← H(5,𝔽2)×(C3⋊D3)⋊C3 #13164951
Order 1728.
3309 conjugacy classes of subgroups.
The subgroup lattice has 334 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | H(3,𝔽3)×H(5,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11722638 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | #41×(C3⋊D3)⋊C3 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #64361⋊C3 | C2 | 1 | 9 | yes | maximal, complemented |
| 5 | C2×D4×(C3⋊D3)⋊C3 | C2 | 1 | 9 | yes | maximal, complemented |
| 6 | C3⋊D3×H(5,𝔽2) | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C3×D3×H(5,𝔽2) | — | 3 | 1 | no | maximal |
| 8 | C23×(C3⋊D3)⋊C3 | C22 | 1 | 6 | yes | complemented |
| 9 | #41×H(3,𝔽3) | C22 | 1 | 6 | yes | complemented |
| 10 | C2×D4×H(3,𝔽3) | C22 | 1 | 9 | yes | complemented |
| 11 | C2×#638⋊C3 | C22 | 1 | 18 | yes | complemented |
| 12 | #88722 | C22 | 1 | 6 | yes | complemented |
| 13 | Q8×(C3⋊D3)⋊C3 | C22 | 1 | 2 | yes | complemented |
| 14 | #3830⋊C3 | C22 | 1 | 18 | yes | complemented |
| 15 | D4×(C3⋊D3)⋊C3 | C22 | 1 | 18 | yes | complemented |
| 16 | D4×(C3⋊D3)⋊C3 | C22 | 1 | 36 | yes | complemented |
| 17 | #3828⋊C3 | C22 | 1 | 18 | yes | complemented |
| 18 | C2×C4⋊((C3⋊D3)⋊C3) | C22 | 1 | 9 | yes | complemented |
| 19 | C2×C4×(C3⋊D3)⋊C3 | C22 | 1 | 9 | yes | complemented |
| 20 | C32×H(5,𝔽2) | — | 2 | 1 | no | — |
| 21 | C32×H(5,𝔽2) | D3 | 1 | 1 | yes | characteristic, complemented |
| 22 | C32×H(5,𝔽2) | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 23 | #64366 | C2×C3 | 1 | 6 | yes | complemented |
| 24 | #41×C3⋊D3 | C2×C3 | 1 | 6 | yes | complemented |
| 25 | #64361 | C2×C3 | 1 | 9 | yes | complemented |
| 26 | C2×D4×C3⋊D3 | C2×C3 | 1 | 9 | yes | complemented |
| 27 | C3×#1009 | — | 3 | 6 | no | — |
| 28 | C3×D3×#41 | — | 3 | 6 | no | — |
| 29 | C3×#1004 | — | 3 | 9 | no | — |
| 30 | C2×C3×D3×D4 | — | 3 | 9 | no | — |
| 31 | C23×H(3,𝔽3) | C23 | 1 | 6 | yes | complemented |
| 32 | C22×(C3⋊D3)⋊C3 | — | 4 | 12 | no | — |
| 33 | C22×(C3⋊D3)⋊C3 | C23 | 1 | 9 | yes | — |
| 34 | C22×(C3⋊D3)⋊C3 | C23 | 1 | 18 | yes | complemented |
| 35 | Q8×H(3,𝔽3) | C23 | 1 | 2 | yes | complemented |
| 36 | D4×H(3,𝔽3) | C23 | 1 | 18 | yes | complemented |
| 37 | C2×C4×H(3,𝔽3) | C23 | 1 | 9 | yes | complemented |
