Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1475 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 1475 conjugacy classes of subgroups — too many to draw. Only its 88 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 | C22×C3⋊(C3⋊S4) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×D3×C3⋊S4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×A4×#67 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#64269 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11724205 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11724202 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11724201 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | D4×C3⋊S4 | — | 3 | 1 | no | maximal |
| 9 | #10596473 | — | 3 | 3 | no | maximal |
| 10 | #10595526 | — | 3 | 1 | no | maximal |
| 11 | C22×C32×A4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C2×C3×D3×A4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C2×C3⋊(C3⋊S4) | — | 2 | 2 | no | — |
| 14 | C2×C3⋊(C3⋊S4) | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C3⋊(C3⋊S4) | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C2×C3×C3⋊S4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | D3×C3⋊S4 | — | 2 | 2 | no | — |
| 18 | #89039 | — | 4 | 1 | no | maximal |
| 19 | C3×Dic3×A4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C3×C3⋊SL(2,ℤ/4) | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C22×C3⋊S4 | — | 3 | 1 | no | — |
| 22 | C22×C3⋊S4 | — | 3 | 3 | no | — |
| 23 | C22×C3⋊S4 | — | 3 | 1 | no | — |
| 24 | C22×C3⋊S4 | — | 6 | 1 | no | — |
| 25 | C22×C3⋊S4 | — | 6 | 3 | no | — |
| 26 | C2×D3×S4 | — | 3 | 3 | no | — |
| 27 | C22×#638 | — | 3 | 1 | no | — |
| 28 | C22×C3×#67 | D3 | 1 | 1 | yes | characteristic, complemented |
| 29 | C3×D4×A4 | — | 3 | 1 | no | — |
| 30 | C2×#3811 | — | 3 | 1 | no | — |
| 31 | C2×D3×#67 | — | 3 | 1 | no | — |
| 32 | A4×#67 | D3 | 1 | 3 | yes | complemented |
| 33 | #64269 | — | 3 | 1 | no | — |
| 34 | #64269 | D3 | 1 | 1 | yes | characteristic, complemented |
| 35 | C4⋊(C3⋊S4) | — | 3 | 1 | no | — |
| 36 | C4×C3⋊S4 | — | 3 | 1 | no | — |
| 37 | C3×GL(2,ℤ/4) | — | 3 | 3 | no | — |
| 38 | #64210 | — | 3 | 3 | no | — |
| 39 | #64207 | — | 3 | 3 | no | — |
| 40 | (C3⋊S4)⋊C4 | — | 3 | 3 | no | — |
| 41 | C3×#953 | — | 3 | 1 | no | — |
| 42 | #63983 | — | 3 | 1 | no | — |
| 43 | #63981 | — | 3 | 1 | no | — |
| 44 | #63980 | — | 3 | 1 | no | — |
| 45 | #63979 | — | 3 | 1 | no | — |
| 46 | #63978 | — | 3 | 1 | no | — |
| 47 | #63977 | — | 3 | 1 | no | — |
| 48 | #67⋊Dic3 | — | 3 | 1 | no | — |
| 49 | #63971 | — | 3 | 1 | no | — |
| 50 | #63958 | — | 3 | 1 | no | — |
| 51 | #63952 | — | 3 | 1 | no | — |
| 52 | C22×C3⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 53 | C2×C32×A4 | — | 2 | 1 | no | — |
| 54 | C2×C32×A4 | C23 | 1 | 1 | yes | characteristic |
| 55 | C2×D3×C3⋊D3 | — | 4 | 1 | no | — |
| 56 | C3×D3×A4 | — | 2 | 1 | no | — |
| 57 | C3⋊(C3⋊S4) | — | 2 | 1 | no | — |
| 58 | C3⋊(C3⋊S4) | D4 | 1 | 2 | yes | complemented |
| 59 | C3×C3⋊S4 | — | 2 | 1 | no | — |
| 60 | C3×#638 | — | 4 | 1 | no | — |
| 61 | C32×#67 | — | 4 | 1 | no | — |
| 62 | #6292 | — | 4 | 1 | no | — |
| 63 | #6291 | — | 4 | 1 | no | — |
| 64 | #6289 | — | 4 | 1 | no | — |
| 65 | D4×S4 | — | 9 | 3 | no | — |
| 66 | D4×#67 | — | 9 | 1 | no | — |
| 67 | #5590 | — | 9 | 1 | no | — |
| 68 | C24×C32 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 69 | C23×C3⋊D3 | — | 3 | 1 | no | — |
| 70 | C23×C3×D3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 71 | C22×C3×A4 | — | 2 | 1 | no | — |
| 72 | C22×C3×A4 | — | 2 | 3 | no | — |
| 73 | C22×C3×A4 | — | 3 | 1 | no | — |
| 74 | C22×C3×A4 | C2×D3 | 1 | 3 | yes | complemented |
| 75 | C22×C3×A4 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 76 | C22×D32 | — | 3 | 1 | no | — |
| 77 | C2×D3×A4 | C2×D3 | 1 | 3 | yes | complemented |
| 78 | C2×C3⋊S4 | — | 3 | 1 | no | — |
| 79 | C2×C3⋊S4 | — | 3 | 3 | no | — |
| 80 | C2×C3⋊S4 | — | 3 | 1 | no | — |
| 81 | C2×C3⋊S4 | — | 3 | 3 | no | — |
| 82 | C2×C3⋊S4 | — | 6 | 2 | no | — |
| 83 | C2×C3⋊S4 | — | 6 | 2 | no | — |
| 84 | C2×C3⋊S4 | — | 6 | 6 | no | — |
| 85 | C2×C3⋊S4 | — | 6 | 1 | no | — |
| 86 | C2×C3⋊S4 | — | 6 | 1 | no | — |
| 87 | C2×C3⋊S4 | — | 6 | 3 | no | — |
| 88 | C2×C3⋊S4 | — | 6 | 3 | no | — |
| 89 | C2×C3⋊S4 | — | 6 | 4 | no | — |
| 90 | C2×C3⋊S4 | — | 6 | 12 | no | — |
| 91 | C2×C3⋊S4 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 92 | C2×C3×S4 | — | 3 | 3 | no | — |
| 93 | D3×S4 | — | 6 | 6 | no | — |
| 94 | C2×#638 | — | 3 | 1 | no | — |
| 95 | C2×#638 | — | 3 | 1 | no | — |
| 96 | C2×#638 | — | 3 | 1 | no | — |
| 97 | C2×#638 | — | 3 | 1 | no | — |
| 98 | C2×#638 | — | 6 | 2 | no | — |
| 99 | C2×#638 | — | 6 | 2 | no | — |
| 100 | C22×C3⋊Dic3 | — | 3 | 1 | no | — |
| 101 | D4×C3⋊D3 | — | 12 | 1 | no | — |
| 102 | C2×C3×#67 | — | 3 | 1 | no | — |
| 103 | C2×C3×#67 | — | 3 | 1 | no | — |
| 104 | C2×C3×#67 | — | 3 | 1 | no | — |
| 105 | C2×C3×#67 | — | 3 | 1 | no | — |
| 106 | C2×C3×#67 | — | 3 | 1 | no | — |
| 107 | C2×C3×#67 | — | 3 | 1 | no | — |
| 108 | C2×C3×#67 | — | 3 | 1 | no | — |
| 109 | C22×C3×Dic3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 110 | C3×C4×A4 | — | 3 | 1 | no | — |
| 111 | #3811 | — | 6 | 1 | no | — |
| 112 | #3811 | — | 6 | 1 | no | — |
| 113 | #3811 | — | 6 | 1 | no | — |
| 114 | #3811 | — | 6 | 1 | no | — |
| 115 | #3811 | — | 12 | 3 | no | — |
| 116 | D3×#67 | — | 6 | 2 | no | — |
| 117 | D3×#67 | — | 6 | 2 | no | — |
| 118 | C2×#626 | — | 3 | 1 | no | — |
| 119 | C2×#626 | — | 3 | 1 | no | — |
| 120 | C2×#626 | — | 3 | 1 | no | — |
| 121 | C2×#626 | — | 3 | 1 | no | — |
| 122 | C2×#625 | — | 3 | 1 | no | — |
| 123 | C2×#624 | — | 3 | 1 | no | — |
| 124 | C2×D3×Dic3 | — | 3 | 1 | no | — |
| 125 | Dic3×A4 | C2×D3 | 1 | 3 | yes | complemented |
| 126 | C3⋊SL(2,ℤ/4) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 127 | C3×SL(2,ℤ/4) | — | 3 | 3 | no | — |
| 128 | C3×#217 | — | 3 | 1 | no | — |
| 129 | C3×#217 | — | 3 | 1 | no | — |
| 130 | C3×#217 | — | 3 | 1 | no | — |
| 131 | #3724 | — | 3 | 1 | no | — |
| 132 | Dic3⋊Dic3 | — | 3 | 1 | no | — |
| 133 | #3722 | — | 3 | 1 | no | — |
| 134 | #3722 | — | 3 | 1 | no | — |
| 135 | (C2×D3)⋊Dic3 | — | 3 | 1 | no | — |
| 136 | (C2×D3)⋊Dic3 | — | 3 | 1 | no | — |
| 137 | (C2×D3)⋊Dic3 | — | 3 | 1 | no | — |
| 138 | Dic32 | — | 3 | 1 | no | — |
| 139 | C22×C33 | — | 4 | 1 | no | — |
| 140 | C2×C3⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 141 | C2×C3⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 142 | C2×C3⋊(C3⋊D3) | — | 8 | 2 | no | — |
| 143 | C2×C3×C3⋊D3 | — | 4 | 1 | no | — |
| 144 | C2×C32×D3 | — | 4 | 1 | no | — |
| 145 | C32×A4 | C2×D4 | 1 | 1 | yes | characteristic, complemented |
| 146 | D3×C3⋊D3 | — | 8 | 2 | no | — |
| 147 | C3×C3⋊Dic3 | — | 4 | 1 | no | — |
| 148 | C32×Dic3 | — | 4 | 1 | no | — |
| 149 | C22×S4 | — | 9 | 3 | no | — |
| 150 | C22×S4 | — | 9 | 3 | no | — |
| 151 | C22×S4 | — | 18 | 3 | no | — |
| 152 | C22×C3×D4 | — | 3 | 1 | no | — |
| 153 | C22×#67 | — | 9 | 1 | no | — |
| 154 | C22×#67 | — | 9 | 1 | no | — |
| 155 | C22×#67 | — | 9 | 1 | no | — |
| 156 | C22×#67 | — | 18 | 1 | no | — |
| 157 | C22×#67 | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 158 | C2×D3×D4 | — | 9 | 1 | no | — |
| 159 | C2×D3×D4 | — | 9 | 1 | no | — |
| 160 | C2×D3×D4 | — | 9 | 1 | no | — |
| 161 | D4×A4 | — | 3 | 3 | no | — |
| 162 | GL(2,ℤ/4) | — | 3 | 3 | no | — |
| 163 | GL(2,ℤ/4) | — | 9 | 3 | no | — |
| 164 | C4⋊S4 | — | 9 | 3 | no | — |
| 165 | C4×S4 | — | 9 | 3 | no | — |
| 166 | C3×#120 | — | 9 | 1 | no | — |
| 167 | #953 | — | 3 | 1 | no | — |
| 168 | #953 | — | 9 | 1 | no | — |
| 169 | #940 | — | 9 | 1 | no | — |
| 170 | #940 | — | 9 | 1 | no | — |
| 171 | #939 | — | 9 | 1 | no | — |
| 172 | #939 | — | 9 | 1 | no | — |
| 173 | #939 | — | 9 | 1 | no | — |
| 174 | #939 | — | 9 | 1 | no | — |
| 175 | #938 | — | 9 | 1 | no | — |
| 176 | #937 | — | 9 | 1 | no | — |
| 177 | #937 | — | 9 | 1 | no | — |
| 178 | #937 | — | 9 | 1 | no | — |
| 179 | D4×Dic3 | — | 9 | 1 | no | — |
| 180 | #930 | — | 9 | 1 | no | — |
| 181 | C4×#67 | — | 9 | 1 | no | — |
| 182 | #884 | — | 9 | 1 | no | — |
| 183 | #884 | — | 9 | 1 | no | — |
| 184 | #882 | — | 9 | 1 | no | — |
| 185 | #882 | — | 9 | 1 | no | — |
| 186 | #67⋊C4 | — | 9 | 1 | no | — |
| 187 | #67⋊C4 | — | 9 | 1 | no | — |
| 188 | C23×C32 | — | 2 | 1 | no | — |
| 189 | C23×C32 | — | 3 | 1 | no | — |
| 190 | C23×C32 | — | 3 | 1 | no | — |
| 191 | C23×C32 | — | 6 | 1 | no | — |
| 192 | C23×C32 | C22×D3 | 1 | 1 | yes | characteristic |
| 193 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 194 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 195 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 196 | C22×C3⋊D3 | — | 6 | 1 | no | — |
| 197 | C22×C3⋊D3 | — | 6 | 1 | no | — |
| 198 | C22×C3⋊D3 | — | 12 | 1 | no | — |
| 199 | C22×C3⋊D3 | — | 12 | 1 | no | — |
| 200 | C22×C3⋊D3 | — | 12 | 3 | no | — |
| 201 | C22×C3⋊D3 | — | 12 | 1 | no | — |
| 202 | C22×C3⋊D3 | — | 24 | 1 | no | — |
| 203 | C22×C3⋊D3 | — | 24 | 3 | no | — |
| 204 | C22×C3×D3 | — | 2 | 1 | no | — |
| 205 | C22×C3×D3 | — | 3 | 1 | no | — |
| 206 | C22×C3×D3 | — | 3 | 1 | no | — |
| 207 | C22×C3×D3 | — | 3 | 1 | no | — |
| 208 | C22×C3×D3 | — | 6 | 1 | no | — |
| 209 | C2×C3×A4 | — | 2 | 2 | no | — |
| 210 | C2×C3×A4 | — | 2 | 6 | no | — |
| 211 | C2×C3×A4 | — | 2 | 3 | no | — |
| 212 | C2×C3×A4 | — | 2 | 1 | no | — |
| 213 | C2×C3×A4 | — | 2 | 1 | no | — |
| 214 | C2×C3×A4 | — | 2 | 3 | no | — |
| 215 | C2×C3×A4 | — | 6 | 1 | no | — |
| 216 | C2×C3×A4 | C22×D3 | 1 | 3 | yes | — |
| 217 | C2×C3×A4 | C22×D3 | 1 | 1 | yes | characteristic |
| 218 | C2×D32 | — | 6 | 1 | no | — |
| 219 | C2×D32 | — | 6 | 2 | no | — |
| 220 | C2×D32 | — | 6 | 1 | no | — |
| 221 | C2×D32 | — | 12 | 3 | no | — |
| 222 | C2×D32 | — | 12 | 1 | no | — |
| 223 | D3×A4 | — | 2 | 3 | no | — |
| 224 | C3⋊S4 | — | 2 | 1 | no | — |
| 225 | C3⋊S4 | — | 3 | 2 | no | — |
| 226 | C3⋊S4 | — | 3 | 6 | no | — |
| 227 | C3⋊S4 | — | 6 | 2 | no | — |
| 228 | C3⋊S4 | — | 6 | 6 | no | — |
| 229 | C3⋊S4 | — | 6 | 6 | no | — |
| 230 | C3⋊S4 | — | 6 | 2 | no | — |
| 231 | C3⋊S4 | — | 6 | 1 | no | — |
| 232 | C3⋊S4 | — | 6 | 3 | no | — |
| 233 | C3×S4 | — | 6 | 3 | no | — |
| 234 | C32×D4 | — | 12 | 1 | no | — |
| 235 | #638 | — | 3 | 2 | no | — |
| 236 | #638 | — | 3 | 2 | no | — |
| 237 | #638 | — | 4 | 1 | no | — |
| 238 | #638 | — | 6 | 2 | no | — |
| 239 | #638 | — | 6 | 2 | no | — |
| 240 | #638 | — | 6 | 1 | no | — |
| 241 | #638 | — | 6 | 1 | no | — |
| 242 | #638 | — | 12 | 1 | no | — |
| 243 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 244 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 245 | C2×C3⋊Dic3 | — | 6 | 2 | no | — |
| 246 | C4⋊(C3⋊D3) | — | 12 | 1 | no | — |
| 247 | C4×C3⋊D3 | — | 12 | 1 | no | — |
| 248 | C3×#67 | — | 3 | 1 | no | — |
| 249 | C3×#67 | — | 3 | 1 | no | — |
| 250 | C3×#67 | — | 3 | 1 | no | — |
| 251 | C3×#67 | — | 4 | 3 | no | — |
| 252 | C3×#67 | — | 6 | 1 | no | — |
| 253 | C3×#67 | — | 6 | 1 | no | — |
| 254 | C3×#67 | — | 6 | 1 | no | — |
| 255 | C3×#67 | — | 6 | 1 | no | — |
| 256 | C3×#67 | — | 6 | 1 | no | — |
| 257 | C3×#67 | — | 12 | 3 | no | — |
| 258 | C3×#67 | — | 12 | 1 | no | — |
| 259 | C3×#67 | S4 | 1 | 1 | yes | characteristic, complemented |
| 260 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 261 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 262 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 263 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 264 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 265 | #626 | — | 6 | 1 | no | — |
| 266 | #626 | — | 6 | 1 | no | — |
| 267 | #626 | — | 6 | 2 | no | — |
| 268 | #626 | — | 6 | 1 | no | — |
| 269 | #626 | — | 6 | 1 | no | — |
| 270 | #626 | — | 12 | 3 | no | — |
| 271 | #626 | — | 12 | 3 | no | — |
| 272 | #626 | — | 12 | 1 | no | — |
| 273 | #625 | — | 6 | 2 | no | — |
| 274 | #624 | — | 6 | 1 | no | — |
| 275 | #624 | — | 6 | 1 | no | — |
| 276 | #624 | — | 12 | 3 | no | — |
| 277 | D3×Dic3 | — | 6 | 2 | no | — |
| 278 | D42 | — | 27 | 1 | no | Sylow |
| 279 | C2×C33 | — | 4 | 1 | no | — |
| 280 | C2×C33 | — | 8 | 1 | no | — |
| 281 | C3⋊(C3⋊D3) | — | 4 | 2 | no | — |
| 282 | C3⋊(C3⋊D3) | — | 8 | 1 | no | — |
| 283 | C3×C3⋊D3 | — | 8 | 1 | no | — |
| 284 | C32×D3 | — | 8 | 1 | no | — |
| 285 | C24×C3 | — | 2 | 1 | no | — |
| 286 | C24×C3 | — | 3 | 1 | no | — |
| 287 | C24×C3 | D32 | 1 | 1 | yes | characteristic, complemented |
| 288 | C24×C3 | C2×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 289 | C23×D3 | — | 9 | 1 | no | — |
| 290 | C23×D3 | — | 9 | 1 | no | — |
| 291 | C23×D3 | — | 9 | 1 | no | — |
| 292 | C23×D3 | — | 9 | 1 | no | — |
| 293 | C23×D3 | — | 18 | 1 | no | — |
| 294 | C23×D3 | C2×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 295 | C22×A4 | — | 2 | 3 | no | — |
| 296 | C22×A4 | — | 3 | 3 | no | — |
| 297 | C22×A4 | D32 | 1 | 3 | yes | complemented |
| 298 | C2×S4 | — | 3 | 3 | no | — |
| 299 | C2×S4 | — | 9 | 3 | no | — |
| 300 | C2×S4 | — | 9 | 3 | no | — |
| 301 | C2×S4 | — | 18 | 3 | no | — |
| 302 | C2×S4 | — | 18 | 3 | no | — |
| 303 | C2×S4 | — | 18 | 6 | no | — |
| 304 | C2×S4 | — | 18 | 6 | no | — |
| 305 | C2×S4 | — | 18 | 12 | no | — |
| 306 | C2×C3×D4 | — | 9 | 1 | no | — |
| 307 | C2×C3×D4 | — | 9 | 1 | no | — |
| 308 | C2×C3×D4 | — | 9 | 1 | no | — |
| 309 | C2×C3×D4 | — | 9 | 1 | no | — |
| 310 | C2×C3×D4 | — | 9 | 1 | no | — |
| 311 | C2×C3×D4 | — | 9 | 1 | no | — |
| 312 | C2×C3×D4 | — | 9 | 1 | no | — |
| 313 | C22×C3×C4 | — | 3 | 1 | no | — |
| 314 | C2×#67 | — | 3 | 1 | no | — |
| 315 | C2×#67 | — | 3 | 1 | no | — |
| 316 | C2×#67 | — | 3 | 1 | no | — |
| 317 | C2×#67 | — | 3 | 1 | no | — |
| 318 | C2×#67 | — | 3 | 1 | no | — |
| 319 | C2×#67 | — | 3 | 1 | no | — |
| 320 | C2×#67 | — | 3 | 1 | no | — |
| 321 | C2×#67 | — | 9 | 1 | no | — |
| 322 | C2×#67 | — | 9 | 1 | no | — |
| 323 | C2×#67 | — | 9 | 1 | no | — |
| 324 | C2×#67 | — | 9 | 1 | no | — |
| 325 | C2×#67 | — | 9 | 1 | no | — |
| 326 | C2×#67 | — | 9 | 1 | no | — |
| 327 | C2×#67 | — | 9 | 1 | no | — |
| 328 | C2×#67 | — | 9 | 1 | no | — |
| 329 | C2×#67 | — | 9 | 1 | no | — |
| 330 | C2×#67 | — | 9 | 1 | no | — |
| 331 | C2×#67 | — | 9 | 1 | no | — |
| 332 | C2×#67 | — | 9 | 1 | no | — |
| 333 | C2×#67 | — | 9 | 1 | no | — |
| 334 | C2×#67 | — | 9 | 1 | no | — |
| 335 | C2×#67 | — | 18 | 1 | no | — |
| 336 | C2×#67 | — | 18 | 1 | no | — |
| 337 | C2×#67 | — | 18 | 1 | no | — |
| 338 | C2×#67 | — | 18 | 1 | no | — |
| 339 | C2×#67 | — | 18 | 2 | no | — |
| 340 | C2×#67 | — | 18 | 2 | no | — |
| 341 | C2×#67 | — | 18 | 2 | no | — |
| 342 | C2×#67 | — | 18 | 2 | no | — |
| 343 | C2×#67 | — | 18 | 2 | no | — |
| 344 | C2×#67 | — | 18 | 2 | no | — |
| 345 | C2×#67 | — | 18 | 4 | no | — |
| 346 | C2×#67 | — | 18 | 4 | no | — |
| 347 | C22×Dic3 | — | 9 | 1 | no | — |
| 348 | C22×Dic3 | — | 9 | 1 | no | — |
| 349 | C22×Dic3 | — | 9 | 1 | no | — |
| 350 | C22×Dic3 | — | 18 | 1 | no | — |
| 351 | C22×Dic3 | C2×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 352 | D3×D4 | — | 18 | 1 | no | — |
| 353 | D3×D4 | — | 18 | 1 | no | — |
| 354 | D3×D4 | — | 18 | 1 | no | — |
| 355 | D3×D4 | — | 18 | 1 | no | — |
| 356 | D3×D4 | — | 18 | 1 | no | — |
| 357 | D3×D4 | — | 18 | 1 | no | — |
| 358 | D3×D4 | — | 18 | 1 | no | — |
| 359 | D3×D4 | — | 18 | 2 | no | — |
| 360 | D3×D4 | — | 18 | 2 | no | — |
| 361 | D3×D4 | — | 18 | 1 | no | — |
| 362 | D3×D4 | — | 36 | 3 | no | — |
| 363 | C2×D12 | — | 9 | 1 | no | — |
| 364 | C2×D12 | — | 9 | 1 | no | — |
| 365 | C2×D12 | — | 9 | 1 | no | — |
| 366 | C2×D12 | — | 9 | 1 | no | — |
| 367 | C2×C4×D3 | — | 9 | 1 | no | — |
| 368 | C2×C4×D3 | — | 9 | 1 | no | — |
| 369 | C2×C4×D3 | — | 9 | 1 | no | — |
| 370 | C4×A4 | — | 3 | 3 | no | — |
| 371 | SL(2,ℤ/4) | — | 3 | 3 | no | — |
| 372 | C3×C22⋊C4 | — | 9 | 1 | no | — |
| 373 | C3×C22⋊C4 | — | 9 | 1 | no | — |
| 374 | C3×C22⋊C4 | — | 9 | 1 | no | — |
| 375 | #217 | — | 3 | 1 | no | — |
| 376 | #217 | — | 3 | 1 | no | — |
| 377 | #217 | — | 3 | 1 | no | — |
| 378 | #217 | — | 9 | 1 | no | — |
| 379 | #217 | — | 9 | 1 | no | — |
| 380 | #217 | — | 9 | 1 | no | — |
| 381 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 382 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 383 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 384 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 385 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 386 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 387 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 388 | C4⋊Dic3 | — | 9 | 1 | no | — |
| 389 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 390 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 391 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 392 | C4×Dic3 | — | 9 | 1 | no | — |
| 393 | C4×Dic3 | — | 9 | 1 | no | — |
| 394 | C22×C32 | — | 3 | 1 | no | — |
| 395 | C22×C32 | — | 3 | 1 | no | — |
| 396 | C22×C32 | — | 3 | 1 | no | — |
| 397 | C22×C32 | — | 4 | 1 | no | — |
| 398 | C22×C32 | — | 4 | 3 | no | — |
| 399 | C22×C32 | — | 6 | 1 | no | — |
| 400 | C22×C32 | — | 6 | 1 | no | — |
| 401 | C22×C32 | — | 6 | 1 | no | — |
| 402 | C22×C32 | — | 6 | 1 | no | — |
| 403 | C22×C32 | — | 8 | 3 | no | — |
| 404 | C22×C32 | — | 8 | 1 | no | — |
| 405 | C22×C32 | — | 12 | 1 | no | — |
| 406 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic, complemented |
| 407 | C22×C32 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 408 | C2×C3⋊D3 | — | 3 | 2 | no | — |
| 409 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 410 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 411 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 412 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 413 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 414 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 415 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 416 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 417 | C2×C3⋊D3 | — | 12 | 3 | no | — |
| 418 | C2×C3⋊D3 | — | 12 | 3 | no | — |
| 419 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 420 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 421 | C2×C3⋊D3 | — | 24 | 1 | no | — |
| 422 | C2×C3⋊D3 | — | 24 | 1 | no | — |
| 423 | C2×C3⋊D3 | — | 24 | 3 | no | — |
| 424 | C2×C3⋊D3 | — | 24 | 3 | no | — |
| 425 | C2×C3⋊D3 | — | 24 | 2 | no | — |
| 426 | C2×C3⋊D3 | — | 24 | 2 | no | — |
| 427 | C2×C3⋊D3 | — | 24 | 6 | no | — |
| 428 | C2×C3⋊D3 | — | 24 | 4 | no | — |
| 429 | C2×C3⋊D3 | — | 24 | 12 | no | — |
| 430 | C2×C3×D3 | — | 3 | 1 | no | — |
| 431 | C2×C3×D3 | — | 4 | 3 | no | — |
| 432 | C2×C3×D3 | — | 6 | 1 | no | — |
| 433 | C2×C3×D3 | — | 6 | 1 | no | — |
| 434 | C2×C3×D3 | — | 6 | 1 | no | — |
| 435 | C2×C3×D3 | — | 6 | 1 | no | — |
| 436 | C2×C3×D3 | — | 6 | 1 | no | — |
| 437 | C2×C3×D3 | — | 6 | 1 | no | — |
| 438 | C2×C3×D3 | — | 6 | 1 | no | — |
| 439 | C2×C3×D3 | — | 12 | 3 | no | — |
| 440 | C2×C3×D3 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 441 | C3×A4 | — | 2 | 1 | no | — |
| 442 | C3×A4 | — | 2 | 3 | no | — |
| 443 | C3×A4 | D3×D4 | 1 | 3 | yes | complemented |
| 444 | C3×A4 | D3×D4 | 1 | 1 | yes | characteristic, complemented |
| 445 | D32 | — | 12 | 2 | no | — |
| 446 | D32 | — | 12 | 2 | no | — |
| 447 | D32 | — | 24 | 6 | no | — |
| 448 | C32×C4 | — | 12 | 1 | no | — |
| 449 | C3⋊Dic3 | — | 3 | 2 | no | — |
| 450 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 451 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 452 | C3×Dic3 | — | 3 | 1 | no | — |
| 453 | C3×Dic3 | — | 4 | 3 | no | — |
| 454 | C3×Dic3 | — | 6 | 1 | no | — |
| 455 | C3×Dic3 | — | 6 | 1 | no | — |
| 456 | C3×Dic3 | — | 6 | 1 | no | — |
| 457 | C3×Dic3 | — | 12 | 3 | no | — |
| 458 | C3×Dic3 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 459 | C22×D4 | — | 3 | 1 | no | — |
| 460 | C22×D4 | — | 27 | 1 | no | — |
| 461 | C22×D4 | — | 27 | 1 | no | — |
| 462 | C22×D4 | — | 27 | 1 | no | — |
| 463 | #127 | — | 27 | 1 | no | — |
| 464 | #121 | — | 27 | 1 | no | — |
| 465 | #121 | — | 27 | 1 | no | — |
| 466 | #121 | — | 27 | 1 | no | — |
| 467 | #121 | — | 27 | 1 | no | — |
| 468 | #120 | — | 9 | 1 | no | — |
| 469 | #120 | — | 27 | 1 | no | — |
| 470 | #120 | — | 27 | 1 | no | — |
| 471 | #120 | — | 27 | 1 | no | — |
| 472 | C4×D4 | — | 27 | 1 | no | — |
| 473 | C4×D4 | — | 27 | 1 | no | — |
| 474 | C33 | — | 4 | 1 | no | Sylow |
| 475 | C23×C3 | — | 2 | 2 | no | — |
| 476 | C23×C3 | — | 2 | 1 | no | — |
| 477 | C23×C3 | — | 2 | 1 | no | — |
| 478 | C23×C3 | — | 2 | 1 | no | — |
| 479 | C23×C3 | — | 3 | 1 | no | — |
| 480 | C23×C3 | — | 3 | 1 | no | — |
| 481 | C23×C3 | — | 3 | 1 | no | — |
| 482 | C23×C3 | — | 3 | 1 | no | — |
| 483 | C23×C3 | — | 6 | 1 | no | — |
| 484 | C23×C3 | — | 6 | 1 | no | — |
| 485 | C23×C3 | — | 6 | 1 | no | — |
| 486 | C23×C3 | — | 6 | 1 | no | — |
| 487 | C23×C3 | — | 6 | 2 | no | — |
| 488 | C23×C3 | — | 6 | 1 | no | — |
| 489 | C23×C3 | — | 9 | 1 | no | — |
| 490 | C23×C3 | — | 9 | 1 | no | — |
| 491 | C23×C3 | — | 9 | 1 | no | — |
| 492 | C23×C3 | — | 18 | 1 | no | — |
| 493 | C23×C3 | C2×D32 | 1 | 1 | yes | characteristic |
| 494 | C23×C3 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 495 | C22×D3 | — | 2 | 1 | no | — |
| 496 | C22×D3 | — | 3 | 1 | no | — |
| 497 | C22×D3 | — | 3 | 1 | no | — |
| 498 | C22×D3 | — | 3 | 1 | no | — |
| 499 | C22×D3 | — | 6 | 1 | no | — |
| 500 | C22×D3 | — | 9 | 1 | no | — |
| 501 | C22×D3 | — | 9 | 1 | no | — |
| 502 | C22×D3 | — | 9 | 1 | no | — |
| 503 | C22×D3 | — | 9 | 1 | no | — |
| 504 | C22×D3 | — | 18 | 1 | no | — |
| 505 | C22×D3 | — | 18 | 1 | no | — |
| 506 | C22×D3 | — | 18 | 1 | no | — |
| 507 | C22×D3 | — | 18 | 2 | no | — |
| 508 | C22×D3 | — | 18 | 2 | no | — |
| 509 | C22×D3 | — | 18 | 1 | no | — |
| 510 | C22×D3 | — | 18 | 1 | no | — |
| 511 | C22×D3 | — | 18 | 2 | no | — |
| 512 | C22×D3 | — | 18 | 2 | no | — |
| 513 | C22×D3 | — | 18 | 1 | no | — |
| 514 | C22×D3 | — | 18 | 1 | no | — |
| 515 | C22×D3 | — | 18 | 4 | no | — |
| 516 | C22×D3 | — | 18 | 1 | no | — |
| 517 | C22×D3 | — | 18 | 1 | no | — |
| 518 | C22×D3 | — | 18 | 1 | no | — |
| 519 | C22×D3 | — | 36 | 3 | no | — |
| 520 | C22×D3 | — | 36 | 1 | no | — |
| 521 | C22×D3 | — | 36 | 1 | no | — |
| 522 | C22×D3 | — | 36 | 3 | no | — |
| 523 | C22×D3 | — | 36 | 1 | no | — |
| 524 | C22×D3 | — | 36 | 1 | no | — |
| 525 | C22×D3 | — | 36 | 1 | no | — |
| 526 | C22×D3 | — | 36 | 1 | no | — |
| 527 | C22×D3 | — | 36 | 2 | no | — |
| 528 | C22×D3 | — | 72 | 3 | no | — |
| 529 | C2×A4 | — | 2 | 6 | no | — |
| 530 | C2×A4 | — | 2 | 3 | no | — |
| 531 | C2×A4 | — | 2 | 3 | no | — |
| 532 | C2×A4 | — | 6 | 3 | no | — |
| 533 | C2×A4 | C2×D32 | 1 | 3 | yes | — |
| 534 | S4 | — | 6 | 3 | no | — |
| 535 | S4 | — | 9 | 6 | no | — |
| 536 | S4 | — | 18 | 6 | no | — |
| 537 | S4 | — | 18 | 6 | no | — |
| 538 | S4 | — | 18 | 3 | no | — |
| 539 | C3×D4 | — | 3 | 1 | no | — |
| 540 | C3×D4 | — | 9 | 1 | no | — |
| 541 | C3×D4 | — | 9 | 1 | no | — |
| 542 | C3×D4 | — | 9 | 1 | no | — |
| 543 | C3×D4 | — | 12 | 3 | no | — |
| 544 | C3×D4 | — | 18 | 1 | no | — |
| 545 | C3×D4 | — | 18 | 1 | no | — |
| 546 | C3×D4 | — | 18 | 1 | no | — |
| 547 | C3×D4 | — | 18 | 1 | no | — |
| 548 | C3×D4 | — | 18 | 1 | no | — |
| 549 | C3×D4 | — | 36 | 1 | no | — |
| 550 | C2×C3×C4 | — | 9 | 1 | no | — |
| 551 | C2×C3×C4 | — | 9 | 1 | no | — |
| 552 | C2×C3×C4 | — | 9 | 1 | no | — |
| 553 | C2×C3×C4 | — | 9 | 1 | no | — |
| 554 | C2×C3×C4 | — | 9 | 1 | no | — |
| 555 | #67 | — | 3 | 1 | no | — |
| 556 | #67 | — | 3 | 1 | no | — |
| 557 | #67 | — | 3 | 1 | no | — |
| 558 | #67 | — | 6 | 1 | no | — |
| 559 | #67 | — | 6 | 1 | no | — |
| 560 | #67 | — | 6 | 1 | no | — |
| 561 | #67 | — | 6 | 1 | no | — |
| 562 | #67 | — | 6 | 1 | no | — |
| 563 | #67 | — | 9 | 2 | no | — |
| 564 | #67 | — | 9 | 2 | no | — |
| 565 | #67 | — | 9 | 2 | no | — |
| 566 | #67 | — | 9 | 2 | no | — |
| 567 | #67 | — | 12 | 3 | no | — |
| 568 | #67 | — | 12 | 1 | no | — |
| 569 | #67 | — | 18 | 2 | no | — |
| 570 | #67 | — | 18 | 2 | no | — |
| 571 | #67 | — | 18 | 1 | no | — |
| 572 | #67 | — | 18 | 2 | no | — |
| 573 | #67 | — | 18 | 1 | no | — |
| 574 | #67 | — | 18 | 1 | no | — |
| 575 | #67 | — | 18 | 2 | no | — |
| 576 | #67 | — | 18 | 2 | no | — |
| 577 | #67 | — | 18 | 2 | no | — |
| 578 | #67 | — | 18 | 2 | no | — |
| 579 | #67 | — | 18 | 2 | no | — |
| 580 | #67 | — | 18 | 2 | no | — |
| 581 | #67 | — | 18 | 2 | no | — |
| 582 | #67 | — | 18 | 1 | no | — |
| 583 | #67 | — | 18 | 1 | no | — |
| 584 | #67 | — | 18 | 4 | no | — |
| 585 | #67 | — | 18 | 2 | no | — |
| 586 | #67 | — | 18 | 4 | no | — |
| 587 | #67 | — | 18 | 1 | no | — |
| 588 | #67 | — | 18 | 1 | no | — |
| 589 | #67 | — | 18 | 1 | no | — |
| 590 | #67 | — | 36 | 3 | no | — |
| 591 | #67 | — | 36 | 1 | no | — |
| 592 | #67 | C3⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 593 | C2×Dic3 | — | 3 | 1 | no | — |
| 594 | C2×Dic3 | — | 3 | 1 | no | — |
| 595 | C2×Dic3 | — | 3 | 1 | no | — |
| 596 | C2×Dic3 | — | 3 | 1 | no | — |
| 597 | C2×Dic3 | — | 3 | 1 | no | — |
| 598 | C2×Dic3 | — | 9 | 1 | no | — |
| 599 | C2×Dic3 | — | 9 | 1 | no | — |
| 600 | C2×Dic3 | — | 9 | 1 | no | — |
| 601 | C2×Dic3 | — | 9 | 1 | no | — |
| 602 | C2×Dic3 | — | 18 | 1 | no | — |
| 603 | C2×Dic3 | — | 18 | 1 | no | — |
| 604 | C2×Dic3 | — | 18 | 2 | no | — |
| 605 | C2×Dic3 | — | 18 | 2 | no | — |
| 606 | C2×Dic3 | — | 18 | 2 | no | — |
| 607 | C2×Dic3 | — | 18 | 4 | no | — |
| 608 | D12 | — | 18 | 1 | no | — |
| 609 | D12 | — | 18 | 1 | no | — |
| 610 | D12 | — | 18 | 1 | no | — |
| 611 | D12 | — | 18 | 2 | no | — |
| 612 | D12 | — | 18 | 1 | no | — |
| 613 | D12 | — | 36 | 3 | no | — |
| 614 | D12 | — | 36 | 1 | no | — |
| 615 | C4×D3 | — | 18 | 1 | no | — |
| 616 | C4×D3 | — | 18 | 1 | no | — |
| 617 | C4×D3 | — | 18 | 1 | no | — |
| 618 | C4×D3 | — | 18 | 2 | no | — |
| 619 | C4×D3 | — | 18 | 1 | no | — |
| 620 | C4×D3 | — | 36 | 3 | no | — |
| 621 | C2×C32 | — | 2 | 1 | no | — |
| 622 | C2×C32 | — | 3 | 1 | no | — |
| 623 | C2×C32 | — | 3 | 1 | no | — |
| 624 | C2×C32 | — | 4 | 1 | no | — |
| 625 | C2×C32 | — | 4 | 3 | no | — |
| 626 | C2×C32 | — | 6 | 1 | no | — |
| 627 | C2×C32 | — | 8 | 3 | no | — |
| 628 | C2×C32 | — | 8 | 1 | no | — |
| 629 | C2×C32 | — | 8 | 3 | no | — |
| 630 | C2×C32 | — | 8 | 6 | no | — |
| 631 | C2×C32 | — | 8 | 2 | no | — |
| 632 | C2×C32 | — | 8 | 1 | no | — |
| 633 | C2×C32 | — | 24 | 1 | no | — |
| 634 | C2×C32 | C22×S4 | 1 | 1 | yes | characteristic |
| 635 | C3⋊D3 | — | 6 | 2 | no | — |
| 636 | C3⋊D3 | — | 8 | 1 | no | — |
| 637 | C3⋊D3 | — | 12 | 2 | no | — |
| 638 | C3⋊D3 | — | 12 | 6 | no | — |
| 639 | C3⋊D3 | — | 12 | 1 | no | — |
| 640 | C3⋊D3 | — | 24 | 2 | no | — |
| 641 | C3⋊D3 | — | 24 | 6 | no | — |
| 642 | C3⋊D3 | — | 24 | 1 | no | — |
| 643 | C3⋊D3 | — | 24 | 3 | no | — |
| 644 | C3⋊D3 | — | 24 | 6 | no | — |
| 645 | C3⋊D3 | — | 24 | 2 | no | — |
| 646 | C3×D3 | — | 2 | 1 | no | — |
| 647 | C3×D3 | — | 6 | 1 | no | — |
| 648 | C3×D3 | — | 8 | 3 | no | — |
| 649 | C3×D3 | — | 12 | 1 | no | — |
| 650 | C3×D3 | — | 24 | 3 | no | — |
| 651 | C24 | — | 3 | 1 | no | — |
| 652 | C24 | — | 27 | 1 | no | — |
| 653 | C24 | — | 27 | 1 | no | — |
| 654 | C24 | D3×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 655 | C2×D4 | — | 9 | 1 | no | — |
| 656 | C2×D4 | — | 9 | 1 | no | — |
| 657 | C2×D4 | — | 9 | 1 | no | — |
| 658 | C2×D4 | — | 9 | 1 | no | — |
| 659 | C2×D4 | — | 9 | 1 | no | — |
| 660 | C2×D4 | — | 9 | 1 | no | — |
| 661 | C2×D4 | — | 9 | 1 | no | — |
| 662 | C2×D4 | — | 27 | 1 | no | — |
| 663 | C2×D4 | — | 27 | 1 | no | — |
| 664 | C2×D4 | — | 27 | 1 | no | — |
| 665 | C2×D4 | — | 27 | 1 | no | — |
| 666 | C2×D4 | — | 27 | 1 | no | — |
| 667 | C2×D4 | — | 27 | 1 | no | — |
| 668 | C2×D4 | — | 27 | 1 | no | — |
| 669 | C2×D4 | — | 27 | 1 | no | — |
| 670 | C2×D4 | — | 27 | 1 | no | — |
| 671 | C2×D4 | — | 54 | 1 | no | — |
| 672 | C2×D4 | — | 54 | 1 | no | — |
| 673 | C2×D4 | — | 54 | 1 | no | — |
| 674 | C2×D4 | — | 54 | 1 | no | — |
| 675 | C2×D4 | — | 54 | 2 | no | — |
| 676 | C2×D4 | — | 54 | 2 | no | — |
| 677 | C2×D4 | — | 54 | 2 | no | — |
| 678 | C2×D4 | — | 54 | 2 | no | — |
| 679 | C22×C4 | — | 3 | 1 | no | — |
| 680 | C22×C4 | — | 27 | 1 | no | — |
| 681 | C22×C4 | — | 27 | 1 | no | — |
| 682 | C22×C4 | — | 27 | 1 | no | — |
| 683 | C4⋊C4 | — | 27 | 1 | no | — |
| 684 | C4⋊C4 | — | 27 | 1 | no | — |
| 685 | C22⋊C4 | — | 9 | 1 | no | — |
| 686 | C22⋊C4 | — | 9 | 1 | no | — |
| 687 | C22⋊C4 | — | 9 | 1 | no | — |
| 688 | C22⋊C4 | — | 27 | 1 | no | — |
| 689 | C22⋊C4 | — | 27 | 1 | no | — |
| 690 | C22⋊C4 | — | 27 | 1 | no | — |
| 691 | C22⋊C4 | — | 27 | 1 | no | — |
| 692 | C22⋊C4 | — | 27 | 1 | no | — |
| 693 | C42 | — | 27 | 1 | no | — |
| 694 | C22×C3 | — | 2 | 1 | no | — |
| 695 | C22×C3 | — | 2 | 1 | no | — |
| 696 | C22×C3 | — | 3 | 1 | no | — |
| 697 | C22×C3 | — | 3 | 1 | no | — |
| 698 | C22×C3 | — | 3 | 1 | no | — |
| 699 | C22×C3 | — | 3 | 1 | no | — |
| 700 | C22×C3 | — | 3 | 1 | no | — |
| 701 | C22×C3 | — | 3 | 1 | no | — |
| 702 | C22×C3 | — | 3 | 1 | no | — |
| 703 | C22×C3 | — | 4 | 3 | no | — |
| 704 | C22×C3 | — | 6 | 1 | no | — |
| 705 | C22×C3 | — | 6 | 1 | no | — |
| 706 | C22×C3 | — | 6 | 1 | no | — |
| 707 | C22×C3 | — | 6 | 1 | no | — |
| 708 | C22×C3 | — | 6 | 1 | no | — |
| 709 | C22×C3 | — | 6 | 1 | no | — |
| 710 | C22×C3 | — | 6 | 1 | no | — |
| 711 | C22×C3 | — | 6 | 2 | no | — |
| 712 | C22×C3 | — | 6 | 2 | no | — |
| 713 | C22×C3 | — | 6 | 1 | no | — |
| 714 | C22×C3 | — | 6 | 1 | no | — |
| 715 | C22×C3 | — | 6 | 1 | no | — |
| 716 | C22×C3 | — | 6 | 1 | no | — |
| 717 | C22×C3 | — | 6 | 2 | no | — |
| 718 | C22×C3 | — | 8 | 3 | no | — |
| 719 | C22×C3 | — | 9 | 1 | no | — |
| 720 | C22×C3 | — | 12 | 3 | no | — |
| 721 | C22×C3 | — | 12 | 1 | no | — |
| 722 | C22×C3 | — | 18 | 1 | no | — |
| 723 | C22×C3 | — | 18 | 1 | no | — |
| 724 | C22×C3 | — | 18 | 1 | no | — |
| 725 | C22×C3 | — | 18 | 1 | no | — |
| 726 | C22×C3 | — | 18 | 1 | no | — |
| 727 | C22×C3 | — | 18 | 1 | no | — |
| 728 | C22×C3 | — | 18 | 1 | no | — |
| 729 | C22×C3 | #3811 | 1 | 1 | yes | characteristic, complemented |
| 730 | C22×C3 | D4×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 731 | C22×C3 | D3×S4 | 1 | 1 | yes | characteristic, complemented |
| 732 | C22×C3 | C2×C3⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 733 | C2×D3 | — | 3 | 1 | no | — |
| 734 | C2×D3 | — | 6 | 1 | no | — |
| 735 | C2×D3 | — | 6 | 1 | no | — |
| 736 | C2×D3 | — | 6 | 1 | no | — |
| 737 | C2×D3 | — | 6 | 1 | no | — |
| 738 | C2×D3 | — | 6 | 1 | no | — |
| 739 | C2×D3 | — | 6 | 1 | no | — |
| 740 | C2×D3 | — | 6 | 1 | no | — |
| 741 | C2×D3 | — | 9 | 2 | no | — |
| 742 | C2×D3 | — | 9 | 2 | no | — |
| 743 | C2×D3 | — | 12 | 3 | no | — |
| 744 | C2×D3 | — | 18 | 2 | no | — |
| 745 | C2×D3 | — | 18 | 1 | no | — |
| 746 | C2×D3 | — | 18 | 1 | no | — |
| 747 | C2×D3 | — | 18 | 1 | no | — |
| 748 | C2×D3 | — | 18 | 1 | no | — |
| 749 | C2×D3 | — | 18 | 1 | no | — |
| 750 | C2×D3 | — | 18 | 1 | no | — |
| 751 | C2×D3 | — | 18 | 1 | no | — |
| 752 | C2×D3 | — | 18 | 1 | no | — |
| 753 | C2×D3 | — | 18 | 2 | no | — |
| 754 | C2×D3 | — | 18 | 1 | no | — |
| 755 | C2×D3 | — | 18 | 1 | no | — |
| 756 | C2×D3 | — | 36 | 1 | no | — |
| 757 | C2×D3 | — | 36 | 1 | no | — |
| 758 | C2×D3 | — | 36 | 3 | no | — |
| 759 | C2×D3 | — | 36 | 1 | no | — |
| 760 | C2×D3 | — | 36 | 1 | no | — |
| 761 | C2×D3 | — | 36 | 3 | no | — |
| 762 | C2×D3 | — | 36 | 2 | no | — |
| 763 | C2×D3 | — | 36 | 2 | no | — |
| 764 | C2×D3 | — | 36 | 2 | no | — |
| 765 | C2×D3 | — | 36 | 2 | no | — |
| 766 | C2×D3 | — | 36 | 2 | no | — |
| 767 | C2×D3 | — | 36 | 2 | no | — |
| 768 | C2×D3 | — | 36 | 2 | no | — |
| 769 | C2×D3 | — | 36 | 2 | no | — |
| 770 | C2×D3 | — | 36 | 4 | no | — |
| 771 | C2×D3 | — | 36 | 4 | no | — |
| 772 | C2×D3 | — | 72 | 3 | no | — |
| 773 | C2×D3 | — | 72 | 3 | no | — |
| 774 | C2×D3 | — | 72 | 6 | no | — |
| 775 | C2×D3 | — | 72 | 6 | no | — |
| 776 | C2×D3 | — | 72 | 12 | no | — |
| 777 | C2×D3 | C2×C3⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 778 | A4 | — | 2 | 3 | no | — |
| 779 | A4 | #3811 | 1 | 3 | yes | complemented |
| 780 | C3×C4 | — | 3 | 1 | no | — |
| 781 | C3×C4 | — | 9 | 1 | no | — |
| 782 | C3×C4 | — | 12 | 3 | no | — |
| 783 | C3×C4 | — | 18 | 1 | no | — |
| 784 | C3×C4 | — | 18 | 1 | no | — |
| 785 | C3×C4 | — | 18 | 1 | no | — |
| 786 | Dic3 | — | 3 | 1 | no | — |
| 787 | Dic3 | — | 6 | 1 | no | — |
| 788 | Dic3 | — | 6 | 1 | no | — |
| 789 | Dic3 | — | 6 | 1 | no | — |
| 790 | Dic3 | — | 9 | 2 | no | — |
| 791 | Dic3 | — | 9 | 2 | no | — |
| 792 | Dic3 | — | 12 | 3 | no | — |
| 793 | Dic3 | — | 18 | 2 | no | — |
| 794 | Dic3 | — | 18 | 1 | no | — |
| 795 | Dic3 | — | 18 | 1 | no | — |
| 796 | Dic3 | — | 18 | 2 | no | — |
| 797 | Dic3 | C2×C3⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 798 | C32 | — | 4 | 1 | no | — |
| 799 | C32 | — | 4 | 3 | no | — |
| 800 | C32 | — | 8 | 3 | no | — |
| 801 | C32 | — | 8 | 1 | no | — |
| 802 | C32 | D4×S4 | 1 | 1 | yes | characteristic, complemented |
| 803 | C23 | — | 2 | 1 | no | — |
| 804 | C23 | — | 3 | 1 | no | — |
| 805 | C23 | — | 3 | 1 | no | — |
| 806 | C23 | — | 6 | 1 | no | — |
| 807 | C23 | — | 6 | 1 | no | — |
| 808 | C23 | — | 9 | 1 | no | — |
| 809 | C23 | — | 9 | 1 | no | — |
| 810 | C23 | — | 9 | 1 | no | — |
| 811 | C23 | — | 18 | 1 | no | — |
| 812 | C23 | — | 27 | 1 | no | — |
| 813 | C23 | — | 27 | 1 | no | — |
| 814 | C23 | — | 54 | 1 | no | — |
| 815 | C23 | — | 54 | 1 | no | — |
| 816 | C23 | — | 54 | 2 | no | — |
| 817 | C23 | — | 54 | 1 | no | — |
| 818 | C23 | — | 54 | 2 | no | — |
| 819 | C23 | — | 54 | 1 | no | — |
| 820 | C23 | — | 108 | 1 | no | — |
| 821 | C23 | — | 108 | 1 | no | — |
| 822 | C23 | C2×D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 823 | D4 | — | 3 | 1 | no | — |
| 824 | D4 | — | 9 | 1 | no | — |
| 825 | D4 | — | 9 | 1 | no | — |
| 826 | D4 | — | 9 | 1 | no | — |
| 827 | D4 | — | 18 | 1 | no | — |
| 828 | D4 | — | 18 | 1 | no | — |
| 829 | D4 | — | 18 | 1 | no | — |
| 830 | D4 | — | 18 | 1 | no | — |
| 831 | D4 | — | 18 | 1 | no | — |
| 832 | D4 | — | 27 | 2 | no | — |
| 833 | D4 | — | 27 | 2 | no | — |
| 834 | D4 | — | 36 | 1 | no | — |
| 835 | D4 | — | 54 | 1 | no | — |
| 836 | D4 | — | 54 | 1 | no | — |
| 837 | D4 | — | 54 | 1 | no | — |
| 838 | D4 | — | 54 | 1 | no | — |
| 839 | D4 | — | 54 | 2 | no | — |
| 840 | D4 | — | 54 | 2 | no | — |
| 841 | D4 | — | 54 | 2 | no | — |
| 842 | D4 | — | 54 | 1 | no | — |
| 843 | D4 | — | 54 | 2 | no | — |
| 844 | D4 | — | 54 | 1 | no | — |
| 845 | D4 | — | 108 | 1 | no | — |
| 846 | C2×C4 | — | 9 | 1 | no | — |
| 847 | C2×C4 | — | 9 | 1 | no | — |
| 848 | C2×C4 | — | 9 | 1 | no | — |
| 849 | C2×C4 | — | 9 | 1 | no | — |
| 850 | C2×C4 | — | 9 | 1 | no | — |
| 851 | C2×C4 | — | 27 | 1 | no | — |
| 852 | C2×C4 | — | 27 | 1 | no | — |
| 853 | C2×C4 | — | 54 | 1 | no | — |
| 854 | C2×C4 | — | 54 | 1 | no | — |
| 855 | C2×C4 | — | 54 | 2 | no | — |
| 856 | C2×C4 | — | 54 | 2 | no | — |
| 857 | C2×C3 | — | 2 | 2 | no | — |
| 858 | C2×C3 | — | 2 | 1 | no | — |
| 859 | C2×C3 | — | 2 | 1 | no | — |
| 860 | C2×C3 | — | 2 | 1 | no | — |
| 861 | C2×C3 | — | 3 | 1 | no | — |
| 862 | C2×C3 | — | 3 | 1 | no | — |
| 863 | C2×C3 | — | 3 | 1 | no | — |
| 864 | C2×C3 | — | 3 | 1 | no | — |
| 865 | C2×C3 | — | 4 | 3 | no | — |
| 866 | C2×C3 | — | 6 | 1 | no | — |
| 867 | C2×C3 | — | 6 | 1 | no | — |
| 868 | C2×C3 | — | 6 | 2 | no | — |
| 869 | C2×C3 | — | 6 | 1 | no | — |
| 870 | C2×C3 | — | 6 | 1 | no | — |
| 871 | C2×C3 | — | 6 | 1 | no | — |
| 872 | C2×C3 | — | 8 | 3 | no | — |
| 873 | C2×C3 | — | 8 | 6 | no | — |
| 874 | C2×C3 | — | 8 | 3 | no | — |
| 875 | C2×C3 | — | 18 | 1 | no | — |
| 876 | C2×C3 | — | 24 | 3 | no | — |
| 877 | C2×C3 | — | 36 | 1 | no | — |
| 878 | C2×C3 | C2×D3×S4 | 1 | 1 | yes | characteristic |
| 879 | C2×C3 | C22×C3⋊S4 | 1 | 1 | yes | characteristic |
| 880 | D3 | — | 2 | 1 | no | — |
| 881 | D3 | — | 6 | 1 | no | — |
| 882 | D3 | — | 12 | 1 | no | — |
| 883 | D3 | — | 18 | 2 | no | — |
| 884 | D3 | — | 18 | 2 | no | — |
| 885 | D3 | — | 24 | 3 | no | — |
| 886 | D3 | — | 36 | 2 | no | — |
| 887 | D3 | — | 36 | 6 | no | — |
| 888 | D3 | — | 36 | 2 | no | — |
| 889 | D3 | — | 36 | 1 | no | — |
| 890 | D3 | — | 36 | 1 | no | — |
| 891 | D3 | — | 72 | 6 | no | — |
| 892 | D3 | — | 72 | 3 | no | — |
| 893 | D3 | — | 72 | 6 | no | — |
| 894 | C22 | — | 3 | 1 | no | — |
| 895 | C22 | — | 3 | 1 | no | — |
| 896 | C22 | — | 3 | 1 | no | — |
| 897 | C22 | — | 3 | 1 | no | — |
| 898 | C22 | — | 6 | 1 | no | — |
| 899 | C22 | — | 6 | 1 | no | — |
| 900 | C22 | — | 6 | 1 | no | — |
| 901 | C22 | — | 6 | 1 | no | — |
| 902 | C22 | — | 9 | 1 | no | — |
| 903 | C22 | — | 18 | 1 | no | — |
| 904 | C22 | — | 18 | 1 | no | — |
| 905 | C22 | — | 18 | 1 | no | — |
| 906 | C22 | — | 18 | 1 | no | — |
| 907 | C22 | — | 18 | 1 | no | — |
| 908 | C22 | — | 18 | 1 | no | — |
| 909 | C22 | — | 18 | 1 | no | — |
| 910 | C22 | — | 27 | 2 | no | — |
| 911 | C22 | — | 54 | 1 | no | — |
| 912 | C22 | — | 54 | 1 | no | — |
| 913 | C22 | — | 54 | 1 | no | — |
| 914 | C22 | — | 54 | 1 | no | — |
| 915 | C22 | — | 54 | 1 | no | — |
| 916 | C22 | — | 108 | 2 | no | — |
| 917 | C22 | — | 108 | 2 | no | — |
| 918 | C22 | — | 108 | 2 | no | — |
| 919 | C22 | — | 108 | 2 | no | — |
| 920 | C22 | #89039 | 1 | 1 | yes | characteristic, complemented |
| 921 | C22 | D3×C3⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 922 | C4 | — | 3 | 1 | no | — |
| 923 | C4 | — | 9 | 1 | no | — |
| 924 | C4 | — | 18 | 1 | no | — |
| 925 | C4 | — | 18 | 1 | no | — |
| 926 | C4 | — | 18 | 1 | no | — |
| 927 | C4 | — | 27 | 2 | no | — |
| 928 | C4 | — | 54 | 1 | no | — |
| 929 | C3 | — | 2 | 1 | no | — |
| 930 | C3 | — | 4 | 3 | no | — |
| 931 | C3 | — | 8 | 3 | no | — |
| 932 | C3 | #10596473 | 1 | 1 | yes | characteristic, complemented |
| 933 | C3 | D4×C3⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 934 | C2 | — | 2 | 1 | no | — |
| 935 | C2 | — | 3 | 1 | no | — |
| 936 | C2 | — | 3 | 1 | no | — |
| 937 | C2 | — | 6 | 1 | no | — |
| 938 | C2 | — | 6 | 1 | no | — |
| 939 | C2 | — | 18 | 1 | no | — |
| 940 | C2 | — | 36 | 1 | no | — |
| 941 | C2 | — | 54 | 2 | no | — |
| 942 | C2 | — | 108 | 1 | no | — |
| 943 | 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 | C2×D4 |
| 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. C22×C3⋊(C3⋊S4) | C2 | semidirect |
| 2. C2×D3×C3⋊S4 | C2 | semidirect |
| 3. C3×A4×#67 | C2 | semidirect |
| 4. C3×#64269 | C2 | semidirect |
| 5. #11724205 | C2 | semidirect |
| 6. #11724202 | C2 | semidirect |
| 7. #11724201 | C2 | semidirect |
| 11. C22×C32×A4 | C22 | semidirect |
| 12. C2×C3×D3×A4 | C22 | semidirect |
| 15. C2×C3⋊(C3⋊S4) | C22 | semidirect |
| 16. C2×C3×C3⋊S4 | C22 | semidirect |
| 19. C3×Dic3×A4 | C22 | semidirect |
| 20. C3×C3⋊SL(2,ℤ/4) | C22 | semidirect |
| 28. C22×C3×#67 | D3 | semidirect |
| 32. A4×#67 | D3 | semidirect |
| 34. #64269 | D3 | semidirect |
| 58. C3⋊(C3⋊S4) | D4 | semidirect |
| 68. C24×C32 | C2×D3 | semidirect |
| 70. C23×C3×D3 | C2×D3 | semidirect |
| 74. C22×C3×A4 | C2×D3 | semidirect |
| 75. C22×C3×A4 | C2×D3 | semidirect |
| 77. C2×D3×A4 | C2×D3 | semidirect |
| 91. C2×C3⋊S4 | C2×D3 | semidirect |
| 109. C22×C3×Dic3 | C2×D3 | semidirect |
| 125. Dic3×A4 | C2×D3 | semidirect |
| 126. C3⋊SL(2,ℤ/4) | C2×D3 | semidirect |
| 145. C32×A4 | C2×D4 | semidirect |
| 157. C22×#67 | C3⋊D3 | semidirect |
| 259. C3×#67 | S4 | semidirect |
| 287. C24×C3 | D32 | semidirect |
| 288. C24×C3 | C2×C3⋊D3 | semidirect |
| 294. C23×D3 | C2×C3⋊D3 | semidirect |
| 297. C22×A4 | D32 | semidirect |
| 351. C22×Dic3 | C2×C3⋊D3 | semidirect |
| 406. C22×C32 | D3×D4 | semidirect |
| 407. C22×C32 | C2×S4 | semidirect |
| 440. C2×C3×D3 | C2×S4 | semidirect |
| 443. C3×A4 | D3×D4 | semidirect |
| 444. C3×A4 | D3×D4 | semidirect |
| 458. C3×Dic3 | C2×S4 | semidirect |
| 592. #67 | C3⋊S4 | semidirect |
| 654. C24 | D3×C3⋊D3 | semidirect |
| 729. C22×C3 | #3811 | semidirect |
| 730. C22×C3 | D4×C3⋊D3 | semidirect |
| 731. C22×C3 | D3×S4 | semidirect |
| 732. C22×C3 | C2×C3⋊S4 | semidirect |
| 777. C2×D3 | C2×C3⋊S4 | semidirect |
| 779. A4 | #3811 | semidirect |
| 797. Dic3 | C2×C3⋊S4 | semidirect |
| 802. C32 | D4×S4 | semidirect |
| 920. C22 | #89039 | semidirect |
| 921. C22 | D3×C3⋊S4 | semidirect |
| 932. C3 | #10596473 | semidirect |
| 933. C3 | D4×C3⋊S4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊(C3⋊S4) | 2 |
| C2×D3×C3⋊S4 | 2 |
| C3×A4×#67 | 2 |
| C3×#64269 | 2 |
| #11724205 | 2 |
| #11724202 | 2 |
| #11724201 | 2 |
| D4×C3⋊S4 | 3 |
| #10596473 | 3 |
| #10595526 | 3 |
| #89039 | 4 |