Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
963 conjugacy classes of subgroups.
The subgroup lattice has 750 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11722490 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×((C3⋊D3)⋊C3)⋊Q8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11721788 | 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 | #11721074 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11721069 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11720853 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11720852 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #11720851 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #11720846 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #10594717 | — | 3 | 1 | no | maximal |
| 13 | D3×#909 | — | 3 | 1 | no | maximal |
| 14 | #88740 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#6229 | 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 | #88671 | — | 2 | 1 | no | — |
| 21 | C2×((C3⋊D3)⋊C3)⋊C4 | — | 2 | 1 | no | — |
| 22 | C2×#6196 | — | 2 | 1 | no | — |
| 23 | #88654 | C22 | 1 | 1 | yes | characteristic |
| 24 | C4×((C3⋊D3)⋊C3)⋊C2 | — | 2 | 1 | no | — |
| 25 | #88652 | C22 | 1 | 1 | yes | characteristic |
| 26 | #88650 | — | 2 | 1 | no | — |
| 27 | #88648 | C22 | 1 | 1 | yes | characteristic |
| 28 | ((C3⋊D3)⋊C3)⋊Q8 | — | 2 | 1 | no | — |
| 29 | ((C3⋊D3)⋊C3)⋊Q8 | — | 2 | 1 | no | — |
| 30 | ((C3⋊D3)⋊C3)⋊Q8 | C22 | 1 | 2 | yes | — |
| 31 | ((C3⋊D3)⋊C3)⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 32 | ((C3⋊D3)⋊C3)⋊Q8 | C22 | 1 | 2 | yes | complemented |
| 33 | M16×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | #88530 | 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 | — |
| 40 | #3746⋊C3 | C22 | 1 | 2 | yes | complemented |
| 41 | #88439 | C22 | 1 | 2 | yes | complemented |
| 42 | #88439 | C22 | 1 | 2 | yes | complemented |
| 43 | #88438 | C22 | 1 | 2 | yes | complemented |
| 44 | #88437 | C22 | 1 | 2 | yes | complemented |
| 45 | #64306 | — | 3 | 1 | no | — |
| 46 | D3×#235 | — | 3 | 1 | no | — |
| 47 | C2×#3797 | — | 3 | 1 | no | — |
| 48 | C2×D3×Dic6 | — | 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×#909 | — | 3 | 1 | no | — |
| 53 | C3×#909 | — | 3 | 1 | no | — |
| 54 | C3×#909 | — | 6 | 1 | no | — |
| 55 | C3×D3×M16 | — | 3 | 1 | no | — |
| 56 | #63833 | — | 3 | 1 | no | — |
| 57 | #63831 | — | 3 | 1 | no | — |
| 58 | #63827 | — | 3 | 1 | no | — |
| 59 | #63827 | — | 3 | 1 | no | — |
| 60 | #63811 | — | 3 | 2 | no | — |
| 61 | #63811 | — | 3 | 2 | no | — |
| 62 | #63802 | — | 3 | 2 | no | — |
| 63 | #63801 | — | 3 | 2 | no | — |
| 64 | #63800 | — | 3 | 2 | no | — |
| 65 | D3×Dic12 | — | 3 | 2 | no | — |
| 66 | #63796 | — | 3 | 2 | no | — |
| 67 | D3×#204 | — | 3 | 2 | no | — |
| 68 | C22×(C3⋊D3)⋊C3 | D4 | 1 | 1 | yes | characteristic |
| 69 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 2 | 1 | no | — |
| 70 | C2×C4×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 71 | #6235 | — | 2 | 1 | no | — |
| 72 | C2×#1084 | — | 2 | 1 | no | — |
| 73 | C4⋊#272 | C23 | 1 | 1 | yes | characteristic |
| 74 | C4×#272 | — | 2 | 1 | no | — |
| 75 | #6229 | — | 2 | 1 | no | — |
| 76 | #6229 | C23 | 1 | 2 | yes | — |
| 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 | 2 | yes | — |
| 89 | #634⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 90 | #6200 | — | 2 | 1 | no | — |
| 91 | #6200 | — | 2 | 1 | no | — |
| 92 | #6199 | — | 2 | 1 | no | — |
| 93 | #6198 | — | 2 | 1 | no | — |
| 94 | ((C3⋊D3)⋊C3)⋊C4 | — | 2 | 2 | no | — |
| 95 | ((C3⋊D3)⋊C3)⋊C4 | — | 2 | 2 | no | — |
| 96 | ((C3⋊D3)⋊C3)⋊C4 | — | 2 | 1 | no | — |
| 97 | ((C3⋊D3)⋊C3)⋊C4 | — | 2 | 1 | no | — |
| 98 | #6196 | — | 2 | 2 | no | — |