| 38 | #638⋊C3 | C23 | 1 | 36 | yes | complemented |
| 39 | C2×(C3⋊Dic3)⋊C3 | C23 | 1 | 9 | yes | complemented |
| 40 | C4⋊((C3⋊D3)⋊C3) | C23 | 1 | 18 | yes | complemented |
| 41 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 6 | yes | — |
| 42 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 18 | yes | complemented |
| 43 | #634⋊C3 | C23 | 1 | 6 | yes | complemented |
| 44 | C2×C3×H(5,𝔽2) | — | 9 | 1 | no | — |
| 45 | D3×H(5,𝔽2) | — | 3 | 1 | no | — |
| 46 | D3×H(5,𝔽2) | — | 9 | 1 | no | — |
| 47 | C23×C3⋊D3 | C22×C3 | 1 | 6 | yes | complemented |
| 48 | C23×C3×D3 | — | 3 | 6 | no | — |
| 49 | C32×#41 | — | 2 | 6 | no | — |
| 50 | C32×#41 | C2×D3 | 1 | 6 | yes | complemented |
| 51 | C32×#41 | C22×C3 | 1 | 6 | yes | complemented |
| 52 | C2×C32×D4 | — | 2 | 9 | no | — |
| 53 | C2×C32×D4 | C2×D3 | 1 | 9 | yes | complemented |
| 54 | C2×C32×D4 | C22×C3 | 1 | 9 | yes | complemented |
| 55 | C2×#638 | C22×C3 | 1 | 18 | yes | complemented |
| 56 | #3832 | C22×C3 | 1 | 6 | yes | complemented |
| 57 | Q8×C3⋊D3 | C22×C3 | 1 | 2 | yes | complemented |
| 58 | #3830 | C22×C3 | 1 | 18 | yes | complemented |
| 59 | D4×C3⋊D3 | C22×C3 | 1 | 18 | yes | complemented |
| 60 | D4×C3⋊D3 | C22×C3 | 1 | 36 | yes | complemented |
| 61 | #3828 | C22×C3 | 1 | 18 | yes | complemented |
| 62 | C2×C4⋊(C3⋊D3) | C22×C3 | 1 | 9 | yes | complemented |
| 63 | C2×C4×C3⋊D3 | C22×C3 | 1 | 9 | yes | complemented |
| 64 | C2×C3×#67 | — | 3 | 18 | no | — |
| 65 | C3×#239 | — | 3 | 6 | no | — |
| 66 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 67 | C3×#237 | — | 3 | 18 | no | — |
| 68 | C3×D3×D4 | — | 3 | 18 | no | — |
| 69 | C3×D3×D4 | — | 3 | 36 | no | — |
| 70 | C3×#235 | — | 3 | 18 | no | — |
| 71 | C2×C3×D12 | — | 3 | 9 | no | — |
| 72 | C2×C3×C4×D3 | — | 3 | 9 | no | — |
| 73 | C22×H(3,𝔽3) | — | 4 | 6 | no | — |
| 74 | C22×H(3,𝔽3) | C24 | 1 | 9 | yes | — |
| 75 | C2×(C3⋊D3)⋊C3 | — | 2 | 18 | no | — |
| 76 | C2×(C3⋊D3)⋊C3 | — | 4 | 18 | no | — |
| 77 | C2×(C3⋊D3)⋊C3 | C24 | 1 | 9 | yes | — |
| 78 | C2×(C3⋊D3)⋊C3 | C24 | 1 | 1 | yes | characteristic |
| 79 | C4×H(3,𝔽3) | C24 | 1 | 6 | yes | — |
| 80 | (C3⋊Dic3)⋊C3 | C24 | 1 | 6 | yes | — |
| 81 | C3×H(5,𝔽2) | — | 3 | 1 | no | — |
| 82 | C3×H(5,𝔽2) | — | 3 | 1 | no | — |
| 83 | C3×H(5,𝔽2) | — | 6 | 1 | no | — |
| 84 | C3×H(5,𝔽2) | — | 9 | 9 | no | — |
| 85 | C3×H(5,𝔽2) | — | 9 | 6 | no | — |
| 86 | C3×H(5,𝔽2) | C3×D3 | 1 | 1 | yes | characteristic |
| 87 | C2×C3×#41 | — | 9 | 6 | no | — |
| 88 | C22×C3×D4 | — | 9 | 9 | no | — |
| 89 | #1009 | — | 3 | 6 | no | — |
| 90 | #1009 | — | 9 | 6 | no | — |
| 91 | D3×#41 | — | 3 | 6 | no | — |
| 92 | D3×#41 | — | 9 | 6 | no | — |
| 93 | #1004 | — | 3 | 9 | no | — |
| 94 | #1004 | — | 9 | 9 | no | — |
| 95 | C2×D3×D4 | — | 3 | 9 | no | — |
| 96 | C2×D3×D4 | — | 9 | 9 | no | — |
| 97 | C23×C32 | — | 2 | 6 | no | — |
| 98 | C23×C32 | C22×D3 | 1 | 6 | yes | complemented |
| 99 | C23×C32 | C23×C3 | 1 | 6 | yes | complemented |
| 100 | C22×C3⋊D3 | — | 4 | 12 | no | — |
| 101 | C22×C3⋊D3 | C23×C3 | 1 | 9 | yes | — |
| 102 | C22×C3⋊D3 | C23×C3 | 1 | 18 | yes | complemented |
| 103 | C22×C3×D3 | — | 3 | 9 | no | — |
| 104 | C22×C3×D3 | — | 3 | 18 | no | — |
| 105 | C22×C3×D3 | — | 12 | 12 | no | — |
| 106 | C32×Q8 | — | 2 | 2 | no | — |
| 107 | C32×Q8 | C22×D3 | 1 | 2 | yes | complemented |
| 108 | C32×Q8 | C23×C3 | 1 | 2 | yes | complemented |
| 109 | C32×D4 | — | 2 | 18 | no | — |
| 110 | C32×D4 | C22×D3 | 1 | 18 | yes | complemented |
| 111 | C32×D4 | C23×C3 | 1 | 18 | yes | complemented |
| 112 | C2×C32×C4 | — | 2 | 9 | no | — |
| 113 | C2×C32×C4 | C22×D3 | 1 | 9 | yes | complemented |
| 114 | C2×C32×C4 | C23×C3 | 1 | 9 | yes | complemented |
| 115 | #638 | C23×C3 | 1 | 36 | yes | complemented |
| 116 | C2×C3⋊Dic3 | C23×C3 | 1 | 9 | yes | complemented |
| 117 | C4⋊(C3⋊D3) | C23×C3 | 1 | 18 | yes | complemented |
| 118 | C4×C3⋊D3 | C23×C3 | 1 | 6 | yes | — |
| 119 | C4×C3⋊D3 | C23×C3 | 1 | 18 | yes | complemented |
| 120 | #634 | C23×C3 | 1 | 6 | yes | complemented |
| 121 | C3×#67 | — | 3 | 36 | no | — |
| 122 | C2×C3×Dic3 | — | 3 | 9 | no | — |
| 123 | C3×D12 | — | 3 | 18 | no | — |
| 124 | C3×C4×D3 | — | 3 | 6 | no | — |
| 125 | C3×C4×D3 | — | 3 | 18 | no | — |
| 126 | C3×Dic6 | — | 3 | 6 | no | — |
| 127 | C2×H(5,𝔽2) | — | 9 | 1 | no | Sylow |
| 128 | C2×H(3,𝔽3) | — | 2 | 9 | no | — |
| 129 | C2×H(3,𝔽3) | C25 | 1 | 1 | yes | characteristic |
| 130 | (C3⋊D3)⋊C3 | — | 2 | 9 | no | — |
| 131 | (C3⋊D3)⋊C3 | H(5,𝔽2) | 1 | 2 | yes | direct product factor |
| 132 | C24×C3 | — | 9 | 6 | no | — |
| 133 | C23×D3 | — | 3 | 6 | no | — |
| 134 | C23×D3 | — | 9 | 6 | no | — |
| 135 | C3×#41 | — | 3 | 6 | no | — |
| 136 | C3×#41 | — | 3 | 6 | no | — |
| 137 | C3×#41 | — | 6 | 6 | no | — |
| 138 | C3×#41 | — | 9 | 18 | no | — |
| 139 | C3×#41 | — | 9 | 18 | no | — |
| 140 | C3×#41 | — | 9 | 6 | no | — |
| 141 | C3×#41 | C2×C3×D3 | 1 | 6 | yes | — |
| 142 | C2×C3×Q8 | — | 9 | 2 | no | — |
| 143 | C2×C3×D4 | — | 3 | 9 | no | — |
| 144 | C2×C3×D4 | — | 3 | 9 | no | — |
| 145 | C2×C3×D4 | — | 6 | 9 | no | — |
| 146 | C2×C3×D4 | — | 9 | 9 | no | — |
| 147 | C2×C3×D4 | — | 9 | 18 | no | — |
| 148 | C2×C3×D4 | — | 9 | 36 | no | — |
| 149 | C2×C3×D4 | — | 9 | 18 | no | — |
| 150 | C2×C3×D4 | C2×C3×D3 | 1 | 9 | yes | — |
| 151 | C22×C3×C4 | — | 9 | 9 | no | — |
| 152 | C2×#67 | — | 3 | 18 | no | — |
| 153 | C2×#67 | — | 9 | 18 | no | — |
| 154 | #239 | — | 3 | 6 | no | — |
| 155 | #239 | — | 9 | 6 | no | — |
| 156 | D3×Q8 | — | 3 | 2 | no | — |
| 157 | D3×Q8 | — | 9 | 2 | no | — |
| 158 | #237 | — | 3 | 18 | no | — |
| 159 | #237 | — | 9 | 18 | no | — |
| 160 | D3×D4 | — | 3 | 18 | no | — |
| 161 | D3×D4 | — | 3 | 36 | no | — |
| 162 | D3×D4 | — | 9 | 18 | no | — |
| 163 | D3×D4 | — | 9 | 36 | no | — |
| 164 | #235 | — | 3 | 18 | no | — |
| 165 | #235 | — | 9 | 18 | no | — |
| 166 | C2×D12 | — | 3 | 9 | no | — |
| 167 | C2×D12 | — | 9 | 9 | no | — |
| 168 | C2×C4×D3 | — | 3 | 9 | no | — |
| 169 | C2×C4×D3 | — | 9 | 9 | no | — |
| 170 | C22×C32 | — | 2 | 9 | no | — |
| 171 | C22×C32 | — | 4 | 6 | no | — |
| 172 | C22×C32 | — | 4 | 6 | no | — |
| 173 | C22×C32 | — | 8 | 6 | no | — |
| 174 | C22×C32 | C23×D3 | 1 | 9 | yes | — |
| 175 | C22×C32 | C24×C3 | 1 | 9 | yes | — |
| 176 | C2×C3⋊D3 | — | 2 | 18 | no | — |
| 177 | C2×C3⋊D3 | — | 4 | 18 | no | — |
| 178 | C2×C3⋊D3 | C24×C3 | 1 | 9 | yes | — |
| 179 | C2×C3⋊D3 | C24×C3 | 1 | 1 | yes | characteristic |
| 180 | C2×C3×D3 | — | 3 | 1 | no | — |
| 181 | C2×C3×D3 | — | 3 | 9 | no | — |
| 182 | C2×C3×D3 | — | 6 | 18 | no | — |
| 183 | C2×C3×D3 | — | 12 | 18 | no | — |
| 184 | C32×C4 | — | 2 | 6 | no | — |
| 185 | C32×C4 | C23×D3 | 1 | 6 | yes | — |
| 186 | C32×C4 | C24×C3 | 1 | 6 | yes | — |
| 187 | C3⋊Dic3 | C24×C3 | 1 | 6 | yes | — |
| 188 | C3×Dic3 | — | 3 | 6 | no | — |
| 189 | H(5,𝔽2) | — | 9 | 6 | no | — |
| 190 | H(5,𝔽2) | — | 9 | 9 | no | — |
| 191 | H(5,𝔽2) | (C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic, direct product factor |
| 192 | C2×#41 | — | 9 | 6 | no | — |
| 193 | C22×D4 | — | 9 | 9 | no | — |
| 194 | H(3,𝔽3) | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 195 | C23×C3 | — | 3 | 6 | no | — |
| 196 | C23×C3 | — | 3 | 6 | no | — |
| 197 | C23×C3 | — | 6 | 6 | no | — |
| 198 | C23×C3 | — | 9 | 9 | no | — |
| 199 | C23×C3 | — | 9 | 18 | no | — |
| 200 | C23×C3 | — | 36 | 12 | no | — |
| 201 | C23×C3 | C22×C3×D3 | 1 | 6 | yes | — |
| 202 | C22×D3 | — | 3 | 9 | no | — |
| 203 | C22×D3 | — | 3 | 18 | no | — |
| 204 | C22×D3 | — | 9 | 9 | no | — |
| 205 | C22×D3 | — | 9 | 18 | no | — |
| 206 | C22×D3 | — | 12 | 12 | no | — |
| 207 | C22×D3 | — | 36 | 12 | no | — |
| 208 | C3×Q8 | — | 3 | 2 | no | — |
| 209 | C3×Q8 | — | 3 | 2 | no | — |
| 210 | C3×Q8 | — | 6 | 2 | no | — |
| 211 | C3×Q8 | — | 9 | 6 | no | — |
| 212 | C3×Q8 | C22×C3×D3 | 1 | 2 | yes | — |
| 213 | C3×D4 | — | 3 | 18 | no | — |
| 214 | C3×D4 | — | 3 | 18 | no | — |
| 215 | C3×D4 | — | 6 | 18 | no | — |
| 216 | C3×D4 | — | 9 | 18 | no | — |
| 217 | C3×D4 | — | 9 | 36 | no | — |
| 218 | C3×D4 | C22×C3×D3 | 1 | 18 | yes | — |
| 219 | C2×C3×C4 | — | 3 | 9 | no | — |
| 220 | C2×C3×C4 | — | 3 | 9 | no | — |
| 221 | C2×C3×C4 | — | 6 | 9 | no | — |
| 222 | C2×C3×C4 | — | 9 | 6 | no | — |
| 223 | C2×C3×C4 | — | 9 | 18 | no | — |
| 224 | C2×C3×C4 | — | 9 | 9 | no | — |
| 225 | C2×C3×C4 | C22×C3×D3 | 1 | 9 | yes | — |
| 226 | #67 | — | 3 | 36 | no | — |
| 227 | #67 | — | 9 | 36 | no | — |
| 228 | C2×Dic3 | — | 3 | 9 | no | — |
| 229 | C2×Dic3 | — | 9 | 9 | no | — |
| 230 | D12 | — | 3 | 18 | no | — |
| 231 | D12 | — | 9 | 18 | no | — |
| 232 | C4×D3 | — | 3 | 6 | no | — |
| 233 | C4×D3 | — | 3 | 18 | no | — |
| 234 | C4×D3 | — | 9 | 6 | no | — |
| 235 | C4×D3 | — | 9 | 18 | no | — |
| 236 | Dic6 | — | 3 | 6 | no | — |
| 237 | Dic6 | — | 9 | 6 | no | — |
| 238 | C2×C32 | — | 2 | 9 | no | — |
| 239 | C2×C32 | — | 2 | 9 | no | — |
| 240 | C2×C32 | — | 2 | 1 | no | — |
| 241 | C2×C32 | — | 4 | 9 | no | — |
| 242 | C2×C32 | C24×D3 | 1 | 1 | yes | characteristic |
| 243 | C2×C32 | C25×C3 | 1 | 1 | yes | characteristic |
| 244 | C3⋊D3 | — | 2 | 9 | no | — |
| 245 | C3⋊D3 | C3×H(5,𝔽2) | 1 | 2 | yes | complemented |
| 246 | C3×D3 | — | 3 | 2 | no | — |
| 247 | C3×D3 | — | 6 | 9 | no | — |
| 248 | C24 | — | 9 | 6 | no | — |
| 249 | #41 | — | 9 | 6 | no | — |
| 250 | #41 | — | 9 | 18 | no | — |
| 251 | #41 | — | 9 | 18 | no | — |
| 252 | #41 | C2×(C3⋊D3)⋊C3 | 1 | 6 | yes | complemented |
| 253 | C2×Q8 | — | 9 | 2 | no | — |
| 254 | C2×D4 | — | 9 | 18 | no | — |
| 255 | C2×D4 | — | 9 | 18 | no | — |
| 256 | C2×D4 | — | 9 | 36 | no | — |
| 257 | C2×D4 | — | 9 | 9 | no | — |
| 258 | C2×D4 | C2×(C3⋊D3)⋊C3 | 1 | 9 | yes | complemented |
| 259 | C22×C4 | — | 9 | 9 | no | — |
| 260 | C22×C3 | — | 3 | 9 | no | — |
| 261 | C22×C3 | — | 3 | 9 | no | — |
| 262 | C22×C3 | — | 4 | 6 | no | — |
| 263 | C22×C3 | — | 6 | 9 | no | — |
| 264 | C22×C3 | — | 9 | 1 | no | — |
| 265 | C22×C3 | — | 9 | 9 | no | — |
| 266 | C22×C3 | — | 12 | 6 | no | — |
| 267 | C22×C3 | — | 12 | 6 | no | — |
| 268 | C22×C3 | — | 18 | 18 | no | — |
| 269 | C22×C3 | — | 24 | 6 | no | — |
| 270 | C22×C3 | — | 36 | 18 | no | — |
| 271 | C22×C3 | C23×C3×D3 | 1 | 9 | yes | — |
| 272 | C2×D3 | — | 3 | 1 | no | — |
| 273 | C2×D3 | — | 3 | 9 | no | — |
| 274 | C2×D3 | — | 6 | 18 | no | — |
| 275 | C2×D3 | — | 9 | 1 | no | — |
| 276 | C2×D3 | — | 9 | 9 | no | — |
| 277 | C2×D3 | — | 12 | 18 | no | — |
| 278 | C2×D3 | — | 18 | 18 | no | — |
| 279 | C2×D3 | — | 36 | 18 | no | — |
| 280 | C3×C4 | — | 3 | 6 | no | — |
| 281 | C3×C4 | — | 3 | 6 | no | — |
| 282 | C3×C4 | — | 6 | 6 | no | — |
| 283 | C3×C4 | — | 9 | 6 | no | — |
| 284 | C3×C4 | C23×C3×D3 | 1 | 6 | yes | — |
| 285 | Dic3 | — | 3 | 6 | no | — |
| 286 | Dic3 | — | 9 | 6 | no | — |
| 287 | C32 | — | 2 | 1 | no | — |
| 288 | C32 | D3×H(5,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 289 | C32 | C2×C3×H(5,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 290 | C23 | — | 9 | 9 | no | — |
| 291 | C23 | — | 9 | 18 | no | — |
| 292 | C23 | — | 36 | 12 | no | — |
| 293 | C23 | C22×(C3⋊D3)⋊C3 | 1 | 6 | yes | complemented |
| 294 | Q8 | — | 9 | 6 | no | — |
| 295 | Q8 | C22×(C3⋊D3)⋊C3 | 1 | 2 | yes | complemented |
| 296 | D4 | — | 9 | 36 | no | — |
| 297 | D4 | — | 9 | 18 | no | — |
| 298 | D4 | C22×(C3⋊D3)⋊C3 | 1 | 18 | yes | complemented |
| 299 | C2×C4 | — | 9 | 9 | no | — |
| 300 | C2×C4 | — | 9 | 6 | no | — |
| 301 | C2×C4 | — | 9 | 18 | no | — |
| 302 | C2×C4 | C22×(C3⋊D3)⋊C3 | 1 | 9 | yes | complemented |
| 303 | C2×C3 | — | 2 | 9 | no | — |
| 304 | C2×C3 | — | 3 | 1 | no | — |
| 305 | C2×C3 | — | 3 | 1 | no | — |
| 306 | C2×C3 | — | 6 | 9 | no | — |
| 307 | C2×C3 | — | 6 | 9 | no | — |
| 308 | C2×C3 | — | 6 | 1 | no | — |
| 309 | C2×C3 | — | 9 | 2 | no | — |
| 310 | C2×C3 | — | 12 | 9 | no | — |
| 311 | C2×C3 | — | 18 | 9 | no | — |
| 312 | C2×C3 | C24×C3×D3 | 1 | 1 | yes | characteristic |
| 313 | D3 | — | 3 | 2 | no | — |
| 314 | D3 | — | 6 | 9 | no | — |
| 315 | D3 | — | 9 | 2 | no | — |
| 316 | D3 | — | 18 | 9 | no | — |
| 317 | C22 | — | 4 | 6 | no | — |
| 318 | C22 | — | 9 | 1 | no | — |
| 319 | C22 | — | 9 | 9 | no | — |
| 320 | C22 | — | 18 | 18 | no | — |
| 321 | C22 | — | 36 | 18 | no | — |
| 322 | C22 | C23×(C3⋊D3)⋊C3 | 1 | 9 | yes | — |
| 323 | C4 | — | 9 | 6 | no | — |
| 324 | C4 | C23×(C3⋊D3)⋊C3 | 1 | 6 | yes | — |
| 325 | C3 | — | 3 | 1 | no | — |
| 326 | C3 | — | 3 | 1 | no | — |
| 327 | C3 | — | 6 | 1 | no | — |
| 328 | C3 | C3×D3×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 329 | C2 | — | 2 | 9 | no | — |
| 330 | C2 | — | 9 | 2 | no | — |
| 331 | C2 | — | 18 | 9 | no | — |
| 332 | C2 | C24×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 1. H(3,𝔽3)×H(5,𝔽2) | C2 | semidirect |
| 2. #11722638 | C2 | semidirect |
| 3. #41×(C3⋊D3)⋊C3 | C2 | semidirect |
| 4. #64361⋊C3 | C2 | semidirect |
| 5. C2×D4×(C3⋊D3)⋊C3 | C2 | semidirect |
| 6. C3⋊D3×H(5,𝔽2) | C3 | semidirect |
| 8. C23×(C3⋊D3)⋊C3 | C22 | semidirect |
| 9. #41×H(3,𝔽3) | C22 | semidirect |
| 10. C2×D4×H(3,𝔽3) | C22 | semidirect |
| 11. C2×#638⋊C3 | C22 | semidirect |
| 12. #88722 | C22 | semidirect |
| 13. Q8×(C3⋊D3)⋊C3 | C22 | semidirect |
| 14. #3830⋊C3 | C22 | semidirect |
| 15. D4×(C3⋊D3)⋊C3 | C22 | semidirect |
| 16. D4×(C3⋊D3)⋊C3 | C22 | semidirect |
| 17. #3828⋊C3 | C22 | semidirect |
| 18. C2×C4⋊((C3⋊D3)⋊C3) | C22 | semidirect |
| 19. C2×C4×(C3⋊D3)⋊C3 | C22 | semidirect |
| 21. C32×H(5,𝔽2) | D3 | semidirect |
| 22. C32×H(5,𝔽2) | C2×C3 | semidirect |
| 23. #64366 | C2×C3 | semidirect |
| 24. #41×C3⋊D3 | C2×C3 | semidirect |
| 25. #64361 | C2×C3 | semidirect |
| 26. C2×D4×C3⋊D3 | C2×C3 | semidirect |
| 31. C23×H(3,𝔽3) | C23 | semidirect |
| 34. C22×(C3⋊D3)⋊C3 | C23 | semidirect |
| 35. Q8×H(3,𝔽3) | C23 | semidirect |
| 36. D4×H(3,𝔽3) | C23 | semidirect |
| 37. C2×C4×H(3,𝔽3) | C23 | semidirect |
| 38. #638⋊C3 | C23 | semidirect |
| 39. C2×(C3⋊Dic3)⋊C3 | C23 | semidirect |
| 40. C4⋊((C3⋊D3)⋊C3) | C23 | semidirect |
| 42. C4×(C3⋊D3)⋊C3 | C23 | semidirect |
| 43. #634⋊C3 | C23 | semidirect |
| 47. C23×C3⋊D3 | C22×C3 | semidirect |
| 50. C32×#41 | C2×D3 | semidirect |
| 51. C32×#41 | C22×C3 | semidirect |
| 53. C2×C32×D4 | C2×D3 | semidirect |
| 54. C2×C32×D4 | C22×C3 | semidirect |
| 55. C2×#638 | C22×C3 | semidirect |
| 56. #3832 | C22×C3 | semidirect |
| 57. Q8×C3⋊D3 | C22×C3 | semidirect |
| 58. #3830 | C22×C3 | semidirect |
| 59. D4×C3⋊D3 | C22×C3 | semidirect |
| 60. D4×C3⋊D3 | C22×C3 | semidirect |
| 61. #3828 | C22×C3 | semidirect |
| 62. C2×C4⋊(C3⋊D3) | C22×C3 | semidirect |
| 63. C2×C4×C3⋊D3 | C22×C3 | semidirect |
| 98. C23×C32 | C22×D3 | semidirect |
| 99. C23×C32 | C23×C3 | semidirect |
| 102. C22×C3⋊D3 | C23×C3 | semidirect |
| 107. C32×Q8 | C22×D3 | semidirect |
| 108. C32×Q8 | C23×C3 | semidirect |
| 110. C32×D4 | C22×D3 | semidirect |
| 111. C32×D4 | C23×C3 | semidirect |
| 113. C2×C32×C4 | C22×D3 | semidirect |
| 114. C2×C32×C4 | C23×C3 | semidirect |
| 115. #638 | C23×C3 | semidirect |
| 116. C2×C3⋊Dic3 | C23×C3 | semidirect |
| 117. C4⋊(C3⋊D3) | C23×C3 | semidirect |
| 119. C4×C3⋊D3 | C23×C3 | semidirect |
| 120. #634 | C23×C3 | semidirect |
| 131. (C3⋊D3)⋊C3 | H(5,𝔽2) | direct (N × H) |
| 191. H(5,𝔽2) | (C3⋊D3)⋊C3 | direct (N × H) |
| 194. H(3,𝔽3) | C2×H(5,𝔽2) | semidirect |
| 245. C3⋊D3 | C3×H(5,𝔽2) | semidirect |
| 252. #41 | C2×(C3⋊D3)⋊C3 | semidirect |
| 258. C2×D4 | C2×(C3⋊D3)⋊C3 | semidirect |
| 288. C32 | D3×H(5,𝔽2) | semidirect |
| 289. C32 | C2×C3×H(5,𝔽2) | semidirect |
| 293. C23 | C22×(C3⋊D3)⋊C3 | semidirect |
| 295. Q8 | C22×(C3⋊D3)⋊C3 | semidirect |
| 298. D4 | C22×(C3⋊D3)⋊C3 | semidirect |
| 302. C2×C4 | C22×(C3⋊D3)⋊C3 | semidirect |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta