Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2630 conjugacy classes of subgroups.
The subgroup lattice has 522 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×#3585 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #87298 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #87296 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#5835 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #84100 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #84002 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #84001 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #83943 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | C2×#5199 | C2 | 1 | 6 | yes | maximal, complemented |
| 10 | #83813 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #83810 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #60471 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C3×#585 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C3×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#1009 | C22 | 1 | 1 | yes | characteristic |
| 16 | C3×#577 | — | 2 | 4 | no | — |
| 17 | C3×#576 | — | 2 | 4 | no | — |
| 18 | C3×#575 | C22 | 1 | 6 | yes | complemented |
| 19 | C2×C3×AGL(1,ℤ/8) | C22 | 1 | 6 | yes | complemented |
| 20 | C3×#568 | C22 | 1 | 1 | yes | characteristic |
| 21 | #5837 | — | 2 | 4 | no | — |
| 22 | #5835 | — | 2 | 4 | no | — |
| 23 | #5835 | — | 2 | 4 | no | — |
| 24 | #5835 | — | 2 | 4 | no | — |
| 25 | #5822 | C22 | 1 | 6 | yes | complemented |
| 26 | C2×#950 | C22 | 1 | 3 | yes | complemented |
| 27 | C2×#949 | C22 | 1 | 6 | yes | complemented |
| 28 | C2×#949 | C22 | 1 | 3 | yes | complemented |
| 29 | #5819 | — | 2 | 4 | no | — |
| 30 | #5819 | C22 | 1 | 1 | yes | characteristic |
| 31 | #5819 | C22 | 1 | 1 | yes | characteristic |
| 32 | #5819 | C22 | 1 | 6 | yes | complemented |
| 33 | C2×#948 | — | 2 | 4 | no | — |
| 34 | C2×#948 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×#948 | C22 | 1 | 6 | yes | complemented |
| 36 | C2×#932 | C22 | 1 | 3 | yes | complemented |
| 37 | C22×#213 | C22 | 1 | 3 | yes | complemented |
| 38 | #5237 | C22 | 1 | 6 | yes | complemented |
| 39 | C2×#833 | C22 | 1 | 6 | yes | complemented |
| 40 | #5204 | C22 | 1 | 4 | yes | complemented |
| 41 | #5203 | C22 | 1 | 12 | yes | complemented |
| 42 | #5200 | C22 | 1 | 12 | yes | complemented |
| 43 | #5199 | C22 | 1 | 12 | yes | complemented |
| 44 | #5199 | C22 | 1 | 24 | yes | complemented |
| 45 | #5132 | C22 | 1 | 6 | yes | complemented |
| 46 | C2×#823 | C22 | 1 | 6 | yes | complemented |
| 47 | #5124 | C22 | 1 | 6 | yes | complemented |
| 48 | C2×#822 | C22 | 1 | 6 | yes | complemented |
| 49 | #3585 | — | 3 | 1 | no | — |
| 50 | #3585 | D3 | 1 | 1 | yes | characteristic, complemented |
| 51 | C2×#576 | — | 3 | 1 | no | — |
| 52 | #3573 | — | 3 | 1 | no | — |
| 53 | #3068 | — | 3 | 6 | no | — |
| 54 | #3068 | — | 3 | 6 | no | — |
| 55 | #3067 | — | 3 | 6 | no | — |
| 56 | C2×#472 | — | 3 | 6 | no | — |
| 57 | #2916 | — | 3 | 1 | no | — |
| 58 | #2888 | — | 3 | 1 | no | — |
| 59 | #2888 | — | 3 | 1 | no | — |
| 60 | C3×2−1+4 | — | 2 | 1 | no | — |
| 61 | C3×2−1+4 | D4 | 1 | 4 | yes | — |
| 62 | C3×H(5,𝔽2) | — | 2 | 3 | no | — |
| 63 | C3×H(5,𝔽2) | — | 2 | 4 | no | — |
| 64 | C3×H(5,𝔽2) | — | 2 | 4 | no | — |
| 65 | C3×H(5,𝔽2) | D4 | 1 | 4 | yes | — |
| 66 | C2×C3×#41 | — | 2 | 4 | no | — |
| 67 | C2×C3×#41 | — | 2 | 1 | no | — |
| 68 | C2×C3×#41 | C23 | 1 | 6 | yes | — |
| 69 | C2×C3×#41 | C23 | 1 | 3 | yes | — |
| 70 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 71 | C22×C3×D4 | — | 2 | 3 | no | — |
| 72 | C22×C3×D4 | C23 | 1 | 3 | yes | — |
| 73 | #1009 | — | 2 | 4 | no | — |
| 74 | #1009 | — | 2 | 4 | no | — |
| 75 | C2×#239 | — | 2 | 1 | no | — |
| 76 | C2×D3×D4 | — | 2 | 3 | no | — |
| 77 | C2×#235 | C23 | 1 | 3 | yes | — |
| 78 | C22×D12 | C23 | 1 | 3 | yes | — |
| 79 | C3×#137 | — | 2 | 6 | no | — |
| 80 | C3×#137 | C23 | 1 | 4 | yes | — |
| 81 | C3×AGL(1,ℤ/8) | — | 2 | 12 | no | — |
| 82 | C3×AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 83 | C3×AGL(1,ℤ/8) | C23 | 1 | 12 | yes | — |
| 84 | C3×#135 | — | 2 | 12 | no | — |
| 85 | C2×C3×SD16 | — | 2 | 6 | no | — |
| 86 | C2×C3×D8 | — | 2 | 6 | no | — |
| 87 | C3×#131 | — | 2 | 4 | no | — |
| 88 | C2×C3×M16 | C23 | 1 | 6 | yes | — |
| 89 | #951 | C23 | 1 | 4 | yes | — |
| 90 | #950 | — | 2 | 12 | no | — |
| 91 | #950 | — | 2 | 6 | no | — |
| 92 | #950 | — | 2 | 6 | no | — |
| 93 | #949 | — | 2 | 12 | no | — |
| 94 | #949 | — | 2 | 12 | no | — |
| 95 | #949 | C23 | 1 | 12 | yes | — |
| 96 | #948 | — | 2 | 4 | no | — |
| 97 | #948 | — | 2 | 4 | no | — |
| 98 | #948 | — | 2 | 12 | no | — |
| 99 | #948 | — | 2 | 6 | no | — |
| 100 | #948 | — | 2 | 6 | no | — |
| 101 | #948 | D4 | 1 | 4 | yes | — |
| 102 | #948 | D4 | 1 | 4 | yes | — |
| 103 | #948 | C23 | 1 | 4 | yes | — |
| 104 | #948 | C23 | 1 | 12 | yes | — |
| 105 | C2×#216 | C23 | 1 | 1 | yes | characteristic |
| 106 | #942 | — | 2 | 6 | no | — |
| 107 | C2×#215 | — | 2 | 6 | no | — |
| 108 | C2×#215 | C23 | 1 | 3 | yes | — |
| 109 | C2×#214 | C23 | 1 | 3 | yes | — |
| 110 | #932 | — | 2 | 6 | no | — |
| 111 | #932 | — | 2 | 12 | no | — |
| 112 | C2×#213 | — | 2 | 6 | no | — |
| 113 | C2×#213 | — | 2 | 6 | no | — |
| 114 | C2×#213 | — | 2 | 6 | no | — |
| 115 | C2×#213 | C23 | 1 | 3 | yes | — |
| 116 | C2×#213 | C23 | 1 | 6 | yes | — |
| 117 | C2×#208 | — | 2 | 12 | no | — |
| 118 | C2×#208 | — | 2 | 6 | no | — |
| 119 | C2×#208 | C23 | 1 | 6 | yes | — |
| 120 | C2×#208 | C23 | 1 | 6 | yes | — |
| 121 | C2×#208 | C23 | 1 | 3 | yes | — |
| 122 | C22×C3⋊C8 | — | 2 | 6 | no | — |
| 123 | C22×C3⋊C8 | C23 | 1 | 3 | yes | — |
| 124 | #836 | C23 | 1 | 4 | yes | — |
| 125 | #833 | C23 | 1 | 12 | yes | — |
| 126 | #824 | C23 | 1 | 4 | yes | — |
| 127 | #823 | C23 | 1 | 12 | yes | — |
| 128 | #822 | C23 | 1 | 4 | yes | — |
| 129 | #822 | C23 | 1 | 12 | yes | — |
| 130 | #585 | C2×D3 | 1 | 1 | yes | characteristic |
| 131 | C2×H(5,𝔽2) | — | 3 | 1 | no | — |
| 132 | C2×H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 133 | #577 | — | 2 | 4 | no | — |
| 134 | #577 | — | 6 | 4 | no | — |
| 135 | #576 | — | 2 | 4 | no | — |
| 136 | #576 | — | 6 | 4 | no | — |
| 137 | #576 | — | 6 | 4 | no | — |
| 138 | #576 | — | 6 | 4 | no | — |
| 139 | #575 | — | 3 | 6 | no | — |
| 140 | #575 | C2×D3 | 1 | 6 | yes | complemented |
| 141 | C2×AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 142 | C2×AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 143 | C2×AGL(1,ℤ/8) | — | 3 | 6 | no | — |
| 144 | C2×AGL(1,ℤ/8) | C2×D3 | 1 | 6 | yes | complemented |
| 145 | C2×#135 | — | 3 | 3 | no | — |
| 146 | C22×D8 | — | 3 | 3 | no | — |
| 147 | #568 | — | 3 | 1 | no | — |
| 148 | #568 | — | 3 | 1 | no | — |
| 149 | #568 | — | 3 | 6 | no | — |
| 150 | #568 | — | 6 | 4 | no | — |
| 151 | #568 | C2×D3 | 1 | 1 | yes | characteristic |
| 152 | C2×#131 | — | 3 | 1 | no | — |
| 153 | C2×#131 | — | 3 | 6 | no | — |
| 154 | C2×#131 | — | 6 | 4 | no | — |
| 155 | #473 | — | 3 | 4 | no | — |
| 156 | #472 | — | 3 | 12 | no | — |
| 157 | #472 | — | 3 | 24 | no | — |
| 158 | #471 | — | 3 | 12 | no | — |
| 159 | #471 | — | 3 | 12 | no | — |
| 160 | #430 | — | 3 | 6 | no | — |
| 161 | C2×#108 | — | 3 | 6 | no | — |
| 162 | #413 | — | 3 | 6 | no | — |
| 163 | #413 | — | 3 | 6 | no | — |
| 164 | C2×#100 | — | 3 | 6 | no | — |
| 165 | C2×#100 | — | 3 | 6 | no | — |
| 166 | C24×C3 | — | 2 | 3 | no | — |
| 167 | C23×D3 | — | 2 | 3 | no | — |
| 168 | C3×#41 | — | 2 | 4 | no | — |
| 169 | C3×#41 | — | 2 | 12 | no | — |
| 170 | C3×#41 | — | 2 | 6 | no | — |
| 171 | C3×#41 | — | 2 | 6 | no | — |
| 172 | C3×#41 | — | 2 | 6 | no | — |
| 173 | C3×#41 | — | 2 | 6 | no | — |
| 174 | C3×#41 | — | 4 | 4 | no | — |
| 175 | C3×#41 | C2×D4 | 1 | 4 | yes | — |
| 176 | C3×#41 | C2×D4 | 1 | 12 | yes | — |
| 177 | C3×#41 | C2×D4 | 1 | 4 | yes | — |
| 178 | C3×#41 | C24 | 1 | 4 | yes | — |
| 179 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 180 | C2×C3×Q8 | C2×D4 | 1 | 6 | yes | — |
| 181 | C2×C3×Q8 | #41 | 1 | 1 | yes | characteristic |
| 182 | C2×C3×Q8 | C24 | 1 | 1 | yes | characteristic |
| 183 | C2×C3×D4 | — | 2 | 6 | no | — |
| 184 | C2×C3×D4 | — | 2 | 12 | no | — |
| 185 | C2×C3×D4 | — | 2 | 3 | no | — |
| 186 | C2×C3×D4 | — | 2 | 6 | no | — |
| 187 | C2×C3×D4 | — | 2 | 6 | no | — |
| 188 | C2×C3×D4 | — | 2 | 3 | no | — |
| 189 | C2×C3×D4 | — | 4 | 12 | no | — |
| 190 | C2×C3×D4 | C2×D4 | 1 | 6 | yes | — |
| 191 | C2×C3×D4 | #41 | 1 | 3 | yes | — |
| 192 | C2×C3×D4 | C24 | 1 | 3 | yes | — |
| 193 | C22×C3×C4 | — | 2 | 6 | no | — |
| 194 | C22×C3×C4 | — | 2 | 3 | no | — |
| 195 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 196 | C2×#67 | — | 2 | 3 | no | — |
| 197 | #239 | — | 4 | 4 | no | — |
| 198 | D3×D4 | — | 4 | 12 | no | — |
| 199 | #235 | — | 2 | 6 | no | — |
| 200 | #235 | — | 2 | 6 | no | — |
| 201 | C2×D12 | — | 2 | 6 | no | — |
| 202 | C2×D12 | — | 2 | 6 | no | — |
| 203 | C2×D12 | — | 2 | 3 | no | — |
| 204 | C2×D12 | C24 | 1 | 3 | yes | — |
| 205 | C2×C4×D3 | — | 2 | 3 | no | — |
| 206 | C2×Dic6 | C24 | 1 | 1 | yes | characteristic |
| 207 | C3×Q16 | — | 2 | 4 | no | — |
| 208 | C3×SD16 | — | 2 | 12 | no | — |
| 209 | C3×SD16 | — | 2 | 4 | no | — |
| 210 | C3×D8 | — | 2 | 12 | no | — |
| 211 | C3×M16 | — | 2 | 6 | no | — |
| 212 | C3×M16 | C24 | 1 | 4 | yes | — |
| 213 | C2×C3×C8 | — | 2 | 6 | no | — |
| 214 | #216 | — | 2 | 4 | no | — |
| 215 | #216 | — | 2 | 1 | no | — |
| 216 | #216 | — | 2 | 1 | no | — |
| 217 | #215 | — | 2 | 12 | no | — |
| 218 | #215 | — | 2 | 6 | no | — |
| 219 | #214 | — | 2 | 4 | no | — |
| 220 | #214 | — | 2 | 6 | no | — |
| 221 | #213 | — | 2 | 12 | no | — |
| 222 | #213 | — | 2 | 3 | no | — |
| 223 | #213 | — | 2 | 3 | no | — |
| 224 | #213 | — | 2 | 12 | no | — |
| 225 | #208 | — | 2 | 6 | no | — |
| 226 | #208 | — | 2 | 6 | no | — |
| 227 | #208 | — | 2 | 12 | no | — |
| 228 | #208 | — | 2 | 4 | no | — |
| 229 | #208 | C2×D4 | 1 | 12 | yes | — |
| 230 | #208 | C24 | 1 | 4 | yes | — |
| 231 | #208 | C24 | 1 | 4 | yes | — |
| 232 | C2×C3⋊C8 | — | 2 | 6 | no | — |
| 233 | C2×C3⋊C8 | — | 2 | 6 | no | — |
| 234 | C2×C3⋊C8 | — | 2 | 4 | no | — |
| 235 | C2×C3⋊C8 | — | 2 | 12 | no | — |
| 236 | C2×C3⋊C8 | C2×D4 | 1 | 6 | yes | — |
| 237 | C2×C3⋊C8 | C2×D4 | 1 | 6 | yes | — |
| 238 | C2×C3⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 239 | C2×C3⋊C8 | C24 | 1 | 3 | yes | — |
| 240 | 2−1+4 | — | 2 | 1 | no | — |
| 241 | 2−1+4 | #67 | 1 | 4 | yes | — |
| 242 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 243 | H(5,𝔽2) | — | 2 | 4 | no | — |
| 244 | H(5,𝔽2) | — | 2 | 4 | no | — |
| 245 | H(5,𝔽2) | — | 6 | 4 | no | — |
| 246 | H(5,𝔽2) | — | 6 | 4 | no | — |
| 247 | H(5,𝔽2) | #67 | 1 | 4 | yes | — |
| 248 | C2×#41 | — | 2 | 4 | no | — |
| 249 | C2×#41 | — | 2 | 1 | no | — |
| 250 | C2×#41 | — | 3 | 3 | no | — |
| 251 | C2×#41 | — | 6 | 1 | no | — |
| 252 | C2×#41 | C22×D3 | 1 | 6 | yes | — |
| 253 | C2×#41 | C22×D3 | 1 | 3 | yes | — |
| 254 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 255 | C22×D4 | — | 2 | 3 | no | — |
| 256 | C22×D4 | — | 3 | 3 | no | — |
| 257 | C22×D4 | — | 6 | 3 | no | — |
| 258 | C22×D4 | C22×D3 | 1 | 3 | yes | — |
| 259 | #137 | — | 2 | 6 | no | — |
| 260 | #137 | — | 3 | 4 | no | — |
| 261 | #137 | — | 6 | 6 | no | — |
| 262 | #137 | C22×D3 | 1 | 4 | yes | — |
| 263 | AGL(1,ℤ/8) | — | 2 | 12 | no | — |