| 99 | #6196 | — | 2 | 2 | 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 | D3×#137 | — | 9 | 1 | no | — |
| 104 | D3×#137 | — | 9 | 1 | no | — |
| 105 | C2×#909 | — | 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×C4×D3 | — | 3 | 1 | no | — |
| 114 | C2×C3×Dic6 | — | 3 | 1 | no | — |
| 115 | C2×C3×Dic6 | — | 3 | 1 | no | — |
| 116 | C2×C3×Dic6 | — | 3 | 1 | no | — |
| 117 | C2×C3×Dic6 | — | 6 | 1 | no | — |
| 118 | #3811 | — | 6 | 1 | no | — |
| 119 | D3×#67 | — | 6 | 1 | no | — |
| 120 | C2×#627 | — | 6 | 1 | no | — |
| 121 | C2×#627 | — | 6 | 1 | no | — |
| 122 | C2×#624 | — | 6 | 1 | no | — |
| 123 | #3805 | — | 6 | 1 | no | — |
| 124 | #3804 | — | 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 | 2 | no | — |
| 134 | #3797 | — | 3 | 2 | no | — |
| 135 | #3797 | — | 3 | 1 | no | — |
| 136 | #3797 | — | 6 | 1 | no | — |
| 137 | #3797 | — | 6 | 1 | no | — |
| 138 | #3796 | — | 3 | 1 | no | — |
| 139 | #3796 | — | 3 | 1 | no | — |
| 140 | #3795 | — | 3 | 1 | no | — |
| 141 | D3×Dic6 | — | 3 | 2 | no | — |
| 142 | D3×Dic6 | — | 3 | 2 | no | — |
| 143 | D3×Dic6 | — | 3 | 1 | no | — |
| 144 | D3×Dic6 | — | 6 | 1 | no | — |
| 145 | D3×Dic6 | — | 6 | 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 | — |
| 154 | C3×#208 | — | 3 | 1 | no | — |
| 155 | C3×Dic12 | — | 3 | 2 | no | — |
| 156 | C3×Dic12 | — | 3 | 2 | no | — |
| 157 | C3×Dic12 | — | 3 | 2 | no | — |
| 158 | C3×Dic12 | — | 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 | #3719 | — | 3 | 2 | no | — |
| 167 | #3718 | — | 3 | 2 | no | — |
| 168 | #3718 | — | 3 | 2 | no | — |
| 169 | #3717 | — | 3 | 2 | no | — |
| 170 | #3716 | — | 3 | 2 | no | — |
| 171 | #3715 | — | 3 | 2 | no | — |
| 172 | #3715 | — | 3 | 2 | no | — |
| 173 | C22×H(3,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C2×#272 | — | 2 | 1 | no | — |
| 175 | C2×(C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 176 | C2×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 177 | C2×(C3⋊D3)⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 178 | C2×(C3⋊D3)⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 179 | ((C3⋊D3)⋊C3)⋊C2 | — | 4 | 2 | no | — |
| 180 | C4×H(3,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | C4×H(3,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 182 | #1084 | — | 2 | 2 | no | — |
| 183 | #1084 | — | 2 | 1 | no | — |
| 184 | (C3⋊Dic3)⋊C3 | — | 2 | 2 | no | — |
| 185 | (C3⋊Dic3)⋊C3 | — | 2 | 1 | no | — |
| 186 | (C3⋊Dic3)⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 187 | (C3⋊Dic3)⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 188 | D3×#41 | — | 9 | 1 | no | — |
| 189 | D3×#41 | — | 9 | 1 | no | — |
| 190 | C2×D3×Q8 | — | 9 | 1 | no | — |
| 191 | C2×D3×Q8 | — | 9 | 1 | no | — |
| 192 | C2×#235 | — | 9 | 1 | no | — |
| 193 | C22×Dic6 | — | 9 | 1 | no | — |
| 194 | C3×#137 | — | 9 | 1 | no | — |
| 195 | C3×#137 | — | 9 | 1 | no | — |
| 196 | C2×C3×M16 | — | 9 | 1 | no | — |
| 197 | #951 | — | 9 | 1 | no | — |
| 198 | #951 | — | 9 | 1 | no | — |
| 199 | #942 | — | 9 | 1 | no | — |
| 200 | #942 | — | 9 | 1 | no | — |
| 201 | #918 | — | 9 | 2 | no | — |
| 202 | #918 | — | 9 | 2 | no | — |
| 203 | D3×Q16 | — | 9 | 2 | no | — |
| 204 | D3×Q16 | — | 9 | 2 | no | — |
| 205 | #915 | — | 9 | 2 | no | — |
| 206 | #915 | — | 9 | 2 | no | — |
| 207 | D3×SD16 | — | 9 | 2 | no | — |
| 208 | D3×SD16 | — | 9 | 2 | no | — |
| 209 | #909 | — | 3 | 1 | no | — |
| 210 | #909 | — | 3 | 1 | no | — |
| 211 | #909 | — | 3 | 1 | no | — |
| 212 | #909 | — | 6 | 1 | no | — |
| 213 | #909 | — | 9 | 1 | no | — |
| 214 | #909 | — | 9 | 2 | no | — |
| 215 | #909 | — | 9 | 2 | no | — |
| 216 | #909 | — | 9 | 1 | no | — |
| 217 | #909 | — | 9 | 1 | no | — |
| 218 | D3×M16 | — | 3 | 1 | no | — |
| 219 | D3×M16 | — | 9 | 1 | no | — |
| 220 | C2×Dic12 | — | 9 | 2 | no | — |
| 221 | C2×#204 | — | 9 | 2 | no | — |
| 222 | C22×C3⋊D3 | D12 | 1 | 1 | yes | characteristic |
| 223 | C22×C3×D3 | — | 3 | 1 | no | — |
| 224 | C2×D32 | — | 6 | 1 | no | — |
| 225 | C2×D32 | — | 6 | 1 | no | — |
| 226 | C2×C32×C4 | — | 2 | 1 | no | — |
| 227 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 228 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 229 | #638 | — | 2 | 1 | no | — |
| 230 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 231 | C2×C3⋊Dic3 | D12 | 1 | 1 | yes | characteristic |
| 232 | C4⋊(C3⋊D3) | C22×D3 | 1 | 1 | yes | characteristic |
| 233 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 234 | C4×C3⋊D3 | D12 | 1 | 1 | yes | characteristic |
| 235 | C4×C3⋊D3 | D12 | 1 | 1 | yes | characteristic |
| 236 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 237 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 238 | #634 | — | 2 | 1 | no | — |
| 239 | #634 | C22×D3 | 1 | 2 | yes | — |
| 240 | #634 | C22×D3 | 1 | 1 | yes | characteristic |
| 241 | C3×#67 | — | 6 | 1 | no | — |
| 242 | C3×#67 | — | 6 | 1 | no | — |
| 243 | C3×#67 | — | 6 | 1 | no | — |
| 244 | C3×#67 | — | 12 | 1 | no | — |
| 245 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 246 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 247 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 248 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 249 | C2×C3×Dic3 | — | 12 | 1 | no | — |
| 250 | C3×D12 | — | 3 | 1 | no | — |
| 251 | C3×D12 | — | 3 | 1 | no | — |
| 252 | C3×D12 | — | 3 | 1 | no | — |
| 253 | C3×D12 | — | 6 | 1 | no | — |
| 254 | C3×C4×D3 | — | 3 | 1 | no | — |
| 255 | C3×C4×D3 | — | 3 | 1 | no | — |
| 256 | C3×C4×D3 | — | 3 | 1 | no | — |
| 257 | C3×C4×D3 | — | 3 | 1 | no | — |
| 258 | C3×C4×D3 | — | 6 | 1 | no | — |
| 259 | C3×C4×D3 | — | 6 | 1 | no | — |
| 260 | C3×C4×D3 | — | 6 | 1 | no | — |
| 261 | C3×C4×D3 | — | 12 | 1 | no | — |
| 262 | C3×Dic6 | — | 3 | 2 | no | — |
| 263 | C3×Dic6 | — | 3 | 1 | no | — |
| 264 | C3×Dic6 | — | 3 | 2 | no | — |
| 265 | C3×Dic6 | — | 3 | 2 | no | — |
| 266 | C3×Dic6 | — | 3 | 1 | no | — |
| 267 | C3×Dic6 | — | 3 | 1 | no | — |
| 268 | C3×Dic6 | — | 6 | 2 | no | — |
| 269 | C3×Dic6 | — | 6 | 1 | no | — |
| 270 | C3×Dic6 | — | 6 | 1 | no | — |
| 271 | C3×Dic6 | — | 6 | 1 | no | — |
| 272 | C3×Dic6 | — | 6 | 1 | no | — |
| 273 | C3×Dic6 | — | 12 | 1 | no | — |
| 274 | #627 | — | 6 | 2 | no | — |
| 275 | #627 | — | 6 | 2 | no | — |
| 276 | #627 | — | 6 | 1 | no | — |
| 277 | #627 | — | 6 | 2 | no | — |
| 278 | #627 | — | 6 | 2 | no | — |
| 279 | #627 | — | 6 | 1 | no | — |
| 280 | #626 | — | 6 | 1 | no | — |
| 281 | #626 | — | 6 | 1 | no | — |
| 282 | #626 | — | 6 | 1 | no | — |
| 283 | #626 | — | 6 | 1 | no | — |
| 284 | #625 | — | 6 | 1 | no | — |
| 285 | #625 | — | 6 | 1 | no | — |
| 286 | #624 | — | 6 | 1 | no | — |
| 287 | #624 | — | 6 | 2 | no | — |
| 288 | #624 | — | 6 | 2 | no | — |
| 289 | #624 | — | 6 | 1 | no | — |
| 290 | D3×Dic3 | — | 6 | 1 | no | — |
| 291 | D3×Dic3 | — | 6 | 2 | no | — |
| 292 | D3×Dic3 | — | 6 | 2 | no | — |
| 293 | D3×Dic3 | — | 6 | 1 | no | — |
| 294 | D3×Dic3 | — | 6 | 1 | no | — |
| 295 | D3×Dic3 | — | 6 | 1 | no | — |
| 296 | C32×C8 | — | 2 | 2 | no | — |
| 297 | C32×C8 | C22×D3 | 1 | 2 | yes | — |
| 298 | C32×C8 | C22×D3 | 1 | 2 | yes | — |
| 299 | C3⋊(C3⋊C8) | C22×D3 | 1 | 2 | yes | — |
| 300 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 301 | C2×#137 | — | 27 | 1 | no | Sylow |
| 302 | C2×H(3,𝔽3) | — | 2 | 1 | no | — |
| 303 | C2×H(3,𝔽3) | C22×D4 | 1 | 1 | yes | characteristic |
| 304 | #272 | — | 4 | 1 | no | — |
