Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2688 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 | C2×C3×#578 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #87295 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×D3×#131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #84111 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #83986 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #83985 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #83917 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #83914 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #83887 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | C2×#5188 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #83785 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #60459 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C2×C3×2−1+4 | C22 | 1 | 2 | yes | — |
| 14 | C2×D3×#41 | C22 | 1 | 1 | yes | characteristic |
| 15 | C3×#578 | — | 2 | 8 | no | — |
| 16 | C2×C3×#137 | C22 | 1 | 6 | yes | complemented |
| 17 | C2×C3×#135 | C22 | 1 | 3 | yes | complemented |
| 18 | C22×C3×Q16 | C22 | 1 | 3 | yes | complemented |
| 19 | C2×C3×#131 | C22 | 1 | 1 | yes | characteristic |
| 20 | #5833 | C22 | 1 | 6 | yes | — |
| 21 | #5829 | — | 2 | 6 | no | — |
| 22 | #5828 | C22 | 1 | 6 | yes | — |
| 23 | #5827 | C22 | 1 | 2 | yes | — |
| 24 | #5824 | — | 2 | 6 | no | — |
| 25 | C2×#948 | C22 | 1 | 1 | yes | characteristic |
| 26 | #5817 | — | 2 | 2 | no | — |
| 27 | #5816 | C22 | 1 | 6 | yes | — |
| 28 | Q8×#67 | — | 2 | 2 | no | — |
| 29 | C2×#946 | C22 | 1 | 6 | yes | — |
| 30 | D3×#131 | — | 2 | 8 | no | — |
| 31 | C2×#907 | C22 | 1 | 3 | yes | — |
| 32 | C2×D3×M16 | C22 | 1 | 3 | yes | — |
| 33 | C2×#901 | C22 | 1 | 3 | yes | — |
| 34 | C22×D3×C8 | C22 | 1 | 3 | yes | — |
| 35 | #5233 | C22 | 1 | 6 | yes | complemented |
| 36 | #5232 | C22 | 1 | 6 | yes | complemented |
| 37 | #5225 | C22 | 1 | 6 | yes | complemented |
| 38 | C2×#835 | C22 | 1 | 6 | yes | complemented |
| 39 | #5189 | C22 | 1 | 12 | yes | complemented |
| 40 | #5188 | C22 | 1 | 6 | yes | — |
| 41 | #5188 | C22 | 1 | 3 | yes | — |
| 42 | #5188 | C22 | 1 | 6 | yes | complemented |
| 43 | #5188 | C22 | 1 | 6 | yes | complemented |
| 44 | #5188 | C22 | 1 | 3 | yes | complemented |
| 45 | #5174 | C22 | 1 | 12 | yes | complemented |
| 46 | #5171 | C22 | 1 | 6 | yes | — |
| 47 | #5171 | C22 | 1 | 6 | yes | complemented |
| 48 | #5157 | C22 | 1 | 1 | yes | characteristic |
| 49 | #5157 | C22 | 1 | 3 | yes | complemented |
| 50 | #5121 | C22 | 1 | 6 | yes | complemented |
| 51 | #5106 | C22 | 1 | 3 | yes | complemented |
| 52 | C2×#818 | C22 | 1 | 3 | yes | complemented |
| 53 | C2×#578 | D3 | 1 | 1 | yes | characteristic, complemented |
| 54 | C22×#131 | — | 3 | 1 | no | — |
| 55 | #3489 | — | 3 | 2 | no | — |
| 56 | #3063 | — | 3 | 6 | no | — |
| 57 | #3061 | — | 3 | 3 | no | — |
| 58 | #3059 | — | 3 | 3 | no | — |
| 59 | #3056 | — | 3 | 6 | no | — |
| 60 | #3050 | — | 3 | 3 | no | — |
| 61 | C2×#467 | — | 3 | 3 | no | — |
| 62 | #2913 | — | 3 | 1 | no | — |
| 63 | #2898 | — | 3 | 2 | no | — |
| 64 | C3×2−1+4 | — | 2 | 8 | no | — |
| 65 | C3×2−1+4 | — | 2 | 8 | no | — |
| 66 | C2×C3×#41 | — | 2 | 6 | no | — |
| 67 | C2×C3×#41 | C23 | 1 | 6 | yes | — |
| 68 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 69 | C22×C3×Q8 | — | 2 | 2 | no | — |
| 70 | C22×C3×Q8 | C23 | 1 | 6 | yes | — |
| 71 | D3×#41 | — | 2 | 4 | no | — |
| 72 | D3×#41 | — | 2 | 4 | no | — |
| 73 | C2×#239 | D4 | 1 | 1 | yes | characteristic |
| 74 | C2×D3×Q8 | D4 | 1 | 1 | yes | characteristic |
| 75 | C2×#237 | D4 | 1 | 3 | yes | — |
| 76 | C2×D3×D4 | D4 | 1 | 3 | yes | — |
| 77 | C2×#235 | C23 | 1 | 3 | yes | — |
| 78 | C22×C4×D3 | C23 | 1 | 3 | yes | — |
| 79 | C3×#137 | — | 2 | 24 | no | — |
| 80 | C3×#135 | — | 2 | 12 | no | — |
| 81 | C2×C3×Q16 | — | 2 | 12 | no | — |
| 82 | C2×C3×Q16 | C23 | 1 | 3 | yes | — |
| 83 | C2×C3×Q16 | C23 | 1 | 6 | yes | — |
| 84 | C2×C3×SD16 | C23 | 1 | 6 | yes | — |
| 85 | C2×C3×D8 | C23 | 1 | 1 | yes | characteristic |
| 86 | C3×#131 | D4 | 1 | 8 | yes | complemented |
| 87 | C2×C3×M16 | C23 | 1 | 3 | yes | — |
| 88 | C22×C3×C8 | C23 | 1 | 3 | yes | — |
| 89 | #948 | — | 2 | 4 | no | — |
| 90 | #947 | — | 2 | 6 | no | — |
| 91 | #946 | — | 2 | 6 | no | — |
| 92 | #946 | — | 2 | 6 | no | — |
| 93 | #946 | C23 | 1 | 6 | yes | — |
| 94 | #946 | C23 | 1 | 6 | yes | — |
| 95 | #946 | C23 | 1 | 12 | yes | — |
| 96 | Q8×Dic3 | — | 2 | 2 | no | — |
| 97 | #944 | — | 2 | 6 | no | — |
| 98 | #939 | — | 2 | 12 | no | — |
| 99 | #938 | C23 | 1 | 2 | yes | — |
| 100 | #938 | C23 | 1 | 6 | yes | — |
| 101 | #937 | — | 2 | 6 | no | — |
| 102 | #935 | — | 2 | 6 | no | — |
| 103 | D4×Dic3 | — | 2 | 6 | no | — |
| 104 | #930 | — | 2 | 6 | no | — |
| 105 | #929 | — | 2 | 12 | no | — |
| 106 | C4×#67 | — | 2 | 6 | no | — |
| 107 | C4×#67 | — | 2 | 6 | no | — |
| 108 | C2×(C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 109 | #926 | C23 | 1 | 6 | yes | — |
| 110 | C2×C4⋊Dic3 | C23 | 1 | 6 | yes | — |
| 111 | #924 | — | 2 | 6 | no | — |
| 112 | C2×Dic3⋊C4 | — | 2 | 6 | no | — |
| 113 | C2×#208 | C23 | 1 | 3 | yes | — |
| 114 | C22×C3⋊C8 | C23 | 1 | 3 | yes | — |
| 115 | #907 | — | 2 | 12 | no | — |
| 116 | D3×M16 | — | 2 | 12 | no | — |
| 117 | #901 | — | 2 | 12 | no | — |
| 118 | C2×ΓL(1,𝔽25) | C23 | 1 | 6 | yes | — |
| 119 | C2×D3×C8 | — | 2 | 12 | no | — |
| 120 | C2×D3×C8 | C23 | 1 | 1 | yes | characteristic |
| 121 | C2×D3×C8 | C23 | 1 | 3 | yes | — |
| 122 | C2×D3×C8 | C23 | 1 | 3 | yes | — |
| 123 | C2×D3×C8 | C23 | 1 | 3 | yes | — |
| 124 | #835 | C23 | 1 | 6 | yes | — |
| 125 | #835 | C23 | 1 | 6 | yes | — |
| 126 | #835 | C23 | 1 | 12 | yes | — |
