← C32×D3×H(5,𝔽2) #13181724
Subgroups — C32×D3×H(5,𝔽2) #13181724
Order 1728.
6052 conjugacy classes of subgroups.
The subgroup lattice has 290 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C33×H(5,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C32×#1009 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | C32×D3×#41 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | C32×#1004 | C2 | 1 | 9 | yes | maximal, complemented |
| 5 | C2×C32×D3×D4 | C2 | 1 | 9 | yes | maximal, complemented |
| 6 | C2×C32×H(5,𝔽2) | — | 3 | 1 | no | maximal |
| 7 | C3×D3×H(5,𝔽2) | C3 | 1 | 4 | yes | maximal, direct product factor |
| 8 | C23×C32×D3 | C22 | 1 | 6 | yes | complemented |
| 9 | C33×#41 | C22 | 1 | 6 | yes | complemented |
| 10 | C2×C33×D4 | C22 | 1 | 9 | yes | complemented |
| 11 | C2×C32×#67 | C22 | 1 | 18 | yes | complemented |
| 12 | C32×#239 | C22 | 1 | 6 | yes | complemented |
| 13 | C32×D3×Q8 | C22 | 1 | 2 | yes | complemented |
| 14 | C32×#237 | C22 | 1 | 18 | yes | complemented |
| 15 | C32×D3×D4 | C22 | 1 | 18 | yes | complemented |
| 16 | C32×D3×D4 | C22 | 1 | 36 | yes | complemented |
| 17 | C32×#235 | C22 | 1 | 18 | yes | complemented |
| 18 | C2×C32×D12 | C22 | 1 | 9 | yes | complemented |
| 19 | C2×C32×C4×D3 | C22 | 1 | 9 | yes | complemented |
| 20 | C32×H(5,𝔽2) | — | 2 | 4 | no | — |
| 21 | C32×H(5,𝔽2) | — | 3 | 6 | no | — |
| 22 | C32×H(5,𝔽2) | — | 3 | 9 | no | — |
| 23 | C32×H(5,𝔽2) | D3 | 1 | 1 | yes | characteristic, direct product factor |
| 24 | C32×H(5,𝔽2) | C2×C3 | 1 | 4 | yes | complemented |
| 25 | C2×C32×#41 | — | 3 | 6 | no | — |
| 26 | C22×C32×D4 | — | 3 | 9 | no | — |
| 27 | C3×#1009 | C2×C3 | 1 | 24 | yes | complemented |
| 28 | C3×D3×#41 | C2×C3 | 1 | 24 | yes | complemented |
| 29 | C3×#1004 | C2×C3 | 1 | 36 | yes | complemented |
| 30 | C2×C3×D3×D4 | C2×C3 | 1 | 36 | yes | complemented |
| 31 | C23×C33 | C23 | 1 | 6 | yes | complemented |
| 32 | C22×C32×D3 | — | 4 | 12 | no | — |
| 33 | C22×C32×D3 | C23 | 1 | 9 | yes | — |
| 34 | C22×C32×D3 | C23 | 1 | 18 | yes | complemented |
| 35 | C33×Q8 | C23 | 1 | 2 | yes | complemented |
| 36 | C33×D4 | C23 | 1 | 18 | yes | complemented |
| 37 | C2×C33×C4 | C23 | 1 | 9 | yes | complemented |
| 38 | C32×#67 | C23 | 1 | 36 | yes | complemented |
| 39 | C2×C32×Dic3 | C23 | 1 | 9 | yes | complemented |
| 40 | C32×D12 | C23 | 1 | 18 | yes | complemented |
| 41 | C32×C4×D3 | C23 | 1 | 6 | yes | — |
| 42 | C32×C4×D3 | C23 | 1 | 18 | yes | complemented |
| 43 | C32×Dic6 | C23 | 1 | 6 | yes | complemented |
| 44 | C2×C3×H(5,𝔽2) | — | 3 | 4 | no | — |
