Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2598 conjugacy classes of subgroups.
The subgroup lattice has 592 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D3×#578 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | C3×#3293 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #84018 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #81808 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | D3×#494 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #80947 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | D3×#473 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #80303 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | D3×#456 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #79895 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | D3×#443 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×#3293 | — | 3 | 1 | no | maximal, Sylow |
| 13 | D3×2−1+4 | C22 | 1 | 4 | yes | — |
| 14 | C3×#578 | C22 | 1 | 4 | yes | complemented |
| 15 | #5838 | C22 | 1 | 8 | yes | complemented |
| 16 | #5779 | — | 2 | 8 | no | — |
| 17 | #5779 | C22 | 1 | 8 | yes | complemented |
| 18 | D3×#137 | — | 2 | 8 | no | — |
| 19 | D3×#137 | C22 | 1 | 8 | yes | — |
| 20 | #5771 | — | 2 | 4 | no | — |
| 21 | #5771 | C22 | 1 | 4 | yes | complemented |
| 22 | D3×#135 | — | 2 | 4 | no | — |
| 23 | D3×#135 | C22 | 1 | 2 | yes | — |
| 24 | #5766 | — | 2 | 4 | no | — |
| 25 | #5766 | C22 | 1 | 4 | yes | complemented |
| 26 | C2×D3×Q16 | — | 2 | 4 | no | — |
| 27 | C2×D3×Q16 | C22 | 1 | 4 | yes | — |
| 28 | #5753 | C22 | 1 | 4 | yes | complemented |
| 29 | D3×#131 | C22 | 1 | 4 | yes | — |
| 30 | D3×C4⋊Q8 | C22 | 1 | 2 | yes | — |
| 31 | C3×#494 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | C3×#473 | C22 | 1 | 4 | yes | complemented |
| 33 | C3×#456 | C22 | 1 | 4 | yes | complemented |
| 34 | C3×#443 | C22 | 1 | 2 | yes | complemented |
| 35 | #5246 | C22 | 1 | 4 | yes | complemented |
| 36 | #5205 | C22 | 1 | 8 | yes | complemented |
| 37 | #5204 | C22 | 1 | 8 | yes | complemented |
| 38 | #5196 | C22 | 1 | 2 | yes | complemented |
| 39 | #5192 | C22 | 1 | 4 | yes | complemented |
| 40 | #5183 | C22 | 1 | 4 | yes | complemented |
| 41 | #5144 | C22 | 1 | 4 | yes | complemented |
| 42 | #5143 | C22 | 1 | 4 | yes | complemented |
| 43 | #5095 | C22 | 1 | 4 | yes | complemented |
| 44 | #5092 | C22 | 1 | 2 | yes | complemented |
| 45 | #4896 | C22 | 1 | 4 | yes | complemented |
| 46 | #4895 | C22 | 1 | 2 | yes | complemented |
| 47 | D3×#108 | C22 | 1 | 2 | yes | — |
| 48 | #4826 | C22 | 1 | 8 | yes | complemented |
| 49 | #4824 | C22 | 1 | 4 | yes | complemented |
| 50 | D3×#104 | C22 | 1 | 4 | yes | — |
| 51 | #4755 | C22 | 1 | 8 | yes | complemented |
| 52 | #4752 | C22 | 1 | 4 | yes | complemented |
| 53 | D3×#101 | C22 | 1 | 4 | yes | — |
| 54 | #4700 | C22 | 1 | 2 | yes | complemented |
| 55 | #4699 | C22 | 1 | 1 | yes | characteristic, complemented |
| 56 | C4×D3×C8 | C22 | 1 | 1 | yes | characteristic |
| 57 | C2×#578 | — | 3 | 4 | no | — |
| 58 | #3293 | — | 3 | 1 | no | — |
| 59 | #3293 | — | 3 | 4 | no | — |
| 60 | #3293 | — | 3 | 4 | no | — |
| 61 | #3293 | — | 3 | 2 | no | — |
| 62 | #3293 | — | 3 | 4 | no | — |
| 63 | #3293 | D3 | 1 | 1 | yes | characteristic, direct product factor |
| 64 | C2×#494 | — | 3 | 1 | no | — |
| 65 | C2×#473 | — | 3 | 4 | no | — |
| 66 | C2×#456 | — | 3 | 4 | no | — |
| 67 | C2×#443 | — | 3 | 2 | no | — |
| 68 | C3×2−1+4 | C23 | 1 | 4 | yes | — |
| 69 | #1010 | — | 2 | 8 | no | — |
| 70 | #1010 | — | 4 | 4 | no | — |
| 71 | #1010 | C23 | 1 | 8 | yes | — |
| 72 | D3×#41 | — | 2 | 8 | no | — |
| 73 | D3×#41 | — | 4 | 4 | no | — |
| 74 | D3×#41 | C23 | 1 | 4 | yes | — |
| 75 | #1007 | — | 2 | 8 | no | — |
| 76 | #1007 | C23 | 1 | 4 | yes | — |
| 77 | C2×D3×Q8 | — | 2 | 8 | no | — |
| 78 | C2×D3×Q8 | C23 | 1 | 4 | yes | — |
| 79 | C3×#137 | — | 2 | 8 | no | — |
| 80 | C3×#137 | C23 | 1 | 8 | yes | — |
| 81 | C3×#135 | — | 2 | 4 | no | — |
| 82 | C3×#135 | C23 | 1 | 2 | yes | — |
| 83 | C2×C3×Q16 | — | 2 | 4 | no | — |
| 84 | C2×C3×Q16 | C23 | 1 | 4 | yes | — |
| 85 | C3×#131 | C23 | 1 | 4 | yes | — |
| 86 | C3×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 87 | #951 | — | 2 | 8 | no | — |
| 88 | #951 | C23 | 1 | 8 | yes | — |
| 89 | #950 | — | 2 | 8 | no | — |
| 90 | #950 | C23 | 1 | 4 | yes | — |
| 91 | #948 | C23 | 1 | 4 | yes | — |
| 92 | #944 | C23 | 1 | 4 | yes | — |
| 93 | C2×#216 | — | 2 | 8 | no | — |
| 94 | C2×#216 | C23 | 1 | 8 | yes | — |
| 95 | #942 | — | 2 | 8 | no | — |
| 96 | #942 | C23 | 1 | 8 | yes | — |
| 97 | #919 | — | 2 | 4 | no | — |
| 98 | #919 | D4 | 1 | 2 | yes | — |
| 99 | #918 | — | 2 | 8 | no | — |
| 100 | #918 | — | 2 | 8 | no | — |
| 101 | #918 | — | 2 | 8 | no | — |
| 102 | D3×Q16 | — | 2 | 8 | no | — |
| 103 | D3×Q16 | — | 2 | 4 | no | — |
| 104 | D3×Q16 | — | 2 | 8 | no | — |
| 105 | D3×Q16 | — | 2 | 4 | no | — |
| 106 | D3×Q16 | — | 2 | 4 | no | — |
| 107 | D3×Q16 | — | 2 | 4 | no | — |
| 108 | D3×Q16 | — | 2 | 4 | no | — |
| 109 | D3×Q16 | — | 2 | 4 | no | — |
| 110 | D3×Q16 | D4 | 1 | 2 | yes | — |
| 111 | #916 | — | 2 | 8 | no | — |
| 112 | #916 | D4 | 1 | 4 | yes | — |
| 113 | #915 | — | 2 | 8 | no | — |
| 114 | #915 | — | 2 | 8 | no | — |
| 115 | #915 | — | 2 | 8 | no | — |
| 116 | D3×SD16 | — | 2 | 8 | no | — |
| 117 | D3×SD16 | D4 | 1 | 4 | yes | — |
| 118 | #912 | — | 2 | 4 | no | — |
| 119 | #912 | D4 | 1 | 2 | yes | — |
| 120 | D3×D8 | D4 | 1 | 2 | yes | — |
| 121 | #909 | — | 2 | 8 | no | — |
| 122 | #909 | C23 | 1 | 8 | yes | — |
| 123 | #907 | — | 2 | 4 | no | — |
| 124 | #907 | C23 | 1 | 4 | yes | — |
| 125 | D3×M16 | — | 2 | 4 | no | — |
| 126 | D3×M16 | C23 | 1 | 4 | yes | — |
| 127 | C2×Dic12 | — | 2 | 4 | no | — |
| 128 | C2×Dic12 | C23 | 1 | 4 | yes | — |
| 129 | #904 | — | 2 | 4 | no | — |
| 130 | #904 | C23 | 1 | 2 | yes | — |
| 131 | #901 | — | 2 | 4 | no | — |
| 132 | #901 | C23 | 1 | 4 | yes | — |
| 133 | C2×D3×C8 | — | 2 | 4 | no | — |
| 134 | C2×D3×C8 | C23 | 1 | 2 | yes | — |
| 135 | D3×C4⋊C4 | — | 4 | 2 | no | — |
| 136 | #888 | — | 4 | 2 | no | — |
| 137 | C42×D3 | C23 | 1 | 1 | yes | characteristic |
| 138 | #869 | C23 | 1 | 2 | yes | — |
| 139 | C3×#108 | C23 | 1 | 2 | yes | — |
| 140 | C3×#104 | C23 | 1 | 4 | yes | — |
| 141 | C3×#101 | C23 | 1 | 4 | yes | — |
| 142 | C3×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 143 | #837 | C23 | 1 | 4 | yes | — |
| 144 | #836 | C23 | 1 | 4 | yes | — |
| 145 | #825 | C23 | 1 | 4 | yes | — |
| 146 | #824 | C23 | 1 | 8 | yes | — |
| 147 | #822 | C23 | 1 | 4 | yes | — |
| 148 | #819 | C23 | 1 | 2 | yes | — |
| 149 | C8×Dic3 | C23 | 1 | 2 | yes | — |
| 150 | #805 | C23 | 1 | 4 | yes | — |
| 151 | C4×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 152 | C2×2−1+4 | — | 3 | 4 | no | — |
| 153 | #578 | — | 3 | 8 | no | — |
| 154 | #578 | — | 3 | 8 | no | — |
| 155 | #578 | — | 3 | 4 | no | — |
| 156 | #578 | — | 3 | 4 | no | — |
| 157 | #578 | — | 3 | 4 | no | — |
| 158 | #578 | — | 6 | 4 | no | — |
| 159 | #578 | — | 6 | 4 | no | — |
| 160 | #578 | — | 6 | 8 | no | — |
| 161 | #578 | C2×D3 | 1 | 4 | yes | complemented |
| 162 | C2×#137 | — | 3 | 8 | no | — |
| 163 | C2×#137 | — | 6 | 8 | no | — |
| 164 | C2×#135 | — | 3 | 2 | no | — |
| 165 | C2×#135 | — | 6 | 4 | no | — |
| 166 | C22×Q16 | — | 3 | 4 | no | — |
| 167 | C22×Q16 | — | 6 | 4 | no | — |
| 168 | C2×#131 | — | 3 | 4 | no | — |
| 169 | C2×C4⋊Q8 | — | 3 | 2 | no | — |
| 170 | #494 | — | 3 | 4 | no | — |
| 171 | #494 | — | 3 | 2 | no | — |
| 172 | #494 | — | 3 | 1 | no | — |
| 173 | #494 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 174 | #473 | — | 3 | 8 | no | — |
| 175 | #473 | — | 3 | 4 | no | — |
| 176 | #473 | — | 3 | 4 | no | — |
| 177 | #473 | — | 3 | 4 | no | — |
| 178 | #473 | — | 3 | 8 | no | — |
| 179 | #473 | C2×D3 | 1 | 4 | yes | complemented |
| 180 | #456 | — | 3 | 4 | no | — |
| 181 | #456 | — | 3 | 8 | no | — |
| 182 | #456 | — | 3 | 4 | no | — |
| 183 | #456 | — | 3 | 8 | no | — |
| 184 | #456 | — | 3 | 4 | no | — |
| 185 | #456 | C2×D3 | 1 | 4 | yes | complemented |
| 186 | #443 | — | 3 | 2 | no | — |
| 187 | #443 | — | 3 | 4 | no | — |
| 188 | #443 | — | 3 | 2 | no | — |
| 189 | #443 | — | 3 | 4 | no | — |
| 190 | #443 | — | 3 | 2 | no | — |
| 191 | #443 | C2×D3 | 1 | 2 | yes | complemented |
| 192 | C2×#108 | — | 3 | 2 | no | — |
| 193 | C2×#104 | — | 3 | 4 | no | — |
| 194 | C2×#101 | — | 3 | 4 | no | — |
| 195 | C2×C4×C8 | — | 3 | 1 | no | — |
| 196 | C3×#41 | — | 2 | 8 | no | — |
| 197 | C3×#41 | — | 4 | 4 | no | — |
| 198 | C3×#41 | C24 | 1 | 4 | yes | — |
| 199 | C2×C3×Q8 | — | 2 | 8 | no | — |
| 200 | C2×C3×Q8 | C24 | 1 | 4 | yes | — |
| 201 | #239 | — | 2 | 8 | no | — |
| 202 | #239 | — | 4 | 4 | no | — |
| 203 | #239 | C2×D4 | 1 | 4 | yes | — |
| 204 | D3×Q8 | — | 2 | 8 | no | — |
| 205 | D3×Q8 | — | 2 | 8 | no | — |
| 206 | D3×Q8 | — | 2 | 8 | no | — |
| 207 | D3×Q8 | — | 2 | 8 | no | — |
| 208 | D3×Q8 | — | 4 | 8 | no | — |
| 209 | D3×Q8 | — | 4 | 4 | no | — |
| 210 | D3×Q8 | C2×D4 | 1 | 4 | yes | — |
| 211 | #237 | — | 2 | 4 | no | — |
| 212 | #237 | — | 2 | 8 | no | — |
| 213 | #237 | — | 4 | 8 | no | — |
| 214 | #237 | — | 4 | 8 | no | — |
| 215 | #237 | — | 4 | 4 | no | — |
| 216 | #237 | C2×D4 | 1 | 4 | yes | — |
| 217 | D3×D4 | — | 2 | 4 | no | — |
| 218 | D3×D4 | — | 4 | 4 | no | — |
| 219 | D3×D4 | C2×D4 | 1 | 4 | yes | — |
| 220 | #235 | — | 2 | 4 | no | — |
| 221 | #235 | — | 2 | 8 | no | — |
| 222 | #235 | — | 4 | 8 | no | — |
| 223 | #235 | — | 4 | 8 | no | — |
| 224 | #235 | — | 4 | 4 | no | — |
| 225 | #235 | C24 | 1 | 4 | yes | — |
| 226 | C2×C4×D3 | — | 2 | 1 | no | — |
| 227 | C2×C4×D3 | — | 2 | 4 | no | — |
| 228 | C2×C4×D3 | — | 2 | 4 | no | — |
| 229 | C2×C4×D3 | — | 4 | 8 | no | — |
| 230 | C2×C4×D3 | C24 | 1 | 1 | yes | characteristic |
| 231 | C2×Dic6 | — | 2 | 8 | no | — |
| 232 | C2×Dic6 | — | 2 | 4 | no | — |
| 233 | C2×Dic6 | — | 4 | 8 | no | — |
| 234 | C2×Dic6 | C24 | 1 | 4 | yes | — |
| 235 | C3×Q16 | — | 2 | 8 | no | — |
| 236 | C3×Q16 | — | 2 | 4 | no | — |
| 237 | C3×Q16 | — | 2 | 4 | no | — |
| 238 | C3×Q16 | C2×D4 | 1 | 2 | yes | — |
| 239 | C3×SD16 | — | 2 | 8 | no | — |
| 240 | C3×SD16 | C2×D4 | 1 | 4 | yes | — |
| 241 | C3×D8 | C2×D4 | 1 | 2 | yes | — |
| 242 | C3×M16 | — | 2 | 4 | no | — |
| 243 | C3×M16 | C24 | 1 | 4 | yes | — |
| 244 | C2×C3×C8 | — | 2 | 4 | no | — |
| 245 | C2×C3×C8 | C24 | 1 | 2 | yes | — |
| 246 | C3×C4⋊C4 | — | 4 | 2 | no | — |
| 247 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 248 | #216 | — | 2 | 8 | no | — |
| 249 | #216 | — | 2 | 8 | no | — |
| 250 | #216 | — | 2 | 8 | no | — |
| 251 | #216 | — | 2 | 8 | no | — |
| 252 | #216 | C2×D4 | 1 | 4 | yes | — |
| 253 | #215 | — | 2 | 8 | no | — |
| 254 | #215 | C2×D4 | 1 | 4 | yes | — |
| 255 | #214 | — | 2 | 8 | no | — |
| 256 | #214 | C2×D4 | 1 | 4 | yes | — |
| 257 | #213 | C2×D4 | 1 | 4 | yes | — |
| 258 | C4⋊Dic3 | — | 4 | 2 | no | — |
| 259 | Dic3⋊C4 | — | 4 | 4 | no | — |
| 260 | C4×Dic3 | — | 2 | 1 | no | — |
| 261 | C4×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 262 | #208 | — | 2 | 4 | no | — |
| 263 | #208 | C24 | 1 | 4 | yes | — |
| 264 | C2×C3⋊C8 | — | 2 | 4 | no | — |
| 265 | C2×C3⋊C8 | C24 | 1 | 2 | yes | — |
| 266 | Dic12 | — | 2 | 8 | no | — |
| 267 | Dic12 | — | 2 | 4 | no | — |
| 268 | Dic12 | — | 2 | 4 | no | — |
| 269 | Dic12 | C2×D4 | 1 | 2 | yes | — |
| 270 | D24 | C2×D4 | 1 | 2 | yes | — |
| 271 | #204 | — | 2 | 8 | no | — |
| 272 | #204 | C2×D4 | 1 | 4 | yes | — |
| 273 | ΓL(1,𝔽25) | — | 2 | 4 | no | — |
| 274 | ΓL(1,𝔽25) | — | 2 | 4 | no | — |
| 275 | ΓL(1,𝔽25) | — | 2 | 4 | no | — |
| 276 | D3×C8 | — | 2 | 4 | no | — |
| 277 | D3×C8 | — | 2 | 4 | no | — |
| 278 | D3×C8 | — | 2 | 4 | no | — |
| 279 | D3×C8 | C2×D4 | 1 | 2 | yes | — |
| 280 | D3×C8 | C2×D4 | 1 | 2 | yes | — |
| 281 | D3×C8 | C2×D4 | 1 | 2 | yes | — |
| 282 | D3×C8 | C2×D4 | 1 | 2 | yes | — |
| 283 | 2−1+4 | — | 3 | 8 | no | — |
| 284 | 2−1+4 | — | 3 | 4 | no | — |
| 285 | 2−1+4 | — | 6 | 8 | no | — |
| 286 | 2−1+4 | — | 6 | 8 | no | — |
| 287 | 2−1+4 | — | 12 | 4 | no | — |
| 288 | 2−1+4 | C22×D3 | 1 | 4 | yes | — |
| 289 | C2×#41 | — | 3 | 4 | no | — |
| 290 | C2×#41 | — | 6 | 8 | no | — |
| 291 | C2×#41 | — | 12 | 4 | no | — |
| 292 | C22×Q8 | — | 3 | 4 | no | — |
| 293 | C22×Q8 | — | 6 | 8 | no | — |
| 294 | #137 | — | 2 | 8 | no | — |
| 295 | #137 | — | 3 | 8 | no | — |
| 296 | #137 | — | 3 | 8 | no | — |
| 297 | #137 | — | 3 | 8 | no | — |
| 298 | #137 | — | 6 | 8 | no | — |
| 299 | #137 | — | 6 | 8 | no | — |
| 300 | #137 | — | 6 | 8 | no | — |
| 301 | #137 | — | 6 | 8 | no | — |
| 302 | #137 | — | 6 | 8 | no | — |
| 303 | #137 | — | 6 | 8 | no | — |
| 304 | #137 | — | 6 | 8 | no | — |
| 305 | #137 | — | 6 | 8 | no | — |
| 306 | #137 | — | 6 | 8 | no | — |
| 307 | #137 | C22×D3 | 1 | 8 | yes | — |
| 308 | #135 | — | 2 | 4 | no | — |
| 309 | #135 | — | 3 | 4 | no | — |
| 310 | #135 | — | 3 | 2 | no | — |
| 311 | #135 | — | 3 | 4 | no | — |
| 312 | #135 | — | 3 | 2 | no | — |
| 313 | #135 | — | 3 | 2 | no | — |
| 314 | #135 | — | 6 | 4 | no | — |
| 315 | #135 | — | 6 | 8 | no | — |
| 316 | #135 | — | 6 | 4 | no | — |
| 317 | #135 | — | 6 | 8 | no | — |
| 318 | #135 | — | 6 | 4 | no | — |
| 319 | #135 | C22×D3 | 1 | 2 | yes | — |
| 320 | C2×Q16 | — | 2 | 4 | no | — |
| 321 | C2×Q16 | — | 3 | 2 | no | — |
| 322 | C2×Q16 | — | 3 | 8 | no | — |
| 323 | C2×Q16 | — | 3 | 4 | no | — |
| 324 | C2×Q16 | — | 6 | 4 | no | — |
| 325 | C2×Q16 | — | 6 | 4 | no | — |
| 326 | C2×Q16 | — | 6 | 4 | no | — |
| 327 | C2×Q16 | — | 6 | 4 | no | — |
| 328 | C2×Q16 | — | 6 | 4 | no | — |
| 329 | C2×Q16 | — | 6 | 8 | no | — |
| 330 | C2×Q16 | — | 6 | 4 | no | — |
| 331 | C2×Q16 | — | 6 | 8 | no | — |
| 332 | C2×Q16 | — | 6 | 8 | no | — |
| 333 | C2×Q16 | — | 6 | 4 | no | — |
| 334 | C2×Q16 | C22×D3 | 1 | 4 | yes | — |
| 335 | C2×SD16 | — | 3 | 4 | no | — |
| 336 | C2×SD16 | — | 6 | 8 | no | — |
| 337 | C2×D8 | — | 3 | 2 | no | — |
| 338 | #131 | — | 3 | 4 | no | — |
| 339 | #131 | — | 3 | 4 | no | — |
| 340 | #131 | — | 3 | 4 | no | — |
| 341 | #131 | — | 6 | 4 | no | — |
| 342 | #131 | — | 6 | 4 | no | — |
| 343 | #131 | C22×D3 | 1 | 4 | yes | — |
| 344 | C2×M16 | — | 3 | 4 | no | — |
| 345 | C2×M16 | — | 6 | 4 | no | — |
| 346 | C22×C8 | — | 3 | 2 | no | — |
| 347 | C22×C8 | — | 6 | 4 | no | — |
| 348 | C4⋊Q8 | — | 3 | 4 | no | — |
| 349 | C4⋊Q8 | — | 3 | 2 | no | — |
| 350 | C4⋊Q8 | — | 12 | 2 | no | — |
| 351 | C4⋊Q8 | C22×D3 | 1 | 2 | yes | — |
| 352 | C2×C4⋊C4 | — | 12 | 2 | no | — |
| 353 | C2×C42 | — | 3 | 1 | no | — |
| 354 | #108 | — | 3 | 4 | no | — |
| 355 | #108 | — | 3 | 2 | no | — |
| 356 | #108 | C22×D3 | 1 | 2 | yes | — |
| 357 | #104 | — | 3 | 4 | no | — |
| 358 | #104 | — | 3 | 4 | no | — |
| 359 | #104 | — | 3 | 4 | no | — |
| 360 | #104 | C22×D3 | 1 | 4 | yes | — |
| 361 | #101 | — | 3 | 4 | no | — |
| 362 | #101 | — | 3 | 8 | no | — |
| 363 | #101 | C22×D3 | 1 | 4 | yes | — |
| 364 | C4×C8 | — | 3 | 2 | no | — |
| 365 | C4×C8 | — | 3 | 1 | no | — |
| 366 | C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 367 | C22×D3 | — | 2 | 4 | no | — |
| 368 | C22×D3 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 369 | C3×Q8 | — | 2 | 8 | no | — |
| 370 | C3×Q8 | — | 4 | 4 | no | — |
| 371 | C3×Q8 | C22×D4 | 1 | 4 | yes | — |
| 372 | C3×D4 | — | 2 | 4 | no | — |
| 373 | C3×D4 | — | 4 | 4 | no | — |
| 374 | C3×D4 | C22×D4 | 1 | 4 | yes | — |
| 375 | C2×C3×C4 | — | 2 | 1 | no | — |
| 376 | C2×C3×C4 | — | 2 | 4 | no | — |
| 377 | C2×C3×C4 | — | 2 | 4 | no | — |
| 378 | C2×C3×C4 | — | 4 | 8 | no | — |
| 379 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 380 | #67 | — | 2 | 4 | no | — |
| 381 | #67 | — | 2 | 4 | no | — |
| 382 | #67 | — | 2 | 4 | no | — |
| 383 | #67 | — | 4 | 8 | no | — |
| 384 | C2×Dic3 | — | 2 | 1 | no | — |
| 385 | C2×Dic3 | — | 2 | 4 | no | — |
| 386 | C2×Dic3 | — | 2 | 4 | no | — |
| 387 | C2×Dic3 | — | 4 | 8 | no | — |
| 388 | C2×Dic3 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 389 | D12 | — | 2 | 4 | no | — |
| 390 | D12 | — | 4 | 4 | no | — |
| 391 | D12 | C22×D4 | 1 | 4 | yes | — |
