Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
944 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11724490 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#1007⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×C3×D3×SL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | D32×SL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #64315⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #64316⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | D3×C3⋊(#41⋊C3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | D3×#1007 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | D3×2−1+4⋊C3 | — | 3 | 1 | no | maximal |
| 10 | C2×#1007⋊C3 | — | 3 | 1 | no | maximal |
| 11 | C2×C32×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C3×D3×#67 | — | 4 | 1 | no | maximal |
| 13 | C3⋊D3×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C3⋊(C3⋊(#41⋊C3)) | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C3×D3×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 16 | C3×D3×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C3×D3×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C3×C3⋊(#41⋊C3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #64364 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 20 | C3×#1007 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×C3×D3×Q8 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 22 | C3×2−1+4⋊C3 | — | 3 | 1 | no | — |
| 23 | C22×C3×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 24 | D3×#239 | — | 3 | 1 | no | — |
| 25 | D3×#239 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 26 | D32×Q8 | — | 3 | 1 | no | — |
| 27 | D32×Q8 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 28 | #64316 | — | 3 | 1 | no | — |
| 29 | #64316 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 30 | #64315 | — | 3 | 1 | no | — |
| 31 | #64315 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 32 | D3×#235 | — | 3 | 1 | no | — |
| 33 | D3×#235 | — | 3 | 1 | no | — |
| 34 | #64297 | — | 3 | 1 | no | — |
| 35 | #64297 | — | 3 | 1 | no | — |
| 36 | #1010⋊C3 | — | 3 | 1 | no | — |
| 37 | D3×#41⋊C3 | — | 3 | 1 | no | — |
| 38 | #1007⋊C3 | — | 2 | 1 | no | — |
| 39 | #1007⋊C3 | — | 3 | 1 | no | — |
| 40 | #1007⋊C3 | — | 3 | 1 | no | — |
| 41 | #1007⋊C3 | — | 3 | 1 | no | — |
| 42 | #1007⋊C3 | — | 3 | 1 | no | — |
| 43 | #1007⋊C3 | — | 3 | 1 | no | — |
| 44 | #1007⋊C3 | — | 6 | 1 | no | — |
| 45 | #1007⋊C3 | D3 | 1 | 1 | yes | characteristic, direct product factor |
| 46 | C2×D3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 47 | C2×D3×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 48 | C2×D3×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 49 | C2×D3×SL(2,𝔽3) | D3 | 1 | 1 | yes | characteristic, complemented |
| 50 | C2×C3⋊(#41⋊C3) | — | 3 | 1 | no | — |
| 51 | C22×C32×D3 | — | 4 | 1 | no | — |
| 52 | C2×C3×D32 | — | 4 | 1 | no | — |
| 53 | C3×#638 | — | 4 | 1 | no | — |
| 54 | C32×#67 | — | 4 | 1 | no | — |
| 55 | C32×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 56 | C3×#626 | — | 4 | 1 | no | — |
| 57 | C3×#625 | — | 4 | 1 | no | — |
| 58 | C3×D3×Dic3 | — | 4 | 1 | no | — |
| 59 | D3×2−1+4 | — | 3 | 1 | no | — |
| 60 | C2×#1007 | — | 3 | 1 | no | — |
| 61 | C2×2−1+4⋊C3 | — | 9 | 1 | no | — |
| 62 | C2×C32×Q8 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 63 | #3832 | — | 3 | 1 | no | — |
| 64 | #3832 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 65 | Q8×C3⋊D3 | — | 3 | 1 | no | — |
| 66 | Q8×C3⋊D3 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 67 | #3828 | — | 3 | 1 | no | — |
| 68 | #3828 | — | 3 | 1 | no | — |
| 69 | C2×C3×#67 | — | 12 | 1 | no | — |
| 70 | C3×#239 | — | 3 | 1 | no | — |
| 71 | C3×#239 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 72 | C3×D3×Q8 | — | 3 | 1 | no | — |
| 73 | C3×D3×Q8 | — | 3 | 1 | no | — |
| 74 | C3×D3×Q8 | — | 3 | 1 | no | — |
| 75 | C3×D3×Q8 | C22×C3 | 1 | 1 | yes | characteristic |
| 76 | C3×D3×Q8 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 77 | C3×D3×Q8 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 78 | C3×D3×D4 | — | 12 | 1 | no | — |
| 79 | C3×#235 | — | 3 | 1 | no | — |
| 80 | C3×#235 | — | 3 | 1 | no | — |
| 81 | C2×C3×C4×D3 | — | 3 | 1 | no | — |
| 82 | C2×C3×Dic6 | — | 3 | 1 | no | — |
| 83 | C3×#41⋊C3 | — | 3 | 1 | no | — |
| 84 | C2×C3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 85 | C2×C3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 86 | C2×C3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 87 | C2×C3×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 88 | C2×C3×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 89 | C2×C3×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 90 | C2×C3×SL(2,𝔽3) | — | 4 | 1 | no | — |
| 91 | C2×C3×SL(2,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 92 | C2×C3×SL(2,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 93 | D3×#67 | — | 3 | 1 | no | — |
| 94 | D3×#67 | A4 | 1 | 1 | yes | characteristic |
| 95 | #3804 | — | 3 | 2 | no | — |
| 96 | #3804 | — | 3 | 1 | no | — |
| 97 | #3804 | — | 3 | 1 | no | — |
| 98 | D3×D12 | — | 3 | 1 | no | — |
| 99 | D3×D12 | — | 3 | 1 | no | — |
| 100 | C4×D32 | — | 3 | 2 | no | — |
| 101 | C4×D32 | — | 3 | 1 | no | — |
| 102 | C4×D32 | — | 3 | 1 | no | — |
| 103 | #3799 | — | 3 | 2 | no | — |
| 104 | #3799 | — | 3 | 1 | no | — |
| 105 | #3799 | — | 3 | 1 | no | — |
| 106 | #3799 | — | 3 | 1 | no | — |
| 107 | #3799 | — | 3 | 1 | no | — |
| 108 | #3798 | — | 3 | 2 | no | — |
| 109 | #3798 | — | 3 | 1 | no | — |
| 110 | #3798 | — | 3 | 1 | no | — |
| 111 | #3797 | — | 3 | 2 | no | — |
| 112 | #3797 | — | 3 | 1 | no | — |
| 113 | #3797 | — | 3 | 1 | no | — |
| 114 | #3796 | — | 3 | 2 | no | — |
| 115 | #3796 | — | 3 | 1 | no | — |
| 116 | #3796 | — | 3 | 1 | no | — |
| 117 | #3795 | — | 3 | 1 | no | — |
| 118 | #3795 | — | 3 | 1 | no | — |
| 119 | D3×Dic6 | — | 3 | 2 | no | — |
| 120 | D3×Dic6 | — | 3 | 1 | no | — |
| 121 | D3×Dic6 | — | 3 | 1 | no | — |
| 122 | D3×Dic6 | — | 3 | 1 | no | — |
| 123 | D3×Dic6 | — | 3 | 1 | no | — |
| 124 | D3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 125 | D3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 126 | D3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 127 | D3×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 128 | D3×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 129 | D3×SL(2,𝔽3) | — | 6 | 1 | no | — |
| 130 | D3×SL(2,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic |
| 131 | D3×SL(2,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 132 | D3×SL(2,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 133 | C3⋊(#41⋊C3) | — | 2 | 1 | no | — |
| 134 | C3⋊(#41⋊C3) | — | 3 | 1 | no | — |
| 135 | C3⋊(#41⋊C3) | — | 3 | 1 | no | — |
| 136 | C3⋊(#41⋊C3) | — | 6 | 1 | no | — |
| 137 | C3⋊(#41⋊C3) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 138 | C22×C33 | — | 4 | 1 | no | — |
| 139 | C2×C3×C3⋊D3 | — | 4 | 1 | no | — |
| 140 | C2×C32×D3 | — | 4 | 1 | no | — |
| 141 | C2×C32×D3 | — | 4 | 1 | no | — |
| 142 | C2×C32×D3 | — | 4 | 1 | no | — |
| 143 | C2×C32×D3 | — | 8 | 2 | no | — |
| 144 | C3×D32 | — | 8 | 2 | no | — |
| 145 | C3×C3⋊Dic3 | — | 4 | 1 | no | — |
| 146 | C32×Dic3 | — | 4 | 1 | no | — |
| 147 | C3×2−1+4 | — | 3 | 1 | no | — |
| 148 | C22×C3×Q8 | — | 3 | 1 | no | — |
| 149 | #1010 | — | 3 | 1 | no | — |
| 150 | #1010 | — | 9 | 1 | no | — |
| 151 | #1010 | — | 9 | 1 | no | — |
| 152 | #1010 | — | 9 | 1 | no | — |
| 153 | D3×#41 | — | 3 | 1 | no | — |
| 154 | D3×#41 | — | 9 | 1 | no | — |
| 155 | D3×#41 | — | 9 | 1 | no | — |
| 156 | D3×#41 | — | 9 | 1 | no | — |
| 157 | #1007 | — | 3 | 1 | no | — |
| 158 | #1007 | — | 3 | 1 | no | — |
| 159 | #1007 | — | 3 | 1 | no | — |
| 160 | #1007 | — | 3 | 1 | no | — |
| 161 | #1007 | — | 3 | 1 | no | — |
| 162 | #1007 | — | 6 | 1 | no | — |
| 163 | #1007 | — | 9 | 1 | no | — |
| 164 | #1007 | — | 9 | 1 | no | — |
| 165 | #1007 | — | 9 | 1 | no | — |
| 166 | #1007 | — | 9 | 1 | no | — |
| 167 | #1007 | — | 9 | 1 | no | — |
| 168 | #1007 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 169 | C2×#239 | — | 3 | 1 | no | — |
| 170 | C2×#239 | — | 9 | 1 | no | — |
| 171 | C2×D3×Q8 | — | 3 | 1 | no | — |
| 172 | C2×D3×Q8 | — | 3 | 1 | no | — |
| 173 | C2×D3×Q8 | — | 9 | 1 | no | — |
| 174 | C2×D3×Q8 | — | 9 | 1 | no | — |
| 175 | C2×D3×Q8 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 176 | C2×#235 | — | 9 | 1 | no | — |
| 177 | C2×#235 | — | 9 | 1 | no | — |
| 178 | 2−1+4⋊C3 | — | 3 | 1 | no | — |
| 179 | 2−1+4⋊C3 | — | 6 | 1 | no | — |
| 180 | 2−1+4⋊C3 | — | 9 | 1 | no | — |
| 181 | 2−1+4⋊C3 | — | 9 | 1 | no | — |
| 182 | 2−1+4⋊C3 | — | 9 | 1 | no | — |
| 183 | C2×#41⋊C3 | — | 9 | 1 | no | — |
| 184 | C22×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 185 | C22×SL(2,𝔽3) | — | 6 | 1 | no | — |
| 186 | C22×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 187 | C23×C32 | — | 12 | 1 | no | — |
| 188 | C22×C3×D3 | — | 4 | 1 | no | — |
| 189 | C22×C3×D3 | — | 8 | 1 | no | — |
| 190 | C22×C3×D3 | — | 12 | 1 | no | — |
| 191 | C22×C3×D3 | — | 12 | 1 | no | — |
| 192 | C22×C3×D3 | C2×A4 | 1 | 1 | yes | characteristic |
| 193 | C2×D32 | — | 3 | 1 | no | — |
| 194 | C2×D32 | C2×A4 | 1 | 1 | yes | characteristic |
| 195 | C32×Q8 | — | 3 | 1 | no | — |
| 196 | C32×Q8 | C23×C3 | 1 | 1 | yes | characteristic |
| 197 | C32×D4 | — | 12 | 1 | no | — |
| 198 | C2×C32×C4 | — | 3 | 1 | no | — |
| 199 | #638 | — | 3 | 1 | no | — |
| 200 | #638 | C2×A4 | 1 | 1 | yes | characteristic |
| 201 | C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 202 | C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 203 | C4×C3⋊D3 | — | 3 | 2 | no | — |
| 204 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 205 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 206 | #634 | — | 3 | 1 | no | — |
| 207 | #634 | — | 3 | 1 | no | — |
| 208 | C3×#67 | — | 3 | 1 | no | — |
| 209 | C3×#67 | — | 4 | 1 | no | — |
| 210 | C3×#67 | — | 8 | 1 | no | — |
| 211 | C3×#67 | — | 12 | 1 | no | — |
| 212 | C3×#67 | — | 12 | 1 | no | — |
| 213 | C3×#67 | — | 12 | 1 | no | — |
| 214 | C3×#67 | — | 12 | 1 | no | — |
| 215 | C3×#67 | — | 12 | 1 | no | — |
| 216 | C3×#67 | — | 24 | 1 | no | — |
| 217 | C3×#67 | C2×A4 | 1 | 1 | yes | characteristic |
| 218 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 219 | C2×C3×Dic3 | — | 12 | 1 | no | — |
| 220 | C3×D12 | — | 3 | 1 | no | — |
| 221 | C3×D12 | — | 3 | 1 | no | — |
| 222 | C3×D12 | — | 12 | 1 | no | — |
| 223 | C3×C4×D3 | — | 3 | 2 | no | — |
| 224 | C3×C4×D3 | — | 3 | 1 | no | — |
| 225 | C3×C4×D3 | — | 3 | 1 | no | — |
| 226 | C3×C4×D3 | — | 3 | 1 | no | — |
| 227 | C3×C4×D3 | — | 3 | 1 | no | — |
| 228 | C3×C4×D3 | — | 3 | 1 | no | — |
| 229 | C3×C4×D3 | — | 3 | 1 | no | — |
| 230 | C3×C4×D3 | — | 12 | 1 | no | — |
| 231 | C3×Dic6 | — | 3 | 2 | no | — |
| 232 | C3×Dic6 | — | 3 | 1 | no | — |
| 233 | C3×Dic6 | — | 3 | 1 | no | — |
| 234 | C3×Dic6 | — | 3 | 1 | no | — |
| 235 | C3×Dic6 | — | 3 | 1 | no | — |
| 236 | C3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 237 | C3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 238 | C3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 239 | C3×SL(2,𝔽3) | — | 4 | 1 | no | — |
| 240 | C3×SL(2,𝔽3) | C22×D3 | 1 | 1 | yes | characteristic |
| 241 | C3×SL(2,𝔽3) | C22×D3 | 1 | 1 | yes | characteristic |
| 242 | #627 | — | 3 | 2 | no | — |
| 243 | #627 | — | 3 | 1 | no | — |
| 244 | #627 | — | 3 | 1 | no | — |
| 245 | #626 | — | 3 | 2 | no | — |
| 246 | #626 | — | 3 | 1 | no | — |
| 247 | #626 | — | 3 | 1 | no | — |
| 248 | #626 | — | 3 | 1 | no | — |
| 249 | #626 | C2×A4 | 1 | 1 | yes | characteristic |
| 250 | #625 | — | 3 | 1 | no | — |
| 251 | #625 | C2×A4 | 1 | 1 | yes | characteristic |
| 252 | #624 | — | 3 | 2 | no | — |
| 253 | #624 | — | 3 | 1 | no | — |
| 254 | #624 | — | 3 | 1 | no | — |
| 255 | D3×Dic3 | — | 3 | 2 | no | — |
| 256 | D3×Dic3 | — | 3 | 1 | no | — |
| 257 | D3×Dic3 | — | 3 | 1 | no | — |
| 258 | D3×Dic3 | — | 3 | 1 | no | — |
| 259 | D3×Dic3 | C2×A4 | 1 | 1 | yes | characteristic |
| 260 | C2×2−1+4 | — | 9 | 1 | no | Sylow |
| 261 | C2×C33 | — | 4 | 1 | no | — |
| 262 | C2×C33 | — | 8 | 1 | no | — |
| 263 | C3×C3⋊D3 | — | 8 | 1 | no | — |
| 264 | C32×D3 | — | 4 | 2 | no | — |
| 265 | C32×D3 | — | 8 | 1 | no | — |
| 266 | C32×D3 | — | 8 | 1 | no | — |
| 267 | C3×#41 | — | 3 | 1 | no | — |
| 268 | C3×#41 | — | 9 | 1 | no | — |
| 269 | C3×#41 | — | 9 | 1 | no | — |
| 270 | C3×#41 | — | 9 | 1 | no | — |
| 271 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 272 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 273 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 274 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 275 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 276 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 277 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 278 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 279 | C2×C3×Q8 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 280 | C2×C3×Q8 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 281 | C2×C3×D4 | — | 36 | 1 | no | — |
| 282 | C22×C3×C4 | — | 9 | 1 | no | — |
| 283 | C2×#67 | — | 3 | 1 | no | — |
| 284 | C2×#67 | — | 9 | 1 | no | — |
| 285 | #239 | — | 3 | 1 | no | — |
| 286 | #239 | — | 3 | 1 | no | — |
| 287 | #239 | — | 3 | 1 | no | — |
| 288 | #239 | — | 6 | 1 | no | — |
| 289 | #239 | — | 9 | 1 | no | — |
| 290 | #239 | — | 9 | 2 | no | — |
| 291 | #239 | — | 9 | 1 | no | — |
| 292 | #239 | — | 9 | 1 | no | — |
| 293 | #239 | — | 9 | 1 | no | — |
| 294 | #239 | — | 9 | 2 | no | — |
| 295 | #239 | — | 9 | 1 | no | — |
| 296 | #239 | — | 9 | 1 | no | — |
| 297 | #239 | — | 9 | 1 | no | — |
| 298 | #239 | — | 9 | 1 | no | — |
| 299 | #239 | — | 18 | 1 | no | — |
| 300 | #239 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 301 | D3×Q8 | — | 3 | 1 | no | — |
| 302 | D3×Q8 | — | 3 | 1 | no | — |
| 303 | D3×Q8 | — | 3 | 1 | no | — |
| 304 | D3×Q8 | — | 3 | 1 | no | — |
| 305 | D3×Q8 | — | 3 | 1 | no | — |
| 306 | D3×Q8 | — | 6 | 1 | no | — |
| 307 | D3×Q8 | — | 9 | 2 | no | — |
| 308 | D3×Q8 | — | 9 | 2 | no | — |
| 309 | D3×Q8 | — | 9 | 1 | no | — |
| 310 | D3×Q8 | — | 9 | 1 | no | — |
| 311 | D3×Q8 | — | 9 | 1 | no | — |
| 312 | D3×Q8 | — | 9 | 1 | no | — |
| 313 | D3×Q8 | — | 9 | 1 | no | — |
| 314 | D3×Q8 | — | 9 | 2 | no | — |
| 315 | D3×Q8 | — | 9 | 1 | no | — |
| 316 | D3×Q8 | — | 9 | 1 | no | — |
| 317 | D3×Q8 | — | 9 | 1 | no | — |
| 318 | D3×Q8 | — | 9 | 1 | no | — |
| 319 | D3×Q8 | — | 9 | 1 | no | — |
| 320 | D3×Q8 | — | 18 | 1 | no | — |
| 321 | D3×Q8 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 322 | D3×Q8 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 323 | D3×Q8 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 324 | #237 | — | 9 | 2 | no | — |
| 325 | #237 | — | 9 | 1 | no | — |
| 326 | #237 | — | 9 | 1 | no | — |
| 327 | #237 | — | 9 | 1 | no | — |
| 328 | #237 | — | 9 | 1 | no | — |
| 329 | #237 | — | 9 | 1 | no | — |
| 330 | #237 | — | 9 | 1 | no | — |
| 331 | #237 | — | 9 | 2 | no | — |
| 332 | D3×D4 | — | 3 | 1 | no | — |
| 333 | D3×D4 | — | 9 | 1 | no | — |
| 334 | D3×D4 | — | 9 | 1 | no | — |
| 335 | D3×D4 | — | 9 | 1 | no | — |
| 336 | #235 | — | 3 | 1 | no | — |
| 337 | #235 | — | 3 | 1 | no | — |
| 338 | #235 | — | 9 | 1 | no | — |
| 339 | #235 | — | 9 | 2 | no | — |
| 340 | #235 | — | 9 | 1 | no | — |
| 341 | #235 | — | 9 | 1 | no | — |
| 342 | #235 | — | 9 | 1 | no | — |
| 343 | #235 | — | 9 | 1 | no | — |
| 344 | #235 | — | 9 | 1 | no | — |
| 345 | #235 | — | 9 | 1 | no | — |
| 346 | #235 | — | 9 | 1 | no | — |
| 347 | #235 | — | 9 | 2 | no | — |
| 348 | #235 | — | 9 | 2 | no | — |
| 349 | #235 | — | 9 | 1 | no | — |
| 350 | #235 | — | 9 | 1 | no | — |
| 351 | #235 | — | 9 | 1 | no | — |
| 352 | #235 | — | 9 | 1 | no | — |
| 353 | #235 | — | 9 | 1 | no | — |
| 354 | #235 | — | 9 | 2 | no | — |
| 355 | #235 | — | 9 | 1 | no | — |
| 356 | #235 | — | 9 | 1 | no | — |
| 357 | #235 | — | 9 | 1 | no | — |
| 358 | #235 | — | 18 | 1 | no | — |
| 359 | #235 | — | 18 | 1 | no | — |
| 360 | C2×D12 | — | 9 | 1 | no | — |
| 361 | C2×D12 | — | 9 | 1 | no | — |
| 362 | C2×C4×D3 | — | 3 | 1 | no | — |
| 363 | C2×C4×D3 | — | 9 | 1 | no | — |
| 364 | C2×C4×D3 | — | 9 | 1 | no | — |
| 365 | C2×C4×D3 | — | 9 | 1 | no | — |
| 366 | C2×C4×D3 | — | 9 | 1 | no | — |
| 367 | C2×C4×D3 | — | 9 | 2 | no | — |
| 368 | C2×C4×D3 | — | 9 | 2 | no | — |
| 369 | C2×Dic6 | — | 3 | 1 | no | — |
| 370 | C2×Dic6 | — | 9 | 1 | no | — |
| 371 | C2×Dic6 | — | 9 | 2 | no | — |
| 372 | C2×Dic6 | — | 9 | 1 | no | — |
| 373 | C2×Dic6 | — | 9 | 1 | no | — |
| 374 | C2×Dic6 | — | 9 | 1 | no | — |
| 375 | #41⋊C3 | — | 3 | 1 | no | — |
| 376 | #41⋊C3 | — | 6 | 1 | no | — |
| 377 | #41⋊C3 | — | 9 | 1 | no | — |
| 378 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 379 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 380 | C2×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 381 | C2×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 382 | C2×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 383 | C2×SL(2,𝔽3) | — | 4 | 1 | no | — |
| 384 | C2×SL(2,𝔽3) | — | 6 | 1 | no | — |
| 385 | C2×SL(2,𝔽3) | — | 6 | 1 | no | — |
| 386 | C2×SL(2,𝔽3) | — | 6 | 1 | no | — |
| 387 | C2×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 388 | C2×SL(2,𝔽3) | D32 | 1 | 1 | yes | characteristic, complemented |
| 389 | C22×C32 | — | 4 | 1 | no | — |
| 390 | C22×C32 | — | 4 | 1 | no | — |
| 391 | C22×C32 | — | 8 | 1 | no | — |
| 392 | C22×C32 | — | 8 | 1 | no | — |
| 393 | C22×C32 | — | 8 | 1 | no | — |
| 394 | C22×C32 | — | 12 | 1 | no | — |
| 395 | C22×C32 | — | 12 | 1 | no | — |
| 396 | C22×C32 | — | 12 | 1 | no | — |
| 397 | C22×C32 | — | 16 | 1 | no | — |
| 398 | C22×C32 | — | 24 | 2 | no | — |
| 399 | C22×C32 | C22×A4 | 1 | 1 | yes | characteristic |
| 400 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 401 | C2×C3⋊D3 | C22×A4 | 1 | 1 | yes | characteristic |
| 402 | C2×C3×D3 | — | 2 | 2 | no | — |
| 403 | C2×C3×D3 | — | 3 | 1 | no | — |
| 404 | C2×C3×D3 | — | 4 | 1 | no | — |
| 405 | C2×C3×D3 | — | 4 | 1 | no | — |
| 406 | C2×C3×D3 | — | 4 | 1 | no | — |
| 407 | C2×C3×D3 | — | 8 | 2 | no | — |
| 408 | C2×C3×D3 | — | 8 | 4 | no | — |
| 409 | C2×C3×D3 | — | 8 | 1 | no | — |
| 410 | C2×C3×D3 | — | 8 | 1 | no | — |
| 411 | C2×C3×D3 | — | 8 | 1 | no | — |
| 412 | C2×C3×D3 | — | 12 | 1 | no | — |
| 413 | C2×C3×D3 | — | 12 | 1 | no | — |
| 414 | C2×C3×D3 | — | 24 | 1 | no | — |
| 415 | C2×C3×D3 | — | 24 | 2 | no | — |
| 416 | C2×C3×D3 | — | 24 | 2 | no | — |
| 417 | C2×C3×D3 | C22×A4 | 1 | 1 | yes | characteristic |
| 418 | C2×C3×D3 | C22×A4 | 1 | 1 | yes | characteristic |
| 419 | C2×C3×D3 | C22×A4 | 1 | 1 | yes | characteristic |
| 420 | D32 | — | 2 | 2 | no | — |
| 421 | D32 | — | 6 | 2 | no | — |
| 422 | C32×C4 | — | 3 | 1 | no | — |
| 423 | C32×C4 | — | 3 | 1 | no | — |
| 424 | C32×C4 | — | 12 | 1 | no | — |
| 425 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 426 | C3⋊Dic3 | C22×A4 | 1 | 1 | yes | characteristic |
| 427 | C3×Dic3 | — | 3 | 1 | no | — |
| 428 | C3×Dic3 | — | 3 | 1 | no | — |
| 429 | C3×Dic3 | — | 3 | 1 | no | — |
| 430 | C3×Dic3 | — | 4 | 1 | no | — |
| 431 | C3×Dic3 | — | 8 | 1 | no | — |
| 432 | C3×Dic3 | — | 12 | 1 | no | — |
| 433 | C3×Dic3 | — | 12 | 1 | no | — |
| 434 | C3×Dic3 | — | 24 | 1 | no | — |
| 435 | C3×Dic3 | C22×A4 | 1 | 1 | yes | characteristic |
| 436 | 2−1+4 | — | 3 | 1 | no | — |
| 437 | 2−1+4 | — | 9 | 1 | no | — |
| 438 | 2−1+4 | — | 9 | 1 | no | — |
| 439 | 2−1+4 | — | 9 | 1 | no | — |
| 440 | 2−1+4 | — | 27 | 1 | no | — |
| 441 | 2−1+4 | — | 27 | 1 | no | — |
| 442 | 2−1+4 | — | 27 | 1 | no | — |
| 443 | 2−1+4 | — | 27 | 1 | no | — |
| 444 | C2×#41 | — | 9 | 1 | no | — |
| 445 | C2×#41 | — | 27 | 1 | no | — |
| 446 | C2×#41 | — | 27 | 1 | no | — |
| 447 | C2×#41 | — | 27 | 1 | no | — |
| 448 | C22×Q8 | — | 3 | 1 | no | — |
| 449 | C22×Q8 | — | 9 | 1 | no | — |
| 450 | C22×Q8 | — | 27 | 1 | no | — |
| 451 | C33 | — | 4 | 1 | no | Sylow |
| 452 | C23×C3 | — | 3 | 1 | no | — |
| 453 | C23×C3 | — | 12 | 1 | no | — |
| 454 | C23×C3 | — | 24 | 1 | no | — |
| 455 | C23×C3 | — | 36 | 1 | no | — |
| 456 | C22×D3 | — | 3 | 1 | no | — |
| 457 | C22×D3 | — | 3 | 1 | no | — |
| 458 | C22×D3 | — | 9 | 1 | no | — |
| 459 | C22×D3 | — | 9 | 1 | no | — |
| 460 | C22×D3 | D3×A4 | 1 | 1 | yes | characteristic |
| 461 | C3×Q8 | — | 2 | 1 | no | — |
| 462 | C3×Q8 | — | 3 | 1 | no | — |
| 463 | C3×Q8 | — | 3 | 1 | no | — |
| 464 | C3×Q8 | — | 6 | 1 | no | — |
| 465 | C3×Q8 | — | 9 | 1 | no | — |
| 466 | C3×Q8 | — | 9 | 1 | no | — |
| 467 | C3×Q8 | — | 9 | 1 | no | — |
| 468 | C3×Q8 | — | 9 | 1 | no | — |
| 469 | C3×Q8 | — | 9 | 2 | no | — |
| 470 | C3×Q8 | C22×C3×D3 | 1 | 1 | yes | characteristic |
| 471 | C3×Q8 | C22×C3×D3 | 1 | 1 | yes | characteristic |
| 472 | C3×D4 | — | 3 | 1 | no | — |
| 473 | C3×D4 | — | 9 | 1 | no | — |
| 474 | C3×D4 | — | 9 | 1 | no | — |
| 475 | C3×D4 | — | 9 | 1 | no | — |
| 476 | C3×D4 | — | 12 | 1 | no | — |
| 477 | C3×D4 | — | 24 | 1 | no | — |
| 478 | C3×D4 | — | 36 | 1 | no | — |
| 479 | C3×D4 | — | 36 | 1 | no | — |
| 480 | C3×D4 | — | 36 | 1 | no | — |
| 481 | C2×C3×C4 | — | 3 | 1 | no | — |
| 482 | C2×C3×C4 | — | 3 | 1 | no | — |
| 483 | C2×C3×C4 | — | 6 | 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 | — | 9 | 1 | no | — |
| 488 | C2×C3×C4 | — | 9 | 1 | no | — |
| 489 | C2×C3×C4 | — | 9 | 1 | no | — |
| 490 | C2×C3×C4 | — | 9 | 2 | no | — |
| 491 | C2×C3×C4 | — | 9 | 1 | no | — |
| 492 | C2×C3×C4 | — | 36 | 1 | no | — |
| 493 | #67 | — | 3 | 1 | no | — |
| 494 | #67 | — | 3 | 1 | no | — |
| 495 | #67 | — | 3 | 1 | no | — |
| 496 | #67 | — | 3 | 1 | no | — |
| 497 | #67 | — | 3 | 1 | no | — |
| 498 | #67 | — | 3 | 1 | no | — |
| 499 | #67 | — | 6 | 1 | no | — |
| 500 | #67 | — | 9 | 1 | no | — |
| 501 | #67 | — | 9 | 1 | no | — |
| 502 | #67 | — | 9 | 1 | no | — |
| 503 | #67 | — | 9 | 2 | no | — |
| 504 | #67 | — | 9 | 1 | no | — |
| 505 | #67 | — | 9 | 1 | no | — |
| 506 | #67 | — | 9 | 1 | no | — |
| 507 | #67 | — | 9 | 1 | no | — |
| 508 | #67 | — | 18 | 1 | no | — |
| 509 | #67 | D3×A4 | 1 | 1 | yes | characteristic |
| 510 | C2×Dic3 | — | 3 | 1 | no | — |
| 511 | C2×Dic3 | — | 3 | 1 | no | — |
| 512 | C2×Dic3 | — | 9 | 1 | no | — |
| 513 | C2×Dic3 | — | 9 | 1 | no | — |
| 514 | C2×Dic3 | — | 9 | 1 | no | — |
| 515 | C2×Dic3 | — | 9 | 2 | no | — |
| 516 | D12 | — | 3 | 1 | no | — |
| 517 | D12 | — | 3 | 1 | no | — |
| 518 | D12 | — | 3 | 1 | no | — |
| 519 | D12 | — | 9 | 1 | no | — |
| 520 | D12 | — | 9 | 1 | no | — |
| 521 | D12 | — | 9 | 1 | no | — |
| 522 | D12 | — | 9 | 1 | no | — |
| 523 | D12 | — | 9 | 1 | no | — |
| 524 | D12 | — | 9 | 2 | no | — |
| 525 | D12 | — | 9 | 1 | no | — |
| 526 | D12 | — | 9 | 1 | no | — |
| 527 | D12 | — | 18 | 1 | no | — |
| 528 | D12 | — | 18 | 1 | no | — |
| 529 | C4×D3 | — | 3 | 2 | no | — |
| 530 | C4×D3 | — | 3 | 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 | — | 3 | 1 | no | — |
| 536 | C4×D3 | — | 3 | 1 | no | — |
| 537 | C4×D3 | — | 9 | 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 | — | 9 | 1 | no | — |
| 543 | C4×D3 | — | 9 | 2 | no | — |
| 544 | C4×D3 | — | 9 | 2 | no | — |
| 545 | C4×D3 | — | 9 | 1 | no | — |
| 546 | C4×D3 | — | 9 | 1 | no | — |
| 547 | C4×D3 | — | 9 | 2 | no | — |
| 548 | C4×D3 | — | 9 | 2 | no | — |
| 549 | C4×D3 | — | 9 | 2 | no | — |
| 550 | C4×D3 | — | 9 | 1 | no | — |
| 551 | C4×D3 | — | 9 | 1 | no | — |
| 552 | C4×D3 | — | 9 | 1 | no | — |
| 553 | C4×D3 | — | 18 | 1 | no | — |
| 554 | C4×D3 | — | 18 | 1 | no | — |
| 555 | C4×D3 | — | 18 | 2 | no | — |
| 556 | Dic6 | — | 3 | 2 | no | — |
| 557 | Dic6 | — | 3 | 1 | no | — |
| 558 | Dic6 | — | 3 | 1 | no | — |
| 559 | Dic6 | — | 3 | 1 | no | — |
| 560 | Dic6 | — | 3 | 1 | no | — |
| 561 | Dic6 | — | 9 | 1 | no | — |
| 562 | Dic6 | — | 9 | 1 | no | — |
| 563 | Dic6 | — | 9 | 1 | no | — |
| 564 | Dic6 | — | 9 | 1 | no | — |
| 565 | Dic6 | — | 9 | 1 | no | — |
| 566 | Dic6 | — | 9 | 2 | no | — |
| 567 | Dic6 | — | 9 | 2 | no | — |
| 568 | Dic6 | — | 9 | 1 | no | — |
| 569 | Dic6 | — | 9 | 1 | no | — |
| 570 | Dic6 | — | 9 | 1 | no | — |
| 571 | Dic6 | — | 18 | 1 | no | — |
| 572 | Dic6 | — | 18 | 1 | no | — |
| 573 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 574 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 575 | SL(2,𝔽3) | — | 4 | 1 | no | — |
| 576 | SL(2,𝔽3) | C2×D32 | 1 | 1 | yes | characteristic |
| 577 | C2×C32 | — | 2 | 1 | no | — |
| 578 | C2×C32 | — | 4 | 1 | no | — |
| 579 | C2×C32 | — | 4 | 1 | no | — |
| 580 | C2×C32 | — | 8 | 1 | no | — |
| 581 | C2×C32 | — | 8 | 1 | no | — |
| 582 | C2×C32 | — | 8 | 1 | no | — |
| 583 | C2×C32 | — | 8 | 2 | no | — |
| 584 | C2×C32 | — | 8 | 1 | no | — |
| 585 | C2×C32 | — | 8 | 1 | no | — |
| 586 | C2×C32 | — | 12 | 2 | no | — |
| 587 | C2×C32 | — | 16 | 1 | no | — |
| 588 | C2×C32 | — | 16 | 1 | no | — |
| 589 | C2×C32 | — | 16 | 1 | no | — |
| 590 | C2×C32 | — | 16 | 2 | no | — |
| 591 | C2×C32 | — | 24 | 1 | no | — |
| 592 | C2×C32 | — | 24 | 1 | no | — |
| 593 | C2×C32 | C23×A4 | 1 | 1 | yes | characteristic |
| 594 | C3⋊D3 | — | 2 | 1 | no | — |
| 595 | C3⋊D3 | — | 6 | 1 | no | — |
| 596 | C3×D3 | — | 2 | 1 | no | — |
| 597 | C3×D3 | — | 2 | 1 | no | — |
| 598 | C3×D3 | — | 4 | 2 | no | — |
| 599 | C3×D3 | — | 6 | 1 | no | — |
| 600 | C3×D3 | — | 8 | 1 | no | — |
| 601 | C3×D3 | — | 8 | 1 | no | — |
| 602 | C3×D3 | — | 8 | 2 | no | — |
| 603 | C3×D3 | — | 8 | 2 | no | — |
| 604 | C3×D3 | — | 16 | 1 | no | — |
| 605 | C3×D3 | — | 24 | 1 | no | — |
| 606 | C3×D3 | — | 24 | 1 | no | — |
| 607 | C3×D3 | — | 48 | 1 | no | — |
| 608 | C3×D3 | 2−1+4⋊C3 | 1 | 2 | yes | complemented |
| 609 | #41 | — | 3 | 1 | no | — |
| 610 | #41 | — | 9 | 1 | no | — |
| 611 | #41 | — | 9 | 1 | no | — |
| 612 | #41 | — | 9 | 1 | no | — |
| 613 | #41 | — | 9 | 1 | no | — |
| 614 | #41 | — | 27 | 1 | no | — |
| 615 | #41 | — | 27 | 1 | no | — |
| 616 | #41 | — | 27 | 1 | no | — |
| 617 | #41 | — | 27 | 1 | no | — |
| 618 | #41 | — | 27 | 2 | no | — |
| 619 | #41 | — | 27 | 1 | no | — |
| 620 | #41 | — | 27 | 1 | no | — |
| 621 | #41 | — | 27 | 1 | no | — |
| 622 | #41 | — | 27 | 1 | no | — |
| 623 | #41 | — | 27 | 2 | no | — |
| 624 | #41 | — | 27 | 1 | no | — |
| 625 | #41 | — | 27 | 2 | no | — |
| 626 | #41 | — | 27 | 1 | no | — |
| 627 | #41 | — | 27 | 1 | no | — |
| 628 | #41 | — | 27 | 1 | no | — |
| 629 | #41 | — | 27 | 2 | no | — |
| 630 | #41 | — | 27 | 1 | no | — |
| 631 | #41 | — | 27 | 1 | no | — |
| 632 | #41 | — | 27 | 1 | no | — |
| 633 | C2×Q8 | — | 3 | 1 | no | — |
| 634 | C2×Q8 | — | 3 | 1 | no | — |
| 635 | C2×Q8 | — | 3 | 1 | no | — |
| 636 | C2×Q8 | — | 9 | 1 | no | — |
| 637 | C2×Q8 | — | 9 | 1 | no | — |
| 638 | C2×Q8 | — | 9 | 1 | no | — |
| 639 | C2×Q8 | — | 9 | 1 | no | — |
| 640 | C2×Q8 | — | 9 | 1 | no | — |
| 641 | C2×Q8 | — | 27 | 1 | no | — |
| 642 | C2×Q8 | — | 27 | 1 | no | — |
| 643 | C2×Q8 | — | 27 | 2 | no | — |
| 644 | C2×Q8 | — | 27 | 1 | no | — |
| 645 | C2×Q8 | — | 27 | 1 | no | — |
| 646 | C2×Q8 | — | 27 | 1 | no | — |
| 647 | C2×Q8 | — | 27 | 1 | no | — |
| 648 | C2×Q8 | — | 27 | 2 | no | — |
| 649 | C2×Q8 | — | 27 | 1 | no | — |
| 650 | C2×Q8 | C3×D32 | 1 | 1 | yes | characteristic, complemented |
| 651 | C2×D4 | — | 9 | 1 | no | — |
| 652 | C2×D4 | — | 27 | 1 | no | — |
| 653 | C2×D4 | — | 27 | 1 | no | — |
| 654 | C2×D4 | — | 27 | 1 | no | — |
| 655 | C22×C4 | — | 9 | 1 | no | — |
| 656 | C22×C4 | — | 27 | 1 | no | — |
| 657 | C22×C4 | — | 27 | 1 | no | — |
| 658 | C22×C4 | — | 27 | 2 | no | — |
| 659 | C22×C3 | — | 2 | 1 | no | — |
| 660 | C22×C3 | — | 3 | 1 | no | — |
| 661 | C22×C3 | — | 3 | 1 | no | — |
| 662 | C22×C3 | — | 3 | 1 | no | — |
| 663 | C22×C3 | — | 4 | 1 | no | — |
| 664 | C22×C3 | — | 6 | 2 | no | — |
| 665 | C22×C3 | — | 8 | 1 | no | — |
| 666 | C22×C3 | — | 8 | 1 | no | — |
| 667 | C22×C3 | — | 9 | 1 | no | — |
| 668 | C22×C3 | — | 12 | 1 | no | — |
| 669 | C22×C3 | — | 12 | 1 | no | — |
| 670 | C22×C3 | — | 12 | 1 | no | — |
| 671 | C22×C3 | — | 16 | 1 | no | — |
| 672 | C22×C3 | — | 24 | 1 | no | — |
| 673 | C22×C3 | — | 24 | 1 | no | — |
| 674 | C22×C3 | — | 24 | 1 | no | — |
| 675 | C22×C3 | — | 24 | 2 | no | — |
| 676 | C22×C3 | — | 24 | 4 | no | — |
| 677 | C22×C3 | — | 36 | 1 | no | — |
| 678 | C22×C3 | — | 72 | 2 | no | — |
| 679 | C22×C3 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 680 | C22×C3 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 681 | C2×D3 | — | 2 | 2 | no | — |
| 682 | C2×D3 | — | 3 | 1 | no | — |
| 683 | C2×D3 | — | 3 | 1 | no | — |
| 684 | C2×D3 | — | 3 | 1 | no | — |
| 685 | C2×D3 | — | 6 | 1 | no | — |
| 686 | C2×D3 | — | 6 | 2 | no | — |
| 687 | C2×D3 | — | 6 | 2 | no | — |
| 688 | C2×D3 | — | 9 | 1 | no | — |
| 689 | C2×D3 | — | 9 | 1 | no | — |
| 690 | C2×D3 | — | 18 | 1 | no | — |
| 691 | C2×D3 | — | 18 | 2 | no | — |
| 692 | C2×D3 | — | 18 | 2 | no | — |
| 693 | C2×D3 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 694 | C2×D3 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 695 | C2×D3 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 696 | C3×C4 | — | 3 | 1 | no | — |
| 697 | C3×C4 | — | 3 | 1 | no | — |
| 698 | C3×C4 | — | 3 | 1 | no | — |
| 699 | C3×C4 | — | 3 | 1 | no | — |
| 700 | C3×C4 | — | 3 | 1 | no | — |
| 701 | C3×C4 | — | 6 | 1 | no | — |
| 702 | C3×C4 | — | 6 | 1 | no | — |
| 703 | C3×C4 | — | 9 | 1 | no | — |
| 704 | C3×C4 | — | 9 | 1 | no | — |
| 705 | C3×C4 | — | 9 | 1 | no | — |
| 706 | C3×C4 | — | 12 | 1 | no | — |
| 707 | C3×C4 | — | 24 | 1 | no | — |
| 708 | C3×C4 | — | 36 | 1 | no | — |
| 709 | Dic3 | — | 3 | 1 | no | — |
| 710 | Dic3 | — | 3 | 1 | no | — |
| 711 | Dic3 | — | 3 | 1 | no | — |
| 712 | Dic3 | — | 3 | 1 | no | — |
| 713 | Dic3 | — | 3 | 1 | no | — |
| 714 | Dic3 | — | 6 | 1 | no | — |
| 715 | Dic3 | — | 9 | 1 | no | — |
| 716 | Dic3 | — | 9 | 1 | no | — |
| 717 | Dic3 | — | 18 | 1 | no | — |
| 718 | Dic3 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 719 | C32 | — | 4 | 1 | no | — |
| 720 | C32 | — | 4 | 1 | no | — |
| 721 | C32 | — | 8 | 1 | no | — |
| 722 | C32 | — | 8 | 1 | no | — |
| 723 | C32 | — | 8 | 1 | no | — |
| 724 | C32 | — | 16 | 1 | no | — |
| 725 | C32 | C2×2−1+4⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 726 | C23 | — | 3 | 1 | no | — |
| 727 | C23 | — | 9 | 1 | no | — |
| 728 | C23 | — | 27 | 1 | no | — |
| 729 | Q8 | — | 3 | 1 | no | — |
| 730 | Q8 | — | 9 | 1 | no | — |
| 731 | Q8 | — | 9 | 1 | no | — |
| 732 | Q8 | — | 9 | 1 | no | — |
| 733 | Q8 | — | 9 | 1 | no | — |
| 734 | Q8 | — | 9 | 2 | no | — |
| 735 | Q8 | — | 27 | 1 | no | — |
| 736 | Q8 | — | 27 | 1 | no | — |
| 737 | Q8 | — | 27 | 1 | no | — |
| 738 | Q8 | — | 27 | 1 | no | — |
| 739 | Q8 | — | 27 | 2 | no | — |
| 740 | Q8 | C2×C3×D32 | 1 | 1 | yes | characteristic |
| 741 | D4 | — | 3 | 1 | no | — |
| 742 | D4 | — | 9 | 1 | no | — |
| 743 | D4 | — | 9 | 1 | no | — |
| 744 | D4 | — | 9 | 1 | no | — |
| 745 | D4 | — | 9 | 1 | no | — |
| 746 | D4 | — | 9 | 1 | no | — |
| 747 | D4 | — | 9 | 1 | no | — |
| 748 | D4 | — | 27 | 1 | no | — |
| 749 | D4 | — | 27 | 1 | no | — |
| 750 | D4 | — | 27 | 1 | no | — |
| 751 | D4 | — | 27 | 1 | no | — |
| 752 | D4 | — | 27 | 1 | no | — |
| 753 | D4 | — | 27 | 2 | no | — |
| 754 | D4 | — | 27 | 1 | no | — |
| 755 | D4 | — | 27 | 1 | no | — |
| 756 | C2×C4 | — | 3 | 1 | no | — |
| 757 | C2×C4 | — | 9 | 1 | no | — |
| 758 | C2×C4 | — | 9 | 1 | no | — |
| 759 | C2×C4 | — | 9 | 1 | no | — |
| 760 | C2×C4 | — | 9 | 1 | no | — |
| 761 | C2×C4 | — | 9 | 1 | no | — |
| 762 | C2×C4 | — | 9 | 1 | no | — |
| 763 | C2×C4 | — | 9 | 1 | no | — |
| 764 | C2×C4 | — | 9 | 2 | no | — |
| 765 | C2×C4 | — | 9 | 1 | no | — |
| 766 | C2×C4 | — | 27 | 1 | no | — |
| 767 | C2×C4 | — | 27 | 1 | no | — |
| 768 | C2×C4 | — | 27 | 1 | no | — |
| 769 | C2×C4 | — | 27 | 2 | no | — |
| 770 | C2×C4 | — | 27 | 1 | no | — |
| 771 | C2×C4 | — | 27 | 1 | no | — |
| 772 | C2×C4 | — | 27 | 2 | no | — |
| 773 | C2×C4 | — | 27 | 1 | no | — |
| 774 | C2×C4 | — | 27 | 1 | no | — |
| 775 | C2×C4 | — | 27 | 2 | no | — |
| 776 | C2×C3 | — | 2 | 1 | no | — |
| 777 | C2×C3 | — | 2 | 1 | no | — |
| 778 | C2×C3 | — | 2 | 1 | no | — |
| 779 | C2×C3 | — | 3 | 2 | no | — |
| 780 | C2×C3 | — | 4 | 1 | no | — |
| 781 | C2×C3 | — | 4 | 1 | no | — |
| 782 | C2×C3 | — | 6 | 1 | no | — |
| 783 | C2×C3 | — | 6 | 1 | no | — |
| 784 | C2×C3 | — | 8 | 1 | no | — |
| 785 | C2×C3 | — | 8 | 2 | no | — |
| 786 | C2×C3 | — | 8 | 1 | no | — |
| 787 | C2×C3 | — | 8 | 1 | no | — |
| 788 | C2×C3 | — | 12 | 2 | no | — |
| 789 | C2×C3 | — | 16 | 1 | no | — |
| 790 | C2×C3 | — | 16 | 2 | no | — |
| 791 | C2×C3 | — | 16 | 1 | no | — |
| 792 | C2×C3 | — | 18 | 1 | no | — |
| 793 | C2×C3 | — | 24 | 2 | no | — |
| 794 | C2×C3 | — | 24 | 1 | no | — |
| 795 | C2×C3 | — | 24 | 1 | no | — |
| 796 | C2×C3 | — | 24 | 2 | no | — |
| 797 | C2×C3 | — | 48 | 1 | no | — |
| 798 | C2×C3 | — | 72 | 1 | no | — |
| 799 | C2×C3 | C22×D3×A4 | 1 | 1 | yes | characteristic |
| 800 | C2×C3 | C22×D3×A4 | 1 | 1 | yes | characteristic |
| 801 | D3 | — | 2 | 1 | no | — |
| 802 | D3 | — | 2 | 1 | no | — |
| 803 | D3 | — | 6 | 1 | no | — |
| 804 | D3 | — | 6 | 1 | no | — |
| 805 | D3 | — | 6 | 1 | no | — |
| 806 | D3 | — | 12 | 1 | no | — |
| 807 | D3 | — | 18 | 1 | no | — |
| 808 | D3 | — | 18 | 1 | no | — |
| 809 | D3 | — | 36 | 1 | no | — |
| 810 | D3 | #1007⋊C3 | 1 | 2 | yes | direct product factor |
| 811 | C22 | — | 3 | 1 | no | — |
| 812 | C22 | — | 3 | 1 | no | — |
| 813 | C22 | — | 3 | 1 | no | — |
| 814 | C22 | — | 6 | 2 | no | — |
| 815 | C22 | — | 9 | 1 | no | — |
| 816 | C22 | — | 9 | 1 | no | — |
| 817 | C22 | — | 18 | 2 | no | — |
| 818 | C22 | — | 27 | 1 | no | — |
| 819 | C22 | — | 54 | 2 | no | — |
| 820 | C22 | D32×A4 | 1 | 1 | yes | characteristic |
| 821 | C4 | — | 3 | 1 | no | — |
| 822 | C4 | — | 3 | 1 | no | — |
| 823 | C4 | — | 3 | 1 | no | — |
| 824 | C4 | — | 9 | 1 | no | — |
| 825 | C4 | — | 9 | 1 | no | — |
| 826 | C4 | — | 9 | 1 | no | — |
| 827 | C4 | — | 9 | 1 | no | — |
| 828 | C4 | — | 27 | 1 | no | — |
| 829 | C3 | — | 2 | 1 | no | — |
| 830 | C3 | — | 4 | 1 | no | — |
| 831 | C3 | — | 8 | 1 | no | — |
| 832 | C3 | — | 8 | 1 | no | — |
| 833 | C3 | — | 16 | 1 | no | — |
| 834 | C3 | C2×#1007⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 835 | C3 | D3×2−1+4⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 836 | C2 | — | 2 | 1 | no | — |
| 837 | C2 | — | 3 | 2 | no | — |
| 838 | C2 | — | 6 | 1 | no | — |
| 839 | C2 | — | 6 | 1 | no | — |
| 840 | C2 | — | 18 | 1 | no | — |
| 841 | C2 | — | 18 | 1 | no | — |
| 842 | C2 | — | 54 | 1 | no | — |
| 843 | C2 | C2×D32×A4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D32×A4 |
| commutator, cosocle, hypocenter | C32×Q8 | C23×C3 |
| Fitting | C2×C32×Q8 | C22×C3 |
| socle | C2×C32 | C23×A4 |
| hypercenter | C22 | D32×A4 |
| LCS | G ▷ C32×Q8 | |
| UCS | C1 ◁ C2 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11724490 | C2 | semidirect |
| 2. C3×#1007⋊C3 | C2 | semidirect |
| 3. C2×C3×D3×SL(2,𝔽3) | C2 | semidirect |
| 4. D32×SL(2,𝔽3) | C2 | semidirect |
| 5. #64315⋊C3 | C2 | semidirect |
| 6. #64316⋊C3 | C2 | semidirect |
| 7. D3×C3⋊(#41⋊C3) | C2 | semidirect |
| 8. D3×#1007 | C3 | semidirect |
| 11. C2×C32×SL(2,𝔽3) | C22 | semidirect |
| 13. C3⋊D3×SL(2,𝔽3) | C22 | semidirect |
| 14. C3⋊(C3⋊(#41⋊C3)) | C22 | semidirect |
| 16. C3×D3×SL(2,𝔽3) | C22 | semidirect |
| 17. C3×D3×SL(2,𝔽3) | C22 | semidirect |
| 18. C3×C3⋊(#41⋊C3) | C22 | semidirect |
| 19. #64364 | C2×C3 | semidirect |
| 20. C3×#1007 | C2×C3 | semidirect |
| 21. C2×C3×D3×Q8 | C2×C3 | semidirect |
| 25. D3×#239 | C2×C3 | semidirect |
| 27. D32×Q8 | C2×C3 | semidirect |
| 29. #64316 | C2×C3 | semidirect |
| 31. #64315 | C2×C3 | semidirect |
| 45. #1007⋊C3 | D3 | direct (N × H) |
| 49. C2×D3×SL(2,𝔽3) | D3 | semidirect |
| 62. C2×C32×Q8 | C22×C3 | semidirect |
| 64. #3832 | C22×C3 | semidirect |
| 66. Q8×C3⋊D3 | C22×C3 | semidirect |
| 71. C3×#239 | C22×C3 | semidirect |
| 76. C3×D3×Q8 | C22×C3 | semidirect |
| 77. C3×D3×Q8 | C22×C3 | semidirect |
| 91. C2×C3×SL(2,𝔽3) | C2×D3 | semidirect |
| 92. C2×C3×SL(2,𝔽3) | C2×D3 | semidirect |
| 131. D3×SL(2,𝔽3) | C2×D3 | semidirect |
| 132. D3×SL(2,𝔽3) | C2×D3 | semidirect |
| 137. C3⋊(#41⋊C3) | C2×D3 | semidirect |
| 168. #1007 | C3×D3 | semidirect |
| 175. C2×D3×Q8 | C3×D3 | semidirect |
| 279. C2×C3×Q8 | C2×C3×D3 | semidirect |
| 280. C2×C3×Q8 | C2×C3×D3 | semidirect |
| 300. #239 | C2×C3×D3 | semidirect |
| 322. D3×Q8 | C2×C3×D3 | semidirect |
| 323. D3×Q8 | C2×C3×D3 | semidirect |
| 388. C2×SL(2,𝔽3) | D32 | semidirect |
| 608. C3×D3 | 2−1+4⋊C3 | semidirect |
| 650. C2×Q8 | C3×D32 | semidirect |
| 725. C32 | C2×2−1+4⋊C3 | semidirect |
| 810. D3 | #1007⋊C3 | direct (N × H) |
| 834. C3 | C2×#1007⋊C3 | semidirect |
| 835. C3 | D3×2−1+4⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724490 | 2 |
| C3×#1007⋊C3 | 2 |
| C2×C3×D3×SL(2,𝔽3) | 2 |
| D32×SL(2,𝔽3) | 2 |
| #64315⋊C3 | 2 |
| #64316⋊C3 | 2 |
| D3×C3⋊(#41⋊C3) | 2 |
| D3×#1007 | 3 |
| D3×2−1+4⋊C3 | 3 |
| C2×#1007⋊C3 | 3 |
| C3×D3×#67 | 4 |