| 264 | AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 265 | AGL(1,ℤ/8) | — | 3 | 12 | no | — |
| 266 | AGL(1,ℤ/8) | — | 6 | 12 | no | — |
| 267 | AGL(1,ℤ/8) | — | 6 | 12 | no | — |
| 268 | AGL(1,ℤ/8) | — | 6 | 12 | no | — |
| 269 | AGL(1,ℤ/8) | — | 6 | 6 | no | — |
| 270 | AGL(1,ℤ/8) | C22×D3 | 1 | 12 | yes | — |
| 271 | #135 | — | 2 | 12 | no | — |
| 272 | #135 | — | 6 | 6 | no | — |
| 273 | #135 | — | 6 | 6 | no | — |
| 274 | #135 | — | 6 | 12 | no | — |
| 275 | C2×Q16 | — | 3 | 1 | no | — |
| 276 | C2×SD16 | — | 2 | 6 | no | — |
| 277 | C2×SD16 | — | 3 | 3 | no | — |
| 278 | C2×SD16 | — | 3 | 3 | no | — |
| 279 | C2×SD16 | — | 6 | 6 | no | — |
| 280 | C2×D8 | — | 2 | 6 | no | — |
| 281 | C2×D8 | — | 3 | 3 | no | — |
| 282 | C2×D8 | — | 3 | 6 | no | — |
| 283 | C2×D8 | — | 6 | 6 | no | — |
| 284 | C2×D8 | — | 6 | 6 | no | — |
| 285 | C2×D8 | — | 6 | 6 | no | — |
| 286 | #131 | — | 2 | 4 | no | — |
| 287 | #131 | — | 3 | 4 | no | — |
| 288 | #131 | — | 3 | 4 | no | — |
| 289 | #131 | — | 3 | 4 | no | — |
| 290 | #131 | — | 3 | 12 | no | — |
| 291 | #131 | — | 6 | 6 | no | — |
| 292 | #131 | — | 6 | 6 | no | — |
| 293 | #131 | — | 6 | 12 | no | — |
| 294 | #131 | — | 6 | 4 | no | — |
| 295 | #131 | — | 6 | 4 | no | — |
| 296 | C2×M16 | — | 3 | 3 | no | — |
| 297 | C2×M16 | — | 3 | 6 | no | — |
| 298 | C2×M16 | — | 3 | 6 | no | — |
| 299 | C2×M16 | — | 6 | 6 | no | — |
| 300 | C2×M16 | — | 6 | 12 | no | — |
| 301 | C2×M16 | C22×D3 | 1 | 6 | yes | — |
| 302 | C22×C8 | — | 3 | 3 | no | — |
| 303 | C22×C8 | — | 6 | 6 | no | — |
| 304 | #108 | — | 3 | 4 | no | — |
| 305 | #108 | — | 3 | 12 | no | — |
| 306 | #101 | — | 3 | 4 | no | — |
| 307 | #101 | — | 3 | 4 | no | — |
| 308 | #100 | — | 3 | 12 | no | — |
| 309 | #100 | — | 3 | 12 | no | — |
| 310 | C23×C3 | — | 2 | 6 | no | — |
| 311 | C23×C3 | — | 2 | 3 | no | — |
| 312 | C23×C3 | — | 4 | 6 | no | — |
| 313 | C23×C3 | — | 16 | 3 | no | — |
| 314 | C23×C3 | C2×#41 | 1 | 3 | yes | — |
| 315 | C22×D3 | — | 2 | 3 | no | — |
| 316 | C22×D3 | — | 4 | 6 | no | — |
| 317 | C22×D3 | — | 16 | 3 | no | — |
| 318 | C3×Q8 | — | 2 | 6 | no | — |
| 319 | C3×Q8 | — | 2 | 1 | no | — |
| 320 | C3×Q8 | — | 2 | 1 | no | — |
| 321 | C3×Q8 | #121 | 1 | 4 | yes | — |
| 322 | C3×Q8 | C22×D4 | 1 | 4 | yes | — |
| 323 | C3×D4 | — | 2 | 12 | no | — |
| 324 | C3×D4 | — | 2 | 4 | no | — |
| 325 | C3×D4 | — | 2 | 6 | no | — |
| 326 | C3×D4 | — | 2 | 3 | no | — |
| 327 | C3×D4 | — | 2 | 3 | no | — |
| 328 | C3×D4 | — | 4 | 6 | no | — |
| 329 | C3×D4 | — | 4 | 6 | no | — |
| 330 | C3×D4 | #121 | 1 | 12 | yes | — |
| 331 | C3×D4 | C22×D4 | 1 | 4 | yes | — |
| 332 | C2×C3×C4 | — | 2 | 6 | no | — |
| 333 | C2×C3×C4 | — | 2 | 12 | no | — |
| 334 | C2×C3×C4 | — | 2 | 4 | no | — |
| 335 | C2×C3×C4 | — | 2 | 1 | no | — |
| 336 | C2×C3×C4 | — | 4 | 6 | no | — |
| 337 | C2×C3×C4 | C22×D4 | 1 | 6 | yes | — |
