Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
3147 conjugacy classes of subgroups.
The subgroup lattice has 478 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3⋊D3×#120 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#5594 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10595529 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10595527 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10595278 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #10595262 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #10595170 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #10594311 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | #10594288 | C2 | 1 | 6 | yes | maximal, complemented |
| 10 | D3×H(3,𝔽4) | — | 3 | 2 | no | maximal |
| 11 | C24×C3⋊D3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C23×D32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C2×D4×C3⋊D3 | C22 | 1 | 3 | yes | — |
| 14 | C2×#3811 | C22 | 1 | 6 | yes | — |
| 15 | C2×#3797 | C22 | 1 | 3 | yes | complemented |
| 16 | C32×#120 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | #64162 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | #64146 | C22 | 1 | 3 | yes | complemented |
| 19 | #64091 | C22 | 1 | 3 | yes | complemented |
| 20 | C22⋊C4×C3⋊D3 | C22 | 1 | 3 | yes | complemented |
| 21 | C3×#953 | C22 | 1 | 4 | yes | complemented |
| 22 | C3×#937 | C22 | 1 | 6 | yes | complemented |
| 23 | C3×#936 | C22 | 1 | 6 | yes | complemented |
| 24 | C3×#885 | C22 | 1 | 12 | yes | complemented |
| 25 | #63983 | C22 | 1 | 6 | yes | complemented |
| 26 | #63981 | C22 | 1 | 12 | yes | complemented |
| 27 | #63977 | C22 | 1 | 6 | yes | complemented |
| 28 | #63974 | C22 | 1 | 3 | yes | complemented |
| 29 | #63974 | C22 | 1 | 6 | yes | complemented |
| 30 | #63959 | C22 | 1 | 12 | yes | complemented |
| 31 | #63953 | C22 | 1 | 6 | yes | complemented |
| 32 | #63953 | C22 | 1 | 6 | yes | complemented |
| 33 | #63923 | C22 | 1 | 6 | yes | complemented |
| 34 | #63921 | C22 | 1 | 6 | yes | complemented |
| 35 | #63907 | C22 | 1 | 12 | yes | complemented |
| 36 | C4×#624 | C22 | 1 | 3 | yes | complemented |
| 37 | #63864 | C22 | 1 | 6 | yes | complemented |
| 38 | #63852 | C22 | 1 | 12 | yes | complemented |
| 39 | C3×H(3,𝔽4) | — | 3 | 2 | no | — |
| 40 | #5683 | — | 3 | 6 | no | — |
| 41 | #5683 | — | 3 | 12 | no | — |
| 42 | D3×#124 | — | 3 | 6 | no | — |
| 43 | D3×#124 | — | 3 | 12 | no | — |
| 44 | #5594 | — | 3 | 4 | no | — |
| 45 | #5594 | — | 3 | 6 | no | — |
| 46 | #5594 | D3 | 1 | 2 | yes | complemented |
| 47 | D3×#120 | — | 3 | 2 | no | — |
| 48 | D3×#120 | — | 3 | 4 | no | — |
| 49 | D3×#120 | — | 3 | 6 | no | — |
| 50 | D3×#120 | — | 6 | 1 | no | — |
| 51 | C24×C32 | C23 | 1 | 1 | yes | characteristic, complemented |
| 52 | C23×C3⋊D3 | — | 4 | 6 | no | — |