| 45 | D3×H(5,𝔽2) | C32 | 1 | 1 | yes | characteristic, direct product factor |
| 46 | C24×C32 | — | 3 | 6 | no | — |
| 47 | C23×C3×D3 | C22×C3 | 1 | 24 | yes | complemented |
| 48 | C32×#41 | — | 2 | 24 | no | — |
| 49 | C32×#41 | — | 3 | 6 | no | — |
| 50 | C32×#41 | — | 3 | 18 | no | — |
| 51 | C32×#41 | — | 3 | 18 | no | — |
| 52 | C32×#41 | C2×D3 | 1 | 6 | yes | complemented |
| 53 | C32×#41 | C22×C3 | 1 | 24 | yes | complemented |
| 54 | C2×C32×Q8 | — | 3 | 2 | no | — |
| 55 | C2×C32×D4 | — | 2 | 36 | no | — |
| 56 | C2×C32×D4 | — | 3 | 18 | no | — |
| 57 | C2×C32×D4 | — | 3 | 18 | no | — |
| 58 | C2×C32×D4 | — | 3 | 36 | no | — |
| 59 | C2×C32×D4 | — | 3 | 9 | no | — |
| 60 | C2×C32×D4 | C2×D3 | 1 | 9 | yes | complemented |
| 61 | C2×C32×D4 | C22×C3 | 1 | 36 | yes | complemented |
| 62 | C22×C32×C4 | — | 3 | 9 | no | — |
| 63 | C2×C3×#67 | C22×C3 | 1 | 72 | yes | complemented |
| 64 | C3×#239 | C22×C3 | 1 | 24 | yes | complemented |
| 65 | C3×D3×Q8 | C22×C3 | 1 | 8 | yes | complemented |
| 66 | C3×#237 | C22×C3 | 1 | 72 | yes | complemented |
| 67 | C3×D3×D4 | C22×C3 | 1 | 72 | yes | complemented |
| 68 | C3×D3×D4 | C22×C3 | 1 | 144 | yes | complemented |
| 69 | C3×#235 | C22×C3 | 1 | 72 | yes | complemented |
| 70 | C2×C3×D12 | C22×C3 | 1 | 36 | yes | complemented |
| 71 | C2×C3×C4×D3 | C22×C3 | 1 | 36 | yes | complemented |
| 72 | C22×C33 | — | 4 | 6 | no | — |
| 73 | C22×C33 | C24 | 1 | 9 | yes | — |
| 74 | C2×C32×D3 | — | 2 | 18 | no | — |
| 75 | C2×C32×D3 | — | 4 | 18 | no | — |
| 76 | C2×C32×D3 | C24 | 1 | 9 | yes | — |
| 77 | C2×C32×D3 | C24 | 1 | 1 | yes | characteristic |
| 78 | C33×C4 | C24 | 1 | 6 | yes | — |
| 79 | C32×Dic3 | C24 | 1 | 6 | yes | — |
| 80 | C3×H(5,𝔽2) | — | 2 | 4 | no | — |
| 81 | C3×H(5,𝔽2) | — | 3 | 24 | no | — |
| 82 | C3×H(5,𝔽2) | — | 3 | 36 | no | — |
| 83 | C3×H(5,𝔽2) | C3×D3 | 1 | 4 | yes | direct product factor |
| 84 | C3×H(5,𝔽2) | C2×C32 | 1 | 1 | yes | characteristic, complemented |
| 85 | C2×C3×#41 | — | 3 | 24 | no | — |
| 86 | C22×C3×D4 | — | 3 | 36 | no | — |
| 87 | #1009 | C2×C32 | 1 | 6 | yes | complemented |
| 88 | D3×#41 | C2×C32 | 1 | 6 | yes | complemented |
| 89 | #1004 | C2×C32 | 1 | 9 | yes | complemented |
| 90 | C2×D3×D4 | C2×C32 | 1 | 9 | yes | complemented |
| 91 | C23×C32 | — | 2 | 24 | no | — |
| 92 | C23×C32 | — | 3 | 9 | no | — |
| 93 | C23×C32 | — | 3 | 18 | no | — |
| 94 | C23×C32 | — | 12 | 12 | no | — |
| 95 | C23×C32 | C22×D3 | 1 | 6 | yes | complemented |
| 96 | C23×C32 | C23×C3 | 1 | 24 | yes | complemented |
| 97 | C22×C3×D3 | — | 4 | 48 | no | — |
| 98 | C22×C3×D3 | C23×C3 | 1 | 36 | yes | — |