| 127 | #832 | C23 | 1 | 2 | yes | — |
| 128 | #832 | C23 | 1 | 6 | yes | — |
| 129 | #818 | C23 | 1 | 6 | yes | — |
| 130 | #818 | C23 | 1 | 1 | yes | characteristic |
| 131 | #818 | C23 | 1 | 3 | yes | — |
| 132 | #817 | C23 | 1 | 6 | yes | — |
| 133 | C2×2−1+4 | C2×D3 | 1 | 2 | yes | — |
| 134 | C22×#41 | — | 3 | 1 | no | — |
| 135 | #578 | — | 2 | 8 | no | — |
| 136 | C2×#137 | C2×D3 | 1 | 6 | yes | complemented |
| 137 | C2×#135 | C2×D3 | 1 | 3 | yes | complemented |
| 138 | C22×Q16 | C2×D3 | 1 | 3 | yes | complemented |
| 139 | C2×#131 | — | 3 | 1 | no | — |
| 140 | C2×#131 | — | 3 | 3 | no | — |
| 141 | C2×#131 | — | 3 | 3 | no | — |
| 142 | C2×#131 | — | 6 | 8 | no | — |
| 143 | C2×#131 | C2×D3 | 1 | 1 | yes | characteristic |
| 144 | C22×M16 | — | 3 | 3 | no | — |
| 145 | C23×C8 | — | 3 | 3 | no | — |
| 146 | D4×Q8 | — | 6 | 2 | no | — |
| 147 | #548 | — | 6 | 2 | no | — |
| 148 | #547 | — | 6 | 6 | no | — |
| 149 | #546 | — | 6 | 6 | no | — |
| 150 | #537 | — | 3 | 6 | no | — |
| 151 | #536 | — | 3 | 6 | no | — |
| 152 | #525 | — | 3 | 6 | no | — |
| 153 | C2×C22⋊Q8 | — | 3 | 6 | no | — |
| 154 | #520 | — | 3 | 2 | no | — |
| 155 | #470 | — | 3 | 12 | no | — |
| 156 | #468 | — | 3 | 12 | no | — |
| 157 | #467 | — | 3 | 3 | no | — |
| 158 | #467 | — | 3 | 6 | no | — |
| 159 | #467 | — | 3 | 6 | no | — |
| 160 | #467 | — | 3 | 6 | no | — |
| 161 | #467 | — | 3 | 3 | no | — |
| 162 | #466 | — | 3 | 1 | no | — |
| 163 | #466 | — | 3 | 3 | no | — |
| 164 | #465 | — | 3 | 6 | no | — |
| 165 | #465 | — | 3 | 6 | no | — |
| 166 | #428 | — | 3 | 6 | no | — |
| 167 | #427 | — | 3 | 3 | no | — |
| 168 | C2×#107 | — | 3 | 3 | no | — |
| 169 | #419 | — | 3 | 6 | no | — |
| 170 | #417 | — | 3 | 6 | no | — |
| 171 | #416 | — | 3 | 6 | no | — |
| 172 | C2×#103 | — | 3 | 6 | no | — |
| 173 | C23×D3 | C2×D4 | 1 | 3 | yes | — |
| 174 | C3×#41 | — | 2 | 12 | no | — |
| 175 | C3×#41 | — | 2 | 12 | no | — |
| 176 | C3×#41 | — | 4 | 24 | no | — |
| 177 | C3×#41 | C2×D4 | 1 | 4 | yes | — |
| 178 | C3×#41 | #41 | 1 | 4 | yes | — |
| 179 | C2×C3×Q8 | — | 2 | 6 | no | — |
| 180 | C2×C3×Q8 | — | 2 | 12 | no | — |
| 181 | C2×C3×Q8 | — | 2 | 12 | no | — |
| 182 | C2×C3×Q8 | — | 4 | 8 | no | — |
| 183 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 184 | C2×C3×Q8 | C24 | 1 | 6 | yes | — |
| 185 | C2×C3×D4 | — | 2 | 6 | no | — |
| 186 | C2×C3×D4 | C2×D4 | 1 | 3 | yes | — |
| 187 | C2×C3×D4 | C24 | 1 | 2 | yes | — |
| 188 | C22×C3×C4 | — | 2 | 6 | no | — |
| 189 | C22×C3×C4 | — | 2 | 6 | no | — |
| 190 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 191 | C2×#67 | — | 2 | 2 | no | — |
| 192 | C2×#67 | — | 2 | 6 | no | — |
| 193 | C2×#67 | C2×D4 | 1 | 6 | yes | — |
| 194 | C22×Dic3 | — | 2 | 6 | no | — |
| 195 | C22×Dic3 | C2×D4 | 1 | 3 | yes | — |
| 196 | #239 | — | 2 | 4 | no | — |
| 197 | D3×Q8 | — | 2 | 4 | no | — |
| 198 | #237 | — | 2 | 12 | no | — |
