Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1010 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 1010 conjugacy classes of subgroups — too many to draw. Only its 96 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 | A4×#638 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×A4×#67 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×C3×Dic3×A4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | A4×#627 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | A4×#626 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | A4×#624 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | D3×Dic3×A4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C22×#3804 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | A4×#237 | — | 3 | 1 | no | maximal |
| 10 | A4×#235 | — | 3 | 1 | no | maximal |
| 11 | C22×C32×A4 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×A4×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C3×D3×A4 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×#3804 | — | 4 | 1 | no | maximal |
| 15 | A4×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 16 | C3×Dic3×A4 | C22 | 1 | 1 | yes | characteristic |
| 17 | C3×Dic3×A4 | C22 | 1 | 1 | yes | characteristic |
| 18 | C3×Dic3×A4 | C22 | 1 | 1 | yes | characteristic |
| 19 | C22×#638 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 20 | C22×C3×#67 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 21 | C23×C3×Dic3 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 22 | C3×D4×A4 | — | 3 | 1 | no | — |
| 23 | C2×C3×C4×A4 | — | 3 | 1 | no | — |
| 24 | C22×#627 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 25 | C22×#626 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 26 | C22×#624 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 27 | C2×#3804 | — | 3 | 1 | no | — |
| 28 | C2×#3804 | — | 3 | 1 | no | — |
| 29 | C2×#3804 | — | 3 | 1 | no | — |
| 30 | C2×#3804 | — | 3 | 1 | no | — |
| 31 | C2×#3804 | — | 3 | 1 | no | — |
| 32 | C2×#3804 | — | 3 | 1 | no | — |
| 33 | C2×#3804 | — | 3 | 1 | no | — |
| 34 | C2×#3804 | — | 3 | 1 | no | — |
| 35 | C22×D3×Dic3 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 36 | A4×#67 | — | 2 | 1 | no | — |
| 37 | A4×#67 | — | 3 | 1 | no | — |
| 38 | A4×#67 | — | 3 | 1 | no | — |
| 39 | A4×#67 | — | 3 | 1 | no | — |
| 40 | A4×#67 | — | 6 | 1 | no | — |
| 41 | A4×#67 | D3 | 1 | 1 | yes | characteristic, complemented |
| 42 | C2×Dic3×A4 | — | 2 | 1 | no | — |
| 43 | C2×Dic3×A4 | — | 3 | 1 | no | — |
| 44 | C2×Dic3×A4 | D3 | 1 | 1 | yes | characteristic, complemented |
| 45 | A4×D12 | — | 3 | 1 | no | — |
| 46 | C4×D3×A4 | — | 3 | 1 | no | — |
| 47 | C4×D3×A4 | — | 3 | 1 | no | — |
| 48 | C4×D3×A4 | — | 3 | 1 | no | — |
| 49 | A4×Dic6 | — | 3 | 1 | no | — |
| 50 | A4×Dic6 | — | 3 | 1 | no | — |
| 51 | C2×C32×A4 | — | 2 | 1 | no | — |
| 52 | C2×C32×A4 | C23 | 1 | 1 | yes | characteristic |
| 53 | A4×C3⋊D3 | — | 2 | 1 | no | — |
| 54 | C3×D3×A4 | — | 2 | 1 | no | — |
| 55 | C3×#638 | — | 4 | 1 | no | — |
| 56 | C32×#67 | — | 4 | 1 | no | — |
| 57 | C2×C32×Dic3 | — | 4 | 1 | no | — |
| 58 | C3×#627 | — | 4 | 1 | no | — |
| 59 | C3×#626 | — | 4 | 1 | no | — |
| 60 | C3×#624 | — | 4 | 1 | no | — |
| 61 | C3×D3×Dic3 | — | 4 | 1 | no | — |
| 62 | C22×#237 | — | 3 | 1 | no | — |
| 63 | C22×#235 | — | 3 | 1 | no | — |
| 64 | A4×#41 | — | 9 | 1 | no | — |
| 65 | C24×C32 | C22×C3 | 1 | 1 | yes | characteristic |
| 66 | C23×C3⋊D3 | C22×C3 | 1 | 1 | yes | characteristic |
| 67 | C23×C3×D3 | C22×C3 | 1 | 1 | yes | characteristic |
| 68 | C22×C3×A4 | — | 2 | 1 | no | — |
| 69 | C22×C3×A4 | — | 2 | 1 | no | — |
| 70 | C22×C3×A4 | — | 2 | 1 | no | — |
| 71 | C22×C3×A4 | — | 3 | 1 | no | — |
| 72 | C22×C3×A4 | — | 4 | 1 | no | — |
| 73 | C22×C3×A4 | C2×D3 | 1 | 1 | yes | characteristic |
| 74 | C22×C3×A4 | C2×D3 | 1 | 1 | yes | characteristic |
| 75 | C2×D3×A4 | — | 2 | 1 | no | — |
| 76 | C2×D3×A4 | — | 3 | 1 | no | — |
| 77 | C2×D3×A4 | — | 3 | 1 | no | — |
| 78 | C2×D3×A4 | — | 6 | 1 | no | — |
| 79 | C2×D3×A4 | C2×D3 | 1 | 1 | yes | characteristic |
| 80 | C2×#638 | — | 3 | 1 | no | — |
| 81 | C2×#638 | — | 3 | 1 | no | — |
| 82 | C2×#638 | — | 3 | 1 | no | — |
| 83 | C2×#638 | — | 3 | 1 | no | — |
| 84 | C22×C3⋊Dic3 | C22×C3 | 1 | 1 | yes | characteristic |
| 85 | C2×C3×#67 | — | 3 | 1 | no | — |
| 86 | C2×C3×#67 | — | 3 | 1 | no | — |
| 87 | C2×C3×#67 | — | 3 | 1 | no | — |
| 88 | C2×C3×#67 | — | 3 | 1 | no | — |
| 89 | C22×C3×Dic3 | — | 3 | 1 | no | — |
| 90 | C22×C3×Dic3 | — | 3 | 1 | no | — |
| 91 | C22×C3×Dic3 | — | 3 | 1 | no | — |
| 92 | C22×C3×Dic3 | — | 3 | 1 | no | — |
| 93 | C22×C3×Dic3 | C22×C3 | 1 | 1 | yes | characteristic |
| 94 | C22×C3×Dic3 | C22×C3 | 1 | 1 | yes | characteristic |
| 95 | C22×C3×Dic3 | C22×C3 | 1 | 1 | yes | characteristic |
| 96 | C3×#237 | — | 12 | 1 | no | — |
| 97 | C3×#235 | — | 12 | 1 | no | — |
| 98 | C3×C4×A4 | — | 3 | 1 | no | — |
| 99 | C3×C4×A4 | — | 3 | 1 | no | — |
| 100 | C3×C4×A4 | — | 3 | 1 | no | — |
| 101 | C2×#627 | — | 3 | 1 | no | — |
| 102 | C2×#627 | — | 3 | 1 | no | — |
| 103 | C2×#627 | — | 3 | 1 | no | — |
| 104 | C2×#627 | — | 3 | 1 | no | — |
| 105 | C2×#626 | — | 3 | 1 | no | — |
| 106 | C2×#626 | — | 3 | 1 | no | — |
| 107 | C2×#626 | — | 3 | 1 | no | — |
| 108 | C2×#626 | — | 3 | 1 | no | — |
| 109 | C2×#624 | — | 3 | 1 | no | — |
| 110 | C2×#624 | — | 3 | 1 | no | — |
| 111 | C2×#624 | — | 3 | 1 | no | — |
| 112 | C2×#624 | — | 3 | 1 | no | — |
| 113 | #3804 | — | 3 | 2 | no | — |
| 114 | #3804 | — | 3 | 2 | no | — |
| 115 | #3804 | — | 3 | 2 | no | — |
| 116 | #3804 | — | 3 | 2 | no | — |
| 117 | #3804 | — | 3 | 2 | no | — |
| 118 | #3804 | — | 3 | 2 | no | — |
| 119 | #3804 | — | 3 | 2 | no | — |
| 120 | #3804 | — | 3 | 1 | no | — |
| 121 | #3804 | — | 3 | 1 | no | — |
| 122 | #3804 | — | 3 | 1 | no | — |
| 123 | #3804 | — | 3 | 1 | no | — |
| 124 | #3804 | — | 3 | 1 | no | — |
| 125 | #3804 | — | 3 | 1 | no | — |
| 126 | #3804 | — | 3 | 1 | no | — |
| 127 | #3804 | A4 | 1 | 1 | yes | characteristic, direct product factor |
| 128 | C2×D3×Dic3 | — | 3 | 1 | no | — |
| 129 | C2×D3×Dic3 | — | 3 | 1 | no | — |
| 130 | C2×D3×Dic3 | — | 3 | 1 | no | — |
| 131 | C2×D3×Dic3 | — | 3 | 1 | no | — |
| 132 | Dic3×A4 | — | 2 | 1 | no | — |
| 133 | Dic3×A4 | — | 2 | 1 | no | — |
| 134 | Dic3×A4 | — | 2 | 1 | no | — |
| 135 | Dic3×A4 | — | 3 | 1 | no | — |
| 136 | Dic3×A4 | — | 3 | 1 | no | — |
| 137 | Dic3×A4 | — | 6 | 1 | no | — |
| 138 | Dic3×A4 | C2×D3 | 1 | 1 | yes | characteristic |
| 139 | Dic3×A4 | C2×D3 | 1 | 1 | yes | characteristic |
| 140 | Dic3×A4 | C2×D3 | 1 | 1 | yes | characteristic |
| 141 | C22×C33 | — | 4 | 1 | no | — |
| 142 | C2×C3×C3⋊D3 | — | 4 | 1 | no | — |
| 143 | C2×C32×D3 | — | 4 | 1 | no | — |
| 144 | C32×A4 | #41 | 1 | 1 | yes | characteristic, complemented |
| 145 | C3×C3⋊Dic3 | — | 4 | 1 | no | — |
| 146 | C32×Dic3 | — | 4 | 1 | no | — |
| 147 | C32×Dic3 | — | 4 | 1 | no | — |
| 148 | C32×Dic3 | — | 4 | 1 | no | — |
| 149 | C22×C3×D4 | — | 3 | 1 | no | — |
| 150 | C23×C3×C4 | — | 3 | 1 | no | — |
| 151 | C22×#67 | — | 3 | 1 | no | — |
| 152 | C22×#67 | — | 3 | 1 | no | — |
| 153 | C22×#67 | — | 3 | 1 | no | — |
| 154 | C22×#67 | — | 6 | 1 | no | — |
| 155 | C22×#67 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 156 | C23×Dic3 | — | 3 | 1 | no | — |
| 157 | C23×Dic3 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 158 | C2×#237 | — | 9 | 1 | no | — |
| 159 | C2×#237 | — | 9 | 1 | no | — |
| 160 | C2×#237 | — | 9 | 1 | no | — |
| 161 | C2×#237 | — | 9 | 1 | no | — |
| 162 | C2×#237 | — | 9 | 1 | no | — |
| 163 | C2×#237 | — | 9 | 1 | no | — |
| 164 | C2×#237 | — | 9 | 1 | no | — |
| 165 | C2×#237 | — | 9 | 1 | no | — |
| 166 | C2×#235 | — | 9 | 1 | no | — |
| 167 | C2×#235 | — | 9 | 1 | no | — |
| 168 | C2×#235 | — | 9 | 1 | no | — |
| 169 | C2×#235 | — | 9 | 1 | no | — |
| 170 | C2×#235 | — | 9 | 1 | no | — |
| 171 | C2×#235 | — | 9 | 1 | no | — |
| 172 | C2×#235 | — | 9 | 1 | no | — |
| 173 | C2×#235 | — | 9 | 1 | no | — |
| 174 | C22×D12 | — | 3 | 1 | no | — |
| 175 | C22×C4×D3 | — | 3 | 1 | no | — |
| 176 | C22×C4×D3 | — | 3 | 1 | no | — |
| 177 | C22×C4×D3 | — | 3 | 1 | no | — |
| 178 | C22×Dic6 | — | 3 | 1 | no | — |
| 179 | C22×Dic6 | — | 3 | 1 | no | — |
| 180 | Q8×A4 | — | 9 | 1 | no | — |
| 181 | D4×A4 | — | 3 | 1 | no | — |
| 182 | D4×A4 | — | 6 | 1 | no | — |
| 183 | D4×A4 | — | 9 | 1 | no | — |
| 184 | D4×A4 | — | 9 | 1 | no | — |
| 185 | C2×C4×A4 | — | 3 | 1 | no | — |
| 186 | C2×C4×A4 | — | 6 | 1 | no | — |
| 187 | C2×C4×A4 | — | 9 | 1 | no | — |
| 188 | C2×C4×A4 | — | 9 | 1 | no | — |
| 189 | C23×C32 | — | 2 | 1 | no | — |
| 190 | C23×C32 | — | 3 | 1 | no | — |
| 191 | C23×C32 | — | 3 | 1 | no | — |
| 192 | C23×C32 | — | 6 | 1 | no | — |
| 193 | C23×C32 | C23×C3 | 1 | 1 | yes | characteristic |
| 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 | — | 6 | 1 | no | — |
| 198 | C22×C3×D3 | — | 2 | 1 | no | — |
| 199 | C22×C3×D3 | — | 3 | 1 | no | — |
| 200 | C22×C3×D3 | — | 3 | 1 | no | — |
| 201 | C22×C3×D3 | — | 6 | 1 | no | — |
| 202 | C2×C3×A4 | — | 2 | 1 | no | — |
| 203 | C2×C3×A4 | — | 2 | 2 | no | — |
| 204 | C2×C3×A4 | — | 2 | 1 | no | — |
| 205 | C2×C3×A4 | — | 2 | 1 | no | — |
| 206 | C2×C3×A4 | — | 2 | 1 | no | — |
| 207 | C2×C3×A4 | — | 2 | 1 | no | — |
| 208 | C2×C3×A4 | — | 4 | 1 | no | — |
| 209 | C2×C3×A4 | — | 4 | 1 | no | — |
| 210 | C2×C3×A4 | — | 4 | 2 | no | — |
| 211 | C2×C3×A4 | — | 4 | 1 | no | — |
| 212 | C2×C3×A4 | — | 6 | 1 | no | — |
| 213 | C2×C3×A4 | C22×D3 | 1 | 1 | yes | characteristic |
| 214 | C2×C3×A4 | C22×D3 | 1 | 1 | yes | characteristic |
| 215 | D3×A4 | — | 2 | 1 | no | — |
| 216 | D3×A4 | — | 4 | 1 | no | — |
| 217 | D3×A4 | — | 6 | 1 | no | — |
| 218 | D3×A4 | — | 6 | 1 | no | — |
| 219 | D3×A4 | — | 12 | 1 | no | — |
| 220 | C32×D4 | — | 12 | 1 | no | — |
| 221 | C2×C32×C4 | — | 12 | 1 | no | — |
| 222 | #638 | — | 3 | 2 | no | — |
| 223 | #638 | — | 3 | 1 | no | — |
| 224 | #638 | — | 3 | 1 | no | — |
| 225 | #638 | — | 3 | 1 | no | — |
| 226 | #638 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 227 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 228 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 229 | C3×#67 | — | 3 | 2 | no | — |
| 230 | C3×#67 | — | 3 | 1 | no | — |
| 231 | C3×#67 | — | 3 | 1 | no | — |
| 232 | C3×#67 | — | 3 | 1 | no | — |
| 233 | C3×#67 | — | 4 | 1 | no | — |
| 234 | C3×#67 | — | 8 | 1 | no | — |
| 235 | C3×#67 | — | 12 | 1 | no | — |
| 236 | C3×#67 | — | 12 | 1 | no | — |
| 237 | C3×#67 | — | 12 | 1 | no | — |
| 238 | C3×#67 | — | 24 | 1 | no | — |
| 239 | C3×#67 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 240 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 241 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 242 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 243 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 244 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 245 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 246 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 247 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 248 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 249 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 250 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 251 | C2×C3×Dic3 | — | 8 | 1 | no | — |
| 252 | C2×C3×Dic3 | — | 12 | 1 | no | — |
| 253 | C2×C3×Dic3 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 254 | C3×D12 | — | 12 | 1 | no | — |
| 255 | C3×C4×D3 | — | 12 | 1 | no | — |
| 256 | C3×C4×D3 | — | 12 | 1 | no | — |
| 257 | C3×C4×D3 | — | 12 | 1 | no | — |
| 258 | C3×Dic6 | — | 12 | 1 | no | — |
| 259 | C3×Dic6 | — | 12 | 1 | no | — |
| 260 | #627 | — | 3 | 2 | no | — |
| 261 | #627 | — | 3 | 1 | no | — |
| 262 | #627 | — | 3 | 1 | no | — |
| 263 | #627 | — | 3 | 1 | no | — |
| 264 | #627 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 265 | #626 | — | 3 | 2 | no | — |
| 266 | #626 | — | 3 | 1 | no | — |
| 267 | #626 | — | 3 | 1 | no | — |
| 268 | #626 | — | 3 | 1 | no | — |
| 269 | #626 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 270 | #624 | — | 3 | 2 | no | — |
| 271 | #624 | — | 3 | 1 | no | — |
| 272 | #624 | — | 3 | 1 | no | — |
| 273 | #624 | — | 3 | 1 | no | — |
| 274 | #624 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 275 | D3×Dic3 | — | 3 | 2 | no | — |
| 276 | D3×Dic3 | — | 3 | 1 | no | — |
| 277 | D3×Dic3 | — | 3 | 1 | no | — |
| 278 | D3×Dic3 | — | 3 | 1 | no | — |
| 279 | D3×Dic3 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 280 | C22×#41 | — | 9 | 1 | no | Sylow |
| 281 | C2×C33 | — | 4 | 1 | no | — |
| 282 | C2×C33 | — | 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 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 288 | C24×C3 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 289 | C23×D3 | — | 3 | 1 | no | — |
| 290 | C23×D3 | — | 3 | 1 | no | — |
| 291 | C23×D3 | — | 6 | 1 | no | — |
| 292 | C23×D3 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 293 | C22×A4 | — | 2 | 1 | no | — |
| 294 | C22×A4 | — | 2 | 1 | no | — |
| 295 | C22×A4 | — | 3 | 1 | no | — |
| 296 | C22×A4 | — | 4 | 1 | no | — |
| 297 | C22×A4 | — | 6 | 1 | no | — |
| 298 | C22×A4 | — | 9 | 1 | no | — |
| 299 | C22×A4 | D32 | 1 | 1 | yes | characteristic |
| 300 | C3×#41 | — | 36 | 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 | C22×C3×C4 | — | 3 | 1 | no | — |
| 306 | C22×C3×C4 | — | 3 | 1 | no | — |
| 307 | C22×C3×C4 | — | 3 | 1 | no | — |
| 308 | C22×C3×C4 | — | 9 | 1 | no | — |
| 309 | C22×C3×C4 | — | 9 | 1 | no | — |
| 310 | C22×C3×C4 | — | 9 | 1 | no | — |
| 311 | C22×C3×C4 | — | 9 | 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 | — | 9 | 1 | no | — |
| 317 | C2×#67 | — | 9 | 1 | no | — |
| 318 | C2×#67 | — | 9 | 1 | no | — |
| 319 | C2×#67 | — | 9 | 1 | no | — |
| 320 | C2×#67 | — | 9 | 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 | — | 18 | 1 | no | — |
| 329 | C2×#67 | — | 18 | 1 | no | — |
| 330 | C2×#67 | — | 18 | 1 | no | — |
| 331 | C2×#67 | — | 18 | 1 | no | — |
| 332 | C22×Dic3 | — | 3 | 1 | no | — |
| 333 | C22×Dic3 | — | 3 | 1 | no | — |
| 334 | C22×Dic3 | — | 3 | 1 | no | — |
| 335 | C22×Dic3 | — | 3 | 1 | no | — |
| 336 | C22×Dic3 | — | 3 | 1 | no | — |
| 337 | C22×Dic3 | — | 3 | 1 | no | — |
| 338 | C22×Dic3 | — | 6 | 1 | no | — |
| 339 | C22×Dic3 | — | 9 | 1 | no | — |
| 340 | C22×Dic3 | — | 9 | 1 | no | — |
| 341 | C22×Dic3 | — | 9 | 1 | no | — |
| 342 | C22×Dic3 | — | 9 | 1 | no | — |
| 343 | C22×Dic3 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 344 | C22×Dic3 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 345 | C22×Dic3 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 346 | #237 | — | 3 | 1 | no | — |
| 347 | #237 | — | 9 | 1 | no | — |
| 348 | #237 | — | 9 | 1 | no | — |
| 349 | #237 | — | 9 | 1 | no | — |
| 350 | #237 | — | 9 | 1 | no | — |
| 351 | #237 | — | 9 | 1 | no | — |
| 352 | #237 | — | 9 | 1 | no | — |
| 353 | #237 | — | 9 | 2 | no | — |
| 354 | #237 | — | 9 | 2 | no | — |
| 355 | #237 | — | 9 | 2 | no | — |
| 356 | #237 | — | 9 | 2 | no | — |
| 357 | #237 | — | 9 | 2 | no | — |
| 358 | #237 | — | 9 | 2 | no | — |
| 359 | #237 | — | 9 | 2 | no | — |
| 360 | #237 | — | 9 | 1 | no | — |
| 361 | #235 | — | 3 | 1 | no | — |
| 362 | #235 | — | 9 | 1 | no | — |
| 363 | #235 | — | 9 | 1 | no | — |
| 364 | #235 | — | 9 | 1 | no | — |
| 365 | #235 | — | 9 | 1 | no | — |
| 366 | #235 | — | 9 | 1 | no | — |
| 367 | #235 | — | 9 | 1 | no | — |
| 368 | #235 | — | 9 | 2 | no | — |
| 369 | #235 | — | 9 | 2 | no | — |
| 370 | #235 | — | 9 | 2 | no | — |
| 371 | #235 | — | 9 | 2 | no | — |
| 372 | #235 | — | 9 | 2 | no | — |
| 373 | #235 | — | 9 | 2 | no | — |
| 374 | #235 | — | 9 | 2 | no | — |
| 375 | #235 | — | 9 | 1 | no | — |
| 376 | C2×D12 | — | 9 | 1 | no | — |
| 377 | C2×D12 | — | 9 | 1 | no | — |
| 378 | C2×D12 | — | 9 | 1 | no | — |
| 379 | C2×D12 | — | 9 | 1 | no | — |
| 380 | C2×C4×D3 | — | 9 | 1 | no | — |
| 381 | C2×C4×D3 | — | 9 | 1 | no | — |
| 382 | C2×C4×D3 | — | 9 | 1 | no | — |
| 383 | C2×C4×D3 | — | 9 | 1 | no | — |
| 384 | C2×C4×D3 | — | 9 | 1 | no | — |
| 385 | C2×C4×D3 | — | 9 | 1 | no | — |
| 386 | C2×C4×D3 | — | 9 | 1 | no | — |
| 387 | C2×C4×D3 | — | 9 | 1 | no | — |
| 388 | C2×C4×D3 | — | 9 | 1 | no | — |
| 389 | C2×C4×D3 | — | 9 | 1 | no | — |
| 390 | C2×C4×D3 | — | 9 | 1 | no | — |
| 391 | C2×C4×D3 | — | 9 | 1 | no | — |
| 392 | C2×Dic6 | — | 9 | 1 | no | — |
| 393 | C2×Dic6 | — | 9 | 1 | no | — |
| 394 | C2×Dic6 | — | 9 | 1 | no | — |
| 395 | C2×Dic6 | — | 9 | 1 | no | — |
| 396 | C2×Dic6 | — | 9 | 1 | no | — |
| 397 | C2×Dic6 | — | 9 | 1 | no | — |
| 398 | C2×Dic6 | — | 9 | 1 | no | — |
| 399 | C2×Dic6 | — | 9 | 1 | no | — |
| 400 | C4×A4 | — | 3 | 1 | no | — |
| 401 | C4×A4 | — | 3 | 1 | no | — |
| 402 | C4×A4 | — | 3 | 1 | no | — |
| 403 | C4×A4 | — | 6 | 1 | no | — |
| 404 | C4×A4 | — | 6 | 1 | no | — |
| 405 | C4×A4 | — | 6 | 1 | no | — |
| 406 | C4×A4 | — | 9 | 1 | no | — |
| 407 | C22×C32 | — | 3 | 1 | no | — |
| 408 | C22×C32 | — | 3 | 1 | no | — |
| 409 | C22×C32 | — | 3 | 1 | no | — |
| 410 | C22×C32 | — | 4 | 1 | no | — |
| 411 | C22×C32 | — | 4 | 1 | no | — |
| 412 | C22×C32 | — | 6 | 1 | no | — |
| 413 | C22×C32 | — | 6 | 1 | no | — |
| 414 | C22×C32 | — | 6 | 1 | no | — |
| 415 | C22×C32 | — | 6 | 1 | no | — |
| 416 | C22×C32 | — | 8 | 1 | no | — |
| 417 | C22×C32 | — | 8 | 1 | no | — |
| 418 | C22×C32 | — | 8 | 1 | no | — |
| 419 | C22×C32 | — | 12 | 1 | no | — |
| 420 | C22×C32 | — | 16 | 1 | no | — |
| 421 | C22×C32 | C3×#41 | 1 | 1 | yes | characteristic, complemented |
| 422 | C22×C32 | C22×A4 | 1 | 1 | yes | characteristic |
| 423 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 424 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 425 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 426 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 427 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 428 | C2×C3⋊D3 | C22×A4 | 1 | 1 | yes | characteristic |
| 429 | C2×C3×D3 | — | 3 | 1 | no | — |
| 430 | C2×C3×D3 | — | 4 | 1 | no | — |
| 431 | C2×C3×D3 | — | 6 | 1 | 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 | — | 8 | 1 | no | — |
| 436 | C2×C3×D3 | — | 12 | 1 | no | — |
| 437 | C2×C3×D3 | — | 12 | 1 | no | — |
| 438 | C2×C3×D3 | — | 24 | 1 | no | — |
| 439 | C2×C3×D3 | C22×A4 | 1 | 1 | yes | characteristic |
| 440 | C3×A4 | — | 2 | 1 | no | — |
| 441 | C3×A4 | — | 2 | 1 | no | — |
| 442 | C3×A4 | — | 2 | 1 | no | — |
| 443 | C3×A4 | — | 4 | 1 | no | — |
| 444 | C3×A4 | #235 | 1 | 1 | yes | characteristic, complemented |
| 445 | C3×A4 | #237 | 1 | 1 | yes | characteristic, complemented |
| 446 | C32×C4 | — | 12 | 1 | no | — |
| 447 | C32×C4 | — | 12 | 1 | no | — |
| 448 | C32×C4 | — | 12 | 1 | no | — |
| 449 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 450 | C3⋊Dic3 | C22×A4 | 1 | 1 | yes | characteristic |
| 451 | C3×Dic3 | — | 3 | 1 | no | — |
| 452 | C3×Dic3 | — | 3 | 1 | no | — |
| 453 | C3×Dic3 | — | 3 | 1 | no | — |
| 454 | C3×Dic3 | — | 4 | 1 | no | — |
| 455 | C3×Dic3 | — | 4 | 1 | no | — |
| 456 | C3×Dic3 | — | 4 | 1 | no | — |
| 457 | C3×Dic3 | — | 8 | 1 | no | — |
| 458 | C3×Dic3 | — | 8 | 1 | no | — |
| 459 | C3×Dic3 | — | 8 | 1 | no | — |
| 460 | C3×Dic3 | — | 12 | 1 | no | — |
| 461 | C3×Dic3 | — | 12 | 1 | no | — |
| 462 | C3×Dic3 | — | 24 | 1 | no | — |
| 463 | C3×Dic3 | C22×A4 | 1 | 1 | yes | characteristic |
| 464 | C3×Dic3 | C22×A4 | 1 | 1 | yes | characteristic |
| 465 | C3×Dic3 | C22×A4 | 1 | 1 | yes | characteristic |
| 466 | C2×#41 | — | 27 | 1 | no | — |
| 467 | C2×#41 | — | 27 | 1 | no | — |
| 468 | C2×#41 | — | 27 | 1 | no | — |
| 469 | C2×#41 | — | 27 | 1 | no | — |
| 470 | C2×#41 | — | 27 | 1 | no | — |
| 471 | C2×#41 | — | 27 | 1 | no | — |
| 472 | C2×#41 | — | 27 | 1 | no | — |
| 473 | C2×#41 | — | 27 | 1 | no | — |
| 474 | C22×Q8 | — | 9 | 1 | no | — |
| 475 | C22×D4 | — | 3 | 1 | no | — |
| 476 | C22×D4 | — | 9 | 1 | no | — |
| 477 | C22×D4 | — | 9 | 1 | no | — |
| 478 | C23×C4 | — | 3 | 1 | no | — |
| 479 | C23×C4 | — | 9 | 1 | no | — |
| 480 | C23×C4 | — | 9 | 1 | no | — |
| 481 | C33 | — | 4 | 1 | no | Sylow |
| 482 | C23×C3 | — | 2 | 1 | no | — |
| 483 | C23×C3 | — | 2 | 1 | no | — |
| 484 | C23×C3 | — | 2 | 1 | no | — |
| 485 | C23×C3 | — | 3 | 1 | no | — |
| 486 | C23×C3 | — | 3 | 1 | no | — |
| 487 | C23×C3 | — | 3 | 1 | no | — |
| 488 | C23×C3 | — | 3 | 1 | no | — |
| 489 | C23×C3 | — | 4 | 1 | no | — |
| 490 | C23×C3 | — | 6 | 1 | no | — |
| 491 | C23×C3 | — | 6 | 1 | no | — |
| 492 | C23×C3 | — | 6 | 1 | no | — |
| 493 | C23×C3 | — | 6 | 1 | no | — |
| 494 | C23×C3 | — | 6 | 1 | no | — |
| 495 | C23×C3 | — | 9 | 1 | no | — |
| 496 | C23×C3 | — | 9 | 1 | no | — |
| 497 | C23×C3 | — | 12 | 1 | no | — |
| 498 | C23×C3 | — | 18 | 1 | no | — |
| 499 | C23×C3 | C22×C3×D3 | 1 | 1 | yes | characteristic |
| 500 | C23×C3 | C22×C3×D3 | 1 | 1 | yes | characteristic |
| 501 | C22×D3 | — | 2 | 1 | no | — |
| 502 | C22×D3 | — | 3 | 1 | no | — |
| 503 | C22×D3 | — | 3 | 1 | no | — |
| 504 | C22×D3 | — | 6 | 1 | no | — |
| 505 | C22×D3 | — | 6 | 1 | no | — |
| 506 | C22×D3 | — | 6 | 1 | no | — |
| 507 | C22×D3 | — | 9 | 1 | no | — |
| 508 | C22×D3 | — | 9 | 1 | no | — |
| 509 | C22×D3 | — | 9 | 1 | no | — |
| 510 | C22×D3 | — | 9 | 1 | no | — |
| 511 | C22×D3 | — | 12 | 1 | no | — |
| 512 | C22×D3 | — | 18 | 1 | no | — |
| 513 | C22×D3 | — | 18 | 1 | no | — |
| 514 | C22×D3 | — | 18 | 1 | no | — |
| 515 | C22×D3 | — | 18 | 1 | no | — |
| 516 | C22×D3 | — | 36 | 1 | no | — |
| 517 | C2×A4 | — | 2 | 2 | no | — |
| 518 | C2×A4 | — | 2 | 1 | no | — |
| 519 | C2×A4 | — | 2 | 1 | no | — |
| 520 | C2×A4 | — | 2 | 1 | no | — |
| 521 | C2×A4 | — | 4 | 1 | no | — |
| 522 | C2×A4 | — | 4 | 2 | no | — |
| 523 | C2×A4 | — | 4 | 1 | no | — |
| 524 | C2×A4 | — | 6 | 1 | no | — |
| 525 | C2×A4 | — | 12 | 1 | no | — |
| 526 | C2×A4 | — | 18 | 1 | no | — |
| 527 | C2×A4 | C2×D32 | 1 | 1 | yes | characteristic |
| 528 | C3×Q8 | — | 36 | 1 | no | — |
| 529 | C3×D4 | — | 3 | 1 | no | — |
| 530 | C3×D4 | — | 9 | 1 | no | — |
| 531 | C3×D4 | — | 9 | 1 | no | — |
| 532 | C3×D4 | — | 9 | 2 | no | — |
| 533 | C3×D4 | — | 9 | 1 | no | — |
| 534 | C3×D4 | — | 12 | 1 | no | — |
| 535 | C3×D4 | — | 24 | 1 | no | — |
| 536 | C3×D4 | — | 36 | 1 | no | — |
| 537 | C3×D4 | — | 36 | 1 | no | — |
| 538 | C2×C3×C4 | — | 3 | 1 | no | — |
| 539 | C2×C3×C4 | — | 9 | 1 | no | — |
| 540 | C2×C3×C4 | — | 9 | 1 | no | — |
| 541 | C2×C3×C4 | — | 9 | 1 | no | — |
| 542 | C2×C3×C4 | — | 9 | 1 | no | — |
| 543 | C2×C3×C4 | — | 9 | 1 | no | — |
| 544 | C2×C3×C4 | — | 9 | 2 | no | — |
| 545 | C2×C3×C4 | — | 9 | 1 | no | — |
| 546 | C2×C3×C4 | — | 9 | 1 | no | — |
| 547 | C2×C3×C4 | — | 9 | 1 | no | — |
| 548 | C2×C3×C4 | — | 9 | 1 | no | — |
| 549 | C2×C3×C4 | — | 12 | 1 | no | — |
| 550 | C2×C3×C4 | — | 24 | 1 | no | — |
| 551 | C2×C3×C4 | — | 36 | 1 | no | — |
| 552 | C2×C3×C4 | — | 36 | 1 | no | — |
| 553 | #67 | — | 3 | 2 | no | — |
| 554 | #67 | — | 3 | 1 | no | — |
| 555 | #67 | — | 3 | 1 | no | — |
| 556 | #67 | — | 3 | 1 | no | — |
| 557 | #67 | — | 3 | 1 | no | — |
| 558 | #67 | — | 3 | 1 | no | — |
| 559 | #67 | — | 3 | 1 | no | — |
| 560 | #67 | — | 6 | 1 | no | — |
| 561 | #67 | — | 9 | 1 | no | — |
| 562 | #67 | — | 9 | 1 | no | — |
| 563 | #67 | — | 9 | 1 | no | — |
| 564 | #67 | — | 9 | 1 | no | — |
| 565 | #67 | — | 9 | 2 | no | — |
| 566 | #67 | — | 9 | 1 | no | — |
| 567 | #67 | — | 9 | 1 | no | — |
| 568 | #67 | — | 9 | 2 | no | — |
| 569 | #67 | — | 9 | 2 | no | — |
| 570 | #67 | — | 9 | 1 | no | — |
| 571 | #67 | — | 9 | 1 | no | — |
| 572 | #67 | — | 9 | 1 | no | — |
| 573 | #67 | — | 18 | 1 | no | — |
| 574 | #67 | — | 18 | 1 | no | — |
| 575 | #67 | — | 18 | 1 | no | — |
| 576 | #67 | — | 18 | 2 | no | — |
| 577 | #67 | D3×A4 | 1 | 1 | yes | characteristic, complemented |
| 578 | C2×Dic3 | — | 3 | 2 | no | — |
| 579 | C2×Dic3 | — | 3 | 1 | no | — |
| 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 | — | 3 | 1 | no | — |
| 585 | C2×Dic3 | — | 3 | 1 | no | — |
| 586 | C2×Dic3 | — | 3 | 1 | no | — |
| 587 | C2×Dic3 | — | 3 | 1 | no | — |
| 588 | C2×Dic3 | — | 3 | 1 | no | — |
| 589 | C2×Dic3 | — | 9 | 1 | no | — |
| 590 | C2×Dic3 | — | 9 | 1 | no | — |
| 591 | C2×Dic3 | — | 9 | 1 | no | — |
| 592 | C2×Dic3 | — | 9 | 1 | no | — |
| 593 | C2×Dic3 | — | 9 | 2 | no | — |
| 594 | C2×Dic3 | — | 9 | 1 | no | — |
| 595 | C2×Dic3 | — | 9 | 1 | no | — |
| 596 | C2×Dic3 | — | 9 | 1 | no | — |
| 597 | C2×Dic3 | — | 18 | 1 | no | — |
| 598 | C2×Dic3 | — | 18 | 1 | no | — |
| 599 | C2×Dic3 | D3×A4 | 1 | 1 | yes | characteristic, complemented |
| 600 | D12 | — | 3 | 1 | no | — |
| 601 | D12 | — | 9 | 1 | no | — |
| 602 | D12 | — | 9 | 1 | no | — |
| 603 | D12 | — | 9 | 2 | no | — |
| 604 | D12 | — | 9 | 1 | no | — |
| 605 | C4×D3 | — | 3 | 1 | no | — |
| 606 | C4×D3 | — | 3 | 1 | no | — |
| 607 | C4×D3 | — | 3 | 1 | no | — |
| 608 | C4×D3 | — | 9 | 1 | no | — |
| 609 | C4×D3 | — | 9 | 1 | no | — |
| 610 | C4×D3 | — | 9 | 1 | no | — |
| 611 | C4×D3 | — | 9 | 1 | no | — |
| 612 | C4×D3 | — | 9 | 1 | no | — |
| 613 | C4×D3 | — | 9 | 2 | no | — |
| 614 | C4×D3 | — | 9 | 2 | no | — |
| 615 | C4×D3 | — | 9 | 1 | no | — |
| 616 | C4×D3 | — | 9 | 2 | no | — |
| 617 | C4×D3 | — | 9 | 1 | no | — |
| 618 | C4×D3 | — | 9 | 1 | no | — |
| 619 | C4×D3 | — | 9 | 1 | no | — |
| 620 | Dic6 | — | 3 | 1 | no | — |
| 621 | Dic6 | — | 3 | 1 | no | — |
| 622 | Dic6 | — | 9 | 1 | no | — |
| 623 | Dic6 | — | 9 | 1 | no | — |
| 624 | Dic6 | — | 9 | 1 | no | — |
| 625 | Dic6 | — | 9 | 1 | no | — |
| 626 | Dic6 | — | 9 | 2 | no | — |
| 627 | Dic6 | — | 9 | 2 | no | — |
| 628 | Dic6 | — | 9 | 1 | no | — |
| 629 | Dic6 | — | 9 | 1 | no | — |
| 630 | C2×C32 | — | 2 | 1 | no | — |
| 631 | C2×C32 | — | 3 | 1 | no | — |
| 632 | C2×C32 | — | 3 | 1 | no | — |
| 633 | C2×C32 | — | 4 | 1 | no | — |
| 634 | C2×C32 | — | 4 | 1 | no | — |
| 635 | C2×C32 | — | 6 | 1 | no | — |
| 636 | C2×C32 | — | 8 | 1 | no | — |
| 637 | C2×C32 | — | 8 | 1 | no | — |
| 638 | C2×C32 | — | 8 | 1 | no | — |
| 639 | C2×C32 | — | 8 | 2 | no | — |
| 640 | C2×C32 | — | 8 | 1 | no | — |
| 641 | C2×C32 | — | 8 | 1 | no | — |
| 642 | C2×C32 | — | 16 | 1 | no | — |
| 643 | C2×C32 | — | 16 | 1 | no | — |
| 644 | C2×C32 | — | 16 | 1 | no | — |
| 645 | C2×C32 | — | 16 | 2 | no | — |
| 646 | C2×C32 | — | 24 | 1 | no | — |
| 647 | C2×C32 | C23×A4 | 1 | 1 | yes | characteristic |
| 648 | C3⋊D3 | — | 2 | 1 | no | — |
| 649 | C3⋊D3 | — | 6 | 1 | no | — |
| 650 | C3×D3 | — | 2 | 1 | no | — |
| 651 | C3×D3 | — | 6 | 1 | no | — |
| 652 | C3×D3 | — | 8 | 1 | no | — |
| 653 | C3×D3 | — | 16 | 1 | no | — |
| 654 | C3×D3 | — | 24 | 1 | no | — |
| 655 | C3×D3 | — | 24 | 1 | no | — |
| 656 | C3×D3 | — | 48 | 1 | no | — |
| 657 | C24 | — | 3 | 1 | no | — |
| 658 | C24 | — | 9 | 1 | no | — |
| 659 | C24 | C3×D32 | 1 | 1 | yes | characteristic |
| 660 | #41 | — | 9 | 1 | no | — |
| 661 | #41 | — | 27 | 1 | no | — |
| 662 | #41 | — | 27 | 1 | no | — |
| 663 | #41 | — | 27 | 1 | no | — |
| 664 | #41 | — | 27 | 1 | no | — |
| 665 | #41 | — | 27 | 1 | no | — |
| 666 | #41 | — | 27 | 1 | no | — |
| 667 | #41 | — | 27 | 1 | no | — |
| 668 | #41 | — | 27 | 2 | no | — |
| 669 | #41 | — | 27 | 2 | no | — |
| 670 | #41 | — | 27 | 2 | no | — |
| 671 | #41 | — | 27 | 2 | no | — |
| 672 | #41 | — | 27 | 2 | no | — |
| 673 | #41 | — | 27 | 2 | no | — |
| 674 | #41 | — | 27 | 2 | no | — |
| 675 | C2×Q8 | — | 27 | 1 | no | — |
| 676 | C2×Q8 | — | 27 | 1 | no | — |
| 677 | C2×Q8 | — | 27 | 1 | no | — |
| 678 | C2×Q8 | — | 27 | 1 | no | — |
| 679 | C2×D4 | — | 9 | 1 | no | — |
| 680 | C2×D4 | — | 9 | 1 | no | — |
| 681 | C2×D4 | — | 9 | 1 | no | — |
| 682 | C2×D4 | — | 9 | 1 | no | — |
| 683 | C2×D4 | — | 27 | 1 | no | — |
| 684 | C2×D4 | — | 27 | 1 | no | — |
| 685 | C2×D4 | — | 27 | 1 | no | — |
| 686 | C2×D4 | — | 27 | 1 | no | — |
| 687 | C2×D4 | — | 27 | 1 | no | — |
| 688 | C2×D4 | — | 27 | 1 | no | — |
| 689 | C2×D4 | — | 27 | 1 | no | — |
| 690 | C2×D4 | — | 27 | 1 | no | — |
| 691 | C22×C4 | — | 3 | 1 | no | — |
| 692 | C22×C4 | — | 3 | 1 | no | — |
| 693 | C22×C4 | — | 3 | 1 | no | — |
| 694 | C22×C4 | — | 9 | 1 | no | — |
| 695 | C22×C4 | — | 9 | 1 | no | — |
| 696 | C22×C4 | — | 9 | 1 | no | — |
| 697 | C22×C4 | — | 9 | 1 | no | — |
| 698 | C22×C4 | — | 9 | 1 | no | — |
| 699 | C22×C4 | — | 27 | 1 | no | — |
| 700 | C22×C4 | — | 27 | 1 | no | — |
| 701 | C22×C4 | — | 27 | 1 | no | — |
| 702 | C22×C4 | — | 27 | 1 | no | — |
| 703 | C22×C4 | — | 27 | 1 | no | — |
| 704 | C22×C4 | — | 27 | 1 | no | — |
| 705 | C22×C4 | — | 27 | 1 | no | — |
| 706 | C22×C4 | — | 27 | 1 | no | — |
| 707 | C22×C3 | — | 2 | 1 | no | — |
| 708 | C22×C3 | — | 2 | 1 | no | — |
| 709 | C22×C3 | — | 3 | 1 | no | — |
| 710 | C22×C3 | — | 3 | 1 | no | — |
| 711 | C22×C3 | — | 3 | 1 | no | — |
| 712 | C22×C3 | — | 3 | 1 | no | — |
| 713 | C22×C3 | — | 3 | 1 | no | — |
| 714 | C22×C3 | — | 3 | 1 | no | — |
| 715 | C22×C3 | — | 3 | 1 | no | — |
| 716 | C22×C3 | — | 4 | 1 | no | — |
| 717 | C22×C3 | — | 6 | 1 | no | — |
| 718 | C22×C3 | — | 6 | 1 | no | — |
| 719 | C22×C3 | — | 6 | 1 | no | — |
| 720 | C22×C3 | — | 6 | 1 | no | — |
| 721 | C22×C3 | — | 6 | 1 | no | — |
| 722 | C22×C3 | — | 6 | 1 | no | — |
| 723 | C22×C3 | — | 6 | 1 | no | — |
| 724 | C22×C3 | — | 6 | 1 | no | — |
| 725 | C22×C3 | — | 6 | 1 | no | — |
| 726 | C22×C3 | — | 6 | 1 | no | — |
| 727 | C22×C3 | — | 6 | 1 | no | — |
| 728 | C22×C3 | — | 8 | 1 | no | — |
| 729 | C22×C3 | — | 8 | 1 | no | — |
| 730 | C22×C3 | — | 9 | 1 | no | — |
| 731 | C22×C3 | — | 12 | 1 | no | — |
| 732 | C22×C3 | — | 12 | 1 | no | — |
| 733 | C22×C3 | — | 12 | 1 | no | — |
| 734 | C22×C3 | — | 12 | 1 | no | — |
| 735 | C22×C3 | — | 12 | 1 | no | — |
| 736 | C22×C3 | — | 16 | 1 | no | — |
| 737 | C22×C3 | — | 18 | 1 | no | — |
| 738 | C22×C3 | — | 18 | 1 | no | — |
| 739 | C22×C3 | — | 18 | 1 | no | — |
| 740 | C22×C3 | — | 18 | 1 | no | — |
| 741 | C22×C3 | — | 24 | 1 | no | — |
| 742 | C22×C3 | — | 36 | 1 | no | — |
| 743 | C22×C3 | C3×#235 | 1 | 1 | yes | characteristic, complemented |
| 744 | C22×C3 | C3×#237 | 1 | 1 | yes | characteristic, complemented |
| 745 | C22×C3 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 746 | C22×C3 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 747 | C2×D3 | — | 3 | 1 | no | — |
| 748 | C2×D3 | — | 3 | 1 | no | — |
| 749 | C2×D3 | — | 3 | 1 | no | — |
| 750 | C2×D3 | — | 6 | 1 | no | — |
| 751 | C2×D3 | — | 6 | 1 | no | — |
| 752 | C2×D3 | — | 6 | 1 | no | — |
| 753 | C2×D3 | — | 6 | 1 | no | — |
| 754 | C2×D3 | — | 6 | 1 | no | — |
| 755 | C2×D3 | — | 9 | 1 | no | — |
| 756 | C2×D3 | — | 9 | 1 | no | — |
| 757 | C2×D3 | — | 18 | 1 | no | — |
| 758 | C2×D3 | — | 18 | 1 | no | — |
| 759 | C2×D3 | — | 18 | 1 | no | — |
| 760 | C2×D3 | — | 18 | 1 | no | — |
| 761 | C2×D3 | — | 18 | 1 | no | — |
| 762 | C2×D3 | — | 18 | 1 | no | — |
| 763 | C2×D3 | — | 18 | 1 | no | — |
| 764 | C2×D3 | — | 18 | 1 | no | — |
| 765 | C2×D3 | — | 18 | 1 | no | — |
| 766 | C2×D3 | — | 36 | 1 | no | — |
| 767 | C2×D3 | — | 36 | 1 | no | — |
| 768 | C2×D3 | — | 36 | 1 | no | — |
| 769 | C2×D3 | — | 36 | 1 | no | — |
| 770 | C2×D3 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 771 | A4 | — | 2 | 1 | no | — |
| 772 | A4 | — | 2 | 1 | no | — |
| 773 | A4 | — | 4 | 1 | no | — |
| 774 | A4 | #3804 | 1 | 1 | yes | characteristic, direct product factor |
| 775 | C3×C4 | — | 3 | 1 | no | — |
| 776 | C3×C4 | — | 3 | 1 | no | — |
| 777 | C3×C4 | — | 3 | 1 | no | — |
| 778 | C3×C4 | — | 9 | 1 | no | — |
| 779 | C3×C4 | — | 9 | 1 | no | — |
| 780 | C3×C4 | — | 9 | 1 | no | — |
| 781 | C3×C4 | — | 12 | 1 | no | — |
| 782 | C3×C4 | — | 12 | 1 | no | — |
| 783 | C3×C4 | — | 12 | 1 | no | — |
| 784 | C3×C4 | — | 24 | 1 | no | — |
| 785 | C3×C4 | — | 24 | 1 | no | — |
| 786 | C3×C4 | — | 24 | 1 | no | — |
| 787 | C3×C4 | — | 36 | 1 | no | — |
| 788 | Dic3 | — | 3 | 1 | no | — |
| 789 | Dic3 | — | 3 | 1 | no | — |
| 790 | Dic3 | — | 3 | 1 | no | — |
| 791 | Dic3 | — | 3 | 1 | no | — |
| 792 | Dic3 | — | 3 | 1 | no | — |
| 793 | Dic3 | — | 6 | 1 | no | — |
| 794 | Dic3 | — | 9 | 1 | no | — |
| 795 | Dic3 | — | 9 | 1 | no | — |
| 796 | Dic3 | — | 18 | 1 | no | — |
| 797 | Dic3 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 798 | Dic3 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 799 | Dic3 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 800 | C32 | — | 4 | 1 | no | — |
| 801 | C32 | — | 4 | 1 | no | — |
| 802 | C32 | — | 8 | 1 | no | — |
| 803 | C32 | — | 8 | 1 | no | — |
| 804 | C32 | — | 8 | 1 | no | — |
| 805 | C32 | — | 16 | 1 | no | — |
| 806 | C32 | A4×#41 | 1 | 1 | yes | characteristic, complemented |
| 807 | C23 | — | 2 | 1 | no | — |
| 808 | C23 | — | 3 | 1 | no | — |
| 809 | C23 | — | 3 | 1 | no | — |
| 810 | C23 | — | 6 | 1 | no | — |
| 811 | C23 | — | 6 | 1 | no | — |
| 812 | C23 | — | 9 | 1 | no | — |
| 813 | C23 | — | 9 | 1 | no | — |
| 814 | C23 | — | 18 | 1 | no | — |
| 815 | C23 | — | 18 | 1 | no | — |
| 816 | C23 | — | 27 | 1 | no | — |
| 817 | C23 | — | 27 | 1 | no | — |
| 818 | C23 | — | 54 | 1 | no | — |
| 819 | C23 | C2×C3×D32 | 1 | 1 | yes | characteristic |
| 820 | Q8 | — | 9 | 1 | no | — |
| 821 | Q8 | — | 27 | 1 | no | — |
| 822 | Q8 | — | 27 | 1 | no | — |
| 823 | Q8 | — | 27 | 1 | no | — |
| 824 | Q8 | — | 27 | 2 | no | — |
| 825 | D4 | — | 3 | 1 | no | — |
| 826 | D4 | — | 9 | 1 | no | — |
| 827 | D4 | — | 9 | 1 | no | — |
| 828 | D4 | — | 9 | 1 | no | — |
| 829 | D4 | — | 9 | 2 | no | — |
| 830 | D4 | — | 9 | 1 | no | — |
| 831 | D4 | — | 9 | 1 | no | — |
| 832 | D4 | — | 27 | 1 | no | — |
| 833 | D4 | — | 27 | 1 | no | — |
| 834 | D4 | — | 27 | 1 | no | — |
| 835 | D4 | — | 27 | 1 | no | — |
| 836 | D4 | — | 27 | 2 | no | — |
| 837 | D4 | — | 27 | 1 | no | — |
| 838 | D4 | — | 27 | 2 | no | — |
| 839 | D4 | — | 27 | 1 | no | — |
| 840 | C2×C4 | — | 3 | 1 | no | — |
| 841 | C2×C4 | — | 9 | 1 | no | — |
| 842 | C2×C4 | — | 9 | 1 | no | — |
| 843 | C2×C4 | — | 9 | 1 | no | — |
| 844 | C2×C4 | — | 9 | 1 | no | — |
| 845 | C2×C4 | — | 9 | 1 | no | — |
| 846 | C2×C4 | — | 9 | 1 | no | — |
| 847 | C2×C4 | — | 9 | 1 | no | — |
| 848 | C2×C4 | — | 9 | 2 | no | — |
| 849 | C2×C4 | — | 9 | 1 | no | — |
| 850 | C2×C4 | — | 9 | 1 | no | — |
| 851 | C2×C4 | — | 9 | 1 | no | — |
| 852 | C2×C4 | — | 9 | 1 | no | — |
| 853 | C2×C4 | — | 27 | 1 | no | — |
| 854 | C2×C4 | — | 27 | 1 | no | — |
| 855 | C2×C4 | — | 27 | 1 | no | — |
| 856 | C2×C4 | — | 27 | 1 | no | — |
| 857 | C2×C4 | — | 27 | 1 | no | — |
| 858 | C2×C4 | — | 27 | 2 | no | — |
| 859 | C2×C4 | — | 27 | 1 | no | — |
| 860 | C2×C4 | — | 27 | 1 | no | — |
| 861 | C2×C4 | — | 27 | 2 | no | — |
| 862 | C2×C4 | — | 27 | 1 | no | — |
| 863 | C2×C3 | — | 2 | 1 | no | — |
| 864 | C2×C3 | — | 2 | 1 | no | — |
| 865 | C2×C3 | — | 2 | 1 | no | — |
| 866 | C2×C3 | — | 3 | 1 | no | — |
| 867 | C2×C3 | — | 3 | 1 | no | — |
| 868 | C2×C3 | — | 3 | 1 | no | — |
| 869 | C2×C3 | — | 3 | 1 | no | — |
| 870 | C2×C3 | — | 4 | 1 | no | — |
| 871 | C2×C3 | — | 4 | 1 | no | — |
| 872 | C2×C3 | — | 6 | 1 | no | — |
| 873 | C2×C3 | — | 6 | 1 | no | — |
| 874 | C2×C3 | — | 6 | 1 | no | — |
| 875 | C2×C3 | — | 6 | 1 | no | — |
| 876 | C2×C3 | — | 6 | 1 | no | — |
| 877 | C2×C3 | — | 8 | 1 | no | — |
| 878 | C2×C3 | — | 8 | 2 | no | — |
| 879 | C2×C3 | — | 8 | 1 | no | — |
| 880 | C2×C3 | — | 8 | 1 | no | — |
| 881 | C2×C3 | — | 12 | 1 | no | — |
| 882 | C2×C3 | — | 16 | 1 | no | — |
| 883 | C2×C3 | — | 16 | 2 | no | — |
| 884 | C2×C3 | — | 16 | 1 | no | — |
| 885 | C2×C3 | — | 18 | 1 | no | — |
| 886 | C2×C3 | — | 24 | 1 | no | — |
| 887 | C2×C3 | — | 48 | 1 | no | — |
| 888 | C2×C3 | — | 72 | 1 | no | — |
| 889 | C2×C3 | C22×D3×A4 | 1 | 1 | yes | characteristic |
| 890 | C2×C3 | C22×D3×A4 | 1 | 1 | yes | characteristic |
| 891 | D3 | — | 2 | 1 | no | — |
| 892 | D3 | — | 6 | 1 | no | — |
| 893 | D3 | — | 6 | 1 | no | — |
| 894 | D3 | — | 6 | 1 | no | — |
| 895 | D3 | — | 12 | 1 | no | — |
| 896 | D3 | — | 18 | 1 | no | — |
| 897 | D3 | — | 18 | 1 | no | — |
| 898 | D3 | — | 36 | 1 | no | — |
| 899 | C22 | — | 3 | 1 | no | — |
| 900 | C22 | — | 3 | 1 | no | — |
| 901 | C22 | — | 3 | 1 | no | — |
| 902 | C22 | — | 3 | 1 | no | — |
| 903 | C22 | — | 6 | 1 | no | — |
| 904 | C22 | — | 6 | 1 | no | — |
| 905 | C22 | — | 6 | 1 | no | — |
| 906 | C22 | — | 6 | 1 | no | — |
| 907 | C22 | — | 9 | 1 | no | — |
| 908 | C22 | — | 9 | 1 | no | — |
| 909 | C22 | — | 18 | 1 | no | — |
| 910 | C22 | — | 18 | 1 | no | — |
| 911 | C22 | — | 18 | 1 | no | — |
| 912 | C22 | — | 18 | 1 | no | — |
| 913 | C22 | — | 27 | 1 | no | — |
| 914 | C22 | — | 54 | 1 | no | — |
| 915 | C22 | — | 54 | 1 | no | — |
| 916 | C22 | — | 54 | 1 | no | — |
| 917 | C22 | — | 54 | 1 | no | — |
| 918 | C22 | C3×#3804 | 1 | 1 | yes | characteristic, complemented |
| 919 | C22 | D32×A4 | 1 | 1 | yes | characteristic |
| 920 | C4 | — | 3 | 1 | no | — |
| 921 | C4 | — | 3 | 1 | no | — |
| 922 | C4 | — | 3 | 1 | no | — |
| 923 | C4 | — | 9 | 1 | no | — |
| 924 | C4 | — | 9 | 1 | no | — |
| 925 | C4 | — | 9 | 1 | no | — |
| 926 | C4 | — | 9 | 1 | no | — |
| 927 | C4 | — | 27 | 1 | no | — |
| 928 | C3 | — | 2 | 1 | no | — |
| 929 | C3 | — | 4 | 1 | no | — |
| 930 | C3 | — | 8 | 1 | no | — |
| 931 | C3 | — | 8 | 1 | no | — |
| 932 | C3 | — | 16 | 1 | no | — |
| 933 | C3 | A4×#235 | 1 | 1 | yes | characteristic, complemented |
| 934 | C3 | A4×#237 | 1 | 1 | yes | characteristic, complemented |
| 935 | C2 | — | 2 | 1 | no | — |
| 936 | C2 | — | 3 | 1 | no | — |
| 937 | C2 | — | 3 | 1 | no | — |
| 938 | C2 | — | 6 | 1 | no | — |
| 939 | C2 | — | 6 | 1 | no | — |
| 940 | C2 | — | 18 | 1 | no | — |
| 941 | C2 | — | 18 | 1 | no | — |
| 942 | C2 | — | 54 | 1 | no | — |
| 943 | C2 | C2×D32×A4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D32×A4 |
| commutator, socle, cosocle | C23×C32 | C23×C3 |
| Fitting | C24×C32 | C22×C3 |
| hypercenter | C22 | D32×A4 |
| hypocenter | C22×C32 | C3×#41 |
| LCS | G ▷ C23×C32 ▷ C22×C32 | |
| UCS | C1 ◁ C2 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. A4×#638 | C2 | semidirect |
| 2. C3×A4×#67 | C2 | semidirect |
| 3. C2×C3×Dic3×A4 | C2 | semidirect |
| 4. A4×#627 | C2 | semidirect |
| 5. A4×#626 | C2 | semidirect |
| 6. A4×#624 | C2 | semidirect |
| 7. D3×Dic3×A4 | C2 | semidirect |
| 8. C22×#3804 | C3 | semidirect |
| 19. C22×#638 | C2×C3 | semidirect |
| 20. C22×C3×#67 | C2×C3 | semidirect |
| 21. C23×C3×Dic3 | C2×C3 | semidirect |
| 24. C22×#627 | C2×C3 | semidirect |
| 25. C22×#626 | C2×C3 | semidirect |
| 26. C22×#624 | C2×C3 | semidirect |
| 35. C22×D3×Dic3 | C2×C3 | semidirect |
| 41. A4×#67 | D3 | semidirect |
| 44. C2×Dic3×A4 | D3 | semidirect |
| 127. #3804 | A4 | direct (N × H) |
| 144. C32×A4 | #41 | semidirect |
| 155. C22×#67 | C3×D3 | semidirect |
| 157. C23×Dic3 | C3×D3 | semidirect |
| 226. #638 | C2×A4 | semidirect |
| 239. C3×#67 | C2×A4 | semidirect |
| 253. C2×C3×Dic3 | C2×A4 | semidirect |
| 264. #627 | C2×A4 | semidirect |
| 269. #626 | C2×A4 | semidirect |
| 274. #624 | C2×A4 | semidirect |
| 279. D3×Dic3 | C2×A4 | semidirect |
| 421. C22×C32 | C3×#41 | semidirect |
| 444. C3×A4 | #235 | semidirect |
| 445. C3×A4 | #237 | semidirect |
| 577. #67 | D3×A4 | semidirect |
| 599. C2×Dic3 | D3×A4 | semidirect |
| 743. C22×C3 | C3×#235 | semidirect |
| 744. C22×C3 | C3×#237 | semidirect |
| 774. A4 | #3804 | direct (N × H) |
| 806. C32 | A4×#41 | semidirect |
| 918. C22 | C3×#3804 | semidirect |
| 933. C3 | A4×#235 | semidirect |
| 934. C3 | A4×#237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#638 | 2 |
| C3×A4×#67 | 2 |
| C2×C3×Dic3×A4 | 2 |
| A4×#627 | 2 |
| A4×#626 | 2 |
| A4×#624 | 2 |
| D3×Dic3×A4 | 2 |
| C22×#3804 | 3 |
| A4×#237 | 3 |
| A4×#235 | 3 |
| C3×#3804 | 4 |