| 392 | C4×D3 | — | 2 | 4 | no | — |
| 393 | C4×D3 | — | 2 | 4 | no | — |
| 394 | C4×D3 | — | 2 | 4 | no | — |
| 395 | C4×D3 | — | 2 | 4 | no | — |
| 396 | C4×D3 | — | 4 | 8 | no | — |
| 397 | C4×D3 | — | 4 | 8 | no | — |
| 398 | C4×D3 | — | 4 | 4 | no | — |
| 399 | C4×D3 | — | 4 | 4 | no | — |
| 400 | C4×D3 | C22×D4 | 1 | 2 | yes | — |
| 401 | C4×D3 | C22×D4 | 1 | 2 | yes | — |
| 402 | Dic6 | — | 2 | 4 | no | — |
| 403 | Dic6 | — | 2 | 8 | no | — |
| 404 | Dic6 | — | 4 | 4 | no | — |
| 405 | Dic6 | — | 4 | 8 | no | — |
| 406 | Dic6 | — | 4 | 8 | no | — |
| 407 | Dic6 | C22×D4 | 1 | 4 | yes | — |
| 408 | C3×C8 | — | 2 | 4 | no | — |
| 409 | C3×C8 | C22×D4 | 1 | 2 | yes | — |
| 410 | C3×C8 | C22×D4 | 1 | 2 | yes | — |
| 411 | C3⋊C8 | — | 2 | 4 | no | — |
| 412 | C3⋊C8 | C22×D4 | 1 | 2 | yes | — |
| 413 | C3⋊C8 | C22×D4 | 1 | 2 | yes | — |
| 414 | #41 | — | 2 | 8 | no | — |
| 415 | #41 | — | 3 | 4 | no | — |
| 416 | #41 | — | 3 | 4 | no | — |
| 417 | #41 | — | 3 | 4 | no | — |
| 418 | #41 | — | 4 | 4 | no | — |
| 419 | #41 | — | 6 | 4 | no | — |
| 420 | #41 | — | 6 | 8 | no | — |
| 421 | #41 | — | 6 | 4 | no | — |
| 422 | #41 | — | 6 | 8 | no | — |
| 423 | #41 | — | 6 | 8 | no | — |
| 424 | #41 | — | 12 | 4 | no | — |
| 425 | #41 | — | 12 | 8 | no | — |
| 426 | #41 | — | 12 | 8 | no | — |
| 427 | #41 | — | 12 | 8 | no | — |
| 428 | #41 | — | 12 | 8 | no | — |
| 429 | #41 | — | 12 | 4 | no | — |
| 430 | #41 | — | 12 | 4 | no | — |
| 431 | #41 | C23×D3 | 1 | 4 | yes | — |
| 432 | C2×Q8 | — | 2 | 8 | no | — |
| 433 | C2×Q8 | — | 3 | 4 | no | — |
| 434 | C2×Q8 | — | 3 | 4 | no | — |
| 435 | C2×Q8 | — | 6 | 4 | no | — |
| 436 | C2×Q8 | — | 6 | 8 | no | — |
| 437 | C2×Q8 | — | 6 | 8 | no | — |
| 438 | C2×Q8 | — | 6 | 8 | no | — |
| 439 | C2×Q8 | — | 6 | 8 | no | — |
| 440 | C2×Q8 | — | 6 | 8 | no | — |
| 441 | C2×Q8 | — | 12 | 8 | no | — |
| 442 | C2×Q8 | — | 12 | 4 | no | — |
| 443 | C2×Q8 | — | 12 | 8 | no | — |
| 444 | C2×Q8 | C23×D3 | 1 | 4 | yes | — |
| 445 | C2×D4 | — | 3 | 4 | no | — |
| 446 | C2×D4 | — | 6 | 4 | no | — |
| 447 | C2×D4 | — | 12 | 4 | no | — |
| 448 | C22×C4 | — | 3 | 1 | no | — |
| 449 | C22×C4 | — | 6 | 4 | no | — |
| 450 | C22×C4 | — | 6 | 1 | no | — |
| 451 | C22×C4 | — | 6 | 4 | no | — |
| 452 | C22×C4 | — | 12 | 8 | no | — |
| 453 | Q16 | — | 2 | 8 | no | — |
| 454 | Q16 | — | 2 | 4 | no | — |
| 455 | Q16 | — | 2 | 4 | no | — |
| 456 | Q16 | — | 3 | 4 | no | — |
| 457 | Q16 | — | 3 | 2 | no | — |
| 458 | Q16 | — | 6 | 8 | no | — |
| 459 | Q16 | — | 6 | 8 | no | — |
| 460 | Q16 | — | 6 | 8 | no | — |
| 461 | Q16 | — | 6 | 8 | no | — |
| 462 | Q16 | — | 6 | 8 | no | — |
| 463 | Q16 | — | 6 | 4 | no | — |
| 464 | Q16 | — | 6 | 4 | no | — |
| 465 | Q16 | D3×D4 | 1 | 2 | yes | — |
| 466 | SD16 | — | 2 | 8 | no | — |
| 467 | SD16 | — | 3 | 4 | no | — |
| 468 | SD16 | — | 3 | 4 | no | — |
| 469 | SD16 | — | 3 | 4 | no | — |
| 470 | SD16 | — | 6 | 8 | no | — |
| 471 | SD16 | — | 6 | 8 | no | — |
| 472 | SD16 | — | 6 | 8 | no | — |
| 473 | SD16 | D3×D4 | 1 | 4 | yes | — |
| 474 | D8 | — | 3 | 4 | no | — |
| 475 | D8 | — | 3 | 2 | no | — |
| 476 | D8 | D3×D4 | 1 | 2 | yes | — |
| 477 | M16 | — | 2 | 4 | no | — |
| 478 | M16 | — | 3 | 4 | no | — |
| 479 | M16 | — | 6 | 4 | no | — |
| 480 | M16 | — | 6 | 4 | no | — |
| 481 | M16 | — | 6 | 4 | no | — |
| 482 | M16 | — | 6 | 4 | no | — |
| 483 | M16 | C23×D3 | 1 | 4 | yes | — |
| 484 | C2×C8 | — | 2 | 4 | no | — |
| 485 | C2×C8 | — | 3 | 2 | no | — |
| 486 | C2×C8 | — | 3 | 2 | no | — |
| 487 | C2×C8 | — | 3 | 2 | no | — |
| 488 | C2×C8 | — | 3 | 2 | no | — |
| 489 | C2×C8 | — | 3 | 2 | no | — |
| 490 | C2×C8 | — | 6 | 4 | no | — |
| 491 | C2×C8 | — | 6 | 4 | no | — |
| 492 | C2×C8 | — | 6 | 4 | no | — |
| 493 | C2×C8 | — | 6 | 4 | no | — |
| 494 | C2×C8 | C23×D3 | 1 | 2 | yes | — |
| 495 | C4⋊C4 | — | 4 | 2 | no | — |
| 496 | C4⋊C4 | — | 12 | 4 | no | — |
| 497 | C4⋊C4 | — | 12 | 2 | no | — |
| 498 | C42 | — | 3 | 1 | no | — |
| 499 | C42 | — | 6 | 1 | no | — |
| 500 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 501 | C22×C3 | — | 2 | 4 | no | — |
| 502 | C22×C3 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 503 | C2×D3 | — | 2 | 2 | no | — |
| 504 | C2×D3 | — | 2 | 4 | no | — |
| 505 | C2×D3 | — | 4 | 8 | no | — |
| 506 | C2×D3 | D42 | 1 | 1 | yes | characteristic |
| 507 | C2×D3 | D42 | 1 | 1 | yes | characteristic |
| 508 | C3×C4 | — | 2 | 2 | no | — |
| 509 | C3×C4 | — | 2 | 4 | no | — |
| 510 | C3×C4 | — | 4 | 4 | no | — |
| 511 | C3×C4 | C23×D4 | 1 | 2 | yes | — |
| 512 | Dic3 | — | 2 | 2 | no | — |
| 513 | Dic3 | — | 2 | 4 | no | — |
| 514 | Dic3 | — | 4 | 4 | no | — |
| 515 | Dic3 | D42 | 1 | 2 | yes | — |
| 516 | C23 | — | 3 | 1 | no | — |
| 517 | C23 | — | 6 | 4 | no | — |
| 518 | Q8 | — | 2 | 8 | no | — |
| 519 | Q8 | — | 3 | 4 | no | — |
| 520 | Q8 | — | 4 | 4 | no | — |
| 521 | Q8 | — | 6 | 4 | no | — |
| 522 | Q8 | — | 6 | 8 | no | — |
| 523 | Q8 | — | 12 | 8 | no | — |
| 524 | Q8 | — | 12 | 8 | no | — |
| 525 | Q8 | — | 12 | 4 | no | — |
| 526 | Q8 | C2×D3×D4 | 1 | 4 | yes | — |
| 527 | D4 | — | 2 | 4 | no | — |
| 528 | D4 | — | 3 | 4 | no | — |
| 529 | D4 | — | 4 | 4 | no | — |
| 530 | D4 | — | 6 | 4 | no | — |
| 531 | D4 | — | 6 | 4 | no | — |
| 532 | D4 | — | 6 | 4 | no | — |
| 533 | D4 | — | 6 | 4 | no | — |
| 534 | D4 | — | 12 | 4 | no | — |
| 535 | D4 | — | 12 | 8 | no | — |
| 536 | D4 | C2×D3×D4 | 1 | 4 | yes | — |
| 537 | C2×C4 | — | 2 | 1 | no | — |
| 538 | C2×C4 | — | 2 | 4 | no | — |
| 539 | C2×C4 | — | 2 | 4 | no | — |
| 540 | C2×C4 | — | 3 | 1 | no | — |
| 541 | C2×C4 | — | 3 | 2 | no | — |
| 542 | C2×C4 | — | 3 | 2 | no | — |
| 543 | C2×C4 | — | 4 | 8 | no | — |
| 544 | C2×C4 | — | 6 | 4 | no | — |
| 545 | C2×C4 | — | 6 | 4 | no | — |
| 546 | C2×C4 | — | 6 | 4 | no | — |
| 547 | C2×C4 | — | 6 | 4 | no | — |
| 548 | C2×C4 | — | 6 | 1 | no | — |
| 549 | C2×C4 | — | 6 | 4 | no | — |
| 550 | C2×C4 | — | 6 | 4 | no | — |
| 551 | C2×C4 | — | 12 | 8 | no | — |
| 552 | C2×C4 | — | 12 | 8 | no | — |
| 553 | C2×C4 | — | 12 | 4 | no | — |
| 554 | C2×C4 | — | 12 | 4 | no | — |
| 555 | C2×C4 | — | 12 | 8 | no | — |
| 556 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 557 | C8 | — | 2 | 4 | no | — |
| 558 | C8 | — | 3 | 2 | no | — |
| 559 | C8 | — | 3 | 2 | no | — |
| 560 | C8 | — | 6 | 4 | no | — |
| 561 | C8 | C2×D3×D4 | 1 | 2 | yes | — |
| 562 | C8 | C2×D3×D4 | 1 | 2 | yes | — |
| 563 | C2×C3 | — | 2 | 1 | no | — |
| 564 | C2×C3 | — | 4 | 4 | no | — |
| 565 | C2×C3 | C2×D42 | 1 | 1 | yes | characteristic |
| 566 | D3 | — | 2 | 1 | no | — |
| 567 | D3 | — | 4 | 4 | no | — |
| 568 | D3 | #3293 | 1 | 2 | yes | direct product factor |
| 569 | C22 | — | 2 | 4 | no | — |
| 570 | C22 | — | 3 | 1 | no | — |
| 571 | C22 | — | 3 | 1 | no | — |
| 572 | C22 | — | 6 | 2 | no | — |
| 573 | C22 | — | 6 | 4 | no | — |
| 574 | C22 | — | 12 | 8 | no | — |
| 575 | C22 | D3×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 576 | C4 | — | 2 | 2 | no | — |
| 577 | C4 | — | 2 | 4 | no | — |
| 578 | C4 | — | 3 | 2 | no | — |
| 579 | C4 | — | 4 | 4 | no | — |
| 580 | C4 | — | 6 | 2 | no | — |
| 581 | C4 | — | 6 | 4 | no | — |
| 582 | C4 | — | 12 | 4 | no | — |
| 583 | C4 | C22×D3×D4 | 1 | 2 | yes | — |
| 584 | C3 | C2×#3293 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 585 | C2 | — | 2 | 1 | no | — |
| 586 | C2 | — | 3 | 2 | no | — |
| 587 | C2 | — | 4 | 4 | no | — |
| 588 | C2 | — | 6 | 1 | no | — |
| 589 | C2 | — | 12 | 4 | no | — |
| 590 | C2 | D3×D42 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D3×D42 |
| commutator, cosocle | C2×C3×C4 | C25 |
| Frattini | C2×C4 | C24×D3 |
| Fitting | C3×#3293 | C2 |
| socle | C2×C3 | C2×D42 |
| hypercenter | #3293 | D3 |
| hypocenter | C3 | C2×#3293 |
| LCS | G ▷ C2×C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #3293 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D3×#578 | C2 | semidirect |
| 2. C3×#3293 | C2 | semidirect |
| 3. #84018 | C2 | semidirect |
| 4. #81808 | C2 | semidirect |
| 5. D3×#494 | C2 | semidirect |
| 6. #80947 | C2 | semidirect |
| 7. D3×#473 | C2 | semidirect |
| 8. #80303 | C2 | semidirect |
| 9. D3×#456 | C2 | semidirect |
| 10. #79895 | C2 | semidirect |
| 11. D3×#443 | C2 | semidirect |
| 14. C3×#578 | C22 | semidirect |
| 15. #5838 | C22 | semidirect |
| 17. #5779 | C22 | semidirect |
| 21. #5771 | C22 | semidirect |
| 25. #5766 | C22 | semidirect |
| 28. #5753 | C22 | semidirect |
| 31. C3×#494 | C22 | semidirect |
| 32. C3×#473 | C22 | semidirect |
| 33. C3×#456 | C22 | semidirect |
| 34. C3×#443 | C22 | semidirect |
| 35. #5246 | C22 | semidirect |
| 36. #5205 | C22 | semidirect |
| 37. #5204 | C22 | semidirect |
| 38. #5196 | C22 | semidirect |
| 39. #5192 | C22 | semidirect |
| 40. #5183 | C22 | semidirect |
| 41. #5144 | C22 | semidirect |
| 42. #5143 | C22 | semidirect |
| 43. #5095 | C22 | semidirect |
| 44. #5092 | C22 | semidirect |
| 45. #4896 | C22 | semidirect |
| 46. #4895 | C22 | semidirect |
| 48. #4826 | C22 | semidirect |
| 49. #4824 | C22 | semidirect |
| 51. #4755 | C22 | semidirect |
| 52. #4752 | C22 | semidirect |
| 54. #4700 | C22 | semidirect |
| 55. #4699 | C22 | semidirect |
| 63. #3293 | D3 | direct (N × H) |
| 161. #578 | C2×D3 | semidirect |
| 173. #494 | C2×D3 | semidirect |
| 179. #473 | C2×D3 | semidirect |
| 185. #456 | C2×D3 | semidirect |
| 191. #443 | C2×D3 | semidirect |
| 568. D3 | #3293 | direct (N × H) |
| 584. C3 | C2×#3293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#578 | 2 |
| C3×#3293 | 2 |
| #84018 | 2 |
| #81808 | 2 |
| D3×#494 | 2 |
| #80947 | 2 |
| D3×#473 | 2 |
| #80303 | 2 |
| D3×#456 | 2 |
| #79895 | 2 |
| D3×#443 | 2 |
| C2×#3293 | 3 |