Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3001 conjugacy classes of subgroups.
The subgroup lattice has 833 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11722664 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #64361⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#3830⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11722545 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | C2×#88671 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #11722507 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11722505 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #11722504 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #11722502 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #11722490 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #11722482 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #10596679 | — | 3 | 1 | no | maximal |
| 13 | #10596678 | — | 3 | 1 | no | maximal |
| 14 | C2×D4×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C2×#6235 | C22 | 1 | 4 | yes | complemented |
| 16 | #88744 | C22 | 1 | 4 | yes | complemented |
| 17 | D4×#272 | C22 | 1 | 4 | yes | complemented |
| 18 | #88740 | C22 | 1 | 2 | yes | complemented |
| 19 | C2×#638⋊C3 | C22 | 1 | 4 | yes | complemented |
| 20 | C2×#638⋊C3 | C22 | 1 | 2 | yes | complemented |
| 21 | C22×(C3⋊Dic3)⋊C3 | C22 | 1 | 2 | yes | complemented |
| 22 | #3830⋊C3 | C22 | 1 | 4 | yes | complemented |
| 23 | #3830⋊C3 | C22 | 1 | 4 | yes | complemented |
| 24 | #3830⋊C3 | C22 | 1 | 4 | yes | complemented |
| 25 | D4×(C3⋊D3)⋊C3 | C22 | 1 | 4 | yes | complemented |
| 26 | #3828⋊C3 | C22 | 1 | 2 | yes | complemented |
| 27 | C2×C4×(C3⋊D3)⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | C2×#634⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #88677 | C22 | 1 | 8 | yes | complemented |
| 30 | #88676 | C22 | 1 | 8 | yes | complemented |
| 31 | #88676 | C22 | 1 | 4 | yes | complemented |
| 32 | C2×#6200 | C22 | 1 | 4 | yes | complemented |
| 33 | C2×#6199 | C22 | 1 | 4 | yes | complemented |
| 34 | #88672 | C22 | 1 | 8 | yes | complemented |
| 35 | #88671 | C22 | 1 | 8 | yes | complemented |
| 36 | #88671 | C22 | 1 | 8 | yes | complemented |
| 37 | #88671 | C22 | 1 | 8 | yes | complemented |
| 38 | #88671 | C22 | 1 | 4 | yes | complemented |
| 39 | #88671 | C22 | 1 | 8 | yes | complemented |
| 40 | C2×((C3⋊D3)⋊C3)⋊C4 | C22 | 1 | 4 | yes | complemented |
| 41 | C2×#6196 | C22 | 1 | 4 | yes | complemented |
| 42 | #88654 | C22 | 1 | 2 | yes | complemented |
| 43 | C4×((C3⋊D3)⋊C3)⋊C2 | C22 | 1 | 4 | yes | complemented |
| 44 | #88652 | C22 | 1 | 2 | yes | complemented |
| 45 | #88652 | C22 | 1 | 4 | yes | complemented |
| 46 | #88651 | C22 | 1 | 4 | yes | complemented |
| 47 | #88650 | C22 | 1 | 4 | yes | complemented |
| 48 | #88649 | C22 | 1 | 4 | yes | complemented |
| 49 | #88648 | C22 | 1 | 2 | yes | complemented |
| 50 | ((C3⋊D3)⋊C3)⋊Q8 | C22 | 1 | 2 | yes | complemented |
| 51 | ((C3⋊D3)⋊C3)⋊Q8 | C22 | 1 | 4 | yes | complemented |
| 52 | #64361 | D3 | 1 | 1 | yes | characteristic, complemented |
| 53 | C2×#3830 | D3 | 1 | 1 | yes | characteristic, complemented |
| 54 | C3×#1004 | — | 3 | 1 | no | — |
| 55 | C3×#1004 | — | 3 | 1 | no | — |
| 56 | C3×#1004 | — | 3 | 1 | no | — |
| 57 | C3×#1004 | — | 6 | 1 | no | — |
| 58 | C2×C3×#237 | — | 3 | 1 | no | — |
| 59 | #64330 | — | 3 | 4 | no | — |
| 60 | #64330 | — | 3 | 4 | no | — |
| 61 | C2×#3805 | — | 3 | 4 | no | — |
| 62 | C2×#3804 | — | 3 | 4 | no | — |
| 63 | #64314 | — | 3 | 4 | no | — |
| 64 | #64313 | — | 3 | 4 | no | — |
| 65 | #64312 | — | 3 | 4 | no | — |
| 66 | D3×#237 | — | 3 | 4 | no | — |
| 67 | D3×#237 | — | 3 | 4 | no | — |
| 68 | D3×#237 | — | 3 | 4 | no | — |
| 69 | #64309 | — | 3 | 4 | no | — |
| 70 | #64309 | — | 3 | 4 | no | — |
| 71 | #64306 | — | 3 | 2 | no | — |
| 72 | D3×#235 | — | 3 | 2 | no | — |
| 73 | #64298 | — | 3 | 2 | no | — |
| 74 | #64297 | — | 3 | 2 | no | — |
| 75 | C23×H(3,𝔽3) | C23 | 1 | 2 | yes | — |
| 76 | C22×#272 | C23 | 1 | 4 | yes | — |
| 77 | C22×(C3⋊D3)⋊C3 | C23 | 1 | 4 | yes | — |
| 78 | C22×(C3⋊D3)⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 79 | C2×((C3⋊D3)⋊C3)⋊C2 | C23 | 1 | 4 | yes | — |
| 80 | D4×H(3,𝔽3) | C23 | 1 | 4 | yes | — |
| 81 | C2×C4×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 82 | #6235 | C23 | 1 | 4 | yes | — |
| 83 | #6235 | C23 | 1 | 8 | yes | — |
| 84 | C2×#1084 | C23 | 1 | 4 | yes | — |
| 85 | C4⋊#272 | C23 | 1 | 2 | yes | — |
| 86 | C4×#272 | C23 | 1 | 4 | yes | — |
| 87 | #6229 | C23 | 1 | 2 | yes | — |
| 88 | #638⋊C3 | C23 | 1 | 4 | yes | — |
| 89 | #638⋊C3 | C23 | 1 | 8 | yes | — |
