Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1446 conjugacy classes of subgroups.
The subgroup lattice has 580 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×#64367 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#64366 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#64157 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11723663 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | C2×#88811 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #11723661 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #11723660 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #10595448 | — | 3 | 1 | no | maximal |
| 9 | #10595447 | — | 3 | 1 | no | maximal |
| 10 | #10595446 | — | 3 | 1 | no | maximal |
| 11 | C33×#41 | C22 | 1 | 1 | yes | characteristic |
| 12 | C3×#3832 | — | 2 | 1 | no | — |
| 13 | C3×Q8×C3⋊D3 | — | 2 | 1 | no | — |
| 14 | C3×#3830 | — | 2 | 3 | no | — |
| 15 | C3×D4×C3⋊D3 | — | 2 | 3 | no | — |
| 16 | C3×#3828 | C22 | 1 | 3 | yes | — |
| 17 | C3×#3828 | C22 | 1 | 3 | yes | complemented |
| 18 | C2×C3×C4⋊(C3⋊D3) | C22 | 1 | 3 | yes | — |
| 19 | C2×C3×#634 | C22 | 1 | 3 | yes | complemented |
| 20 | C3×#3748 | C22 | 1 | 3 | yes | complemented |
| 21 | C2×C3×C3⋊(C3⋊C8) | C22 | 1 | 3 | yes | complemented |
| 22 | #88812 | C22 | 1 | 3 | yes | complemented |
| 23 | #88811 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #88811 | C22 | 1 | 3 | yes | complemented |
| 25 | #88811 | C22 | 1 | 6 | yes | complemented |
| 26 | #88810 | C22 | 1 | 3 | yes | complemented |
| 27 | #64367 | D3 | 1 | 1 | yes | characteristic, complemented |
| 28 | #64366 | D3 | 1 | 1 | yes | characteristic, complemented |
| 29 | C3×#1010 | — | 3 | 1 | no | — |
| 30 | C3×#1010 | — | 3 | 1 | no | — |
| 31 | C3×#1010 | — | 6 | 1 | no | — |
| 32 | C3×#1009 | — | 3 | 1 | no | — |
| 33 | C3×#1009 | — | 3 | 1 | no | — |
| 34 | C3×#1009 | — | 6 | 1 | no | — |
| 35 | #64157 | D3 | 1 | 1 | yes | characteristic, complemented |
| 36 | C3×#948 | — | 3 | 1 | no | — |
| 37 | C3×#948 | — | 3 | 1 | no | — |
| 38 | C3×#948 | — | 6 | 1 | no | — |
| 39 | #63833 | — | 3 | 3 | no | — |
| 40 | C2×#3717 | — | 3 | 3 | no | — |
| 41 | #63831 | — | 3 | 3 | no | — |
| 42 | #63830 | — | 3 | 3 | no | — |
| 43 | #63829 | — | 3 | 3 | no | — |
| 44 | #63829 | — | 3 | 3 | no | — |
| 45 | C2×#3716 | — | 3 | 3 | no | — |
| 46 | #63827 | — | 3 | 3 | no | — |
| 47 | C2×#3715 | — | 3 | 3 | no | — |
| 48 | #63825 | — | 3 | 3 | no | — |
| 49 | #63823 | — | 3 | 3 | no | — |
| 50 | #63822 | — | 3 | 3 | no | — |
| 51 | C22×C3×C3⋊D3 | — | 2 | 3 | no | — |
| 52 | C33×Q8 | D4 | 1 | 1 | yes | characteristic |
| 53 | C33×D4 | D4 | 1 | 3 | yes | — |
| 54 | C2×C33×C4 | C23 | 1 | 3 | yes | — |
| 55 | C3×#638 | — | 2 | 3 | no | — |
| 56 | C3×#638 | — | 2 | 3 | no | — |
| 57 | C2×C3×C3⋊Dic3 | — | 2 | 3 | no | — |
| 58 | C3×C4⋊(C3⋊D3) | — | 2 | 3 | no | — |
| 59 | C3×C4⋊(C3⋊D3) | C23 | 1 | 3 | yes | — |
| 60 | C3×C4⋊(C3⋊D3) | C23 | 1 | 1 | yes | characteristic |
| 61 | C3×C4×C3⋊D3 | — | 2 | 3 | no | — |
| 62 | C3×C4×C3⋊D3 | — | 2 | 3 | no | — |
| 63 | C3×#634 | — | 2 | 3 | no | — |
| 64 | C3×#634 | C23 | 1 | 3 | yes | — |
| 65 | C3×#634 | C23 | 1 | 1 | yes | characteristic |
