← C3×#63090 #10681697
Subgroups — C3×#63090 #10681697
Order 768.
10836 conjugacy classes of subgroups.
The subgroup lattice has 366 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×C3×#585 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C3×#3586 | C2 | 1 | 16 | yes | maximal, complemented |
| 3 | C3×#3585 | C2 | 1 | 16 | yes | maximal, complemented |
| 4 | C3×#3584 | C2 | 1 | 16 | yes | maximal, complemented |
| 5 | C2×C3×#575 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | C2×C3×#568 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #63090 | C3 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 8 | C3×#585 | — | 2 | 8 | no | — |
| 9 | C3×#585 | — | 2 | 8 | no | — |
| 10 | C3×#585 | C22 | 1 | 16 | yes | complemented |
| 11 | C3×#585 | C22 | 1 | 16 | yes | complemented |
| 12 | C2×C3×2−1+4 | — | 2 | 2 | no | — |
| 13 | C2×C3×2−1+4 | C22 | 1 | 8 | yes | complemented |
| 14 | C2×C3×H(5,𝔽2) | — | 2 | 6 | no | — |
| 15 | C2×C3×H(5,𝔽2) | C22 | 1 | 8 | yes | complemented |
| 16 | C22×C3×#41 | — | 2 | 8 | no | — |
| 17 | C22×C3×#41 | C22 | 1 | 1 | yes | characteristic |
| 18 | C22×C3×#41 | C22 | 1 | 12 | yes | complemented |
| 19 | C3×#578 | C22 | 1 | 64 | yes | complemented |
| 20 | C3×#577 | C22 | 1 | 128 | yes | complemented |
| 21 | C3×#576 | C22 | 1 | 64 | yes | complemented |
| 22 | C3×#575 | C22 | 1 | 16 | yes | complemented |
| 23 | C3×#575 | C22 | 1 | 96 | yes | complemented |
| 24 | C3×#575 | C22 | 1 | 48 | yes | complemented |
| 25 | C2×C3×#137 | C22 | 1 | 48 | yes | complemented |
| 26 | C2×C3×AGL(1,ℤ/8) | C22 | 1 | 48 | yes | complemented |
| 27 | C2×C3×#135 | C22 | 1 | 48 | yes | complemented |
| 28 | C3×#568 | C22 | 1 | 16 | yes | complemented |
| 29 | C2×C3×#131 | C22 | 1 | 8 | yes | complemented |
| 30 | C22×C3×M16 | C22 | 1 | 6 | yes | complemented |
| 31 | C2×#585 | C2×C3 | 1 | 2 | yes | complemented |
| 32 | #3586 | C2×C3 | 1 | 16 | yes | complemented |
| 33 | #3585 | C2×C3 | 1 | 16 | yes | complemented |
| 34 | #3584 | C2×C3 | 1 | 16 | yes | complemented |
| 35 | C2×#575 | C2×C3 | 1 | 12 | yes | complemented |
| 36 | C2×#568 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 37 | C3×2−1+4 | — | 2 | 32 | no | — |
| 38 | C3×2−1+4 | — | 2 | 16 | no | — |
| 39 | C3×2−1+4 | — | 2 | 16 | no | — |
| 40 | C3×2−1+4 | C23 | 1 | 64 | yes | complemented |
| 41 | C3×H(5,𝔽2) | — | 2 | 32 | no | — |
| 42 | C3×H(5,𝔽2) | — | 2 | 48 | no | — |
| 43 | C3×H(5,𝔽2) | — | 2 | 48 | no | — |
| 44 | C3×H(5,𝔽2) | C23 | 1 | 64 | yes | complemented |
| 45 | C2×C3×#41 | — | 2 | 64 | no | — |
| 46 | C2×C3×#41 | — | 2 | 64 | no | — |
| 47 | C2×C3×#41 | — | 2 | 8 | no | — |
| 48 | C2×C3×#41 | — | 2 | 24 | no | — |
| 49 | C2×C3×#41 | — | 2 | 12 | no | — |
| 50 | C2×C3×#41 | — | 2 | 12 | no | — |
| 51 | C2×C3×#41 | — | 2 | 24 | no | — |
| 52 | C2×C3×#41 | — | 2 | 24 | no | — |
| 53 | C2×C3×#41 | D4 | 1 | 8 | yes | — |
| 54 | C2×C3×#41 | D4 | 1 | 4 | yes | — |
| 55 | C2×C3×#41 | C23 | 1 | 48 | yes | — |
| 56 | C2×C3×#41 | C23 | 1 | 8 | yes | — |
| 57 | C2×C3×#41 | C23 | 1 | 4 | yes | — |
| 58 | C2×C3×#41 | C23 | 1 | 8 | yes | — |
| 59 | C2×C3×#41 | C23 | 1 | 48 | yes | complemented |
| 60 | C2×C3×#41 | C23 | 1 | 24 | yes | complemented |
| 61 | C22×C3×Q8 | — | 2 | 8 | no | — |
| 62 | C22×C3×Q8 | D4 | 1 | 1 | yes | characteristic |
| 63 | C22×C3×Q8 | C23 | 1 | 12 | yes | complemented |
| 64 | C22×C3×D4 | — | 2 | 12 | no | — |
| 65 | C22×C3×D4 | — | 2 | 24 | no | — |
| 66 | C22×C3×D4 | D4 | 1 | 3 | yes | — |
| 67 | C22×C3×D4 | C23 | 1 | 12 | yes | complemented |
| 68 | C23×C3×C4 | — | 2 | 12 | no | — |
| 69 | C23×C3×C4 | C23 | 1 | 3 | yes | — |
| 70 | C3×#137 | C23 | 1 | 64 | yes | complemented |
| 71 | C3×#137 | C23 | 1 | 192 | yes | complemented |
| 72 | C3×AGL(1,ℤ/8) | C23 | 1 | 64 | yes | complemented |
| 73 | C3×AGL(1,ℤ/8) | C23 | 1 | 192 | yes | complemented |
| 74 | C3×#135 | C23 | 1 | 64 | yes | complemented |
| 75 | C3×#135 | C23 | 1 | 192 | yes | complemented |
| 76 | C2×C3×Q16 | C23 | 1 | 48 | yes | complemented |
| 77 | C2×C3×SD16 | C23 | 1 | 96 | yes | complemented |
| 78 | C2×C3×D8 | C23 | 1 | 48 | yes | complemented |
| 79 | C3×#131 | C23 | 1 | 64 | yes | complemented |
| 80 | C2×C3×M16 | C23 | 1 | 4 | yes | — |
| 81 | C2×C3×M16 | C23 | 1 | 12 | yes | complemented |
| 82 | C2×C3×M16 | C23 | 1 | 48 | yes | complemented |
| 83 | C22×C3×C8 | C23 | 1 | 12 | yes | complemented |
| 84 | #585 | — | 2 | 8 | no | — |
| 85 | #585 | — | 2 | 8 | no | — |
| 86 | #585 | C22×C3 | 1 | 16 | yes | complemented |
| 87 | #585 | C22×C3 | 1 | 16 | yes | complemented |
| 88 | C2×2−1+4 | — | 2 | 2 | no | — |
| 89 | C2×2−1+4 | C22×C3 | 1 | 8 | yes | complemented |
| 90 | C2×H(5,𝔽2) | — | 2 | 6 | no | — |
| 91 | C2×H(5,𝔽2) | C22×C3 | 1 | 8 | yes | complemented |
| 92 | C22×#41 | — | 2 | 8 | no | — |
| 93 | C22×#41 | C22×C3 | 1 | 1 | yes | characteristic |
| 94 | C22×#41 | C22×C3 | 1 | 12 | yes | complemented |
| 95 | #578 | C22×C3 | 1 | 64 | yes | complemented |
| 96 | #577 | C22×C3 | 1 | 128 | yes | complemented |
| 97 | #576 | C22×C3 | 1 | 64 | yes | complemented |
| 98 | #575 | C22×C3 | 1 | 16 | yes | complemented |
| 99 | #575 | C22×C3 | 1 | 96 | yes | complemented |
| 100 | #575 | C22×C3 | 1 | 48 | yes | complemented |
| 101 | C2×#137 | C22×C3 | 1 | 48 | yes | complemented |
| 102 | C2×AGL(1,ℤ/8) | C22×C3 | 1 | 48 | yes | complemented |
| 103 | C2×#135 | C22×C3 | 1 | 48 | yes | complemented |
| 104 | #568 | C22×C3 | 1 | 16 | yes | complemented |
| 105 | C2×#131 | C22×C3 | 1 | 8 | yes | complemented |
| 106 | C22×M16 | C22×C3 | 1 | 6 | yes | complemented |
| 107 | C24×C3 | — | 2 | 12 | no | — |
| 108 | C24×C3 | C2×D4 | 1 | 3 | yes | — |
| 109 | C3×#41 | — | 2 | 64 | no | — |
| 110 | C3×#41 | — | 2 | 192 | no | — |
| 111 | C3×#41 | — | 2 | 48 | no | — |
| 112 | C3×#41 | — | 2 | 8 | no | — |
| 113 | C3×#41 | — | 2 | 8 | no | — |
| 114 | C3×#41 | — | 2 | 48 | no | — |
| 115 | C3×#41 | — | 2 | 48 | no | — |
| 116 | C3×#41 | — | 2 | 48 | no | — |
| 117 | C3×#41 | — | 2 | 48 | no | — |
| 118 | C3×#41 | C2×D4 | 1 | 16 | yes | — |
| 119 | C3×#41 | C2×D4 | 1 | 32 | yes | — |
| 120 | C3×#41 | C24 | 1 | 16 | yes | — |
| 121 | C3×#41 | C24 | 1 | 96 | yes | — |
| 122 | C3×#41 | C24 | 1 | 16 | yes | — |
| 123 | C3×#41 | C24 | 1 | 16 | yes | — |
| 124 | C2×C3×Q8 | — | 2 | 64 | no | — |
| 125 | C2×C3×Q8 | — | 2 | 12 | no | — |
| 126 | C2×C3×Q8 | — | 2 | 24 | no | — |
| 127 | C2×C3×Q8 | C2×D4 | 1 | 8 | yes | — |
| 128 | C2×C3×Q8 | C2×D4 | 1 | 4 | yes | — |
| 129 | C2×C3×Q8 | C24 | 1 | 48 | yes | — |
| 130 | C2×C3×Q8 | C24 | 1 | 8 | yes | — |
| 131 | C2×C3×D4 | — | 2 | 8 | no | — |
| 132 | C2×C3×D4 | — | 2 | 24 | no | — |
| 133 | C2×C3×D4 | — | 2 | 48 | no | — |
| 134 | C2×C3×D4 | — | 2 | 48 | no | — |
| 135 | C2×C3×D4 | — | 2 | 192 | no | — |
| 136 | C2×C3×D4 | — | 2 | 12 | no | — |
| 137 | C2×C3×D4 | — | 2 | 24 | no | — |
| 138 | C2×C3×D4 | C2×D4 | 1 | 24 | yes | — |
| 139 | C2×C3×D4 | C2×D4 | 1 | 12 | yes | — |
| 140 | C2×C3×D4 | C24 | 1 | 48 | yes | — |
| 141 | C2×C3×D4 | C24 | 1 | 8 | yes | — |
| 142 | C22×C3×C4 | — | 2 | 12 | no | — |
| 143 | C22×C3×C4 | — | 2 | 8 | no | — |
| 144 | C22×C3×C4 | — | 2 | 24 | no | — |
| 145 | C22×C3×C4 | — | 2 | 48 | no | — |
| 146 | C22×C3×C4 | — | 2 | 48 | no | — |
| 147 | C22×C3×C4 | C2×D4 | 1 | 12 | yes | — |
| 148 | C22×C3×C4 | C2×D4 | 1 | 3 | yes | — |
| 149 | C22×C3×C4 | C2×D4 | 1 | 6 | yes | — |
| 150 | C22×C3×C4 | C24 | 1 | 6 | yes | — |
| 151 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 152 | C22×C3×C4 | C24 | 1 | 12 | yes | — |