| 90 | #638⋊C3 | C23 | 1 | 8 | yes | — |
| 91 | C2×(C3⋊Dic3)⋊C3 | C23 | 1 | 4 | yes | — |
| 92 | C2×(C3⋊Dic3)⋊C3 | C23 | 1 | 4 | yes | — |
| 93 | C2×(C3⋊Dic3)⋊C3 | C23 | 1 | 4 | yes | — |
| 94 | C2×(C3⋊Dic3)⋊C3 | C23 | 1 | 2 | yes | — |
| 95 | C2×(C3⋊Dic3)⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 96 | C4⋊((C3⋊D3)⋊C3) | C23 | 1 | 2 | yes | — |
| 97 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 2 | yes | — |
| 98 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 4 | yes | — |
| 99 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 2 | yes | — |
| 100 | #634⋊C3 | C23 | 1 | 4 | yes | — |
| 101 | #634⋊C3 | C23 | 1 | 2 | yes | — |
| 102 | #6200 | C23 | 1 | 8 | yes | — |
| 103 | #6200 | C23 | 1 | 4 | yes | — |
| 104 | #6200 | C23 | 1 | 4 | yes | — |
| 105 | #6199 | C23 | 1 | 8 | yes | — |
| 106 | #6199 | C23 | 1 | 4 | yes | — |
| 107 | #6198 | C23 | 1 | 4 | yes | — |
| 108 | ((C3⋊D3)⋊C3)⋊C4 | C23 | 1 | 8 | yes | — |
| 109 | ((C3⋊D3)⋊C3)⋊C4 | C23 | 1 | 4 | yes | — |
| 110 | ((C3⋊D3)⋊C3)⋊C4 | C23 | 1 | 4 | yes | — |
| 111 | #6196 | C23 | 1 | 4 | yes | — |
| 112 | #6196 | C23 | 1 | 8 | yes | — |
| 113 | #5966 | — | 9 | 1 | no | — |
| 114 | #5966 | — | 9 | 1 | no | — |
| 115 | #5964 | — | 9 | 1 | no | — |
| 116 | C2×C32×D4 | — | 2 | 1 | no | — |
| 117 | C2×C32×D4 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 118 | C2×C32×D4 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 119 | C2×#638 | C2×D3 | 1 | 4 | yes | complemented |
| 120 | C2×#638 | C2×D3 | 1 | 2 | yes | complemented |
| 121 | C22×C3⋊Dic3 | C2×D3 | 1 | 2 | yes | complemented |
| 122 | #3830 | C2×D3 | 1 | 4 | yes | complemented |
| 123 | #3830 | C2×D3 | 1 | 4 | yes | complemented |
| 124 | #3830 | C2×D3 | 1 | 4 | yes | complemented |
| 125 | D4×C3⋊D3 | C2×D3 | 1 | 4 | yes | complemented |
| 126 | #3828 | C2×D3 | 1 | 2 | yes | complemented |
| 127 | C2×C4×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 128 | C2×#634 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 129 | C2×C3×#67 | — | 3 | 4 | no | — |
| 130 | C2×C3×#67 | — | 3 | 4 | no | — |
| 131 | C2×C3×#67 | — | 3 | 4 | no | — |
| 132 | C2×C3×#67 | — | 3 | 2 | no | — |
| 133 | C2×C3×#67 | — | 6 | 4 | no | — |
| 134 | C22×C3×Dic3 | — | 3 | 2 | no | — |
| 135 | C3×#237 | — | 3 | 4 | no | — |
| 136 | C3×#237 | — | 3 | 4 | no | — |
| 137 | C3×#237 | — | 3 | 4 | no | — |
| 138 | C3×#237 | — | 3 | 4 | no | — |
| 139 | C3×#237 | — | 3 | 4 | no | — |
| 140 | C3×#237 | — | 6 | 4 | no | — |
| 141 | C3×D3×D4 | — | 3 | 4 | no | — |
| 142 | C3×D3×D4 | — | 3 | 4 | no | — |
| 143 | C3×D3×D4 | — | 3 | 4 | no | — |
| 144 | C3×D3×D4 | — | 6 | 4 | no | — |
| 145 | C3×#235 | — | 3 | 2 | no | — |
| 146 | C3×#235 | — | 3 | 2 | no | — |
| 147 | C3×#235 | — | 3 | 2 | no | — |
| 148 | C3×#235 | — | 6 | 2 | no | — |
| 149 | C2×C3×C4×D3 | — | 3 | 1 | no | — |
| 150 | C2×C3×Dic6 | — | 3 | 1 | no | — |
| 151 | #3811 | — | 3 | 4 | no | — |
| 152 | #3811 | — | 3 | 8 | no | — |
| 153 | D3×#67 | — | 3 | 4 | no | — |
| 154 | D3×#67 | — | 3 | 8 | no | — |
| 155 | D3×#67 | — | 3 | 8 | no | — |
| 156 | D3×#67 | — | 3 | 8 | no | — |
| 157 | C2×#627 | — | 3 | 4 | no | — |
| 158 | C2×#627 | — | 3 | 4 | no | — |
| 159 | C2×#626 | — | 3 | 4 | no | — |
| 160 | C2×#625 | — | 3 | 4 | no | — |
| 161 | C2×#624 | — | 3 | 4 | no | — |
| 162 | #3805 | — | 3 | 8 | no | — |
| 163 | #3805 | — | 3 | 4 | no | — |
| 164 | #3805 | — | 3 | 8 | no | — |
| 165 | #3805 | — | 3 | 8 | no | — |
| 166 | #3805 | — | 3 | 8 | no | — |
| 167 | #3804 | — | 3 | 8 | no | — |
| 168 | #3804 | — | 3 | 4 | no | — |
| 169 | #3804 | — | 3 | 8 | no | — |
| 170 | #3804 | — | 3 | 8 | no | — |
| 171 | #3804 | — | 3 | 8 | no | — |
| 172 | #3804 | — | 3 | 8 | no | — |
| 173 | #3804 | — | 3 | 8 | no | — |
| 174 | C2×D3×Dic3 | — | 3 | 4 | no | — |
| 175 | C2×D3×Dic3 | — | 3 | 4 | no | — |
| 176 | C2×D3×Dic3 | — | 3 | 4 | no | — |
| 177 | #3802 | — | 3 | 2 | no | — |
| 178 | D3×D12 | — | 3 | 2 | no | — |
| 179 | C4×D32 | — | 3 | 4 | no | — |
| 180 | C4×D32 | — | 3 | 4 | no | — |
| 181 | #3799 | — | 3 | 4 | no | — |
| 182 | #3799 | — | 3 | 2 | no | — |
| 183 | #3798 | — | 3 | 4 | no | — |
| 184 | #3798 | — | 3 | 4 | no | — |
| 185 | #3797 | — | 3 | 4 | no | — |
| 186 | #3797 | — | 3 | 2 | no | — |
| 187 | #3796 | — | 3 | 4 | no | — |
| 188 | #3796 | — | 3 | 2 | no | — |
| 189 | #3796 | — | 3 | 2 | no | — |
| 190 | #3795 | — | 3 | 4 | no | — |
| 191 | #3795 | — | 3 | 4 | no | — |
| 192 | #3795 | — | 3 | 2 | no | — |
| 193 | D3×Dic6 | — | 3 | 4 | no | — |
| 194 | D3×Dic6 | — | 3 | 4 | no | — |
| 195 | D3×Dic6 | — | 3 | 4 | no | — |
| 196 | D3×Dic6 | — | 3 | 2 | no | — |