| 305 | (C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 306 | (C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 307 | (C3⋊D3)⋊C3 | #137 | 1 | 2 | yes | complemented |
| 308 | C3×#41 | — | 9 | 1 | no | — |
| 309 | C3×#41 | — | 9 | 1 | no | — |
| 310 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 311 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 312 | C22×C3×C4 | — | 9 | 1 | no | — |
| 313 | C2×#67 | — | 18 | 1 | no | — |
| 314 | C22×Dic3 | — | 18 | 1 | no | — |
| 315 | #239 | — | 9 | 1 | no | — |
| 316 | #239 | — | 9 | 1 | no | — |
| 317 | D3×Q8 | — | 9 | 2 | no | — |
| 318 | D3×Q8 | — | 9 | 2 | no | — |
| 319 | D3×Q8 | — | 9 | 1 | no | — |
| 320 | D3×Q8 | — | 9 | 2 | no | — |
| 321 | D3×Q8 | — | 9 | 2 | no | — |
| 322 | D3×Q8 | — | 9 | 1 | no | — |
| 323 | D3×Q8 | — | 18 | 1 | no | — |
| 324 | D3×Q8 | — | 18 | 1 | no | — |
| 325 | D3×Q8 | — | 18 | 1 | no | — |
| 326 | D3×Q8 | — | 18 | 1 | no | — |
| 327 | #237 | — | 9 | 1 | no | — |
| 328 | #237 | — | 9 | 1 | no | — |
| 329 | #237 | — | 18 | 1 | no | — |
| 330 | #237 | — | 18 | 1 | no | — |
| 331 | D3×D4 | — | 9 | 1 | no | — |
| 332 | D3×D4 | — | 9 | 1 | no | — |
| 333 | D3×D4 | — | 18 | 1 | no | — |
| 334 | D3×D4 | — | 18 | 1 | no | — |
| 335 | #235 | — | 3 | 1 | no | — |
| 336 | #235 | — | 3 | 1 | no | — |
| 337 | #235 | — | 3 | 1 | no | — |
| 338 | #235 | — | 6 | 1 | no | — |
| 339 | #235 | — | 9 | 1 | no | — |
| 340 | #235 | — | 9 | 1 | no | — |
| 341 | #235 | — | 9 | 1 | no | — |
| 342 | #235 | — | 18 | 1 | no | — |
| 343 | #235 | — | 18 | 1 | no | — |
| 344 | #235 | — | 18 | 1 | no | — |
| 345 | #235 | — | 18 | 1 | no | — |
| 346 | C2×D12 | — | 9 | 1 | no | — |
| 347 | C2×C4×D3 | — | 3 | 1 | no | — |
| 348 | C2×C4×D3 | — | 9 | 1 | no | — |
| 349 | C2×C4×D3 | — | 18 | 1 | no | — |
| 350 | C2×C4×D3 | — | 18 | 1 | no | — |
| 351 | C2×C4×D3 | — | 18 | 1 | no | — |
| 352 | C2×C4×D3 | — | 18 | 1 | no | — |
| 353 | C2×C4×D3 | — | 18 | 1 | no | — |
| 354 | C2×Dic6 | — | 3 | 1 | no | — |
| 355 | C2×Dic6 | — | 3 | 1 | no | — |
| 356 | C2×Dic6 | — | 3 | 1 | no | — |
| 357 | C2×Dic6 | — | 6 | 1 | no | — |
| 358 | C2×Dic6 | — | 9 | 1 | no | — |
| 359 | C2×Dic6 | — | 9 | 2 | no | — |
| 360 | C2×Dic6 | — | 9 | 1 | no | — |
| 361 | C2×Dic6 | — | 9 | 2 | no | — |
| 362 | C2×Dic6 | — | 18 | 1 | no | — |
| 363 | C2×Dic6 | — | 18 | 1 | no | — |
| 364 | C2×Dic6 | — | 18 | 1 | no | — |
| 365 | C2×Dic6 | — | 18 | 1 | no | — |
| 366 | C2×Dic6 | — | 18 | 1 | no | — |
| 367 | C3×Q16 | — | 9 | 2 | no | — |
| 368 | C3×Q16 | — | 9 | 2 | no | — |
| 369 | C3×SD16 | — | 9 | 2 | no | — |
| 370 | C3×SD16 | — | 9 | 2 | no | — |
| 371 | C3×M16 | — | 3 | 1 | no | — |
| 372 | C3×M16 | — | 3 | 1 | no | — |
| 373 | C3×M16 | — | 6 | 1 | no | — |
| 374 | C3×M16 | — | 9 | 2 | no | — |
| 375 | C3×M16 | — | 9 | 1 | no | — |
| 376 | C3×M16 | D32 | 1 | 1 | yes | characteristic |
| 377 | C2×C3×C8 | — | 9 | 2 | no | — |
| 378 | #216 | — | 9 | 2 | no | — |
| 379 | #216 | — | 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 | #208 | — | 3 | 1 | no | — |
| 387 | #208 | — | 9 | 1 | no | — |
| 388 | Dic12 | — | 3 | 2 | no | — |
| 389 | Dic12 | — | 3 | 2 | no | — |
| 390 | Dic12 | — | 3 | 2 | no | — |
| 391 | Dic12 | — | 6 | 2 | no | — |
| 392 | Dic12 | — | 9 | 2 | no | — |
| 393 | Dic12 | — | 9 | 2 | no | — |
| 394 | Dic12 | — | 9 | 2 | no | — |
| 395 | #204 | — | 3 | 2 | no | — |
| 396 | #204 | — | 3 | 2 | no | — |
| 397 | #204 | — | 3 | 2 | no | — |
| 398 | #204 | — | 6 | 2 | no | — |
| 399 | #204 | — | 9 | 2 | no | — |
| 400 | #204 | — | 9 | 2 | no | — |
| 401 | #204 | — | 9 | 2 | no | — |
| 402 | ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 403 | ΓL(1,𝔽25) | — | 9 | 2 | no | — |
| 404 | D3×C8 | — | 3 | 2 | no | — |
| 405 | D3×C8 | — | 9 | 2 | no | — |
| 406 | C22×C32 | — | 2 | 1 | no | — |
| 407 | C22×C32 | C2×D12 | 1 | 1 | yes | characteristic |
| 408 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic |
| 409 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 410 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 411 | C2×C3⋊D3 | C2×D12 | 1 | 1 | yes | characteristic |
| 412 | C2×C3⋊D3 | C2×D12 | 1 | 1 | yes | characteristic |
| 413 | C2×C3×D3 | — | 3 | 1 | no | — |
| 414 | C2×C3×D3 | — | 3 | 1 | no | — |
| 415 | C2×C3×D3 | — | 6 | 2 | no | — |
| 416 | C2×C3×D3 | — | 6 | 1 | no | — |
| 417 | C2×C3×D3 | — | 6 | 1 | no | — |
| 418 | C2×C3×D3 | — | 6 | 1 | no | — |
| 419 | C2×C3×D3 | — | 12 | 1 | no | — |
| 420 | D32 | — | 12 | 2 | no | — |
| 421 | D32 | — | 12 | 2 | no | — |
| 422 | C32×C4 | — | 2 | 1 | no | — |
| 423 | C32×C4 | — | 2 | 1 | no | — |
| 424 | C32×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 425 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 426 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 427 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 428 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 429 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 430 | C3⋊Dic3 | C2×D12 | 1 | 1 | yes | characteristic |
| 431 | C3⋊Dic3 | C2×D12 | 1 | 1 | yes | characteristic |
| 432 | C3×Dic3 | — | 3 | 1 | no | — |
| 433 | C3×Dic3 | — | 3 | 1 | no | — |
| 434 | C3×Dic3 | — | 6 | 1 | no | — |
| 435 | C3×Dic3 | — | 6 | 2 | no | — |
| 436 | C3×Dic3 | — | 6 | 1 | no | — |
| 437 | C3×Dic3 | — | 6 | 2 | no | — |
| 438 | C3×Dic3 | — | 6 | 2 | no | — |
| 439 | C3×Dic3 | — | 6 | 1 | no | — |
| 440 | C3×Dic3 | — | 12 | 2 | no | — |
| 441 | C3×Dic3 | — | 12 | 1 | no | — |
| 442 | C2×#41 | — | 27 | 1 | no | — |
| 443 | C22×Q8 | — | 27 | 1 | no | — |
| 444 | #137 | — | 9 | 1 | no | — |
| 445 | #137 | — | 9 | 1 | no | — |
| 446 | #137 | — | 27 | 2 | no | — |
| 447 | #137 | — | 27 | 2 | no | — |
| 448 | #137 | — | 27 | 1 | no | — |
| 449 | #137 | — | 27 | 1 | no | — |
| 450 | C2×Q16 | — | 27 | 2 | no | — |
| 451 | C2×SD16 | — | 27 | 2 | no | — |
| 452 | C2×M16 | — | 9 | 1 | no | — |
| 453 | H(3,𝔽3) | C2×#137 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 454 | C23×C3 | — | 9 | 1 | no | — |
| 455 | C22×D3 | — | 3 | 1 | no | — |
| 456 | C22×D3 | — | 9 | 1 | no | — |
| 457 | C22×D3 | — | 18 | 1 | no | — |
| 458 | C22×D3 | — | 18 | 1 | no | — |
| 459 | C22×D3 | — | 18 | 1 | no | — |
| 460 | C3×Q8 | — | 9 | 2 | no | — |
| 461 | C3×Q8 | — | 9 | 1 | no | — |
| 462 | C3×Q8 | — | 9 | 2 | no | — |
| 463 | C3×Q8 | — | 9 | 1 | no | — |
| 464 | C3×Q8 | — | 18 | 1 | no | — |
| 465 | C3×Q8 | — | 18 | 1 | no | — |
| 466 | C3×D4 | — | 9 | 1 | no | — |
| 467 | C3×D4 | — | 9 | 1 | no | — |
| 468 | C3×D4 | — | 18 | 1 | no | — |
| 469 | C3×D4 | — | 18 | 1 | no | — |
| 470 | C2×C3×C4 | — | 3 | 1 | no | — |
| 471 | C2×C3×C4 | — | 3 | 1 | no | — |
| 472 | C2×C3×C4 | — | 6 | 1 | no | — |
| 473 | C2×C3×C4 | — | 9 | 1 | no | — |
| 474 | C2×C3×C4 | — | 9 | 1 | no | — |
| 475 | C2×C3×C4 | — | 9 | 1 | no | — |
| 476 | C2×C3×C4 | — | 9 | 1 | no | — |
| 477 | C2×C3×C4 | — | 9 | 1 | no | — |
| 478 | C2×C3×C4 | — | 18 | 1 | no | — |
| 479 | C2×C3×C4 | — | 18 | 1 | no | — |
| 480 | C2×C3×C4 | — | 18 | 1 | no | — |
| 481 | C2×C3×C4 | — | 18 | 1 | no | — |
| 482 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 483 | #67 | — | 6 | 1 | no | — |
| 484 | #67 | — | 6 | 1 | no | — |
| 485 | #67 | — | 6 | 1 | no | — |
| 486 | #67 | — | 12 | 1 | no | — |
| 487 | #67 | — | 18 | 1 | no | — |
| 488 | #67 | — | 18 | 1 | no | — |
| 489 | #67 | — | 18 | 1 | no | — |
| 490 | #67 | — | 18 | 1 | no | — |
| 491 | #67 | — | 18 | 1 | no | — |
| 492 | #67 | — | 18 | 1 | no | — |
| 493 | #67 | — | 18 | 1 | no | — |
| 494 | C2×Dic3 | — | 3 | 1 | no | — |
| 495 | C2×Dic3 | — | 6 | 1 | no | — |
| 496 | C2×Dic3 | — | 6 | 1 | no | — |
| 497 | C2×Dic3 | — | 6 | 1 | no | — |
| 498 | C2×Dic3 | — | 9 | 1 | no | — |
| 499 | C2×Dic3 | — | 12 | 1 | no | — |
| 500 | C2×Dic3 | — | 18 | 1 | no | — |
| 501 | C2×Dic3 | — | 18 | 1 | no | — |
| 502 | C2×Dic3 | — | 18 | 1 | no | — |
| 503 | C2×Dic3 | — | 18 | 2 | no | — |
| 504 | C2×Dic3 | — | 18 | 2 | no | — |
| 505 | C2×Dic3 | — | 18 | 1 | no | — |
| 506 | D12 | — | 3 | 1 | no | — |
| 507 | D12 | — | 3 | 1 | no | — |
| 508 | D12 | — | 3 | 1 | no | — |
| 509 | D12 | — | 6 | 1 | no | — |
| 510 | D12 | — | 9 | 1 | no | — |
| 511 | D12 | — | 18 | 1 | no | — |
| 512 | D12 | — | 18 | 1 | no | — |
| 513 | D12 | — | 18 | 1 | no | — |
| 514 | C4×D3 | — | 3 | 1 | no | — |
| 515 | C4×D3 | — | 3 | 1 | no | — |
| 516 | C4×D3 | — | 3 | 1 | no | — |
| 517 | C4×D3 | — | 3 | 1 | no | — |
| 518 | C4×D3 | — | 6 | 1 | no | — |
| 519 | C4×D3 | — | 6 | 1 | no | — |
| 520 | C4×D3 | — | 6 | 1 | no | — |
| 521 | C4×D3 | — | 9 | 1 | no | — |
| 522 | C4×D3 | — | 9 | 1 | no | — |
| 523 | C4×D3 | — | 9 | 1 | no | — |
| 524 | C4×D3 | — | 9 | 1 | no | — |
| 525 | C4×D3 | — | 12 | 1 | no | — |
| 526 | C4×D3 | — | 18 | 1 | no | — |
| 527 | C4×D3 | — | 18 | 1 | no | — |
| 528 | C4×D3 | — | 18 | 1 | no | — |
| 529 | C4×D3 | — | 18 | 1 | no | — |
| 530 | C4×D3 | — | 18 | 2 | no | — |
| 531 | C4×D3 | — | 18 | 2 | no | — |
| 532 | C4×D3 | — | 18 | 1 | no | — |
| 533 | C4×D3 | — | 18 | 2 | no | — |
| 534 | C4×D3 | — | 18 | 2 | no | — |
| 535 | C4×D3 | — | 18 | 1 | no | — |
| 536 | C4×D3 | — | 18 | 1 | no | — |
| 537 | Dic6 | — | 3 | 2 | no | — |
| 538 | Dic6 | — | 3 | 2 | no | — |
| 539 | Dic6 | — | 3 | 1 | no | — |
| 540 | Dic6 | — | 3 | 1 | no | — |
| 541 | Dic6 | — | 3 | 2 | no | — |
| 542 | Dic6 | — | 3 | 1 | no | — |
| 543 | Dic6 | — | 6 | 2 | no | — |
| 544 | Dic6 | — | 6 | 1 | no | — |
| 545 | Dic6 | — | 6 | 1 | no | — |
| 546 | Dic6 | — | 6 | 1 | no | — |
| 547 | Dic6 | — | 6 | 1 | no | — |
| 548 | Dic6 | — | 9 | 2 | no | — |
| 549 | Dic6 | — | 9 | 1 | no | — |
| 550 | Dic6 | — | 12 | 1 | no | — |
| 551 | Dic6 | — | 18 | 1 | no | — |
| 552 | Dic6 | — | 18 | 2 | no | — |
| 553 | Dic6 | — | 18 | 2 | no | — |
| 554 | Dic6 | — | 18 | 1 | no | — |
| 555 | Dic6 | — | 18 | 2 | no | — |
| 556 | Dic6 | — | 18 | 2 | no | — |
| 557 | Dic6 | — | 18 | 1 | no | — |
| 558 | Dic6 | — | 18 | 2 | no | — |
| 559 | Dic6 | — | 18 | 2 | no | — |
| 560 | Dic6 | — | 18 | 1 | no | — |
| 561 | C3×C8 | — | 3 | 2 | no | — |
| 562 | C3×C8 | — | 3 | 2 | no | — |
| 563 | C3×C8 | — | 6 | 2 | no | — |
| 564 | C3×C8 | — | 9 | 2 | no | — |
| 565 | C3×C8 | C2×D32 | 1 | 2 | yes | — |
| 566 | C3⋊C8 | — | 3 | 2 | no | — |
| 567 | C3⋊C8 | — | 9 | 2 | no | — |
| 568 | C2×C32 | — | 2 | 1 | no | — |
| 569 | C2×C32 | — | 2 | 1 | no | — |
| 570 | C2×C32 | — | 2 | 1 | no | — |
| 571 | C2×C32 | — | 4 | 1 | no | — |
| 572 | C2×C32 | C22×D12 | 1 | 1 | yes | characteristic |
| 573 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 574 | C3⋊D3 | — | 2 | 1 | no | — |
| 575 | C3⋊D3 | — | 4 | 1 | no | — |
| 576 | C3⋊D3 | #909 | 1 | 2 | yes | complemented |
| 577 | C3×D3 | — | 3 | 2 | no | — |
| 578 | C3×D3 | — | 6 | 1 | no | — |
| 579 | C3×D3 | — | 12 | 1 | no | — |
| 580 | C3×D3 | — | 12 | 1 | no | — |
| 581 | C3×D3 | — | 12 | 1 | no | — |
| 582 | C3×D3 | — | 24 | 1 | no | — |
| 583 | #41 | — | 9 | 1 | no | — |
| 584 | #41 | — | 9 | 1 | no | — |
| 585 | #41 | — | 27 | 1 | no | — |
| 586 | #41 | — | 27 | 1 | no | — |
| 587 | #41 | — | 54 | 1 | no | — |
| 588 | #41 | — | 54 | 1 | no | — |
| 589 | C2×Q8 | — | 9 | 1 | no | — |
| 590 | C2×Q8 | — | 9 | 1 | no | — |
| 591 | C2×Q8 | — | 27 | 2 | no | — |
| 592 | C2×Q8 | — | 27 | 1 | no | — |
| 593 | C2×Q8 | — | 27 | 2 | no | — |
| 594 | C2×Q8 | — | 54 | 1 | no | — |
| 595 | C2×Q8 | — | 54 | 1 | no | — |
| 596 | C2×Q8 | — | 54 | 1 | no | — |
| 597 | C2×D4 | — | 27 | 1 | no | — |
| 598 | C2×D4 | — | 54 | 1 | no | — |
| 599 | C22×C4 | — | 9 | 1 | no | — |
| 600 | C22×C4 | — | 54 | 1 | no | — |
| 601 | C22×C4 | — | 54 | 1 | no | — |
| 602 | Q16 | — | 9 | 2 | no | — |
| 603 | Q16 | — | 9 | 2 | no | — |
| 604 | Q16 | — | 27 | 2 | no | — |
| 605 | Q16 | — | 27 | 2 | no | — |
| 606 | SD16 | — | 9 | 2 | no | — |
| 607 | SD16 | — | 9 | 2 | no | — |
| 608 | SD16 | — | 27 | 2 | no | — |
| 609 | SD16 | — | 27 | 2 | no | — |
| 610 | M16 | — | 9 | 1 | no | — |
| 611 | M16 | — | 9 | 2 | no | — |
| 612 | M16 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 613 | C2×C8 | — | 9 | 2 | no | — |
| 614 | C22×C3 | — | 3 | 1 | no | — |
| 615 | C22×C3 | — | 3 | 1 | no | — |
| 616 | C22×C3 | — | 6 | 1 | no | — |
| 617 | C22×C3 | — | 9 | 1 | no | — |
| 618 | C22×C3 | — | 9 | 1 | no | — |
| 619 | C22×C3 | — | 18 | 1 | no | — |
| 620 | C22×C3 | — | 18 | 2 | no | — |
| 621 | C22×C3 | — | 18 | 1 | no | — |
| 622 | C22×C3 | D3×D12 | 1 | 1 | yes | characteristic |
| 623 | C2×D3 | — | 3 | 1 | no | — |
| 624 | C2×D3 | — | 3 | 1 | no | — |
| 625 | C2×D3 | — | 6 | 2 | no | — |
| 626 | C2×D3 | — | 6 | 1 | no | — |
| 627 | C2×D3 | — | 6 | 1 | no | — |
| 628 | C2×D3 | — | 6 | 1 | no | — |
| 629 | C2×D3 | — | 9 | 1 | no | — |
| 630 | C2×D3 | — | 9 | 1 | no | — |
| 631 | C2×D3 | — | 12 | 1 | no | — |
| 632 | C2×D3 | — | 18 | 2 | no | — |
| 633 | C2×D3 | — | 18 | 1 | no | — |
| 634 | C2×D3 | — | 36 | 2 | no | — |
| 635 | C2×D3 | — | 36 | 2 | no | — |
| 636 | C2×D3 | — | 36 | 2 | no | — |
| 637 | C3×C4 | — | 3 | 1 | no | — |
| 638 | C3×C4 | — | 3 | 1 | no | — |
| 639 | C3×C4 | — | 3 | 1 | no | — |
| 640 | C3×C4 | — | 3 | 1 | no | — |
| 641 | C3×C4 | — | 6 | 1 | no | — |
| 642 | C3×C4 | — | 6 | 1 | no | — |
| 643 | C3×C4 | — | 9 | 1 | no | — |
| 644 | C3×C4 | — | 9 | 1 | no | — |
| 645 | C3×C4 | — | 18 | 2 | no | — |
| 646 | C3×C4 | — | 18 | 1 | no | — |
| 647 | C3×C4 | — | 18 | 2 | no | — |
| 648 | C3×C4 | — | 18 | 1 | no | — |
| 649 | C3×C4 | D3×D12 | 1 | 1 | yes | characteristic |
| 650 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 651 | Dic3 | — | 3 | 1 | no | — |
| 652 | Dic3 | — | 3 | 1 | no | — |
| 653 | Dic3 | — | 6 | 2 | no | — |
| 654 | Dic3 | — | 6 | 2 | no | — |
| 655 | Dic3 | — | 6 | 1 | no | — |
| 656 | Dic3 | — | 6 | 1 | no | — |
| 657 | Dic3 | — | 6 | 2 | no | — |
| 658 | Dic3 | — | 6 | 1 | no | — |
| 659 | Dic3 | — | 9 | 1 | no | — |
| 660 | Dic3 | — | 9 | 1 | no | — |
| 661 | Dic3 | — | 12 | 2 | no | — |
| 662 | Dic3 | — | 12 | 1 | no | — |
| 663 | Dic3 | — | 18 | 2 | no | — |
| 664 | Dic3 | — | 18 | 1 | no | — |
| 665 | C32 | — | 2 | 1 | no | — |
| 666 | C32 | C2×#909 | 1 | 1 | yes | characteristic, complemented |
| 667 | C32 | D3×#137 | 1 | 1 | yes | characteristic, complemented |
| 668 | C23 | — | 9 | 1 | no | — |
| 669 | C23 | — | 54 | 1 | no | — |
| 670 | Q8 | — | 9 | 2 | no | — |
| 671 | Q8 | — | 9 | 2 | no | — |
| 672 | Q8 | — | 9 | 1 | no | — |
| 673 | Q8 | — | 9 | 1 | no | — |
| 674 | Q8 | — | 18 | 1 | no | — |
| 675 | Q8 | — | 18 | 1 | no | — |
| 676 | Q8 | — | 54 | 2 | no | — |
| 677 | Q8 | — | 54 | 2 | no | — |
| 678 | Q8 | — | 54 | 1 | no | — |
| 679 | D4 | — | 9 | 1 | no | — |
| 680 | D4 | — | 9 | 1 | no | — |
| 681 | D4 | — | 18 | 1 | no | — |
| 682 | D4 | — | 18 | 1 | no | — |
| 683 | D4 | — | 54 | 1 | no | — |
| 684 | D4 | — | 54 | 1 | no | — |
| 685 | D4 | — | 54 | 1 | no | — |
| 686 | C2×C4 | — | 9 | 1 | no | — |
| 687 | C2×C4 | — | 9 | 1 | no | — |
| 688 | C2×C4 | — | 9 | 1 | no | — |
| 689 | C2×C4 | — | 9 | 1 | no | — |
| 690 | C2×C4 | — | 9 | 1 | no | — |
| 691 | C2×C4 | — | 18 | 1 | no | — |
| 692 | C2×C4 | — | 18 | 1 | no | — |
| 693 | C2×C4 | — | 18 | 1 | no | — |
| 694 | C2×C4 | — | 18 | 1 | no | — |
| 695 | C2×C4 | — | 54 | 1 | no | — |
| 696 | C2×C4 | — | 54 | 1 | no | — |
| 697 | C2×C4 | — | 54 | 1 | no | — |
| 698 | C2×C4 | — | 54 | 2 | no | — |
| 699 | C2×C4 | — | 54 | 2 | no | — |
| 700 | C2×C4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 701 | C8 | — | 9 | 2 | no | — |
| 702 | C8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 2 | yes | — |
| 703 | C2×C3 | — | 2 | 1 | no | — |
| 704 | C2×C3 | — | 3 | 1 | no | — |
| 705 | C2×C3 | — | 3 | 1 | no | — |
| 706 | C2×C3 | — | 6 | 1 | no | — |
| 707 | C2×C3 | — | 6 | 1 | no | — |
| 708 | C2×C3 | — | 6 | 1 | no | — |
| 709 | C2×C3 | — | 9 | 2 | no | — |
| 710 | C2×C3 | — | 12 | 1 | no | — |
| 711 | C2×C3 | — | 18 | 1 | no | — |
| 712 | C2×C3 | — | 36 | 1 | no | — |
| 713 | C2×C3 | — | 36 | 1 | no | — |
| 714 | C2×C3 | C2×D3×D12 | 1 | 1 | yes | characteristic |
| 715 | D3 | — | 3 | 2 | no | — |
| 716 | D3 | — | 6 | 1 | no | — |
| 717 | D3 | — | 9 | 2 | no | — |
| 718 | D3 | — | 12 | 1 | no | — |
| 719 | D3 | — | 12 | 1 | no | — |
| 720 | D3 | — | 12 | 1 | no | — |
| 721 | D3 | — | 18 | 1 | no | — |
| 722 | D3 | — | 24 | 1 | no | — |
| 723 | D3 | — | 36 | 1 | no | — |
| 724 | C22 | — | 9 | 1 | no | — |
| 725 | C22 | — | 9 | 1 | no | — |
| 726 | C22 | — | 18 | 2 | no | — |
| 727 | C22 | — | 18 | 1 | no | — |
| 728 | C22 | — | 18 | 1 | no | — |
| 729 | C22 | — | 108 | 2 | no | — |
| 730 | C22 | #88654 | 1 | 1 | yes | characteristic |
| 731 | C4 | — | 9 | 1 | no | — |
| 732 | C4 | — | 9 | 1 | no | — |
| 733 | C4 | — | 18 | 1 | no | — |
| 734 | C4 | — | 18 | 1 | no | — |
| 735 | C4 | — | 18 | 2 | no | — |
| 736 | C4 | — | 18 | 2 | no | — |
| 737 | C4 | #88654 | 1 | 1 | yes | characteristic |
| 738 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 739 | C3 | — | 3 | 1 | no | — |
| 740 | C3 | — | 3 | 1 | no | — |
| 741 | C3 | — | 6 | 1 | no | — |
| 742 | C3 | D3×#909 | 1 | 1 | yes | characteristic |
| 743 | C2 | — | 2 | 1 | no | — |
| 744 | C2 | — | 9 | 2 | no | — |
| 745 | C2 | — | 18 | 1 | no | — |
| 746 | C2 | — | 36 | 1 | no | — |
| 747 | C2 | — | 36 | 1 | no | — |
| 748 | C2 | C2×#88654 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×((C3⋊D3)⋊C3)⋊Q8 | C2 | semidirect |
| 3. #11721788 | C2 | semidirect |
| 4. #64118⋊C3 | C2 | semidirect |
| 5. M16×(C3⋊D3)⋊C3 | C2 | semidirect |
| 6. #11721074 | C2 | semidirect |
| 7. #11721069 | C2 | semidirect |
| 8. #11720853 | C2 | semidirect |
| 9. #11720852 | C2 | semidirect |
| 10. #11720851 | C2 | semidirect |
| 11. #11720846 | C2 | semidirect |
| 15. C2×#6229 | C22 | semidirect |
| 18. C2×#634⋊C3 | C22 | semidirect |
| 32. ((C3⋊D3)⋊C3)⋊Q8 | C22 | semidirect |
| 33. M16×H(3,𝔽3) | C22 | semidirect |
| 34. #88530 | C22 | semidirect |
| 35. #88528 | C22 | semidirect |
| 36. #3748⋊C3 | C22 | semidirect |
| 37. #3744⋊C3 | C22 | semidirect |
| 38. #3743⋊C3 | C22 | semidirect |
| 40. #3746⋊C3 | C22 | semidirect |
| 41. #88439 | C22 | semidirect |
| 42. #88439 | C22 | semidirect |
| 43. #88438 | C22 | semidirect |
| 44. #88437 | 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 |
| 307. (C3⋊D3)⋊C3 | #137 | semidirect |
| 453. H(3,𝔽3) | C2×#137 | semidirect |
| 576. C3⋊D3 | #909 | semidirect |
| 612. M16 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 666. C32 | C2×#909 | semidirect |
| 667. C32 | D3×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722490 | 2 |
| C2×((C3⋊D3)⋊C3)⋊Q8 | 2 |
| #11721788 | 2 |
| #64118⋊C3 | 2 |
| M16×(C3⋊D3)⋊C3 | 2 |
| #11721074 | 2 |
| #11721069 | 2 |
| #11720853 | 2 |
| #11720852 | 2 |
| #11720851 | 2 |
| #11720846 | 2 |
| #10594717 | 3 |
| D3×#909 | 3 |