| 66 | C3×C3⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 67 | C3×C3⋊(C3⋊C8) | C23 | 1 | 3 | yes | — |
| 68 | #5837 | — | 9 | 1 | no | — |
| 69 | #5836 | — | 9 | 1 | no | — |
| 70 | #5751 | — | 9 | 1 | no | — |
| 71 | C32×#41 | — | 2 | 1 | no | — |
| 72 | C32×#41 | — | 2 | 1 | no | — |
| 73 | C32×#41 | — | 2 | 1 | no | — |
| 74 | C32×#41 | — | 4 | 1 | no | — |
| 75 | C32×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 76 | C32×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 77 | C32×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 78 | #3832 | — | 2 | 1 | no | — |
| 79 | Q8×C3⋊D3 | — | 2 | 1 | no | — |
| 80 | #3830 | — | 2 | 3 | no | — |
| 81 | D4×C3⋊D3 | — | 2 | 3 | no | — |
| 82 | #3828 | C2×D3 | 1 | 3 | yes | — |
| 83 | #3828 | C2×D3 | 1 | 3 | yes | complemented |
| 84 | C2×C4⋊(C3⋊D3) | C2×D3 | 1 | 3 | yes | — |
| 85 | C2×#634 | C2×D3 | 1 | 3 | yes | complemented |
| 86 | C3×#239 | — | 6 | 2 | no | — |
| 87 | C3×#239 | — | 6 | 1 | no | — |
| 88 | C3×#239 | — | 6 | 1 | no | — |
| 89 | C3×D3×Q8 | — | 6 | 2 | no | — |
| 90 | C3×D3×Q8 | — | 6 | 1 | no | — |
| 91 | C3×D3×Q8 | — | 6 | 1 | no | — |
| 92 | C3×#237 | — | 6 | 6 | no | — |
| 93 | C3×#237 | — | 6 | 3 | no | — |
| 94 | C3×#237 | — | 6 | 3 | no | — |
| 95 | C3×D3×D4 | — | 6 | 6 | no | — |
| 96 | C3×D3×D4 | — | 6 | 3 | no | — |
| 97 | C3×D3×D4 | — | 6 | 3 | no | — |
| 98 | C3×#235 | — | 3 | 3 | no | — |
| 99 | C3×#235 | — | 3 | 3 | no | — |
| 100 | C3×#235 | — | 3 | 3 | no | — |
| 101 | C3×#235 | — | 3 | 3 | no | — |
| 102 | C3×#235 | — | 6 | 3 | no | — |
| 103 | C3×#235 | — | 6 | 3 | no | — |
| 104 | C2×C3×D12 | — | 3 | 3 | no | — |
| 105 | C2×C3×D12 | — | 3 | 3 | no | — |
| 106 | C2×C3×D12 | — | 6 | 3 | no | — |
| 107 | C2×C3×Dic6 | — | 3 | 3 | no | — |
| 108 | C2×C3×Dic6 | — | 3 | 3 | no | — |
| 109 | C2×C3×Dic6 | — | 6 | 3 | no | — |
| 110 | #3748 | C2×D3 | 1 | 3 | yes | complemented |
| 111 | C2×C3⋊(C3⋊C8) | C2×D3 | 1 | 3 | yes | complemented |
| 112 | C3×#208 | — | 3 | 3 | no | — |
| 113 | C3×#208 | — | 3 | 3 | no | — |
| 114 | C3×#208 | — | 6 | 3 | no | — |
| 115 | C2×C3×C3⋊C8 | — | 3 | 3 | no | — |
| 116 | C2×C3×C3⋊C8 | — | 3 | 3 | no | — |
| 117 | C2×C3×C3⋊C8 | — | 6 | 3 | no | — |
| 118 | #3719 | — | 3 | 3 | no | — |
| 119 | #3719 | — | 3 | 3 | no | — |
| 120 | #3718 | — | 3 | 3 | no | — |
| 121 | #3717 | — | 3 | 6 | no | — |
| 122 | #3717 | — | 3 | 1 | no | — |
| 123 | #3717 | — | 3 | 3 | no | — |
| 124 | #3716 | — | 3 | 3 | no | — |
| 125 | #3716 | — | 3 | 6 | no | — |
| 126 | #3716 | — | 3 | 1 | no | — |
| 127 | #3715 | — | 3 | 1 | no | — |
| 128 | #3715 | — | 3 | 3 | no | — |
| 129 | #3715 | — | 3 | 6 | no | — |
| 130 | #3714 | — | 3 | 3 | no | — |
| 131 | #3714 | — | 3 | 3 | no | — |
| 132 | #3713 | — | 3 | 3 | no | — |
| 133 | C22×C33 | C2×D4 | 1 | 3 | yes | — |
| 134 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 135 | C2×C3×C3⋊D3 | — | 2 | 3 | no | — |
| 136 | C2×C3×C3⋊D3 | — | 8 | 3 | no | — |
| 137 | C33×C4 | C2×D4 | 1 | 3 | yes | — |
| 138 | C33×C4 | C24 | 1 | 1 | yes | characteristic |
| 139 | C3×C3⋊Dic3 | — | 2 | 3 | no | — |
| 140 | C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 141 | C3×2−1+4 | — | 9 | 1 | no | — |
| 142 | C3×H(5,𝔽2) | — | 9 | 1 | no | — |
| 143 | #1010 | — | 3 | 1 | no | — |
| 144 | #1010 | — | 3 | 1 | no | — |
| 145 | #1010 | — | 6 | 1 | no | — |
| 146 | #1009 | — | 3 | 1 | no | — |
| 147 | #1009 | — | 3 | 1 | no | — |
| 148 | #1009 | — | 6 | 1 | no | — |
| 149 | C3×#131 | — | 9 | 1 | no | — |
| 150 | #951 | — | 9 | 3 | no | — |
| 151 | #950 | — | 9 | 3 | no | — |
| 152 | #950 | — | 9 | 3 | no | — |
| 153 | #949 | — | 9 | 3 | no | — |
| 154 | #948 | — | 3 | 1 | no | — |
| 155 | #948 | — | 3 | 1 | no | — |
| 156 | #948 | — | 6 | 1 | no | — |
| 157 | #942 | — | 9 | 3 | no | — |
| 158 | C2×#215 | — | 9 | 3 | no | — |
| 159 | C2×#214 | — | 9 | 3 | no | — |
| 160 | #932 | — | 9 | 3 | no | — |
| 161 | #909 | — | 9 | 3 | no | — |
| 162 | #908 | — | 9 | 3 | no | — |
| 163 | #904 | — | 9 | 3 | no | — |
| 164 | C2×#204 | — | 9 | 3 | no | — |
| 165 | C22×C3⋊D3 | — | 2 | 3 | no | — |
| 166 | C22×C3×D3 | — | 6 | 6 | no | — |
| 167 | C22×C3×D3 | — | 6 | 3 | no | — |
| 168 | C22×C3×D3 | — | 6 | 3 | no | — |
| 169 | C32×Q8 | — | 2 | 1 | no | — |
| 170 | C32×Q8 | — | 2 | 1 | no | — |
| 171 | C32×Q8 | — | 2 | 1 | no | — |
| 172 | C32×Q8 | — | 4 | 1 | no | — |
| 173 | C32×Q8 | D12 | 1 | 1 | yes | characteristic |
| 174 | C32×Q8 | #67 | 1 | 1 | yes | characteristic |
| 175 | C32×Q8 | #67 | 1 | 1 | yes | characteristic |
| 176 | C32×D4 | — | 2 | 3 | no | — |
| 177 | C32×D4 | — | 2 | 3 | no | — |
| 178 | C32×D4 | — | 2 | 3 | no | — |
| 179 | C32×D4 | — | 4 | 3 | no | — |
| 180 | C32×D4 | D12 | 1 | 3 | yes | — |
| 181 | C32×D4 | #67 | 1 | 3 | yes | — |
| 182 | C32×D4 | #67 | 1 | 3 | yes | — |
| 183 | C2×C32×C4 | — | 2 | 3 | no | — |
| 184 | C2×C32×C4 | — | 2 | 3 | no | — |
| 185 | C2×C32×C4 | — | 2 | 3 | no | — |
| 186 | C2×C32×C4 | — | 4 | 3 | no | — |
| 187 | C2×C32×C4 | C22×D3 | 1 | 3 | yes | — |
| 188 | C2×C32×C4 | C22×D3 | 1 | 3 | yes | — |
| 189 | C2×C32×C4 | C22×D3 | 1 | 3 | yes | — |
| 190 | #638 | — | 2 | 3 | no | — |
| 191 | #638 | — | 2 | 3 | no | — |
| 192 | C2×C3⋊Dic3 | — | 2 | 3 | no | — |
| 193 | C4⋊(C3⋊D3) | — | 2 | 3 | no | — |
| 194 | C4⋊(C3⋊D3) | C22×D3 | 1 | 1 | yes | characteristic |
| 195 | C4⋊(C3⋊D3) | C22×D3 | 1 | 3 | yes | — |
| 196 | C4×C3⋊D3 | — | 2 | 3 | no | — |
| 197 | C4×C3⋊D3 | — | 2 | 3 | no | — |
| 198 | #634 | — | 2 | 3 | no | — |
| 199 | #634 | C22×D3 | 1 | 3 | yes | — |
| 200 | #634 | C22×D3 | 1 | 1 | yes | characteristic |
| 201 | C3×#67 | — | 6 | 6 | no | — |
| 202 | C3×#67 | — | 6 | 6 | no | — |
| 203 | C3×#67 | — | 6 | 3 | no | — |
| 204 | C3×#67 | — | 6 | 3 | no | — |
| 205 | C3×#67 | — | 6 | 3 | no | — |
| 206 | C3×#67 | — | 6 | 3 | no | — |
| 207 | C2×C3×Dic3 | — | 6 | 6 | no | — |
| 208 | C2×C3×Dic3 | — | 6 | 3 | no | — |
| 209 | C2×C3×Dic3 | — | 6 | 3 | no | — |
| 210 | C3×D12 | — | 3 | 1 | no | — |
| 211 | C3×D12 | — | 3 | 3 | no | — |
| 212 | C3×D12 | — | 3 | 1 | no | — |
| 213 | C3×D12 | — | 3 | 3 | no | — |
| 214 | C3×D12 | — | 6 | 3 | no | — |
| 215 | C3×D12 | — | 6 | 1 | no | — |
| 216 | C3×D12 | — | 6 | 6 | no | — |
| 217 | C3×D12 | — | 6 | 3 | no | — |
| 218 | C3×D12 | — | 6 | 3 | no | — |
| 219 | C3×C4×D3 | — | 6 | 6 | no | — |
| 220 | C3×C4×D3 | — | 6 | 6 | no | — |
| 221 | C3×C4×D3 | — | 6 | 3 | no | — |
| 222 | C3×C4×D3 | — | 6 | 3 | no | — |
| 223 | C3×C4×D3 | — | 6 | 3 | no | — |
| 224 | C3×C4×D3 | — | 6 | 3 | no | — |
| 225 | C3×Dic6 | — | 3 | 3 | no | — |
| 226 | C3×Dic6 | — | 3 | 1 | no | — |
| 227 | C3×Dic6 | — | 3 | 3 | no | — |
| 228 | C3×Dic6 | — | 3 | 1 | no | — |
| 229 | C3×Dic6 | — | 6 | 3 | no | — |
| 230 | C3×Dic6 | — | 6 | 1 | no | — |
| 231 | C3×Dic6 | — | 6 | 6 | no | — |
| 232 | C3×Dic6 | — | 6 | 3 | no | — |
| 233 | C3×Dic6 | — | 6 | 3 | no | — |
| 234 | C3⋊(C3⋊C8) | C22×D3 | 1 | 3 | yes | — |
| 235 | C3⋊(C3⋊C8) | C22×D3 | 1 | 1 | yes | characteristic |
| 236 | C3×C3⋊C8 | — | 3 | 3 | no | — |
| 237 | C3×C3⋊C8 | — | 3 | 3 | no | — |
| 238 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 239 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 240 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 241 | C3×C3⋊C8 | — | 6 | 3 | no | — |
| 242 | #577 | — | 27 | 1 | no | Sylow |
| 243 | C2×C33 | — | 2 | 3 | no | — |
| 244 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 245 | C3×C3⋊D3 | — | 4 | 1 | no | — |
| 246 | C3×C3⋊D3 | — | 4 | 3 | no | — |
| 247 | C3×#41 | — | 2 | 1 | no | — |
| 248 | C3×#41 | — | 2 | 1 | no | — |
| 249 | C3×#41 | — | 2 | 1 | no | — |
| 250 | C3×#41 | — | 4 | 1 | no | — |
| 251 | C3×#41 | — | 9 | 3 | no | — |
| 252 | C3×#41 | — | 9 | 3 | no | — |
| 253 | C3×#41 | — | 18 | 1 | no | — |
| 254 | C3×#41 | — | 18 | 3 | no | — |
| 255 | C3×#41 | D32 | 1 | 1 | yes | characteristic |
| 256 | C3×#41 | D32 | 1 | 1 | yes | characteristic |
| 257 | C3×#41 | D32 | 1 | 1 | yes | characteristic |
| 258 | C2×C3×Q8 | — | 9 | 3 | no | — |
| 259 | C2×C3×Q8 | — | 18 | 1 | no | — |
| 260 | C2×C3×D4 | — | 9 | 3 | no | — |
| 261 | C2×C3×D4 | — | 18 | 3 | no | — |
| 262 | #239 | — | 6 | 2 | no | — |
| 263 | #239 | — | 6 | 1 | no | — |
| 264 | #239 | — | 6 | 1 | no | — |
| 265 | D3×Q8 | — | 6 | 2 | no | — |
| 266 | D3×Q8 | — | 6 | 1 | no | — |
| 267 | D3×Q8 | — | 6 | 1 | no | — |
| 268 | #237 | — | 6 | 6 | no | — |
| 269 | #237 | — | 6 | 3 | no | — |
| 270 | #237 | — | 6 | 3 | no | — |
| 271 | D3×D4 | — | 6 | 6 | no | — |
| 272 | D3×D4 | — | 6 | 3 | no | — |
| 273 | D3×D4 | — | 6 | 3 | no | — |
| 274 | #235 | — | 3 | 3 | no | — |
| 275 | #235 | — | 3 | 3 | no | — |
| 276 | #235 | — | 3 | 3 | no | — |
| 277 | #235 | — | 3 | 3 | no | — |
| 278 | #235 | — | 6 | 3 | no | — |
| 279 | #235 | — | 6 | 3 | no | — |
| 280 | C2×D12 | — | 3 | 3 | no | — |
| 281 | C2×D12 | — | 3 | 3 | no | — |
| 282 | C2×D12 | — | 6 | 3 | no | — |
| 283 | C2×Dic6 | — | 3 | 3 | no | — |
| 284 | C2×Dic6 | — | 3 | 3 | no | — |
| 285 | C2×Dic6 | — | 6 | 3 | no | — |
| 286 | C3×M16 | — | 9 | 3 | no | — |
| 287 | C2×C3×C8 | — | 9 | 3 | no | — |
| 288 | #216 | — | 9 | 3 | no | — |
| 289 | #216 | — | 9 | 3 | no | — |
| 290 | #215 | — | 9 | 3 | no | — |
| 291 | #215 | — | 9 | 6 | no | — |
| 292 | #215 | — | 9 | 1 | no | — |
| 293 | #214 | — | 9 | 6 | no | — |
| 294 | #214 | — | 9 | 3 | no | — |
| 295 | #214 | — | 9 | 1 | no | — |
| 296 | #213 | — | 9 | 3 | no | — |
| 297 | #213 | — | 9 | 3 | no | — |
| 298 | #208 | — | 3 | 3 | no | — |
| 299 | #208 | — | 3 | 3 | no | — |
| 300 | #208 | — | 6 | 3 | no | — |
| 301 | C2×C3⋊C8 | — | 3 | 3 | no | — |
| 302 | C2×C3⋊C8 | — | 3 | 3 | no | — |
| 303 | C2×C3⋊C8 | — | 6 | 3 | no | — |
| 304 | Dic12 | — | 9 | 3 | no | — |
| 305 | D24 | — | 9 | 3 | no | — |
| 306 | #204 | — | 9 | 3 | no | — |
| 307 | #204 | — | 9 | 6 | no | — |
| 308 | #204 | — | 9 | 1 | no | — |
| 309 | C22×C32 | — | 2 | 3 | no | — |
| 310 | C22×C32 | — | 2 | 3 | no | — |
| 311 | C22×C32 | — | 2 | 3 | no | — |
| 312 | C22×C32 | — | 4 | 3 | no | — |
| 313 | C22×C32 | C2×D12 | 1 | 3 | yes | — |
| 314 | C22×C32 | C2×#67 | 1 | 3 | yes | — |
| 315 | C22×C32 | C2×#67 | 1 | 3 | yes | — |
| 316 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 317 | C2×C3⋊D3 | — | 2 | 3 | no | — |
| 318 | C2×C3⋊D3 | — | 8 | 3 | no | — |
| 319 | C2×C3×D3 | — | 6 | 2 | no | — |
| 320 | C2×C3×D3 | — | 6 | 6 | no | — |
| 321 | C2×C3×D3 | — | 6 | 1 | no | — |
| 322 | C2×C3×D3 | — | 6 | 3 | no | — |
| 323 | C2×C3×D3 | — | 6 | 1 | no | — |
| 324 | C2×C3×D3 | — | 6 | 3 | no | — |
| 325 | C2×C3×D3 | — | 24 | 3 | no | — |
| 326 | C2×C3×D3 | — | 24 | 3 | no | — |
| 327 | C2×C3×D3 | — | 24 | 6 | no | — |
| 328 | C32×C4 | — | 2 | 1 | no | — |
| 329 | C32×C4 | — | 2 | 1 | no | — |
| 330 | C32×C4 | — | 2 | 1 | no | — |
| 331 | C32×C4 | — | 2 | 3 | no | — |
| 332 | C32×C4 | — | 2 | 3 | no | — |
| 333 | C32×C4 | — | 2 | 3 | no | — |
| 334 | C32×C4 | — | 4 | 3 | no | — |
| 335 | C32×C4 | — | 4 | 1 | no | — |
| 336 | C32×C4 | C2×D12 | 1 | 3 | yes | — |
| 337 | C32×C4 | C2×#67 | 1 | 3 | yes | — |
| 338 | C32×C4 | C2×#67 | 1 | 3 | yes | — |
| 339 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 340 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 341 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 342 | C3⋊Dic3 | — | 2 | 3 | no | — |
| 343 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 344 | C3×Dic3 | — | 6 | 6 | no | — |
| 345 | C3×Dic3 | — | 6 | 2 | no | — |
| 346 | C3×Dic3 | — | 6 | 3 | no | — |
| 347 | C3×Dic3 | — | 6 | 1 | no | — |
| 348 | C3×Dic3 | — | 6 | 3 | no | — |
| 349 | C3×Dic3 | — | 6 | 1 | no | — |
| 350 | 2−1+4 | — | 9 | 1 | no | — |
| 351 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 352 | #137 | — | 27 | 3 | no | — |
| 353 | AGL(1,ℤ/8) | — | 27 | 3 | no | — |
| 354 | #135 | — | 27 | 3 | no | — |
| 355 | C2×SD16 | — | 27 | 3 | no | — |
| 356 | #131 | — | 9 | 1 | no | — |
| 357 | C33 | #577 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 358 | C23×C3 | — | 18 | 3 | no | — |
| 359 | C22×D3 | — | 6 | 6 | no | — |
| 360 | C22×D3 | — | 6 | 3 | no | — |
| 361 | C22×D3 | — | 6 | 3 | no | — |
| 362 | C3×Q8 | — | 2 | 1 | no | — |
| 363 | C3×Q8 | — | 2 | 1 | no | — |
| 364 | C3×Q8 | — | 2 | 1 | no | — |
| 365 | C3×Q8 | — | 4 | 1 | no | — |
| 366 | C3×Q8 | — | 9 | 3 | no | — |
| 367 | C3×Q8 | — | 9 | 1 | no | — |
| 368 | C3×Q8 | — | 18 | 3 | no | — |
| 369 | C3×Q8 | #625 | 1 | 1 | yes | characteristic |
| 370 | C3×Q8 | #626 | 1 | 1 | yes | characteristic |
| 371 | C3×Q8 | #626 | 1 | 1 | yes | characteristic |
| 372 | C3×D4 | — | 2 | 3 | no | — |
| 373 | C3×D4 | — | 2 | 3 | no | — |
| 374 | C3×D4 | — | 2 | 3 | no | — |
| 375 | C3×D4 | — | 4 | 3 | no | — |
| 376 | C3×D4 | — | 9 | 1 | no | — |