| 338 | C2×C3×C4 | C22×D4 | 1 | 6 | yes | — |
| 339 | C2×C3×C4 | C2×#41 | 1 | 3 | yes | — |
| 340 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 341 | #67 | — | 4 | 6 | no | — |
| 342 | C2×Dic3 | — | 2 | 1 | no | — |
| 343 | D12 | — | 2 | 3 | no | — |
| 344 | D12 | — | 2 | 3 | no | — |
| 345 | D12 | — | 4 | 6 | no | — |
| 346 | C4×D3 | — | 4 | 6 | no | — |
| 347 | Dic6 | — | 2 | 1 | no | — |
| 348 | Dic6 | — | 2 | 1 | no | — |
| 349 | C3×C8 | — | 2 | 4 | no | — |
| 350 | C3⋊C8 | — | 2 | 4 | no | — |
| 351 | C3⋊C8 | — | 2 | 4 | no | — |
| 352 | C3⋊C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 353 | C3⋊C8 | C22×D4 | 1 | 6 | yes | — |
| 354 | C3⋊C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 355 | C24 | — | 2 | 3 | no | — |
| 356 | C24 | — | 6 | 3 | no | — |
| 357 | #41 | — | 2 | 4 | no | — |
| 358 | #41 | — | 2 | 12 | no | — |
| 359 | #41 | — | 2 | 6 | no | — |
| 360 | #41 | — | 2 | 6 | no | — |
| 361 | #41 | — | 2 | 6 | no | — |
| 362 | #41 | — | 2 | 6 | no | — |
| 363 | #41 | — | 4 | 4 | no | — |
| 364 | #41 | — | 6 | 6 | no | — |
| 365 | #41 | — | 6 | 6 | no | — |
| 366 | #41 | — | 12 | 4 | no | — |
| 367 | #41 | D3×D4 | 1 | 4 | yes | — |
| 368 | #41 | C2×#67 | 1 | 12 | yes | — |
| 369 | #41 | C2×#67 | 1 | 4 | yes | — |
| 370 | #41 | C23×D3 | 1 | 4 | yes | — |
| 371 | C2×Q8 | — | 2 | 4 | no | — |
| 372 | C2×Q8 | — | 3 | 1 | no | — |
| 373 | C2×Q8 | #237 | 1 | 1 | yes | characteristic |
| 374 | C2×Q8 | C2×#67 | 1 | 6 | yes | — |
| 375 | C2×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 376 | C2×D4 | — | 2 | 6 | no | — |
| 377 | C2×D4 | — | 2 | 12 | no | — |
| 378 | C2×D4 | — | 2 | 3 | no | — |
| 379 | C2×D4 | — | 2 | 6 | no | — |
| 380 | C2×D4 | — | 2 | 3 | no | — |
| 381 | C2×D4 | — | 2 | 6 | no | — |
| 382 | C2×D4 | — | 3 | 3 | no | — |
| 383 | C2×D4 | — | 4 | 12 | no | — |
| 384 | C2×D4 | — | 6 | 3 | no | — |
| 385 | C2×D4 | — | 6 | 6 | no | — |
| 386 | C2×D4 | — | 6 | 3 | no | — |
| 387 | C2×D4 | — | 6 | 6 | no | — |
| 388 | C2×D4 | — | 12 | 12 | no | — |
| 389 | C2×D4 | #237 | 1 | 3 | yes | — |
| 390 | C2×D4 | C2×#67 | 1 | 6 | yes | — |
| 391 | C2×D4 | C23×D3 | 1 | 3 | yes | — |
| 392 | C22×C4 | — | 2 | 6 | no | — |
| 393 | C22×C4 | — | 2 | 3 | no | — |
| 394 | C22×C4 | — | 6 | 3 | no | — |
| 395 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 396 | Q16 | — | 2 | 4 | no | — |
| 397 | Q16 | — | 6 | 1 | no | — |
| 398 | Q16 | — | 6 | 1 | no | — |
| 399 | Q16 | — | 6 | 4 | no | — |
| 400 | SD16 | — | 2 | 12 | no | — |
| 401 | SD16 | — | 2 | 4 | no | — |
| 402 | SD16 | — | 6 | 6 | no | — |
| 403 | SD16 | — | 6 | 6 | no | — |
| 404 | SD16 | — | 6 | 12 | no | — |
| 405 | SD16 | — | 6 | 4 | no | — |
| 406 | D8 | — | 2 | 12 | no | — |
| 407 | D8 | — | 6 | 3 | no | — |
| 408 | D8 | — | 6 | 3 | no | — |
| 409 | D8 | — | 6 | 12 | no | — |
| 410 | D8 | — | 6 | 12 | no | — |
| 411 | M16 | — | 2 | 6 | no | — |
| 412 | M16 | — | 3 | 12 | no | — |
| 413 | M16 | — | 3 | 4 | no | — |
| 414 | M16 | — | 3 | 4 | no | — |
| 415 | M16 | — | 6 | 4 | no | — |
| 416 | M16 | — | 6 | 12 | no | — |
| 417 | M16 | — | 6 | 6 | no | — |
| 418 | M16 | — | 6 | 6 | no | — |
| 419 | M16 | C23×D3 | 1 | 4 | yes | — |
| 420 | C2×C8 | — | 2 | 6 | no | — |
| 421 | C2×C8 | — | 3 | 6 | no | — |
| 422 | C2×C8 | — | 3 | 6 | no | — |
| 423 | C2×C8 | — | 3 | 1 | no | — |
| 424 | C2×C8 | — | 3 | 3 | no | — |
| 425 | C2×C8 | — | 6 | 4 | no | — |
| 426 | C2×C8 | — | 6 | 12 | no | — |
| 427 | C2×C8 | — | 6 | 6 | no | — |
| 428 | C2×C8 | — | 6 | 6 | no | — |
| 429 | C22×C3 | — | 2 | 4 | no | — |
| 430 | C22×C3 | — | 4 | 3 | no | — |
| 431 | C22×C3 | — | 4 | 3 | no | — |
| 432 | C22×C3 | — | 8 | 6 | no | — |
| 433 | C22×C3 | — | 8 | 3 | no | — |
| 434 | C22×C3 | — | 16 | 6 | no | — |
| 435 | C22×C3 | C2×#121 | 1 | 6 | yes | — |
| 436 | C22×C3 | C22×#41 | 1 | 1 | yes | characteristic |
| 437 | C2×D3 | — | 4 | 3 | no | — |
| 438 | C2×D3 | — | 8 | 3 | no | — |
| 439 | C2×D3 | — | 16 | 6 | no | — |
| 440 | C3×C4 | — | 2 | 4 | no | — |
| 441 | C3×C4 | — | 4 | 1 | no | — |
| 442 | C3×C4 | C2×#121 | 1 | 6 | yes | — |
| 443 | C3×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 444 | C3×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 445 | Dic3 | — | 4 | 1 | no | — |
| 446 | C23 | — | 2 | 6 | no | — |
| 447 | C23 | — | 2 | 3 | no | — |
| 448 | C23 | — | 4 | 6 | no | — |
| 449 | C23 | — | 6 | 3 | no | — |
| 450 | C23 | — | 12 | 6 | no | — |
| 451 | C23 | — | 16 | 3 | no | — |
| 452 | C23 | — | 48 | 3 | no | — |
| 453 | C23 | C2×#237 | 1 | 3 | yes | — |
| 454 | Q8 | — | 2 | 6 | no | — |
| 455 | Q8 | — | 2 | 1 | no | — |
| 456 | Q8 | — | 2 | 1 | no | — |
| 457 | Q8 | — | 6 | 1 | no | — |
| 458 | Q8 | — | 6 | 1 | no | — |
| 459 | Q8 | #939 | 1 | 4 | yes | — |
| 460 | Q8 | C22×#67 | 1 | 4 | yes | — |
| 461 | D4 | — | 2 | 4 | no | — |
| 462 | D4 | — | 2 | 12 | no | — |
| 463 | D4 | — | 2 | 3 | no | — |
| 464 | D4 | — | 2 | 3 | no | — |
| 465 | D4 | — | 2 | 6 | no | — |
| 466 | D4 | — | 4 | 6 | no | — |
| 467 | D4 | — | 4 | 6 | no | — |
| 468 | D4 | — | 6 | 3 | no | — |
| 469 | D4 | — | 6 | 3 | no | — |
| 470 | D4 | — | 12 | 6 | no | — |
| 471 | D4 | — | 12 | 6 | no | — |
| 472 | D4 | #939 | 1 | 12 | yes | — |
| 473 | D4 | C22×#67 | 1 | 4 | yes | — |
| 474 | C2×C4 | — | 2 | 6 | no | — |
| 475 | C2×C4 | — | 2 | 4 | no | — |
| 476 | C2×C4 | — | 2 | 12 | no | — |
| 477 | C2×C4 | — | 2 | 1 | no | — |
| 478 | C2×C4 | — | 4 | 6 | no | — |
| 479 | C2×C4 | — | 6 | 1 | no | — |
| 480 | C2×C4 | — | 12 | 6 | no | — |
| 481 | C2×C4 | C2×D3×D4 | 1 | 6 | yes | — |
| 482 | C2×C4 | C2×#237 | 1 | 3 | yes | — |
| 483 | C2×C4 | C22×#67 | 1 | 6 | yes | — |
| 484 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 485 | C8 | — | 2 | 4 | no | — |
| 486 | C8 | — | 3 | 1 | no | — |
| 487 | C8 | — | 3 | 1 | no | — |
| 488 | C8 | — | 3 | 6 | no | — |
| 489 | C8 | — | 6 | 4 | no | — |
| 490 | C8 | — | 6 | 4 | no | — |
| 491 | C2×C3 | — | 2 | 1 | no | — |
| 492 | C2×C3 | — | 2 | 6 | no | — |
| 493 | C2×C3 | — | 4 | 4 | no | — |
| 494 | C2×C3 | — | 8 | 3 | no | — |
| 495 | C2×C3 | C22×#121 | 1 | 1 | yes | characteristic |
| 496 | D3 | — | 8 | 3 | no | — |
| 497 | C22 | — | 2 | 4 | no | — |
| 498 | C22 | — | 4 | 3 | no | — |
| 499 | C22 | — | 4 | 3 | no | — |
| 500 | C22 | — | 8 | 6 | no | — |
| 501 | C22 | — | 8 | 3 | no | — |
| 502 | C22 | — | 12 | 3 | no | — |
| 503 | C22 | — | 16 | 6 | no | — |
| 504 | C22 | — | 24 | 3 | no | — |
| 505 | C22 | — | 48 | 6 | no | — |
| 506 | C22 | C2×#939 | 1 | 6 | yes | — |
| 507 | C22 | C22×#237 | 1 | 1 | yes | characteristic |
| 508 | C4 | — | 2 | 4 | no | — |
| 509 | C4 | — | 4 | 1 | no | — |
| 510 | C4 | — | 12 | 1 | no | — |
| 511 | C4 | C2×#939 | 1 | 6 | yes | — |
| 512 | C4 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 513 | C4 | C23×#67 | 1 | 1 | yes | characteristic |
| 514 | C3 | #60471 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 515 | C2 | — | 2 | 1 | no | — |
| 516 | C2 | — | 2 | 6 | no | — |
| 517 | C2 | — | 4 | 4 | no | — |
| 518 | C2 | — | 8 | 3 | no | — |
| 519 | C2 | — | 24 | 3 | no | — |
| 520 | C2 | C22×#939 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#3585 | C2 | semidirect |
| 2. #87298 | C2 | semidirect |
| 3. #87296 | C2 | semidirect |
| 4. C2×#5835 | C2 | semidirect |
| 5. #84100 | C2 | semidirect |
| 6. #84002 | C2 | semidirect |
| 7. #84001 | C2 | semidirect |
| 8. #83943 | C2 | semidirect |
| 9. C2×#5199 | C2 | semidirect |
| 10. #83813 | C2 | semidirect |
| 11. #83810 | C2 | semidirect |
| 18. C3×#575 | C22 | semidirect |
| 19. C2×C3×AGL(1,ℤ/8) | C22 | semidirect |
| 25. #5822 | C22 | semidirect |
| 26. C2×#950 | C22 | semidirect |
| 27. C2×#949 | C22 | semidirect |
| 28. C2×#949 | C22 | semidirect |
| 32. #5819 | C22 | semidirect |
| 35. C2×#948 | C22 | semidirect |
| 36. C2×#932 | C22 | semidirect |
| 37. C22×#213 | C22 | semidirect |
| 38. #5237 | C22 | semidirect |
| 39. C2×#833 | C22 | semidirect |
| 40. #5204 | C22 | semidirect |
| 41. #5203 | C22 | semidirect |
| 42. #5200 | C22 | semidirect |
| 43. #5199 | C22 | semidirect |
| 44. #5199 | C22 | semidirect |
| 45. #5132 | C22 | semidirect |
| 46. C2×#823 | C22 | semidirect |
| 47. #5124 | C22 | semidirect |
| 48. C2×#822 | C22 | semidirect |
| 50. #3585 | D3 | semidirect |
| 140. #575 | C2×D3 | semidirect |
| 144. C2×AGL(1,ℤ/8) | C2×D3 | semidirect |
| 514. C3 | #60471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3585 | 2 |
| #87298 | 2 |
| #87296 | 2 |
| C2×#5835 | 2 |
| #84100 | 2 |
| #84002 | 2 |
| #84001 | 2 |
| #83943 | 2 |
| C2×#5199 | 2 |
| #83813 | 2 |
| #83810 | 2 |
| #60471 | 3 |