| 199 | D3×D4 | — | 2 | 12 | no | — |
| 200 | #235 | — | 2 | 6 | no | — |
| 201 | #235 | — | 2 | 6 | no | — |
| 202 | C2×D12 | C2×D4 | 1 | 3 | yes | — |
| 203 | C2×C4×D3 | — | 2 | 6 | no | — |
| 204 | C2×C4×D3 | — | 2 | 6 | no | — |
| 205 | C2×C4×D3 | C2×D4 | 1 | 3 | yes | — |
| 206 | C2×C4×D3 | C2×D4 | 1 | 3 | yes | — |
| 207 | C2×C4×D3 | C24 | 1 | 1 | yes | characteristic |
| 208 | C2×C4×D3 | C24 | 1 | 3 | yes | — |
| 209 | C2×Dic6 | C2×D4 | 1 | 3 | yes | — |
| 210 | C3×Q16 | — | 2 | 6 | no | — |
| 211 | C3×Q16 | — | 2 | 12 | no | — |
| 212 | C3×SD16 | — | 2 | 12 | no | — |
| 213 | C3×D8 | — | 2 | 2 | no | — |
| 214 | C3×M16 | C2×D4 | 1 | 12 | yes | — |
| 215 | C2×C3×C8 | C2×D4 | 1 | 12 | yes | — |
| 216 | C2×C3×C8 | C24 | 1 | 3 | yes | — |
| 217 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 218 | #217 | — | 2 | 6 | no | — |
| 219 | #217 | — | 2 | 6 | no | — |
| 220 | #217 | — | 2 | 2 | no | — |
| 221 | (C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 222 | (C2×D3)⋊C4 | — | 2 | 12 | no | — |
| 223 | (C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 224 | C4⋊Dic3 | — | 2 | 6 | no | — |
| 225 | C4⋊Dic3 | C24 | 1 | 2 | yes | — |
| 226 | C4⋊Dic3 | C24 | 1 | 6 | yes | — |
| 227 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 228 | Dic3⋊C4 | — | 2 | 12 | no | — |
| 229 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 230 | C4×Dic3 | — | 2 | 6 | no | — |
| 231 | #208 | — | 2 | 6 | no | — |
| 232 | C2×C3⋊C8 | — | 2 | 6 | no | — |
| 233 | C2×C3⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 234 | C2×C3⋊C8 | C24 | 1 | 3 | yes | — |
| 235 | ΓL(1,𝔽25) | — | 2 | 12 | no | — |
| 236 | D3×C8 | — | 2 | 2 | no | — |
| 237 | D3×C8 | — | 2 | 6 | no | — |
| 238 | D3×C8 | — | 2 | 6 | no | — |
| 239 | D3×C8 | — | 2 | 6 | no | — |
| 240 | 2−1+4 | — | 2 | 8 | no | — |
| 241 | 2−1+4 | — | 2 | 8 | no | — |
| 242 | C2×#41 | — | 2 | 6 | no | — |
| 243 | C2×#41 | — | 3 | 1 | no | — |
| 244 | C2×#41 | — | 3 | 3 | no | — |
| 245 | C2×#41 | — | 3 | 3 | no | — |
| 246 | C2×#41 | — | 6 | 4 | no | — |
| 247 | C2×#41 | — | 6 | 4 | no | — |
| 248 | C2×#41 | C22×D3 | 1 | 6 | yes | — |
| 249 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 250 | C22×Q8 | — | 2 | 2 | no | — |
| 251 | C22×Q8 | — | 3 | 1 | no | — |
| 252 | C22×Q8 | C22×D3 | 1 | 6 | yes | — |
| 253 | C22×D4 | — | 3 | 3 | no | — |
| 254 | C23×C4 | — | 3 | 3 | no | — |
| 255 | #137 | — | 2 | 24 | no | — |
| 256 | #135 | — | 2 | 12 | no | — |
| 257 | C2×Q16 | — | 2 | 12 | no | — |
| 258 | C2×Q16 | C22×D3 | 1 | 3 | yes | — |
| 259 | C2×Q16 | C22×D3 | 1 | 6 | yes | — |
| 260 | C2×SD16 | C22×D3 | 1 | 6 | yes | — |
| 261 | C2×D8 | C22×D3 | 1 | 1 | yes | characteristic |
| 262 | #131 | — | 6 | 4 | no | — |
| 263 | #131 | — | 6 | 12 | no | — |
| 264 | #131 | — | 6 | 12 | no | — |
| 265 | #131 | #67 | 1 | 8 | yes | complemented |