| 53 | C23×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 54 | C23×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 55 | C23×C3⋊D3 | C23 | 1 | 3 | yes | complemented |
| 56 | C23×C3×D3 | C23 | 1 | 2 | yes | complemented |
| 57 | C22×D32 | — | 4 | 6 | no | — |
| 58 | C22×D32 | C23 | 1 | 2 | yes | — |
| 59 | C22×D32 | C23 | 1 | 2 | yes | complemented |
| 60 | C2×C32×D4 | C23 | 1 | 3 | yes | — |
| 61 | C2×#638 | C23 | 1 | 3 | yes | — |
| 62 | C2×#638 | C23 | 1 | 3 | yes | — |
| 63 | D4×C3⋊D3 | — | 4 | 6 | no | — |
| 64 | C2×C4⋊(C3⋊D3) | C23 | 1 | 3 | yes | — |
| 65 | C2×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 66 | C2×C3×#67 | C23 | 1 | 12 | yes | — |
| 67 | C2×C3×Dic6 | C23 | 1 | 6 | yes | complemented |
| 68 | #3811 | — | 4 | 12 | no | — |
| 69 | C2×#627 | C23 | 1 | 6 | yes | complemented |
| 70 | C2×#626 | C23 | 1 | 12 | yes | — |
| 71 | C2×#624 | C23 | 1 | 6 | yes | — |
| 72 | #3797 | — | 4 | 6 | no | — |
| 73 | C32×C22⋊C4 | C23 | 1 | 3 | yes | complemented |
| 74 | #3757 | C23 | 1 | 3 | yes | complemented |
| 75 | #3752 | C23 | 1 | 6 | yes | complemented |
| 76 | C3×#217 | C23 | 1 | 12 | yes | complemented |
| 77 | C3×#217 | C23 | 1 | 6 | yes | complemented |
| 78 | C3×(C2×D3)⋊C4 | C23 | 1 | 12 | yes | complemented |
| 79 | C3×C4×Dic3 | C23 | 1 | 6 | yes | complemented |
| 80 | #3722 | C23 | 1 | 12 | yes | complemented |
| 81 | #3722 | C23 | 1 | 6 | yes | complemented |
| 82 | (C2×D3)⋊Dic3 | C23 | 1 | 12 | yes | complemented |
| 83 | Dic32 | C23 | 1 | 6 | yes | complemented |
| 84 | C2×H(3,𝔽4) | — | 9 | 1 | no | Sylow |
| 85 | C24×D3 | — | 3 | 2 | no | — |
| 86 | C24×D3 | — | 3 | 2 | no | — |
| 87 | C24×D3 | — | 6 | 1 | no | — |
| 88 | C2×D3×Q8 | — | 3 | 6 | no | — |
| 89 | C2×D3×D4 | — | 3 | 6 | no | — |
| 90 | C2×D3×D4 | — | 3 | 12 | no | — |
| 91 | C2×D3×D4 | — | 6 | 3 | no | — |
| 92 | C3×#124 | — | 3 | 6 | no | — |
| 93 | C3×#124 | — | 3 | 12 | no | — |
| 94 | C3×#120 | — | 2 | 1 | no | — |
| 95 | C3×#120 | — | 3 | 4 | no | — |
| 96 | C3×#120 | — | 3 | 6 | no | — |
| 97 | C3×#120 | C2×D3 | 1 | 2 | yes | complemented |
| 98 | #953 | — | 3 | 2 | no | — |
| 99 | #953 | — | 3 | 6 | no | — |
| 100 | #953 | — | 6 | 1 | no | — |
| 101 | #953 | C2×D3 | 1 | 4 | yes | complemented |
| 102 | #947 | — | 3 | 12 | no | — |
| 103 | #947 | — | 3 | 6 | no | — |
| 104 | #937 | — | 3 | 6 | no | — |
| 105 | #937 | — | 3 | 12 | no | — |
| 106 | #937 | — | 3 | 12 | no | — |
| 107 | #937 | — | 6 | 3 | no | — |
| 108 | #937 | C2×D3 | 1 | 6 | yes | complemented |
| 109 | #936 | — | 3 | 12 | no | — |
| 110 | #936 | C2×D3 | 1 | 6 | yes | complemented |
| 111 | #885 | — | 3 | 12 | no | — |
| 112 | #885 | — | 3 | 12 | no | — |
| 113 | #885 | — | 3 | 12 | no | — |
| 114 | #885 | — | 3 | 12 | no | — |
| 115 | #885 | — | 3 | 12 | no | — |
| 116 | #885 | C2×D3 | 1 | 12 | yes | complemented |
| 117 | #882 | — | 3 | 6 | no | — |
| 118 | #882 | — | 3 | 12 | no | — |
| 119 | #882 | — | 3 | 6 | no | — |
| 120 | #882 | — | 3 | 12 | no | — |
| 121 | #882 | — | 6 | 3 | no | — |
| 122 | D3×C22⋊C4 | — | 3 | 6 | no | — |
| 123 | D3×C22⋊C4 | — | 3 | 6 | no | — |
| 124 | D3×C22⋊C4 | — | 3 | 12 | no | — |
| 125 | D3×C22⋊C4 | — | 3 | 12 | no | — |
| 126 | D3×C22⋊C4 | — | 6 | 3 | no | — |
| 127 | #875 | — | 3 | 6 | no | — |
| 128 | #875 | — | 3 | 12 | no | — |
| 129 | C42×D3 | — | 3 | 6 | no | — |
| 130 | C23×C32 | — | 4 | 3 | no | — |
| 131 | C23×C32 | C24 | 1 | 1 | yes | characteristic |
| 132 | C23×C32 | C24 | 1 | 3 | yes | — |
| 133 | C22×C3⋊D3 | — | 2 | 6 | no | — |
| 134 | C22×C3⋊D3 | — | 2 | 6 | no | — |
| 135 | C22×C3⋊D3 | — | 2 | 12 | no | — |
| 136 | C22×C3⋊D3 | — | 4 | 6 | no | — |
| 137 | C22×C3⋊D3 | — | 4 | 3 | no | — |
| 138 | C22×C3⋊D3 | — | 4 | 16 | no | — |
| 139 | C22×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 140 | C22×C3⋊D3 | C24 | 1 | 3 | yes | — |
| 141 | C22×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 142 | C22×C3×D3 | — | 4 | 6 | no | — |
| 143 | C22×C3×D3 | C24 | 1 | 4 | yes | — |
| 144 | C2×D32 | — | 2 | 12 | no | — |
| 145 | C2×D32 | — | 4 | 6 | no | — |
| 146 | C2×D32 | — | 4 | 16 | no | — |
| 147 | C32×D4 | — | 4 | 3 | no | — |
| 148 | C2×C32×C4 | C24 | 1 | 3 | yes | — |
| 149 | #638 | — | 4 | 3 | no | — |
| 150 | #638 | — | 4 | 3 | no | — |
| 151 | C2×C3⋊Dic3 | C24 | 1 | 3 | yes | — |
| 152 | C4⋊(C3⋊D3) | — | 4 | 3 | no | — |
| 153 | C4×C3⋊D3 | — | 2 | 6 | no | — |
| 154 | C3×#67 | — | 4 | 12 | no | — |
| 155 | C2×C3×Dic3 | C24 | 1 | 12 | yes | — |
| 156 | C3×Dic6 | — | 4 | 6 | no | — |
| 157 | #627 | — | 4 | 6 | no | — |
| 158 | #626 | — | 4 | 12 | no | — |
| 159 | #624 | — | 2 | 12 | no | — |
| 160 | H(3,𝔽4) | — | 3 | 2 | no | — |
| 161 | H(3,𝔽4) | — | 9 | 2 | no | — |
| 162 | H(3,𝔽4) | — | 9 | 6 | no | — |
| 163 | H(3,𝔽4) | — | 9 | 6 | no | — |
| 164 | C2×#124 | — | 9 | 3 | no | — |
| 165 | C2×#124 | — | 9 | 6 | no | — |
| 166 | C2×#120 | — | 9 | 2 | no | — |
| 167 | C2×#120 | — | 9 | 3 | no | — |
| 168 | C2×#120 | — | 9 | 1 | no | — |
| 169 | C24×C3 | — | 2 | 1 | no | — |
| 170 | C24×C3 | — | 3 | 2 | no | — |
| 171 | C24×C3 | C22×D3 | 1 | 2 | yes | complemented |
| 172 | C23×D3 | — | 3 | 6 | no | — |
| 173 | C23×D3 | — | 3 | 2 | no | — |
| 174 | C23×D3 | — | 3 | 6 | no | — |
| 175 | C23×D3 | — | 3 | 4 | no | — |
| 176 | C23×D3 | — | 3 | 4 | no | — |
| 177 | C23×D3 | — | 6 | 3 | no | — |
| 178 | C23×D3 | — | 6 | 1 | no | — |
| 179 | C23×D3 | — | 6 | 3 | no | — |
| 180 | C23×D3 | — | 12 | 12 | no | — |
| 181 | C23×D3 | — | 12 | 12 | no | — |
| 182 | C23×D3 | — | 12 | 12 | no | — |
| 183 | C23×D3 | C22×D3 | 1 | 2 | yes | complemented |
| 184 | C2×C3×Q8 | — | 3 | 6 | no | — |
| 185 | C2×C3×D4 | — | 2 | 3 | no | — |
| 186 | C2×C3×D4 | — | 3 | 12 | no | — |
| 187 | C2×C3×D4 | C22×D3 | 1 | 6 | yes | — |
| 188 | C2×#67 | — | 3 | 6 | no | — |
| 189 | C2×#67 | — | 3 | 6 | no | — |
| 190 | C2×#67 | — | 3 | 12 | no | — |
| 191 | C2×#67 | — | 6 | 3 | no | — |
| 192 | C2×#67 | — | 6 | 3 | no | — |
| 193 | C2×#67 | C22×D3 | 1 | 12 | yes | — |
| 194 | D3×Q8 | — | 12 | 12 | no | — |
| 195 | D3×D4 | — | 12 | 24 | no | — |
| 196 | D3×D4 | — | 12 | 12 | no | — |
| 197 | D3×D4 | — | 12 | 12 | no | — |
| 198 | C2×D12 | — | 3 | 12 | no | — |
| 199 | C2×D12 | — | 3 | 6 | no | — |
| 200 | C2×D12 | — | 6 | 3 | no | — |
| 201 | C2×C4×D3 | — | 3 | 6 | no | — |
| 202 | C2×C4×D3 | — | 3 | 12 | no | — |
| 203 | C2×C4×D3 | — | 6 | 3 | no | — |
| 204 | C2×Dic6 | — | 3 | 12 | no | — |
| 205 | C2×Dic6 | C22×D3 | 1 | 6 | yes | complemented |
| 206 | C3×C22⋊C4 | — | 2 | 3 | no | — |
| 207 | C3×C22⋊C4 | — | 3 | 12 | no | — |
| 208 | C3×C22⋊C4 | — | 3 | 6 | no | — |
| 209 | C3×C22⋊C4 | — | 3 | 12 | no | — |
| 210 | C3×C22⋊C4 | C22×D3 | 1 | 6 | yes | complemented |
| 211 | C3×C42 | — | 3 | 6 | no | — |
| 212 | #217 | — | 3 | 6 | no | — |
| 213 | #217 | — | 3 | 12 | no | — |
| 214 | #217 | — | 6 | 3 | no | — |
| 215 | #217 | C22×D3 | 1 | 6 | yes | complemented |
| 216 | #217 | C22×D3 | 1 | 12 | yes | complemented |
| 217 | (C2×D3)⋊C4 | — | 3 | 12 | no | — |
| 218 | (C2×D3)⋊C4 | — | 3 | 12 | no | — |
| 219 | (C2×D3)⋊C4 | — | 3 | 12 | no | — |
| 220 | (C2×D3)⋊C4 | — | 3 | 12 | no | — |
| 221 | (C2×D3)⋊C4 | — | 3 | 12 | no | — |
| 222 | (C2×D3)⋊C4 | — | 6 | 6 | no | — |
| 223 | (C2×D3)⋊C4 | C22×D3 | 1 | 12 | yes | complemented |
| 224 | C4×Dic3 | — | 3 | 12 | no | — |
| 225 | C4×Dic3 | C22×D3 | 1 | 6 | yes | complemented |
| 226 | C22×C32 | — | 2 | 3 | no | — |
| 227 | C22×C32 | — | 2 | 6 | no | — |
| 228 | C22×C32 | — | 2 | 3 | no | — |
| 229 | C22×C32 | — | 4 | 4 | no | — |
| 230 | C22×C32 | C25 | 1 | 1 | yes | characteristic |
| 231 | C2×C3⋊D3 | — | 2 | 3 | no | — |
| 232 | C2×C3⋊D3 | — | 2 | 6 | no | — |
| 233 | C2×C3⋊D3 | — | 2 | 3 | no | — |
| 234 | C2×C3⋊D3 | — | 4 | 12 | no | — |
| 235 | C2×C3⋊D3 | — | 4 | 12 | no | — |
| 236 | C2×C3⋊D3 | — | 4 | 4 | no | — |
| 237 | C2×C3⋊D3 | H(5,𝔽2) | 1 | 6 | yes | — |
| 238 | C2×C3×D3 | — | 2 | 12 | no | — |
| 239 | C2×C3×D3 | — | 4 | 8 | no | — |
| 240 | D32 | — | 4 | 8 | no | — |
| 241 | D32 | — | 4 | 8 | no | — |
| 242 | C32×C4 | — | 2 | 3 | no | — |
| 243 | C3⋊Dic3 | — | 2 | 3 | no | — |
| 244 | C3×Dic3 | — | 2 | 12 | no | — |
| 245 | C25 | — | 9 | 1 | no | — |
| 246 | C25 | — | 9 | 1 | no | — |
| 247 | C22×Q8 | — | 9 | 3 | no | — |
| 248 | C22×D4 | — | 9 | 6 | no | — |
| 249 | C22×D4 | — | 9 | 3 | no | — |
| 250 | #124 | — | 3 | 6 | no | — |
| 251 | #124 | — | 3 | 12 | no | — |
| 252 | #124 | — | 9 | 12 | no | — |
| 253 | #124 | — | 9 | 6 | no | — |
| 254 | #124 | — | 9 | 6 | no | — |
| 255 | #124 | — | 9 | 6 | no | — |
| 256 | #124 | — | 9 | 12 | no | — |
| 257 | #124 | — | 9 | 12 | no | — |
| 258 | #120 | — | 3 | 4 | no | — |
| 259 | #120 | — | 3 | 6 | no | — |
| 260 | #120 | — | 9 | 6 | no | — |
| 261 | #120 | — | 9 | 12 | no | — |
| 262 | #120 | — | 9 | 6 | no | — |
| 263 | #120 | — | 9 | 6 | no | — |
| 264 | #120 | — | 9 | 1 | no | — |
| 265 | #120 | — | 9 | 3 | no | — |
| 266 | #120 | — | 9 | 3 | no | — |
| 267 | #120 | D32 | 1 | 1 | yes | characteristic, complemented |
| 268 | C2×C22⋊C4 | — | 9 | 3 | no | — |
| 269 | C2×C22⋊C4 | — | 9 | 6 | no | — |
| 270 | C2×C22⋊C4 | — | 9 | 6 | no | — |
| 271 | C2×C22⋊C4 | — | 9 | 3 | no | — |
| 272 | C2×C42 | — | 9 | 3 | no | — |
| 273 | C23×C3 | — | 2 | 3 | no | — |
| 274 | C23×C3 | — | 2 | 1 | no | — |
| 275 | C23×C3 | — | 3 | 4 | no | — |
| 276 | C23×C3 | — | 4 | 6 | no | — |
| 277 | C23×C3 | — | 4 | 6 | no | — |
| 278 | C23×C3 | — | 12 | 6 | no | — |
| 279 | C23×C3 | C23×D3 | 1 | 6 | yes | — |
| 280 | C23×C3 | C23×D3 | 1 | 2 | yes | — |
| 281 | C22×D3 | — | 3 | 2 | no | — |
| 282 | C22×D3 | — | 3 | 2 | no | — |
| 283 | C22×D3 | — | 3 | 6 | no | — |
| 284 | C22×D3 | — | 4 | 6 | no | — |
| 285 | C22×D3 | — | 6 | 1 | no | — |
| 286 | C22×D3 | — | 6 | 3 | no | — |
| 287 | C22×D3 | — | 6 | 1 | no | — |
| 288 | C22×D3 | — | 6 | 24 | no | — |
| 289 | C22×D3 | — | 6 | 12 | no | — |
| 290 | C22×D3 | — | 6 | 24 | no | — |
| 291 | C22×D3 | — | 6 | 12 | no | — |
| 292 | C22×D3 | — | 6 | 12 | no | — |
| 293 | C22×D3 | — | 12 | 12 | no | — |
| 294 | C22×D3 | — | 12 | 6 | no | — |
| 295 | C22×D3 | — | 12 | 12 | no | — |
| 296 | C22×D3 | — | 12 | 32 | no | — |
| 297 | C22×D3 | — | 12 | 12 | no | — |
| 298 | C22×D3 | — | 12 | 6 | no | — |
| 299 | C22×D3 | — | 12 | 12 | no | — |
| 300 | C22×D3 | — | 12 | 6 | no | — |
| 301 | C22×D3 | — | 12 | 32 | no | — |
| 302 | C22×D3 | — | 12 | 32 | no | — |
| 303 | C22×D3 | C23×D3 | 1 | 4 | yes | — |
| 304 | C3×Q8 | — | 12 | 6 | no | — |
| 305 | C3×D4 | — | 4 | 6 | no | — |
| 306 | C3×D4 | — | 4 | 6 | no | — |
| 307 | C3×D4 | — | 12 | 12 | no | — |
| 308 | C2×C3×C4 | — | 2 | 3 | no | — |
| 309 | C2×C3×C4 | — | 3 | 12 | no | — |
| 310 | C2×C3×C4 | C23×D3 | 1 | 6 | yes | — |
| 311 | #67 | — | 4 | 12 | no | — |
| 312 | #67 | — | 12 | 12 | no | — |
| 313 | #67 | — | 12 | 6 | no | — |
| 314 | #67 | — | 12 | 6 | no | — |
| 315 | #67 | — | 12 | 6 | no | — |
| 316 | #67 | — | 12 | 6 | no | — |
| 317 | C2×Dic3 | — | 3 | 6 | no | — |
| 318 | C2×Dic3 | — | 6 | 3 | no | — |
| 319 | C2×Dic3 | C23×D3 | 1 | 12 | yes | — |
| 320 | D12 | — | 12 | 6 | no | — |
| 321 | D12 | — | 12 | 6 | no | — |
| 322 | D12 | — | 12 | 12 | no | — |
| 323 | C4×D3 | — | 6 | 24 | no | — |
| 324 | C4×D3 | — | 6 | 12 | no | — |
| 325 | C4×D3 | — | 12 | 6 | no | — |
| 326 | Dic6 | — | 4 | 6 | no | — |
| 327 | Dic6 | — | 12 | 12 | no | — |
| 328 | C2×C32 | — | 4 | 3 | no | — |
| 329 | C2×C32 | — | 4 | 1 | no | — |
| 330 | C2×C32 | C2×H(5,𝔽2) | 1 | 3 | yes | — |
| 331 | C3⋊D3 | — | 4 | 3 | no | — |
| 332 | C3⋊D3 | — | 4 | 1 | no | — |
| 333 | C3⋊D3 | H(3,𝔽4) | 1 | 4 | yes | complemented |
| 334 | C3×D3 | — | 4 | 4 | no | — |
| 335 | C24 | — | 3 | 2 | no | — |
| 336 | C24 | — | 9 | 2 | no | — |
| 337 | C24 | — | 9 | 2 | no | — |
| 338 | C24 | — | 9 | 3 | no | — |
| 339 | C24 | — | 9 | 1 | no | — |
| 340 | C24 | — | 9 | 3 | no | — |
| 341 | C24 | — | 36 | 6 | no | — |
| 342 | C24 | — | 36 | 6 | no | — |
| 343 | C24 | C2×D32 | 1 | 1 | yes | characteristic, complemented |
| 344 | C2×Q8 | — | 3 | 6 | no | — |
| 345 | C2×Q8 | — | 9 | 6 | no | — |
| 346 | C2×Q8 | — | 36 | 6 | no | — |
| 347 | C2×D4 | — | 3 | 12 | no | — |
| 348 | C2×D4 | — | 9 | 12 | no | — |
| 349 | C2×D4 | — | 9 | 3 | no | — |
| 350 | C2×D4 | — | 9 | 3 | no | — |
| 351 | C2×D4 | — | 9 | 3 | no | — |
| 352 | C2×D4 | — | 36 | 6 | no | — |
| 353 | C2×D4 | — | 36 | 12 | no | — |
| 354 | C2×D4 | C2×D32 | 1 | 3 | yes | — |
| 355 | C22×C4 | — | 9 | 6 | no | — |
| 356 | C22×C4 | — | 9 | 3 | no | — |
| 357 | C22⋊C4 | — | 3 | 6 | no | — |
| 358 | C22⋊C4 | — | 3 | 12 | no | — |
| 359 | C22⋊C4 | — | 3 | 12 | no | — |
| 360 | C22⋊C4 | — | 9 | 6 | no | — |
| 361 | C22⋊C4 | — | 9 | 12 | no | — |
| 362 | C22⋊C4 | — | 9 | 12 | no | — |
| 363 | C22⋊C4 | — | 9 | 3 | no | — |
| 364 | C22⋊C4 | — | 9 | 6 | no | — |
| 365 | C22⋊C4 | C2×D32 | 1 | 3 | yes | complemented |
| 366 | C42 | — | 3 | 6 | no | — |
| 367 | C42 | — | 9 | 6 | no | — |
| 368 | C22×C3 | — | 2 | 6 | no | — |
| 369 | C22×C3 | — | 2 | 12 | no | — |
| 370 | C22×C3 | — | 2 | 6 | no | — |
| 371 | C22×C3 | — | 2 | 6 | no | — |
| 372 | C22×C3 | — | 2 | 1 | no | — |
| 373 | C22×C3 | — | 4 | 6 | no | — |
| 374 | C22×C3 | — | 4 | 3 | no | — |
| 375 | C22×C3 | — | 4 | 8 | no | — |
| 376 | C22×C3 | — | 4 | 8 | no | — |
| 377 | C22×C3 | — | 6 | 12 | no | — |
| 378 | C22×C3 | — | 12 | 8 | no | — |
| 379 | C22×C3 | C24×D3 | 1 | 2 | yes | — |
| 380 | C2×D3 | — | 2 | 12 | no | — |
| 381 | C2×D3 | — | 3 | 12 | no | — |
| 382 | C2×D3 | — | 4 | 8 | no | — |
| 383 | C2×D3 | — | 6 | 6 | no | — |
| 384 | C2×D3 | — | 6 | 6 | no | — |
| 385 | C2×D3 | — | 6 | 6 | no | — |
| 386 | C2×D3 | — | 6 | 6 | no | — |
| 387 | C2×D3 | — | 6 | 12 | no | — |
| 388 | C2×D3 | — | 12 | 6 | no | — |
| 389 | C2×D3 | — | 12 | 3 | no | — |
| 390 | C2×D3 | — | 12 | 16 | no | — |
| 391 | C2×D3 | — | 12 | 24 | no | — |
| 392 | C2×D3 | — | 12 | 8 | no | — |
| 393 | C2×D3 | — | 12 | 16 | no | — |
| 394 | C2×D3 | — | 12 | 24 | no | — |
| 395 | C2×D3 | — | 12 | 24 | no | — |
| 396 | C2×D3 | — | 12 | 24 | no | — |
| 397 | C2×D3 | — | 24 | 4 | no | — |
| 398 | C3×C4 | — | 2 | 6 | no | — |
| 399 | C3×C4 | — | 4 | 3 | no | — |
| 400 | C3×C4 | — | 6 | 12 | no | — |
| 401 | Dic3 | — | 2 | 12 | no | — |
| 402 | Dic3 | — | 6 | 6 | no | — |
| 403 | Dic3 | — | 12 | 3 | no | — |
| 404 | C32 | C2×H(3,𝔽4) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 405 | C23 | — | 3 | 4 | no | — |
| 406 | C23 | — | 4 | 3 | no | — |
| 407 | C23 | — | 9 | 1 | no | — |
| 408 | C23 | — | 9 | 3 | no | — |
| 409 | C23 | — | 9 | 1 | no | — |
| 410 | C23 | — | 12 | 6 | no | — |
| 411 | C23 | — | 18 | 6 | no | — |
| 412 | C23 | — | 18 | 6 | no | — |
| 413 | C23 | — | 18 | 12 | no | — |
| 414 | C23 | — | 18 | 12 | no | — |
| 415 | C23 | — | 36 | 3 | no | — |
| 416 | C23 | — | 36 | 6 | no | — |
| 417 | C23 | — | 36 | 16 | no | — |
| 418 | C23 | — | 36 | 6 | no | — |
| 419 | C23 | — | 36 | 16 | no | — |
| 420 | C23 | C22×D32 | 1 | 1 | yes | characteristic |
| 421 | C23 | C22×D32 | 1 | 3 | yes | — |
| 422 | Q8 | — | 12 | 6 | no | — |
| 423 | Q8 | — | 36 | 6 | no | — |
| 424 | D4 | — | 4 | 3 | no | — |
| 425 | D4 | — | 12 | 12 | no | — |
| 426 | D4 | — | 36 | 3 | no | — |
| 427 | D4 | — | 36 | 12 | no | — |
| 428 | D4 | — | 36 | 3 | no | — |
| 429 | D4 | — | 36 | 3 | no | — |
| 430 | C2×C4 | — | 3 | 12 | no | — |
| 431 | C2×C4 | — | 9 | 3 | no | — |
| 432 | C2×C4 | — | 18 | 6 | no | — |
| 433 | C2×C4 | — | 18 | 12 | no | — |
| 434 | C2×C4 | C22×D32 | 1 | 3 | yes | — |
| 435 | C2×C3 | — | 2 | 3 | no | — |
| 436 | C2×C3 | — | 4 | 6 | no | — |
| 437 | C2×C3 | — | 4 | 2 | no | — |
| 438 | C2×C3 | — | 4 | 6 | no | — |
| 439 | C2×C3 | — | 8 | 1 | no | — |
| 440 | C2×C3 | — | 12 | 4 | no | — |
| 441 | C2×C3 | D3×H(5,𝔽2) | 1 | 6 | yes | — |
| 442 | D3 | — | 3 | 8 | no | — |
| 443 | D3 | — | 4 | 4 | no | — |
| 444 | D3 | — | 6 | 4 | no | — |
| 445 | D3 | — | 12 | 6 | no | — |
| 446 | D3 | — | 12 | 6 | no | — |
| 447 | D3 | — | 12 | 2 | no | — |
| 448 | D3 | — | 24 | 1 | no | — |
| 449 | C22 | — | 2 | 3 | no | — |
| 450 | C22 | — | 2 | 3 | no | — |
| 451 | C22 | — | 2 | 6 | no | — |
| 452 | C22 | — | 4 | 4 | no | — |
| 453 | C22 | — | 6 | 12 | no | — |
| 454 | C22 | — | 9 | 6 | no | — |
| 455 | C22 | — | 12 | 8 | no | — |
| 456 | C22 | — | 18 | 3 | no | — |
| 457 | C22 | — | 18 | 6 | no | — |
| 458 | C22 | — | 18 | 3 | no | — |
| 459 | C22 | — | 36 | 12 | no | — |
| 460 | C22 | — | 36 | 4 | no | — |
| 461 | C22 | — | 36 | 12 | no | — |
| 462 | C22 | — | 36 | 8 | no | — |
| 463 | C22 | — | 36 | 8 | no | — |
| 464 | C22 | C23×D32 | 1 | 1 | yes | characteristic |
| 465 | C4 | — | 2 | 3 | no | — |
| 466 | C4 | — | 6 | 12 | no | — |
| 467 | C4 | — | 18 | 3 | no | — |
| 468 | C3 | — | 2 | 1 | no | — |
| 469 | C3 | D3×H(3,𝔽4) | 1 | 2 | yes | complemented |
| 470 | C2 | — | 4 | 3 | no | — |
| 471 | C2 | — | 4 | 1 | no | — |
| 472 | C2 | — | 9 | 4 | no | — |
| 473 | C2 | — | 12 | 4 | no | — |
| 474 | C2 | — | 36 | 3 | no | — |
| 475 | C2 | — | 36 | 1 | no | — |
| 476 | C2 | #10596675 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D32 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C32×#120 | C22 |
| hypercenter | #120 | D32 |
| hypocenter | C32 | C2×H(3,𝔽4) |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3⋊D3×#120 | C2 | semidirect |
| 2. C3×#5594 | C2 | semidirect |
| 3. #10595529 | C2 | semidirect |
| 4. #10595527 | C2 | semidirect |
| 5. #10595278 | C2 | semidirect |
| 6. #10595262 | C2 | semidirect |
| 7. #10595170 | C2 | semidirect |
| 8. #10594311 | C2 | semidirect |
| 9. #10594288 | C2 | semidirect |
| 11. C24×C3⋊D3 | C22 | semidirect |
| 12. C23×D32 | C22 | semidirect |
| 15. C2×#3797 | C22 | semidirect |
| 16. C32×#120 | C22 | semidirect |
| 17. #64162 | C22 | semidirect |
| 18. #64146 | C22 | semidirect |
| 19. #64091 | C22 | semidirect |
| 20. C22⋊C4×C3⋊D3 | C22 | semidirect |
| 21. C3×#953 | C22 | semidirect |
| 22. C3×#937 | C22 | semidirect |
| 23. C3×#936 | C22 | semidirect |
| 24. C3×#885 | C22 | semidirect |
| 25. #63983 | C22 | semidirect |
| 26. #63981 | C22 | semidirect |
| 27. #63977 | C22 | semidirect |
| 28. #63974 | C22 | semidirect |
| 29. #63974 | C22 | semidirect |
| 30. #63959 | C22 | semidirect |
| 31. #63953 | C22 | semidirect |
| 32. #63953 | C22 | semidirect |
| 33. #63923 | C22 | semidirect |
| 34. #63921 | C22 | semidirect |
| 35. #63907 | C22 | semidirect |
| 36. C4×#624 | C22 | semidirect |
| 37. #63864 | C22 | semidirect |
| 38. #63852 | C22 | semidirect |
| 46. #5594 | D3 | semidirect |
| 51. C24×C32 | C23 | semidirect |
| 55. C23×C3⋊D3 | C23 | semidirect |
| 56. C23×C3×D3 | C23 | semidirect |
| 59. C22×D32 | C23 | semidirect |
| 67. C2×C3×Dic6 | C23 | semidirect |
| 69. C2×#627 | C23 | semidirect |
| 73. C32×C22⋊C4 | C23 | semidirect |
| 74. #3757 | C23 | semidirect |
| 75. #3752 | C23 | semidirect |
| 76. C3×#217 | C23 | semidirect |
| 77. C3×#217 | C23 | semidirect |
| 78. C3×(C2×D3)⋊C4 | C23 | semidirect |
| 79. C3×C4×Dic3 | C23 | semidirect |
| 80. #3722 | C23 | semidirect |
| 81. #3722 | C23 | semidirect |
| 82. (C2×D3)⋊Dic3 | C23 | semidirect |
| 83. Dic32 | C23 | semidirect |
| 97. C3×#120 | C2×D3 | semidirect |
| 101. #953 | C2×D3 | semidirect |
| 108. #937 | C2×D3 | semidirect |
| 110. #936 | C2×D3 | semidirect |
| 116. #885 | C2×D3 | semidirect |
| 171. C24×C3 | C22×D3 | semidirect |
| 183. C23×D3 | C22×D3 | semidirect |
| 205. C2×Dic6 | C22×D3 | semidirect |
| 210. C3×C22⋊C4 | C22×D3 | semidirect |
| 215. #217 | C22×D3 | semidirect |
| 216. #217 | C22×D3 | semidirect |
| 223. (C2×D3)⋊C4 | C22×D3 | semidirect |
| 225. C4×Dic3 | C22×D3 | semidirect |
| 267. #120 | D32 | semidirect |
| 333. C3⋊D3 | H(3,𝔽4) | semidirect |
| 343. C24 | C2×D32 | semidirect |
| 365. C22⋊C4 | C2×D32 | semidirect |
| 404. C32 | C2×H(3,𝔽4) | semidirect |
| 469. C3 | D3×H(3,𝔽4) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×#120 | 2 |
| C3×#5594 | 2 |
| #10595529 | 2 |
| #10595527 | 2 |
| #10595278 | 2 |
| #10595262 | 2 |
| #10595170 | 2 |
| #10594311 | 2 |
| #10594288 | 2 |
| D3×H(3,𝔽4) | 3 |