| 377 | C3×D4 | — | 9 | 3 | no | — |
| 378 | C3×D4 | — | 18 | 3 | no | — |
| 379 | C3×D4 | — | 18 | 3 | no | — |
| 380 | C3×D4 | — | 18 | 3 | no | — |
| 381 | C3×D4 | #625 | 1 | 3 | yes | — |
| 382 | C3×D4 | #626 | 1 | 3 | yes | — |
| 383 | C3×D4 | #626 | 1 | 3 | yes | — |
| 384 | C2×C3×C4 | — | 2 | 3 | no | — |
| 385 | C2×C3×C4 | — | 2 | 3 | no | — |
| 386 | C2×C3×C4 | — | 2 | 3 | no | — |
| 387 | C2×C3×C4 | — | 4 | 3 | no | — |
| 388 | C2×C3×C4 | — | 18 | 3 | no | — |
| 389 | C2×C3×C4 | — | 18 | 3 | no | — |
| 390 | C2×C3×C4 | — | 18 | 3 | no | — |
| 391 | C2×C3×C4 | C2×D32 | 1 | 3 | yes | — |
| 392 | C2×C3×C4 | C2×D32 | 1 | 3 | yes | — |
| 393 | C2×C3×C4 | C2×D32 | 1 | 3 | yes | — |
| 394 | #67 | — | 6 | 6 | no | — |
| 395 | #67 | — | 6 | 6 | no | — |
| 396 | #67 | — | 6 | 3 | no | — |
| 397 | #67 | — | 6 | 3 | no | — |
| 398 | #67 | — | 6 | 3 | no | — |
| 399 | #67 | — | 6 | 3 | no | — |
| 400 | C2×Dic3 | — | 6 | 6 | no | — |
| 401 | C2×Dic3 | — | 6 | 3 | no | — |
| 402 | C2×Dic3 | — | 6 | 3 | no | — |
| 403 | D12 | — | 3 | 3 | no | — |
| 404 | D12 | — | 3 | 1 | no | — |
| 405 | D12 | — | 3 | 1 | no | — |
| 406 | D12 | — | 3 | 3 | no | — |
| 407 | D12 | — | 6 | 3 | no | — |
| 408 | D12 | — | 6 | 1 | no | — |
| 409 | D12 | — | 6 | 6 | no | — |
| 410 | D12 | — | 6 | 3 | no | — |
| 411 | D12 | — | 6 | 3 | no | — |
| 412 | C4×D3 | — | 6 | 6 | no | — |
| 413 | C4×D3 | — | 6 | 6 | no | — |
| 414 | C4×D3 | — | 6 | 3 | no | — |
| 415 | C4×D3 | — | 6 | 3 | no | — |
| 416 | C4×D3 | — | 6 | 3 | no | — |
| 417 | C4×D3 | — | 6 | 3 | no | — |
| 418 | Dic6 | — | 3 | 3 | no | — |
| 419 | Dic6 | — | 3 | 1 | no | — |
| 420 | Dic6 | — | 3 | 3 | no | — |
| 421 | Dic6 | — | 3 | 1 | no | — |
| 422 | Dic6 | — | 6 | 3 | no | — |
| 423 | Dic6 | — | 6 | 1 | no | — |
| 424 | Dic6 | — | 6 | 6 | no | — |
| 425 | Dic6 | — | 6 | 3 | no | — |
| 426 | Dic6 | — | 6 | 3 | no | — |
| 427 | C3×C8 | — | 9 | 1 | no | — |
| 428 | C3×C8 | — | 9 | 3 | no | — |
| 429 | C3⋊C8 | — | 3 | 1 | no | — |
| 430 | C3⋊C8 | — | 3 | 1 | no | — |
| 431 | C3⋊C8 | — | 3 | 3 | no | — |
| 432 | C3⋊C8 | — | 3 | 3 | no | — |
| 433 | C3⋊C8 | — | 6 | 1 | no | — |
| 434 | C3⋊C8 | — | 6 | 3 | no | — |
| 435 | C2×C32 | — | 2 | 3 | no | — |
| 436 | C2×C32 | — | 2 | 3 | no | — |
| 437 | C2×C32 | — | 2 | 3 | no | — |
| 438 | C2×C32 | — | 2 | 1 | no | — |
| 439 | C2×C32 | — | 2 | 1 | no | — |
| 440 | C2×C32 | — | 2 | 1 | no | — |
| 441 | C2×C32 | — | 4 | 1 | no | — |
| 442 | C2×C32 | — | 4 | 3 | no | — |
| 443 | C2×C32 | — | 4 | 3 | no | — |
| 444 | C2×C32 | — | 4 | 3 | no | — |
| 445 | C2×C32 | — | 8 | 3 | no | — |
| 446 | C2×C32 | C22×D12 | 1 | 1 | yes | characteristic |
| 447 | C2×C32 | C22×#67 | 1 | 1 | yes | characteristic |
| 448 | C2×C32 | C22×#67 | 1 | 1 | yes | characteristic |
| 449 | C3⋊D3 | — | 4 | 3 | no | — |
| 450 | C3⋊D3 | — | 4 | 1 | no | — |
| 451 | C3×D3 | — | 12 | 2 | no | — |
| 452 | C3×D3 | — | 12 | 6 | no | — |
| 453 | C3×D3 | — | 12 | 1 | no | — |
| 454 | C3×D3 | — | 12 | 3 | no | — |
| 455 | C3×D3 | — | 12 | 1 | no | — |
| 456 | C3×D3 | — | 12 | 3 | no | — |
| 457 | #41 | — | 9 | 3 | no | — |
| 458 | #41 | — | 9 | 3 | no | — |
| 459 | #41 | — | 18 | 1 | no | — |
| 460 | #41 | — | 18 | 3 | no | — |
| 461 | #41 | #1113 | 1 | 1 | yes | characteristic |
| 462 | C2×Q8 | — | 9 | 3 | no | — |
| 463 | C2×Q8 | — | 18 | 1 | no | — |
| 464 | C2×D4 | — | 9 | 3 | no | — |
| 465 | C2×D4 | — | 18 | 3 | no | — |
| 466 | Q16 | — | 27 | 3 | no | — |
| 467 | SD16 | — | 27 | 3 | no | — |
| 468 | SD16 | — | 27 | 6 | no | — |
| 469 | SD16 | — | 27 | 1 | no | — |
| 470 | D8 | — | 27 | 3 | no | — |
| 471 | M16 | — | 9 | 3 | no | — |
| 472 | C2×C8 | — | 9 | 3 | no | — |
| 473 | C22×C3 | — | 2 | 3 | no | — |
| 474 | C22×C3 | — | 2 | 3 | no | — |
| 475 | C22×C3 | — | 2 | 3 | no | — |
| 476 | C22×C3 | — | 4 | 3 | no | — |
| 477 | C22×C3 | — | 18 | 1 | no | — |
| 478 | C22×C3 | — | 18 | 3 | no | — |
| 479 | C22×C3 | — | 72 | 3 | no | — |
| 480 | C22×C3 | C2×#625 | 1 | 3 | yes | — |
| 481 | C22×C3 | C2×#626 | 1 | 3 | yes | — |
| 482 | C22×C3 | C2×#626 | 1 | 3 | yes | — |
| 483 | C2×D3 | — | 6 | 2 | no | — |
| 484 | C2×D3 | — | 6 | 6 | no | — |
| 485 | C2×D3 | — | 6 | 1 | no | — |
| 486 | C2×D3 | — | 6 | 3 | no | — |
| 487 | C2×D3 | — | 6 | 1 | no | — |
| 488 | C2×D3 | — | 6 | 3 | no | — |
| 489 | C2×D3 | — | 24 | 3 | no | — |
| 490 | C2×D3 | — | 24 | 3 | no | — |
| 491 | C2×D3 | — | 24 | 6 | no | — |
| 492 | C3×C4 | — | 2 | 1 | no | — |
| 493 | C3×C4 | — | 2 | 1 | no | — |
| 494 | C3×C4 | — | 2 | 1 | no | — |
| 495 | C3×C4 | — | 2 | 3 | no | — |
| 496 | C3×C4 | — | 2 | 3 | no | — |
| 497 | C3×C4 | — | 2 | 3 | no | — |
| 498 | C3×C4 | — | 4 | 1 | no | — |
| 499 | C3×C4 | — | 4 | 3 | no | — |
| 500 | C3×C4 | — | 18 | 1 | no | — |
| 501 | C3×C4 | — | 18 | 3 | no | — |
| 502 | C3×C4 | C2×#625 | 1 | 3 | yes | — |
| 503 | C3×C4 | C2×#626 | 1 | 3 | yes | — |
| 504 | C3×C4 | C2×#626 | 1 | 3 | yes | — |
| 505 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 506 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 507 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 508 | Dic3 | — | 6 | 6 | no | — |
| 509 | Dic3 | — | 6 | 2 | no | — |
| 510 | Dic3 | — | 6 | 3 | no | — |
| 511 | Dic3 | — | 6 | 1 | no | — |
| 512 | Dic3 | — | 6 | 3 | no | — |
| 513 | Dic3 | — | 6 | 1 | no | — |
| 514 | C32 | — | 2 | 1 | no | — |
| 515 | C32 | — | 2 | 1 | no | — |
| 516 | C32 | — | 2 | 1 | no | — |
| 517 | C32 | — | 4 | 1 | no | — |
| 518 | C32 | #5751 | 1 | 1 | yes | characteristic, complemented |
| 519 | C32 | #5836 | 1 | 1 | yes | characteristic, complemented |
| 520 | C32 | #5837 | 1 | 1 | yes | characteristic, complemented |
| 521 | C23 | — | 18 | 3 | no | — |
| 522 | Q8 | — | 9 | 3 | no | — |
| 523 | Q8 | — | 9 | 1 | no | — |
| 524 | Q8 | — | 18 | 3 | no | — |
| 525 | Q8 | #6295 | 1 | 1 | yes | characteristic |
| 526 | D4 | — | 9 | 1 | no | — |
| 527 | D4 | — | 9 | 3 | no | — |
| 528 | D4 | — | 18 | 3 | no | — |
| 529 | D4 | — | 18 | 3 | no | — |
| 530 | D4 | — | 18 | 3 | no | — |
| 531 | D4 | #6295 | 1 | 3 | yes | — |
| 532 | C2×C4 | — | 18 | 3 | no | — |
| 533 | C2×C4 | — | 18 | 3 | no | — |
| 534 | C2×C4 | — | 18 | 3 | no | — |
| 535 | C2×C4 | C2×#1113 | 1 | 3 | yes | — |
| 536 | C8 | — | 9 | 1 | no | — |
| 537 | C8 | — | 9 | 3 | no | — |
| 538 | C2×C3 | — | 2 | 3 | no | — |
| 539 | C2×C3 | — | 2 | 3 | no | — |
| 540 | C2×C3 | — | 2 | 3 | no | — |
| 541 | C2×C3 | — | 2 | 1 | no | — |
| 542 | C2×C3 | — | 2 | 1 | no | — |
| 543 | C2×C3 | — | 2 | 1 | no | — |
| 544 | C2×C3 | — | 4 | 3 | no | — |
| 545 | C2×C3 | — | 4 | 3 | no | — |
| 546 | C2×C3 | — | 4 | 3 | no | — |
| 547 | C2×C3 | — | 4 | 1 | no | — |
| 548 | C2×C3 | — | 8 | 3 | no | — |
| 549 | C2×C3 | — | 36 | 1 | no | — |
| 550 | C2×C3 | — | 36 | 3 | no | — |
| 551 | C2×C3 | C22×#625 | 1 | 1 | yes | characteristic |
| 552 | C2×C3 | C22×#626 | 1 | 1 | yes | characteristic |
| 553 | C2×C3 | C22×#626 | 1 | 1 | yes | characteristic |
| 554 | D3 | — | 12 | 6 | no | — |
| 555 | D3 | — | 12 | 2 | no | — |
| 556 | D3 | — | 12 | 3 | no | — |
| 557 | D3 | — | 12 | 1 | no | — |
| 558 | D3 | — | 12 | 3 | no | — |
| 559 | D3 | — | 12 | 1 | no | — |
| 560 | C22 | — | 18 | 1 | no | — |
| 561 | C22 | — | 18 | 3 | no | — |
| 562 | C22 | — | 72 | 3 | no | — |
| 563 | C22 | C2×#6295 | 1 | 3 | yes | — |
| 564 | C4 | — | 18 | 1 | no | — |
| 565 | C4 | — | 18 | 3 | no | — |
| 566 | C4 | C2×#6295 | 1 | 3 | yes | — |
| 567 | C4 | C22×#1113 | 1 | 1 | yes | characteristic |
| 568 | C3 | — | 2 | 1 | no | — |
| 569 | C3 | — | 2 | 1 | no | — |
| 570 | C3 | — | 2 | 1 | no | — |
| 571 | C3 | — | 4 | 1 | no | — |
| 572 | C3 | #10595446 | 1 | 1 | yes | characteristic, complemented |
| 573 | C3 | #10595447 | 1 | 1 | yes | characteristic, complemented |
| 574 | C3 | #10595448 | 1 | 1 | yes | characteristic, complemented |
| 575 | C2 | — | 2 | 3 | no | — |
| 576 | C2 | — | 36 | 3 | no | — |
| 577 | C2 | — | 36 | 1 | no | — |
| 578 | C2 | C22×#6295 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×#6295 |
| commutator, cosocle | C33×C4 | C24 |
| Frattini | C4 | C22×#1113 |
| Fitting | C33×#41 | C22 |
| socle | C2×C33 | C22×D4 |
| hypercenter | #41 | #1113 |
| hypocenter | C33 | #577 |
| LCS | G ▷ C33×C4 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#64367 | C2 | semidirect |
| 2. C3×#64366 | C2 | semidirect |
| 3. C3×#64157 | C2 | semidirect |
| 4. #11723663 | C2 | semidirect |
| 5. C2×#88811 | C2 | semidirect |
| 6. #11723661 | C2 | semidirect |
| 7. #11723660 | C2 | semidirect |
| 17. C3×#3828 | C22 | semidirect |
| 19. C2×C3×#634 | C22 | semidirect |
| 20. C3×#3748 | C22 | semidirect |
| 21. C2×C3×C3⋊(C3⋊C8) | C22 | semidirect |
| 22. #88812 | C22 | semidirect |
| 23. #88811 | C22 | semidirect |
| 24. #88811 | C22 | semidirect |
| 25. #88811 | C22 | semidirect |
| 26. #88810 | C22 | semidirect |
| 27. #64367 | D3 | semidirect |
| 28. #64366 | D3 | semidirect |
| 35. #64157 | D3 | semidirect |
| 83. #3828 | C2×D3 | semidirect |
| 85. C2×#634 | C2×D3 | semidirect |
| 110. #3748 | C2×D3 | semidirect |
| 111. C2×C3⋊(C3⋊C8) | C2×D3 | semidirect |
| 357. C33 | #577 | semidirect |
| 518. C32 | #5751 | semidirect |
| 519. C32 | #5836 | semidirect |
| 520. C32 | #5837 | semidirect |
| 572. C3 | #10595446 | semidirect |
| 573. C3 | #10595447 | semidirect |
| 574. C3 | #10595448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64367 | 2 |
| C3×#64366 | 2 |
| C3×#64157 | 2 |
| #11723663 | 2 |
| C2×#88811 | 2 |
| #11723661 | 2 |
| #11723660 | 2 |
| #10595448 | 3 |
| #10595447 | 3 |
| #10595446 | 3 |