| 197 | C22×H(3,𝔽3) | — | 4 | 2 | no | — |
| 198 | C22×H(3,𝔽3) | C24 | 1 | 4 | yes | — |
| 199 | C22×H(3,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 200 | C2×#272 | — | 4 | 4 | no | — |
| 201 | C2×#272 | C24 | 1 | 4 | yes | — |
| 202 | C2×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 203 | C2×(C3⋊D3)⋊C3 | — | 4 | 4 | no | — |
| 204 | C2×(C3⋊D3)⋊C3 | C24 | 1 | 4 | yes | — |
| 205 | C2×(C3⋊D3)⋊C3 | C24 | 1 | 2 | yes | — |
| 206 | ((C3⋊D3)⋊C3)⋊C2 | — | 4 | 4 | no | — |
| 207 | C4×H(3,𝔽3) | C24 | 1 | 2 | yes | — |
| 208 | #1084 | C24 | 1 | 4 | yes | — |
| 209 | (C3⋊Dic3)⋊C3 | C24 | 1 | 1 | yes | characteristic |
| 210 | (C3⋊Dic3)⋊C3 | C24 | 1 | 4 | yes | — |
| 211 | (C3⋊Dic3)⋊C3 | C24 | 1 | 4 | yes | — |
| 212 | (C3⋊Dic3)⋊C3 | C24 | 1 | 1 | yes | characteristic |
| 213 | C3×H(5,𝔽2) | — | 9 | 1 | no | — |
| 214 | C3×H(5,𝔽2) | — | 9 | 1 | no | — |
| 215 | C2×C3×#41 | — | 9 | 1 | no | — |
| 216 | #1010 | — | 9 | 2 | no | — |
| 217 | #1010 | — | 9 | 2 | no | — |
| 218 | #1010 | — | 9 | 4 | no | — |
| 219 | #1010 | — | 9 | 4 | no | — |
| 220 | #1010 | — | 9 | 4 | no | — |
| 221 | #1009 | — | 9 | 4 | no | — |
| 222 | D3×#41 | — | 9 | 2 | no | — |
| 223 | D3×#41 | — | 9 | 2 | no | — |
| 224 | D3×#41 | — | 9 | 4 | no | — |
| 225 | D3×#41 | — | 9 | 4 | no | — |
| 226 | D3×#41 | — | 9 | 4 | no | — |
| 227 | D3×#41 | — | 9 | 4 | no | — |
| 228 | #1007 | — | 9 | 2 | no | — |
| 229 | #1004 | — | 3 | 1 | no | — |
| 230 | #1004 | — | 3 | 1 | no | — |
| 231 | #1004 | — | 3 | 1 | no | — |
| 232 | #1004 | — | 6 | 1 | no | — |
| 233 | #1004 | — | 9 | 1 | no | — |
| 234 | #1004 | — | 9 | 4 | no | — |
| 235 | #1004 | — | 9 | 4 | no | — |
| 236 | #1004 | — | 9 | 4 | no | — |
| 237 | #1004 | — | 9 | 4 | no | — |
| 238 | #1004 | — | 9 | 4 | no | — |
| 239 | C2×#237 | — | 3 | 1 | no | — |
| 240 | C2×#237 | — | 9 | 1 | no | — |
| 241 | C2×#237 | — | 9 | 4 | no | — |
| 242 | C2×#237 | — | 9 | 4 | no | — |
| 243 | C2×#237 | — | 9 | 4 | no | — |
| 244 | C2×#237 | — | 9 | 4 | no | — |
| 245 | C2×#235 | — | 9 | 2 | no | — |
| 246 | C2×#235 | — | 9 | 4 | no | — |
| 247 | C23×C32 | — | 2 | 2 | no | — |
| 248 | C23×C32 | C22×D3 | 1 | 2 | yes | — |
| 249 | C23×C32 | C22×D3 | 1 | 2 | yes | — |
| 250 | C22×C3⋊D3 | C22×D3 | 1 | 4 | yes | — |
| 251 | C22×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 252 | C22×C3×D3 | — | 3 | 4 | no | — |
| 253 | C22×C3×D3 | — | 3 | 1 | no | — |
| 254 | C22×C3×D3 | — | 3 | 4 | no | — |
| 255 | C22×C3×D3 | — | 3 | 4 | no | — |
| 256 | C22×C3×D3 | — | 6 | 4 | no | — |
| 257 | C2×D32 | — | 3 | 4 | no | — |
| 258 | C2×D32 | — | 3 | 4 | no | — |
| 259 | C32×D4 | — | 2 | 4 | no | — |
| 260 | C32×D4 | C22×D3 | 1 | 4 | yes | — |
| 261 | C32×D4 | C22×D3 | 1 | 4 | yes | — |
| 262 | C2×C32×C4 | — | 2 | 1 | no | — |
| 263 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 264 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 265 | #638 | C22×D3 | 1 | 4 | yes | — |
| 266 | #638 | C22×D3 | 1 | 8 | yes | — |
| 267 | #638 | C22×D3 | 1 | 8 | yes | — |
| 268 | C2×C3⋊Dic3 | C22×D3 | 1 | 4 | yes | — |
| 269 | C2×C3⋊Dic3 | C22×D3 | 1 | 4 | yes | — |
| 270 | C2×C3⋊Dic3 | C22×D3 | 1 | 2 | yes | — |
| 271 | C2×C3⋊Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 272 | C2×C3⋊Dic3 | C22×D3 | 1 | 4 | yes | — |
| 273 | C4⋊(C3⋊D3) | C22×D3 | 1 | 2 | yes | — |
| 274 | C4×C3⋊D3 | C22×D3 | 1 | 2 | yes | — |
| 275 | C4×C3⋊D3 | C22×D3 | 1 | 4 | yes | — |
| 276 | C4×C3⋊D3 | C22×D3 | 1 | 2 | yes | — |
| 277 | #634 | C22×D3 | 1 | 2 | yes | — |
| 278 | #634 | C22×D3 | 1 | 4 | yes | — |
| 279 | C3×#67 | — | 3 | 8 | no | — |
| 280 | C3×#67 | — | 3 | 8 | no | — |
| 281 | C3×#67 | — | 3 | 4 | no | — |
| 282 | C3×#67 | — | 3 | 4 | no | — |
| 283 | C3×#67 | — | 3 | 8 | no | — |
| 284 | C3×#67 | — | 3 | 8 | no | — |
| 285 | C3×#67 | — | 3 | 4 | no | — |
| 286 | C3×#67 | — | 6 | 4 | no | — |
| 287 | C3×#67 | — | 6 | 8 | no | — |
| 288 | C2×C3×Dic3 | — | 3 | 4 | no | — |
| 289 | C2×C3×Dic3 | — | 3 | 4 | no | — |
| 290 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 291 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 292 | C2×C3×Dic3 | — | 3 | 4 | no | — |
| 293 | C2×C3×Dic3 | — | 3 | 4 | no | — |
| 294 | C2×C3×Dic3 | — | 3 | 4 | no | — |
| 295 | C2×C3×Dic3 | — | 6 | 4 | no | — |
| 296 | C3×D12 | — | 3 | 2 | no | — |
| 297 | C3×D12 | — | 3 | 2 | no | — |
| 298 | C3×D12 | — | 3 | 2 | no | — |
| 299 | C3×D12 | — | 6 | 2 | no | — |
| 300 | C3×C4×D3 | — | 3 | 4 | no | — |
| 301 | C3×C4×D3 | — | 3 | 2 | no | — |
| 302 | C3×C4×D3 | — | 3 | 2 | no | — |
| 303 | C3×C4×D3 | — | 3 | 4 | no | — |
| 304 | C3×C4×D3 | — | 3 | 4 | no | — |
| 305 | C3×C4×D3 | — | 6 | 4 | no | — |
| 306 | C3×Dic6 | — | 3 | 2 | no | — |
| 307 | C3×Dic6 | — | 3 | 4 | no | — |
| 308 | C3×Dic6 | — | 3 | 2 | no | — |
| 309 | C3×Dic6 | — | 3 | 2 | no | — |
| 310 | C3×Dic6 | — | 6 | 2 | no | — |
| 311 | #627 | — | 3 | 8 | no | — |
| 312 | #627 | — | 3 | 8 | no | — |
| 313 | #627 | — | 3 | 4 | no | — |
| 314 | #627 | — | 3 | 4 | no | — |
| 315 | #626 | — | 3 | 4 | no | — |
| 316 | #626 | — | 3 | 4 | no | — |
| 317 | #626 | — | 3 | 4 | no | — |
| 318 | #626 | — | 3 | 8 | no | — |
| 319 | #626 | — | 3 | 4 | no | — |
| 320 | #625 | — | 3 | 8 | no | — |
| 321 | #625 | — | 3 | 4 | no | — |
| 322 | #625 | — | 3 | 4 | no | — |
| 323 | #624 | — | 3 | 8 | no | — |
| 324 | #624 | — | 3 | 4 | no | — |
| 325 | #624 | — | 3 | 4 | no | — |
| 326 | D3×Dic3 | — | 3 | 8 | no | — |
| 327 | D3×Dic3 | — | 3 | 4 | no | — |
| 328 | D3×Dic3 | — | 3 | 4 | no | — |
| 329 | D3×Dic3 | — | 3 | 8 | no | — |
| 330 | D3×Dic3 | — | 3 | 8 | no | — |
| 331 | D3×Dic3 | — | 3 | 4 | no | — |
| 332 | D3×Dic3 | — | 3 | 4 | no | — |
| 333 | #585 | — | 27 | 1 | no | Sylow |
| 334 | C2×H(3,𝔽3) | — | 2 | 4 | no | — |
| 335 | C2×H(3,𝔽3) | — | 2 | 1 | no | — |
| 336 | C2×H(3,𝔽3) | C25 | 1 | 1 | yes | characteristic |
| 337 | #272 | — | 2 | 4 | no | — |
| 338 | (C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 339 | (C3⋊D3)⋊C3 | — | 2 | 4 | no | — |
| 340 | C3×#41 | — | 9 | 2 | no | — |
| 341 | C3×#41 | — | 9 | 4 | no | — |
| 342 | C3×#41 | — | 9 | 4 | no | — |
| 343 | C3×#41 | — | 9 | 4 | no | — |
| 344 | C3×#41 | — | 9 | 4 | no | — |
| 345 | C3×#41 | — | 9 | 2 | no | — |
| 346 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 347 | C2×C3×D4 | — | 3 | 1 | no | — |
| 348 | C2×C3×D4 | — | 3 | 1 | no | — |
| 349 | C2×C3×D4 | — | 6 | 1 | no | — |
| 350 | C2×C3×D4 | — | 9 | 4 | no | — |
| 351 | C2×C3×D4 | — | 9 | 4 | no | — |
| 352 | C2×C3×D4 | — | 9 | 2 | no | — |
| 353 | C2×C3×D4 | — | 9 | 4 | no | — |
| 354 | C2×C3×D4 | — | 9 | 4 | no | — |
| 355 | C2×C3×D4 | D32 | 1 | 1 | yes | characteristic |
| 356 | C22×C3×C4 | — | 9 | 1 | no | — |
| 357 | C22×C3×C4 | — | 9 | 2 | no | — |
| 358 | C2×#67 | — | 3 | 4 | no | — |
| 359 | C2×#67 | — | 3 | 4 | no | — |
| 360 | C2×#67 | — | 3 | 2 | no | — |
| 361 | C2×#67 | — | 3 | 4 | no | — |
| 362 | C2×#67 | — | 6 | 4 | no | — |
| 363 | C2×#67 | — | 9 | 4 | no | — |
| 364 | C2×#67 | — | 9 | 2 | no | — |
| 365 | C2×#67 | — | 9 | 4 | no | — |
| 366 | C2×#67 | — | 9 | 8 | no | — |
| 367 | C2×#67 | — | 9 | 4 | no | — |
| 368 | C2×#67 | — | 9 | 8 | no | — |
| 369 | C2×#67 | — | 9 | 4 | no | — |
| 370 | C22×Dic3 | — | 3 | 2 | no | — |
| 371 | C22×Dic3 | — | 9 | 2 | no | — |
| 372 | C22×Dic3 | — | 9 | 4 | no | — |
| 373 | C22×Dic3 | — | 9 | 4 | no | — |
| 374 | #239 | — | 9 | 2 | no | — |
| 375 | #239 | — | 9 | 4 | no | — |
| 376 | #239 | — | 9 | 4 | no | — |
| 377 | #239 | — | 9 | 2 | no | — |
| 378 | D3×Q8 | — | 9 | 4 | no | — |
| 379 | D3×Q8 | — | 9 | 2 | no | — |
| 380 | D3×Q8 | — | 9 | 4 | no | — |
| 381 | D3×Q8 | — | 9 | 2 | no | — |
| 382 | D3×Q8 | — | 9 | 4 | no | — |
| 383 | D3×Q8 | — | 9 | 4 | no | — |
| 384 | #237 | — | 3 | 4 | no | — |
| 385 | #237 | — | 3 | 4 | no | — |
| 386 | #237 | — | 3 | 4 | no | — |
| 387 | #237 | — | 3 | 4 | no | — |
| 388 | #237 | — | 3 | 4 | no | — |
| 389 | #237 | — | 6 | 4 | no | — |
| 390 | #237 | — | 9 | 4 | no | — |
| 391 | #237 | — | 9 | 4 | no | — |
| 392 | #237 | — | 9 | 4 | no | — |
| 393 | #237 | — | 9 | 2 | no | — |
| 394 | #237 | — | 9 | 4 | no | — |
| 395 | #237 | — | 9 | 2 | no | — |
| 396 | #237 | — | 9 | 4 | no | — |
| 397 | #237 | — | 9 | 4 | no | — |
| 398 | #237 | — | 9 | 8 | no | — |
| 399 | #237 | — | 9 | 8 | no | — |
| 400 | #237 | — | 9 | 8 | no | — |
| 401 | #237 | — | 9 | 8 | no | — |
| 402 | #237 | — | 9 | 8 | no | — |
| 403 | #237 | — | 9 | 8 | no | — |
| 404 | #237 | — | 9 | 4 | no | — |
| 405 | #237 | — | 9 | 8 | no | — |
| 406 | #237 | — | 9 | 8 | no | — |
| 407 | #237 | — | 9 | 8 | no | — |
| 408 | #237 | — | 9 | 8 | no | — |
| 409 | D3×D4 | — | 3 | 4 | no | — |
| 410 | D3×D4 | — | 3 | 4 | no | — |
| 411 | D3×D4 | — | 3 | 4 | no | — |
| 412 | D3×D4 | — | 6 | 4 | no | — |
| 413 | D3×D4 | — | 9 | 4 | no | — |
| 414 | D3×D4 | — | 9 | 2 | no | — |
| 415 | D3×D4 | — | 9 | 2 | no | — |
| 416 | D3×D4 | — | 9 | 4 | no | — |
| 417 | D3×D4 | — | 9 | 8 | no | — |
| 418 | D3×D4 | — | 9 | 4 | no | — |
| 419 | D3×D4 | — | 9 | 8 | no | — |
| 420 | D3×D4 | — | 9 | 8 | no | — |
| 421 | D3×D4 | — | 9 | 8 | no | — |
| 422 | #235 | — | 3 | 2 | no | — |
| 423 | #235 | — | 3 | 2 | no | — |
| 424 | #235 | — | 3 | 2 | no | — |
| 425 | #235 | — | 6 | 2 | no | — |
| 426 | #235 | — | 9 | 2 | no | — |
| 427 | #235 | — | 9 | 4 | no | — |
| 428 | #235 | — | 9 | 2 | no | — |
| 429 | #235 | — | 9 | 4 | no | — |
| 430 | #235 | — | 9 | 4 | no | — |
| 431 | #235 | — | 9 | 4 | no | — |
| 432 | #235 | — | 9 | 2 | no | — |
| 433 | #235 | — | 9 | 4 | no | — |
| 434 | #235 | — | 9 | 8 | no | — |
| 435 | #235 | — | 9 | 4 | no | — |
| 436 | #235 | — | 9 | 8 | no | — |
| 437 | #235 | — | 9 | 8 | no | — |
| 438 | #235 | — | 9 | 8 | no | — |
| 439 | #235 | — | 9 | 8 | no | — |
| 440 | C2×D12 | — | 9 | 2 | no | — |
| 441 | C2×D12 | — | 9 | 4 | no | — |
| 442 | C2×C4×D3 | — | 3 | 1 | no | — |
| 443 | C2×C4×D3 | — | 9 | 1 | no | — |
| 444 | C2×C4×D3 | — | 9 | 4 | no | — |
| 445 | C2×C4×D3 | — | 9 | 4 | no | — |
| 446 | C2×C4×D3 | — | 9 | 4 | no | — |
| 447 | C2×C4×D3 | — | 9 | 4 | no | — |
| 448 | C2×C4×D3 | — | 9 | 4 | no | — |
| 449 | C2×C4×D3 | — | 9 | 4 | no | — |
| 450 | C2×C4×D3 | — | 9 | 4 | no | — |
| 451 | C2×Dic6 | — | 3 | 1 | no | — |
| 452 | C2×Dic6 | — | 9 | 1 | no | — |
| 453 | C2×Dic6 | — | 9 | 4 | no | — |
| 454 | C2×Dic6 | — | 9 | 2 | no | — |
| 455 | C2×Dic6 | — | 9 | 4 | no | — |
| 456 | C2×Dic6 | — | 9 | 4 | no | — |
| 457 | C2×Dic6 | — | 9 | 4 | no | — |
| 458 | C2×Dic6 | — | 9 | 4 | no | — |
| 459 | C22×C32 | — | 2 | 4 | no | — |
| 460 | C22×C32 | — | 2 | 1 | no | — |
| 461 | C22×C32 | — | 4 | 2 | no | — |
| 462 | C22×C32 | — | 4 | 2 | no | — |
| 463 | C22×C32 | — | 8 | 2 | no | — |
| 464 | C22×C32 | C23×D3 | 1 | 4 | yes | — |
| 465 | C22×C32 | C23×D3 | 1 | 1 | yes | characteristic |
| 466 | C22×C32 | C23×D3 | 1 | 4 | yes | — |
| 467 | C22×C32 | C23×D3 | 1 | 1 | yes | characteristic |
| 468 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 469 | C2×C3⋊D3 | — | 4 | 4 | no | — |
| 470 | C2×C3⋊D3 | C23×D3 | 1 | 4 | yes | — |
| 471 | C2×C3⋊D3 | C23×D3 | 1 | 2 | yes | — |
| 472 | C2×C3×D3 | — | 3 | 4 | no | — |
| 473 | C2×C3×D3 | — | 3 | 2 | no | — |
| 474 | C2×C3×D3 | — | 3 | 4 | no | — |
| 475 | C2×C3×D3 | — | 3 | 4 | no | — |
| 476 | C2×C3×D3 | — | 6 | 4 | no | — |
| 477 | C2×C3×D3 | — | 12 | 4 | no | — |
| 478 | C2×C3×D3 | — | 12 | 1 | no | — |
| 479 | C2×C3×D3 | — | 12 | 4 | no | — |
| 480 | C2×C3×D3 | — | 12 | 4 | no | — |
| 481 | C2×C3×D3 | — | 24 | 4 | no | — |
| 482 | D32 | — | 12 | 4 | no | — |
| 483 | D32 | — | 12 | 4 | no | — |
| 484 | C32×C4 | — | 2 | 2 | no | — |
| 485 | C32×C4 | C23×D3 | 1 | 2 | yes | — |
| 486 | C32×C4 | C23×D3 | 1 | 2 | yes | — |
| 487 | C3⋊Dic3 | C23×D3 | 1 | 1 | yes | characteristic |
| 488 | C3⋊Dic3 | C23×D3 | 1 | 4 | yes | — |
| 489 | C3⋊Dic3 | C23×D3 | 1 | 4 | yes | — |
| 490 | C3⋊Dic3 | C23×D3 | 1 | 1 | yes | characteristic |
| 491 | C3×Dic3 | — | 3 | 1 | no | — |
| 492 | C3×Dic3 | — | 3 | 4 | no | — |
| 493 | C3×Dic3 | — | 3 | 4 | no | — |
| 494 | C3×Dic3 | — | 3 | 1 | no | — |
| 495 | C3×Dic3 | — | 3 | 4 | no | — |
| 496 | C3×Dic3 | — | 3 | 4 | no | — |
| 497 | C3×Dic3 | — | 6 | 4 | no | — |
| 498 | 2−1+4 | — | 27 | 2 | no | — |
| 499 | 2−1+4 | — | 27 | 4 | no | — |
| 500 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 501 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 502 | H(5,𝔽2) | — | 27 | 4 | no | — |
| 503 | H(5,𝔽2) | — | 27 | 4 | no | — |
| 504 | C2×#41 | — | 9 | 1 | no | — |
| 505 | C2×#41 | — | 27 | 4 | no | — |
| 506 | C2×#41 | — | 27 | 2 | no | — |
| 507 | C2×#41 | — | 27 | 4 | no | — |
| 508 | C2×#41 | — | 27 | 4 | no | — |
| 509 | H(3,𝔽3) | #585 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 510 | C23×C3 | — | 3 | 2 | no | — |
| 511 | C23×C3 | — | 3 | 2 | no | — |
| 512 | C23×C3 | — | 6 | 2 | no | — |
| 513 | C23×C3 | — | 9 | 4 | no | — |
| 514 | C23×C3 | — | 9 | 1 | no | — |
| 515 | C23×C3 | — | 9 | 4 | no | — |
| 516 | C23×C3 | C2×D32 | 1 | 2 | yes | — |
| 517 | C22×D3 | — | 3 | 4 | no | — |
| 518 | C22×D3 | — | 3 | 4 | no | — |
| 519 | C22×D3 | — | 3 | 1 | no | — |
| 520 | C22×D3 | — | 3 | 4 | no | — |
| 521 | C22×D3 | — | 6 | 4 | no | — |
| 522 | C22×D3 | — | 9 | 4 | no | — |
| 523 | C22×D3 | — | 9 | 1 | no | — |
| 524 | C22×D3 | — | 9 | 4 | no | — |
| 525 | C22×D3 | — | 9 | 4 | no | — |
| 526 | C22×D3 | — | 9 | 4 | no | — |
| 527 | C3×Q8 | — | 9 | 2 | no | — |
| 528 | C3×Q8 | — | 9 | 4 | no | — |
| 529 | C3×Q8 | — | 9 | 2 | no | — |
| 530 | C3×D4 | — | 3 | 4 | no | — |
| 531 | C3×D4 | — | 3 | 4 | no | — |
| 532 | C3×D4 | — | 6 | 4 | no | — |
| 533 | C3×D4 | — | 9 | 2 | no | — |
| 534 | C3×D4 | — | 9 | 8 | no | — |
| 535 | C3×D4 | — | 9 | 8 | no | — |
| 536 | C3×D4 | — | 9 | 4 | no | — |
| 537 | C3×D4 | — | 9 | 8 | no | — |
| 538 | C3×D4 | — | 9 | 4 | no | — |
| 539 | C3×D4 | — | 9 | 2 | no | — |
| 540 | C3×D4 | C2×D32 | 1 | 4 | yes | — |
| 541 | C2×C3×C4 | — | 3 | 1 | no | — |
| 542 | C2×C3×C4 | — | 3 | 1 | no | — |
| 543 | C2×C3×C4 | — | 6 | 1 | no | — |
| 544 | C2×C3×C4 | — | 9 | 4 | no | — |
| 545 | C2×C3×C4 | — | 9 | 2 | no | — |
| 546 | C2×C3×C4 | — | 9 | 2 | no | — |
| 547 | C2×C3×C4 | — | 9 | 4 | no | — |
| 548 | C2×C3×C4 | — | 9 | 4 | no | — |
| 549 | C2×C3×C4 | — | 9 | 4 | no | — |
| 550 | C2×C3×C4 | — | 9 | 1 | no | — |
| 551 | C2×C3×C4 | — | 9 | 2 | no | — |
| 552 | C2×C3×C4 | — | 9 | 4 | no | — |
| 553 | C2×C3×C4 | — | 9 | 4 | no | — |
| 554 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 555 | #67 | — | 3 | 4 | no | — |
| 556 | #67 | — | 3 | 4 | no | — |
| 557 | #67 | — | 3 | 8 | no | — |
| 558 | #67 | — | 3 | 8 | no | — |
| 559 | #67 | — | 3 | 4 | no | — |
| 560 | #67 | — | 3 | 8 | no | — |
| 561 | #67 | — | 3 | 8 | no | — |
| 562 | #67 | — | 6 | 4 | no | — |
| 563 | #67 | — | 6 | 8 | no | — |
| 564 | #67 | — | 9 | 4 | no | — |
| 565 | #67 | — | 9 | 8 | no | — |
| 566 | #67 | — | 9 | 8 | no | — |
| 567 | #67 | — | 9 | 8 | no | — |
| 568 | #67 | — | 9 | 4 | no | — |
| 569 | #67 | — | 9 | 4 | no | — |
| 570 | #67 | — | 9 | 4 | no | — |
| 571 | #67 | — | 9 | 4 | no | — |
| 572 | #67 | — | 9 | 4 | no | — |
| 573 | #67 | — | 9 | 8 | no | — |
| 574 | #67 | — | 9 | 4 | no | — |
| 575 | C2×Dic3 | — | 3 | 4 | no | — |
| 576 | C2×Dic3 | — | 3 | 4 | no | — |
| 577 | C2×Dic3 | — | 3 | 2 | no | — |
| 578 | C2×Dic3 | — | 3 | 4 | no | — |
| 579 | C2×Dic3 | — | 3 | 4 | no | — |
| 580 | C2×Dic3 | — | 3 | 1 | no | — |
| 581 | C2×Dic3 | — | 3 | 4 | no | — |
| 582 | C2×Dic3 | — | 6 | 4 | no | — |
| 583 | C2×Dic3 | — | 9 | 4 | no | — |
| 584 | C2×Dic3 | — | 9 | 2 | no | — |
| 585 | C2×Dic3 | — | 9 | 4 | no | — |
| 586 | C2×Dic3 | — | 9 | 1 | no | — |
| 587 | C2×Dic3 | — | 9 | 4 | no | — |
| 588 | C2×Dic3 | — | 9 | 8 | no | — |
| 589 | C2×Dic3 | — | 9 | 4 | no | — |
| 590 | C2×Dic3 | — | 9 | 4 | no | — |
| 591 | C2×Dic3 | — | 9 | 8 | no | — |
| 592 | C2×Dic3 | — | 9 | 4 | no | — |
| 593 | D12 | — | 3 | 2 | no | — |
| 594 | D12 | — | 3 | 2 | no | — |
| 595 | D12 | — | 3 | 2 | no | — |
| 596 | D12 | — | 6 | 2 | no | — |
| 597 | D12 | — | 9 | 2 | no | — |
| 598 | D12 | — | 9 | 4 | no | — |
| 599 | D12 | — | 9 | 4 | no | — |
| 600 | D12 | — | 9 | 8 | no | — |
| 601 | D12 | — | 9 | 4 | no | — |
| 602 | C4×D3 | — | 3 | 4 | no | — |
| 603 | C4×D3 | — | 3 | 4 | no | — |
| 604 | C4×D3 | — | 3 | 2 | no | — |
| 605 | C4×D3 | — | 3 | 2 | no | — |
| 606 | C4×D3 | — | 3 | 4 | no | — |
| 607 | C4×D3 | — | 6 | 4 | no | — |
| 608 | C4×D3 | — | 9 | 2 | no | — |
| 609 | C4×D3 | — | 9 | 2 | no | — |
| 610 | C4×D3 | — | 9 | 4 | no | — |
| 611 | C4×D3 | — | 9 | 4 | no | — |
| 612 | C4×D3 | — | 9 | 8 | no | — |
| 613 | C4×D3 | — | 9 | 4 | no | — |
| 614 | C4×D3 | — | 9 | 4 | no | — |
| 615 | C4×D3 | — | 9 | 4 | no | — |
| 616 | C4×D3 | — | 9 | 8 | no | — |
| 617 | C4×D3 | — | 9 | 4 | no | — |
| 618 | C4×D3 | — | 9 | 4 | no | — |
| 619 | C4×D3 | — | 9 | 8 | no | — |
| 620 | C4×D3 | — | 9 | 8 | no | — |
| 621 | Dic6 | — | 3 | 2 | no | — |
| 622 | Dic6 | — | 3 | 2 | no | — |
| 623 | Dic6 | — | 3 | 4 | no | — |
| 624 | Dic6 | — | 3 | 2 | no | — |
| 625 | Dic6 | — | 6 | 2 | no | — |
| 626 | Dic6 | — | 9 | 4 | no | — |
| 627 | Dic6 | — | 9 | 2 | no | — |
| 628 | Dic6 | — | 9 | 8 | no | — |
| 629 | Dic6 | — | 9 | 4 | no | — |
| 630 | Dic6 | — | 9 | 4 | no | — |
| 631 | Dic6 | — | 9 | 8 | no | — |
| 632 | Dic6 | — | 9 | 4 | no | — |
| 633 | Dic6 | — | 9 | 8 | no | — |
| 634 | C2×C32 | — | 2 | 4 | no | — |
| 635 | C2×C32 | — | 2 | 1 | no | — |
| 636 | C2×C32 | — | 2 | 4 | no | — |
| 637 | C2×C32 | — | 2 | 1 | no | — |
| 638 | C2×C32 | — | 2 | 1 | no | — |
| 639 | C2×C32 | — | 4 | 4 | no | — |
| 640 | C2×C32 | — | 4 | 1 | no | — |
| 641 | C2×C32 | C24×D3 | 1 | 1 | yes | characteristic |
| 642 | C2×C32 | C24×D3 | 1 | 1 | yes | characteristic |
| 643 | C3⋊D3 | — | 2 | 2 | no | — |
| 644 | C3⋊D3 | — | 2 | 4 | no | — |
| 645 | C3×D3 | — | 6 | 4 | no | — |
| 646 | C3×D3 | — | 6 | 4 | no | — |
| 647 | C3×D3 | — | 6 | 2 | no | — |
| 648 | C3×D3 | — | 6 | 4 | no | — |
| 649 | C3×D3 | — | 12 | 4 | no | — |
| 650 | #41 | — | 9 | 4 | no | — |
| 651 | #41 | — | 9 | 4 | no | — |
| 652 | #41 | — | 9 | 4 | no | — |
| 653 | #41 | — | 9 | 4 | no | — |
| 654 | #41 | — | 9 | 2 | no | — |
| 655 | #41 | — | 9 | 2 | no | — |
| 656 | #41 | — | 27 | 4 | no | — |
| 657 | #41 | — | 27 | 4 | no | — |
| 658 | #41 | — | 27 | 8 | no | — |
| 659 | #41 | — | 27 | 8 | no | — |
| 660 | #41 | — | 27 | 8 | no | — |
| 661 | #41 | — | 27 | 8 | no | — |
| 662 | #41 | — | 27 | 8 | no | — |
| 663 | #41 | — | 27 | 2 | no | — |
| 664 | #41 | — | 27 | 2 | no | — |
| 665 | #41 | — | 27 | 4 | no | — |
| 666 | #41 | — | 27 | 4 | no | — |
| 667 | C2×Q8 | — | 9 | 1 | no | — |
| 668 | C2×Q8 | — | 27 | 4 | no | — |
| 669 | C2×Q8 | — | 27 | 2 | no | — |
| 670 | C2×Q8 | — | 27 | 4 | no | — |
| 671 | C2×Q8 | — | 27 | 4 | no | — |
| 672 | C2×D4 | — | 9 | 2 | no | — |
| 673 | C2×D4 | — | 9 | 4 | no | — |
| 674 | C2×D4 | — | 9 | 4 | no | — |
| 675 | C2×D4 | — | 9 | 4 | no | — |
| 676 | C2×D4 | — | 9 | 4 | no | — |
| 677 | C2×D4 | — | 27 | 2 | no | — |
| 678 | C2×D4 | — | 27 | 4 | no | — |
| 679 | C2×D4 | — | 27 | 4 | no | — |
| 680 | C2×D4 | — | 27 | 8 | no | — |
| 681 | C2×D4 | — | 27 | 8 | no | — |
| 682 | C2×D4 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 683 | C22×C4 | — | 9 | 2 | no | — |
| 684 | C22×C4 | — | 9 | 1 | no | — |
| 685 | C22×C4 | — | 27 | 4 | no | — |
| 686 | C22×C4 | — | 27 | 4 | no | — |
| 687 | C22×C4 | — | 27 | 4 | no | — |
| 688 | C22×C3 | — | 3 | 4 | no | — |
| 689 | C22×C3 | — | 3 | 4 | no | — |
| 690 | C22×C3 | — | 3 | 1 | no | — |
| 691 | C22×C3 | — | 3 | 1 | no | — |
| 692 | C22×C3 | — | 4 | 2 | no | — |
| 693 | C22×C3 | — | 6 | 4 | no | — |
| 694 | C22×C3 | — | 6 | 1 | no | — |
| 695 | C22×C3 | — | 9 | 4 | no | — |
| 696 | C22×C3 | — | 9 | 2 | no | — |
| 697 | C22×C3 | — | 9 | 4 | no | — |
| 698 | C22×C3 | — | 12 | 2 | no | — |
| 699 | C22×C3 | — | 12 | 2 | no | — |
| 700 | C22×C3 | — | 24 | 2 | no | — |
| 701 | C22×C3 | — | 36 | 4 | no | — |
| 702 | C22×C3 | — | 36 | 4 | no | — |
| 703 | C22×C3 | — | 36 | 1 | no | — |
| 704 | C22×C3 | C22×D32 | 1 | 4 | yes | — |
| 705 | C22×C3 | C22×D32 | 1 | 1 | yes | characteristic |
| 706 | C2×D3 | — | 3 | 4 | no | — |
| 707 | C2×D3 | — | 3 | 4 | no | — |
| 708 | C2×D3 | — | 3 | 2 | no | — |
| 709 | C2×D3 | — | 3 | 4 | no | — |
| 710 | C2×D3 | — | 6 | 4 | no | — |
| 711 | C2×D3 | — | 9 | 4 | no | — |
| 712 | C2×D3 | — | 9 | 2 | no | — |
| 713 | C2×D3 | — | 12 | 4 | no | — |
| 714 | C2×D3 | — | 12 | 1 | no | — |
| 715 | C2×D3 | — | 12 | 4 | no | — |
| 716 | C2×D3 | — | 12 | 4 | no | — |
| 717 | C2×D3 | — | 24 | 4 | no | — |
| 718 | C2×D3 | — | 36 | 4 | no | — |
| 719 | C2×D3 | — | 36 | 1 | no | — |
| 720 | C2×D3 | — | 36 | 4 | no | — |
| 721 | C2×D3 | — | 36 | 4 | no | — |
| 722 | C2×D3 | — | 36 | 4 | no | — |
| 723 | C3×C4 | — | 3 | 2 | no | — |
| 724 | C3×C4 | — | 3 | 2 | no | — |
| 725 | C3×C4 | — | 6 | 2 | no | — |
| 726 | C3×C4 | — | 9 | 1 | no | — |
| 727 | C3×C4 | — | 9 | 4 | no | — |
| 728 | C3×C4 | — | 9 | 4 | no | — |
| 729 | C3×C4 | — | 9 | 1 | no | — |
| 730 | C3×C4 | — | 9 | 4 | no | — |
| 731 | C3×C4 | C22×D32 | 1 | 2 | yes | — |
| 732 | Dic3 | — | 3 | 4 | no | — |
| 733 | Dic3 | — | 3 | 4 | no | — |
| 734 | Dic3 | — | 3 | 4 | no | — |
| 735 | Dic3 | — | 3 | 4 | no | — |
| 736 | Dic3 | — | 3 | 1 | no | — |
| 737 | Dic3 | — | 3 | 1 | no | — |
| 738 | Dic3 | — | 6 | 4 | no | — |
| 739 | Dic3 | — | 9 | 4 | no | — |
| 740 | Dic3 | — | 9 | 1 | no | — |
| 741 | Dic3 | — | 9 | 4 | no | — |
| 742 | Dic3 | — | 9 | 1 | no | — |
| 743 | C32 | — | 2 | 1 | no | — |
| 744 | C32 | #5964 | 1 | 1 | yes | characteristic, complemented |
| 745 | C32 | #5966 | 1 | 1 | yes | characteristic, complemented |
| 746 | C23 | — | 9 | 1 | no | — |
| 747 | C23 | — | 9 | 4 | no | — |
| 748 | C23 | — | 9 | 4 | no | — |
| 749 | C23 | — | 27 | 4 | no | — |
| 750 | C23 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 2 | yes | — |
| 751 | Q8 | — | 9 | 4 | no | — |
| 752 | Q8 | — | 9 | 2 | no | — |
| 753 | Q8 | — | 9 | 2 | no | — |
| 754 | Q8 | — | 27 | 4 | no | — |
| 755 | Q8 | — | 27 | 8 | no | — |
| 756 | D4 | — | 9 | 8 | no | — |
| 757 | D4 | — | 9 | 4 | no | — |
| 758 | D4 | — | 9 | 8 | no | — |
| 759 | D4 | — | 9 | 4 | no | — |
| 760 | D4 | — | 9 | 8 | no | — |
| 761 | D4 | — | 9 | 2 | no | — |
| 762 | D4 | — | 9 | 2 | no | — |
| 763 | D4 | — | 27 | 4 | no | — |
| 764 | D4 | — | 27 | 4 | no | — |
| 765 | D4 | — | 27 | 4 | no | — |
| 766 | D4 | — | 27 | 8 | no | — |
| 767 | D4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 4 | yes | — |
| 768 | C2×C4 | — | 9 | 1 | no | — |
| 769 | C2×C4 | — | 9 | 4 | no | — |
| 770 | C2×C4 | — | 9 | 2 | no | — |
| 771 | C2×C4 | — | 9 | 4 | no | — |
| 772 | C2×C4 | — | 9 | 4 | no | — |
| 773 | C2×C4 | — | 9 | 4 | no | — |
| 774 | C2×C4 | — | 9 | 2 | no | — |
| 775 | C2×C4 | — | 9 | 2 | no | — |
| 776 | C2×C4 | — | 9 | 4 | no | — |
| 777 | C2×C4 | — | 9 | 4 | no | — |
| 778 | C2×C4 | — | 27 | 4 | no | — |
| 779 | C2×C4 | — | 27 | 4 | no | — |
| 780 | C2×C4 | — | 27 | 4 | no | — |
| 781 | C2×C4 | — | 27 | 8 | no | — |
| 782 | C2×C4 | — | 27 | 8 | no | — |
| 783 | C2×C4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 784 | C2×C3 | — | 2 | 1 | no | — |
| 785 | C2×C3 | — | 2 | 4 | no | — |
| 786 | C2×C3 | — | 3 | 1 | no | — |
| 787 | C2×C3 | — | 3 | 1 | no | — |
| 788 | C2×C3 | — | 6 | 4 | no | — |
| 789 | C2×C3 | — | 6 | 4 | no | — |
| 790 | C2×C3 | — | 6 | 1 | no | — |
| 791 | C2×C3 | — | 6 | 1 | no | — |
| 792 | C2×C3 | — | 6 | 1 | no | — |
| 793 | C2×C3 | — | 12 | 4 | no | — |
| 794 | C2×C3 | — | 12 | 1 | no | — |
| 795 | C2×C3 | — | 18 | 2 | no | — |
| 796 | C2×C3 | — | 18 | 4 | no | — |
| 797 | C2×C3 | — | 18 | 4 | no | — |
| 798 | C2×C3 | C23×D32 | 1 | 1 | yes | characteristic |
| 799 | D3 | — | 6 | 4 | no | — |
| 800 | D3 | — | 6 | 4 | no | — |
| 801 | D3 | — | 6 | 4 | no | — |
| 802 | D3 | — | 6 | 2 | no | — |
| 803 | D3 | — | 12 | 4 | no | — |
| 804 | D3 | — | 18 | 4 | no | — |
| 805 | D3 | — | 18 | 2 | no | — |
| 806 | C22 | — | 4 | 2 | no | — |
| 807 | C22 | — | 9 | 2 | no | — |
| 808 | C22 | — | 9 | 4 | no | — |
| 809 | C22 | — | 9 | 4 | no | — |
| 810 | C22 | — | 36 | 4 | no | — |
| 811 | C22 | — | 36 | 1 | no | — |
| 812 | C22 | — | 36 | 4 | no | — |
| 813 | C22 | — | 108 | 4 | no | — |
| 814 | C22 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 4 | yes | — |
| 815 | C22 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 816 | C4 | — | 9 | 1 | no | — |
| 817 | C4 | — | 9 | 1 | no | — |
| 818 | C4 | — | 9 | 4 | no | — |
| 819 | C4 | — | 9 | 4 | no | — |
| 820 | C4 | — | 9 | 4 | no | — |
| 821 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 2 | yes | — |
| 822 | C3 | — | 3 | 1 | no | — |
| 823 | C3 | — | 3 | 1 | no | — |
| 824 | C3 | — | 6 | 1 | no | — |
| 825 | C3 | #10596678 | 1 | 1 | yes | characteristic |
| 826 | C2 | — | 2 | 1 | no | — |
| 827 | C2 | — | 2 | 4 | no | — |
| 828 | C2 | — | 18 | 4 | no | — |
| 829 | C2 | — | 18 | 4 | no | — |
| 830 | C2 | — | 18 | 2 | no | — |
| 831 | C2 | C23×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11722664 | C2 | semidirect |
| 2. #64361⋊C3 | C2 | semidirect |
| 3. C2×#3830⋊C3 | C2 | semidirect |
| 4. #11722545 | C2 | semidirect |
| 5. C2×#88671 | C2 | semidirect |
| 6. #11722507 | C2 | semidirect |
| 7. #11722505 | C2 | semidirect |
| 8. #11722504 | C2 | semidirect |
| 9. #11722502 | C2 | semidirect |
| 10. #11722490 | C2 | semidirect |
| 11. #11722482 | C2 | semidirect |
| 14. C2×D4×H(3,𝔽3) | C22 | semidirect |
| 15. C2×#6235 | C22 | semidirect |
| 16. #88744 | C22 | semidirect |
| 17. D4×#272 | C22 | semidirect |
| 18. #88740 | C22 | semidirect |
| 19. C2×#638⋊C3 | C22 | semidirect |
| 20. C2×#638⋊C3 | C22 | semidirect |
| 21. C22×(C3⋊Dic3)⋊C3 | C22 | semidirect |
| 22. #3830⋊C3 | C22 | semidirect |
| 23. #3830⋊C3 | C22 | semidirect |
| 24. #3830⋊C3 | C22 | semidirect |
| 25. D4×(C3⋊D3)⋊C3 | C22 | semidirect |
| 26. #3828⋊C3 | C22 | semidirect |
| 27. C2×C4×(C3⋊D3)⋊C3 | C22 | semidirect |
| 28. C2×#634⋊C3 | C22 | semidirect |
| 29. #88677 | C22 | semidirect |
| 30. #88676 | C22 | semidirect |
| 31. #88676 | C22 | semidirect |
| 32. C2×#6200 | C22 | semidirect |
| 33. C2×#6199 | C22 | semidirect |
| 34. #88672 | C22 | semidirect |
| 35. #88671 | C22 | semidirect |
| 36. #88671 | C22 | semidirect |
| 37. #88671 | C22 | semidirect |
| 38. #88671 | C22 | semidirect |
| 39. #88671 | C22 | semidirect |
| 40. C2×((C3⋊D3)⋊C3)⋊C4 | C22 | semidirect |
| 41. C2×#6196 | C22 | semidirect |
| 42. #88654 | C22 | semidirect |
| 43. C4×((C3⋊D3)⋊C3)⋊C2 | C22 | semidirect |
| 44. #88652 | C22 | semidirect |
| 45. #88652 | C22 | semidirect |
| 46. #88651 | C22 | semidirect |
| 47. #88650 | C22 | semidirect |
| 48. #88649 | C22 | semidirect |
| 49. #88648 | C22 | semidirect |
| 50. ((C3⋊D3)⋊C3)⋊Q8 | C22 | semidirect |
| 51. ((C3⋊D3)⋊C3)⋊Q8 | C22 | semidirect |
| 52. #64361 | D3 | semidirect |
| 53. C2×#3830 | D3 | semidirect |
| 117. C2×C32×D4 | C2×D3 | semidirect |
| 118. C2×C32×D4 | C2×D3 | semidirect |
| 119. C2×#638 | C2×D3 | semidirect |
| 120. C2×#638 | C2×D3 | semidirect |
| 121. C22×C3⋊Dic3 | C2×D3 | semidirect |
| 122. #3830 | C2×D3 | semidirect |
| 123. #3830 | C2×D3 | semidirect |
| 124. #3830 | C2×D3 | semidirect |
| 125. D4×C3⋊D3 | C2×D3 | semidirect |
| 126. #3828 | C2×D3 | semidirect |
| 127. C2×C4×C3⋊D3 | C2×D3 | semidirect |
| 128. C2×#634 | C2×D3 | semidirect |
| 509. H(3,𝔽3) | #585 | semidirect |
| 682. C2×D4 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 744. C32 | #5964 | semidirect |
| 745. C32 | #5966 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722664 | 2 |
| #64361⋊C3 | 2 |
| C2×#3830⋊C3 | 2 |
| #11722545 | 2 |
| C2×#88671 | 2 |
| #11722507 | 2 |
| #11722505 | 2 |
| #11722504 | 2 |
| #11722502 | 2 |
| #11722490 | 2 |
| #11722482 | 2 |
| #10596679 | 3 |
| #10596678 | 3 |