Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
985 conjugacy classes of subgroups.
The subgroup lattice has 768 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11722490 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#88652 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11721787 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #64118⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | M16×(C3⋊D3)⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11721069 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11721068 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11720854 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11720853 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #11720850 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #11720848 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #10594718 | — | 3 | 1 | no | maximal |
| 13 | #10594712 | — | 3 | 1 | no | maximal |
| 14 | #88740 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C4⋊#272 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | #3828⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C4×(C3⋊D3)⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#634⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #88676 | — | 2 | 1 | no | — |
| 20 | C2×#6200 | — | 2 | 1 | no | — |
| 21 | C2×#6199 | — | 2 | 1 | no | — |
| 22 | #88671 | — | 2 | 1 | no | — |
| 23 | #88654 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | C4×((C3⋊D3)⋊C3)⋊C2 | — | 2 | 1 | no | — |
| 25 | #88652 | — | 2 | 1 | no | — |
| 26 | #88652 | — | 2 | 1 | no | — |
| 27 | #88652 | C22 | 1 | 2 | yes | — |
| 28 | #88652 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #88652 | C22 | 1 | 2 | yes | complemented |
| 30 | #88650 | — | 2 | 1 | no | — |
| 31 | #88648 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | ((C3⋊D3)⋊C3)⋊Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | M16×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | #88529 | C22 | 1 | 2 | yes | complemented |
| 35 | #88528 | C22 | 1 | 2 | yes | complemented |
| 36 | #3748⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #3744⋊C3 | C22 | 1 | 2 | yes | complemented |
| 38 | #3743⋊C3 | C22 | 1 | 2 | yes | complemented |
| 39 | C8×(C3⋊D3)⋊C3 | C22 | 1 | 2 | yes | complemented |
| 40 | #3746⋊C3 | C22 | 1 | 2 | yes | complemented |
| 41 | #88439 | C22 | 1 | 2 | yes | complemented |
| 42 | #88437 | C22 | 1 | 2 | yes | complemented |
| 43 | #88437 | C22 | 1 | 2 | yes | complemented |
| 44 | #88436 | C22 | 1 | 2 | yes | complemented |
| 45 | #64306 | — | 3 | 1 | no | — |
| 46 | D3×#235 | — | 3 | 1 | no | — |
| 47 | C2×#3796 | — | 3 | 1 | no | — |
| 48 | C2×#3795 | — | 3 | 1 | no | — |
| 49 | #64118 | D3 | 1 | 1 | yes | characteristic, complemented |
| 50 | M16×C3⋊D3 | D3 | 1 | 1 | yes | characteristic, complemented |
| 51 | C3×#909 | — | 3 | 1 | no | — |
| 52 | C3×#908 | — | 3 | 1 | no | — |
| 53 | C3×#908 | — | 3 | 1 | no | — |
| 54 | C3×#908 | — | 6 | 1 | no | — |
| 55 | C3×D3×M16 | — | 3 | 1 | no | — |
| 56 | #63831 | — | 3 | 1 | no | — |
| 57 | #63830 | — | 3 | 1 | no | — |
| 58 | #63827 | — | 3 | 1 | no | — |
| 59 | #63823 | — | 3 | 1 | no | — |
| 60 | #63811 | — | 3 | 2 | no | — |
| 61 | #63810 | — | 3 | 2 | no | — |
| 62 | #63809 | — | 3 | 2 | no | — |
| 63 | #63807 | — | 3 | 2 | no | — |
| 64 | #63806 | — | 3 | 2 | no | — |
| 65 | #63800 | — | 3 | 2 | no | — |
| 66 | #63798 | — | 3 | 2 | no | — |
| 67 | #63795 | — | 3 | 2 | no | — |
| 68 | C22×#272 | — | 2 | 1 | no | — |
| 69 | C22×(C3⋊D3)⋊C3 | D4 | 1 | 1 | yes | characteristic |
| 70 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 2 | 1 | no | — |
| 71 | C2×C4×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 72 | #6235 | — | 2 | 1 | no | — |
| 73 | C4⋊#272 | — | 2 | 1 | no | — |
| 74 | C4⋊#272 | C23 | 1 | 2 | yes | — |
| 75 | C4⋊#272 | C23 | 1 | 1 | yes | characteristic |
| 76 | C4×#272 | — | 2 | 1 | no | — |
| 77 | #6229 | C23 | 1 | 1 | yes | characteristic |
| 78 | #638⋊C3 | — | 2 | 1 | no | — |
| 79 | C2×(C3⋊Dic3)⋊C3 | — | 2 | 1 | no | — |
| 80 | C2×(C3⋊Dic3)⋊C3 | D4 | 1 | 1 | yes | characteristic |
| 81 | C4⋊((C3⋊D3)⋊C3) | C23 | 1 | 1 | yes | characteristic |