| 266 | C2×M16 | — | 3 | 3 | no | — |
| 267 | C2×M16 | — | 3 | 6 | no | — |
| 268 | C2×M16 | — | 6 | 12 | no | — |
| 269 | C2×M16 | C22×D3 | 1 | 3 | yes | — |
| 270 | C22×C8 | — | 3 | 3 | no | — |
| 271 | C22×C8 | — | 3 | 1 | no | — |
| 272 | C22×C8 | — | 3 | 3 | no | — |
| 273 | C22×C8 | — | 3 | 3 | no | — |
| 274 | C22×C8 | — | 3 | 3 | no | — |
| 275 | C22×C8 | — | 6 | 12 | no | — |
| 276 | C22×C8 | C22×D3 | 1 | 3 | yes | — |
| 277 | C4⋊Q8 | — | 6 | 6 | no | — |
| 278 | #124 | — | 6 | 6 | no | — |
| 279 | #123 | — | 6 | 12 | no | — |
| 280 | #123 | — | 6 | 6 | no | — |
| 281 | C22⋊Q8 | — | 3 | 6 | no | — |
| 282 | C22⋊Q8 | — | 3 | 12 | no | — |
| 283 | C22⋊Q8 | — | 3 | 6 | no | — |
| 284 | C22⋊Q8 | — | 6 | 6 | no | — |
| 285 | C22⋊Q8 | — | 6 | 6 | no | — |
| 286 | C22⋊Q8 | — | 6 | 6 | no | — |
| 287 | #121 | — | 3 | 2 | no | — |
| 288 | #121 | — | 3 | 6 | no | — |
| 289 | #121 | — | 6 | 6 | no | — |
| 290 | #121 | — | 6 | 12 | no | — |
| 291 | #120 | — | 6 | 6 | no | — |
| 292 | C4×Q8 | — | 6 | 2 | no | — |
| 293 | C4×D4 | — | 6 | 6 | no | — |
| 294 | C4×D4 | — | 6 | 6 | no | — |
| 295 | C4×D4 | — | 6 | 6 | no | — |
| 296 | #117 | — | 3 | 6 | no | — |
| 297 | C2×C4⋊C4 | — | 3 | 6 | no | — |
| 298 | C2×C4⋊C4 | — | 6 | 6 | no | — |
| 299 | C2×C22⋊C4 | — | 6 | 6 | no | — |
| 300 | #107 | — | 3 | 3 | no | — |
| 301 | #107 | — | 3 | 6 | no | — |
| 302 | #107 | — | 3 | 1 | no | — |
| 303 | #106 | — | 3 | 6 | no | — |
| 304 | #103 | — | 3 | 6 | no | — |
| 305 | #103 | — | 3 | 12 | no | — |
| 306 | #103 | — | 3 | 6 | no | — |
| 307 | #102 | — | 3 | 2 | no | — |
| 308 | #102 | — | 3 | 6 | no | — |
| 309 | C23×C3 | — | 2 | 2 | no | — |
| 310 | C23×C3 | C22×D4 | 1 | 3 | yes | — |
| 311 | C22×D3 | — | 2 | 6 | no | — |
| 312 | C22×D3 | — | 2 | 6 | no | — |
| 313 | C22×D3 | — | 4 | 3 | no | — |
| 314 | C22×D3 | C22×D4 | 1 | 3 | yes | — |
| 315 | C22×D3 | C22×D4 | 1 | 1 | yes | characteristic |
| 316 | C3×Q8 | — | 2 | 6 | no | — |
| 317 | C3×Q8 | — | 2 | 6 | no | — |
| 318 | C3×Q8 | — | 4 | 12 | no | — |
| 319 | C3×Q8 | #121 | 1 | 4 | yes | — |
| 320 | C3×D4 | — | 2 | 2 | no | — |
| 321 | C3×D4 | — | 2 | 2 | no | — |
| 322 | C3×D4 | — | 4 | 12 | no | — |
| 323 | C3×D4 | #121 | 1 | 12 | yes | — |
| 324 | C2×C3×C4 | — | 2 | 6 | no | — |
| 325 | C2×C3×C4 | — | 4 | 12 | no | — |
| 326 | C2×C3×C4 | — | 4 | 12 | no | — |
| 327 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 328 | C2×C3×C4 | C22×D4 | 1 | 6 | yes | — |
| 329 | C2×C3×C4 | C2×#41 | 1 | 6 | yes | — |
| 330 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 331 | #67 | — | 2 | 12 | no | — |
| 332 | #67 | — | 4 | 4 | no | — |
| 333 | #67 | — | 8 | 6 | no | — |
| 334 | C2×Dic3 | — | 2 | 6 | no | — |
| 335 | C2×Dic3 | — | 2 | 2 | no | — |
| 336 | C2×Dic3 | — | 2 | 6 | no | — |
| 337 | C2×Dic3 | — | 8 | 6 | no | — |
| 338 | C2×Dic3 | C22×D4 | 1 | 3 | yes | — |
| 339 | C2×Dic3 | C22×D4 | 1 | 1 | yes | characteristic |
| 340 | D12 | — | 2 | 6 | no | — |
| 341 | C4×D3 | — | 2 | 6 | no | — |
| 342 | C4×D3 | — | 2 | 6 | no | — |
| 343 | C4×D3 | — | 2 | 1 | no | — |
| 344 | C4×D3 | — | 2 | 3 | no | — |
| 345 | C4×D3 | — | 2 | 1 | no | — |
| 346 | C4×D3 | — | 2 | 3 | no | — |
| 347 | Dic6 | — | 2 | 6 | no | — |
| 348 | C3×C8 | C22×D4 | 1 | 2 | yes | — |
| 349 | C3×C8 | C22×D4 | 1 | 6 | yes | — |
| 350 | C3⋊C8 | — | 2 | 1 | no | — |
| 351 | C3⋊C8 | — | 2 | 3 | no | — |
| 352 | C24 | — | 3 | 3 | no | — |
| 353 | #41 | — | 2 | 12 | no | — |
| 354 | #41 | — | 2 | 12 | no | — |
| 355 | #41 | — | 4 | 24 | no | — |
| 356 | #41 | — | 6 | 4 | no | — |
| 357 | #41 | — | 6 | 12 | no | — |
| 358 | #41 | — | 6 | 6 | no | — |
| 359 | #41 | — | 6 | 6 | no | — |
| 360 | #41 | #237 | 1 | 4 | yes | — |
| 361 | #41 | C2×#67 | 1 | 4 | yes | — |
| 362 | C2×Q8 | — | 2 | 6 | no | — |
| 363 | C2×Q8 | — | 2 | 12 | no | — |
| 364 | C2×Q8 | — | 2 | 12 | no | — |
| 365 | C2×Q8 | — | 3 | 3 | no | — |
| 366 | C2×Q8 | — | 4 | 8 | no | — |
| 367 | C2×Q8 | — | 6 | 4 | no | — |
| 368 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 369 | C2×Q8 | C23×D3 | 1 | 6 | yes | — |
| 370 | C2×D4 | — | 2 | 6 | no | — |
| 371 | C2×D4 | — | 3 | 6 | no | — |
| 372 | C2×D4 | — | 3 | 3 | no | — |
| 373 | C2×D4 | — | 6 | 12 | no | — |
| 374 | C2×D4 | — | 6 | 2 | no | — |
| 375 | C2×D4 | — | 6 | 6 | no | — |
| 376 | C2×D4 | D3×D4 | 1 | 3 | yes | — |
| 377 | C2×D4 | C23×D3 | 1 | 2 | yes | — |
| 378 | C22×C4 | — | 2 | 6 | no | — |
| 379 | C22×C4 | — | 2 | 6 | no | — |
| 380 | C22×C4 | — | 3 | 3 | no | — |
| 381 | C22×C4 | — | 3 | 3 | no | — |
| 382 | C22×C4 | — | 3 | 3 | no | — |
| 383 | C22×C4 | — | 3 | 1 | no | — |
| 384 | C22×C4 | — | 3 | 3 | no | — |
| 385 | C22×C4 | — | 6 | 6 | no | — |
| 386 | C22×C4 | — | 6 | 6 | no | — |
| 387 | C22×C4 | — | 6 | 6 | no | — |
| 388 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 389 | Q16 | — | 2 | 6 | no | — |
| 390 | Q16 | — | 2 | 12 | no | — |
| 391 | SD16 | — | 2 | 12 | no | — |
| 392 | D8 | — | 2 | 2 | no | — |
| 393 | M16 | — | 6 | 6 | no | — |
| 394 | M16 | — | 6 | 12 | no | — |
| 395 | M16 | C2×#67 | 1 | 12 | yes | — |
| 396 | C2×C8 | — | 3 | 1 | no | — |
| 397 | C2×C8 | — | 3 | 3 | no | — |
| 398 | C2×C8 | — | 6 | 6 | no | — |
| 399 | C2×C8 | — | 6 | 2 | no | — |
| 400 | C2×C8 | — | 6 | 6 | no | — |
| 401 | C2×C8 | — | 6 | 6 | no | — |
| 402 | C2×C8 | — | 6 | 6 | no | — |
| 403 | C2×C8 | C2×#67 | 1 | 12 | yes | — |
| 404 | C2×C8 | C23×D3 | 1 | 3 | yes | — |
| 405 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 406 | C4⋊C4 | — | 3 | 2 | no | — |
| 407 | C4⋊C4 | — | 3 | 6 | no | — |
| 408 | C4⋊C4 | — | 6 | 6 | no | — |
| 409 | C4⋊C4 | — | 6 | 12 | no | — |
| 410 | C4⋊C4 | — | 6 | 6 | no | — |
| 411 | C4⋊C4 | — | 6 | 6 | no | — |
| 412 | C22⋊C4 | — | 6 | 6 | no | — |
