 122 | C2×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 123 | C2×#135 | — | 3 | 1 | no | — |
| 124 | C2×#135 | — | 6 | 1 | no | — |
| 125 | C22×Q16 | — | 6 | 1 | no | — |
| 126 | C22×Q16 | C2×D3 | 1 | 1 | yes | characteristic |
| 127 | C22×D8 | — | 3 | 1 | no | — |
| 128 | C2×#131 | — | 3 | 1 | no | — |
| 129 | #509 | — | 3 | 4 | no | — |
| 130 | #509 | — | 6 | 2 | no | — |
| 131 | C2×SD32 | — | 3 | 4 | no | — |
| 132 | C2×SD32 | — | 6 | 1 | no | — |
| 133 | C2×SD32 | — | 6 | 2 | no | — |
| 134 | C2×SD32 | — | 6 | 2 | no | — |
| 135 | C2×D16 | — | 6 | 1 | no | — |
| 136 | C2×M32 | C2×D3 | 1 | 1 | yes | characteristic |
| 137 | C22×C16 | — | 3 | 1 | no | — |
| 138 | #472 | — | 3 | 4 | no | — |
| 139 | #472 | — | 6 | 2 | no | — |
| 140 | C2×#108 | C2×D3 | 1 | 1 | yes | characteristic |
| 141 | C2×#100 | — | 6 | 1 | no | — |
| 142 | #362 | C2×D3 | 1 | 4 | yes | complemented |
| 143 | #359 | — | 3 | 4 | no | — |
| 144 | #350 | — | 3 | 4 | no | — |
| 145 | C23×D3 | — | 4 | 1 | no | — |
| 146 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 147 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 148 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 149 | C2×C3×Q8 | — | 4 | 1 | no | — |
| 150 | C2×C3×Q8 | — | 4 | 1 | no | — |
| 151 | C2×C3×Q8 | — | 4 | 1 | no | — |
| 152 | C22×C3×C4 | — | 4 | 1 | no | — |
| 153 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C2×#67 | — | 2 | 1 | no | — |
| 155 | C2×#67 | — | 4 | 1 | no | — |
| 156 | #239 | — | 2 | 8 | no | — |
| 157 | #239 | — | 4 | 4 | no | — |
| 158 | #239 | — | 4 | 4 | no | — |
| 159 | #239 | — | 4 | 4 | no | — |
| 160 | D3×Q8 | — | 2 | 8 | no | — |
| 161 | D3×Q8 | — | 4 | 4 | no | — |
| 162 | D3×Q8 | — | 4 | 4 | no | — |
| 163 | D3×Q8 | — | 4 | 4 | no | — |
| 164 | #235 | — | 2 | 1 | no | — |
| 165 | #235 | — | 2 | 1 | no | — |
| 166 | #235 | — | 2 | 2 | no | — |
| 167 | #235 | — | 2 | 2 | no | — |
| 168 | #235 | — | 4 | 8 | no | — |
| 169 | #235 | — | 4 | 8 | no | — |
| 170 | #235 | — | 4 | 1 | no | — |
| 171 | #235 | — | 4 | 1 | no | — |
| 172 | #235 | D8 | 1 | 2 | yes | — |
| 173 | #235 | C2×D4 | 1 | 2 | yes | — |
| 174 | C2×D12 | — | 2 | 1 | no | — |
| 175 | C2×D12 | — | 2 | 2 | no | — |
| 176 | C2×D12 | — | 4 | 2 | no | — |
| 177 | C2×D12 | — | 4 | 1 | no | — |
| 178 | C2×D12 | — | 4 | 1 | no | — |
| 179 | C2×D12 | — | 4 | 1 | no | — |
| 180 | C2×D12 | — | 4 | 1 | no | — |
| 181 | C2×D12 | — | 4 | 1 | no | — |
| 182 | C2×D12 | D8 | 1 | 1 | yes | characteristic |
| 183 | C2×C4×D3 | — | 2 | 1 | no | — |
| 184 | C2×C4×D3 | — | 4 | 2 | no | — |
| 185 | C2×C4×D3 | — | 4 | 2 | no | — |
| 186 | C2×C4×D3 | — | 4 | 1 | no | — |
| 187 | C2×Dic6 | — | 2 | 1 | no | — |
| 188 | C2×Dic6 | — | 4 | 2 | no | — |
| 189 | C2×Dic6 | D8 | 1 | 1 | yes | characteristic |
| 190 | C3×Q16 | — | 2 | 2 | no | — |
| 191 | C3×Q16 | — | 2 | 2 | no | — |
| 192 | C3×Q16 | — | 2 | 2 | no | — |
| 193 | C3×Q16 | C2×D4 | 1 | 4 | yes | — |
| 194 | C3×M16 | — | 2 | 2 | no | — |
| 195 | C3×M16 | — | 4 | 1 | no | — |
| 196 | C2×C3×C8 | — | 4 | 1 | no | — |
| 197 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 198 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 199 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 200 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 201 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 202 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 203 | #216 | — | 2 | 8 | no | — |
| 204 | #215 | — | 2 | 8 | no | — |
| 205 | #208 | — | 2 | 1 | no | — |
| 206 | #208 | C2×D4 | 1 | 2 | yes | — |
| 207 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 208 | Dic12 | — | 2 | 1 | no | — |
| 209 | Dic12 | C2×D4 | 1 | 2 | yes | — |
| 210 | D24 | — | 2 | 1 | no | — |
| 211 | D24 | — | 2 | 2 | no | — |
| 212 | D24 | — | 2 | 2 | no | — |
| 213 | D24 | — | 4 | 4 | no | — |
| 214 | D24 | — | 4 | 1 | no | — |
| 215 | D24 | — | 4 | 1 | no | — |
| 216 | D24 | C2×D4 | 1 | 2 | yes | — |
| 217 | #204 | — | 2 | 2 | no | — |
| 218 | #204 | — | 2 | 2 | no | — |
| 219 | #204 | — | 4 | 4 | no | — |
| 220 | ΓL(1,𝔽25) | — | 2 | 2 | no | — |
| 221 | ΓL(1,𝔽25) | — | 2 | 2 | no | — |
| 222 | D3×C8 | — | 2 | 2 | no | — |
| 223 | D3×C8 | — | 2 | 2 | no | — |
| 224 | C3×C16 | — | 2 | 2 | no | — |
| 225 | C3⋊C16 | — | 2 | 2 | no | — |
| 226 | 2−1+4 | — | 6 | 4 | no | — |
| 227 | 2−1+4 | — | 6 | 4 | no | — |
| 228 | 2−1+4 | — | 12 | 2 | no | — |
| 229 | 2−1+4 | — | 12 | 2 | no | — |
| 230 | C2×#41 | — | 3 | 1 | no | — |
| 231 | C2×#41 | — | 6 | 2 | no | — |
| 232 | C2×#41 | — | 6 | 1 | no | — |
| 233 | C2×#41 | — | 12 | 2 | no | — |
| 234 | C2×#41 | — | 12 | 1 | no | — |
| 235 | C22×Q8 | — | 2 | 1 | no | — |
| 236 | C22×Q8 | — | 6 | 2 | no | — |
| 237 | C22×Q8 | — | 12 | 1 | no | — |
| 238 | C22×D4 | — | 6 | 1 | no | — |
| 239 | #137 | — | 6 | 4 | no | — |
| 240 | #137 | — | 6 | 8 | no | — |
| 241 | #137 | — | 6 | 4 | no | — |
| 242 | #137 | — | 6 | 8 | no | — |
| 243 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 244 | AGL(1,ℤ/8) | — | 12 | 2 | no | — |
| 245 | #135 | — | 3 | 2 | no | — |
| 246 | #135 | — | 3 | 2 | no | — |
| 247 | #135 | — | 6 | 4 | no | — |
| 248 | #135 | — | 6 | 4 | no | — |
| 249 | #135 | — | 6 | 1 | no | — |
| 250 | #135 | — | 6 | 1 | no | — |
| 251 | C2×Q16 | — | 2 | 1 | no | — |
| 252 | C2×Q16 | — | 2 | 1 | no | — |
| 253 | C2×Q16 | — | 2 | 1 | no | — |
| 254 | C2×Q16 | — | 3 | 1 | no | — |
| 255 | C2×Q16 | — | 6 | 4 | no | — |
| 256 | C2×Q16 | — | 6 | 4 | no | — |
| 257 | C2×Q16 | — | 6 | 2 | no | — |
| 258 | C2×Q16 | D12 | 1 | 2 | yes | — |
| 259 | C2×Q16 | D12 | 1 | 2 | yes | — |
| 260 | C2×Q16 | C22×D3 | 1 | 2 | yes | — |
| 261 | C2×SD16 | — | 6 | 2 | no | — |
| 262 | C2×SD16 | — | 6 | 1 | no | — |
| 263 | C2×SD16 | — | 12 | 1 | no | — |
| 264 | C2×D8 | — | 3 | 1 | no | — |
| 265 | C2×D8 | — | 3 | 2 | no | — |
| 266 | C2×D8 | — | 6 | 1 | no | — |
| 267 | C2×D8 | — | 6 | 1 | no | — |
| 268 | C2×D8 | — | 6 | 1 | no | — |
| 269 | C2×D8 | — | 6 | 1 | no | — |
| 270 | C2×D8 | — | 6 | 1 | no | — |
| 271 | C2×D8 | — | 12 | 1 | no | — |
| 272 | #131 | — | 3 | 2 | no | — |
| 273 | #131 | — | 3 | 2 | no | — |
| 274 | #131 | — | 6 | 1 | no | — |
| 275 | #131 | — | 6 | 1 | no | — |
| 276 | C2×M16 | — | 2 | 1 | no | — |
| 277 | C2×M16 | — | 3 | 1 | no | — |
| 278 | C2×M16 | — | 6 | 1 | no | — |
| 279 | C22×C8 | — | 6 | 1 | no | — |
| 280 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 281 | SD32 | — | 6 | 4 | no | — |
| 282 | SD32 | — | 6 | 8 | no | — |
| 283 | D16 | — | 6 | 4 | no | — |
| 284 | M32 | — | 2 | 1 | no | — |
| 285 | M32 | C22×D3 | 1 | 2 | yes | — |
| 286 | C2×C16 | — | 2 | 1 | no | — |
| 287 | C2×C16 | — | 3 | 2 | no | — |
| 288 | C2×C16 | — | 6 | 1 | no | — |
| 289 | C2×C16 | — | 6 | 1 | no | — |
| 290 | #108 | — | 2 | 1 | no | — |
| 291 | #108 | C22×D3 | 1 | 2 | yes | — |
| 292 | #100 | — | 6 | 4 | no | — |
| 293 | C23×C3 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 294 | C22×D3 | — | 2 | 1 | no | — |
| 295 | C22×D3 | — | 4 | 1 | no | — |
| 296 | C22×D3 | — | 4 | 2 | no | — |
| 297 | C22×D3 | — | 8 | 1 | no | — |
| 298 | C22×D3 | — | 8 | 1 | no | — |
| 299 | C22×D3 | — | 16 | 2 | no | — |
| 300 | C3×Q8 | — | 2 | 4 | no | — |
| 301 | C3×Q8 | — | 4 | 2 | no | — |
| 302 | C3×Q8 | — | 4 | 2 | no | — |
| 303 | C3×Q8 | — | 4 | 2 | no | — |
| 304 | C2×C3×C4 | — | 4 | 2 | no | — |
| 305 | C2×C3×C4 | — | 4 | 2 | no | — |
| 306 | C2×C3×C4 | — | 4 | 2 | no | — |
| 307 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 308 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 309 | C2×C3×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 310 | C2×C3×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 311 | C2×C3×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 312 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 313 | #67 | — | 2 | 2 | no | — |
| 314 | #67 | — | 2 | 2 | no | — |
| 315 | #67 | — | 4 | 2 | no | — |
| 316 | #67 | — | 4 | 2 | no | — |
| 317 | C2×Dic3 | — | 2 | 1 | no | — |
| 318 | C2×Dic3 | — | 4 | 1 | no | — |
| 319 | D12 | — | 2 | 2 | no | — |
| 320 | D12 | — | 2 | 1 | no | — |
| 321 | D12 | — | 4 | 8 | no | — |
| 322 | D12 | — | 4 | 2 | no | — |
| 323 | D12 | — | 4 | 2 | no | — |
| 324 | D12 | — | 4 | 1 | no | — |
| 325 | D12 | — | 8 | 1 | no | — |
| 326 | D12 | — | 8 | 1 | no | — |
| 327 | D12 | C2×D8 | 1 | 2 | yes | — |
| 328 | C4×D3 | — | 2 | 2 | no | — |
| 329 | C4×D3 | — | 2 | 2 | no | — |
| 330 | C4×D3 | — | 4 | 8 | no | — |
| 331 | C4×D3 | — | 4 | 8 | no | — |
| 332 | C4×D3 | — | 4 | 2 | no | — |
| 333 | C4×D3 | — | 4 | 2 | no | — |
| 334 | Dic6 | — | 2 | 1 | no | — |
| 335 | Dic6 | — | 2 | 2 | no | — |
| 336 | Dic6 | — | 4 | 8 | no | — |
| 337 | Dic6 | — | 4 | 1 | no | — |
| 338 | Dic6 | C2×D8 | 1 | 2 | yes | — |
| 339 | C3×C8 | — | 4 | 2 | no | — |
| 340 | C3×C8 | #120 | 1 | 1 | yes | characteristic |
| 341 | C3×C8 | #120 | 1 | 1 | yes | characteristic |
| 342 | C3×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 343 | C3×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 344 | C3⋊C8 | — | 2 | 2 | no | — |
| 345 | C24 | — | 12 | 1 | no | — |
| 346 | #41 | — | 3 | 2 | no | — |
| 347 | #41 | — | 3 | 2 | no | — |
| 348 | #41 | — | 6 | 1 | no | — |
| 349 | #41 | — | 6 | 1 | no | — |
| 350 | #41 | — | 6 | 8 | no | — |
| 351 | #41 | — | 6 | 2 | no | — |
| 352 | #41 | — | 6 | 2 | no | — |
| 353 | #41 | — | 12 | 8 | no | — |
| 354 | #41 | — | 12 | 8 | no | — |
| 355 | #41 | — | 12 | 4 | no | — |
| 356 | #41 | — | 12 | 4 | no | — |
| 357 | #41 | — | 12 | 4 | no | — |
| 358 | #41 | — | 12 | 1 | no | — |
| 359 | #41 | — | 12 | 1 | no | — |
| 360 | C2×Q8 | — | 2 | 2 | no | — |
| 361 | C2×Q8 | — | 2 | 2 | no | — |
| 362 | C2×Q8 | — | 2 | 2 | no | — |
| 363 | C2×Q8 | — | 3 | 1 | no | — |
| 364 | C2×Q8 | — | 4 | 1 | no | — |
| 365 | C2×Q8 | — | 4 | 1 | no | — |
| 366 | C2×Q8 | — | 4 | 1 | no | — |
| 367 | C2×Q8 | — | 6 | 8 | no | — |
| 368 | C2×Q8 | — | 6 | 1 | no | — |
| 369 | C2×Q8 | — | 12 | 2 | no | — |
| 370 | C2×Q8 | — | 12 | 4 | no | — |
| 371 | C2×Q8 | — | 12 | 4 | no | — |
| 372 | C2×Q8 | — | 12 | 4 | no | — |
| 373 | C2×D4 | — | 3 | 1 | no | — |
| 374 | C2×D4 | — | 6 | 1 | no | — |
| 375 | C2×D4 | — | 6 | 1 | no | — |
| 376 | C2×D4 | — | 6 | 2 | no | — |
| 377 | C2×D4 | — | 12 | 2 | no | — |
| 378 | C2×D4 | — | 12 | 1 | no | — |
| 379 | C2×D4 | — | 12 | 1 | no | — |
| 380 | C2×D4 | — | 12 | 1 | no | — |
| 381 | C2×D4 | — | 12 | 1 | no | — |
| 382 | C2×D4 | — | 12 | 1 | no | — |
| 383 | C2×D4 | — | 12 | 1 | no | — |
| 384 | C22×C4 | — | 4 | 1 | no | — |
| 385 | C22×C4 | — | 6 | 1 | no | — |
| 386 | C22×C4 | — | 12 | 2 | no | — |
| 387 | C22×C4 | — | 12 | 2 | no | — |
| 388 | C22×C4 | — | 12 | 1 | no | — |
| 389 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 390 | Q16 | — | 2 | 2 | no | — |
| 391 | Q16 | — | 2 | 2 | no | — |
| 392 | Q16 | — | 2 | 2 | no | — |
| 393 | Q16 | — | 3 | 2 | no | — |
| 394 | Q16 | — | 6 | 8 | no | — |
| 395 | Q16 | — | 6 | 1 | no | — |
| 396 | Q16 | C2×D12 | 1 | 4 | yes | — |
| 397 | SD16 | — | 6 | 8 | no | — |
| 398 | SD16 | — | 6 | 2 | no | — |
| 399 | SD16 | — | 6 | 2 | no | — |
| 400 | SD16 | — | 12 | 4 | no | — |
| 401 | D8 | — | 3 | 2 | no | — |
| 402 | D8 | — | 6 | 1 | no | — |
| 403 | D8 | — | 6 | 2 | no | — |
| 404 | D8 | — | 6 | 2 | no | — |
| 405 | D8 | — | 12 | 4 | no | — |
| 406 | D8 | — | 12 | 1 | no | — |
| 407 | D8 | — | 12 | 1 | no | — |
| 408 | M16 | — | 2 | 2 | no | — |
| 409 | M16 | — | 3 | 2 | no | — |
| 410 | M16 | — | 4 | 1 | no | — |
| 411 | M16 | — | 6 | 1 | no | — |
| 412 | M16 | — | 6 | 2 | no | — |
| 413 | M16 | — | 6 | 2 | no | — |
| 414 | C2×C8 | — | 4 | 1 | no | — |
| 415 | C2×C8 | — | 6 | 1 | no | — |
| 416 | C2×C8 | — | 6 | 2 | no | — |
| 417 | C2×C8 | — | 6 | 2 | no | — |
| 418 | C2×C8 | C2×D12 | 1 | 1 | yes | characteristic |
| 419 | C2×C8 | C2×D12 | 1 | 1 | yes | characteristic |
| 420 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 421 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 422 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 423 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 424 | C16 | — | 2 | 2 | no | — |
| 425 | C16 | — | 6 | 2 | no | — |
| 426 | C22×C3 | — | 2 | 2 | no | — |
| 427 | C22×C3 | #447 | 1 | 1 | yes | characteristic |
| 428 | C22×C3 | #447 | 1 | 1 | yes | characteristic |
| 429 | C22×C3 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 430 | C2×D3 | — | 2 | 2 | no | — |
| 431 | C2×D3 | — | 4 | 2 | no | — |
| 432 | C2×D3 | — | 4 | 2 | no | — |
| 433 | C2×D3 | — | 8 | 2 | no | — |
| 434 | C2×D3 | — | 8 | 2 | no | — |
| 435 | C2×D3 | — | 16 | 2 | no | — |
| 436 | C2×D3 | — | 16 | 2 | no | — |
| 437 | C2×D3 | — | 16 | 2 | no | — |
| 438 | C3×C4 | — | 4 | 4 | no | — |
| 439 | C3×C4 | #447 | 1 | 1 | yes | characteristic |
| 440 | C3×C4 | #447 | 1 | 1 | yes | characteristic |
| 441 | C3×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 442 | C3×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 443 | Dic3 | — | 2 | 2 | no | — |
| 444 | Dic3 | — | 4 | 2 | no | — |
| 445 | C23 | — | 6 | 1 | no | — |
| 446 | C23 | — | 12 | 1 | no | — |
| 447 | C23 | — | 12 | 2 | no | — |
| 448 | C23 | — | 24 | 1 | no | — |
| 449 | C23 | — | 24 | 1 | no | — |
| 450 | C23 | — | 48 | 2 | no | — |
| 451 | C23 | #914 | 1 | 1 | yes | characteristic |
| 452 | Q8 | — | 2 | 4 | no | — |
| 453 | Q8 | — | 3 | 2 | no | — |
| 454 | Q8 | — | 4 | 2 | no | — |
| 455 | Q8 | — | 4 | 2 | no | — |
| 456 | Q8 | — | 4 | 2 | no | — |
| 457 | Q8 | — | 6 | 1 | no | — |
| 458 | Q8 | — | 6 | 2 | no | — |
| 459 | Q8 | — | 12 | 8 | no | — |
| 460 | Q8 | — | 12 | 1 | no | — |
| 461 | D4 | — | 3 | 2 | no | — |
| 462 | D4 | — | 6 | 2 | no | — |
| 463 | D4 | — | 6 | 2 | no | — |
| 464 | D4 | — | 6 | 2 | no | — |
| 465 | D4 | — | 6 | 1 | no | — |
| 466 | D4 | — | 12 | 8 | no | — |
| 467 | D4 | — | 12 | 2 | no | — |
| 468 | D4 | — | 12 | 2 | no | — |
| 469 | D4 | — | 12 | 2 | no | — |
| 470 | D4 | — | 12 | 2 | no | — |
| 471 | D4 | — | 12 | 1 | no | — |
| 472 | D4 | — | 24 | 1 | no | — |
| 473 | D4 | — | 24 | 1 | no | — |
| 474 | C2×C4 | — | 4 | 2 | no | — |
| 475 | C2×C4 | — | 4 | 2 | no | — |
| 476 | C2×C4 | — | 4 | 2 | no | — |
| 477 | C2×C4 | — | 6 | 1 | no | — |
| 478 | C2×C4 | — | 6 | 2 | no | — |
| 479 | C2×C4 | — | 6 | 2 | no | — |
| 480 | C2×C4 | — | 12 | 8 | no | — |
| 481 | C2×C4 | — | 12 | 8 | no | — |
| 482 | C2×C4 | — | 12 | 1 | no | — |
| 483 | C2×C4 | — | 12 | 2 | no | — |
| 484 | C2×C4 | — | 12 | 2 | no | — |
| 485 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 486 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 487 | C2×C4 | D3×D8 | 1 | 1 | yes | characteristic |
| 488 | C2×C4 | D3×D8 | 1 | 1 | yes | characteristic |
| 489 | C2×C4 | #914 | 1 | 1 | yes | characteristic |
| 490 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 491 | C8 | — | 4 | 2 | no | — |
| 492 | C8 | — | 6 | 2 | no | — |
| 493 | C8 | #882 | 1 | 1 | yes | characteristic |
| 494 | C8 | #882 | 1 | 1 | yes | characteristic |
| 495 | C8 | C22×D12 | 1 | 1 | yes | characteristic |
| 496 | C8 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 497 | C2×C3 | — | 2 | 1 | no | — |
| 498 | C2×C3 | — | 2 | 1 | no | — |
| 499 | C2×C3 | #2193 | 1 | 2 | yes | complemented |
| 500 | C2×C3 | C2×#447 | 1 | 1 | yes | characteristic |
| 501 | D3 | — | 4 | 2 | no | — |
| 502 | D3 | — | 8 | 2 | no | — |
| 503 | D3 | — | 16 | 2 | no | — |
| 504 | C22 | — | 2 | 2 | no | — |
| 505 | C22 | — | 6 | 2 | no | — |
| 506 | C22 | — | 12 | 2 | no | — |
| 507 | C22 | — | 12 | 2 | no | — |
| 508 | C22 | — | 24 | 2 | no | — |
| 509 | C22 | — | 24 | 2 | no | — |
| 510 | C22 | — | 48 | 2 | no | — |
| 511 | C22 | — | 48 | 2 | no | — |
| 512 | C22 | — | 48 | 2 | no | — |
| 513 | C22 | #4773 | 1 | 1 | yes | characteristic |
| 514 | C22 | #4773 | 1 | 1 | yes | characteristic |
| 515 | C22 | C2×#914 | 1 | 1 | yes | characteristic |
| 516 | C4 | — | 4 | 4 | no | — |
| 517 | C4 | — | 6 | 2 | no | — |
| 518 | C4 | — | 12 | 2 | no | — |
| 519 | C4 | #4773 | 1 | 1 | yes | characteristic |
| 520 | C4 | #4773 | 1 | 1 | yes | characteristic |
| 521 | C4 | C2×#882 | 1 | 1 | yes | characteristic |
| 522 | C4 | C2×D3×D8 | 1 | 1 | yes | characteristic |
| 523 | C3 | C2×#2193 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 524 | C2 | — | 2 | 1 | no | — |
| 525 | C2 | — | 2 | 1 | no | — |
| 526 | C2 | — | 12 | 2 | no | — |
| 527 | C2 | — | 24 | 2 | no | — |
| 528 | C2 | — | 48 | 2 | no | — |
| 529 | C2 | #69268 | 1 | 2 | yes | direct product factor |
| 530 | C2 | C2×#4773 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#5766 | C2 | semidirect |
| 2. C22×#828 | C2 | semidirect |
| 3. C2×#4908 | C2 | semidirect |
| 4. C2×#4897 | C2 | semidirect |
| 5. C2×C3×#362 | C2 | semidirect |
| 6. C2×#4515 | C2 | semidirect |
| 7. C2×#4497 | C2 | semidirect |
| 8. #69268 | C2 | direct (N × H) |
| 16. #5766 | C22 | semidirect |
| 28. C2×#828 | C22 | semidirect |
| 32. #4908 | C22 | semidirect |
| 36. #4897 | C22 | semidirect |
| 37. C3×#362 | C22 | semidirect |
| 38. #4515 | C22 | semidirect |
| 39. #4497 | C22 | semidirect |
| 45. C2×#362 | D3 | semidirect |
| 142. #362 | C2×D3 | semidirect |
| 499. C2×C3 | #2193 | semidirect |
| 523. C3 | C2×#2193 | semidirect |
| 529. C2 | #69268 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5766 | 2 |
| C22×#828 | 2 |
| C2×#4908 | 2 |
| C2×#4897 | 2 |
| C2×C3×#362 | 2 |
| C2×#4515 | 2 |
| C2×#4497 | 2 |
| #69268 | 2 |
| C2×#2193 | 3 |