| 82 | C4×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 83 | C4×(C3⋊D3)⋊C3 | D4 | 1 | 1 | yes | characteristic |
| 84 | C4×(C3⋊D3)⋊C3 | D4 | 1 | 1 | yes | characteristic |
| 85 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 86 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 87 | #634⋊C3 | — | 2 | 1 | no | — |
| 88 | #634⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 89 | #634⋊C3 | C23 | 1 | 2 | yes | — |
| 90 | #6200 | — | 2 | 1 | no | — |
| 91 | #6200 | — | 2 | 2 | no | — |
| 92 | #6200 | — | 2 | 2 | no | — |
| 93 | #6200 | — | 2 | 1 | no | — |
| 94 | #6199 | — | 2 | 2 | no | — |
| 95 | #6199 | — | 2 | 2 | no | — |
| 96 | #6199 | — | 2 | 1 | no | — |
| 97 | #6198 | — | 2 | 1 | no | — |
| 98 | ((C3⋊D3)⋊C3)⋊C4 | — | 2 | 1 | no | — |
| 99 | ((C3⋊D3)⋊C3)⋊C4 | — | 2 | 1 | no | — |
| 100 | #6196 | — | 2 | 1 | no | — |
| 101 | C8×H(3,𝔽3) | C23 | 1 | 2 | yes | — |
| 102 | (C3⋊(C3⋊C8))⋊C3 | C23 | 1 | 2 | yes | — |
| 103 | #5777 | — | 9 | 1 | no | — |
| 104 | #5773 | — | 9 | 1 | no | — |
| 105 | #5748 | — | 9 | 1 | no | — |
| 106 | #3828 | C2×D3 | 1 | 1 | yes | characteristic |
| 107 | C2×C4×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 108 | C2×#634 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 109 | C3×#235 | — | 3 | 1 | no | — |
| 110 | C3×#235 | — | 3 | 1 | no | — |
| 111 | C3×#235 | — | 3 | 1 | no | — |
| 112 | C3×#235 | — | 6 | 1 | no | — |
| 113 | C2×C3×D12 | — | 3 | 1 | no | — |
| 114 | C2×C3×D12 | — | 3 | 1 | no | — |
| 115 | C2×C3×D12 | — | 6 | 1 | no | — |
| 116 | C2×C3×C4×D3 | — | 3 | 1 | no | — |
| 117 | C2×C3×Dic6 | — | 3 | 1 | no | — |
| 118 | #3811 | — | 6 | 1 | no | — |
| 119 | D3×#67 | — | 6 | 1 | no | — |
| 120 | C2×#626 | — | 6 | 1 | no | — |
| 121 | C2×#625 | — | 6 | 1 | no | — |
| 122 | #3805 | — | 6 | 1 | no | — |
| 123 | #3804 | — | 6 | 1 | no | — |
| 124 | C2×D3×Dic3 | — | 6 | 1 | no | — |
| 125 | C2×D3×Dic3 | — | 6 | 1 | no | — |
| 126 | #3802 | — | 3 | 1 | no | — |
| 127 | D3×D12 | — | 3 | 1 | no | — |
| 128 | C4×D32 | — | 6 | 1 | no | — |
| 129 | C4×D32 | — | 6 | 1 | no | — |
| 130 | #3799 | — | 3 | 1 | no | — |
| 131 | #3798 | — | 6 | 1 | no | — |
| 132 | #3798 | — | 6 | 1 | no | — |
| 133 | #3797 | — | 3 | 1 | no | — |
| 134 | #3796 | — | 3 | 2 | no | — |
| 135 | #3796 | — | 3 | 2 | no | — |
| 136 | #3796 | — | 3 | 1 | no | — |
| 137 | #3796 | — | 3 | 1 | no | — |
| 138 | #3796 | — | 6 | 1 | no | — |
| 139 | #3796 | — | 6 | 1 | no | — |
| 140 | #3795 | — | 3 | 2 | no | — |
| 141 | #3795 | — | 3 | 2 | no | — |
| 142 | #3795 | — | 3 | 1 | no | — |
| 143 | #3795 | — | 6 | 1 | no | — |
| 144 | #3795 | — | 6 | 1 | no | — |
| 145 | D3×Dic6 | — | 3 | 1 | no | — |
| 146 | C32×M16 | — | 2 | 1 | no | — |
| 147 | C32×M16 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 148 | C32×M16 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 149 | #3748 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 150 | #3746 | C2×D3 | 1 | 2 | yes | complemented |
| 151 | #3744 | C2×D3 | 1 | 2 | yes | complemented |
| 152 | #3743 | C2×D3 | 1 | 2 | yes | complemented |
| 153 | C8×C3⋊D3 | C2×D3 | 1 | 2 | yes | complemented |
| 154 | C3×#208 | — | 3 | 1 | no | — |
| 155 | C3×Dic12 | — | 3 | 2 | no | — |
| 156 | C3×D24 | — | 3 | 2 | no | — |
| 157 | C3×D24 | — | 3 | 2 | no | — |
| 158 | C3×D24 | — | 6 | 2 | no | — |
| 159 | C3×#204 | — | 3 | 2 | no | — |
| 160 | C3×#204 | — | 3 | 2 | no | — |
| 161 | C3×#204 | — | 3 | 2 | no | — |
| 162 | C3×#204 | — | 6 | 2 | no | — |
| 163 | C3×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 164 | C3×D3×C8 | — | 3 | 2 | no | — |
| 165 | #3719 | — | 3 | 2 | no | — |
| 166 | #3718 | — | 3 | 2 | no | — |
| 167 | #3716 | — | 3 | 2 | no | — |
| 168 | #3716 | — | 3 | 2 | no | — |
| 169 | #3715 | — | 3 | 2 | no | — |
| 170 | #3715 | — | 3 | 2 | no | — |
| 171 | #3714 | — | 3 | 2 | no | — |
| 172 | #3713 | — | 3 | 2 | no | — |
| 173 | C22×H(3,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C2×#272 | — | 2 | 2 | no | — |
| 175 | C2×#272 | — | 2 | 1 | no | — |
| 176 | C2×#272 | — | 4 | 2 | no | — |
| 177 | C2×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 178 | C2×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 179 | C2×(C3⋊D3)⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 180 | C2×(C3⋊D3)⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | ((C3⋊D3)⋊C3)⋊C2 | — | 4 | 2 | no | — |
| 182 | C4×H(3,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 183 | C4×H(3,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 184 | #1084 | — | 2 | 1 | no | — |
| 185 | (C3⋊Dic3)⋊C3 | — | 2 | 1 | no | — |
| 186 | (C3⋊Dic3)⋊C3 | — | 2 | 2 | no | — |
| 187 | (C3⋊Dic3)⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 188 | (C3⋊Dic3)⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 189 | D3×#41 | — | 9 | 1 | no | — |
| 190 | D3×#41 | — | 9 | 1 | no | — |
| 191 | C2×#239 | — | 9 | 1 | no | — |
| 192 | C2×#237 | — | 9 | 1 | no | — |
| 193 | C2×#235 | — | 9 | 1 | no | — |
| 194 | C2×#235 | — | 9 | 1 | no | — |
| 195 | C3×#137 | — | 9 | 1 | no | — |
| 196 | C3×AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 197 | C2×C3×M16 | — | 9 | 1 | no | — |
| 198 | #951 | — | 9 | 1 | no | — |
| 199 | #949 | — | 9 | 1 | no | — |
| 200 | #942 | — | 9 | 1 | no | — |
| 201 | #932 | — | 9 | 1 | no | — |
| 202 | #919 | — | 9 | 2 | no | — |
| 203 | #918 | — | 9 | 2 | no | — |
| 204 | #916 | — | 9 | 2 | no | — |
| 205 | #916 | — | 9 | 2 | no | — |
| 206 | #915 | — | 9 | 2 | no | — |
| 207 | #914 | — | 9 | 2 | no | — |
| 208 | #912 | — | 9 | 2 | no | — |
| 209 | #911 | — | 9 | 2 | no | — |
| 210 | #909 | — | 3 | 1 | no | — |
| 211 | #909 | — | 9 | 1 | no | — |
| 212 | #909 | — | 9 | 2 | no | — |
| 213 | #909 | — | 9 | 1 | no | — |
| 214 | #908 | — | 3 | 1 | no | — |
| 215 | #908 | — | 3 | 1 | no | — |
| 216 | #908 | — | 6 | 1 | no | — |
| 217 | #908 | — | 9 | 2 | no | — |
| 218 | #908 | — | 9 | 1 | no | — |
| 219 | D3×M16 | — | 3 | 1 | no | — |
| 220 | D3×M16 | — | 9 | 1 | no | — |
| 221 | #904 | — | 9 | 2 | no | — |
| 222 | #904 | — | 9 | 2 | no | — |
| 223 | C22×C3⋊D3 | D12 | 1 | 1 | yes | characteristic |
| 224 | C22×C3×D3 | — | 3 | 1 | no | — |
| 225 | C22×C3×D3 | — | 6 | 1 | no | — |
| 226 | C22×C3×D3 | — | 6 | 1 | no | — |
| 227 | C22×C3×D3 | — | 12 | 1 | no | — |
| 228 | C2×D32 | — | 6 | 1 | no | — |
| 229 | C2×D32 | — | 6 | 1 | no | — |
| 230 | C2×C32×C4 | — | 2 | 1 | no | — |
| 231 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 232 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 233 | #638 | — | 2 | 1 | no | — |
| 234 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 235 | C2×C3⋊Dic3 | D12 | 1 | 1 | yes | characteristic |
| 236 | C4⋊(C3⋊D3) | C22×D3 | 1 | 1 | yes | characteristic |
| 237 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 238 | C4×C3⋊D3 | D12 | 1 | 1 | yes | characteristic |
| 239 | C4×C3⋊D3 | D12 | 1 | 1 | yes | characteristic |
| 240 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 241 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 242 | #634 | — | 2 | 1 | no | — |
| 243 | #634 | C22×D3 | 1 | 1 | yes | characteristic |
| 244 | #634 | C22×D3 | 1 | 2 | yes | — |
| 245 | C3×#67 | — | 6 | 1 | no | — |
| 246 | C3×#67 | — | 6 | 1 | no | — |
| 247 | C3×#67 | — | 6 | 1 | no | — |
| 248 | C3×#67 | — | 12 | 1 | no | — |
| 249 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 250 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 251 | C3×D12 | — | 3 | 1 | no | — |
| 252 | C3×D12 | — | 3 | 2 | no | — |
| 253 | C3×D12 | — | 3 | 2 | no | — |
| 254 | C3×D12 | — | 3 | 1 | no | — |
| 255 | C3×D12 | — | 3 | 1 | no | — |
| 256 | C3×D12 | — | 6 | 2 | no | — |
| 257 | C3×D12 | — | 6 | 1 | no | — |
| 258 | C3×D12 | — | 6 | 1 | no | — |
| 259 | C3×D12 | — | 6 | 1 | no | — |
| 260 | C3×D12 | — | 12 | 1 | no | — |
| 261 | C3×C4×D3 | — | 3 | 1 | no | — |
| 262 | C3×C4×D3 | — | 3 | 1 | no | — |
| 263 | C3×C4×D3 | — | 3 | 1 | no | — |
| 264 | C3×C4×D3 | — | 3 | 1 | no | — |
| 265 | C3×C4×D3 | — | 6 | 1 | no | — |
| 266 | C3×C4×D3 | — | 6 | 1 | no | — |
| 267 | C3×C4×D3 | — | 6 | 1 | no | — |
| 268 | C3×C4×D3 | — | 12 | 1 | no | — |
| 269 | C3×Dic6 | — | 3 | 1 | no | — |
| 270 | C3×Dic6 | — | 3 | 2 | no | — |
| 271 | C3×Dic6 | — | 3 | 1 | no | — |
| 272 | C3×Dic6 | — | 3 | 1 | no | — |
| 273 | C3×Dic6 | — | 6 | 1 | no | — |
| 274 | C3×Dic6 | — | 6 | 1 | no | — |
| 275 | #627 | — | 6 | 1 | no | — |
| 276 | #627 | — | 6 | 1 | no | — |
| 277 | #626 | — | 6 | 1 | no | — |
| 278 | #626 | — | 6 | 1 | no | — |
| 279 | #626 | — | 6 | 1 | no | — |
| 280 | #626 | — | 6 | 2 | no | — |
| 281 | #626 | — | 6 | 2 | no | — |
| 282 | #626 | — | 6 | 1 | no | — |
| 283 | #625 | — | 6 | 2 | no | — |
| 284 | #625 | — | 6 | 2 | no | — |
| 285 | #625 | — | 6 | 1 | no | — |
| 286 | #625 | — | 6 | 1 | no | — |
| 287 | #624 | — | 6 | 1 | no | — |
| 288 | #624 | — | 6 | 1 | no | — |
| 289 | D3×Dic3 | — | 6 | 2 | no | — |
| 290 | D3×Dic3 | — | 6 | 2 | no | — |
| 291 | D3×Dic3 | — | 6 | 1 | no | — |
| 292 | D3×Dic3 | — | 6 | 1 | no | — |
| 293 | D3×Dic3 | — | 6 | 1 | no | — |
| 294 | D3×Dic3 | — | 6 | 2 | no | — |
| 295 | D3×Dic3 | — | 6 | 2 | no | — |
| 296 | D3×Dic3 | — | 6 | 1 | no | — |
| 297 | C32×C8 | — | 2 | 2 | no | — |
| 298 | C32×C8 | C22×D3 | 1 | 2 | yes | — |
| 299 | C32×C8 | C22×D3 | 1 | 2 | yes | — |
| 300 | C3⋊(C3⋊C8) | C22×D3 | 1 | 2 | yes | — |
| 301 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 302 | #575 | — | 27 | 1 | no | Sylow |
| 303 | C2×H(3,𝔽3) | — | 2 | 1 | no | — |
| 304 | C2×H(3,𝔽3) | C22×D4 | 1 | 1 | yes | characteristic |
| 305 | #272 | — | 4 | 1 | no | — |
| 306 | #272 | — | 4 | 2 | no | — |
| 307 | (C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 308 | (C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 309 | (C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 310 | C3×#41 | — | 9 | 1 | no | — |
| 311 | C3×#41 | — | 9 | 1 | no | — |
| 312 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 313 | C2×C3×D4 | — | 9 | 1 | no | — |
| 314 | C22×C3×C4 | — | 9 | 1 | no | — |
| 315 | C2×#67 | — | 18 | 1 | no | — |
| 316 | C2×#67 | — | 18 | 1 | no | — |
| 317 | C2×#67 | — | 18 | 1 | no | — |
| 318 | C22×Dic3 | — | 18 | 1 | no | — |
| 319 | #239 | — | 9 | 1 | no | — |
| 320 | #239 | — | 9 | 2 | no | — |
| 321 | #239 | — | 9 | 2 | no | — |
| 322 | #239 | — | 9 | 1 | no | — |
| 323 | #239 | — | 18 | 1 | no | — |
| 324 | #239 | — | 18 | 1 | no | — |
| 325 | D3×Q8 | — | 9 | 1 | no | — |
| 326 | D3×Q8 | — | 9 | 1 | no | — |
| 327 | #237 | — | 9 | 2 | no | — |
| 328 | #237 | — | 9 | 1 | no | — |
| 329 | #237 | — | 9 | 2 | no | — |
| 330 | #237 | — | 9 | 1 | no | — |
| 331 | #237 | — | 18 | 1 | no | — |
| 332 | #237 | — | 18 | 1 | no | — |
| 333 | #237 | — | 18 | 1 | no | — |
| 334 | #237 | — | 18 | 1 | no | — |
| 335 | D3×D4 | — | 9 | 1 | no | — |
| 336 | D3×D4 | — | 9 | 1 | no | — |
| 337 | D3×D4 | — | 18 | 1 | no | — |
| 338 | D3×D4 | — | 18 | 1 | no | — |
| 339 | #235 | — | 3 | 1 | no | — |
| 340 | #235 | — | 3 | 1 | no | — |
| 341 | #235 | — | 3 | 1 | no | — |
| 342 | #235 | — | 6 | 1 | no | — |
| 343 | #235 | — | 9 | 1 | no | — |
| 344 | #235 | — | 9 | 1 | no | — |
| 345 | #235 | — | 9 | 2 | no | — |
| 346 | #235 | — | 9 | 1 | no | — |
| 347 | #235 | — | 9 | 2 | no | — |
| 348 | #235 | — | 18 | 1 | no | — |
| 349 | #235 | — | 18 | 1 | no | — |
| 350 | #235 | — | 18 | 1 | no | — |
| 351 | #235 | — | 18 | 1 | no | — |
| 352 | #235 | — | 18 | 1 | no | — |
| 353 | #235 | — | 18 | 1 | no | — |
| 354 | C2×D12 | — | 3 | 1 | no | — |
| 355 | C2×D12 | — | 3 | 1 | no | — |
| 356 | C2×D12 | — | 6 | 1 | no | — |
| 357 | C2×D12 | — | 9 | 1 | no | — |
| 358 | C2×D12 | — | 18 | 1 | no | — |
| 359 | C2×C4×D3 | — | 3 | 1 | no | — |
| 360 | C2×C4×D3 | — | 9 | 1 | no | — |
| 361 | C2×C4×D3 | — | 18 | 1 | no | — |
| 362 | C2×C4×D3 | — | 18 | 1 | no | — |
| 363 | C2×C4×D3 | — | 18 | 1 | no | — |
| 364 | C2×C4×D3 | — | 18 | 1 | no | — |
| 365 | C2×C4×D3 | — | 18 | 1 | no | — |
| 366 | C2×Dic6 | — | 3 | 1 | no | — |
| 367 | C2×Dic6 | — | 9 | 1 | no | — |
| 368 | C2×Dic6 | — | 9 | 1 | no | — |
| 369 | C3×Q16 | — | 9 | 2 | no | — |
| 370 | C3×SD16 | — | 9 | 2 | no | — |
| 371 | C3×SD16 | — | 9 | 2 | no | — |
| 372 | C3×D8 | — | 9 | 2 | no | — |
| 373 | C3×M16 | — | 3 | 1 | no | — |
| 374 | C3×M16 | — | 3 | 1 | no | — |
| 375 | C3×M16 | — | 6 | 1 | no | — |
| 376 | C3×M16 | — | 9 | 2 | no | — |
| 377 | C3×M16 | — | 9 | 1 | no | — |
| 378 | C3×M16 | D32 | 1 | 1 | yes | characteristic |
| 379 | C2×C3×C8 | — | 9 | 2 | no | — |
| 380 | #216 | — | 9 | 2 | no | — |
| 381 | #216 | — | 9 | 2 | no | — |
| 382 | #215 | — | 9 | 2 | no | — |
| 383 | #215 | — | 9 | 2 | no | — |
| 384 | #214 | — | 9 | 2 | no | — |
| 385 | #214 | — | 9 | 2 | no | — |
