Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2219 conjugacy classes of subgroups.
The subgroup lattice has 788 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3⋊D3×#123 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×#5651 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10595276 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10595170 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #10595169 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #10594925 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10594811 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10594399 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10594374 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10594353 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #10594251 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #10594154 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #10594154 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #10594067 | C2 | 1 | 2 | yes | maximal, complemented |
| 15 | #10594036 | C2 | 1 | 2 | yes | maximal, complemented |
| 16 | D3×#563 | — | 3 | 2 | no | maximal |
| 17 | C2×D4×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 18 | C22×C4×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 19 | C22×#624 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#3797 | C22 | 1 | 2 | yes | — |
| 21 | C2×#3797 | C22 | 1 | 1 | yes | characteristic |
| 22 | C32×#123 | C22 | 1 | 1 | yes | characteristic |
| 23 | #64144 | C22 | 1 | 1 | yes | characteristic |
| 24 | #64138 | C22 | 1 | 1 | yes | characteristic |
| 25 | #64103 | C22 | 1 | 2 | yes | — |
| 26 | C4⋊C4×C3⋊D3 | C22 | 1 | 2 | yes | — |
| 27 | #64095 | C22 | 1 | 1 | yes | characteristic |
| 28 | #64092 | C22 | 1 | 2 | yes | — |
| 29 | C22⋊C4×C3⋊D3 | C22 | 1 | 2 | yes | — |
| 30 | C22⋊C4×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 31 | C3×#936 | C22 | 1 | 2 | yes | — |
| 32 | C3×#935 | C22 | 1 | 2 | yes | — |
| 33 | C3×#924 | C22 | 1 | 4 | yes | complemented |
| 34 | C3×#889 | C22 | 1 | 4 | yes | complemented |
| 35 | C3×#888 | C22 | 1 | 4 | yes | complemented |
| 36 | C3×#879 | C22 | 1 | 4 | yes | complemented |
| 37 | C3×#879 | C22 | 1 | 4 | yes | complemented |
| 38 | C3×#878 | C22 | 1 | 4 | yes | complemented |
| 39 | #63982 | C22 | 1 | 4 | yes | complemented |
| 40 | #63975 | C22 | 1 | 2 | yes | — |
| 41 | #63974 | C22 | 1 | 2 | yes | — |
| 42 | #63974 | C22 | 1 | 1 | yes | characteristic |
| 43 | #63974 | C22 | 1 | 2 | yes | — |
| 44 | #63974 | C22 | 1 | 2 | yes | — |
| 45 | #63966 | C22 | 1 | 2 | yes | — |
| 46 | #63964 | C22 | 1 | 4 | yes | complemented |
| 47 | #63956 | C22 | 1 | 4 | yes | complemented |
| 48 | #63956 | C22 | 1 | 4 | yes | complemented |
| 49 | #63953 | C22 | 1 | 2 | yes | — |
| 50 | #63953 | C22 | 1 | 2 | yes | — |
| 51 | #63918 | C22 | 1 | 4 | yes | complemented |
| 52 | #63900 | C22 | 1 | 2 | yes | — |
| 53 | #63900 | C22 | 1 | 2 | yes | — |
| 54 | #63897 | C22 | 1 | 2 | yes | — |
| 55 | #63895 | C22 | 1 | 4 | yes | complemented |
| 56 | #63888 | C22 | 1 | 4 | yes | complemented |
| 57 | #63883 | C22 | 1 | 2 | yes | — |
| 58 | #63883 | C22 | 1 | 2 | yes | — |
| 59 | #63883 | C22 | 1 | 2 | yes | — |
| 60 | #63883 | C22 | 1 | 2 | yes | — |
| 61 | #63883 | C22 | 1 | 2 | yes | — |
| 62 | C4×#624 | C22 | 1 | 2 | yes | — |
| 63 | C4×#624 | C22 | 1 | 1 | yes | characteristic |
| 64 | #63871 | C22 | 1 | 4 | yes | complemented |
| 65 | #63868 | C22 | 1 | 4 | yes | complemented |
| 66 | #63868 | C22 | 1 | 4 | yes | complemented |
| 67 | #63867 | C22 | 1 | 4 | yes | complemented |
| 68 | #63865 | C22 | 1 | 4 | yes | complemented |
| 69 | #63864 | C22 | 1 | 2 | yes | — |
| 70 | #63848 | C22 | 1 | 4 | yes | complemented |
| 71 | #63848 | C22 | 1 | 4 | yes | complemented |
| 72 | #63846 | C22 | 1 | 4 | yes | complemented |
| 73 | #63845 | C22 | 1 | 4 | yes | complemented |
| 74 | #63839 | C22 | 1 | 4 | yes | complemented |
| 75 | #63839 | C22 | 1 | 4 | yes | complemented |
| 76 | C3×#563 | — | 3 | 2 | no | — |
| 77 | #5735 | — | 3 | 4 | no | — |
| 78 | D3×C4⋊Q8 | — | 3 | 4 | no | — |
| 79 | #5712 | — | 3 | 4 | no | — |
| 80 | #5712 | — | 3 | 4 | no | — |
| 81 | D3×#126 | — | 3 | 4 | no | — |
| 82 | D3×#126 | — | 3 | 4 | no | — |
| 83 | #5699 | — | 3 | 4 | no | — |
| 84 | D3×#125 | — | 3 | 4 | no | — |
| 85 | D3×#124 | — | 3 | 2 | no | — |
| 86 | #5672 | — | 3 | 2 | no | — |
| 87 | D3×#123 | — | 3 | 2 | no | — |
| 88 | D3×#123 | — | 3 | 2 | no | — |
| 89 | D3×#123 | — | 6 | 1 | no | — |
| 90 | #5651 | — | 3 | 2 | no | — |
| 91 | #5651 | D3 | 1 | 2 | yes | complemented |
| 92 | #5646 | — | 3 | 4 | no | — |
| 93 | #5646 | — | 3 | 4 | no | — |
| 94 | D3×C22⋊Q8 | — | 3 | 4 | no | — |
| 95 | D3×C22⋊Q8 | — | 3 | 4 | no | — |
| 96 | C23×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 97 | C23×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 98 | C2×C32×D4 | C23 | 1 | 1 | yes | characteristic |
| 99 | C22×C32×C4 | C23 | 1 | 1 | yes | characteristic |
| 100 | C2×#638 | C23 | 1 | 1 | yes | characteristic |
| 101 | C2×#638 | C23 | 1 | 1 | yes | characteristic |
| 102 | C22×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 103 | D4×C3⋊D3 | — | 4 | 2 | no | — |
| 104 | C2×C4⋊(C3⋊D3) | C23 | 1 | 1 | yes | characteristic |
| 105 | C2×C4×C3⋊D3 | — | 4 | 2 | no | — |
| 106 | C2×C4×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 107 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 108 | C2×C4×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 109 | C2×C4×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 110 | C22×C3×Dic3 | C23 | 1 | 2 | yes | — |
| 111 | C2×C3×Dic6 | C23 | 1 | 4 | yes | — |
| 112 | C2×C3×Dic6 | C23 | 1 | 2 | yes | — |
| 113 | C2×#627 | C23 | 1 | 2 | yes | — |
| 114 | C2×#627 | C23 | 1 | 4 | yes | — |
| 115 | C2×#624 | — | 4 | 2 | no | — |
| 116 | C2×#624 | C23 | 1 | 2 | yes | — |
| 117 | C2×#624 | C23 | 1 | 2 | yes | — |
| 118 | C2×#624 | C23 | 1 | 2 | yes | — |
| 119 | C2×#624 | C23 | 1 | 2 | yes | — |
| 120 | C2×#624 | C23 | 1 | 2 | yes | — |
| 121 | #3797 | — | 4 | 2 | no | — |
| 122 | #3797 | — | 4 | 4 | no | — |
| 123 | C32×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 124 | C32×C22⋊C4 | C23 | 1 | 2 | yes | — |
| 125 | C32×C22⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 126 | #3757 | C23 | 1 | 2 | yes | — |
| 127 | #3757 | C23 | 1 | 1 | yes | characteristic |
| 128 | #3752 | C23 | 1 | 2 | yes | — |
| 129 | #3752 | C23 | 1 | 2 | yes | — |
| 130 | #3752 | C23 | 1 | 2 | yes | — |
| 131 | C4⋊(C3⋊Dic3) | C23 | 1 | 2 | yes | — |
| 132 | #3750 | C23 | 1 | 2 | yes | — |
| 133 | #3750 | C23 | 1 | 2 | yes | — |
| 134 | C3×#217 | C23 | 1 | 4 | yes | — |
| 135 | C3×#217 | C23 | 1 | 2 | yes | — |
| 136 | C3×#217 | C23 | 1 | 4 | yes | — |
| 137 | C3×#217 | C23 | 1 | 4 | yes | — |
| 138 | C3×C4⋊Dic3 | C23 | 1 | 4 | yes | — |
| 139 | C3×C4⋊Dic3 | C23 | 1 | 4 | yes | — |
| 140 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 141 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 142 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 143 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 144 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 145 | C3×C4×Dic3 | C23 | 1 | 4 | yes | — |
| 146 | C3×C4×Dic3 | C23 | 1 | 2 | yes | — |
| 147 | #3724 | C23 | 1 | 4 | yes | — |
| 148 | #3724 | C23 | 1 | 4 | yes | — |
| 149 | Dic3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 150 | Dic3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 151 | Dic3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 152 | Dic3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 153 | Dic3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 154 | #3722 | C23 | 1 | 2 | yes | — |
| 155 | #3722 | C23 | 1 | 4 | yes | — |
| 156 | #3722 | C23 | 1 | 4 | yes | — |
| 157 | #3722 | C23 | 1 | 4 | yes | — |
| 158 | Dic32 | C23 | 1 | 4 | yes | — |
| 159 | Dic32 | C23 | 1 | 2 | yes | — |
| 160 | C2×#563 | — | 9 | 1 | no | Sylow |
| 161 | C2×D3×Q8 | — | 3 | 2 | no | — |
| 162 | C2×D3×Q8 | — | 3 | 4 | no | — |
| 163 | C2×D3×D4 | — | 3 | 2 | no | — |
| 164 | C2×D3×D4 | — | 6 | 1 | no | — |
| 165 | C22×C4×D3 | — | 3 | 2 | no | — |
| 166 | C22×C4×D3 | — | 3 | 2 | no | — |
| 167 | C22×C4×D3 | — | 6 | 1 | no | — |
| 168 | C3×C4⋊Q8 | — | 3 | 4 | no | — |
| 169 | C3×#126 | — | 3 | 4 | no | — |
| 170 | C3×#126 | — | 3 | 4 | no | — |
| 171 | C3×#125 | — | 3 | 4 | no | — |
| 172 | C3×#124 | — | 3 | 2 | no | — |
| 173 | C3×#123 | — | 2 | 1 | no | — |
| 174 | C3×#123 | — | 3 | 2 | no | — |
| 175 | C3×#123 | C2×D3 | 1 | 2 | yes | — |
| 176 | C3×C22⋊Q8 | — | 3 | 4 | no | — |
| 177 | C3×C22⋊Q8 | — | 3 | 4 | no | — |
| 178 | #947 | — | 3 | 2 | no | — |
| 179 | #946 | — | 3 | 4 | no | — |
| 180 | #946 | — | 3 | 4 | no | — |
| 181 | #944 | — | 3 | 4 | no | — |
| 182 | #944 | — | 3 | 4 | no | — |
| 183 | #936 | C2×D3 | 1 | 2 | yes | — |
| 184 | #935 | — | 3 | 2 | no | — |
| 185 | #935 | — | 6 | 1 | no | — |
| 186 | #935 | C2×D3 | 1 | 2 | yes | — |
| 187 | #929 | — | 3 | 2 | no | — |
| 188 | #929 | — | 3 | 2 | no | — |
| 189 | #929 | — | 6 | 1 | no | — |
| 190 | #924 | — | 3 | 4 | no | — |
| 191 | #924 | C2×D3 | 1 | 4 | yes | complemented |
| 192 | #898 | — | 3 | 4 | no | — |
| 193 | #898 | — | 3 | 4 | no | — |
| 194 | #898 | — | 3 | 4 | no | — |
| 195 | #898 | — | 3 | 4 | no | — |
| 196 | #898 | — | 3 | 4 | no | — |
| 197 | #898 | — | 3 | 4 | no | — |
| 198 | #897 | — | 3 | 4 | no | — |
| 199 | #897 | — | 3 | 4 | no | — |
| 200 | #896 | — | 3 | 4 | no | — |
| 201 | #896 | — | 3 | 4 | no | — |
| 202 | #896 | — | 3 | 4 | no | — |
| 203 | #896 | — | 3 | 4 | no | — |
| 204 | #894 | — | 3 | 4 | no | — |
| 205 | #894 | — | 3 | 4 | no | — |
| 206 | #894 | — | 6 | 2 | no | — |
| 207 | D3×C4⋊C4 | — | 3 | 4 | no | — |
| 208 | D3×C4⋊C4 | — | 3 | 4 | no | — |
| 209 | D3×C4⋊C4 | — | 3 | 4 | no | — |
| 210 | D3×C4⋊C4 | — | 3 | 4 | no | — |
| 211 | D3×C4⋊C4 | — | 3 | 4 | no | — |
| 212 | D3×C4⋊C4 | — | 3 | 4 | no | — |
| 213 | D3×C4⋊C4 | — | 3 | 4 | no | — |
| 214 | D3×C4⋊C4 | — | 3 | 4 | no | — |
| 215 | D3×C4⋊C4 | — | 6 | 2 | no | — |
| 216 | #890 | — | 3 | 4 | no | — |
| 217 | #890 | — | 3 | 4 | no | — |
| 218 | #889 | — | 3 | 4 | no | — |
| 219 | #889 | — | 3 | 4 | no | — |
| 220 | #889 | — | 3 | 4 | no | — |
| 221 | #889 | C2×D3 | 1 | 4 | yes | complemented |
| 222 | #888 | — | 3 | 4 | no | — |
| 223 | #888 | — | 3 | 4 | no | — |
| 224 | #888 | — | 3 | 4 | no | — |
| 225 | #888 | C2×D3 | 1 | 4 | yes | complemented |
| 226 | #886 | — | 3 | 2 | no | — |
| 227 | #886 | — | 3 | 2 | no | — |
| 228 | #886 | — | 6 | 1 | no | — |
| 229 | #885 | — | 3 | 4 | no | — |
| 230 | #885 | — | 3 | 4 | no | — |
| 231 | #883 | — | 3 | 4 | no | — |
| 232 | #883 | — | 3 | 4 | no | — |
| 233 | #883 | — | 6 | 2 | no | — |
| 234 | D3×C22⋊C4 | — | 3 | 2 | no | — |
| 235 | D3×C22⋊C4 | — | 3 | 4 | no | — |
| 236 | D3×C22⋊C4 | — | 3 | 2 | no | — |
| 237 | D3×C22⋊C4 | — | 3 | 4 | no | — |
| 238 | D3×C22⋊C4 | — | 3 | 4 | no | — |
| 239 | D3×C22⋊C4 | — | 3 | 4 | no | — |
| 240 | D3×C22⋊C4 | — | 6 | 2 | no | — |
| 241 | D3×C22⋊C4 | — | 6 | 1 | no | — |
| 242 | #879 | — | 3 | 4 | no | — |
| 243 | #879 | — | 3 | 4 | no | — |
| 244 | #879 | — | 3 | 4 | no | — |
| 245 | #879 | — | 3 | 4 | no | — |
| 246 | #879 | C2×D3 | 1 | 4 | yes | complemented |
| 247 | #879 | C2×D3 | 1 | 4 | yes | complemented |
| 248 | #878 | — | 3 | 4 | no | — |
| 249 | #878 | — | 3 | 4 | no | — |
| 250 | #878 | — | 3 | 4 | no | — |
| 251 | #878 | C2×D3 | 1 | 4 | yes | complemented |
| 252 | #876 | — | 3 | 4 | no | — |
| 253 | #876 | — | 3 | 4 | no | — |
| 254 | #875 | — | 3 | 2 | no | — |
| 255 | C42×D3 | — | 3 | 2 | no | — |
| 256 | C42×D3 | — | 3 | 4 | no | — |
| 257 | #870 | — | 3 | 4 | no | — |
| 258 | #869 | — | 3 | 4 | no | — |
| 259 | C23×C32 | C24 | 1 | 1 | yes | characteristic |
| 260 | C23×C32 | C24 | 1 | 1 | yes | characteristic |
| 261 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 262 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 263 | C22×C3⋊D3 | — | 2 | 4 | no | — |
| 264 | C22×C3⋊D3 | — | 2 | 4 | no | — |
| 265 | C22×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 266 | C22×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 267 | C22×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 268 | C32×D4 | — | 4 | 1 | no | — |
| 269 | C2×C32×C4 | — | 4 | 1 | no | — |
| 270 | C2×C32×C4 | C24 | 1 | 2 | yes | — |
| 271 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 272 | C2×C32×C4 | C24 | 1 | 2 | yes | — |
| 273 | #638 | — | 4 | 1 | no | — |
| 274 | #638 | — | 4 | 1 | no | — |
| 275 | C2×C3⋊Dic3 | — | 4 | 1 | no | — |
| 276 | C2×C3⋊Dic3 | C24 | 1 | 2 | yes | — |
| 277 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 278 | C2×C3⋊Dic3 | C24 | 1 | 2 | yes | — |
| 279 | C4⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 280 | C4×C3⋊D3 | — | 2 | 4 | no | — |
| 281 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 282 | C4×C3⋊D3 | — | 2 | 4 | no | — |
| 283 | C4×C3⋊D3 | — | 4 | 2 | no | — |
| 284 | C2×C3×Dic3 | — | 4 | 2 | no | — |
| 285 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 286 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 287 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 288 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 289 | C3×Dic6 | — | 4 | 4 | no | — |
| 290 | C3×Dic6 | — | 4 | 2 | no | — |
| 291 | #627 | — | 4 | 4 | no | — |
| 292 | #627 | — | 4 | 2 | no | — |
| 293 | #624 | — | 2 | 4 | no | — |
| 294 | #624 | — | 2 | 4 | no | — |
| 295 | #624 | — | 2 | 4 | no | — |
| 296 | #624 | — | 2 | 4 | no | — |
| 297 | #624 | — | 4 | 2 | no | — |
| 298 | #563 | — | 3 | 2 | no | — |
| 299 | #563 | — | 9 | 2 | no | — |
| 300 | #563 | — | 9 | 4 | no | — |
| 301 | #563 | — | 9 | 2 | no | — |
| 302 | #563 | — | 9 | 4 | no | — |
| 303 | #563 | — | 9 | 2 | no | — |
| 304 | C2×C4⋊Q8 | — | 9 | 2 | no | — |
| 305 | C2×#126 | — | 9 | 2 | no | — |
| 306 | C2×#126 | — | 9 | 2 | no | — |
| 307 | C2×#125 | — | 9 | 2 | no | — |
| 308 | C2×#124 | — | 9 | 1 | no | — |
| 309 | C2×#123 | — | 9 | 1 | no | — |
| 310 | C2×#123 | — | 9 | 1 | no | — |
| 311 | C2×C22⋊Q8 | — | 9 | 2 | no | — |
| 312 | C2×C22⋊Q8 | — | 9 | 2 | no | — |
| 313 | C23×D3 | — | 3 | 2 | no | — |
| 314 | C23×D3 | — | 3 | 2 | no | — |
| 315 | C23×D3 | — | 6 | 1 | no | — |
| 316 | C23×D3 | — | 6 | 1 | no | — |
| 317 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 318 | C2×C3×Q8 | — | 3 | 4 | no | — |
| 319 | C2×C3×D4 | — | 2 | 1 | no | — |
| 320 | C2×C3×D4 | C22×D3 | 1 | 2 | yes | — |
| 321 | C22×C3×C4 | — | 2 | 1 | no | — |
| 322 | C22×C3×C4 | — | 3 | 2 | no | — |
| 323 | C22×C3×C4 | C22×D3 | 1 | 2 | yes | — |
| 324 | C2×#67 | — | 3 | 2 | no | — |
| 325 | C2×#67 | — | 3 | 2 | no | — |
| 326 | C2×#67 | — | 6 | 1 | no | — |
| 327 | C2×#67 | — | 6 | 1 | no | — |
| 328 | C22×Dic3 | — | 3 | 2 | no | — |
| 329 | C22×Dic3 | — | 6 | 1 | no | — |
| 330 | C22×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 331 | D3×Q8 | — | 12 | 8 | no | — |
| 332 | D3×Q8 | — | 12 | 4 | no | — |
| 333 | D3×D4 | — | 12 | 4 | no | — |
| 334 | D3×D4 | — | 12 | 4 | no | — |
| 335 | C2×D12 | — | 3 | 2 | no | — |
| 336 | C2×D12 | — | 6 | 1 | no | — |
| 337 | C2×C4×D3 | — | 3 | 4 | no | — |
| 338 | C2×C4×D3 | — | 3 | 2 | no | — |
| 339 | C2×C4×D3 | — | 3 | 4 | no | — |
| 340 | C2×C4×D3 | — | 3 | 4 | no | — |
| 341 | C2×C4×D3 | — | 3 | 4 | no | — |
| 342 | C2×C4×D3 | — | 3 | 4 | no | — |
| 343 | C2×C4×D3 | — | 3 | 4 | no | — |
| 344 | C2×C4×D3 | — | 3 | 4 | no | — |
| 345 | C2×C4×D3 | — | 3 | 4 | no | — |
| 346 | C2×C4×D3 | — | 6 | 2 | no | — |
| 347 | C2×C4×D3 | — | 6 | 2 | no | — |
| 348 | C2×C4×D3 | — | 6 | 2 | no | — |
| 349 | C2×C4×D3 | — | 6 | 1 | no | — |
| 350 | C2×C4×D3 | — | 12 | 4 | no | — |
| 351 | C2×C4×D3 | — | 12 | 4 | no | — |
| 352 | C2×C4×D3 | — | 12 | 4 | no | — |
| 353 | C2×Dic6 | — | 3 | 4 | no | — |
| 354 | C2×Dic6 | — | 3 | 4 | no | — |
| 355 | C2×Dic6 | — | 3 | 4 | no | — |
| 356 | C2×Dic6 | C22×D3 | 1 | 2 | yes | — |
| 357 | C2×Dic6 | C22×D3 | 1 | 4 | yes | — |
| 358 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 359 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 360 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 361 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 362 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 363 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 364 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 365 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 366 | C3×C4⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 367 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 368 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 369 | C3×C22⋊C4 | — | 3 | 4 | no | — |
| 370 | C3×C22⋊C4 | — | 3 | 4 | no | — |
| 371 | C3×C22⋊C4 | — | 3 | 4 | no | — |
| 372 | C3×C22⋊C4 | — | 3 | 2 | no | — |
| 373 | C3×C22⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 374 | C3×C22⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 375 | C3×C42 | — | 3 | 4 | no | — |
| 376 | C3×C42 | — | 3 | 2 | no | — |
| 377 | #217 | — | 3 | 4 | no | — |
| 378 | #217 | — | 3 | 2 | no | — |
| 379 | #217 | — | 6 | 2 | no | — |
| 380 | #217 | — | 6 | 1 | no | — |
| 381 | #217 | C22×D3 | 1 | 4 | yes | — |
| 382 | #217 | C22×D3 | 1 | 4 | yes | — |
| 383 | #217 | C22×D3 | 1 | 4 | yes | — |
| 384 | #217 | C22×D3 | 1 | 2 | yes | — |
| 385 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 386 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 387 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 388 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 389 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 390 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 391 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 392 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 393 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 394 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 395 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 396 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 397 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 398 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 399 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 400 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 401 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 402 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 403 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 404 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 405 | C4⋊Dic3 | C22×D3 | 1 | 4 | yes | — |
| 406 | C4⋊Dic3 | C22×D3 | 1 | 4 | yes | — |
| 407 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 408 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 409 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 410 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 411 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 412 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 413 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 414 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 415 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 416 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 417 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 418 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 419 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 420 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 421 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 422 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 423 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 424 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 425 | C4×Dic3 | — | 3 | 4 | no | — |
| 426 | C4×Dic3 | — | 3 | 4 | no | — |
| 427 | C4×Dic3 | — | 3 | 4 | no | — |
| 428 | C4×Dic3 | C22×D3 | 1 | 4 | yes | — |
| 429 | C4×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 430 | C22×C32 | — | 2 | 1 | no | — |
| 431 | C22×C32 | — | 2 | 1 | no | — |
| 432 | C22×C32 | — | 2 | 2 | no | — |
| 433 | C22×C32 | — | 2 | 2 | no | — |
| 434 | C22×C32 | C25 | 1 | 1 | yes | characteristic |
| 435 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 436 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 437 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 438 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 439 | C2×C3⋊D3 | — | 4 | 4 | no | — |
| 440 | C2×C3⋊D3 | — | 4 | 4 | no | — |
| 441 | C2×C3⋊D3 | H(5,𝔽2) | 1 | 2 | yes | — |
| 442 | C2×C3⋊D3 | 2−1+4 | 1 | 4 | yes | — |
| 443 | C32×C4 | — | 2 | 2 | no | — |
| 444 | C32×C4 | — | 2 | 1 | no | — |
| 445 | C32×C4 | — | 2 | 2 | no | — |
| 446 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 447 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 448 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 449 | C3×Dic3 | — | 2 | 4 | no | — |
| 450 | C3×Dic3 | — | 2 | 4 | no | — |
| 451 | C3×Dic3 | — | 2 | 4 | no | — |
| 452 | C3×Dic3 | — | 2 | 4 | no | — |
| 453 | C22×Q8 | — | 9 | 2 | no | — |
| 454 | C22×Q8 | — | 9 | 1 | no | — |
| 455 | C22×D4 | — | 9 | 1 | no | — |
| 456 | C23×C4 | — | 9 | 1 | no | — |
| 457 | C23×C4 | — | 9 | 1 | no | — |
| 458 | C4⋊Q8 | — | 3 | 4 | no | — |
| 459 | C4⋊Q8 | — | 9 | 4 | no | — |
| 460 | C4⋊Q8 | — | 9 | 4 | no | — |
| 461 | C4⋊Q8 | — | 9 | 4 | no | — |
| 462 | #126 | — | 3 | 4 | no | — |
| 463 | #126 | — | 3 | 4 | no | — |
| 464 | #126 | — | 9 | 4 | no | — |
| 465 | #126 | — | 9 | 4 | no | — |
| 466 | #126 | — | 9 | 4 | no | — |
| 467 | #126 | — | 9 | 4 | no | — |
| 468 | #126 | — | 9 | 4 | no | — |
| 469 | #126 | — | 9 | 4 | no | — |
| 470 | #125 | — | 3 | 4 | no | — |
| 471 | #125 | — | 9 | 4 | no | — |
| 472 | #125 | — | 9 | 4 | no | — |
| 473 | #125 | — | 9 | 4 | no | — |
| 474 | #124 | — | 3 | 2 | no | — |
| 475 | #124 | — | 9 | 2 | no | — |
| 476 | #124 | — | 9 | 2 | no | — |
| 477 | #124 | — | 9 | 2 | no | — |
| 478 | #123 | — | 3 | 2 | no | — |
| 479 | #123 | — | 9 | 2 | no | — |
| 480 | #123 | — | 9 | 2 | no | — |
| 481 | #123 | — | 9 | 2 | no | — |
| 482 | #123 | — | 9 | 1 | no | — |
| 483 | #123 | — | 9 | 1 | no | — |
| 484 | #123 | — | 9 | 2 | no | — |
| 485 | #123 | — | 9 | 2 | no | — |
| 486 | #123 | — | 9 | 1 | no | — |
| 487 | #123 | D32 | 1 | 1 | yes | characteristic |
| 488 | C22⋊Q8 | — | 3 | 4 | no | — |
| 489 | C22⋊Q8 | — | 3 | 4 | no | — |
| 490 | C22⋊Q8 | — | 9 | 4 | no | — |
| 491 | C22⋊Q8 | — | 9 | 4 | no | — |
| 492 | C22⋊Q8 | — | 9 | 4 | no | — |
| 493 | C22⋊Q8 | — | 9 | 4 | no | — |
| 494 | C22⋊Q8 | — | 9 | 4 | no | — |
| 495 | C22⋊Q8 | — | 9 | 4 | no | — |
| 496 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 497 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 498 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 499 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 500 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 501 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 502 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 503 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 504 | C2×C22⋊C4 | — | 9 | 2 | no | — |
| 505 | C2×C22⋊C4 | — | 9 | 2 | no | — |
| 506 | C2×C22⋊C4 | — | 9 | 2 | no | — |
| 507 | C2×C22⋊C4 | — | 9 | 1 | no | — |
| 508 | C2×C22⋊C4 | — | 9 | 2 | no | — |
| 509 | C2×C22⋊C4 | — | 9 | 1 | no | — |
| 510 | C2×C42 | — | 9 | 1 | no | — |
| 511 | C2×C42 | — | 9 | 2 | no | — |
| 512 | C23×C3 | — | 2 | 1 | no | — |
| 513 | C23×C3 | — | 2 | 1 | no | — |
| 514 | C23×C3 | C23×D3 | 1 | 2 | yes | — |
| 515 | C23×C3 | C23×D3 | 1 | 2 | yes | — |
| 516 | C22×D3 | — | 3 | 2 | no | — |
| 517 | C22×D3 | — | 3 | 2 | no | — |
| 518 | C22×D3 | — | 3 | 2 | no | — |
| 519 | C22×D3 | — | 6 | 1 | no | — |
| 520 | C22×D3 | — | 6 | 1 | no | — |
| 521 | C22×D3 | — | 6 | 1 | no | — |
| 522 | C22×D3 | — | 6 | 4 | no | — |
| 523 | C22×D3 | — | 6 | 4 | no | — |
| 524 | C22×D3 | — | 6 | 8 | no | — |
| 525 | C22×D3 | — | 6 | 8 | no | — |
| 526 | C22×D3 | — | 6 | 4 | no | — |
| 527 | C22×D3 | — | 12 | 4 | no | — |
| 528 | C22×D3 | — | 12 | 2 | no | — |
| 529 | C22×D3 | — | 12 | 4 | no | — |
| 530 | C3×Q8 | — | 12 | 4 | no | — |
| 531 | C3×Q8 | — | 12 | 2 | no | — |
| 532 | C3×D4 | — | 4 | 2 | no | — |
| 533 | C3×D4 | — | 4 | 2 | no | — |
| 534 | C2×C3×C4 | — | 2 | 1 | no | — |
| 535 | C2×C3×C4 | — | 2 | 2 | no | — |
| 536 | C2×C3×C4 | — | 2 | 2 | no | — |
| 537 | C2×C3×C4 | — | 3 | 4 | no | — |
| 538 | C2×C3×C4 | — | 3 | 4 | no | — |
| 539 | C2×C3×C4 | — | 3 | 4 | no | — |
| 540 | C2×C3×C4 | — | 3 | 4 | no | — |
| 541 | C2×C3×C4 | — | 4 | 2 | no | — |
| 542 | C2×C3×C4 | — | 4 | 2 | no | — |
| 543 | C2×C3×C4 | — | 12 | 2 | no | — |
| 544 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 545 | C2×C3×C4 | C23×D3 | 1 | 4 | yes | — |
| 546 | C2×C3×C4 | C23×D3 | 1 | 4 | yes | — |
| 547 | #67 | — | 12 | 2 | no | — |
| 548 | #67 | — | 12 | 2 | no | — |
| 549 | #67 | — | 12 | 2 | no | — |
| 550 | #67 | — | 12 | 2 | no | — |
| 551 | C2×Dic3 | — | 3 | 4 | no | — |
| 552 | C2×Dic3 | — | 3 | 2 | no | — |
| 553 | C2×Dic3 | — | 3 | 4 | no | — |
| 554 | C2×Dic3 | — | 4 | 2 | no | — |
| 555 | C2×Dic3 | — | 6 | 1 | no | — |
| 556 | C2×Dic3 | — | 6 | 2 | no | — |
| 557 | C2×Dic3 | — | 6 | 2 | no | — |
| 558 | C2×Dic3 | — | 12 | 2 | no | — |
| 559 | C2×Dic3 | — | 12 | 2 | no | — |
| 560 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 561 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 562 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 563 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 564 | D12 | — | 12 | 2 | no | — |
| 565 | D12 | — | 12 | 2 | no | — |
| 566 | C4×D3 | — | 6 | 8 | no | — |
| 567 | C4×D3 | — | 6 | 8 | no | — |
| 568 | C4×D3 | — | 6 | 8 | no | — |
| 569 | C4×D3 | — | 6 | 8 | no | — |
| 570 | C4×D3 | — | 6 | 8 | no | — |
| 571 | C4×D3 | — | 6 | 8 | no | — |
| 572 | C4×D3 | — | 6 | 4 | no | — |
| 573 | C4×D3 | — | 12 | 4 | no | — |
| 574 | C4×D3 | — | 12 | 4 | no | — |
| 575 | C4×D3 | — | 12 | 2 | no | — |
| 576 | C4×D3 | — | 12 | 4 | no | — |
| 577 | C4×D3 | — | 12 | 4 | no | — |
| 578 | C4×D3 | — | 12 | 4 | no | — |
| 579 | Dic6 | — | 4 | 2 | no | — |
| 580 | Dic6 | — | 4 | 4 | no | — |
| 581 | Dic6 | — | 12 | 4 | no | — |
| 582 | Dic6 | — | 12 | 4 | no | — |
| 583 | Dic6 | — | 12 | 4 | no | — |
| 584 | C2×C32 | — | 4 | 1 | no | — |
| 585 | C2×C32 | — | 4 | 1 | no | — |
| 586 | C2×C32 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 587 | C2×C32 | C2×2−1+4 | 1 | 2 | yes | — |
| 588 | C3⋊D3 | — | 4 | 1 | no | — |
| 589 | C3⋊D3 | — | 4 | 1 | no | — |
| 590 | C3⋊D3 | #563 | 1 | 4 | yes | complemented |
| 591 | C24 | — | 9 | 1 | no | — |
| 592 | C24 | — | 9 | 1 | no | — |
| 593 | C2×Q8 | — | 3 | 4 | no | — |
| 594 | C2×Q8 | — | 3 | 2 | no | — |
| 595 | C2×Q8 | — | 9 | 4 | no | — |
| 596 | C2×Q8 | — | 9 | 2 | no | — |
| 597 | C2×Q8 | — | 36 | 4 | no | — |
| 598 | C2×Q8 | — | 36 | 2 | no | — |
| 599 | C2×D4 | — | 9 | 1 | no | — |
| 600 | C2×D4 | — | 9 | 1 | no | — |
| 601 | C2×D4 | — | 9 | 1 | no | — |
| 602 | C2×D4 | — | 36 | 2 | no | — |
| 603 | C2×D4 | C2×D32 | 1 | 1 | yes | characteristic |
| 604 | C22×C4 | — | 3 | 2 | no | — |
| 605 | C22×C4 | — | 9 | 2 | no | — |
| 606 | C22×C4 | — | 9 | 2 | no | — |
| 607 | C22×C4 | — | 9 | 2 | no | — |
| 608 | C22×C4 | — | 9 | 2 | no | — |
| 609 | C22×C4 | — | 9 | 2 | no | — |
| 610 | C22×C4 | — | 9 | 1 | no | — |
| 611 | C22×C4 | — | 9 | 2 | no | — |
| 612 | C22×C4 | — | 9 | 1 | no | — |
| 613 | C22×C4 | — | 9 | 2 | no | — |
| 614 | C22×C4 | — | 9 | 2 | no | — |
| 615 | C22×C4 | — | 36 | 2 | no | — |
| 616 | C22×C4 | — | 36 | 2 | no | — |
| 617 | C22×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 618 | C4⋊C4 | — | 3 | 4 | no | — |
| 619 | C4⋊C4 | — | 3 | 4 | no | — |
| 620 | C4⋊C4 | — | 3 | 4 | no | — |
| 621 | C4⋊C4 | — | 3 | 4 | no | — |
| 622 | C4⋊C4 | — | 3 | 4 | no | — |
| 623 | C4⋊C4 | — | 3 | 4 | no | — |
| 624 | C4⋊C4 | — | 3 | 4 | no | — |
| 625 | C4⋊C4 | — | 9 | 4 | no | — |
| 626 | C4⋊C4 | — | 9 | 4 | no | — |
| 627 | C4⋊C4 | — | 9 | 4 | no | — |
| 628 | C4⋊C4 | — | 9 | 4 | no | — |
| 629 | C4⋊C4 | — | 9 | 4 | no | — |
| 630 | C4⋊C4 | — | 9 | 4 | no | — |
| 631 | C4⋊C4 | — | 9 | 4 | no | — |
| 632 | C4⋊C4 | — | 9 | 2 | no | — |
| 633 | C4⋊C4 | — | 9 | 2 | no | — |
| 634 | C4⋊C4 | — | 9 | 2 | no | — |
| 635 | C4⋊C4 | C2×D32 | 1 | 2 | yes | — |
| 636 | C22⋊C4 | — | 3 | 4 | no | — |
| 637 | C22⋊C4 | — | 3 | 4 | no | — |
| 638 | C22⋊C4 | — | 3 | 4 | no | — |
| 639 | C22⋊C4 | — | 3 | 2 | no | — |
| 640 | C22⋊C4 | — | 9 | 4 | no | — |
| 641 | C22⋊C4 | — | 9 | 4 | no | — |
| 642 | C22⋊C4 | — | 9 | 4 | no | — |
| 643 | C22⋊C4 | — | 9 | 2 | no | — |
| 644 | C22⋊C4 | — | 9 | 2 | no | — |
| 645 | C22⋊C4 | — | 9 | 1 | no | — |
| 646 | C22⋊C4 | — | 9 | 2 | no | — |
| 647 | C22⋊C4 | — | 9 | 2 | no | — |
| 648 | C22⋊C4 | — | 9 | 2 | no | — |
| 649 | C22⋊C4 | C2×D32 | 1 | 2 | yes | — |
| 650 | C22⋊C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 651 | C42 | — | 3 | 2 | no | — |
| 652 | C42 | — | 3 | 4 | no | — |
| 653 | C42 | — | 9 | 2 | no | — |
| 654 | C42 | — | 9 | 4 | no | — |
| 655 | C22×C3 | — | 2 | 2 | no | — |
| 656 | C22×C3 | — | 2 | 2 | no | — |
| 657 | C22×C3 | — | 2 | 2 | no | — |
| 658 | C22×C3 | — | 2 | 4 | no | — |
| 659 | C22×C3 | — | 2 | 4 | no | — |
| 660 | C22×C3 | — | 2 | 1 | no | — |
| 661 | C22×C3 | — | 4 | 2 | no | — |
| 662 | C22×C3 | — | 4 | 1 | no | — |
| 663 | C22×C3 | — | 4 | 2 | no | — |
| 664 | C22×C3 | C24×D3 | 1 | 2 | yes | — |
| 665 | C2×D3 | — | 3 | 4 | no | — |
| 666 | C2×D3 | — | 3 | 8 | no | — |
| 667 | C2×D3 | — | 6 | 2 | no | — |
| 668 | C2×D3 | — | 6 | 4 | no | — |
| 669 | C2×D3 | — | 6 | 2 | no | — |
| 670 | C2×D3 | — | 6 | 2 | no | — |
| 671 | C2×D3 | — | 6 | 2 | no | — |
| 672 | C2×D3 | — | 6 | 4 | no | — |
| 673 | C2×D3 | — | 6 | 4 | no | — |
| 674 | C2×D3 | — | 12 | 2 | no | — |
| 675 | C2×D3 | — | 12 | 1 | no | — |
| 676 | C2×D3 | — | 12 | 2 | no | — |
| 677 | C2×D3 | — | 12 | 8 | no | — |
| 678 | C2×D3 | — | 12 | 8 | no | — |
| 679 | C2×D3 | — | 12 | 8 | no | — |
| 680 | C2×D3 | — | 24 | 4 | no | — |
| 681 | C3×C4 | — | 2 | 4 | no | — |
| 682 | C3×C4 | — | 2 | 2 | no | — |
| 683 | C3×C4 | — | 2 | 4 | no | — |
| 684 | C3×C4 | — | 4 | 2 | no | — |
| 685 | C3×C4 | — | 4 | 1 | no | — |
| 686 | C3×C4 | — | 4 | 2 | no | — |
| 687 | C3×C4 | — | 6 | 4 | no | — |
| 688 | C3×C4 | — | 6 | 4 | no | — |
| 689 | C3×C4 | — | 6 | 4 | no | — |
| 690 | C3×C4 | — | 6 | 4 | no | — |
| 691 | Dic3 | — | 2 | 4 | no | — |
| 692 | Dic3 | — | 2 | 4 | no | — |
| 693 | Dic3 | — | 2 | 4 | no | — |
| 694 | Dic3 | — | 2 | 4 | no | — |
| 695 | Dic3 | — | 6 | 4 | no | — |
| 696 | Dic3 | — | 6 | 2 | no | — |
| 697 | Dic3 | — | 6 | 4 | no | — |
| 698 | Dic3 | — | 12 | 2 | no | — |
| 699 | Dic3 | — | 12 | 1 | no | — |
| 700 | Dic3 | — | 12 | 2 | no | — |
| 701 | C32 | C2×#563 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 702 | C23 | — | 9 | 1 | no | — |
| 703 | C23 | — | 9 | 1 | no | — |
| 704 | C23 | — | 9 | 1 | no | — |
| 705 | C23 | — | 18 | 2 | no | — |
| 706 | C23 | — | 18 | 2 | no | — |
| 707 | C23 | — | 18 | 4 | no | — |
| 708 | C23 | — | 18 | 4 | no | — |
| 709 | C23 | C22×D32 | 1 | 1 | yes | characteristic |
| 710 | C23 | C22×D32 | 1 | 1 | yes | characteristic |
| 711 | Q8 | — | 12 | 4 | no | — |
| 712 | Q8 | — | 12 | 2 | no | — |
| 713 | Q8 | — | 36 | 4 | no | — |
| 714 | Q8 | — | 36 | 2 | no | — |
| 715 | D4 | — | 4 | 1 | no | — |
| 716 | D4 | — | 36 | 1 | no | — |
| 717 | D4 | — | 36 | 1 | no | — |
| 718 | D4 | — | 36 | 1 | no | — |
| 719 | C2×C4 | — | 3 | 4 | no | — |
| 720 | C2×C4 | — | 3 | 4 | no | — |
| 721 | C2×C4 | — | 3 | 4 | no | — |
| 722 | C2×C4 | — | 3 | 4 | no | — |
| 723 | C2×C4 | — | 4 | 1 | no | — |
| 724 | C2×C4 | — | 9 | 2 | no | — |
| 725 | C2×C4 | — | 9 | 1 | no | — |
| 726 | C2×C4 | — | 9 | 2 | no | — |
| 727 | C2×C4 | — | 12 | 2 | no | — |
| 728 | C2×C4 | — | 18 | 4 | no | — |
| 729 | C2×C4 | — | 18 | 2 | no | — |
| 730 | C2×C4 | — | 18 | 4 | no | — |
| 731 | C2×C4 | — | 18 | 4 | no | — |
| 732 | C2×C4 | — | 18 | 4 | no | — |
| 733 | C2×C4 | — | 18 | 4 | no | — |
| 734 | C2×C4 | — | 18 | 4 | no | — |
| 735 | C2×C4 | — | 36 | 2 | no | — |
| 736 | C2×C4 | — | 36 | 2 | no | — |
| 737 | C2×C4 | — | 36 | 1 | no | — |
| 738 | C2×C4 | C22×D32 | 1 | 2 | yes | — |
| 739 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 740 | C2×C4 | C22×D32 | 1 | 2 | yes | — |
| 741 | C2×C3 | — | 2 | 1 | no | — |
| 742 | C2×C3 | — | 2 | 2 | no | — |
| 743 | C2×C3 | — | 4 | 2 | no | — |
| 744 | C2×C3 | — | 4 | 2 | no | — |
| 745 | C2×C3 | — | 4 | 2 | no | — |
| 746 | C2×C3 | — | 8 | 1 | no | — |
| 747 | C2×C3 | D3×H(5,𝔽2) | 1 | 2 | yes | — |
| 748 | C2×C3 | D3×2−1+4 | 1 | 4 | yes | — |
| 749 | D3 | — | 3 | 8 | no | — |
| 750 | D3 | — | 6 | 4 | no | — |
| 751 | D3 | — | 12 | 2 | no | — |
| 752 | D3 | — | 12 | 2 | no | — |
| 753 | D3 | — | 12 | 2 | no | — |
| 754 | D3 | — | 24 | 1 | no | — |
| 755 | C22 | — | 2 | 1 | no | — |
| 756 | C22 | — | 2 | 1 | no | — |
| 757 | C22 | — | 2 | 2 | no | — |
| 758 | C22 | — | 2 | 2 | no | — |
| 759 | C22 | — | 9 | 2 | no | — |
| 760 | C22 | — | 9 | 4 | no | — |
| 761 | C22 | — | 18 | 1 | no | — |
| 762 | C22 | — | 18 | 1 | no | — |
| 763 | C22 | — | 18 | 2 | no | — |
| 764 | C22 | — | 18 | 2 | no | — |
| 765 | C22 | — | 36 | 4 | no | — |
| 766 | C22 | — | 36 | 4 | no | — |
| 767 | C22 | C23×D32 | 1 | 1 | yes | characteristic |
| 768 | C4 | — | 2 | 2 | no | — |
| 769 | C4 | — | 2 | 1 | no | — |
| 770 | C4 | — | 2 | 2 | no | — |
| 771 | C4 | — | 6 | 4 | no | — |
| 772 | C4 | — | 6 | 4 | no | — |
| 773 | C4 | — | 6 | 4 | no | — |
| 774 | C4 | — | 6 | 4 | no | — |
| 775 | C4 | — | 18 | 2 | no | — |
| 776 | C4 | — | 18 | 1 | no | — |
| 777 | C4 | — | 18 | 2 | no | — |
| 778 | C3 | — | 2 | 1 | no | — |
| 779 | C3 | D3×#563 | 1 | 2 | yes | complemented |
| 780 | C2 | — | 4 | 1 | no | — |
| 781 | C2 | — | 4 | 1 | no | — |
| 782 | C2 | — | 9 | 4 | no | — |
| 783 | C2 | — | 36 | 1 | no | — |
| 784 | C2 | — | 36 | 1 | no | — |
| 785 | C2 | #10596675 | 1 | 1 | yes | characteristic |
| 786 | C2 | #10596694 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D32 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C32×#123 | C22 |
| prime radical | C2×D4×C3⋊D3 | C22 |
| hypercenter | #123 | D32 |
| hypocenter | C32 | C2×#563 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#5651 | C2 | semidirect |
| 3. #10595276 | C2 | semidirect |
| 6. #10594925 | C2 | semidirect |
| 7. #10594811 | C2 | semidirect |
| 8. #10594399 | C2 | semidirect |
| 9. #10594374 | C2 | semidirect |
| 10. #10594353 | C2 | semidirect |
| 11. #10594251 | C2 | semidirect |
| 12. #10594154 | C2 | semidirect |
| 13. #10594154 | C2 | semidirect |
| 14. #10594067 | C2 | semidirect |
| 15. #10594036 | C2 | semidirect |
| 33. C3×#924 | C22 | semidirect |
| 34. C3×#889 | C22 | semidirect |
| 35. C3×#888 | C22 | semidirect |
| 36. C3×#879 | C22 | semidirect |
| 37. C3×#879 | C22 | semidirect |
| 38. C3×#878 | C22 | semidirect |
| 39. #63982 | C22 | semidirect |
| 46. #63964 | C22 | semidirect |
| 47. #63956 | C22 | semidirect |
| 48. #63956 | C22 | semidirect |
| 51. #63918 | C22 | semidirect |
| 55. #63895 | C22 | semidirect |
| 56. #63888 | C22 | semidirect |
| 64. #63871 | C22 | semidirect |
| 65. #63868 | C22 | semidirect |
| 66. #63868 | C22 | semidirect |
| 67. #63867 | C22 | semidirect |
| 68. #63865 | C22 | semidirect |
| 70. #63848 | C22 | semidirect |
| 71. #63848 | C22 | semidirect |
| 72. #63846 | C22 | semidirect |
| 73. #63845 | C22 | semidirect |
| 74. #63839 | C22 | semidirect |
| 75. #63839 | C22 | semidirect |
| 91. #5651 | D3 | semidirect |
| 191. #924 | C2×D3 | semidirect |
| 221. #889 | C2×D3 | semidirect |
| 225. #888 | C2×D3 | semidirect |
| 246. #879 | C2×D3 | semidirect |
| 247. #879 | C2×D3 | semidirect |
| 251. #878 | C2×D3 | semidirect |
| 590. C3⋊D3 | #563 | semidirect |
| 701. C32 | C2×#563 | semidirect |
| 779. C3 | D3×#563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×#123 | 2 |
| C3×#5651 | 2 |
| #10595276 | 2 |
| #10595170 | 2 |
| #10595169 | 2 |
| #10594925 | 2 |
| #10594811 | 2 |
| #10594399 | 2 |
| #10594374 | 2 |
| #10594353 | 2 |
| #10594251 | 2 |
| #10594154 | 2 |
| #10594067 | 2 |
| #10594036 | 2 |
| D3×#563 | 3 |