| 99 | C22×C3×D3 | C23×C3 | 1 | 72 | yes | complemented |
| 100 | C32×Q8 | — | 2 | 8 | no | — |
| 101 | C32×Q8 | — | 3 | 6 | no | — |
| 102 | C32×Q8 | C22×D3 | 1 | 2 | yes | complemented |
| 103 | C32×Q8 | C23×C3 | 1 | 8 | yes | complemented |
| 104 | C32×D4 | — | 2 | 72 | no | — |
| 105 | C32×D4 | — | 3 | 36 | no | — |
| 106 | C32×D4 | — | 3 | 18 | no | — |
| 107 | C32×D4 | C22×D3 | 1 | 18 | yes | complemented |
| 108 | C32×D4 | C23×C3 | 1 | 72 | yes | complemented |
| 109 | C2×C32×C4 | — | 2 | 36 | no | — |
| 110 | C2×C32×C4 | — | 3 | 9 | no | — |
| 111 | C2×C32×C4 | — | 3 | 6 | no | — |
| 112 | C2×C32×C4 | — | 3 | 18 | no | — |
| 113 | C2×C32×C4 | C22×D3 | 1 | 9 | yes | complemented |
| 114 | C2×C32×C4 | C23×C3 | 1 | 36 | yes | complemented |
| 115 | C3×#67 | C23×C3 | 1 | 144 | yes | complemented |
| 116 | C2×C3×Dic3 | C23×C3 | 1 | 36 | yes | complemented |
| 117 | C3×D12 | C23×C3 | 1 | 72 | yes | complemented |
| 118 | C3×C4×D3 | C23×C3 | 1 | 24 | yes | — |
| 119 | C3×C4×D3 | C23×C3 | 1 | 72 | yes | complemented |
| 120 | C3×Dic6 | C23×C3 | 1 | 24 | yes | complemented |
| 121 | C2×H(5,𝔽2) | — | 3 | 1 | no | Sylow |
| 122 | C2×C33 | — | 2 | 9 | no | — |
| 123 | C2×C33 | C25 | 1 | 1 | yes | characteristic |
| 124 | C32×D3 | — | 2 | 9 | no | — |
| 125 | C32×D3 | H(5,𝔽2) | 1 | 2 | yes | direct product factor |
| 126 | C24×C3 | — | 3 | 24 | no | — |
| 127 | C23×D3 | C22×C32 | 1 | 6 | yes | complemented |
| 128 | C3×#41 | — | 2 | 24 | no | — |
| 129 | C3×#41 | — | 3 | 24 | no | — |
| 130 | C3×#41 | — | 3 | 72 | no | — |
| 131 | C3×#41 | — | 3 | 72 | no | — |
| 132 | C3×#41 | C2×C3×D3 | 1 | 24 | yes | complemented |
| 133 | C3×#41 | C22×C32 | 1 | 6 | yes | complemented |
| 134 | C2×C3×Q8 | — | 3 | 8 | no | — |
| 135 | C2×C3×D4 | — | 2 | 36 | no | — |
| 136 | C2×C3×D4 | — | 3 | 72 | no | — |
| 137 | C2×C3×D4 | — | 3 | 72 | no | — |
| 138 | C2×C3×D4 | — | 3 | 144 | no | — |
| 139 | C2×C3×D4 | — | 3 | 36 | no | — |
| 140 | C2×C3×D4 | C2×C3×D3 | 1 | 36 | yes | complemented |
| 141 | C2×C3×D4 | C22×C32 | 1 | 9 | yes | complemented |
| 142 | C22×C3×C4 | — | 3 | 36 | no | — |
| 143 | C2×#67 | C22×C32 | 1 | 18 | yes | complemented |
| 144 | #239 | C22×C32 | 1 | 6 | yes | complemented |
| 145 | D3×Q8 | C22×C32 | 1 | 2 | yes | complemented |
| 146 | #237 | C22×C32 | 1 | 18 | yes | complemented |
| 147 | D3×D4 | C22×C32 | 1 | 18 | yes | complemented |
| 148 | D3×D4 | C22×C32 | 1 | 36 | yes | complemented |
| 149 | #235 | C22×C32 | 1 | 18 | yes | complemented |
| 150 | C2×D12 | C22×C32 | 1 | 9 | yes | complemented |
| 151 | C2×C4×D3 | C22×C32 | 1 | 9 | yes | complemented |
| 152 | C22×C32 | — | 2 | 36 | no | — |