| 386 | #213 | — | 9 | 2 | no | — |
| 387 | #213 | — | 9 | 2 | no | — |
| 388 | #208 | — | 3 | 1 | no | — |
| 389 | #208 | — | 9 | 1 | no | — |
| 390 | Dic12 | — | 3 | 2 | no | — |
| 391 | Dic12 | — | 9 | 2 | no | — |
| 392 | Dic12 | — | 9 | 2 | no | — |
| 393 | D24 | — | 3 | 2 | no | — |
| 394 | D24 | — | 3 | 2 | no | — |
| 395 | D24 | — | 6 | 2 | no | — |
| 396 | D24 | — | 9 | 2 | no | — |
| 397 | #204 | — | 3 | 2 | no | — |
| 398 | #204 | — | 3 | 2 | no | — |
| 399 | #204 | — | 3 | 2 | no | — |
| 400 | #204 | — | 6 | 2 | no | — |
| 401 | #204 | — | 9 | 2 | no | — |
| 402 | #204 | — | 9 | 2 | no | — |
| 403 | #204 | — | 9 | 2 | no | — |
| 404 | ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 405 | ΓL(1,𝔽25) | — | 9 | 2 | no | — |
| 406 | D3×C8 | — | 3 | 2 | no | — |
| 407 | D3×C8 | — | 9 | 2 | no | — |
| 408 | C22×C32 | — | 2 | 1 | no | — |
| 409 | C22×C32 | C2×D12 | 1 | 1 | yes | characteristic |
| 410 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic |
| 411 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 412 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 413 | C2×C3⋊D3 | C2×D12 | 1 | 1 | yes | characteristic |
| 414 | C2×C3⋊D3 | C2×D12 | 1 | 1 | yes | characteristic |
| 415 | C2×C3×D3 | — | 3 | 1 | no | — |
| 416 | C2×C3×D3 | — | 3 | 1 | no | — |
| 417 | C2×C3×D3 | — | 6 | 1 | no | — |
| 418 | C2×C3×D3 | — | 6 | 2 | no | — |
| 419 | C2×C3×D3 | — | 6 | 1 | no | — |
| 420 | C2×C3×D3 | — | 6 | 2 | no | — |
| 421 | C2×C3×D3 | — | 6 | 1 | no | — |
| 422 | C2×C3×D3 | — | 12 | 1 | no | — |
| 423 | C2×C3×D3 | — | 12 | 2 | no | — |
| 424 | C2×C3×D3 | — | 12 | 1 | no | — |
| 425 | C2×C3×D3 | — | 12 | 2 | no | — |
| 426 | C2×C3×D3 | — | 12 | 2 | no | — |
| 427 | C2×C3×D3 | — | 24 | 2 | no | — |
| 428 | D32 | — | 12 | 2 | no | — |
| 429 | D32 | — | 12 | 2 | no | — |
| 430 | C32×C4 | — | 2 | 1 | no | — |
| 431 | C32×C4 | — | 2 | 1 | no | — |
| 432 | C32×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 433 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 434 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 435 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 436 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 437 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 438 | C3⋊Dic3 | C2×D12 | 1 | 1 | yes | characteristic |
| 439 | C3⋊Dic3 | C2×D12 | 1 | 1 | yes | characteristic |
| 440 | C3×Dic3 | — | 3 | 1 | no | — |
| 441 | C3×Dic3 | — | 3 | 1 | no | — |
| 442 | C3×Dic3 | — | 6 | 2 | no | — |
| 443 | C3×Dic3 | — | 6 | 1 | no | — |
| 444 | C3×Dic3 | — | 6 | 1 | no | — |
| 445 | C3×Dic3 | — | 6 | 1 | no | — |
| 446 | C3×Dic3 | — | 12 | 1 | no | — |
| 447 | C2×#41 | — | 27 | 1 | no | — |
| 448 | C2×#41 | — | 27 | 1 | no | — |
| 449 | #137 | — | 9 | 1 | no | — |
| 450 | #137 | — | 27 | 2 | no | — |
| 451 | #137 | — | 27 | 1 | no | — |
| 452 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 453 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 454 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 455 | #135 | — | 27 | 2 | no | — |
| 456 | #135 | — | 27 | 2 | no | — |
| 457 | C2×M16 | — | 9 | 1 | no | — |
| 458 | H(3,𝔽3) | #575 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 459 | C23×C3 | — | 9 | 1 | no | — |
| 460 | C23×C3 | — | 18 | 1 | no | — |
| 461 | C22×D3 | — | 3 | 1 | no | — |
| 462 | C22×D3 | — | 6 | 1 | no | — |
| 463 | C22×D3 | — | 6 | 1 | no | — |
| 464 | C22×D3 | — | 9 | 1 | no | — |
| 465 | C22×D3 | — | 12 | 1 | no | — |
| 466 | C22×D3 | — | 18 | 1 | no | — |
| 467 | C22×D3 | — | 18 | 1 | no | — |
| 468 | C22×D3 | — | 18 | 1 | no | — |
| 469 | C3×Q8 | — | 9 | 1 | no | — |
| 470 | C3×Q8 | — | 9 | 2 | no | — |
| 471 | C3×Q8 | — | 9 | 1 | no | — |
| 472 | C3×Q8 | — | 18 | 1 | no | — |
| 473 | C3×D4 | — | 9 | 1 | no | — |
| 474 | C3×D4 | — | 9 | 2 | no | — |
| 475 | C3×D4 | — | 9 | 1 | no | — |
| 476 | C3×D4 | — | 18 | 1 | no | — |
| 477 | C3×D4 | — | 18 | 1 | no | — |
| 478 | C3×D4 | — | 18 | 1 | no | — |
| 479 | C2×C3×C4 | — | 3 | 1 | no | — |
| 480 | C2×C3×C4 | — | 3 | 1 | no | — |
| 481 | C2×C3×C4 | — | 6 | 1 | no | — |
| 482 | C2×C3×C4 | — | 9 | 1 | no | — |
| 483 | C2×C3×C4 | — | 9 | 1 | no | — |
| 484 | C2×C3×C4 | — | 9 | 1 | no | — |
| 485 | C2×C3×C4 | — | 9 | 1 | no | — |
| 486 | C2×C3×C4 | — | 9 | 1 | no | — |
| 487 | C2×C3×C4 | — | 18 | 1 | no | — |
| 488 | C2×C3×C4 | — | 18 | 1 | no | — |
| 489 | C2×C3×C4 | — | 18 | 1 | no | — |
| 490 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 491 | #67 | — | 6 | 1 | no | — |
| 492 | #67 | — | 6 | 1 | no | — |
| 493 | #67 | — | 6 | 1 | no | — |
| 494 | #67 | — | 12 | 1 | no | — |
| 495 | #67 | — | 18 | 1 | no | — |
| 496 | #67 | — | 18 | 1 | no | — |
| 497 | #67 | — | 18 | 1 | no | — |
| 498 | #67 | — | 18 | 2 | no | — |
| 499 | #67 | — | 18 | 2 | no | — |
| 500 | #67 | — | 18 | 1 | no | — |
| 501 | #67 | — | 18 | 1 | no | — |
| 502 | #67 | — | 18 | 1 | no | — |
| 503 | #67 | — | 18 | 1 | no | — |
| 504 | #67 | — | 18 | 2 | no | — |
| 505 | #67 | — | 18 | 2 | no | — |
| 506 | C2×Dic3 | — | 3 | 1 | no | — |
| 507 | C2×Dic3 | — | 6 | 1 | no | — |
| 508 | C2×Dic3 | — | 9 | 1 | no | — |
| 509 | C2×Dic3 | — | 18 | 1 | no | — |
| 510 | C2×Dic3 | — | 18 | 1 | no | — |
| 511 | C2×Dic3 | — | 18 | 2 | no | — |
| 512 | C2×Dic3 | — | 18 | 2 | no | — |
| 513 | C2×Dic3 | — | 18 | 1 | no | — |
| 514 | C2×Dic3 | — | 18 | 1 | no | — |
| 515 | D12 | — | 3 | 2 | no | — |
| 516 | D12 | — | 3 | 2 | no | — |
| 517 | D12 | — | 3 | 1 | no | — |
| 518 | D12 | — | 3 | 1 | no | — |
| 519 | D12 | — | 3 | 1 | no | — |
| 520 | D12 | — | 6 | 2 | no | — |
| 521 | D12 | — | 6 | 1 | no | — |
| 522 | D12 | — | 6 | 1 | no | — |
| 523 | D12 | — | 6 | 1 | no | — |
| 524 | D12 | — | 9 | 1 | no | — |
| 525 | D12 | — | 12 | 1 | no | — |
| 526 | D12 | — | 18 | 1 | no | — |
| 527 | D12 | — | 18 | 1 | no | — |
| 528 | D12 | — | 18 | 2 | no | — |
| 529 | D12 | — | 18 | 2 | no | — |
| 530 | D12 | — | 18 | 1 | no | — |
| 531 | C4×D3 | — | 3 | 1 | no | — |
| 532 | C4×D3 | — | 3 | 1 | no | — |
| 533 | C4×D3 | — | 3 | 1 | no | — |
| 534 | C4×D3 | — | 3 | 1 | no | — |
| 535 | C4×D3 | — | 6 | 1 | no | — |
| 536 | C4×D3 | — | 6 | 1 | no | — |
| 537 | C4×D3 | — | 6 | 1 | no | — |
| 538 | C4×D3 | — | 9 | 1 | no | — |
| 539 | C4×D3 | — | 9 | 1 | no | — |
| 540 | C4×D3 | — | 9 | 1 | no | — |
| 541 | C4×D3 | — | 9 | 1 | no | — |
| 542 | C4×D3 | — | 12 | 1 | no | — |
| 543 | C4×D3 | — | 18 | 1 | no | — |
| 544 | C4×D3 | — | 18 | 1 | no | — |
| 545 | C4×D3 | — | 18 | 1 | no | — |
| 546 | C4×D3 | — | 18 | 1 | no | — |
| 547 | C4×D3 | — | 18 | 1 | no | — |
| 548 | C4×D3 | — | 18 | 1 | no | — |
| 549 | C4×D3 | — | 18 | 2 | no | — |
| 550 | C4×D3 | — | 18 | 2 | no | — |
| 551 | C4×D3 | — | 18 | 2 | no | — |
| 552 | C4×D3 | — | 18 | 1 | no | — |
| 553 | C4×D3 | — | 18 | 2 | no | — |
| 554 | Dic6 | — | 3 | 1 | no | — |
| 555 | Dic6 | — | 3 | 1 | no | — |
| 556 | Dic6 | — | 3 | 2 | no | — |
| 557 | Dic6 | — | 3 | 1 | no | — |
| 558 | Dic6 | — | 6 | 1 | no | — |
| 559 | Dic6 | — | 6 | 1 | no | — |
| 560 | Dic6 | — | 9 | 2 | no | — |
| 561 | Dic6 | — | 9 | 1 | no | — |
| 562 | Dic6 | — | 18 | 1 | no | — |
| 563 | Dic6 | — | 18 | 1 | no | — |
| 564 | Dic6 | — | 18 | 1 | no | — |
| 565 | Dic6 | — | 18 | 1 | no | — |
| 566 | C3×C8 | — | 3 | 2 | no | — |
| 567 | C3×C8 | — | 3 | 2 | no | — |
| 568 | C3×C8 | — | 6 | 2 | no | — |
| 569 | C3×C8 | — | 9 | 2 | no | — |
| 570 | C3×C8 | C2×D32 | 1 | 2 | yes | — |
| 571 | C3⋊C8 | — | 3 | 2 | no | — |
| 572 | C3⋊C8 | — | 9 | 2 | no | — |
| 573 | C2×C32 | — | 2 | 1 | no | — |
| 574 | C2×C32 | — | 2 | 1 | no | — |
| 575 | C2×C32 | — | 2 | 1 | no | — |
| 576 | C2×C32 | — | 4 | 1 | no | — |
| 577 | C2×C32 | C22×D12 | 1 | 1 | yes | characteristic |
| 578 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 579 | C3⋊D3 | — | 2 | 1 | no | — |
| 580 | C3⋊D3 | — | 2 | 1 | no | — |
| 581 | C3⋊D3 | — | 4 | 1 | no | — |
| 582 | C3×D3 | — | 6 | 1 | no | — |
| 583 | C3×D3 | — | 6 | 1 | no | — |
| 584 | C3×D3 | — | 12 | 1 | no | — |
| 585 | C3×D3 | — | 12 | 1 | no | — |
| 586 | C3×D3 | — | 12 | 2 | no | — |
| 587 | C3×D3 | — | 12 | 1 | no | — |
| 588 | C3×D3 | — | 12 | 2 | no | — |
| 589 | C3×D3 | — | 24 | 1 | no | — |
| 590 | C3×D3 | — | 24 | 2 | no | — |
| 591 | #41 | — | 9 | 1 | no | — |
| 592 | #41 | — | 9 | 1 | no | — |
| 593 | #41 | — | 27 | 1 | no | — |
| 594 | #41 | — | 27 | 2 | no | — |
| 595 | #41 | — | 27 | 1 | no | — |
| 596 | #41 | — | 27 | 2 | no | — |
| 597 | #41 | — | 54 | 1 | no | — |
| 598 | #41 | — | 54 | 1 | no | — |
| 599 | #41 | — | 54 | 1 | no | — |
| 600 | #41 | — | 54 | 1 | no | — |
| 601 | C2×Q8 | — | 9 | 1 | no | — |
| 602 | C2×Q8 | — | 27 | 1 | no | — |
| 603 | C2×D4 | — | 9 | 1 | no | — |
| 604 | C2×D4 | — | 27 | 1 | no | — |
| 605 | C2×D4 | — | 54 | 1 | no | — |
| 606 | C2×D4 | — | 54 | 1 | no | — |
| 607 | C22×C4 | — | 9 | 1 | no | — |
| 608 | C22×C4 | — | 54 | 1 | no | — |
| 609 | C22×C4 | — | 54 | 1 | no | — |
| 610 | Q16 | — | 9 | 2 | no | — |
| 611 | Q16 | — | 27 | 2 | no | — |
| 612 | SD16 | — | 9 | 2 | no | — |
| 613 | SD16 | — | 9 | 2 | no | — |
| 614 | SD16 | — | 27 | 2 | no | — |
| 615 | SD16 | — | 27 | 2 | no | — |
| 616 | D8 | — | 9 | 2 | no | — |
| 617 | D8 | — | 27 | 2 | no | — |
| 618 | M16 | — | 9 | 1 | no | — |
| 619 | M16 | — | 9 | 2 | no | — |
| 620 | M16 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 621 | C2×C8 | — | 9 | 2 | no | — |
| 622 | C22×C3 | — | 3 | 1 | no | — |
| 623 | C22×C3 | — | 3 | 1 | no | — |
| 624 | C22×C3 | — | 6 | 1 | no | — |
| 625 | C22×C3 | — | 9 | 1 | no | — |
| 626 | C22×C3 | — | 9 | 1 | no | — |
| 627 | C22×C3 | — | 18 | 1 | no | — |
| 628 | C22×C3 | — | 18 | 2 | no | — |
| 629 | C22×C3 | — | 18 | 1 | no | — |
| 630 | C22×C3 | — | 36 | 2 | no | — |
| 631 | C22×C3 | — | 36 | 1 | no | — |
| 632 | C22×C3 | D3×D12 | 1 | 1 | yes | characteristic |
| 633 | C2×D3 | — | 3 | 1 | no | — |
| 634 | C2×D3 | — | 3 | 1 | no | — |
| 635 | C2×D3 | — | 6 | 1 | no | — |
| 636 | C2×D3 | — | 6 | 1 | no | — |
| 637 | C2×D3 | — | 6 | 2 | no | — |
| 638 | C2×D3 | — | 6 | 2 | no | — |
| 639 | C2×D3 | — | 6 | 1 | no | — |
| 640 | C2×D3 | — | 9 | 1 | no | — |
| 641 | C2×D3 | — | 9 | 1 | no | — |
| 642 | C2×D3 | — | 12 | 1 | no | — |
| 643 | C2×D3 | — | 12 | 2 | no | — |
| 644 | C2×D3 | — | 12 | 1 | no | — |
| 645 | C2×D3 | — | 12 | 2 | no | — |
| 646 | C2×D3 | — | 12 | 2 | no | — |
| 647 | C2×D3 | — | 18 | 1 | no | — |
| 648 | C2×D3 | — | 24 | 2 | no | — |
| 649 | C2×D3 | — | 36 | 1 | no | — |
| 650 | C2×D3 | — | 36 | 2 | no | — |
| 651 | C2×D3 | — | 36 | 2 | no | — |
| 652 | C2×D3 | — | 36 | 2 | no | — |
| 653 | C3×C4 | — | 3 | 1 | no | — |
| 654 | C3×C4 | — | 3 | 1 | no | — |
| 655 | C3×C4 | — | 3 | 1 | no | — |
| 656 | C3×C4 | — | 3 | 1 | no | — |
| 657 | C3×C4 | — | 6 | 1 | no | — |
| 658 | C3×C4 | — | 6 | 1 | no | — |
| 659 | C3×C4 | — | 9 | 1 | no | — |
| 660 | C3×C4 | — | 9 | 1 | no | — |
| 661 | C3×C4 | — | 18 | 1 | no | — |
| 662 | C3×C4 | — | 18 | 2 | no | — |
| 663 | C3×C4 | — | 18 | 1 | no | — |
| 664 | C3×C4 | D3×D12 | 1 | 1 | yes | characteristic |
| 665 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 666 | Dic3 | — | 3 | 1 | no | — |
| 667 | Dic3 | — | 3 | 1 | no | — |
| 668 | Dic3 | — | 6 | 1 | no | — |
| 669 | Dic3 | — | 6 | 1 | no | — |
| 670 | Dic3 | — | 6 | 2 | no | — |
| 671 | Dic3 | — | 6 | 1 | no | — |
| 672 | Dic3 | — | 9 | 1 | no | — |
| 673 | Dic3 | — | 9 | 1 | no | — |
| 674 | Dic3 | — | 12 | 1 | no | — |
| 675 | Dic3 | — | 18 | 1 | no | — |
| 676 | Dic3 | — | 18 | 2 | no | — |
| 677 | C32 | — | 2 | 1 | no | — |
| 678 | C32 | #5748 | 1 | 1 | yes | characteristic, complemented |
| 679 | C32 | #5777 | 1 | 1 | yes | characteristic, complemented |
| 680 | C23 | — | 9 | 1 | no | — |
| 681 | C23 | — | 18 | 1 | no | — |
| 682 | C23 | — | 54 | 1 | no | — |
| 683 | Q8 | — | 9 | 1 | no | — |
| 684 | Q8 | — | 9 | 2 | no | — |
| 685 | Q8 | — | 9 | 1 | no | — |
| 686 | Q8 | — | 18 | 1 | no | — |
| 687 | Q8 | — | 54 | 1 | no | — |
| 688 | D4 | — | 9 | 1 | no | — |
| 689 | D4 | — | 9 | 2 | no | — |
| 690 | D4 | — | 9 | 1 | no | — |
| 691 | D4 | — | 18 | 1 | no | — |
| 692 | D4 | — | 18 | 1 | no | — |
| 693 | D4 | — | 18 | 1 | no | — |
| 694 | D4 | — | 54 | 1 | no | — |
| 695 | D4 | — | 54 | 1 | no | — |
| 696 | D4 | — | 54 | 1 | no | — |
| 697 | D4 | — | 54 | 2 | no | — |
| 698 | D4 | — | 54 | 2 | no | — |
| 699 | C2×C4 | — | 9 | 1 | no | — |
| 700 | C2×C4 | — | 9 | 1 | no | — |
| 701 | C2×C4 | — | 9 | 1 | no | — |
| 702 | C2×C4 | — | 9 | 1 | no | — |
| 703 | C2×C4 | — | 9 | 1 | no | — |
| 704 | C2×C4 | — | 18 | 1 | no | — |
| 705 | C2×C4 | — | 18 | 1 | no | — |
| 706 | C2×C4 | — | 18 | 1 | no | — |
| 707 | C2×C4 | — | 54 | 1 | no | — |
| 708 | C2×C4 | — | 54 | 1 | no | — |
| 709 | C2×C4 | — | 54 | 2 | no | — |
| 710 | C2×C4 | — | 54 | 2 | no | — |
| 711 | C2×C4 | — | 54 | 1 | no | — |
| 712 | C2×C4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 713 | C8 | — | 9 | 2 | no | — |
| 714 | C8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 2 | yes | — |
| 715 | C2×C3 | — | 2 | 1 | no | — |
| 716 | C2×C3 | — | 3 | 1 | no | — |
| 717 | C2×C3 | — | 3 | 1 | no | — |
| 718 | C2×C3 | — | 6 | 1 | no | — |
| 719 | C2×C3 | — | 6 | 1 | no | — |
| 720 | C2×C3 | — | 6 | 1 | no | — |
| 721 | C2×C3 | — | 12 | 1 | no | — |
| 722 | C2×C3 | — | 18 | 1 | no | — |
| 723 | C2×C3 | — | 18 | 1 | no | — |
| 724 | C2×C3 | — | 36 | 1 | no | — |
| 725 | C2×C3 | — | 36 | 1 | no | — |
| 726 | C2×C3 | — | 36 | 2 | no | — |
| 727 | C2×C3 | C2×D3×D12 | 1 | 1 | yes | characteristic |
| 728 | D3 | — | 6 | 1 | no | — |
| 729 | D3 | — | 6 | 1 | no | — |
| 730 | D3 | — | 12 | 2 | no | — |
| 731 | D3 | — | 12 | 2 | no | — |
| 732 | D3 | — | 12 | 1 | no | — |
| 733 | D3 | — | 12 | 1 | no | — |
| 734 | D3 | — | 12 | 1 | no | — |
| 735 | D3 | — | 18 | 1 | no | — |
| 736 | D3 | — | 18 | 1 | no | — |
| 737 | D3 | — | 24 | 2 | no | — |
| 738 | D3 | — | 24 | 1 | no | — |
| 739 | D3 | — | 36 | 1 | no | — |
| 740 | C22 | — | 9 | 1 | no | — |
| 741 | C22 | — | 9 | 1 | no | — |
| 742 | C22 | — | 18 | 1 | no | — |
| 743 | C22 | — | 18 | 1 | no | — |
| 744 | C22 | — | 18 | 2 | no | — |
| 745 | C22 | — | 36 | 1 | no | — |
| 746 | C22 | — | 36 | 2 | no | — |
| 747 | C22 | — | 108 | 2 | no | — |
| 748 | C22 | #88654 | 1 | 1 | yes | characteristic |
| 749 | C4 | — | 9 | 1 | no | — |
| 750 | C4 | — | 9 | 1 | no | — |
| 751 | C4 | — | 18 | 1 | no | — |
| 752 | C4 | — | 18 | 1 | no | — |
| 753 | C4 | — | 18 | 2 | no | — |
| 754 | C4 | #88654 | 1 | 1 | yes | characteristic |
| 755 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 756 | C3 | — | 3 | 1 | no | — |
| 757 | C3 | — | 3 | 1 | no | — |
| 758 | C3 | — | 6 | 1 | no | — |
| 759 | C3 | #10594711 | 1 | 1 | yes | characteristic |
| 760 | C2 | — | 2 | 1 | no | — |
| 761 | C2 | — | 18 | 1 | no | — |
| 762 | C2 | — | 18 | 1 | no | — |
| 763 | C2 | — | 36 | 2 | no | — |
| 764 | C2 | — | 36 | 1 | no | — |
| 765 | C2 | — | 36 | 1 | no | — |
| 766 | C2 | C2×#88654 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11722490 | C2 | semidirect |
| 2. C2×#88652 | C2 | semidirect |
| 3. #11721787 | C2 | semidirect |
| 4. #64118⋊C3 | C2 | semidirect |
| 5. M16×(C3⋊D3)⋊C3 | C2 | semidirect |
| 6. #11721069 | C2 | semidirect |
| 7. #11721068 | C2 | semidirect |
| 8. #11720854 | C2 | semidirect |
| 9. #11720853 | C2 | semidirect |
| 10. #11720850 | C2 | semidirect |
| 11. #11720848 | C2 | semidirect |
| 15. C2×C4⋊#272 | C22 | semidirect |
| 18. C2×#634⋊C3 | C22 | semidirect |
| 23. #88654 | C22 | semidirect |
| 28. #88652 | C22 | semidirect |
| 29. #88652 | C22 | semidirect |
| 31. #88648 | C22 | semidirect |
| 32. ((C3⋊D3)⋊C3)⋊Q8 | C22 | semidirect |
| 33. M16×H(3,𝔽3) | C22 | semidirect |
| 34. #88529 | C22 | semidirect |
| 35. #88528 | C22 | semidirect |
| 36. #3748⋊C3 | C22 | semidirect |
| 37. #3744⋊C3 | C22 | semidirect |
| 38. #3743⋊C3 | C22 | semidirect |
| 39. C8×(C3⋊D3)⋊C3 | C22 | semidirect |
| 40. #3746⋊C3 | C22 | semidirect |
| 41. #88439 | C22 | semidirect |
| 42. #88437 | C22 | semidirect |
| 43. #88437 | C22 | semidirect |
| 44. #88436 | C22 | semidirect |
| 49. #64118 | D3 | semidirect |
| 50. M16×C3⋊D3 | D3 | semidirect |
| 108. C2×#634 | C2×D3 | semidirect |
| 147. C32×M16 | C2×D3 | semidirect |
| 148. C32×M16 | C2×D3 | semidirect |
| 149. #3748 | C2×D3 | semidirect |
| 150. #3746 | C2×D3 | semidirect |
| 151. #3744 | C2×D3 | semidirect |
| 152. #3743 | C2×D3 | semidirect |
| 153. C8×C3⋊D3 | C2×D3 | semidirect |
| 458. H(3,𝔽3) | #575 | semidirect |
| 620. M16 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 678. C32 | #5748 | semidirect |
| 679. C32 | #5777 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722490 | 2 |
| C2×#88652 | 2 |
| #11721787 | 2 |
| #64118⋊C3 | 2 |
| M16×(C3⋊D3)⋊C3 | 2 |
| #11721069 | 2 |
| #11721068 | 2 |
| #11720854 | 2 |
| #11720853 | 2 |
| #11720850 | 2 |
| #11720848 | 2 |
| #10594718 | 3 |
| #10594712 | 3 |