| 153 | C3×Q16 | C24 | 1 | 64 | yes | — |
| 154 | C3×SD16 | C24 | 1 | 128 | yes | — |
| 155 | C3×D8 | C24 | 1 | 64 | yes | — |
| 156 | C3×M16 | C24 | 1 | 16 | yes | — |
| 157 | C3×M16 | C24 | 1 | 48 | yes | — |
| 158 | C2×C3×C8 | C24 | 1 | 8 | yes | — |
| 159 | C2×C3×C8 | C24 | 1 | 48 | yes | — |
| 160 | 2−1+4 | — | 2 | 32 | no | — |
| 161 | 2−1+4 | — | 2 | 16 | no | — |
| 162 | 2−1+4 | — | 2 | 16 | no | — |
| 163 | 2−1+4 | C23×C3 | 1 | 64 | yes | complemented |
| 164 | H(5,𝔽2) | — | 2 | 32 | no | — |
| 165 | H(5,𝔽2) | — | 2 | 48 | no | — |
| 166 | H(5,𝔽2) | — | 2 | 48 | no | — |
| 167 | H(5,𝔽2) | C23×C3 | 1 | 64 | yes | complemented |
| 168 | C2×#41 | — | 2 | 64 | no | — |
| 169 | C2×#41 | — | 2 | 64 | no | — |
| 170 | C2×#41 | — | 2 | 8 | no | — |
| 171 | C2×#41 | — | 2 | 24 | no | — |
| 172 | C2×#41 | — | 2 | 12 | no | — |
| 173 | C2×#41 | — | 2 | 12 | no | — |
| 174 | C2×#41 | — | 2 | 24 | no | — |
| 175 | C2×#41 | — | 2 | 24 | no | — |
| 176 | C2×#41 | C3×D4 | 1 | 8 | yes | — |
| 177 | C2×#41 | C3×D4 | 1 | 4 | yes | — |
| 178 | C2×#41 | C23×C3 | 1 | 48 | yes | — |
| 179 | C2×#41 | C23×C3 | 1 | 8 | yes | — |
| 180 | C2×#41 | C23×C3 | 1 | 4 | yes | — |
| 181 | C2×#41 | C23×C3 | 1 | 8 | yes | — |
| 182 | C2×#41 | C23×C3 | 1 | 48 | yes | complemented |
| 183 | C2×#41 | C23×C3 | 1 | 24 | yes | complemented |
| 184 | C22×Q8 | — | 2 | 8 | no | — |
| 185 | C22×Q8 | C3×D4 | 1 | 1 | yes | characteristic |
| 186 | C22×Q8 | C23×C3 | 1 | 12 | yes | complemented |
| 187 | C22×D4 | — | 2 | 12 | no | — |
| 188 | C22×D4 | — | 2 | 24 | no | — |
| 189 | C22×D4 | C3×D4 | 1 | 3 | yes | — |
| 190 | C22×D4 | C23×C3 | 1 | 12 | yes | complemented |
| 191 | C23×C4 | — | 2 | 12 | no | — |
| 192 | C23×C4 | C23×C3 | 1 | 3 | yes | — |
| 193 | #137 | C23×C3 | 1 | 64 | yes | complemented |
| 194 | #137 | C23×C3 | 1 | 192 | yes | complemented |
| 195 | AGL(1,ℤ/8) | C23×C3 | 1 | 64 | yes | complemented |
| 196 | AGL(1,ℤ/8) | C23×C3 | 1 | 192 | yes | complemented |
| 197 | #135 | C23×C3 | 1 | 64 | yes | complemented |
| 198 | #135 | C23×C3 | 1 | 192 | yes | complemented |
| 199 | C2×Q16 | C23×C3 | 1 | 48 | yes | complemented |
| 200 | C2×SD16 | C23×C3 | 1 | 96 | yes | complemented |
| 201 | C2×D8 | C23×C3 | 1 | 48 | yes | complemented |
| 202 | #131 | C23×C3 | 1 | 64 | yes | complemented |
| 203 | C2×M16 | C23×C3 | 1 | 4 | yes | — |
| 204 | C2×M16 | C23×C3 | 1 | 12 | yes | complemented |
| 205 | C2×M16 | C23×C3 | 1 | 48 | yes | complemented |
| 206 | C22×C8 | C23×C3 | 1 | 12 | yes | complemented |
| 207 | C23×C3 | — | 2 | 8 | no | — |
| 208 | C23×C3 | — | 2 | 48 | no | — |
| 209 | C23×C3 | — | 8 | 3 | no | — |
| 210 | C23×C3 | — | 8 | 24 | no | — |
| 211 | C23×C3 | C22×D4 | 1 | 12 | yes | — |
| 212 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 213 | C23×C3 | C22×D4 | 1 | 6 | yes | — |
| 214 | C3×Q8 | — | 2 | 8 | no | — |
| 215 | C3×Q8 | — | 2 | 48 | no | — |
| 216 | C3×Q8 | C22×D4 | 1 | 16 | yes | — |
| 217 | C3×Q8 | C25 | 1 | 16 | yes | — |
| 218 | C3×D4 | — | 2 | 16 | no | — |
| 219 | C3×D4 | — | 2 | 96 | no | — |
| 220 | C3×D4 | — | 2 | 16 | no | — |
| 221 | C3×D4 | — | 2 | 8 | no | — |
| 222 | C3×D4 | — | 2 | 48 | no | — |
| 223 | C3×D4 | C22×D4 | 1 | 48 | yes | — |
| 224 | C3×D4 | C25 | 1 | 16 | yes | — |
| 225 | C2×C3×C4 | — | 2 | 8 | no | — |
| 226 | C2×C3×C4 | — | 2 | 48 | no | — |
| 227 | C2×C3×C4 | — | 2 | 16 | no | — |
| 228 | C2×C3×C4 | — | 2 | 96 | no | — |
| 229 | C2×C3×C4 | — | 2 | 16 | no | — |
| 230 | C2×C3×C4 | C22×D4 | 1 | 12 | yes | — |
| 231 | C2×C3×C4 | C22×D4 | 1 | 24 | yes | — |
| 232 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 233 | C2×C3×C4 | C22×D4 | 1 | 6 | yes | — |
| 234 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 235 | C2×C3×C4 | C22×D4 | 1 | 12 | yes | — |
| 236 | C2×C3×C4 | C25 | 1 | 12 | yes | — |
| 237 | C2×C3×C4 | C25 | 1 | 2 | yes | — |
| 238 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 239 | C3×C8 | C25 | 1 | 16 | yes | — |
| 240 | C24 | — | 2 | 12 | no | — |
| 241 | C24 | C2×C3×D4 | 1 | 3 | yes | — |
| 242 | #41 | — | 2 | 64 | no | — |
| 243 | #41 | — | 2 | 192 | no | — |
| 244 | #41 | — | 2 | 8 | no | — |
| 245 | #41 | — | 2 | 48 | no | — |
| 246 | #41 | — | 2 | 8 | no | — |
| 247 | #41 | — | 2 | 48 | no | — |
| 248 | #41 | — | 2 | 48 | no | — |
| 249 | #41 | — | 2 | 48 | no | — |
| 250 | #41 | — | 2 | 48 | no | — |
| 251 | #41 | C2×C3×D4 | 1 | 16 | yes | — |
| 252 | #41 | C2×C3×D4 | 1 | 32 | yes | — |
| 253 | #41 | C24×C3 | 1 | 16 | yes | — |
| 254 | #41 | C24×C3 | 1 | 96 | yes | — |
| 255 | #41 | C24×C3 | 1 | 16 | yes | — |
| 256 | #41 | C24×C3 | 1 | 16 | yes | — |
| 257 | C2×Q8 | — | 2 | 64 | no | — |
| 258 | C2×Q8 | — | 2 | 12 | no | — |
| 259 | C2×Q8 | — | 2 | 24 | no | — |
| 260 | C2×Q8 | C2×C3×D4 | 1 | 8 | yes | — |
| 261 | C2×Q8 | C2×C3×D4 | 1 | 4 | yes | — |
| 262 | C2×Q8 | C24×C3 | 1 | 48 | yes | — |
| 263 | C2×Q8 | C24×C3 | 1 | 8 | yes | — |
| 264 | C2×D4 | — | 2 | 8 | no | — |
| 265 | C2×D4 | — | 2 | 24 | no | — |
| 266 | C2×D4 | — | 2 | 48 | no | — |
| 267 | C2×D4 | — | 2 | 48 | no | — |
| 268 | C2×D4 | — | 2 | 192 | no | — |
| 269 | C2×D4 | — | 2 | 12 | no | — |
| 270 | C2×D4 | — | 2 | 24 | no | — |
| 271 | C2×D4 | C2×C3×D4 | 1 | 24 | yes | — |
| 272 | C2×D4 | C2×C3×D4 | 1 | 12 | yes | — |
| 273 | C2×D4 | C24×C3 | 1 | 48 | yes | — |
| 274 | C2×D4 | C24×C3 | 1 | 8 | yes | — |
| 275 | C22×C4 | — | 2 | 12 | no | — |
| 276 | C22×C4 | — | 2 | 8 | no | — |
| 277 | C22×C4 | — | 2 | 24 | no | — |
| 278 | C22×C4 | — | 2 | 48 | no | — |
| 279 | C22×C4 | — | 2 | 48 | no | — |
| 280 | C22×C4 | C2×C3×D4 | 1 | 12 | yes | — |
| 281 | C22×C4 | C2×C3×D4 | 1 | 3 | yes | — |
| 282 | C22×C4 | C2×C3×D4 | 1 | 6 | yes | — |
| 283 | C22×C4 | C24×C3 | 1 | 6 | yes | — |
| 284 | C22×C4 | C24×C3 | 1 | 1 | yes | characteristic |
| 285 | C22×C4 | C24×C3 | 1 | 12 | yes | — |
| 286 | Q16 | C24×C3 | 1 | 64 | yes | — |
| 287 | SD16 | C24×C3 | 1 | 128 | yes | — |
| 288 | D8 | C24×C3 | 1 | 64 | yes | — |
| 289 | M16 | C24×C3 | 1 | 16 | yes | — |
| 290 | M16 | C24×C3 | 1 | 48 | yes | — |
| 291 | C2×C8 | C24×C3 | 1 | 8 | yes | — |
| 292 | C2×C8 | C24×C3 | 1 | 48 | yes | — |
| 293 | C22×C3 | — | 2 | 16 | no | — |
| 294 | C22×C3 | — | 4 | 1 | no | — |
| 295 | C22×C3 | — | 4 | 12 | no | — |
| 296 | C22×C3 | — | 4 | 6 | no | — |
| 297 | C22×C3 | — | 4 | 16 | no | — |
| 298 | C22×C3 | — | 8 | 48 | no | — |
| 299 | C22×C3 | C23×D4 | 1 | 2 | yes | — |
| 300 | C22×C3 | C23×D4 | 1 | 12 | yes | — |
| 301 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 302 | C3×C4 | — | 2 | 16 | no | — |
| 303 | C3×C4 | C23×D4 | 1 | 2 | yes | — |
| 304 | C3×C4 | C23×D4 | 1 | 12 | yes | — |
| 305 | C3×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 306 | C3×C4 | C26 | 1 | 1 | yes | characteristic |
| 307 | C23 | — | 2 | 8 | no | — |
| 308 | C23 | — | 2 | 48 | no | — |
| 309 | C23 | — | 8 | 3 | no | — |
| 310 | C23 | — | 8 | 24 | no | — |
| 311 | C23 | C22×C3×D4 | 1 | 12 | yes | — |
| 312 | C23 | C22×C3×D4 | 1 | 1 | yes | characteristic |
| 313 | C23 | C22×C3×D4 | 1 | 6 | yes | — |
| 314 | Q8 | — | 2 | 8 | no | — |
| 315 | Q8 | — | 2 | 48 | no | — |
| 316 | Q8 | C22×C3×D4 | 1 | 16 | yes | — |
| 317 | Q8 | C25×C3 | 1 | 16 | yes | — |
| 318 | D4 | — | 2 | 16 | no | — |
| 319 | D4 | — | 2 | 96 | no | — |
| 320 | D4 | — | 2 | 16 | no | — |
| 321 | D4 | — | 2 | 8 | no | — |
| 322 | D4 | — | 2 | 48 | no | — |
| 323 | D4 | C22×C3×D4 | 1 | 48 | yes | — |
| 324 | D4 | C25×C3 | 1 | 16 | yes | — |
| 325 | C2×C4 | — | 2 | 8 | no | — |
| 326 | C2×C4 | — | 2 | 48 | no | — |
| 327 | C2×C4 | — | 2 | 16 | no | — |
| 328 | C2×C4 | — | 2 | 16 | no | — |
| 329 | C2×C4 | — | 2 | 96 | no | — |
| 330 | C2×C4 | C22×C3×D4 | 1 | 2 | yes | — |
| 331 | C2×C4 | C22×C3×D4 | 1 | 12 | yes | — |
| 332 | C2×C4 | C22×C3×D4 | 1 | 12 | yes | — |
| 333 | C2×C4 | C22×C3×D4 | 1 | 24 | yes | — |
| 334 | C2×C4 | C22×C3×D4 | 1 | 1 | yes | characteristic |
| 335 | C2×C4 | C22×C3×D4 | 1 | 6 | yes | — |
| 336 | C2×C4 | C25×C3 | 1 | 1 | yes | characteristic |
| 337 | C2×C4 | C25×C3 | 1 | 12 | yes | — |
| 338 | C2×C4 | C25×C3 | 1 | 2 | yes | — |
| 339 | C8 | C25×C3 | 1 | 16 | yes | — |
| 340 | C2×C3 | — | 2 | 2 | no | — |
| 341 | C2×C3 | — | 2 | 1 | no | — |
| 342 | C2×C3 | — | 2 | 12 | no | — |
| 343 | C2×C3 | — | 4 | 16 | no | — |
| 344 | C2×C3 | C24×D4 | 1 | 1 | yes | characteristic |
| 345 | C22 | — | 2 | 16 | no | — |
| 346 | C22 | — | 4 | 1 | no | — |
| 347 | C22 | — | 4 | 12 | no | — |
| 348 | C22 | — | 4 | 6 | no | — |
| 349 | C22 | — | 4 | 16 | no | — |
| 350 | C22 | — | 8 | 48 | no | — |
| 351 | C22 | C23×C3×D4 | 1 | 2 | yes | — |
| 352 | C22 | C23×C3×D4 | 1 | 12 | yes | — |
| 353 | C22 | C23×C3×D4 | 1 | 1 | yes | characteristic |
| 354 | C4 | — | 2 | 16 | no | — |
| 355 | C4 | C23×C3×D4 | 1 | 1 | yes | characteristic |
| 356 | C4 | C23×C3×D4 | 1 | 2 | yes | — |
| 357 | C4 | C23×C3×D4 | 1 | 12 | yes | — |
| 358 | C4 | C26×C3 | 1 | 1 | yes | characteristic |
| 359 | C3 | #63090 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 360 | C2 | — | 2 | 2 | no | — |
| 361 | C2 | — | 2 | 1 | no | — |
| 362 | C2 | — | 2 | 12 | no | — |
| 363 | C2 | — | 4 | 16 | no | — |
| 364 | C2 | C24×C3×D4 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 1. C2×C3×#585 | C2 | semidirect |
| 2. C3×#3586 | C2 | semidirect |
| 3. C3×#3585 | C2 | semidirect |
| 4. C3×#3584 | C2 | semidirect |
| 5. C2×C3×#575 | C2 | semidirect |
| 6. C2×C3×#568 | C2 | semidirect |
| 7. #63090 | C3 | direct (N × H) |
| 10. C3×#585 | C22 | semidirect |
| 11. C3×#585 | C22 | semidirect |
| 13. C2×C3×2−1+4 | C22 | semidirect |
| 15. C2×C3×H(5,𝔽2) | C22 | semidirect |
| 18. C22×C3×#41 | C22 | semidirect |
| 19. C3×#578 | C22 | semidirect |
| 20. C3×#577 | C22 | semidirect |
| 21. C3×#576 | C22 | semidirect |
| 22. C3×#575 | C22 | semidirect |
| 23. C3×#575 | C22 | semidirect |
| 24. C3×#575 | C22 | semidirect |
| 25. C2×C3×#137 | C22 | semidirect |
| 26. C2×C3×AGL(1,ℤ/8) | C22 | semidirect |
| 27. C2×C3×#135 | C22 | semidirect |
| 28. C3×#568 | C22 | semidirect |
| 29. C2×C3×#131 | C22 | semidirect |
| 30. C22×C3×M16 | C22 | semidirect |
| 31. C2×#585 | C2×C3 | semidirect |
| 32. #3586 | C2×C3 | semidirect |
| 33. #3585 | C2×C3 | semidirect |
| 34. #3584 | C2×C3 | semidirect |
| 35. C2×#575 | C2×C3 | semidirect |
| 36. C2×#568 | C2×C3 | semidirect |
| 40. C3×2−1+4 | C23 | semidirect |
| 44. C3×H(5,𝔽2) | C23 | semidirect |
| 59. C2×C3×#41 | C23 | semidirect |
| 60. C2×C3×#41 | C23 | semidirect |
| 63. C22×C3×Q8 | C23 | semidirect |
| 67. C22×C3×D4 | C23 | semidirect |
| 70. C3×#137 | C23 | semidirect |
| 71. C3×#137 | C23 | semidirect |
| 72. C3×AGL(1,ℤ/8) | C23 | semidirect |
| 73. C3×AGL(1,ℤ/8) | C23 | semidirect |
| 74. C3×#135 | C23 | semidirect |
| 75. C3×#135 | C23 | semidirect |
| 76. C2×C3×Q16 | C23 | semidirect |
| 77. C2×C3×SD16 | C23 | semidirect |
| 78. C2×C3×D8 | C23 | semidirect |
| 79. C3×#131 | C23 | semidirect |
| 81. C2×C3×M16 | C23 | semidirect |
| 82. C2×C3×M16 | C23 | semidirect |
| 83. C22×C3×C8 | C23 | semidirect |
| 86. #585 | C22×C3 | semidirect |
| 87. #585 | C22×C3 | semidirect |
| 89. C2×2−1+4 | C22×C3 | semidirect |
| 91. C2×H(5,𝔽2) | C22×C3 | semidirect |
| 94. C22×#41 | C22×C3 | semidirect |
| 95. #578 | C22×C3 | semidirect |
| 96. #577 | C22×C3 | semidirect |
| 97. #576 | C22×C3 | semidirect |
| 98. #575 | C22×C3 | semidirect |
| 99. #575 | C22×C3 | semidirect |
| 100. #575 | C22×C3 | semidirect |
| 101. C2×#137 | C22×C3 | semidirect |
| 102. C2×AGL(1,ℤ/8) | C22×C3 | semidirect |
| 103. C2×#135 | C22×C3 | semidirect |
| 104. #568 | C22×C3 | semidirect |
| 105. C2×#131 | C22×C3 | semidirect |
| 106. C22×M16 | C22×C3 | semidirect |
| 163. 2−1+4 | C23×C3 | semidirect |
| 167. H(5,𝔽2) | C23×C3 | semidirect |
| 182. C2×#41 | C23×C3 | semidirect |
| 183. C2×#41 | C23×C3 | semidirect |
| 186. C22×Q8 | C23×C3 | semidirect |
| 190. C22×D4 | C23×C3 | semidirect |
| 193. #137 | C23×C3 | semidirect |
| 194. #137 | C23×C3 | semidirect |
| 195. AGL(1,ℤ/8) | C23×C3 | semidirect |
| 196. AGL(1,ℤ/8) | C23×C3 | semidirect |
| 197. #135 | C23×C3 | semidirect |
| 198. #135 | C23×C3 | semidirect |
| 199. C2×Q16 | C23×C3 | semidirect |
| 200. C2×SD16 | C23×C3 | semidirect |
| 201. C2×D8 | C23×C3 | semidirect |
| 202. #131 | C23×C3 | semidirect |
| 204. C2×M16 | C23×C3 | semidirect |
| 205. C2×M16 | C23×C3 | semidirect |
| 206. C22×C8 | C23×C3 | semidirect |
| 359. C3 | #63090 | direct (N × H) |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta