Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1010 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 1010 conjugacy classes of subgroups — too many to draw. Only its 86 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 | C3×A4×#67 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11724473 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×C3×C3⋊SL(2,ℤ/4) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11724205 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | D3×C3⋊SL(2,ℤ/4) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11724201 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11724199 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10596577 | — | 3 | 1 | no | maximal |
| 9 | #10596467 | — | 3 | 3 | no | maximal |
| 10 | #10595493 | — | 3 | 1 | no | maximal |
| 11 | C22×C32×A4 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C3×D3×A4 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C3⋊(C3⋊S4) | C22 | 1 | 1 | yes | characteristic |
| 14 | #89028 | — | 4 | 1 | no | maximal |
| 15 | C3×Dic3×A4 | C22 | 1 | 1 | yes | characteristic |
| 16 | C3⋊(C3⋊SL(2,ℤ/4)) | C22 | 1 | 1 | yes | characteristic |
| 17 | C3×C3⋊SL(2,ℤ/4) | C22 | 1 | 1 | yes | characteristic |
| 18 | C3×C3⋊SL(2,ℤ/4) | C22 | 1 | 1 | yes | characteristic |
| 19 | C22×C3×#67 | D3 | 1 | 1 | yes | characteristic, complemented |
| 20 | C3×D4×A4 | — | 3 | 1 | no | — |
| 21 | C2×#3804 | — | 3 | 1 | no | — |
| 22 | A4×#67 | D3 | 1 | 3 | yes | complemented |
| 23 | #64269 | — | 3 | 1 | no | — |
| 24 | #64269 | — | 3 | 1 | no | — |
| 25 | #64269 | — | 3 | 3 | no | — |
| 26 | #64269 | — | 6 | 1 | no | — |
| 27 | #64269 | — | 6 | 3 | no | — |
| 28 | C2×C3⋊SL(2,ℤ/4) | — | 3 | 1 | no | — |
| 29 | C2×C3⋊SL(2,ℤ/4) | D3 | 1 | 1 | yes | characteristic, complemented |
| 30 | C4×C3⋊S4 | — | 3 | 1 | no | — |
| 31 | #64259 | — | 3 | 1 | no | — |
| 32 | C2×C3×SL(2,ℤ/4) | — | 3 | 3 | no | — |
| 33 | #64210 | — | 3 | 3 | no | — |
| 34 | D3×SL(2,ℤ/4) | — | 3 | 3 | no | — |
| 35 | (C3⋊S4)⋊C4 | — | 3 | 3 | no | — |
| 36 | #64204 | — | 3 | 3 | no | — |
| 37 | #64162 | — | 3 | 1 | no | — |
| 38 | C2×C3×#217 | — | 3 | 1 | no | — |
| 39 | #63978 | — | 3 | 1 | no | — |
| 40 | #63977 | — | 3 | 1 | no | — |
| 41 | Dic3×#67 | — | 3 | 1 | no | — |
| 42 | #63971 | — | 3 | 1 | no | — |
| 43 | #63969 | — | 3 | 1 | no | — |
| 44 | D3×#217 | — | 3 | 1 | no | — |
| 45 | #63964 | — | 3 | 1 | no | — |
| 46 | #63961 | — | 3 | 1 | no | — |
| 47 | #63959 | — | 3 | 1 | no | — |
| 48 | #63958 | — | 3 | 1 | no | — |
| 49 | #63952 | — | 3 | 1 | no | — |
| 50 | C2×C32×A4 | — | 2 | 1 | no | — |
| 51 | C2×C32×A4 | C23 | 1 | 1 | yes | characteristic |
| 52 | C3×D3×A4 | — | 2 | 1 | no | — |
| 53 | C3⋊(C3⋊S4) | — | 2 | 1 | no | — |
| 54 | #6312 | — | 4 | 1 | no | — |
| 55 | C2×C3×C3⋊Dic3 | — | 4 | 1 | no | — |
| 56 | C32×#67 | — | 4 | 1 | no | — |
| 57 | #6293 | — | 4 | 1 | no | — |
| 58 | #6291 | — | 4 | 1 | no | — |
| 59 | #6289 | — | 4 | 1 | no | — |
| 60 | D3×C3⋊Dic3 | — | 4 | 1 | no | — |
| 61 | #5914 | — | 9 | 3 | no | — |
| 62 | #5806 | — | 9 | 1 | no | — |
| 63 | #5490 | — | 9 | 1 | no | — |
| 64 | C24×C32 | C2×D3 | 1 | 1 | yes | characteristic |
| 65 | C23×C3×D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 66 | C22×C3×A4 | — | 2 | 1 | no | — |
| 67 | C22×C3×A4 | — | 2 | 3 | no | — |
| 68 | C22×C3×A4 | — | 3 | 1 | no | — |
| 69 | C22×C3×A4 | C2×D3 | 1 | 3 | yes | — |
| 70 | C22×C3×A4 | C2×D3 | 1 | 1 | yes | characteristic |
| 71 | C2×D3×A4 | C2×D3 | 1 | 3 | yes | — |
| 72 | C2×C3⋊S4 | — | 3 | 1 | no | — |
| 73 | C2×C3⋊S4 | — | 3 | 3 | no | — |
| 74 | C2×C3⋊S4 | — | 6 | 1 | no | — |
| 75 | C2×C3⋊S4 | — | 6 | 3 | no | — |
| 76 | C2×#638 | — | 3 | 1 | no | — |
| 77 | C2×#638 | — | 3 | 1 | no | — |
| 78 | C2×#638 | — | 3 | 1 | no | — |
| 79 | #3830 | — | 12 | 1 | no | — |
| 80 | C2×C3×#67 | — | 3 | 1 | no | — |
| 81 | C2×C3×#67 | — | 3 | 1 | no | — |
| 82 | C2×C3×#67 | — | 3 | 1 | no | — |
| 83 | C2×C3×#67 | — | 3 | 1 | no | — |
| 84 | C22×C3×Dic3 | — | 3 | 1 | no | — |
| 85 | C22×C3×Dic3 | — | 3 | 1 | no | — |
| 86 | C22×C3×Dic3 | C2×D3 | 1 | 1 | yes | characteristic |
| 87 | C3×C4×A4 | — | 3 | 1 | no | — |
| 88 | C2×#627 | — | 3 | 1 | no | — |