| 413 | C22⋊C4 | — | 6 | 12 | no | — |
| 414 | C22⋊C4 | — | 6 | 6 | no | — |
| 415 | C22⋊C4 | — | 6 | 2 | no | — |
| 416 | C22⋊C4 | — | 6 | 6 | no | — |
| 417 | C22⋊C4 | — | 6 | 6 | no | — |
| 418 | C42 | — | 6 | 6 | no | — |
| 419 | C22×C3 | — | 2 | 3 | no | — |
| 420 | C22×C3 | — | 2 | 3 | no | — |
| 421 | C22×C3 | — | 4 | 2 | no | — |
| 422 | C22×C3 | — | 4 | 2 | no | — |
| 423 | C22×C3 | — | 4 | 2 | no | — |
| 424 | C22×C3 | C2×#121 | 1 | 6 | yes | — |
| 425 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 426 | C2×D3 | — | 2 | 1 | no | — |
| 427 | C2×D3 | — | 2 | 1 | no | — |
| 428 | C2×D3 | — | 2 | 3 | no | — |
| 429 | C2×D3 | — | 2 | 3 | no | — |
| 430 | C2×D3 | — | 2 | 3 | no | — |
| 431 | C2×D3 | — | 4 | 12 | no | — |
| 432 | C2×D3 | #578 | 1 | 2 | yes | complemented |
| 433 | C3×C4 | — | 4 | 6 | no | — |
| 434 | C3×C4 | C2×#121 | 1 | 6 | yes | — |
| 435 | C3×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 436 | C3×C4 | C22×#41 | 1 | 1 | yes | characteristic |
| 437 | Dic3 | — | 2 | 3 | no | — |
| 438 | Dic3 | — | 2 | 1 | no | — |
| 439 | Dic3 | — | 4 | 6 | no | — |
| 440 | Dic3 | — | 4 | 2 | no | — |
| 441 | C23 | — | 2 | 2 | no | — |
| 442 | C23 | — | 3 | 1 | no | — |
| 443 | C23 | — | 3 | 3 | no | — |
| 444 | C23 | — | 6 | 6 | no | — |
| 445 | C23 | — | 6 | 6 | no | — |
| 446 | C23 | — | 12 | 3 | no | — |
| 447 | C23 | C2×D3×D4 | 1 | 3 | yes | — |
| 448 | Q8 | — | 2 | 6 | no | — |
| 449 | Q8 | — | 2 | 6 | no | — |
| 450 | Q8 | — | 4 | 12 | no | — |
| 451 | Q8 | — | 6 | 6 | no | — |
| 452 | Q8 | #938 | 1 | 4 | yes | — |
| 453 | D4 | — | 2 | 2 | no | — |
| 454 | D4 | — | 2 | 2 | no | — |
| 455 | D4 | — | 4 | 12 | no | — |
| 456 | D4 | — | 6 | 12 | no | — |
| 457 | D4 | — | 6 | 6 | no | — |
| 458 | D4 | — | 12 | 4 | no | — |
| 459 | D4 | — | 24 | 6 | no | — |
| 460 | D4 | #938 | 1 | 12 | yes | — |
| 461 | C2×C4 | — | 2 | 6 | no | — |
| 462 | C2×C4 | — | 3 | 1 | no | — |
| 463 | C2×C4 | — | 3 | 3 | no | — |
| 464 | C2×C4 | — | 4 | 12 | no | — |
| 465 | C2×C4 | — | 4 | 12 | no | — |
| 466 | C2×C4 | — | 6 | 6 | no | — |
| 467 | C2×C4 | — | 6 | 1 | no | — |
| 468 | C2×C4 | — | 6 | 3 | no | — |
| 469 | C2×C4 | — | 6 | 1 | no | — |
| 470 | C2×C4 | — | 6 | 3 | no | — |
| 471 | C2×C4 | — | 6 | 6 | no | — |
| 472 | C2×C4 | — | 6 | 6 | no | — |
| 473 | C2×C4 | — | 6 | 2 | no | — |
| 474 | C2×C4 | — | 6 | 6 | no | — |
| 475 | C2×C4 | — | 24 | 6 | no | — |
| 476 | C2×C4 | C2×D3×D4 | 1 | 3 | yes | — |
| 477 | C2×C4 | C2×#237 | 1 | 6 | yes | — |
| 478 | C2×C4 | C22×#67 | 1 | 6 | yes | — |
| 479 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 480 | C8 | — | 6 | 1 | no | — |
| 481 | C8 | — | 6 | 3 | no | — |
| 482 | C8 | C22×#67 | 1 | 2 | yes | — |
| 483 | C8 | C22×#67 | 1 | 6 | yes | — |
| 484 | C2×C3 | — | 2 | 6 | no | — |
| 485 | C2×C3 | — | 8 | 2 | no | — |
| 486 | C2×C3 | C22×#121 | 1 | 1 | yes | characteristic |
| 487 | C2×C3 | C2×#578 | 1 | 1 | yes | characteristic |
| 488 | C2×C3 | #3584 | 1 | 1 | yes | characteristic |
| 489 | D3 | — | 2 | 2 | no | — |
| 490 | D3 | — | 4 | 3 | no | — |
| 491 | C22 | — | 2 | 3 | no | — |
| 492 | C22 | — | 2 | 3 | no | — |
| 493 | C22 | — | 3 | 2 | no | — |
| 494 | C22 | — | 4 | 2 | no | — |
| 495 | C22 | — | 4 | 2 | no | — |
| 496 | C22 | — | 4 | 2 | no | — |
| 497 | C22 | — | 6 | 1 | no | — |
| 498 | C22 | — | 6 | 1 | no | — |
| 499 | C22 | — | 6 | 3 | no | — |
| 500 | C22 | — | 6 | 3 | no | — |
| 501 | C22 | — | 6 | 3 | no | — |
| 502 | C22 | — | 12 | 12 | no | — |
| 503 | C22 | C2×#938 | 1 | 6 | yes | — |
| 504 | C22 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 505 | C4 | — | 4 | 6 | no | — |
| 506 | C4 | — | 6 | 1 | no | — |
| 507 | C4 | — | 6 | 3 | no | — |
| 508 | C4 | — | 12 | 2 | no | — |
| 509 | C4 | — | 12 | 6 | no | — |
| 510 | C4 | C2×#938 | 1 | 6 | yes | — |
| 511 | C4 | C22×#237 | 1 | 1 | yes | characteristic |
| 512 | C4 | C23×#67 | 1 | 1 | yes | characteristic |
| 513 | C3 | #60459 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 514 | C2 | — | 2 | 6 | no | — |
| 515 | C2 | — | 6 | 2 | no | — |
| 516 | C2 | — | 8 | 2 | no | — |
| 517 | C2 | — | 12 | 3 | no | — |
| 518 | C2 | D3×#578 | 1 | 1 | yes | characteristic |
| 519 | C2 | #87210 | 1 | 1 | yes | characteristic |
| 520 | C2 | C22×#938 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×#578 | C2 | semidirect |
| 2. #87295 | C2 | semidirect |
| 3. C2×D3×#131 | C2 | semidirect |
| 4. #84111 | C2 | semidirect |
| 5. #83986 | C2 | semidirect |
| 6. #83985 | C2 | semidirect |
| 7. #83917 | C2 | semidirect |
| 8. #83914 | C2 | semidirect |
| 9. #83887 | C2 | semidirect |
| 10. C2×#5188 | C2 | semidirect |
| 11. #83785 | C2 | semidirect |
| 16. C2×C3×#137 | C22 | semidirect |
| 17. C2×C3×#135 | C22 | semidirect |
| 18. C22×C3×Q16 | C22 | semidirect |
| 35. #5233 | C22 | semidirect |
| 36. #5232 | C22 | semidirect |
| 37. #5225 | C22 | semidirect |
| 38. C2×#835 | C22 | semidirect |
| 39. #5189 | C22 | semidirect |
| 42. #5188 | C22 | semidirect |
| 43. #5188 | C22 | semidirect |
| 44. #5188 | C22 | semidirect |
| 45. #5174 | C22 | semidirect |
| 47. #5171 | C22 | semidirect |
| 49. #5157 | C22 | semidirect |
| 50. #5121 | C22 | semidirect |
| 51. #5106 | C22 | semidirect |
| 52. C2×#818 | C22 | semidirect |
| 53. C2×#578 | D3 | semidirect |
| 86. C3×#131 | D4 | semidirect |
| 136. C2×#137 | C2×D3 | semidirect |
| 137. C2×#135 | C2×D3 | semidirect |
| 138. C22×Q16 | C2×D3 | semidirect |
| 265. #131 | #67 | semidirect |
| 432. C2×D3 | #578 | semidirect |
| 513. C3 | #60459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#578 | 2 |
| #87295 | 2 |
| C2×D3×#131 | 2 |
| #84111 | 2 |
| #83986 | 2 |
| #83985 | 2 |
| #83917 | 2 |
| #83914 | 2 |
| #83887 | 2 |
| C2×#5188 | 2 |
| #83785 | 2 |
| #60459 | 3 |