Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1310 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 1310 conjugacy classes of subgroups — too many to draw. Only its 90 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 | #11724473 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11724204 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11724202 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | Dic3×C3⋊S4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | D4×C3⋊S4 | — | 3 | 1 | no | maximal |
| 9 | #67×S4 | — | 3 | 3 | no | maximal |
| 10 | #672 | — | 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) | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C2×C3×C3⋊S4 | — | 2 | 2 | no | — |
| 15 | C2×C3×C3⋊S4 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×C3×C3⋊S4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | D3×C3⋊S4 | — | 2 | 2 | no | — |
| 18 | C3⋊D3×#67 | — | 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 | D3 | 1 | 1 | yes | characteristic, complemented |
| 23 | C22×C3×S4 | — | 3 | 3 | no | — |
| 24 | C2×D3×S4 | — | 3 | 3 | no | — |
| 25 | C22×C3×#67 | — | 3 | 1 | no | — |
| 26 | C22×C3×#67 | D3 | 1 | 1 | yes | characteristic, complemented |
| 27 | C3×D4×A4 | — | 3 | 1 | no | — |
| 28 | C2×D3×#67 | — | 3 | 1 | no | — |
| 29 | C2×D3×#67 | — | 3 | 1 | no | — |
| 30 | A4×#67 | D3 | 1 | 3 | yes | complemented |
| 31 | #64269 | — | 3 | 1 | no | — |
| 32 | #64269 | — | 3 | 3 | no | — |
| 33 | #64269 | — | 3 | 1 | no | — |
| 34 | #64269 | — | 6 | 1 | no | — |
| 35 | #64269 | — | 6 | 3 | no | — |
| 36 | C4⋊(C3⋊S4) | — | 3 | 1 | no | — |
| 37 | C4×C3⋊S4 | — | 3 | 1 | no | — |
| 38 | #64209 | — | 3 | 3 | no | — |
| 39 | #64207 | — | 3 | 3 | no | — |
| 40 | Dic3×S4 | — | 3 | 3 | no | — |
| 41 | #64162 | — | 3 | 1 | no | — |
| 42 | #63983 | — | 3 | 1 | no | — |
| 43 | #63979 | — | 3 | 1 | no | — |
| 44 | #63978 | — | 3 | 1 | no | — |
| 45 | #63978 | — | 3 | 1 | no | — |
| 46 | #63976 | — | 3 | 1 | no | — |
| 47 | #63976 | — | 3 | 1 | no | — |
| 48 | Dic3×#67 | — | 3 | 1 | no | — |
| 49 | Dic3×#67 | — | 3 | 1 | no | — |
| 50 | #63970 | — | 3 | 1 | no | — |
| 51 | #63970 | — | 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 | — | 2 | 1 | no | — |
| 59 | C3×C3⋊S4 | D4 | 1 | 2 | yes | complemented |
| 60 | #6312 | — | 4 | 1 | no | — |
| 61 | C32×#67 | — | 4 | 1 | no | — |
| 62 | #6292 | — | 4 | 1 | no | — |
| 63 | #6290 | — | 4 | 1 | no | — |
| 64 | Dic3×C3⋊D3 | — | 4 | 1 | no | — |
| 65 | D4×S4 | — | 9 | 3 | no | — |
| 66 | D4×#67 | — | 9 | 1 | no | — |
| 67 | D4×#67 | — | 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 | — | 2 | 2 | no | — |
| 79 | C2×C3⋊S4 | — | 3 | 1 | no | — |
| 80 | C2×C3⋊S4 | — | 3 | 3 | no | — |
| 81 | C2×C3⋊S4 | — | 6 | 2 | no | — |
| 82 | C2×C3⋊S4 | — | 6 | 1 | no | — |
| 83 | C2×C3⋊S4 | — | 6 | 3 | no | — |
| 84 | C2×C3⋊S4 | C2×D3 | 1 | 1 | yes | characteristic |
| 85 | C2×C3⋊S4 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 86 | C2×C3×S4 | — | 3 | 3 | no | — |
| 87 | C2×C3×S4 | — | 3 | 3 | no | — |
| 88 | C2×C3×S4 | — | 6 | 6 | no | — |
| 89 | D3×S4 | — | 6 | 6 | no | — |
| 90 | C2×#638 | — | 3 | 1 | no | — |
| 91 | C2×#638 | — | 3 | 1 | no | — |
| 92 | C2×#638 | — | 3 | 1 | no | — |
| 93 | D4×C3⋊D3 | — | 12 | 1 | no | — |
| 94 | C2×C3×#67 | — | 3 | 1 | no | — |
| 95 | C2×C3×#67 | — | 3 | 1 | no | — |
| 96 | C2×C3×#67 | — | 3 | 1 | no | — |
| 97 | C2×C3×#67 | — | 3 | 1 | no | — |
| 98 | C2×C3×#67 | — | 3 | 1 | no | — |
| 99 | C2×C3×#67 | — | 3 | 1 | no | — |
| 100 | C2×C3×#67 | — | 3 | 1 | no | — |
| 101 | C2×C3×#67 | — | 3 | 1 | no | — |
| 102 | C2×C3×#67 | — | 6 | 2 | no | — |
| 103 | C2×C3×#67 | — | 6 | 2 | no | — |
| 104 | C22×C3×Dic3 | — | 3 | 1 | no | — |
| 105 | C22×C3×Dic3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 106 | C3×C4×A4 | — | 3 | 1 | no | — |
| 107 | D3×#67 | — | 6 | 2 | no | — |
| 108 | D3×#67 | — | 6 | 2 | no | — |
| 109 | D3×#67 | — | 6 | 1 | no | — |
| 110 | D3×#67 | — | 6 | 1 | no | — |
| 111 | D3×#67 | — | 6 | 1 | no | — |
| 112 | D3×#67 | — | 6 | 1 | no | — |
| 113 | D3×#67 | — | 12 | 3 | no | — |
| 114 | C2×#626 | — | 3 | 1 | no | — |
| 115 | C2×#626 | — | 3 | 1 | no | — |
| 116 | C2×#625 | — | 3 | 1 | no | — |
| 117 | C2×#625 | — | 3 | 1 | no | — |
| 118 | C2×#625 | — | 3 | 1 | no | — |
| 119 | C2×D3×Dic3 | — | 3 | 1 | no | — |
| 120 | C2×D3×Dic3 | — | 3 | 1 | no | — |
| 121 | Dic3×A4 | C2×D3 | 1 | 3 | yes | complemented |
| 122 | C3⋊SL(2,ℤ/4) | — | 3 | 1 | no | — |
| 123 | C3⋊SL(2,ℤ/4) | — | 3 | 3 | no | — |
| 124 | C3⋊SL(2,ℤ/4) | — | 6 | 1 | no | — |
| 125 | C3⋊SL(2,ℤ/4) | — | 6 | 3 | no | — |
| 126 | #3757 | — | 3 | 1 | no | — |
| 127 | #3757 | — | 3 | 1 | no | — |
| 128 | #3757 | — | 3 | 1 | no | — |
| 129 | Dic3⋊Dic3 | — | 3 | 1 | no | — |
| 130 | Dic3⋊Dic3 | — | 3 | 1 | no | — |
| 131 | #3722 | — | 3 | 1 | no | — |
| 132 | (C2×D3)⋊Dic3 | — | 3 | 1 | no | — |
| 133 | (C2×D3)⋊Dic3 | — | 3 | 1 | no | — |
| 134 | (C2×D3)⋊Dic3 | — | 3 | 1 | no | — |
| 135 | (C2×D3)⋊Dic3 | — | 3 | 1 | no | — |
| 136 | Dic32 | — | 3 | 1 | no | — |
| 137 | C22×C33 | — | 4 | 1 | no | — |
| 138 | C2×C3⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 139 | C2×C3×C3⋊D3 | — | 4 | 1 | no | — |
| 140 | C2×C3×C3⋊D3 | — | 4 | 1 | no | — |
| 141 | C2×C3×C3⋊D3 | — | 8 | 2 | no | — |
| 142 | C2×C32×D3 | — | 4 | 1 | no | — |
| 143 | C32×A4 | C2×D4 | 1 | 1 | yes | characteristic, complemented |
| 144 | D3×C3⋊D3 | — | 8 | 2 | no | — |
| 145 | C3⋊(C3⋊Dic3) | — | 4 | 1 | no | — |
| 146 | C32×Dic3 | — | 4 | 1 | no | — |
| 147 | C22×S4 | — | 3 | 3 | no | — |
| 148 | C22×S4 | — | 9 | 3 | no | — |
| 149 | C22×C3×D4 | — | 3 | 1 | no | — |
| 150 | C22×C3×D4 | — | 9 | 1 | no | — |
| 151 | C22×#67 | — | 3 | 1 | no | — |
| 152 | C22×#67 | — | 9 | 1 | no | — |
| 153 | C22×#67 | — | 9 | 1 | no | — |
| 154 | C22×#67 | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 155 | C2×D3×D4 | — | 9 | 1 | no | — |
| 156 | C2×D3×D4 | — | 9 | 1 | no | — |
| 157 | D4×A4 | — | 3 | 3 | no | — |
| 158 | GL(2,ℤ/4) | — | 9 | 3 | no | — |
| 159 | GL(2,ℤ/4) | — | 9 | 3 | no | — |
| 160 | GL(2,ℤ/4) | — | 18 | 3 | no | — |
| 161 | C4⋊S4 | — | 9 | 3 | no | — |
| 162 | C4×S4 | — | 9 | 3 | no | — |
| 163 | #953 | — | 9 | 1 | no | — |
| 164 | #953 | — | 9 | 1 | no | — |
| 165 | #953 | — | 9 | 1 | no | — |
| 166 | #953 | — | 9 | 1 | no | — |
| 167 | #953 | — | 18 | 1 | no | — |
| 168 | #940 | — | 9 | 1 | no | — |
| 169 | #940 | — | 9 | 1 | no | — |
| 170 | #939 | — | 9 | 1 | no | — |
| 171 | #939 | — | 9 | 1 | no | — |
| 172 | #939 | — | 9 | 1 | no | — |
| 173 | #939 | — | 9 | 1 | no | — |
| 174 | #938 | — | 9 | 1 | no | — |
| 175 | #938 | — | 9 | 1 | no | — |
| 176 | #937 | — | 9 | 1 | no | — |
| 177 | #937 | — | 9 | 1 | no | — |
| 178 | #937 | — | 9 | 1 | no | — |
| 179 | #937 | — | 9 | 1 | no | — |
| 180 | D4×Dic3 | — | 9 | 1 | no | — |
| 181 | D4×Dic3 | — | 9 | 1 | no | — |
| 182 | #930 | — | 9 | 1 | no | — |
| 183 | #930 | — | 9 | 1 | no | — |
| 184 | C4×#67 | — | 9 | 1 | no | — |
| 185 | C4×#67 | — | 9 | 1 | no | — |
| 186 | C23×C32 | — | 2 | 1 | no | — |
| 187 | C23×C32 | — | 3 | 1 | no | — |
| 188 | C23×C32 | — | 3 | 1 | no | — |
| 189 | C23×C32 | — | 6 | 1 | no | — |
| 190 | C23×C32 | C22×D3 | 1 | 1 | yes | characteristic |
| 191 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 192 | C22×C3⋊D3 | — | 4 | 1 | no | — |
| 193 | C22×C3⋊D3 | — | 12 | 1 | no | — |
| 194 | C22×C3×D3 | — | 2 | 1 | no | — |
| 195 | C22×C3×D3 | — | 3 | 1 | no | — |
| 196 | C22×C3×D3 | — | 3 | 1 | no | — |
| 197 | C22×C3×D3 | — | 3 | 1 | no | — |
| 198 | C22×C3×D3 | — | 3 | 1 | no | — |
| 199 | C22×C3×D3 | — | 6 | 2 | no | — |
| 200 | C22×C3×D3 | — | 6 | 1 | no | — |
| 201 | C22×C3×D3 | — | 6 | 1 | no | — |
| 202 | C22×C3×D3 | — | 6 | 1 | no | — |
| 203 | C22×C3×D3 | — | 12 | 3 | no | — |
| 204 | C22×C3×D3 | — | 12 | 1 | no | — |
| 205 | C2×C3×A4 | — | 2 | 1 | no | — |
| 206 | C2×C3×A4 | — | 2 | 1 | no | — |
| 207 | C2×C3×A4 | — | 2 | 3 | no | — |
| 208 | C2×C3×A4 | — | 2 | 3 | no | — |
| 209 | C2×C3×A4 | — | 4 | 3 | no | — |
| 210 | C2×C3×A4 | — | 4 | 1 | no | — |
| 211 | C2×C3×A4 | — | 6 | 1 | no | — |
| 212 | C2×C3×A4 | C22×D3 | 1 | 3 | yes | — |
| 213 | C2×C3×A4 | C22×D3 | 1 | 1 | yes | characteristic |
| 214 | C2×D32 | — | 6 | 2 | no | — |
| 215 | C2×D32 | — | 6 | 1 | no | — |
| 216 | C2×D32 | — | 6 | 1 | no | — |
| 217 | C2×D32 | — | 12 | 3 | no | — |
| 218 | C2×D32 | — | 12 | 1 | no | — |
| 219 | D3×A4 | — | 2 | 3 | no | — |
| 220 | C3⋊S4 | — | 2 | 1 | no | — |
| 221 | C3⋊S4 | — | 6 | 1 | no | — |
| 222 | C3⋊S4 | — | 6 | 3 | no | — |
| 223 | C3⋊S4 | — | 12 | 1 | no | — |
| 224 | C3⋊S4 | — | 12 | 3 | no | — |
| 225 | C3⋊S4 | #67 | 1 | 2 | yes | direct product factor |
| 226 | C3×S4 | — | 3 | 6 | no | — |
| 227 | C3×S4 | — | 6 | 3 | no | — |
| 228 | C32×D4 | — | 12 | 1 | no | — |
| 229 | #638 | — | 6 | 1 | no | — |
| 230 | #638 | — | 6 | 1 | no | — |
| 231 | #638 | — | 6 | 1 | no | — |
| 232 | #638 | — | 6 | 1 | no | — |
| 233 | #638 | — | 12 | 1 | no | — |
| 234 | #638 | — | 12 | 1 | no | — |
| 235 | #638 | — | 12 | 3 | no | — |
| 236 | #638 | — | 12 | 1 | no | — |
| 237 | #638 | — | 24 | 1 | no | — |
| 238 | #638 | — | 24 | 3 | no | — |
| 239 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 240 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 241 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 242 | C4⋊(C3⋊D3) | — | 12 | 1 | no | — |
| 243 | C4×C3⋊D3 | — | 12 | 1 | no | — |
| 244 | C3×#67 | — | 3 | 2 | no | — |
| 245 | C3×#67 | — | 3 | 2 | no | — |
| 246 | C3×#67 | — | 3 | 1 | no | — |
| 247 | C3×#67 | — | 3 | 1 | no | — |
| 248 | C3×#67 | — | 3 | 1 | no | — |
| 249 | C3×#67 | — | 4 | 3 | no | — |
| 250 | C3×#67 | — | 6 | 1 | no | — |
| 251 | C3×#67 | — | 6 | 2 | no | — |
| 252 | C3×#67 | — | 6 | 2 | no | — |
| 253 | C3×#67 | — | 6 | 1 | no | — |
| 254 | C3×#67 | — | 6 | 1 | no | — |
| 255 | C3×#67 | S4 | 1 | 1 | yes | characteristic, complemented |
| 256 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 257 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 258 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 259 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 260 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 261 | #626 | — | 6 | 2 | no | — |
| 262 | #626 | — | 6 | 1 | no | — |
| 263 | #626 | — | 6 | 1 | no | — |
| 264 | #626 | — | 12 | 3 | no | — |
| 265 | #625 | — | 6 | 2 | no | — |
| 266 | #625 | — | 6 | 1 | no | — |
| 267 | #625 | — | 6 | 1 | no | — |
| 268 | #625 | — | 12 | 3 | no | — |
| 269 | #625 | — | 12 | 1 | no | — |
| 270 | D3×Dic3 | — | 6 | 2 | no | — |
| 271 | D3×Dic3 | — | 6 | 1 | no | — |
| 272 | D3×Dic3 | — | 6 | 1 | no | — |
| 273 | D3×Dic3 | — | 12 | 3 | no | — |
| 274 | D42 | — | 27 | 1 | no | Sylow |
| 275 | C2×C33 | — | 4 | 1 | no | — |
| 276 | C2×C33 | — | 8 | 1 | no | — |
| 277 | C3⋊(C3⋊D3) | — | 8 | 1 | no | — |
| 278 | C3×C3⋊D3 | — | 4 | 2 | no | — |
| 279 | C3×C3⋊D3 | — | 8 | 1 | no | — |
| 280 | C32×D3 | — | 8 | 1 | no | — |
| 281 | C24×C3 | — | 2 | 1 | no | — |
| 282 | C24×C3 | — | 3 | 1 | no | — |
| 283 | C24×C3 | — | 9 | 1 | no | — |
| 284 | C24×C3 | D32 | 1 | 1 | yes | characteristic, complemented |
| 285 | C24×C3 | C2×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 286 | C23×D3 | — | 3 | 1 | no | — |
| 287 | C23×D3 | — | 9 | 1 | no | — |
| 288 | C23×D3 | — | 9 | 1 | no | — |
| 289 | C23×D3 | C2×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 290 | C22×A4 | — | 2 | 3 | no | — |
| 291 | C22×A4 | — | 3 | 3 | no | — |
| 292 | C22×A4 | D32 | 1 | 3 | yes | complemented |
| 293 | C2×S4 | — | 3 | 3 | no | — |
| 294 | C2×S4 | — | 3 | 3 | no | — |
| 295 | C2×S4 | — | 6 | 6 | no | — |
| 296 | C2×S4 | — | 9 | 3 | no | — |
| 297 | C2×S4 | — | 18 | 3 | no | — |
| 298 | C2×S4 | — | 18 | 6 | no | — |
| 299 | C2×C3×D4 | — | 9 | 1 | no | — |
| 300 | C2×C3×D4 | — | 9 | 1 | no | — |
| 301 | C2×C3×D4 | — | 9 | 1 | no | — |
| 302 | C2×C3×D4 | — | 9 | 1 | no | — |
| 303 | C2×C3×D4 | — | 9 | 1 | no | — |
| 304 | C2×C3×D4 | — | 9 | 1 | no | — |
| 305 | C2×C3×D4 | — | 9 | 1 | no | — |
| 306 | C2×C3×D4 | — | 9 | 1 | no | — |
| 307 | C2×C3×D4 | — | 18 | 2 | no | — |
| 308 | C2×C3×D4 | — | 18 | 2 | no | — |
| 309 | C22×C3×C4 | — | 3 | 1 | no | — |
| 310 | C22×C3×C4 | — | 9 | 1 | no | — |
| 311 | C2×#67 | — | 3 | 1 | no | — |
| 312 | C2×#67 | — | 3 | 1 | no | — |
| 313 | C2×#67 | — | 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 | — | 6 | 2 | no | — |
| 320 | C2×#67 | — | 6 | 2 | 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 | 2 | no | — |
| 339 | C2×#67 | — | 18 | 2 | no | — |
| 340 | C2×#67 | — | 18 | 1 | no | — |
| 341 | C2×#67 | — | 18 | 1 | no | — |
| 342 | C2×#67 | — | 18 | 1 | no | — |
| 343 | C2×#67 | — | 18 | 1 | no | — |
| 344 | C22×Dic3 | — | 3 | 1 | no | — |
| 345 | C22×Dic3 | — | 9 | 1 | no | — |
| 346 | C22×Dic3 | — | 9 | 1 | no | — |
| 347 | C22×Dic3 | C2×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 348 | D3×D4 | — | 18 | 1 | no | — |
| 349 | D3×D4 | — | 18 | 2 | no | — |
| 350 | D3×D4 | — | 18 | 1 | no | — |
| 351 | D3×D4 | — | 18 | 1 | no | — |
| 352 | D3×D4 | — | 18 | 2 | no | — |
| 353 | D3×D4 | — | 18 | 1 | no | — |
| 354 | D3×D4 | — | 36 | 3 | no | — |
| 355 | C2×D12 | — | 9 | 1 | no | — |
| 356 | C2×D12 | — | 9 | 1 | no | — |
| 357 | C2×C4×D3 | — | 9 | 1 | no | — |
| 358 | C2×C4×D3 | — | 9 | 1 | no | — |
| 359 | C4×A4 | — | 3 | 3 | no | — |
| 360 | SL(2,ℤ/4) | — | 9 | 3 | no | — |
| 361 | SL(2,ℤ/4) | — | 18 | 3 | no | — |
| 362 | #217 | — | 9 | 1 | no | — |
| 363 | #217 | — | 9 | 1 | no | — |
| 364 | #217 | — | 9 | 1 | no | — |
| 365 | #217 | — | 9 | 1 | no | — |
| 366 | #217 | — | 9 | 1 | no | — |
| 367 | #217 | — | 9 | 1 | no | — |
| 368 | #217 | — | 9 | 1 | no | — |
| 369 | #217 | — | 9 | 1 | no | — |
| 370 | #217 | — | 9 | 1 | no | — |
| 371 | #217 | — | 9 | 1 | no | — |
| 372 | #217 | — | 18 | 1 | no | — |
| 373 | #217 | — | 18 | 1 | no | — |
| 374 | #217 | — | 18 | 1 | no | — |
| 375 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 376 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 377 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 378 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 379 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 380 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 381 | C4⋊Dic3 | — | 9 | 1 | no | — |
| 382 | C4⋊Dic3 | — | 9 | 1 | no | — |
| 383 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 384 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 385 | C4×Dic3 | — | 9 | 1 | no | — |
| 386 | C4×Dic3 | — | 9 | 1 | no | — |
| 387 | C22×C32 | — | 3 | 1 | no | — |
| 388 | C22×C32 | — | 3 | 1 | no | — |
| 389 | C22×C32 | — | 3 | 1 | no | — |
| 390 | C22×C32 | — | 4 | 1 | no | — |
| 391 | C22×C32 | — | 4 | 3 | no | — |
| 392 | C22×C32 | — | 6 | 1 | no | — |
| 393 | C22×C32 | — | 6 | 1 | no | — |
| 394 | C22×C32 | — | 6 | 1 | no | — |
| 395 | C22×C32 | — | 6 | 1 | no | — |
| 396 | C22×C32 | — | 8 | 3 | no | — |
| 397 | C22×C32 | — | 8 | 1 | no | — |
| 398 | C22×C32 | — | 12 | 1 | no | — |
| 399 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic, complemented |
| 400 | C22×C32 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 401 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 402 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 403 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 404 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 405 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 406 | C2×C3⋊D3 | — | 8 | 2 | no | — |
| 407 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 408 | C2×C3⋊D3 | — | 12 | 3 | no | — |
| 409 | C2×C3⋊D3 | — | 24 | 1 | no | — |
| 410 | C2×C3⋊D3 | — | 24 | 3 | no | — |
| 411 | C2×C3⋊D3 | — | 24 | 2 | no | — |
| 412 | C2×C3×D3 | — | 3 | 2 | no | — |
| 413 | C2×C3×D3 | — | 3 | 1 | no | — |
| 414 | C2×C3×D3 | — | 4 | 3 | no | — |
| 415 | C2×C3×D3 | — | 6 | 1 | no | — |
| 416 | C2×C3×D3 | — | 6 | 1 | no | — |
| 417 | C2×C3×D3 | — | 6 | 1 | no | — |
| 418 | C2×C3×D3 | — | 6 | 1 | no | — |
| 419 | C2×C3×D3 | — | 6 | 1 | no | — |
| 420 | C2×C3×D3 | — | 6 | 1 | no | — |
| 421 | C2×C3×D3 | — | 6 | 1 | no | — |
| 422 | C2×C3×D3 | — | 6 | 1 | no | — |
| 423 | C2×C3×D3 | — | 6 | 1 | no | — |
| 424 | C2×C3×D3 | — | 12 | 3 | no | — |
| 425 | C2×C3×D3 | — | 12 | 3 | no | — |
| 426 | C2×C3×D3 | — | 12 | 2 | no | — |
| 427 | C2×C3×D3 | — | 12 | 2 | no | — |
| 428 | C2×C3×D3 | — | 24 | 6 | no | — |
| 429 | C2×C3×D3 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 430 | C3×A4 | — | 2 | 1 | no | — |
| 431 | C3×A4 | — | 2 | 3 | no | — |
| 432 | C3×A4 | D3×D4 | 1 | 3 | yes | complemented |
| 433 | C3×A4 | C2×#67 | 1 | 1 | yes | characteristic, complemented |
| 434 | D32 | — | 12 | 2 | no | — |
| 435 | D32 | — | 12 | 2 | no | — |
| 436 | D32 | — | 24 | 6 | no | — |
| 437 | C32×C4 | — | 12 | 1 | no | — |
| 438 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 439 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 440 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 441 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 442 | C3⋊Dic3 | — | 12 | 3 | no | — |
| 443 | C3⋊Dic3 | — | 24 | 1 | no | — |
| 444 | C3⋊Dic3 | — | 24 | 3 | no | — |
| 445 | C3×Dic3 | — | 3 | 2 | no | — |
| 446 | C3×Dic3 | — | 3 | 1 | no | — |
| 447 | C3×Dic3 | — | 4 | 3 | no | — |
| 448 | C3×Dic3 | — | 6 | 1 | no | — |
| 449 | C3×Dic3 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 450 | C22×D4 | — | 3 | 1 | no | — |
| 451 | C22×D4 | — | 9 | 1 | no | — |
| 452 | C22×D4 | — | 27 | 1 | no | — |
| 453 | C22×D4 | — | 27 | 1 | no | — |
| 454 | #127 | — | 27 | 1 | no | — |
| 455 | #121 | — | 27 | 1 | no | — |
| 456 | #121 | — | 27 | 1 | no | — |
| 457 | #121 | — | 27 | 1 | no | — |
| 458 | #121 | — | 27 | 1 | no | — |
| 459 | #120 | — | 27 | 1 | no | — |
| 460 | #120 | — | 27 | 1 | no | — |
| 461 | #120 | — | 27 | 1 | no | — |
| 462 | #120 | — | 27 | 1 | no | — |
| 463 | C4×D4 | — | 27 | 1 | no | — |
| 464 | C4×D4 | — | 27 | 1 | no | — |
| 465 | C33 | — | 4 | 1 | no | Sylow |
| 466 | C23×C3 | — | 2 | 1 | no | — |
| 467 | C23×C3 | — | 2 | 1 | no | — |
| 468 | C23×C3 | — | 2 | 1 | no | — |
| 469 | C23×C3 | — | 3 | 1 | no | — |
| 470 | C23×C3 | — | 3 | 1 | no | — |
| 471 | C23×C3 | — | 3 | 1 | no | — |
| 472 | C23×C3 | — | 3 | 1 | no | — |
| 473 | C23×C3 | — | 4 | 1 | no | — |
| 474 | C23×C3 | — | 6 | 1 | no | — |
| 475 | C23×C3 | — | 6 | 1 | no | — |
| 476 | C23×C3 | — | 6 | 1 | no | — |
| 477 | C23×C3 | — | 6 | 1 | no | — |
| 478 | C23×C3 | — | 6 | 1 | no | — |
| 479 | C23×C3 | — | 9 | 1 | no | — |
| 480 | C23×C3 | — | 9 | 1 | no | — |
| 481 | C23×C3 | — | 9 | 1 | no | — |
| 482 | C23×C3 | — | 9 | 1 | no | — |
| 483 | C23×C3 | — | 12 | 1 | no | — |
| 484 | C23×C3 | — | 18 | 1 | no | — |
| 485 | C23×C3 | — | 18 | 1 | no | — |
| 486 | C23×C3 | — | 18 | 2 | no | — |
| 487 | C23×C3 | — | 18 | 1 | no | — |
| 488 | C23×C3 | — | 36 | 1 | no | — |
| 489 | C23×C3 | C2×D32 | 1 | 1 | yes | characteristic |
| 490 | C23×C3 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 491 | C22×D3 | — | 2 | 1 | no | — |
| 492 | C22×D3 | — | 3 | 1 | no | — |
| 493 | C22×D3 | — | 3 | 1 | no | — |
| 494 | C22×D3 | — | 3 | 1 | no | — |
| 495 | C22×D3 | — | 3 | 1 | no | — |
| 496 | C22×D3 | — | 6 | 2 | no | — |
| 497 | C22×D3 | — | 6 | 1 | no | — |
| 498 | C22×D3 | — | 6 | 1 | no | — |
| 499 | C22×D3 | — | 6 | 1 | no | — |
| 500 | C22×D3 | — | 9 | 1 | no | — |
| 501 | C22×D3 | — | 9 | 1 | no | — |
| 502 | C22×D3 | — | 12 | 3 | no | — |
| 503 | C22×D3 | — | 12 | 1 | no | — |
| 504 | C22×D3 | — | 18 | 1 | no | — |
| 505 | C22×D3 | — | 18 | 2 | no | — |
| 506 | C22×D3 | — | 18 | 1 | no | — |
| 507 | C22×D3 | — | 18 | 1 | no | — |
| 508 | C22×D3 | — | 18 | 2 | no | — |
| 509 | C22×D3 | — | 18 | 1 | no | — |
| 510 | C22×D3 | — | 18 | 1 | no | — |
| 511 | C22×D3 | — | 36 | 3 | no | — |
| 512 | C22×D3 | — | 36 | 1 | no | — |
| 513 | C22×D3 | — | 36 | 1 | no | — |
| 514 | C2×A4 | — | 2 | 3 | no | — |
| 515 | C2×A4 | — | 2 | 3 | no | — |
| 516 | C2×A4 | — | 4 | 3 | no | — |
| 517 | C2×A4 | — | 6 | 3 | no | — |
| 518 | C2×A4 | C2×D32 | 1 | 3 | yes | — |
| 519 | S4 | — | 3 | 6 | no | — |
| 520 | S4 | — | 6 | 3 | no | — |
| 521 | S4 | — | 18 | 3 | no | — |
| 522 | S4 | — | 36 | 3 | no | — |
| 523 | C3×D4 | — | 3 | 1 | no | — |
| 524 | C3×D4 | — | 9 | 1 | no | — |
| 525 | C3×D4 | — | 9 | 1 | no | — |
| 526 | C3×D4 | — | 9 | 2 | no | — |
| 527 | C3×D4 | — | 9 | 1 | no | — |
| 528 | C3×D4 | — | 9 | 2 | no | — |
| 529 | C3×D4 | — | 12 | 3 | no | — |
| 530 | C3×D4 | — | 18 | 1 | no | — |
| 531 | C3×D4 | — | 18 | 2 | no | — |
| 532 | C3×D4 | — | 18 | 1 | no | — |
| 533 | C3×D4 | — | 18 | 2 | no | — |
| 534 | C3×D4 | — | 18 | 1 | no | — |
| 535 | C2×C3×C4 | — | 9 | 1 | no | — |
| 536 | C2×C3×C4 | — | 9 | 1 | no | — |
| 537 | C2×C3×C4 | — | 9 | 1 | no | — |
| 538 | C2×C3×C4 | — | 9 | 1 | no | — |
| 539 | C2×C3×C4 | — | 18 | 2 | no | — |
| 540 | #67 | — | 3 | 2 | no | — |
| 541 | #67 | — | 3 | 1 | no | — |
| 542 | #67 | — | 3 | 2 | no | — |
| 543 | #67 | — | 3 | 1 | no | — |
| 544 | #67 | — | 3 | 1 | no | — |
| 545 | #67 | — | 6 | 1 | no | — |
| 546 | #67 | — | 6 | 2 | no | — |
| 547 | #67 | — | 6 | 2 | no | — |
| 548 | #67 | — | 6 | 1 | no | — |
| 549 | #67 | — | 6 | 1 | no | — |
| 550 | #67 | — | 18 | 2 | no | — |
| 551 | #67 | — | 18 | 1 | no | — |
| 552 | #67 | — | 18 | 2 | no | — |
| 553 | #67 | — | 18 | 1 | no | — |
| 554 | #67 | — | 18 | 1 | no | — |
| 555 | #67 | — | 18 | 2 | no | — |
| 556 | #67 | — | 18 | 1 | no | — |
| 557 | #67 | — | 18 | 1 | no | — |
| 558 | #67 | — | 18 | 1 | no | — |
| 559 | #67 | — | 18 | 1 | no | — |
| 560 | #67 | — | 18 | 1 | no | — |
| 561 | #67 | — | 18 | 1 | no | — |
| 562 | #67 | — | 18 | 1 | no | — |
| 563 | #67 | — | 18 | 1 | no | — |
| 564 | #67 | — | 18 | 1 | no | — |
| 565 | #67 | — | 18 | 1 | no | — |
| 566 | #67 | — | 18 | 1 | no | — |
| 567 | #67 | — | 36 | 3 | no | — |
| 568 | #67 | — | 36 | 1 | no | — |
| 569 | #67 | — | 36 | 1 | no | — |
| 570 | #67 | — | 36 | 3 | no | — |
| 571 | #67 | — | 36 | 1 | no | — |
| 572 | #67 | — | 36 | 1 | no | — |
| 573 | #67 | — | 36 | 1 | no | — |
| 574 | #67 | — | 36 | 1 | no | — |
| 575 | #67 | — | 36 | 1 | no | — |
| 576 | #67 | — | 36 | 1 | no | — |
| 577 | #67 | — | 36 | 2 | no | — |
| 578 | #67 | — | 72 | 3 | no | — |
| 579 | #67 | C3⋊S4 | 1 | 1 | yes | characteristic, direct product factor |
| 580 | C2×Dic3 | — | 3 | 1 | no | — |
| 581 | C2×Dic3 | — | 3 | 1 | no | — |
| 582 | C2×Dic3 | — | 3 | 1 | no | — |
| 583 | C2×Dic3 | — | 3 | 1 | no | — |
| 584 | C2×Dic3 | — | 6 | 2 | no | — |
| 585 | C2×Dic3 | — | 9 | 1 | no | — |
| 586 | C2×Dic3 | — | 9 | 1 | no | — |
| 587 | C2×Dic3 | — | 9 | 1 | no | — |
| 588 | C2×Dic3 | — | 9 | 1 | no | — |
| 589 | C2×Dic3 | — | 9 | 1 | no | — |
| 590 | C2×Dic3 | — | 9 | 1 | no | — |
| 591 | C2×Dic3 | — | 18 | 1 | no | — |
| 592 | C2×Dic3 | — | 18 | 1 | no | — |
| 593 | C2×Dic3 | — | 18 | 1 | no | — |
| 594 | C2×Dic3 | — | 18 | 2 | no | — |
| 595 | C2×Dic3 | — | 18 | 1 | no | — |
| 596 | C2×Dic3 | — | 18 | 1 | no | — |
| 597 | D12 | — | 18 | 1 | no | — |
| 598 | D12 | — | 18 | 2 | no | — |
| 599 | D12 | — | 18 | 1 | no | — |
| 600 | D12 | — | 36 | 3 | no | — |
| 601 | C4×D3 | — | 18 | 1 | no | — |
| 602 | C4×D3 | — | 18 | 2 | no | — |
| 603 | C4×D3 | — | 18 | 1 | no | — |
| 604 | C4×D3 | — | 36 | 3 | no | — |
| 605 | C2×C32 | — | 2 | 1 | no | — |
| 606 | C2×C32 | — | 3 | 1 | no | — |
| 607 | C2×C32 | — | 3 | 1 | no | — |
| 608 | C2×C32 | — | 4 | 1 | no | — |
| 609 | C2×C32 | — | 4 | 3 | no | — |
| 610 | C2×C32 | — | 6 | 1 | no | — |
| 611 | C2×C32 | — | 8 | 3 | no | — |
| 612 | C2×C32 | — | 8 | 1 | no | — |
| 613 | C2×C32 | — | 8 | 3 | no | — |
| 614 | C2×C32 | — | 8 | 1 | no | — |
| 615 | C2×C32 | — | 16 | 1 | no | — |
| 616 | C2×C32 | — | 16 | 3 | no | — |
| 617 | C2×C32 | — | 24 | 1 | no | — |
| 618 | C2×C32 | C22×S4 | 1 | 1 | yes | characteristic |
| 619 | C3⋊D3 | — | 4 | 2 | no | — |
| 620 | C3⋊D3 | — | 8 | 1 | no | — |
| 621 | C3⋊D3 | — | 12 | 1 | no | — |
| 622 | C3⋊D3 | — | 24 | 1 | no | — |
| 623 | C3⋊D3 | — | 24 | 3 | no | — |
| 624 | C3⋊D3 | — | 48 | 1 | no | — |
| 625 | C3⋊D3 | — | 48 | 3 | no | — |
| 626 | C3×D3 | — | 2 | 1 | no | — |
| 627 | C3×D3 | — | 6 | 2 | no | — |
| 628 | C3×D3 | — | 6 | 1 | no | — |
| 629 | C3×D3 | — | 8 | 3 | no | — |
| 630 | C3×D3 | — | 12 | 6 | no | — |
| 631 | C3×D3 | — | 12 | 1 | no | — |
| 632 | C3×D3 | — | 24 | 3 | no | — |
| 633 | C24 | — | 3 | 1 | no | — |
| 634 | C24 | — | 9 | 1 | no | — |
| 635 | C24 | — | 27 | 1 | no | — |
| 636 | C24 | D3×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 637 | C2×D4 | — | 9 | 1 | no | — |
| 638 | C2×D4 | — | 9 | 1 | no | — |
| 639 | C2×D4 | — | 9 | 1 | no | — |
| 640 | C2×D4 | — | 9 | 1 | no | — |
| 641 | C2×D4 | — | 9 | 1 | no | — |
| 642 | C2×D4 | — | 9 | 1 | no | — |
| 643 | C2×D4 | — | 9 | 1 | no | — |
| 644 | C2×D4 | — | 9 | 1 | no | — |
| 645 | C2×D4 | — | 18 | 2 | no | — |
| 646 | C2×D4 | — | 18 | 2 | no | — |
| 647 | C2×D4 | — | 27 | 1 | no | — |
| 648 | C2×D4 | — | 27 | 1 | no | — |
| 649 | C2×D4 | — | 27 | 1 | no | — |
| 650 | C2×D4 | — | 27 | 1 | no | — |
| 651 | C2×D4 | — | 27 | 1 | no | — |
| 652 | C2×D4 | — | 27 | 1 | no | — |
| 653 | C2×D4 | — | 27 | 1 | no | — |
| 654 | C2×D4 | — | 27 | 1 | no | — |
| 655 | C2×D4 | — | 54 | 1 | no | — |
| 656 | C2×D4 | — | 54 | 2 | no | — |
| 657 | C2×D4 | — | 54 | 1 | no | — |
| 658 | C2×D4 | — | 54 | 1 | no | — |
| 659 | C2×D4 | — | 54 | 2 | no | — |
| 660 | C2×D4 | — | 54 | 1 | no | — |
| 661 | C22×C4 | — | 3 | 1 | no | — |
| 662 | C22×C4 | — | 9 | 1 | no | — |
| 663 | C22×C4 | — | 27 | 1 | no | — |
| 664 | C22×C4 | — | 27 | 1 | no | — |
| 665 | C4⋊C4 | — | 27 | 1 | no | — |
| 666 | C4⋊C4 | — | 27 | 1 | no | — |
| 667 | C22⋊C4 | — | 27 | 1 | no | — |
| 668 | C22⋊C4 | — | 27 | 1 | no | — |
| 669 | C22⋊C4 | — | 27 | 1 | no | — |
| 670 | C22⋊C4 | — | 27 | 1 | no | — |
| 671 | C22⋊C4 | — | 27 | 1 | no | — |
| 672 | C22⋊C4 | — | 27 | 1 | no | — |
| 673 | C22⋊C4 | — | 27 | 1 | no | — |
| 674 | C22⋊C4 | — | 27 | 1 | no | — |
| 675 | C42 | — | 27 | 1 | no | — |
| 676 | C22×C3 | — | 2 | 1 | no | — |
| 677 | C22×C3 | — | 2 | 1 | no | — |
| 678 | C22×C3 | — | 3 | 1 | no | — |
| 679 | C22×C3 | — | 3 | 1 | no | — |
| 680 | C22×C3 | — | 3 | 1 | no | — |
| 681 | C22×C3 | — | 3 | 1 | no | — |
| 682 | C22×C3 | — | 3 | 1 | no | — |
| 683 | C22×C3 | — | 3 | 1 | no | — |
| 684 | C22×C3 | — | 3 | 1 | no | — |
| 685 | C22×C3 | — | 4 | 3 | no | — |
| 686 | C22×C3 | — | 6 | 1 | no | — |
| 687 | C22×C3 | — | 6 | 1 | no | — |
| 688 | C22×C3 | — | 6 | 1 | no | — |
| 689 | C22×C3 | — | 6 | 1 | no | — |
| 690 | C22×C3 | — | 6 | 1 | no | — |
| 691 | C22×C3 | — | 6 | 1 | no | — |
| 692 | C22×C3 | — | 6 | 1 | no | — |
| 693 | C22×C3 | — | 6 | 1 | no | — |
| 694 | C22×C3 | — | 6 | 1 | no | — |
| 695 | C22×C3 | — | 6 | 1 | no | — |
| 696 | C22×C3 | — | 6 | 1 | no | — |
| 697 | C22×C3 | — | 6 | 2 | no | — |
| 698 | C22×C3 | — | 8 | 3 | no | — |
| 699 | C22×C3 | — | 9 | 2 | no | — |
| 700 | C22×C3 | — | 9 | 1 | no | — |
| 701 | C22×C3 | — | 12 | 3 | no | — |
| 702 | C22×C3 | — | 12 | 1 | no | — |
| 703 | C22×C3 | — | 12 | 1 | no | — |
| 704 | C22×C3 | — | 12 | 1 | no | — |
| 705 | C22×C3 | — | 18 | 1 | no | — |
| 706 | C22×C3 | — | 18 | 1 | no | — |
| 707 | C22×C3 | — | 18 | 1 | no | — |
| 708 | C22×C3 | — | 18 | 1 | no | — |
| 709 | C22×C3 | — | 18 | 1 | no | — |
| 710 | C22×C3 | — | 18 | 1 | no | — |
| 711 | C22×C3 | — | 18 | 1 | no | — |
| 712 | C22×C3 | — | 18 | 1 | no | — |
| 713 | C22×C3 | — | 18 | 1 | no | — |
| 714 | C22×C3 | — | 36 | 2 | no | — |
| 715 | C22×C3 | — | 36 | 2 | no | — |
| 716 | C22×C3 | D3×#67 | 1 | 1 | yes | characteristic, complemented |
| 717 | C22×C3 | D4×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 718 | C22×C3 | D3×S4 | 1 | 1 | yes | characteristic, complemented |
| 719 | C22×C3 | C2×C3⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 720 | C2×D3 | — | 3 | 2 | no | — |
| 721 | C2×D3 | — | 3 | 1 | no | — |
| 722 | C2×D3 | — | 6 | 1 | no | — |
| 723 | C2×D3 | — | 6 | 1 | no | — |
| 724 | C2×D3 | — | 6 | 1 | no | — |
| 725 | C2×D3 | — | 6 | 1 | no | — |
| 726 | C2×D3 | — | 6 | 1 | no | — |
| 727 | C2×D3 | — | 6 | 1 | no | — |
| 728 | C2×D3 | — | 6 | 1 | no | — |
| 729 | C2×D3 | — | 6 | 1 | no | — |
| 730 | C2×D3 | — | 6 | 1 | no | — |
| 731 | C2×D3 | — | 12 | 3 | no | — |
| 732 | C2×D3 | — | 12 | 3 | no | — |
| 733 | C2×D3 | — | 12 | 2 | no | — |
| 734 | C2×D3 | — | 12 | 2 | no | — |
| 735 | C2×D3 | — | 18 | 1 | no | — |
| 736 | C2×D3 | — | 18 | 1 | no | — |
| 737 | C2×D3 | — | 18 | 1 | no | — |
| 738 | C2×D3 | — | 18 | 1 | no | — |
| 739 | C2×D3 | — | 18 | 1 | no | — |
| 740 | C2×D3 | — | 18 | 1 | no | — |
| 741 | C2×D3 | — | 24 | 6 | no | — |
| 742 | C2×D3 | — | 36 | 1 | no | — |
| 743 | C2×D3 | — | 36 | 3 | no | — |
| 744 | C2×D3 | — | 36 | 1 | no | — |
| 745 | C2×D3 | — | 36 | 1 | no | — |
| 746 | C2×D3 | — | 36 | 2 | no | — |
| 747 | C2×D3 | — | 36 | 2 | no | — |
| 748 | C2×D3 | — | 36 | 2 | no | — |
| 749 | C2×D3 | — | 36 | 2 | no | — |
| 750 | C2×D3 | — | 72 | 3 | no | — |
| 751 | C2×D3 | — | 72 | 6 | no | — |
| 752 | C2×D3 | C2×C3⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 753 | A4 | — | 2 | 3 | no | — |
| 754 | A4 | D3×#67 | 1 | 3 | yes | complemented |
| 755 | C3×C4 | — | 3 | 1 | no | — |
| 756 | C3×C4 | — | 9 | 2 | no | — |
| 757 | C3×C4 | — | 9 | 1 | no | — |
| 758 | C3×C4 | — | 12 | 3 | no | — |
| 759 | C3×C4 | — | 18 | 1 | no | — |
| 760 | Dic3 | — | 3 | 2 | no | — |
| 761 | Dic3 | — | 3 | 1 | no | — |
| 762 | Dic3 | — | 6 | 1 | no | — |
| 763 | Dic3 | — | 18 | 1 | no | — |
| 764 | Dic3 | — | 18 | 1 | no | — |
| 765 | Dic3 | — | 18 | 1 | no | — |
| 766 | Dic3 | — | 18 | 1 | no | — |
| 767 | Dic3 | — | 18 | 1 | no | — |
| 768 | Dic3 | — | 18 | 1 | no | — |
| 769 | Dic3 | — | 36 | 1 | no | — |
| 770 | Dic3 | — | 36 | 3 | no | — |
| 771 | Dic3 | — | 36 | 1 | no | — |
| 772 | Dic3 | — | 36 | 1 | no | — |
| 773 | Dic3 | — | 72 | 3 | no | — |
| 774 | Dic3 | C2×C3⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 775 | C32 | — | 4 | 1 | no | — |
| 776 | C32 | — | 4 | 3 | no | — |
| 777 | C32 | — | 8 | 3 | no | — |
| 778 | C32 | — | 8 | 1 | no | — |
| 779 | C32 | D4×S4 | 1 | 1 | yes | characteristic, complemented |
| 780 | C23 | — | 2 | 1 | no | — |
| 781 | C23 | — | 3 | 1 | no | — |
| 782 | C23 | — | 3 | 1 | no | — |
| 783 | C23 | — | 6 | 1 | no | — |
| 784 | C23 | — | 6 | 1 | no | — |
| 785 | C23 | — | 9 | 1 | no | — |
| 786 | C23 | — | 9 | 1 | no | — |
| 787 | C23 | — | 9 | 1 | no | — |
| 788 | C23 | — | 9 | 1 | no | — |
| 789 | C23 | — | 18 | 1 | no | — |
| 790 | C23 | — | 18 | 1 | no | — |
| 791 | C23 | — | 18 | 2 | no | — |
| 792 | C23 | — | 18 | 1 | no | — |
| 793 | C23 | — | 27 | 1 | no | — |
| 794 | C23 | — | 36 | 1 | no | — |
| 795 | C23 | — | 54 | 1 | no | — |
| 796 | C23 | — | 54 | 2 | no | — |
| 797 | C23 | — | 54 | 1 | no | — |
| 798 | C23 | — | 108 | 1 | no | — |
| 799 | C23 | C2×D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 800 | D4 | — | 3 | 1 | no | — |
| 801 | D4 | — | 9 | 1 | no | — |
| 802 | D4 | — | 9 | 1 | no | — |
| 803 | D4 | — | 9 | 2 | no | — |
| 804 | D4 | — | 9 | 1 | no | — |
| 805 | D4 | — | 9 | 2 | no | — |
| 806 | D4 | — | 18 | 1 | no | — |
| 807 | D4 | — | 18 | 2 | no | — |
| 808 | D4 | — | 18 | 1 | no | — |
| 809 | D4 | — | 18 | 2 | no | — |
| 810 | D4 | — | 18 | 1 | no | — |
| 811 | D4 | — | 54 | 1 | no | — |
| 812 | D4 | — | 54 | 2 | no | — |
| 813 | D4 | — | 54 | 1 | no | — |
| 814 | D4 | — | 54 | 1 | no | — |
| 815 | D4 | — | 54 | 1 | no | — |
| 816 | D4 | — | 54 | 1 | no | — |
| 817 | D4 | — | 54 | 2 | no | — |
| 818 | D4 | — | 54 | 1 | no | — |
| 819 | D4 | — | 54 | 1 | no | — |
| 820 | D4 | — | 54 | 1 | no | — |
| 821 | D4 | — | 108 | 1 | no | — |
| 822 | D4 | — | 108 | 1 | no | — |
| 823 | C2×C4 | — | 9 | 1 | no | — |
| 824 | C2×C4 | — | 9 | 1 | no | — |
| 825 | C2×C4 | — | 9 | 1 | no | — |
| 826 | C2×C4 | — | 9 | 1 | no | — |
| 827 | C2×C4 | — | 18 | 2 | no | — |
| 828 | C2×C4 | — | 27 | 1 | no | — |
| 829 | C2×C4 | — | 27 | 1 | no | — |
| 830 | C2×C4 | — | 27 | 1 | no | — |
| 831 | C2×C4 | — | 54 | 1 | no | — |
| 832 | C2×C4 | — | 54 | 2 | no | — |
| 833 | C2×C4 | — | 54 | 1 | no | — |
| 834 | C2×C3 | — | 2 | 1 | no | — |
| 835 | C2×C3 | — | 2 | 1 | no | — |
| 836 | C2×C3 | — | 2 | 1 | no | — |
| 837 | C2×C3 | — | 3 | 1 | no | — |
| 838 | C2×C3 | — | 3 | 1 | no | — |
| 839 | C2×C3 | — | 3 | 1 | no | — |
| 840 | C2×C3 | — | 3 | 1 | no | — |
| 841 | C2×C3 | — | 4 | 1 | no | — |
| 842 | C2×C3 | — | 4 | 3 | no | — |
| 843 | C2×C3 | — | 6 | 1 | no | — |
| 844 | C2×C3 | — | 6 | 1 | no | — |
| 845 | C2×C3 | — | 6 | 1 | no | — |
| 846 | C2×C3 | — | 6 | 1 | no | — |
| 847 | C2×C3 | — | 6 | 1 | no | — |
| 848 | C2×C3 | — | 8 | 3 | no | — |
| 849 | C2×C3 | — | 8 | 3 | no | — |
| 850 | C2×C3 | — | 12 | 1 | no | — |
| 851 | C2×C3 | — | 16 | 3 | no | — |
| 852 | C2×C3 | — | 18 | 1 | no | — |
| 853 | C2×C3 | — | 18 | 2 | no | — |
| 854 | C2×C3 | — | 24 | 3 | no | — |
| 855 | C2×C3 | — | 36 | 1 | no | — |
| 856 | C2×C3 | C2×D3×S4 | 1 | 1 | yes | characteristic |
| 857 | C2×C3 | C22×C3⋊S4 | 1 | 1 | yes | characteristic |
| 858 | D3 | — | 2 | 1 | no | — |
| 859 | D3 | — | 6 | 2 | no | — |
| 860 | D3 | — | 6 | 1 | no | — |
| 861 | D3 | — | 12 | 6 | no | — |
| 862 | D3 | — | 12 | 1 | no | — |
| 863 | D3 | — | 24 | 3 | no | — |
| 864 | D3 | — | 36 | 1 | no | — |
| 865 | D3 | — | 36 | 1 | no | — |
| 866 | D3 | — | 72 | 1 | no | — |
| 867 | D3 | — | 72 | 3 | no | — |
| 868 | D3 | — | 144 | 3 | no | — |
| 869 | C22 | — | 3 | 1 | no | — |
| 870 | C22 | — | 3 | 1 | no | — |
| 871 | C22 | — | 3 | 1 | no | — |
| 872 | C22 | — | 3 | 1 | no | — |
| 873 | C22 | — | 6 | 1 | no | — |
| 874 | C22 | — | 6 | 1 | no | — |
| 875 | C22 | — | 6 | 1 | no | — |
| 876 | C22 | — | 6 | 1 | no | — |
| 877 | C22 | — | 9 | 2 | no | — |
| 878 | C22 | — | 9 | 1 | no | — |
| 879 | C22 | — | 18 | 1 | no | — |
| 880 | C22 | — | 18 | 1 | no | — |
| 881 | C22 | — | 18 | 1 | no | — |
| 882 | C22 | — | 18 | 1 | no | — |
| 883 | C22 | — | 18 | 1 | no | — |
| 884 | C22 | — | 18 | 1 | no | — |
| 885 | C22 | — | 18 | 1 | no | — |
| 886 | C22 | — | 18 | 1 | no | — |
| 887 | C22 | — | 18 | 1 | no | — |
| 888 | C22 | — | 36 | 2 | no | — |
| 889 | C22 | — | 36 | 2 | no | — |
| 890 | C22 | — | 54 | 1 | no | — |
| 891 | C22 | — | 54 | 1 | no | — |
| 892 | C22 | — | 54 | 1 | no | — |
| 893 | C22 | — | 108 | 2 | no | — |
| 894 | C22 | — | 108 | 2 | no | — |
| 895 | C22 | C3⋊D3×#67 | 1 | 1 | yes | characteristic, complemented |
| 896 | C22 | D3×C3⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 897 | C4 | — | 3 | 1 | no | — |
| 898 | C4 | — | 9 | 2 | no | — |
| 899 | C4 | — | 9 | 1 | no | — |
| 900 | C4 | — | 18 | 1 | no | — |
| 901 | C4 | — | 54 | 1 | no | — |
| 902 | C4 | — | 54 | 1 | no | — |
| 903 | C4 | — | 54 | 1 | no | — |
| 904 | C3 | — | 2 | 1 | no | — |
| 905 | C3 | — | 4 | 3 | no | — |
| 906 | C3 | — | 8 | 3 | no | — |
| 907 | C3 | #67×S4 | 1 | 1 | yes | characteristic, complemented |
| 908 | C3 | D4×C3⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 909 | C2 | — | 2 | 1 | no | — |
| 910 | C2 | — | 3 | 1 | no | — |
| 911 | C2 | — | 3 | 1 | no | — |
| 912 | C2 | — | 6 | 1 | no | — |
| 913 | C2 | — | 6 | 1 | no | — |
| 914 | C2 | — | 18 | 1 | no | — |
| 915 | C2 | — | 18 | 2 | no | — |
| 916 | C2 | — | 36 | 1 | no | — |
| 917 | C2 | — | 108 | 1 | no | — |
| 918 | 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. #11724473 | C2 | semidirect |
| 5. #11724204 | C2 | semidirect |
| 6. #11724202 | C2 | semidirect |
| 7. Dic3×C3⋊S4 | C2 | semidirect |
| 11. C22×C32×A4 | C22 | semidirect |
| 12. C2×C3×D3×A4 | C22 | semidirect |
| 13. 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 |
| 22. C22×C3⋊S4 | D3 | semidirect |
| 26. C22×C3×#67 | D3 | semidirect |
| 30. A4×#67 | D3 | semidirect |
| 59. 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 |
| 85. C2×C3⋊S4 | C2×D3 | semidirect |
| 105. C22×C3×Dic3 | C2×D3 | semidirect |
| 121. Dic3×A4 | C2×D3 | semidirect |
| 143. C32×A4 | C2×D4 | semidirect |
| 154. C22×#67 | C3⋊D3 | semidirect |
| 225. C3⋊S4 | #67 | direct (N × H) |
| 255. C3×#67 | S4 | semidirect |
| 284. C24×C3 | D32 | semidirect |
| 285. C24×C3 | C2×C3⋊D3 | semidirect |
| 289. C23×D3 | C2×C3⋊D3 | semidirect |
| 292. C22×A4 | D32 | semidirect |
| 347. C22×Dic3 | C2×C3⋊D3 | semidirect |
| 399. C22×C32 | D3×D4 | semidirect |
| 400. C22×C32 | C2×S4 | semidirect |
| 429. C2×C3×D3 | C2×S4 | semidirect |
| 432. C3×A4 | D3×D4 | semidirect |
| 433. C3×A4 | C2×#67 | semidirect |
| 449. C3×Dic3 | C2×S4 | semidirect |
| 579. #67 | C3⋊S4 | direct (N × H) |
| 636. C24 | D3×C3⋊D3 | semidirect |
| 716. C22×C3 | D3×#67 | semidirect |
| 717. C22×C3 | D4×C3⋊D3 | semidirect |
| 718. C22×C3 | D3×S4 | semidirect |
| 719. C22×C3 | C2×C3⋊S4 | semidirect |
| 752. C2×D3 | C2×C3⋊S4 | semidirect |
| 754. A4 | D3×#67 | semidirect |
| 774. Dic3 | C2×C3⋊S4 | semidirect |
| 779. C32 | D4×S4 | semidirect |
| 895. C22 | C3⋊D3×#67 | semidirect |
| 896. C22 | D3×C3⋊S4 | semidirect |
| 907. C3 | #67×S4 | semidirect |
| 908. 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 |
| #11724473 | 2 |
| #11724204 | 2 |
| #11724202 | 2 |
| Dic3×C3⋊S4 | 2 |
| D4×C3⋊S4 | 3 |
| #67×S4 | 3 |
| #672 | 3 |
| C3⋊D3×#67 | 4 |