| 89 | C2×#626 | — | 3 | 1 | no | — |
| 90 | C2×#626 | — | 3 | 1 | no | — |
| 91 | C2×#624 | — | 3 | 1 | no | — |
| 92 | #3804 | — | 6 | 1 | no | — |
| 93 | #3804 | — | 6 | 1 | no | — |
| 94 | #3804 | — | 6 | 1 | no | — |
| 95 | #3804 | — | 6 | 1 | no | — |
| 96 | #3804 | — | 12 | 3 | no | — |
| 97 | C2×D3×Dic3 | — | 3 | 1 | no | — |
| 98 | C2×D3×Dic3 | — | 3 | 1 | no | — |
| 99 | Dic3×A4 | C2×D3 | 1 | 3 | yes | — |
| 100 | C3⋊SL(2,ℤ/4) | — | 3 | 1 | no | — |
| 101 | C3⋊SL(2,ℤ/4) | — | 3 | 3 | no | — |
| 102 | C3⋊SL(2,ℤ/4) | — | 6 | 1 | no | — |
| 103 | C3⋊SL(2,ℤ/4) | — | 6 | 3 | no | — |
| 104 | C3⋊SL(2,ℤ/4) | C2×D3 | 1 | 1 | yes | characteristic |
| 105 | C3⋊SL(2,ℤ/4) | C2×D3 | 1 | 1 | yes | characteristic |
| 106 | C3×SL(2,ℤ/4) | — | 3 | 3 | no | — |
| 107 | C3×SL(2,ℤ/4) | — | 3 | 3 | no | — |
| 108 | #3757 | — | 3 | 1 | no | — |
| 109 | #3757 | — | 3 | 1 | no | — |
| 110 | #3757 | — | 3 | 1 | no | — |
| 111 | C3×#217 | — | 3 | 1 | no | — |
| 112 | C3×#217 | — | 3 | 1 | no | — |
| 113 | C3×#217 | — | 3 | 1 | no | — |
| 114 | C3×#217 | — | 3 | 1 | no | — |
| 115 | #3724 | — | 3 | 1 | no | — |
| 116 | #3724 | — | 3 | 1 | no | — |
| 117 | Dic3⋊Dic3 | — | 3 | 1 | no | — |
| 118 | Dic3⋊Dic3 | — | 3 | 1 | no | — |
| 119 | #3722 | — | 3 | 1 | no | — |
| 120 | (C2×D3)⋊Dic3 | — | 3 | 1 | no | — |
| 121 | (C2×D3)⋊Dic3 | — | 3 | 1 | no | — |
| 122 | (C2×D3)⋊Dic3 | — | 3 | 1 | no | — |
| 123 | (C2×D3)⋊Dic3 | — | 3 | 1 | no | — |
| 124 | Dic32 | — | 3 | 1 | no | — |
| 125 | C22×C33 | — | 4 | 1 | no | — |
| 126 | C2×C3⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 127 | C2×C32×D3 | — | 4 | 1 | no | — |
| 128 | C32×A4 | #41 | 1 | 1 | yes | characteristic, complemented |
| 129 | C3⋊(C3⋊Dic3) | — | 4 | 1 | no | — |
| 130 | C3×C3⋊Dic3 | — | 4 | 1 | no | — |
| 131 | C3×C3⋊Dic3 | — | 4 | 1 | no | — |
| 132 | C32×Dic3 | — | 4 | 1 | no | — |
| 133 | C22×C3×D4 | — | 3 | 1 | no | — |
| 134 | C22×#67 | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 135 | C2×#237 | — | 9 | 1 | no | — |
| 136 | C2×#235 | — | 9 | 1 | no | — |
| 137 | D4×A4 | — | 3 | 3 | no | — |
| 138 | GL(2,ℤ/4) | — | 9 | 3 | no | — |
| 139 | GL(2,ℤ/4) | — | 9 | 3 | no | — |
| 140 | GL(2,ℤ/4) | — | 18 | 3 | no | — |
| 141 | C2×SL(2,ℤ/4) | — | 3 | 3 | no | — |
| 142 | C2×SL(2,ℤ/4) | — | 9 | 3 | no | — |
| 143 | C4×S4 | — | 9 | 3 | no | — |
| 144 | A4⋊Q8 | — | 9 | 3 | no | — |
| 145 | C2×C3×C22⋊C4 | — | 9 | 1 | no | — |
| 146 | #953 | — | 9 | 1 | no | — |
| 147 | #953 | — | 9 | 1 | no | — |
| 148 | #953 | — | 9 | 1 | no | — |
| 149 | #953 | — | 18 | 1 | no | — |
| 150 | C2×#217 | — | 3 | 1 | no | — |
| 151 | C2×#217 | — | 9 | 1 | no | — |
| 152 | #939 | — | 9 | 1 | no | — |
| 153 | #939 | — | 9 | 1 | no | — |
| 154 | #938 | — | 9 | 1 | no | — |
| 155 | #936 | — | 9 | 1 | no | — |
| 156 | #935 | — | 9 | 1 | no | — |
| 157 | #935 | — | 9 | 1 | no | — |
| 158 | D4×Dic3 | — | 9 | 1 | no | — |
| 159 | #930 | — | 9 | 1 | no | — |
| 160 | #929 | — | 9 | 1 | no | — |
| 161 | C4×#67 | — | 9 | 1 | no | — |
| 162 | C4×#67 | — | 9 | 1 | no | — |
| 163 | #924 | — | 9 | 1 | no | — |
| 164 | #885 | — | 9 | 1 | no | — |
| 165 | #884 | — | 9 | 1 | no | — |
| 166 | #884 | — | 9 | 1 | no | — |
| 167 | #883 | — | 9 | 1 | no | — |
| 168 | #882 | — | 9 | 1 | no | — |
| 169 | #67⋊C4 | — | 9 | 1 | no | — |
| 170 | D3×C22⋊C4 | — | 9 | 1 | no | — |
| 171 | #878 | — | 9 | 1 | no | — |
| 172 | C23×C32 | — | 2 | 1 | no | — |
| 173 | C23×C32 | — | 3 | 1 | no | — |
| 174 | C23×C32 | — | 3 | 1 | no | — |
| 175 | C23×C32 | — | 6 | 1 | no | — |
| 176 | C23×C32 | C22×D3 | 1 | 1 | yes | characteristic |
| 177 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 178 | C22×C3×D3 | — | 2 | 1 | no | — |
| 179 | C22×C3×D3 | — | 3 | 1 | no | — |
| 180 | C22×C3×D3 | — | 3 | 1 | no | — |
| 181 | C22×C3×D3 | — | 6 | 1 | no | — |
| 182 | C2×C3×A4 | — | 2 | 1 | no | — |
| 183 | C2×C3×A4 | — | 2 | 1 | no | — |
| 184 | C2×C3×A4 | — | 2 | 3 | no | — |
| 185 | C2×C3×A4 | — | 2 | 3 | no | — |
| 186 | C2×C3×A4 | — | 4 | 3 | no | — |
| 187 | C2×C3×A4 | — | 4 | 1 | no | — |
| 188 | C2×C3×A4 | — | 6 | 1 | no | — |
| 189 | C2×C3×A4 | C22×D3 | 1 | 3 | yes | — |
| 190 | C2×C3×A4 | C22×D3 | 1 | 1 | yes | characteristic |
| 191 | D3×A4 | — | 2 | 3 | no | — |
| 192 | C3⋊S4 | — | 6 | 1 | no | — |
| 193 | C3⋊S4 | — | 6 | 3 | no | — |
| 194 | C3⋊S4 | — | 12 | 1 | no | — |
| 195 | C3⋊S4 | — | 12 | 3 | no | — |
| 196 | C32×D4 | — | 12 | 1 | no | — |
| 197 | #638 | — | 6 | 1 | no | — |
| 198 | #638 | — | 6 | 1 | no | — |
| 199 | #638 | — | 6 | 1 | no | — |
| 200 | #638 | — | 6 | 1 | no | — |
| 201 | #638 | — | 12 | 1 | no | — |
| 202 | #638 | — | 12 | 1 | no | — |
| 203 | #638 | — | 12 | 3 | no | — |
| 204 | #638 | — | 12 | 1 | no | — |
| 205 | #638 | — | 24 | 1 | no | — |
| 206 | #638 | — | 24 | 3 | no | — |
| 207 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 208 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 209 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 210 | C2×C3⋊Dic3 | — | 4 | 1 | no | — |
| 211 | C2×C3⋊Dic3 | — | 12 | 1 | no | — |
| 212 | C4×C3⋊D3 | — | 12 | 1 | no | — |
| 213 | #634 | — | 12 | 1 | no | — |
| 214 | C3×#67 | — | 3 | 1 | no | — |
| 215 | C3×#67 | — | 3 | 1 | no | — |
| 216 | C3×#67 | — | 3 | 1 | no | — |
| 217 | C3×#67 | — | 4 | 3 | no | — |
| 218 | C3×#67 | — | 6 | 1 | no | — |
| 219 | C3×#67 | S4 | 1 | 1 | yes | characteristic, complemented |
| 220 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 221 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 222 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 223 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 224 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 225 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 226 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 227 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 228 | C2×C3×Dic3 | — | 12 | 3 | no | — |
| 229 | C2×C3×Dic3 | — | 12 | 1 | no | — |
| 230 | #627 | — | 6 | 1 | no | — |
| 231 | #627 | — | 6 | 1 | no | — |
| 232 | #627 | — | 12 | 3 | no | — |
| 233 | #626 | — | 6 | 1 | no | — |
| 234 | #626 | — | 6 | 1 | no | — |
| 235 | #626 | — | 12 | 3 | no | — |
| 236 | #626 | — | 12 | 1 | no | — |
| 237 | #624 | — | 6 | 1 | no | — |
| 238 | #624 | — | 6 | 1 | no | — |
| 239 | #624 | — | 12 | 3 | no | — |
| 240 | D3×Dic3 | — | 6 | 1 | no | — |
| 241 | D3×Dic3 | — | 6 | 1 | no | — |
| 242 | D3×Dic3 | — | 12 | 3 | no | — |
| 243 | D3×Dic3 | — | 12 | 1 | no | — |
| 244 | #546 | — | 27 | 1 | no | Sylow |
| 245 | C2×C33 | — | 4 | 1 | no | — |
| 246 | C2×C33 | — | 8 | 1 | no | — |
| 247 | C3⋊(C3⋊D3) | — | 8 | 1 | no | — |
| 248 | C32×D3 | — | 8 | 1 | no | — |
| 249 | C24×C3 | — | 2 | 1 | no | — |
| 250 | C24×C3 | — | 3 | 1 | no | — |
| 251 | C24×C3 | D32 | 1 | 1 | yes | characteristic |
| 252 | C24×C3 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 253 | C23×D3 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 254 | C22×A4 | — | 2 | 3 | no | — |
| 255 | C22×A4 | — | 3 | 3 | no | — |
| 256 | C22×A4 | D32 | 1 | 3 | yes | — |
| 257 | C2×S4 | — | 9 | 3 | no | — |
| 258 | C2×S4 | — | 18 | 3 | no | — |
| 259 | C2×C3×D4 | — | 9 | 1 | no | — |
| 260 | C2×C3×D4 | — | 9 | 1 | no | — |
| 261 | C2×C3×D4 | — | 9 | 1 | no | — |
| 262 | C2×C3×D4 | — | 9 | 1 | no | — |
| 263 | C22×C3×C4 | — | 3 | 1 | no | — |
| 264 | C22×C3×C4 | — | 9 | 1 | no | — |
| 265 | C22×C3×C4 | — | 9 | 1 | no | — |
| 266 | C2×#67 | — | 3 | 1 | no | — |
| 267 | C2×#67 | — | 3 | 1 | no | — |
| 268 | C2×#67 | — | 3 | 1 | no | — |
| 269 | C2×#67 | — | 3 | 1 | no | — |
| 270 | C2×#67 | — | 9 | 1 | no | — |
| 271 | C2×#67 | — | 9 | 1 | no | — |
| 272 | C2×#67 | — | 9 | 1 | no | — |
| 273 | C2×#67 | — | 9 | 1 | no | — |
| 274 | C2×#67 | — | 9 | 1 | no | — |
| 275 | C2×#67 | — | 9 | 1 | no | — |
| 276 | C2×#67 | — | 9 | 1 | no | — |
| 277 | C2×#67 | — | 9 | 1 | no | — |
| 278 | C2×#67 | — | 18 | 1 | no | — |
| 279 | C2×#67 | — | 18 | 1 | no | — |
| 280 | C2×#67 | — | 18 | 1 | no | — |
| 281 | C22×Dic3 | — | 3 | 1 | no | — |
| 282 | C22×Dic3 | — | 3 | 1 | no | — |
| 283 | C22×Dic3 | — | 9 | 1 | no | — |
| 284 | C22×Dic3 | — | 9 | 1 | no | — |
| 285 | C22×Dic3 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 286 | #237 | — | 18 | 1 | no | — |
| 287 | #237 | — | 18 | 1 | no | — |
| 288 | #237 | — | 18 | 1 | no | — |
| 289 | #237 | — | 18 | 1 | no | — |
| 290 | #237 | — | 36 | 3 | no | — |
| 291 | #235 | — | 18 | 1 | no | — |
| 292 | #235 | — | 18 | 1 | no | — |
| 293 | #235 | — | 18 | 1 | no | — |
| 294 | #235 | — | 18 | 1 | no | — |
| 295 | C2×D12 | — | 9 | 1 | no | — |
| 296 | C2×D12 | — | 9 | 1 | no | — |
| 297 | C2×C4×D3 | — | 9 | 1 | no | — |
| 298 | C2×C4×D3 | — | 9 | 1 | no | — |
| 299 | C2×C4×D3 | — | 9 | 1 | no | — |
| 300 | C2×C4×D3 | — | 9 | 1 | no | — |
| 301 | C2×Dic6 | — | 9 | 1 | no | — |
| 302 | C2×Dic6 | — | 9 | 1 | no | — |
| 303 | C4×A4 | — | 3 | 3 | no | — |
| 304 | SL(2,ℤ/4) | — | 3 | 3 | no | — |
| 305 | SL(2,ℤ/4) | — | 3 | 3 | no | — |
| 306 | SL(2,ℤ/4) | — | 9 | 3 | no | — |
| 307 | SL(2,ℤ/4) | — | 18 | 3 | no | — |
| 308 | C3×C22⋊C4 | — | 9 | 1 | no | — |
| 309 | C3×C22⋊C4 | — | 9 | 1 | no | — |
| 310 | C3×C22⋊C4 | — | 9 | 1 | no | — |
| 311 | C3×C22⋊C4 | — | 9 | 1 | no | — |
| 312 | #217 | — | 3 | 1 | no | — |
| 313 | #217 | — | 3 | 1 | no | — |
| 314 | #217 | — | 3 | 1 | no | — |
| 315 | #217 | — | 3 | 1 | no | — |
| 316 | #217 | — | 9 | 1 | no | — |
| 317 | #217 | — | 9 | 1 | no | — |
| 318 | #217 | — | 9 | 1 | no | — |
| 319 | #217 | — | 9 | 1 | no | — |
| 320 | #217 | — | 9 | 1 | no | — |
| 321 | #217 | — | 9 | 1 | no | — |
| 322 | #217 | — | 9 | 1 | no | — |
| 323 | #217 | — | 9 | 1 | no | — |
| 324 | #217 | — | 9 | 1 | no | — |
| 325 | #217 | — | 9 | 1 | no | — |
| 326 | #217 | — | 18 | 1 | no | — |
| 327 | #217 | — | 18 | 1 | no | — |
| 328 | #217 | — | 18 | 1 | no | — |
| 329 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 330 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 331 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 332 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 333 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 334 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 335 | C4⋊Dic3 | — | 9 | 1 | no | — |
| 336 | C4⋊Dic3 | — | 9 | 1 | no | — |
| 337 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 338 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 339 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 340 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 341 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 342 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 343 | C4×Dic3 | — | 9 | 1 | no | — |
| 344 | C4×Dic3 | — | 9 | 1 | no | — |
| 345 | C22×C32 | — | 3 | 1 | no | — |
| 346 | C22×C32 | — | 3 | 1 | no | — |
| 347 | C22×C32 | — | 3 | 1 | no | — |
| 348 | C22×C32 | — | 4 | 1 | no | — |
| 349 | C22×C32 | — | 4 | 3 | no | — |
| 350 | C22×C32 | — | 6 | 1 | no | — |
| 351 | C22×C32 | — | 6 | 1 | no | — |
| 352 | C22×C32 | — | 6 | 1 | no | — |
| 353 | C22×C32 | — | 6 | 1 | no | — |
| 354 | C22×C32 | — | 8 | 3 | no | — |
| 355 | C22×C32 | — | 8 | 1 | no | — |
| 356 | C22×C32 | — | 12 | 1 | no | — |
| 357 | C22×C32 | #237 | 1 | 1 | yes | characteristic, complemented |
| 358 | C22×C32 | C2×S4 | 1 | 1 | yes | characteristic |
| 359 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 360 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 361 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 362 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 363 | C2×C3⋊D3 | — | 12 | 3 | no | — |
| 364 | C2×C3⋊D3 | — | 24 | 1 | no | — |
| 365 | C2×C3⋊D3 | — | 24 | 3 | no | — |
| 366 | C2×C3×D3 | — | 3 | 1 | no | — |
| 367 | C2×C3×D3 | — | 4 | 3 | no | — |
| 368 | C2×C3×D3 | — | 6 | 1 | no | — |
| 369 | C2×C3×D3 | — | 6 | 1 | no | — |
| 370 | C2×C3×D3 | — | 6 | 1 | no | — |
| 371 | C2×C3×D3 | — | 6 | 1 | no | — |
| 372 | C2×C3×D3 | C2×S4 | 1 | 1 | yes | characteristic |
| 373 | C3×A4 | — | 2 | 1 | no | — |
| 374 | C3×A4 | — | 2 | 3 | no | — |
| 375 | C3×A4 | #235 | 1 | 1 | yes | characteristic, complemented |
| 376 | C3×A4 | #237 | 1 | 3 | yes | complemented |
| 377 | C32×C4 | — | 12 | 1 | no | — |
| 378 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 379 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 380 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 381 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 382 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 383 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 384 | C3⋊Dic3 | — | 12 | 3 | no | — |
| 385 | C3⋊Dic3 | — | 24 | 1 | no | — |
| 386 | C3⋊Dic3 | — | 24 | 3 | no | — |
| 387 | C3×Dic3 | — | 3 | 1 | no | — |
| 388 | C3×Dic3 | — | 4 | 3 | no | — |
| 389 | C3×Dic3 | — | 6 | 1 | no | — |
| 390 | C3×Dic3 | — | 6 | 1 | no | — |
| 391 | C3×Dic3 | — | 6 | 1 | no | — |
| 392 | C3×Dic3 | — | 6 | 1 | no | — |
| 393 | C3×Dic3 | — | 12 | 3 | no | — |
| 394 | C3×Dic3 | — | 12 | 3 | no | — |
| 395 | C3×Dic3 | C2×S4 | 1 | 1 | yes | characteristic |
| 396 | C2×#41 | — | 27 | 1 | no | — |
| 397 | C22×D4 | — | 3 | 1 | no | — |
| 398 | #124 | — | 27 | 1 | no | — |
| 399 | #123 | — | 27 | 1 | no | — |
| 400 | #123 | — | 27 | 1 | no | — |
| 401 | C22⋊Q8 | — | 27 | 1 | no | — |
| 402 | #121 | — | 27 | 1 | no | — |
| 403 | #121 | — | 27 | 1 | no | — |
| 404 | #121 | — | 27 | 1 | no | — |
| 405 | #120 | — | 27 | 1 | no | — |
| 406 | #120 | — | 27 | 1 | no | — |
| 407 | C4×D4 | — | 27 | 1 | no | — |
| 408 | C4×D4 | — | 27 | 1 | no | — |
| 409 | C2×C22⋊C4 | — | 9 | 1 | no | — |
| 410 | C2×C22⋊C4 | — | 27 | 1 | no | — |
| 411 | C33 | — | 4 | 1 | no | Sylow |
| 412 | C23×C3 | — | 2 | 1 | no | — |
| 413 | C23×C3 | — | 2 | 1 | no | — |
| 414 | C23×C3 | — | 2 | 1 | no | — |
| 415 | C23×C3 | — | 3 | 1 | no | — |
| 416 | C23×C3 | — | 3 | 1 | no | — |
| 417 | C23×C3 | — | 3 | 1 | no | — |
| 418 | C23×C3 | — | 3 | 1 | no | — |
| 419 | C23×C3 | — | 4 | 1 | no | — |
| 420 | C23×C3 | — | 6 | 1 | no | — |
| 421 | C23×C3 | — | 6 | 1 | no | — |
| 422 | C23×C3 | — | 6 | 1 | no | — |
| 423 | C23×C3 | — | 6 | 1 | no | — |
| 424 | C23×C3 | — | 6 | 1 | no | — |
| 425 | C23×C3 | — | 9 | 1 | no | — |
| 426 | C23×C3 | — | 9 | 1 | no | — |
| 427 | C23×C3 | — | 12 | 1 | no | — |
| 428 | C23×C3 | — | 18 | 1 | no | — |
| 429 | C23×C3 | C2×D32 | 1 | 1 | yes | characteristic |
| 430 | C23×C3 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 431 | C22×D3 | — | 2 | 1 | no | — |
| 432 | C22×D3 | — | 3 | 1 | no | — |
| 433 | C22×D3 | — | 3 | 1 | no | — |
| 434 | C22×D3 | — | 6 | 1 | no | — |
| 435 | C22×D3 | — | 9 | 1 | no | — |
| 436 | C22×D3 | — | 9 | 1 | no | — |
| 437 | C22×D3 | — | 18 | 1 | no | — |
| 438 | C2×A4 | — | 2 | 3 | no | — |
| 439 | C2×A4 | — | 2 | 3 | no | — |
| 440 | C2×A4 | — | 4 | 3 | no | — |
| 441 | C2×A4 | — | 6 | 3 | no | — |
| 442 | C2×A4 | C2×D32 | 1 | 3 | yes | — |
| 443 | S4 | — | 18 | 3 | no | — |
| 444 | S4 | — | 36 | 3 | no | — |
| 445 | C3×D4 | — | 3 | 1 | no | — |
| 446 | C3×D4 | — | 9 | 1 | no | — |
| 447 | C3×D4 | — | 9 | 1 | no | — |
| 448 | C3×D4 | — | 9 | 1 | no | — |
| 449 | C3×D4 | — | 12 | 3 | no | — |
| 450 | C3×D4 | — | 18 | 1 | no | — |
| 451 | C2×C3×C4 | — | 9 | 1 | no | — |
| 452 | C2×C3×C4 | — | 9 | 1 | no | — |
| 453 | C2×C3×C4 | — | 9 | 1 | no | — |
| 454 | C2×C3×C4 | — | 9 | 1 | no | — |
| 455 | C2×C3×C4 | — | 9 | 1 | no | — |
| 456 | C2×C3×C4 | — | 9 | 1 | no | — |
| 457 | C2×C3×C4 | — | 18 | 1 | no | — |
| 458 | C2×C3×C4 | — | 18 | 1 | no | — |
| 459 | C2×C3×C4 | — | 36 | 1 | no | — |
| 460 | #67 | — | 3 | 1 | no | — |
| 461 | #67 | — | 3 | 1 | no | — |
| 462 | #67 | — | 3 | 1 | no | — |
| 463 | #67 | — | 6 | 1 | no | — |
| 464 | #67 | — | 18 | 1 | no | — |
| 465 | #67 | — | 18 | 1 | no | — |
| 466 | #67 | — | 18 | 1 | no | — |
| 467 | #67 | — | 18 | 1 | no | — |
| 468 | #67 | — | 18 | 1 | no | — |
| 469 | #67 | — | 18 | 1 | no | — |
| 470 | #67 | — | 18 | 1 | no | — |
| 471 | #67 | — | 18 | 1 | no | — |
| 472 | #67 | — | 18 | 1 | no | — |
| 473 | #67 | — | 18 | 1 | no | — |
| 474 | #67 | — | 36 | 3 | no | — |
| 475 | #67 | — | 36 | 1 | no | — |
| 476 | #67 | — | 36 | 1 | no | — |
| 477 | #67 | — | 36 | 3 | no | — |
| 478 | #67 | — | 36 | 1 | no | — |
| 479 | #67 | — | 36 | 1 | no | — |
| 480 | #67 | — | 36 | 1 | no | — |
| 481 | #67 | — | 36 | 1 | no | — |
| 482 | #67 | — | 36 | 1 | no | — |
| 483 | #67 | — | 36 | 2 | no | — |
| 484 | #67 | — | 72 | 3 | no | — |
| 485 | #67 | C3⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 486 | C2×Dic3 | — | 3 | 1 | no | — |
| 487 | C2×Dic3 | — | 3 | 1 | no | — |
| 488 | C2×Dic3 | — | 3 | 1 | no | — |
| 489 | C2×Dic3 | — | 3 | 1 | no | — |
| 490 | C2×Dic3 | — | 3 | 1 | no | — |
| 491 | C2×Dic3 | — | 3 | 1 | no | — |
| 492 | C2×Dic3 | — | 6 | 1 | no | — |
| 493 | C2×Dic3 | — | 6 | 1 | no | — |
| 494 | C2×Dic3 | — | 9 | 1 | no | — |
| 495 | C2×Dic3 | — | 9 | 1 | no | — |
| 496 | C2×Dic3 | — | 9 | 1 | no | — |
| 497 | C2×Dic3 | — | 9 | 1 | no | — |
| 498 | C2×Dic3 | — | 9 | 1 | no | — |
| 499 | C2×Dic3 | — | 9 | 1 | no | — |
| 500 | C2×Dic3 | — | 12 | 3 | no | — |
| 501 | C2×Dic3 | — | 12 | 1 | no | — |
| 502 | C2×Dic3 | — | 18 | 1 | no | — |
| 503 | C2×Dic3 | — | 18 | 1 | no | — |
| 504 | C2×Dic3 | — | 18 | 1 | no | — |
| 505 | C2×Dic3 | — | 18 | 1 | no | — |
| 506 | C2×Dic3 | — | 18 | 1 | no | — |
| 507 | C2×Dic3 | — | 36 | 3 | no | — |
| 508 | C2×Dic3 | — | 36 | 1 | no | — |
| 509 | D12 | — | 18 | 1 | no | — |
| 510 | D12 | — | 18 | 1 | no | — |
| 511 | D12 | — | 36 | 1 | no | — |
| 512 | C4×D3 | — | 18 | 1 | no | — |
| 513 | C4×D3 | — | 18 | 1 | no | — |
| 514 | C4×D3 | — | 18 | 1 | no | — |
| 515 | C4×D3 | — | 18 | 1 | no | — |
| 516 | C4×D3 | — | 18 | 1 | no | — |
| 517 | C4×D3 | — | 18 | 1 | no | — |
| 518 | C4×D3 | — | 36 | 3 | no | — |
| 519 | C4×D3 | — | 36 | 1 | no | — |
| 520 | Dic6 | — | 18 | 1 | no | — |
| 521 | Dic6 | — | 18 | 1 | no | — |
| 522 | Dic6 | — | 18 | 1 | no | — |
| 523 | Dic6 | — | 18 | 1 | no | — |
| 524 | Dic6 | — | 36 | 3 | no | — |
| 525 | C2×C32 | — | 2 | 1 | no | — |
| 526 | C2×C32 | — | 3 | 1 | no | — |
| 527 | C2×C32 | — | 3 | 1 | no | — |
| 528 | C2×C32 | — | 4 | 1 | no | — |
| 529 | C2×C32 | — | 4 | 3 | no | — |
| 530 | C2×C32 | — | 6 | 1 | no | — |
| 531 | C2×C32 | — | 8 | 3 | no | — |
| 532 | C2×C32 | — | 8 | 1 | no | — |
| 533 | C2×C32 | — | 8 | 3 | no | — |
| 534 | C2×C32 | — | 8 | 1 | no | — |
| 535 | C2×C32 | — | 16 | 1 | no | — |
| 536 | C2×C32 | — | 16 | 3 | no | — |
| 537 | C2×C32 | — | 24 | 1 | no | — |
| 538 | C2×C32 | C22×S4 | 1 | 1 | yes | characteristic |
| 539 | C3⋊D3 | — | 12 | 1 | no | — |
| 540 | C3⋊D3 | — | 24 | 1 | no | — |
| 541 | C3⋊D3 | — | 24 | 3 | no | — |
| 542 | C3⋊D3 | — | 48 | 1 | no | — |
| 543 | C3⋊D3 | — | 48 | 3 | no | — |
| 544 | C3×D3 | — | 2 | 1 | no | — |
| 545 | C3×D3 | — | 6 | 1 | no | — |
| 546 | C3×D3 | — | 8 | 3 | no | — |
| 547 | C24 | — | 3 | 1 | no | — |
| 548 | C24 | D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 549 | #41 | — | 54 | 1 | no | — |
| 550 | #41 | — | 54 | 1 | no | — |
| 551 | #41 | — | 54 | 1 | no | — |
| 552 | #41 | — | 54 | 1 | no | — |
| 553 | C2×Q8 | — | 27 | 1 | no | — |
| 554 | C2×D4 | — | 9 | 1 | no | — |
| 555 | C2×D4 | — | 9 | 1 | no | — |
| 556 | C2×D4 | — | 9 | 1 | no | — |
| 557 | C2×D4 | — | 9 | 1 | no | — |
| 558 | C2×D4 | — | 27 | 1 | no | — |
| 559 | C2×D4 | — | 27 | 1 | no | — |
| 560 | C2×D4 | — | 27 | 1 | no | — |
| 561 | C2×D4 | — | 27 | 1 | no | — |
| 562 | C2×D4 | — | 27 | 1 | no | — |
| 563 | C22×C4 | — | 3 | 1 | no | — |
| 564 | C22×C4 | — | 9 | 1 | no | — |
| 565 | C22×C4 | — | 9 | 1 | no | — |
| 566 | C22×C4 | — | 27 | 1 | no | — |
| 567 | C22×C4 | — | 27 | 1 | no | — |
| 568 | C22×C4 | — | 27 | 1 | no | — |
| 569 | C4⋊C4 | — | 27 | 1 | no | — |
| 570 | C4⋊C4 | — | 27 | 1 | no | — |
| 571 | C4⋊C4 | — | 27 | 1 | no | — |
| 572 | C4⋊C4 | — | 27 | 1 | no | — |
| 573 | C22⋊C4 | — | 9 | 1 | no | — |
| 574 | C22⋊C4 | — | 9 | 1 | no | — |
| 575 | C22⋊C4 | — | 9 | 1 | no | — |
| 576 | C22⋊C4 | — | 9 | 1 | no | — |
| 577 | C22⋊C4 | — | 27 | 1 | no | — |
| 578 | C22⋊C4 | — | 27 | 1 | no | — |
| 579 | C22⋊C4 | — | 27 | 1 | no | — |
| 580 | C22⋊C4 | — | 27 | 1 | no | — |
| 581 | C22⋊C4 | — | 27 | 1 | no | — |
| 582 | C22⋊C4 | — | 27 | 1 | no | — |
| 583 | C22⋊C4 | — | 27 | 1 | no | — |
| 584 | C22⋊C4 | — | 27 | 1 | no | — |
| 585 | C42 | — | 27 | 1 | no | — |
| 586 | C22×C3 | — | 2 | 1 | no | — |
| 587 | C22×C3 | — | 2 | 1 | no | — |
| 588 | C22×C3 | — | 3 | 1 | no | — |
| 589 | C22×C3 | — | 3 | 1 | no | — |
| 590 | C22×C3 | — | 3 | 1 | no | — |
| 591 | C22×C3 | — | 3 | 1 | no | — |
| 592 | C22×C3 | — | 3 | 1 | no | — |
| 593 | C22×C3 | — | 3 | 1 | no | — |
| 594 | C22×C3 | — | 3 | 1 | no | — |
| 595 | C22×C3 | — | 4 | 3 | no | — |
| 596 | C22×C3 | — | 6 | 1 | no | — |
| 597 | C22×C3 | — | 6 | 1 | no | — |
| 598 | C22×C3 | — | 6 | 1 | no | — |
| 599 | C22×C3 | — | 6 | 1 | no | — |
| 600 | C22×C3 | — | 6 | 1 | no | — |
| 601 | C22×C3 | — | 6 | 1 | no | — |
| 602 | C22×C3 | — | 6 | 1 | no | — |
| 603 | C22×C3 | — | 6 | 1 | no | — |
| 604 | C22×C3 | — | 6 | 1 | no | — |
| 605 | C22×C3 | — | 6 | 1 | no | — |
| 606 | C22×C3 | — | 6 | 1 | no | — |
| 607 | C22×C3 | — | 6 | 2 | no | — |
| 608 | C22×C3 | — | 8 | 3 | no | — |
| 609 | C22×C3 | — | 9 | 1 | no | — |
| 610 | C22×C3 | — | 12 | 3 | no | — |
| 611 | C22×C3 | — | 12 | 1 | no | — |
| 612 | C22×C3 | — | 12 | 1 | no | — |
| 613 | C22×C3 | — | 12 | 1 | no | — |
| 614 | C22×C3 | — | 18 | 1 | no | — |
| 615 | C22×C3 | — | 18 | 1 | no | — |
| 616 | C22×C3 | — | 18 | 1 | no | — |
| 617 | C22×C3 | — | 18 | 1 | no | — |
| 618 | C22×C3 | #3804 | 1 | 1 | yes | characteristic, complemented |
| 619 | C22×C3 | #3830 | 1 | 1 | yes | characteristic, complemented |
| 620 | C22×C3 | D3×S4 | 1 | 1 | yes | characteristic |
| 621 | C22×C3 | C2×C3⋊S4 | 1 | 1 | yes | characteristic |
| 622 | C2×D3 | — | 3 | 1 | no | — |
| 623 | C2×D3 | — | 6 | 1 | no | — |
| 624 | C2×D3 | — | 6 | 1 | no | — |
| 625 | C2×D3 | — | 6 | 1 | no | — |
| 626 | C2×D3 | — | 6 | 1 | no | — |
| 627 | C2×D3 | — | 18 | 1 | no | — |
| 628 | C2×D3 | — | 18 | 1 | no | — |
| 629 | C2×D3 | — | 18 | 1 | no | — |
| 630 | C2×D3 | — | 18 | 1 | no | — |
| 631 | C2×D3 | — | 18 | 1 | no | — |
| 632 | C2×D3 | — | 18 | 1 | no | — |
| 633 | C2×D3 | — | 36 | 1 | no | — |
| 634 | C2×D3 | — | 36 | 3 | no | — |
| 635 | C2×D3 | — | 36 | 1 | no | — |
| 636 | C2×D3 | — | 36 | 1 | no | — |
| 637 | C2×D3 | — | 72 | 3 | no | — |
| 638 | C2×D3 | C2×C3⋊S4 | 1 | 1 | yes | characteristic |
| 639 | A4 | — | 2 | 3 | no | — |
| 640 | A4 | #3804 | 1 | 3 | yes | complemented |
| 641 | C3×C4 | — | 3 | 1 | no | — |
| 642 | C3×C4 | — | 9 | 1 | no | — |
| 643 | C3×C4 | — | 12 | 3 | no | — |
| 644 | C3×C4 | — | 18 | 1 | no | — |
| 645 | C3×C4 | — | 18 | 1 | no | — |
| 646 | C3×C4 | — | 18 | 1 | no | — |
| 647 | C3×C4 | — | 18 | 1 | no | — |
| 648 | Dic3 | — | 3 | 1 | no | — |
| 649 | Dic3 | — | 6 | 1 | no | — |
| 650 | Dic3 | — | 6 | 1 | no | — |
| 651 | Dic3 | — | 6 | 1 | no | — |
| 652 | Dic3 | — | 6 | 1 | no | — |
| 653 | Dic3 | — | 12 | 3 | no | — |
| 654 | Dic3 | — | 12 | 3 | no | — |
| 655 | Dic3 | — | 18 | 1 | no | — |
| 656 | Dic3 | — | 18 | 1 | no | — |
| 657 | Dic3 | — | 18 | 1 | no | — |
| 658 | Dic3 | — | 18 | 1 | no | — |
| 659 | Dic3 | — | 18 | 1 | no | — |
| 660 | Dic3 | — | 18 | 1 | no | — |
| 661 | Dic3 | — | 36 | 1 | no | — |
| 662 | Dic3 | — | 36 | 3 | no | — |
| 663 | Dic3 | — | 36 | 1 | no | — |
| 664 | Dic3 | — | 36 | 1 | no | — |
| 665 | Dic3 | — | 72 | 3 | no | — |
| 666 | Dic3 | C2×C3⋊S4 | 1 | 1 | yes | characteristic |
| 667 | C32 | — | 4 | 1 | no | — |
| 668 | C32 | — | 4 | 3 | no | — |
| 669 | C32 | — | 8 | 3 | no | — |
| 670 | C32 | — | 8 | 1 | no | — |
| 671 | C32 | #5914 | 1 | 1 | yes | characteristic, complemented |
| 672 | C23 | — | 2 | 1 | no | — |
| 673 | C23 | — | 3 | 1 | no | — |
| 674 | C23 | — | 3 | 1 | no | — |
| 675 | C23 | — | 6 | 1 | no | — |
| 676 | C23 | — | 6 | 1 | no | — |
| 677 | C23 | — | 9 | 1 | no | — |
| 678 | C23 | — | 9 | 1 | no | — |
| 679 | C23 | — | 18 | 1 | no | — |
| 680 | C23 | — | 27 | 1 | no | — |
| 681 | C23 | C2×D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 682 | Q8 | — | 54 | 1 | no | — |
| 683 | Q8 | — | 54 | 1 | no | — |
| 684 | D4 | — | 3 | 1 | no | — |
| 685 | D4 | — | 9 | 1 | no | — |
| 686 | D4 | — | 9 | 1 | no | — |
| 687 | D4 | — | 9 | 1 | no | — |
| 688 | D4 | — | 18 | 1 | no | — |
| 689 | D4 | — | 54 | 1 | no | — |
| 690 | D4 | — | 54 | 1 | no | — |
| 691 | D4 | — | 54 | 1 | no | — |
| 692 | D4 | — | 54 | 1 | no | — |
| 693 | D4 | — | 54 | 1 | no | — |
| 694 | D4 | — | 54 | 1 | no | — |
| 695 | D4 | — | 108 | 1 | no | — |
| 696 | D4 | — | 108 | 1 | no | — |
| 697 | C2×C4 | — | 9 | 1 | no | — |
| 698 | C2×C4 | — | 9 | 1 | no | — |
| 699 | C2×C4 | — | 9 | 1 | no | — |
| 700 | C2×C4 | — | 9 | 1 | no | — |
| 701 | C2×C4 | — | 9 | 1 | no | — |
| 702 | C2×C4 | — | 9 | 1 | no | — |
| 703 | C2×C4 | — | 18 | 1 | no | — |
| 704 | C2×C4 | — | 18 | 1 | no | — |
| 705 | C2×C4 | — | 27 | 1 | no | — |
| 706 | C2×C4 | — | 27 | 1 | no | — |
| 707 | C2×C4 | — | 27 | 1 | no | — |
| 708 | C2×C4 | — | 36 | 1 | no | — |
| 709 | C2×C4 | — | 54 | 1 | no | — |
| 710 | C2×C4 | — | 54 | 1 | no | — |
| 711 | C2×C4 | — | 54 | 1 | no | — |
| 712 | C2×C4 | — | 54 | 1 | no | — |
| 713 | C2×C4 | — | 108 | 1 | no | — |
| 714 | C2×C3 | — | 2 | 1 | no | — |
| 715 | C2×C3 | — | 2 | 1 | no | — |
| 716 | C2×C3 | — | 2 | 1 | no | — |
| 717 | C2×C3 | — | 3 | 1 | no | — |
| 718 | C2×C3 | — | 3 | 1 | no | — |
| 719 | C2×C3 | — | 3 | 1 | no | — |
| 720 | C2×C3 | — | 3 | 1 | no | — |
| 721 | C2×C3 | — | 4 | 1 | no | — |
| 722 | C2×C3 | — | 4 | 3 | no | — |
| 723 | C2×C3 | — | 6 | 1 | no | — |
| 724 | C2×C3 | — | 6 | 1 | no | — |
| 725 | C2×C3 | — | 6 | 1 | no | — |
| 726 | C2×C3 | — | 6 | 1 | no | — |
| 727 | C2×C3 | — | 6 | 1 | no | — |
| 728 | C2×C3 | — | 8 | 3 | no | — |
| 729 | C2×C3 | — | 8 | 3 | no | — |
| 730 | C2×C3 | — | 12 | 1 | no | — |
| 731 | C2×C3 | — | 16 | 3 | no | — |
| 732 | C2×C3 | — | 18 | 1 | no | — |
| 733 | C2×C3 | — | 24 | 3 | no | — |
| 734 | C2×C3 | C2×D3×S4 | 1 | 1 | yes | characteristic |
| 735 | C2×C3 | C22×C3⋊S4 | 1 | 1 | yes | characteristic |
| 736 | D3 | — | 2 | 1 | no | — |
| 737 | D3 | — | 6 | 1 | no | — |
| 738 | D3 | — | 36 | 1 | no | — |
| 739 | D3 | — | 36 | 1 | no | — |
| 740 | D3 | — | 72 | 1 | no | — |
| 741 | D3 | — | 72 | 3 | no | — |
| 742 | D3 | — | 144 | 3 | no | — |
| 743 | C22 | — | 3 | 1 | no | — |
| 744 | C22 | — | 3 | 1 | no | — |
| 745 | C22 | — | 3 | 1 | no | — |
| 746 | C22 | — | 3 | 1 | no | — |
| 747 | C22 | — | 6 | 1 | no | — |
| 748 | C22 | — | 6 | 1 | no | — |
| 749 | C22 | — | 6 | 1 | no | — |
| 750 | C22 | — | 6 | 1 | no | — |
| 751 | C22 | — | 9 | 1 | no | — |
| 752 | C22 | — | 18 | 1 | no | — |
| 753 | C22 | — | 18 | 1 | no | — |
| 754 | C22 | — | 18 | 1 | no | — |
| 755 | C22 | — | 18 | 1 | no | — |
| 756 | C22 | — | 54 | 1 | no | — |
| 757 | C22 | — | 54 | 1 | no | — |
| 758 | C22 | — | 54 | 1 | no | — |
| 759 | C22 | #89028 | 1 | 1 | yes | characteristic, complemented |
| 760 | C22 | D3×C3⋊S4 | 1 | 1 | yes | characteristic |
| 761 | C4 | — | 3 | 1 | no | — |
| 762 | C4 | — | 9 | 1 | no | — |
| 763 | C4 | — | 18 | 1 | no | — |
| 764 | C4 | — | 18 | 1 | no | — |
| 765 | C4 | — | 18 | 1 | no | — |
| 766 | C4 | — | 18 | 1 | no | — |
| 767 | C4 | — | 54 | 1 | no | — |
| 768 | C4 | — | 54 | 1 | no | — |
| 769 | C4 | — | 54 | 1 | no | — |
| 770 | C3 | — | 2 | 1 | no | — |
| 771 | C3 | — | 4 | 3 | no | — |
| 772 | C3 | — | 8 | 3 | no | — |
| 773 | C3 | #10596467 | 1 | 1 | yes | characteristic, complemented |
| 774 | C3 | #10596577 | 1 | 1 | yes | characteristic, complemented |
| 775 | C2 | — | 2 | 1 | no | — |
| 776 | C2 | — | 3 | 1 | no | — |
| 777 | C2 | — | 3 | 1 | no | — |
| 778 | C2 | — | 6 | 1 | no | — |
| 779 | C2 | — | 6 | 1 | no | — |
| 780 | C2 | — | 18 | 1 | no | — |
| 781 | C2 | — | 108 | 1 | no | — |
| 782 | C2 | C2×D3×C3⋊S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D3×C3⋊S4 |
| commutator, cosocle | C2×C32×A4 | C23 |
| Fitting | C24×C32 | C2×D3 |
| socle | C23×C32 | C22×D3 |
| hypercenter | C22 | D3×C3⋊S4 |
| hypocenter | C32×A4 | #41 |
| LCS | G ▷ C2×C32×A4 ▷ C32×A4 | |
| UCS | C1 ◁ C2 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×A4×#67 | C2 | semidirect |
| 2. #11724473 | C2 | semidirect |
| 3. C2×C3×C3⋊SL(2,ℤ/4) | C2 | semidirect |
| 4. #11724205 | C2 | semidirect |
| 5. D3×C3⋊SL(2,ℤ/4) | C2 | semidirect |
| 6. #11724201 | C2 | semidirect |
| 7. #11724199 | C2 | semidirect |
| 19. C22×C3×#67 | D3 | semidirect |
| 22. A4×#67 | D3 | semidirect |
| 29. C2×C3⋊SL(2,ℤ/4) | D3 | semidirect |
| 128. C32×A4 | #41 | semidirect |
| 134. C22×#67 | C3⋊D3 | semidirect |
| 219. C3×#67 | S4 | semidirect |
| 357. C22×C32 | #237 | semidirect |
| 375. C3×A4 | #235 | semidirect |
| 376. C3×A4 | #237 | semidirect |
| 485. #67 | C3⋊S4 | semidirect |
| 618. C22×C3 | #3804 | semidirect |
| 619. C22×C3 | #3830 | semidirect |
| 640. A4 | #3804 | semidirect |
| 671. C32 | #5914 | semidirect |
| 759. C22 | #89028 | semidirect |
| 773. C3 | #10596467 | semidirect |
| 774. C3 | #10596577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×A4×#67 | 2 |
| #11724473 | 2 |
| C2×C3×C3⋊SL(2,ℤ/4) | 2 |
| #11724205 | 2 |
| D3×C3⋊SL(2,ℤ/4) | 2 |
| #11724201 | 2 |
| #11724199 | 2 |
| #10596577 | 3 |
| #10596467 | 3 |
| #10595493 | 3 |
| #89028 | 4 |