| 153 | C22×C32 | — | 3 | 1 | no | — |
| 154 | C22×C32 | — | 3 | 9 | no | — |
| 155 | C22×C32 | — | 4 | 6 | no | — |
| 156 | C22×C32 | — | 4 | 24 | no | — |
| 157 | C22×C32 | — | 6 | 18 | no | — |
| 158 | C22×C32 | — | 8 | 24 | no | — |
| 159 | C22×C32 | — | 12 | 18 | no | — |
| 160 | C22×C32 | C23×D3 | 1 | 9 | yes | — |
| 161 | C22×C32 | C24×C3 | 1 | 36 | yes | — |
| 162 | C2×C3×D3 | — | 2 | 72 | no | — |
| 163 | C2×C3×D3 | — | 4 | 72 | no | — |
| 164 | C2×C3×D3 | C24×C3 | 1 | 36 | yes | — |
| 165 | C2×C3×D3 | C24×C3 | 1 | 4 | yes | — |
| 166 | C32×C4 | — | 2 | 24 | no | — |
| 167 | C32×C4 | — | 3 | 6 | no | — |
| 168 | C32×C4 | C23×D3 | 1 | 6 | yes | — |
| 169 | C32×C4 | C24×C3 | 1 | 24 | yes | — |
| 170 | C3×Dic3 | C24×C3 | 1 | 24 | yes | — |
| 171 | H(5,𝔽2) | — | 3 | 6 | no | — |
| 172 | H(5,𝔽2) | — | 3 | 9 | no | — |
| 173 | H(5,𝔽2) | C32×D3 | 1 | 1 | yes | characteristic, direct product factor |
| 174 | C2×#41 | — | 3 | 6 | no | — |
| 175 | C22×D4 | — | 3 | 9 | no | — |
| 176 | C33 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 177 | C23×C3 | — | 2 | 24 | no | — |
| 178 | C23×C3 | — | 3 | 36 | no | — |
| 179 | C23×C3 | — | 3 | 72 | no | — |
| 180 | C23×C3 | — | 12 | 48 | no | — |
| 181 | C23×C3 | C22×C3×D3 | 1 | 24 | yes | complemented |
| 182 | C23×C3 | C23×C32 | 1 | 6 | yes | complemented |
| 183 | C22×D3 | — | 4 | 12 | no | — |
| 184 | C22×D3 | C23×C32 | 1 | 9 | yes | — |
| 185 | C22×D3 | C23×C32 | 1 | 18 | yes | complemented |
| 186 | C3×Q8 | — | 2 | 8 | no | — |
| 187 | C3×Q8 | — | 3 | 24 | no | — |
| 188 | C3×Q8 | C22×C3×D3 | 1 | 8 | yes | complemented |
| 189 | C3×Q8 | C23×C32 | 1 | 2 | yes | complemented |
| 190 | C3×D4 | — | 2 | 72 | no | — |
| 191 | C3×D4 | — | 3 | 144 | no | — |
| 192 | C3×D4 | — | 3 | 72 | no | — |
| 193 | C3×D4 | C22×C3×D3 | 1 | 72 | yes | complemented |
| 194 | C3×D4 | C23×C32 | 1 | 18 | yes | complemented |
| 195 | C2×C3×C4 | — | 2 | 36 | no | — |
| 196 | C2×C3×C4 | — | 3 | 36 | no | — |
| 197 | C2×C3×C4 | — | 3 | 24 | no | — |
| 198 | C2×C3×C4 | — | 3 | 72 | no | — |
| 199 | C2×C3×C4 | C22×C3×D3 | 1 | 36 | yes | complemented |
| 200 | C2×C3×C4 | C23×C32 | 1 | 9 | yes | complemented |
| 201 | #67 | C23×C32 | 1 | 36 | yes | complemented |
| 202 | C2×Dic3 | C23×C32 | 1 | 9 | yes | complemented |
| 203 | D12 | C23×C32 | 1 | 18 | yes | complemented |
| 204 | C4×D3 | C23×C32 | 1 | 6 | yes | — |
| 205 | C4×D3 | C23×C32 | 1 | 18 | yes | complemented |
| 206 | Dic6 | C23×C32 | 1 | 6 | yes | complemented |
| 207 | C2×C32 | — | 2 | 9 | no | — |
| 208 | C2×C32 | — | 2 | 4 | no | — |
| 209 | C2×C32 | — | 2 | 36 | no | — |
| 210 | C2×C32 | — | 3 | 2 | no | — |
| 211 | C2×C32 | — | 4 | 36 | no | — |
| 212 | C2×C32 | — | 6 | 9 | no | — |
| 213 | C2×C32 | C24×D3 | 1 | 1 | yes | characteristic |
| 214 | C2×C32 | C25×C3 | 1 | 4 | yes | — |
| 215 | C3×D3 | — | 2 | 36 | no | — |
| 216 | C3×D3 | C3×H(5,𝔽2) | 1 | 8 | yes | direct product factor |
| 217 | C24 | — | 3 | 6 | no | — |
| 218 | #41 | — | 3 | 6 | no | — |
| 219 | #41 | — | 3 | 18 | no | — |
| 220 | #41 | — | 3 | 18 | no | — |
| 221 | #41 | C2×C32×D3 | 1 | 6 | yes | complemented |
| 222 | C2×Q8 | — | 3 | 2 | no | — |
| 223 | C2×D4 | — | 3 | 18 | no | — |
| 224 | C2×D4 | — | 3 | 18 | no | — |
| 225 | C2×D4 | — | 3 | 36 | no | — |
| 226 | C2×D4 | — | 3 | 9 | no | — |
| 227 | C2×D4 | C2×C32×D3 | 1 | 9 | yes | complemented |
| 228 | C22×C4 | — | 3 | 9 | no | — |
| 229 | C22×C3 | — | 2 | 36 | no | — |
| 230 | C22×C3 | — | 3 | 4 | no | — |
| 231 | C22×C3 | — | 3 | 36 | no | — |
| 232 | C22×C3 | — | 4 | 6 | no | — |
| 233 | C22×C3 | — | 4 | 24 | no | — |
| 234 | C22×C3 | — | 6 | 72 | no | — |
| 235 | C22×C3 | — | 8 | 24 | no | — |
| 236 | C22×C3 | — | 12 | 72 | no | — |
| 237 | C22×C3 | C23×C3×D3 | 1 | 36 | yes | — |
| 238 | C22×C3 | C24×C32 | 1 | 9 | yes | — |
| 239 | C2×D3 | — | 2 | 18 | no | — |
| 240 | C2×D3 | — | 4 | 18 | no | — |
| 241 | C2×D3 | C24×C32 | 1 | 9 | yes | — |
| 242 | C2×D3 | C24×C32 | 1 | 1 | yes | characteristic |
| 243 | C3×C4 | — | 2 | 24 | no | — |
| 244 | C3×C4 | — | 3 | 24 | no | — |
| 245 | C3×C4 | C23×C3×D3 | 1 | 24 | yes | — |
| 246 | C3×C4 | C24×C32 | 1 | 6 | yes | — |
| 247 | Dic3 | C24×C32 | 1 | 6 | yes | — |
| 248 | C32 | — | 2 | 4 | no | — |
| 249 | C32 | D3×H(5,𝔽2) | 1 | 1 | yes | characteristic, direct product factor |
| 250 | C32 | C2×C3×H(5,𝔽2) | 1 | 4 | yes | complemented |
| 251 | C23 | — | 3 | 9 | no | — |
| 252 | C23 | — | 3 | 18 | no | — |
| 253 | C23 | — | 12 | 12 | no | — |
| 254 | C23 | C22×C32×D3 | 1 | 6 | yes | complemented |
| 255 | Q8 | — | 3 | 6 | no | — |
| 256 | Q8 | C22×C32×D3 | 1 | 2 | yes | complemented |
| 257 | D4 | — | 3 | 36 | no | — |
| 258 | D4 | — | 3 | 18 | no | — |
| 259 | D4 | C22×C32×D3 | 1 | 18 | yes | complemented |
| 260 | C2×C4 | — | 3 | 9 | no | — |
| 261 | C2×C4 | — | 3 | 6 | no | — |
| 262 | C2×C4 | — | 3 | 18 | no | — |
| 263 | C2×C4 | C22×C32×D3 | 1 | 9 | yes | complemented |
| 264 | C2×C3 | — | 2 | 36 | no | — |
| 265 | C2×C3 | — | 2 | 9 | no | — |
| 266 | C2×C3 | — | 2 | 4 | no | — |
| 267 | C2×C3 | — | 3 | 8 | no | — |
| 268 | C2×C3 | — | 4 | 36 | no | — |
| 269 | C2×C3 | — | 6 | 36 | no | — |
| 270 | C2×C3 | C24×C3×D3 | 1 | 4 | yes | — |
| 271 | C2×C3 | C25×C32 | 1 | 1 | yes | characteristic |
| 272 | D3 | — | 2 | 9 | no | — |
| 273 | D3 | C32×H(5,𝔽2) | 1 | 2 | yes | direct product factor |
| 274 | C22 | — | 3 | 1 | no | — |
| 275 | C22 | — | 3 | 9 | no | — |
| 276 | C22 | — | 4 | 6 | no | — |
| 277 | C22 | — | 6 | 18 | no | — |
| 278 | C22 | — | 12 | 18 | no | — |
| 279 | C22 | C23×C32×D3 | 1 | 9 | yes | — |
| 280 | C4 | — | 3 | 6 | no | — |
| 281 | C4 | C23×C32×D3 | 1 | 6 | yes | — |
| 282 | C3 | — | 2 | 4 | no | — |
| 283 | C3 | C3×D3×H(5,𝔽2) | 1 | 4 | yes | direct product factor |
| 284 | C3 | C2×C32×H(5,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 285 | C2 | — | 2 | 9 | no | — |
| 286 | C2 | — | 3 | 2 | no | — |
| 287 | C2 | — | 6 | 9 | no | — |
| 288 | C2 | C24×C32×D3 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 1. C33×H(5,𝔽2) | C2 | semidirect |
| 2. C32×#1009 | C2 | semidirect |
| 3. C32×D3×#41 | C2 | semidirect |
| 4. C32×#1004 | C2 | semidirect |
| 5. C2×C32×D3×D4 | C2 | semidirect |
| 7. C3×D3×H(5,𝔽2) | C3 | direct (N × H) |
| 8. C23×C32×D3 | C22 | semidirect |
| 9. C33×#41 | C22 | semidirect |
| 10. C2×C33×D4 | C22 | semidirect |
| 11. C2×C32×#67 | C22 | semidirect |
| 12. C32×#239 | C22 | semidirect |
| 13. C32×D3×Q8 | C22 | semidirect |
| 14. C32×#237 | C22 | semidirect |
| 15. C32×D3×D4 | C22 | semidirect |
| 16. C32×D3×D4 | C22 | semidirect |
| 17. C32×#235 | C22 | semidirect |
| 18. C2×C32×D12 | C22 | semidirect |
| 19. C2×C32×C4×D3 | C22 | semidirect |
| 23. C32×H(5,𝔽2) | D3 | direct (N × H) |
| 24. C32×H(5,𝔽2) | C2×C3 | semidirect |
| 27. C3×#1009 | C2×C3 | semidirect |
| 28. C3×D3×#41 | C2×C3 | semidirect |
| 29. C3×#1004 | C2×C3 | semidirect |
| 30. C2×C3×D3×D4 | C2×C3 | semidirect |
| 31. C23×C33 | C23 | semidirect |
| 34. C22×C32×D3 | C23 | semidirect |
| 35. C33×Q8 | C23 | semidirect |
| 36. C33×D4 | C23 | semidirect |
| 37. C2×C33×C4 | C23 | semidirect |
| 38. C32×#67 | C23 | semidirect |
| 39. C2×C32×Dic3 | C23 | semidirect |
| 40. C32×D12 | C23 | semidirect |
| 42. C32×C4×D3 | C23 | semidirect |
| 43. C32×Dic6 | C23 | semidirect |
| 45. D3×H(5,𝔽2) | C32 | direct (N × H) |
| 47. C23×C3×D3 | C22×C3 | semidirect |
| 52. C32×#41 | C2×D3 | semidirect |
| 53. C32×#41 | C22×C3 | semidirect |
| 60. C2×C32×D4 | C2×D3 | semidirect |
| 61. C2×C32×D4 | C22×C3 | semidirect |
| 63. C2×C3×#67 | C22×C3 | semidirect |
| 64. C3×#239 | C22×C3 | semidirect |
| 65. C3×D3×Q8 | C22×C3 | semidirect |
| 66. C3×#237 | C22×C3 | semidirect |
| 67. C3×D3×D4 | C22×C3 | semidirect |
| 68. C3×D3×D4 | C22×C3 | semidirect |
| 69. C3×#235 | C22×C3 | semidirect |
| 70. C2×C3×D12 | C22×C3 | semidirect |
| 71. C2×C3×C4×D3 | C22×C3 | semidirect |
| 83. C3×H(5,𝔽2) | C3×D3 | direct (N × H) |
| 84. C3×H(5,𝔽2) | C2×C32 | semidirect |
| 87. #1009 | C2×C32 | semidirect |
| 88. D3×#41 | C2×C32 | semidirect |
| 89. #1004 | C2×C32 | semidirect |
| 90. C2×D3×D4 | C2×C32 | semidirect |
| 95. C23×C32 | C22×D3 | semidirect |
| 96. C23×C32 | C23×C3 | semidirect |
| 99. C22×C3×D3 | C23×C3 | semidirect |
| 102. C32×Q8 | C22×D3 | semidirect |
| 103. C32×Q8 | C23×C3 | semidirect |
| 107. C32×D4 | C22×D3 | semidirect |
| 108. C32×D4 | C23×C3 | semidirect |
| 113. C2×C32×C4 | C22×D3 | semidirect |
| 114. C2×C32×C4 | C23×C3 | semidirect |
| 115. C3×#67 | C23×C3 | semidirect |
| 116. C2×C3×Dic3 | C23×C3 | semidirect |
| 117. C3×D12 | C23×C3 | semidirect |
| 119. C3×C4×D3 | C23×C3 | semidirect |
| 120. C3×Dic6 | C23×C3 | semidirect |
| 125. C32×D3 | H(5,𝔽2) | direct (N × H) |
| 127. C23×D3 | C22×C32 | semidirect |
| 132. C3×#41 | C2×C3×D3 | semidirect |
| 133. C3×#41 | C22×C32 | semidirect |
| 140. C2×C3×D4 | C2×C3×D3 | semidirect |
| 141. C2×C3×D4 | C22×C32 | semidirect |
| 143. C2×#67 | C22×C32 | semidirect |
| 144. #239 | C22×C32 | semidirect |
| 145. D3×Q8 | C22×C32 | semidirect |
| 146. #237 | C22×C32 | semidirect |
| 147. D3×D4 | C22×C32 | semidirect |
| 148. D3×D4 | C22×C32 | semidirect |
| 149. #235 | C22×C32 | semidirect |
| 150. C2×D12 | C22×C32 | semidirect |
| 151. C2×C4×D3 | C22×C32 | semidirect |
| 173. H(5,𝔽2) | C32×D3 | direct (N × H) |
| 176. C33 | C2×H(5,𝔽2) | semidirect |
| 181. C23×C3 | C22×C3×D3 | semidirect |
| 182. C23×C3 | C23×C32 | semidirect |
| 185. C22×D3 | C23×C32 | semidirect |
| 188. C3×Q8 | C22×C3×D3 | semidirect |
| 189. C3×Q8 | C23×C32 | semidirect |
| 193. C3×D4 | C22×C3×D3 | semidirect |
| 194. C3×D4 | C23×C32 | semidirect |
| 199. C2×C3×C4 | C22×C3×D3 | semidirect |
| 200. C2×C3×C4 | C23×C32 | semidirect |
| 201. #67 | C23×C32 | semidirect |
| 202. C2×Dic3 | C23×C32 | semidirect |
| 203. D12 | C23×C32 | semidirect |
| 205. C4×D3 | C23×C32 | semidirect |
| 206. Dic6 | C23×C32 | semidirect |
| 216. C3×D3 | C3×H(5,𝔽2) | direct (N × H) |
| 221. #41 | C2×C32×D3 | semidirect |
| 227. C2×D4 | C2×C32×D3 | semidirect |
| 249. C32 | D3×H(5,𝔽2) | direct (N × H) |
| 250. C32 | C2×C3×H(5,𝔽2) | semidirect |
| 254. C23 | C22×C32×D3 | semidirect |
| 256. Q8 | C22×C32×D3 | semidirect |
| 259. D4 | C22×C32×D3 | semidirect |
| 263. C2×C4 | C22×C32×D3 | semidirect |
| 273. D3 | C32×H(5,𝔽2) | direct (N × H) |
| 283. C3 | C3×D3×H(5,𝔽2) | direct (N × H) |
| 284. C3 | C2×C32×H(5,𝔽2) | semidirect |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta