Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1416 conjugacy classes of subgroups.
The subgroup lattice has 812 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D4×#1113 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11724374 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11723560 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C3⋊D3×#214 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#63937 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C3×#63926 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11722880 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11722876 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11722843 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11722831 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11722820 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #10594740 | — | 3 | 1 | no | maximal |
| 13 | D3×#911 | — | 3 | 2 | no | maximal |
| 14 | C22×#1113 | — | 2 | 1 | no | — |
| 15 | C3×D4×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 16 | C3×D4×C3⋊D3 | C22 | 1 | 2 | yes | complemented |
| 17 | #89049 | — | 2 | 1 | no | — |
| 18 | #89049 | — | 2 | 2 | no | — |
| 19 | C4⋊#1113 | C22 | 1 | 1 | yes | characteristic |
| 20 | C4⋊#1113 | C22 | 1 | 2 | yes | complemented |
| 21 | C4×#1113 | C22 | 1 | 1 | yes | characteristic |
| 22 | C3⋊D3×Dic6 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #89014 | C22 | 1 | 2 | yes | complemented |
| 24 | C3×#3802 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C3×#3796 | C22 | 1 | 2 | yes | complemented |
| 26 | #88961 | — | 2 | 2 | no | — |
| 27 | #88953 | — | 2 | 1 | no | — |
| 28 | D32×Dic3 | — | 2 | 1 | no | — |
| 29 | #88861 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | C32×#214 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | C32×#213 | C22 | 1 | 2 | yes | complemented |
| 32 | #88796 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #88796 | C22 | 1 | 2 | yes | complemented |
| 34 | #88793 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | #88789 | C22 | 1 | 2 | yes | complemented |
| 36 | #88787 | C22 | 1 | 2 | yes | complemented |
| 37 | C3⋊D3×C3⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | C3×#3717 | C22 | 1 | 2 | yes | complemented |
| 39 | C3×#3714 | C22 | 1 | 2 | yes | complemented |
| 40 | C3×#3714 | C22 | 1 | 2 | yes | complemented |
| 41 | C3×#3712 | C22 | 1 | 2 | yes | complemented |
| 42 | C3×#3710 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | #64319 | — | 3 | 1 | no | — |
| 44 | D3×#237 | — | 3 | 2 | no | — |
| 45 | D32×D4 | — | 3 | 1 | no | — |
| 46 | D32×D4 | — | 3 | 2 | no | — |
| 47 | SD16×C3⋊D3 | — | 3 | 1 | no | — |
| 48 | #64120 | — | 3 | 2 | no | — |
| 49 | C3×#914 | — | 3 | 2 | no | — |
| 50 | C3×#911 | — | 3 | 2 | no | — |
| 51 | C3×D3×D8 | — | 3 | 2 | no | — |
| 52 | #63940 | — | 3 | 1 | no | — |
| 53 | #63939 | — | 3 | 2 | no | — |
| 54 | #63937 | D3 | 1 | 2 | yes | complemented |
| 55 | #63932 | — | 3 | 2 | no | — |
| 56 | #63932 | — | 3 | 2 | no | — |
| 57 | #63932 | — | 6 | 2 | no | — |
| 58 | D3×#214 | — | 3 | 2 | no | — |
| 59 | D3×#214 | — | 6 | 1 | no | — |
| 60 | #63927 | — | 3 | 2 | no | — |
| 61 | #63926 | D3 | 1 | 1 | yes | characteristic, complemented |
| 62 | #63925 | — | 3 | 2 | no | — |
| 63 | D3×#213 | — | 3 | 2 | no | — |
| 64 | #63798 | — | 3 | 2 | no | — |
| 65 | #63797 | — | 3 | 1 | no | — |
| 66 | #63795 | — | 3 | 2 | no | — |
| 67 | #63795 | — | 3 | 2 | no | — |
| 68 | D3×#204 | — | 3 | 2 | no | — |
| 69 | #63791 | — | 3 | 1 | no | — |
| 70 | D3×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 71 | C22×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 72 | C22×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 73 | C2×#1113 | — | 2 | 1 | no | — |
| 74 | C2×#1113 | — | 2 | 2 | no | — |
| 75 | C2×#1113 | — | 4 | 4 | no | — |
| 76 | C2×#1113 | D4 | 1 | 1 | yes | characteristic |
| 77 | C2×C3×D32 | — | 2 | 1 | no | — |
| 78 | C33×D4 | C23 | 1 | 1 | yes | characteristic |
| 79 | #6308 | C23 | 1 | 1 | yes | characteristic, complemented |
| 80 | C3×#638 | — | 2 | 1 | no | — |
| 81 | C3×#638 | — | 2 | 2 | no | — |
| 82 | C3×C4⋊(C3⋊D3) | C23 | 1 | 1 | yes | characteristic |
| 83 | C3×C4⋊(C3⋊D3) | C23 | 1 | 2 | yes | — |
| 84 | C3×C4×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 85 | C3×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 86 | C32×D12 | C23 | 1 | 2 | yes | complemented |
| 87 | C32×Dic6 | C23 | 1 | 1 | yes | characteristic, complemented |
| 88 | #6295 | — | 2 | 1 | no | — |
| 89 | #6295 | — | 2 | 2 | no | — |
| 90 | #6294 | D4 | 1 | 1 | yes | characteristic |
| 91 | #6294 | D4 | 1 | 2 | yes | — |
| 92 | #6293 | — | 2 | 1 | no | — |
| 93 | #6290 | — | 2 | 2 | no | — |
| 94 | Dic3×C3⋊D3 | — | 2 | 1 | no | — |
| 95 | D3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 96 | C3×#626 | — | 2 | 2 | no | — |
| 97 | C3×#625 | — | 2 | 1 | no | — |
| 98 | C3×D3×Dic3 | — | 2 | 2 | no | — |
| 99 | C3⋊(C3⋊(C3⋊C8)) | C23 | 1 | 1 | yes | characteristic, complemented |
| 100 | C32×C3⋊C8 | C23 | 1 | 2 | yes | complemented |
| 101 | C32×C3⋊C8 | C23 | 1 | 1 | yes | characteristic, complemented |
| 102 | D3×AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 103 | C2×#911 | — | 9 | 1 | no | — |
| 104 | C22×D32 | — | 6 | 1 | no | — |
| 105 | C22×D32 | — | 6 | 2 | no | — |
| 106 | Q8×C3⋊D3 | — | 3 | 1 | no | — |
| 107 | #3830 | — | 3 | 2 | no | — |
| 108 | D4×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 109 | D4×C3⋊D3 | C2×D3 | 1 | 2 | yes | complemented |
| 110 | C3×#239 | — | 3 | 2 | no | — |
| 111 | C3×#237 | — | 3 | 2 | no | — |
| 112 | C3×D3×D4 | — | 3 | 2 | no | — |
| 113 | C3×D3×D4 | — | 3 | 2 | no | — |
| 114 | C3×D3×D4 | — | 3 | 2 | no | — |
| 115 | C3×D3×D4 | — | 3 | 2 | no | — |
| 116 | C3×D3×D4 | — | 6 | 1 | no | — |
| 117 | C3×D3×D4 | — | 6 | 2 | no | — |
| 118 | #3811 | — | 6 | 1 | no | — |
| 119 | #3811 | — | 6 | 2 | no | — |
| 120 | D3×#67 | — | 6 | 2 | no | — |
| 121 | D3×#67 | — | 6 | 2 | no | — |
| 122 | D3×#67 | — | 6 | 2 | no | — |
| 123 | D3×#67 | — | 6 | 2 | no | — |
| 124 | #3805 | — | 6 | 2 | no | — |
| 125 | #3804 | — | 6 | 2 | no | — |
| 126 | C2×D3×Dic3 | — | 6 | 2 | no | — |
| 127 | #3802 | — | 3 | 1 | no | — |
| 128 | #3802 | — | 3 | 2 | no | — |
| 129 | #3802 | — | 6 | 1 | no | — |
| 130 | #3802 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 131 | D3×D12 | — | 3 | 2 | no | — |
| 132 | D3×D12 | — | 3 | 2 | no | — |
| 133 | D3×D12 | — | 3 | 2 | no | — |
| 134 | C4×D32 | — | 3 | 2 | no | — |
| 135 | C4×D32 | — | 3 | 1 | no | — |
| 136 | C4×D32 | — | 6 | 1 | no | — |
| 137 | #3796 | C2×D3 | 1 | 2 | yes | complemented |
| 138 | #3795 | — | 3 | 2 | no | — |
| 139 | #3795 | — | 3 | 2 | no | — |
| 140 | #3795 | — | 6 | 2 | no | — |
| 141 | #3795 | — | 6 | 2 | no | — |
| 142 | D3×Dic6 | — | 3 | 2 | no | — |
| 143 | D3×Dic6 | — | 6 | 1 | no | — |
| 144 | C32×SD16 | — | 3 | 1 | no | — |
| 145 | C32×D8 | — | 3 | 2 | no | — |
| 146 | #3755 | — | 3 | 1 | no | — |
| 147 | #3754 | — | 3 | 2 | no | — |
| 148 | #3754 | — | 3 | 1 | no | — |
| 149 | #3754 | — | 6 | 1 | no | — |
| 150 | #3754 | — | 6 | 2 | no | — |
| 151 | #3754 | — | 12 | 1 | no | — |
| 152 | #3753 | — | 3 | 2 | no | — |
| 153 | #3744 | — | 3 | 2 | no | — |
| 154 | #3744 | — | 3 | 1 | no | — |
| 155 | #3743 | — | 3 | 2 | no | — |
| 156 | C8×C3⋊D3 | — | 3 | 1 | no | — |
| 157 | C3×#215 | — | 3 | 2 | no | — |
| 158 | C3×#214 | — | 2 | 1 | no | — |
| 159 | C3×#214 | C2×D3 | 1 | 2 | yes | complemented |
| 160 | C3×#213 | — | 2 | 2 | no | — |
| 161 | C3×#213 | — | 3 | 2 | no | — |
| 162 | C3×#213 | — | 3 | 2 | no | — |
| 163 | C3×#213 | C2×D3 | 1 | 2 | yes | complemented |
| 164 | C3×#213 | C2×D3 | 1 | 2 | yes | complemented |
| 165 | C3×D24 | — | 3 | 2 | no | — |
| 166 | C3×D24 | — | 3 | 2 | no | — |
| 167 | C3×#204 | — | 3 | 2 | no | — |
| 168 | C3×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 169 | C3×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 170 | C3×D3×C8 | — | 3 | 2 | no | — |
| 171 | #3717 | C2×D3 | 1 | 2 | yes | complemented |
| 172 | #3716 | — | 3 | 2 | no | — |
| 173 | #3716 | — | 3 | 2 | no | — |
| 174 | #3716 | — | 3 | 2 | no | — |
| 175 | #3716 | — | 6 | 1 | no | — |
| 176 | #3716 | — | 6 | 2 | no | — |
| 177 | #3715 | — | 3 | 2 | no | — |
| 178 | #3715 | — | 6 | 1 | no | — |
| 179 | #3714 | C2×D3 | 1 | 2 | yes | complemented |
| 180 | #3714 | C2×D3 | 1 | 2 | yes | complemented |
| 181 | #3713 | — | 3 | 2 | no | — |
| 182 | #3713 | — | 3 | 2 | no | — |
| 183 | #3713 | — | 6 | 2 | no | — |
| 184 | #3712 | C2×D3 | 1 | 2 | yes | complemented |
| 185 | #3711 | — | 3 | 2 | no | — |
| 186 | #3711 | — | 3 | 2 | no | — |
| 187 | #3711 | — | 6 | 2 | no | — |
| 188 | #3710 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 189 | D3×C3⋊C8 | — | 3 | 2 | no | — |
| 190 | D3×C3⋊C8 | — | 6 | 1 | no | — |
| 191 | C22×C33 | — | 2 | 1 | no | — |
| 192 | C2×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 193 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 194 | C2×C3×C3⋊D3 | — | 4 | 4 | no | — |
| 195 | C2×C3×C3⋊D3 | — | 4 | 2 | no | — |
| 196 | C2×C3×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 197 | C2×C3×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 198 | C2×C32×D3 | — | 2 | 2 | no | — |
| 199 | #1113 | — | 2 | 2 | no | — |
| 200 | #1113 | — | 4 | 4 | no | — |
| 201 | #1113 | — | 4 | 2 | no | — |
| 202 | C3×D32 | — | 4 | 2 | no | — |
| 203 | C33×C4 | C24 | 1 | 1 | yes | characteristic |
| 204 | C3⋊(C3⋊Dic3) | — | 2 | 1 | no | — |
| 205 | C3×C3⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 206 | C3×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 207 | C32×Dic3 | — | 2 | 1 | no | — |
| 208 | D3×#41 | — | 9 | 2 | no | — |
| 209 | C2×#237 | — | 9 | 1 | no | — |
| 210 | C2×D3×D4 | — | 9 | 1 | no | — |
| 211 | C2×D3×D4 | — | 9 | 2 | no | — |
| 212 | C3×AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 213 | C2×C3×D8 | — | 9 | 1 | no | — |
| 214 | #949 | — | 9 | 2 | no | — |
| 215 | C2×#214 | — | 9 | 1 | no | — |
| 216 | #932 | — | 9 | 2 | no | — |
| 217 | C2×#213 | — | 9 | 1 | no | — |
| 218 | #914 | — | 3 | 2 | no | — |
| 219 | #914 | — | 9 | 2 | no | — |
| 220 | D3×SD16 | — | 9 | 2 | no | — |
| 221 | D3×SD16 | — | 9 | 2 | no | — |
| 222 | D3×SD16 | — | 18 | 1 | no | — |
| 223 | #911 | — | 3 | 2 | no | — |
| 224 | #911 | — | 9 | 2 | no | — |
| 225 | #911 | — | 9 | 2 | no | — |
| 226 | #911 | — | 9 | 2 | no | — |
| 227 | #911 | — | 9 | 2 | no | — |
| 228 | #911 | — | 9 | 2 | no | — |
| 229 | #911 | — | 18 | 2 | no | — |
| 230 | D3×D8 | — | 3 | 2 | no | — |
| 231 | D3×D8 | — | 9 | 2 | no | — |
| 232 | #908 | — | 9 | 2 | no | — |
| 233 | D3×M16 | — | 9 | 2 | no | — |
| 234 | C2×#204 | — | 9 | 1 | no | — |
| 235 | C2×ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 236 | C22×C3⋊D3 | — | 2 | 1 | no | — |
| 237 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 238 | C22×C3×D3 | — | 6 | 2 | no | — |
| 239 | C22×C3×D3 | — | 6 | 2 | no | — |
| 240 | C22×C3×D3 | — | 6 | 2 | no | — |
| 241 | C22×C3×D3 | — | 6 | 2 | no | — |
| 242 | C22×C3×D3 | — | 12 | 1 | no | — |
| 243 | C22×C3×D3 | — | 12 | 2 | no | — |
| 244 | C2×D32 | — | 2 | 1 | no | — |
| 245 | C2×D32 | — | 3 | 1 | no | — |
| 246 | C2×D32 | — | 3 | 2 | no | — |
| 247 | C2×D32 | — | 6 | 2 | no | — |
| 248 | C2×D32 | — | 6 | 2 | no | — |
| 249 | C2×D32 | — | 6 | 2 | no | — |
| 250 | C2×D32 | — | 6 | 2 | no | — |
| 251 | C2×D32 | — | 6 | 1 | no | — |
| 252 | C2×D32 | — | 12 | 8 | no | — |
| 253 | C2×D32 | — | 12 | 4 | no | — |
| 254 | C32×Q8 | — | 3 | 1 | no | — |
| 255 | C32×D4 | — | 2 | 2 | no | — |
| 256 | C32×D4 | — | 2 | 1 | no | — |
| 257 | C32×D4 | — | 3 | 2 | no | — |
| 258 | C32×D4 | — | 4 | 1 | no | — |
| 259 | C32×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 260 | C32×D4 | C22×D3 | 1 | 2 | yes | — |
| 261 | #638 | — | 2 | 1 | no | — |
| 262 | #638 | — | 2 | 2 | no | — |
| 263 | #638 | — | 6 | 2 | no | — |
| 264 | C2×C3⋊Dic3 | — | 6 | 2 | no | — |
| 265 | C4⋊(C3⋊D3) | C22×D3 | 1 | 1 | yes | characteristic |
| 266 | C4⋊(C3⋊D3) | C22×D3 | 1 | 2 | yes | — |
| 267 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 268 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 269 | C4×C3⋊D3 | C22×D3 | 1 | 2 | yes | — |
| 270 | #634 | — | 3 | 2 | no | — |
| 271 | #634 | — | 3 | 1 | no | — |
| 272 | #634 | — | 6 | 1 | no | — |
| 273 | #634 | — | 6 | 2 | no | — |
| 274 | #634 | — | 6 | 1 | no | — |
| 275 | #634 | — | 12 | 1 | no | — |
| 276 | C3×#67 | — | 6 | 2 | no | — |
| 277 | C3×#67 | — | 6 | 2 | no | — |
| 278 | C3×#67 | — | 6 | 2 | no | — |
| 279 | C3×#67 | — | 6 | 2 | no | — |
| 280 | C3×#67 | — | 6 | 2 | no | — |
| 281 | C3×#67 | — | 12 | 2 | no | — |
| 282 | C3×#67 | — | 12 | 1 | no | — |
| 283 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 284 | C3×D12 | — | 2 | 2 | no | — |
| 285 | C3×D12 | — | 3 | 2 | no | — |
| 286 | C3×D12 | — | 3 | 2 | no | — |
| 287 | C3×D12 | — | 3 | 2 | no | — |
| 288 | C3×D12 | — | 6 | 2 | no | — |
| 289 | C3×D12 | — | 6 | 1 | no | — |
| 290 | C3×D12 | — | 6 | 2 | no | — |
| 291 | C3×D12 | C22×D3 | 1 | 2 | yes | complemented |
| 292 | C3×D12 | C22×D3 | 1 | 2 | yes | complemented |
| 293 | C3×C4×D3 | — | 3 | 2 | no | — |
| 294 | C3×C4×D3 | — | 3 | 2 | no | — |
| 295 | C3×C4×D3 | — | 3 | 2 | no | — |
| 296 | C3×C4×D3 | — | 6 | 1 | no | — |
| 297 | C3×C4×D3 | — | 6 | 2 | no | — |
| 298 | C3×C4×D3 | — | 6 | 2 | no | — |
| 299 | C3×Dic6 | — | 2 | 1 | no | — |
| 300 | C3×Dic6 | C22×D3 | 1 | 2 | yes | complemented |
| 301 | #627 | — | 6 | 2 | no | — |
| 302 | #627 | — | 12 | 1 | no | — |
| 303 | #626 | — | 2 | 2 | no | — |
| 304 | #626 | — | 6 | 2 | no | — |
| 305 | #626 | — | 6 | 2 | no | — |
| 306 | #626 | — | 6 | 2 | no | — |
| 307 | #625 | — | 2 | 1 | no | — |
| 308 | #625 | — | 6 | 2 | no | — |
| 309 | #625 | — | 6 | 2 | no | — |
| 310 | #625 | — | 6 | 2 | no | — |
| 311 | #625 | — | 6 | 1 | no | — |
| 312 | #625 | — | 12 | 2 | no | — |
| 313 | #624 | — | 3 | 1 | no | — |
| 314 | #624 | — | 3 | 2 | no | — |
| 315 | D3×Dic3 | — | 2 | 2 | no | — |
| 316 | D3×Dic3 | — | 3 | 2 | no | — |
| 317 | D3×Dic3 | — | 3 | 2 | no | — |
| 318 | D3×Dic3 | — | 3 | 2 | no | — |
| 319 | D3×Dic3 | — | 6 | 2 | no | — |
| 320 | D3×Dic3 | — | 6 | 2 | no | — |
| 321 | D3×Dic3 | — | 6 | 2 | no | — |
| 322 | D3×Dic3 | — | 12 | 2 | no | — |
| 323 | D3×Dic3 | — | 12 | 1 | no | — |
| 324 | C32×C8 | — | 3 | 2 | no | — |
| 325 | C32×C8 | — | 3 | 1 | no | — |
| 326 | C3⋊(C3⋊C8) | — | 3 | 2 | no | — |
| 327 | C3⋊(C3⋊C8) | — | 3 | 1 | no | — |
| 328 | C3⋊(C3⋊C8) | — | 6 | 1 | no | — |
| 329 | C3⋊(C3⋊C8) | — | 6 | 2 | no | — |
| 330 | C3⋊(C3⋊C8) | — | 12 | 1 | no | — |
| 331 | C3×C3⋊C8 | — | 2 | 1 | no | — |
| 332 | C3×C3⋊C8 | — | 2 | 2 | no | — |
| 333 | C3×C3⋊C8 | C22×D3 | 1 | 2 | yes | complemented |
| 334 | C3×C3⋊C8 | C22×D3 | 1 | 2 | yes | complemented |
| 335 | C3×C3⋊C8 | C22×D3 | 1 | 2 | yes | complemented |
| 336 | C2×AGL(1,ℤ/8) | — | 27 | 1 | no | Sylow |
| 337 | C2×C33 | — | 4 | 1 | no | — |
| 338 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 339 | C3×C3⋊D3 | — | 2 | 2 | no | — |
| 340 | C3×C3⋊D3 | — | 4 | 2 | no | — |
| 341 | C3×C3⋊D3 | — | 4 | 1 | no | — |
| 342 | C3×C3⋊D3 | AGL(1,ℤ/8) | 1 | 2 | yes | complemented |
| 343 | C32×D3 | — | 4 | 2 | no | — |
| 344 | C23×D3 | — | 18 | 2 | no | — |
| 345 | C23×D3 | — | 18 | 1 | no | — |
| 346 | C3×#41 | — | 9 | 2 | no | — |
| 347 | C2×C3×D4 | — | 9 | 1 | no | — |
| 348 | C2×C3×D4 | — | 9 | 2 | no | — |
| 349 | C2×C3×D4 | — | 9 | 1 | no | — |
| 350 | C2×#67 | — | 18 | 2 | no | — |
| 351 | C2×#67 | — | 18 | 1 | no | — |
| 352 | C2×#67 | — | 18 | 1 | no | — |
| 353 | C22×Dic3 | — | 18 | 1 | no | — |
| 354 | #239 | — | 3 | 2 | no | — |
| 355 | D3×Q8 | — | 9 | 2 | no | — |
| 356 | D3×Q8 | — | 18 | 1 | no | — |
| 357 | #237 | — | 3 | 2 | no | — |
| 358 | #237 | — | 9 | 2 | no | — |
| 359 | #237 | — | 9 | 2 | no | — |
| 360 | #237 | — | 18 | 2 | no | — |
| 361 | #237 | — | 18 | 2 | no | — |
| 362 | #237 | — | 18 | 2 | no | — |
| 363 | D3×D4 | — | 3 | 2 | no | — |
| 364 | D3×D4 | — | 3 | 2 | no | — |
| 365 | D3×D4 | — | 3 | 2 | no | — |
| 366 | D3×D4 | — | 3 | 2 | no | — |
| 367 | D3×D4 | — | 6 | 2 | no | — |
| 368 | D3×D4 | — | 6 | 1 | no | — |
| 369 | D3×D4 | — | 9 | 2 | no | — |
| 370 | D3×D4 | — | 9 | 2 | no | — |
| 371 | D3×D4 | — | 9 | 2 | no | — |
| 372 | D3×D4 | — | 18 | 2 | no | — |
| 373 | D3×D4 | — | 18 | 2 | no | — |
| 374 | D3×D4 | — | 18 | 2 | no | — |
| 375 | D3×D4 | — | 18 | 2 | no | — |
| 376 | #235 | — | 9 | 2 | no | — |
| 377 | #235 | — | 18 | 2 | no | — |
| 378 | C2×D12 | — | 9 | 1 | no | — |
| 379 | C2×D12 | — | 9 | 2 | no | — |
| 380 | C2×C4×D3 | — | 9 | 1 | no | — |
| 381 | C2×C4×D3 | — | 9 | 2 | no | — |
| 382 | C2×C4×D3 | — | 18 | 2 | no | — |
| 383 | C2×Dic6 | — | 9 | 1 | no | — |
| 384 | C3×SD16 | — | 3 | 2 | no | — |
| 385 | C3×SD16 | — | 6 | 1 | no | — |
| 386 | C3×SD16 | — | 9 | 2 | no | — |
| 387 | C3×D8 | — | 3 | 2 | no | — |
| 388 | C3×D8 | — | 3 | 2 | no | — |
| 389 | C3×D8 | — | 6 | 2 | no | — |
| 390 | C3×D8 | — | 9 | 2 | no | — |
| 391 | C3×D8 | — | 9 | 2 | no | — |
| 392 | C3×M16 | — | 9 | 2 | no | — |
| 393 | C2×C3×C8 | — | 9 | 1 | no | — |
| 394 | #215 | — | 3 | 2 | no | — |
| 395 | #215 | — | 9 | 2 | no | — |
| 396 | #215 | — | 18 | 1 | no | — |
| 397 | #214 | — | 9 | 1 | no | — |
| 398 | #214 | — | 9 | 2 | no | — |
| 399 | #214 | — | 9 | 1 | no | — |
| 400 | #214 | — | 9 | 1 | no | — |
| 401 | #214 | — | 9 | 2 | no | — |
| 402 | #214 | — | 18 | 2 | no | — |
| 403 | #214 | — | 18 | 1 | no | — |
| 404 | #214 | — | 36 | 1 | no | — |
| 405 | #214 | D32 | 1 | 1 | yes | characteristic, complemented |
| 406 | #213 | — | 3 | 2 | no | — |
| 407 | #213 | — | 3 | 2 | no | — |
| 408 | #213 | — | 9 | 2 | no | — |
| 409 | #213 | — | 9 | 2 | no | — |
| 410 | #213 | — | 9 | 2 | no | — |
| 411 | #213 | — | 18 | 2 | no | — |
| 412 | #213 | D32 | 1 | 2 | yes | complemented |
| 413 | #208 | — | 9 | 2 | no | — |
| 414 | C2×C3⋊C8 | — | 9 | 1 | no | — |
| 415 | D24 | — | 3 | 2 | no | — |
| 416 | D24 | — | 3 | 2 | no | — |
| 417 | #204 | — | 3 | 2 | no | — |
| 418 | #204 | — | 9 | 2 | no | — |
| 419 | #204 | — | 9 | 2 | no | — |
| 420 | #204 | — | 9 | 2 | no | — |
| 421 | #204 | — | 18 | 2 | no | — |
| 422 | #204 | — | 18 | 1 | no | — |
| 423 | ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 424 | ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 425 | ΓL(1,𝔽25) | — | 9 | 2 | no | — |
| 426 | ΓL(1,𝔽25) | — | 9 | 2 | no | — |
| 427 | ΓL(1,𝔽25) | — | 18 | 2 | no | — |
| 428 | D3×C8 | — | 3 | 2 | no | — |
| 429 | D3×C8 | — | 9 | 2 | no | — |
| 430 | D3×C8 | — | 18 | 1 | no | — |
| 431 | C22×C32 | — | 2 | 1 | no | — |
| 432 | C22×C32 | — | 2 | 2 | no | — |
| 433 | C22×C32 | — | 4 | 1 | no | — |
| 434 | C22×C32 | — | 4 | 2 | no | — |
| 435 | C22×C32 | — | 6 | 2 | no | — |
| 436 | C22×C32 | — | 8 | 1 | no | — |
| 437 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 438 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 439 | C2×C3⋊D3 | — | 4 | 4 | no | — |
| 440 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 441 | C2×C3⋊D3 | D3×D4 | 1 | 2 | yes | — |
| 442 | C2×C3⋊D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 443 | C2×C3×D3 | — | 2 | 2 | no | — |
| 444 | C2×C3×D3 | — | 2 | 2 | no | — |
| 445 | C2×C3×D3 | — | 3 | 2 | no | — |
| 446 | C2×C3×D3 | — | 3 | 2 | no | — |
| 447 | C2×C3×D3 | — | 3 | 2 | no | — |
| 448 | C2×C3×D3 | — | 4 | 2 | no | — |
| 449 | C2×C3×D3 | — | 6 | 1 | no | — |
| 450 | C2×C3×D3 | — | 6 | 2 | no | — |
| 451 | C2×C3×D3 | — | 6 | 2 | no | — |
| 452 | C2×C3×D3 | — | 6 | 2 | no | — |
| 453 | C2×C3×D3 | — | 6 | 2 | no | — |
| 454 | C2×C3×D3 | — | 12 | 1 | no | — |
| 455 | C2×C3×D3 | — | 12 | 2 | no | — |
| 456 | C2×C3×D3 | — | 12 | 4 | no | — |
| 457 | C2×C3×D3 | — | 12 | 4 | no | — |
| 458 | C2×C3×D3 | — | 12 | 4 | no | — |
| 459 | C2×C3×D3 | — | 12 | 4 | no | — |
| 460 | C2×C3×D3 | — | 24 | 2 | no | — |
| 461 | C2×C3×D3 | — | 24 | 4 | no | — |
| 462 | D32 | — | 4 | 2 | no | — |
| 463 | D32 | — | 6 | 4 | no | — |
| 464 | D32 | — | 6 | 2 | no | — |
| 465 | D32 | — | 12 | 4 | no | — |
| 466 | D32 | — | 12 | 4 | no | — |
| 467 | D32 | — | 12 | 4 | no | — |
| 468 | D32 | — | 12 | 4 | no | — |
| 469 | D32 | — | 12 | 2 | no | — |
| 470 | C32×C4 | — | 2 | 1 | no | — |
| 471 | C32×C4 | — | 2 | 2 | no | — |
| 472 | C32×C4 | — | 4 | 1 | no | — |
| 473 | C32×C4 | — | 6 | 1 | no | — |
| 474 | C32×C4 | C23×D3 | 1 | 2 | yes | — |
| 475 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 476 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 477 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 478 | C3⋊Dic3 | — | 12 | 2 | no | — |
| 479 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 480 | C3⋊Dic3 | — | 24 | 1 | no | — |
| 481 | C3⋊Dic3 | D3×D4 | 1 | 2 | yes | — |
| 482 | C3⋊Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 483 | C3×Dic3 | — | 2 | 2 | no | — |
| 484 | C3×Dic3 | — | 3 | 2 | no | — |
| 485 | C3×Dic3 | — | 3 | 2 | no | — |
| 486 | C3×Dic3 | — | 3 | 2 | no | — |
| 487 | C3×Dic3 | — | 4 | 1 | no | — |
| 488 | C3×Dic3 | — | 6 | 2 | no | — |
| 489 | C3×Dic3 | — | 6 | 1 | no | — |
| 490 | C2×#41 | — | 27 | 1 | no | — |
| 491 | C22×D4 | — | 27 | 1 | no | — |
| 492 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 493 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 494 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 495 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 496 | C2×SD16 | — | 27 | 1 | no | — |
| 497 | C2×SD16 | — | 27 | 1 | no | — |
| 498 | C2×D8 | — | 9 | 1 | no | — |
| 499 | C2×D8 | — | 27 | 1 | no | — |
| 500 | C2×M16 | — | 27 | 1 | no | — |
| 501 | C33 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 502 | C23×C3 | — | 18 | 1 | no | — |
| 503 | C23×C3 | — | 18 | 2 | no | — |
| 504 | C23×C3 | — | 18 | 1 | no | — |
| 505 | C22×D3 | — | 6 | 2 | no | — |
| 506 | C22×D3 | — | 6 | 2 | no | — |
| 507 | C22×D3 | — | 6 | 2 | no | — |
| 508 | C22×D3 | — | 6 | 2 | no | — |
| 509 | C22×D3 | — | 9 | 2 | no | — |
| 510 | C22×D3 | — | 9 | 1 | no | — |
| 511 | C22×D3 | — | 12 | 1 | no | — |
| 512 | C22×D3 | — | 12 | 2 | no | — |
| 513 | C22×D3 | — | 18 | 2 | no | — |
| 514 | C22×D3 | — | 18 | 2 | no | — |
| 515 | C22×D3 | — | 18 | 2 | no | — |
| 516 | C22×D3 | — | 18 | 1 | no | — |
| 517 | C22×D3 | — | 18 | 2 | no | — |
| 518 | C22×D3 | — | 36 | 8 | no | — |
| 519 | C22×D3 | — | 36 | 4 | no | — |
| 520 | C3×Q8 | — | 3 | 2 | no | — |
| 521 | C3×Q8 | — | 6 | 1 | no | — |
| 522 | C3×D4 | — | 2 | 2 | no | — |
| 523 | C3×D4 | — | 2 | 1 | no | — |
| 524 | C3×D4 | — | 3 | 2 | no | — |
| 525 | C3×D4 | — | 3 | 2 | no | — |
| 526 | C3×D4 | — | 4 | 1 | no | — |
| 527 | C3×D4 | — | 6 | 2 | no | — |
| 528 | C3×D4 | — | 9 | 2 | no | — |
| 529 | C3×D4 | — | 9 | 1 | no | — |
| 530 | C3×D4 | — | 18 | 2 | no | — |
| 531 | C3×D4 | — | 18 | 1 | no | — |
| 532 | C3×D4 | — | 18 | 2 | no | — |
| 533 | C3×D4 | — | 18 | 1 | no | — |
| 534 | C3×D4 | C2×D32 | 1 | 2 | yes | — |
| 535 | C3×D4 | C2×D32 | 1 | 1 | yes | characteristic |
| 536 | C2×C3×C4 | — | 9 | 1 | no | — |
| 537 | C2×C3×C4 | — | 9 | 2 | no | — |
| 538 | C2×C3×C4 | — | 18 | 2 | no | — |
| 539 | #67 | — | 6 | 2 | no | — |
| 540 | #67 | — | 6 | 2 | no | — |
| 541 | #67 | — | 6 | 2 | no | — |
| 542 | #67 | — | 6 | 2 | no | — |
| 543 | #67 | — | 6 | 2 | no | — |
| 544 | #67 | — | 12 | 1 | no | — |
| 545 | #67 | — | 12 | 2 | no | — |
| 546 | #67 | — | 18 | 2 | no | — |
| 547 | #67 | — | 18 | 2 | no | — |
| 548 | #67 | — | 18 | 2 | no | — |
| 549 | #67 | — | 18 | 2 | no | — |
| 550 | #67 | — | 18 | 2 | no | — |
| 551 | #67 | — | 18 | 2 | no | — |
| 552 | #67 | — | 36 | 2 | no | — |
| 553 | C2×Dic3 | — | 6 | 2 | no | — |
| 554 | C2×Dic3 | — | 9 | 2 | no | — |
| 555 | C2×Dic3 | — | 9 | 1 | no | — |
| 556 | C2×Dic3 | — | 18 | 1 | no | — |
| 557 | C2×Dic3 | — | 18 | 2 | no | — |
| 558 | C2×Dic3 | — | 18 | 2 | no | — |
| 559 | C2×Dic3 | — | 36 | 2 | no | — |
| 560 | D12 | — | 3 | 2 | no | — |
| 561 | D12 | — | 3 | 2 | no | — |
| 562 | D12 | — | 3 | 2 | no | — |
| 563 | D12 | — | 6 | 2 | no | — |
| 564 | D12 | — | 6 | 1 | no | — |
| 565 | D12 | — | 6 | 2 | no | — |
| 566 | D12 | — | 18 | 1 | no | — |
| 567 | D12 | — | 18 | 2 | no | — |
| 568 | D12 | C2×D32 | 1 | 2 | yes | complemented |
| 569 | C4×D3 | — | 3 | 2 | no | — |
| 570 | C4×D3 | — | 3 | 2 | no | — |
| 571 | C4×D3 | — | 3 | 2 | no | — |
| 572 | C4×D3 | — | 6 | 1 | no | — |
| 573 | C4×D3 | — | 6 | 2 | no | — |
| 574 | C4×D3 | — | 6 | 2 | no | — |
| 575 | C4×D3 | — | 9 | 2 | no | — |
| 576 | C4×D3 | — | 9 | 2 | no | — |
| 577 | C4×D3 | — | 9 | 2 | no | — |
| 578 | C4×D3 | — | 18 | 2 | no | — |
| 579 | C4×D3 | — | 18 | 2 | no | — |
| 580 | C4×D3 | — | 36 | 1 | no | — |
| 581 | Dic6 | — | 9 | 1 | no | — |
| 582 | Dic6 | — | 9 | 2 | no | — |
| 583 | Dic6 | — | 18 | 2 | no | — |
| 584 | Dic6 | — | 18 | 1 | no | — |
| 585 | Dic6 | — | 18 | 1 | no | — |
| 586 | Dic6 | — | 18 | 2 | no | — |
| 587 | Dic6 | — | 36 | 1 | no | — |
| 588 | Dic6 | — | 36 | 1 | no | — |
| 589 | Dic6 | C2×D32 | 1 | 1 | yes | characteristic, complemented |
| 590 | C3×C8 | — | 3 | 2 | no | — |
| 591 | C3×C8 | — | 3 | 2 | no | — |
| 592 | C3×C8 | — | 3 | 2 | no | — |
| 593 | C3×C8 | — | 6 | 1 | no | — |
| 594 | C3×C8 | — | 6 | 2 | no | — |
| 595 | C3⋊C8 | — | 9 | 2 | no | — |
| 596 | C3⋊C8 | — | 9 | 1 | no | — |
| 597 | C3⋊C8 | — | 18 | 1 | no | — |
| 598 | C3⋊C8 | — | 18 | 2 | no | — |
| 599 | C3⋊C8 | — | 36 | 1 | no | — |
| 600 | C3⋊C8 | C2×D32 | 1 | 2 | yes | complemented |
| 601 | C3⋊C8 | C2×D32 | 1 | 1 | yes | characteristic, complemented |
| 602 | C2×C32 | — | 2 | 1 | no | — |
| 603 | C2×C32 | — | 2 | 2 | no | — |
| 604 | C2×C32 | — | 4 | 1 | no | — |
| 605 | C2×C32 | — | 4 | 1 | no | — |
| 606 | C2×C32 | — | 4 | 2 | no | — |
| 607 | C2×C32 | — | 8 | 2 | no | — |
| 608 | C2×C32 | — | 8 | 1 | no | — |
| 609 | C2×C32 | — | 12 | 2 | no | — |
| 610 | C2×C32 | — | 16 | 1 | no | — |
| 611 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 612 | C2×C32 | C2×D3×D4 | 1 | 2 | yes | — |
| 613 | C3⋊D3 | — | 2 | 2 | no | — |
| 614 | C3⋊D3 | — | 4 | 1 | no | — |
| 615 | C3⋊D3 | — | 4 | 2 | no | — |
| 616 | C3⋊D3 | #911 | 1 | 2 | yes | complemented |
| 617 | C3×D3 | — | 3 | 4 | no | — |
| 618 | C3×D3 | — | 4 | 2 | no | — |
| 619 | C3×D3 | — | 4 | 2 | no | — |
| 620 | C3×D3 | — | 6 | 2 | no | — |
| 621 | C3×D3 | — | 6 | 2 | no | — |
| 622 | C3×D3 | — | 6 | 2 | no | — |
| 623 | C3×D3 | — | 8 | 2 | no | — |
| 624 | C3×D3 | — | 12 | 2 | no | — |
| 625 | C3×D3 | — | 12 | 2 | no | — |
| 626 | C3×D3 | — | 12 | 2 | no | — |
| 627 | C3×D3 | — | 12 | 2 | no | — |
| 628 | C3×D3 | — | 24 | 2 | no | — |
| 629 | C3×D3 | — | 24 | 1 | no | — |
| 630 | C24 | — | 54 | 1 | no | — |
| 631 | #41 | — | 9 | 2 | no | — |
| 632 | #41 | — | 27 | 2 | no | — |
| 633 | #41 | — | 54 | 2 | no | — |
| 634 | C2×Q8 | — | 27 | 1 | no | — |
| 635 | C2×D4 | — | 9 | 1 | no | — |
| 636 | C2×D4 | — | 9 | 1 | no | — |
| 637 | C2×D4 | — | 9 | 2 | no | — |
| 638 | C2×D4 | — | 27 | 1 | no | — |
| 639 | C2×D4 | — | 27 | 2 | no | — |
| 640 | C2×D4 | — | 54 | 1 | no | — |
| 641 | C2×D4 | — | 54 | 2 | no | — |
| 642 | C2×D4 | — | 54 | 1 | no | — |
| 643 | C22×C4 | — | 27 | 1 | no | — |
| 644 | C22×C4 | — | 54 | 1 | no | — |
| 645 | SD16 | — | 3 | 1 | no | — |
| 646 | SD16 | — | 9 | 2 | no | — |
| 647 | SD16 | — | 27 | 2 | no | — |
| 648 | SD16 | — | 27 | 1 | no | — |
| 649 | SD16 | — | 27 | 1 | no | — |
| 650 | SD16 | — | 27 | 1 | no | — |
| 651 | D8 | — | 3 | 2 | no | — |
| 652 | D8 | — | 9 | 2 | no | — |
| 653 | D8 | — | 9 | 2 | no | — |
| 654 | D8 | — | 27 | 2 | no | — |
| 655 | M16 | — | 9 | 2 | no | — |
| 656 | M16 | — | 27 | 2 | no | — |
| 657 | C2×C8 | — | 9 | 1 | no | — |
| 658 | C2×C8 | — | 27 | 1 | no | — |
| 659 | C22×C3 | — | 2 | 2 | no | — |
| 660 | C22×C3 | — | 2 | 1 | no | — |
| 661 | C22×C3 | — | 4 | 1 | no | — |
| 662 | C22×C3 | — | 4 | 2 | no | — |
| 663 | C22×C3 | — | 6 | 2 | no | — |
| 664 | C22×C3 | — | 6 | 2 | no | — |
| 665 | C22×C3 | — | 8 | 1 | no | — |
| 666 | C22×C3 | — | 9 | 1 | no | — |
| 667 | C22×C3 | — | 9 | 2 | no | — |
| 668 | C22×C3 | — | 12 | 2 | no | — |
| 669 | C22×C3 | — | 18 | 2 | no | — |
| 670 | C22×C3 | — | 18 | 1 | no | — |
| 671 | C22×C3 | — | 36 | 2 | no | — |
| 672 | C22×C3 | — | 36 | 4 | no | — |
| 673 | C22×C3 | — | 36 | 2 | no | — |
| 674 | C2×D3 | — | 2 | 2 | no | — |
| 675 | C2×D3 | — | 3 | 2 | no | — |
| 676 | C2×D3 | — | 3 | 2 | no | — |
| 677 | C2×D3 | — | 3 | 2 | no | — |
| 678 | C2×D3 | — | 6 | 1 | no | — |
| 679 | C2×D3 | — | 6 | 2 | no | — |
| 680 | C2×D3 | — | 6 | 2 | no | — |
| 681 | C2×D3 | — | 6 | 2 | no | — |
| 682 | C2×D3 | — | 6 | 2 | no | — |
| 683 | C2×D3 | — | 12 | 1 | no | — |
| 684 | C2×D3 | — | 12 | 2 | no | — |
| 685 | C2×D3 | — | 12 | 4 | no | — |
| 686 | C2×D3 | — | 12 | 4 | no | — |
| 687 | C2×D3 | — | 12 | 4 | no | — |
| 688 | C2×D3 | — | 12 | 4 | no | — |
| 689 | C2×D3 | — | 18 | 4 | no | — |
| 690 | C2×D3 | — | 18 | 2 | no | — |
| 691 | C2×D3 | — | 24 | 2 | no | — |
| 692 | C2×D3 | — | 24 | 4 | no | — |
| 693 | C2×D3 | — | 36 | 4 | no | — |
| 694 | C2×D3 | — | 36 | 4 | no | — |
| 695 | C2×D3 | — | 36 | 4 | no | — |
| 696 | C2×D3 | — | 36 | 2 | no | — |
| 697 | C2×D3 | — | 36 | 4 | no | — |
| 698 | C3×C4 | — | 2 | 2 | no | — |
| 699 | C3×C4 | — | 2 | 1 | no | — |
| 700 | C3×C4 | — | 4 | 1 | no | — |
| 701 | C3×C4 | — | 6 | 2 | no | — |
| 702 | C3×C4 | — | 9 | 1 | no | — |
| 703 | C3×C4 | — | 9 | 2 | no | — |
| 704 | C3×C4 | — | 12 | 1 | no | — |
| 705 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 706 | C3×C4 | C22×D32 | 1 | 2 | yes | — |
| 707 | Dic3 | — | 2 | 1 | no | — |
| 708 | Dic3 | — | 3 | 2 | no | — |
| 709 | Dic3 | — | 3 | 2 | no | — |
| 710 | Dic3 | — | 3 | 2 | no | — |
| 711 | Dic3 | — | 6 | 1 | no | — |
| 712 | Dic3 | — | 6 | 2 | no | — |
| 713 | Dic3 | — | 18 | 2 | no | — |
| 714 | Dic3 | — | 18 | 1 | no | — |
| 715 | Dic3 | — | 36 | 1 | no | — |
| 716 | Dic3 | — | 36 | 2 | no | — |
| 717 | Dic3 | — | 72 | 1 | no | — |
| 718 | C32 | — | 2 | 2 | no | — |
| 719 | C32 | — | 2 | 1 | no | — |
| 720 | C32 | — | 4 | 1 | no | — |
| 721 | C32 | C2×#911 | 1 | 1 | yes | characteristic, complemented |
| 722 | C32 | D3×AGL(1,ℤ/8) | 1 | 2 | yes | complemented |
| 723 | C23 | — | 18 | 1 | no | — |
| 724 | C23 | — | 18 | 2 | no | — |
| 725 | C23 | — | 18 | 1 | no | — |
| 726 | C23 | — | 27 | 1 | no | — |
| 727 | C23 | — | 54 | 1 | no | — |
| 728 | C23 | — | 54 | 2 | no | — |
| 729 | C23 | — | 108 | 4 | no | — |
| 730 | Q8 | — | 3 | 1 | no | — |
| 731 | Q8 | — | 27 | 1 | no | — |
| 732 | Q8 | — | 54 | 1 | no | — |
| 733 | D4 | — | 3 | 2 | no | — |
| 734 | D4 | — | 9 | 1 | no | — |
| 735 | D4 | — | 9 | 2 | no | — |
| 736 | D4 | — | 18 | 2 | no | — |
| 737 | D4 | — | 18 | 2 | no | — |
| 738 | D4 | — | 18 | 1 | no | — |
| 739 | D4 | — | 18 | 1 | no | — |
| 740 | D4 | — | 54 | 2 | no | — |
| 741 | D4 | — | 54 | 1 | no | — |
| 742 | D4 | — | 54 | 2 | no | — |
| 743 | D4 | D33 | 1 | 1 | yes | characteristic |
| 744 | C2×C4 | — | 9 | 1 | no | — |
| 745 | C2×C4 | — | 9 | 2 | no | — |
| 746 | C2×C4 | — | 18 | 2 | no | — |
| 747 | C2×C4 | — | 27 | 1 | no | — |
| 748 | C2×C4 | — | 27 | 2 | no | — |
| 749 | C2×C4 | — | 54 | 1 | no | — |
| 750 | C2×C4 | — | 54 | 2 | no | — |
| 751 | C8 | — | 3 | 2 | no | — |
| 752 | C8 | — | 3 | 1 | no | — |
| 753 | C8 | — | 27 | 1 | no | — |
| 754 | C2×C3 | — | 2 | 1 | no | — |
| 755 | C2×C3 | — | 2 | 2 | no | — |
| 756 | C2×C3 | — | 4 | 2 | no | — |
| 757 | C2×C3 | — | 4 | 1 | no | — |
| 758 | C2×C3 | — | 4 | 1 | no | — |
| 759 | C2×C3 | — | 8 | 1 | no | — |
| 760 | C2×C3 | — | 8 | 2 | no | — |
| 761 | C2×C3 | — | 9 | 2 | no | — |
| 762 | C2×C3 | — | 12 | 2 | no | — |
| 763 | C2×C3 | — | 12 | 2 | no | — |
| 764 | C2×C3 | — | 16 | 1 | no | — |
| 765 | C2×C3 | — | 18 | 2 | no | — |
| 766 | C2×C3 | — | 24 | 2 | no | — |
| 767 | C2×C3 | — | 36 | 2 | no | — |
| 768 | C2×C3 | — | 36 | 1 | no | — |
| 769 | C2×C3 | D32×D4 | 1 | 2 | yes | — |
| 770 | C2×C3 | D32×D4 | 1 | 1 | yes | characteristic |
| 771 | D3 | — | 3 | 4 | no | — |
| 772 | D3 | — | 4 | 2 | no | — |
| 773 | D3 | — | 6 | 2 | no | — |
| 774 | D3 | — | 6 | 2 | no | — |
| 775 | D3 | — | 6 | 2 | no | — |
| 776 | D3 | — | 12 | 2 | no | — |
| 777 | D3 | — | 12 | 2 | no | — |
| 778 | D3 | — | 12 | 2 | no | — |
| 779 | D3 | — | 12 | 2 | no | — |
| 780 | D3 | — | 24 | 1 | no | — |
| 781 | D3 | — | 24 | 2 | no | — |
| 782 | C22 | — | 2 | 1 | no | — |
| 783 | C22 | — | 6 | 2 | no | — |
| 784 | C22 | — | 9 | 1 | no | — |
| 785 | C22 | — | 9 | 2 | no | — |
| 786 | C22 | — | 18 | 1 | no | — |
| 787 | C22 | — | 18 | 2 | no | — |
| 788 | C22 | — | 36 | 2 | no | — |
| 789 | C22 | — | 36 | 4 | no | — |
| 790 | C22 | — | 36 | 2 | no | — |
| 791 | C22 | — | 54 | 2 | no | — |
| 792 | C22 | — | 108 | 2 | no | — |
| 793 | C22 | — | 108 | 4 | no | — |
| 794 | C4 | — | 6 | 1 | no | — |
| 795 | C4 | — | 9 | 2 | no | — |
| 796 | C4 | — | 9 | 1 | no | — |
| 797 | C4 | — | 54 | 1 | no | — |
| 798 | C4 | C2×D33 | 1 | 1 | yes | characteristic |
| 799 | C3 | — | 2 | 1 | no | — |
| 800 | C3 | — | 2 | 2 | no | — |
| 801 | C3 | — | 4 | 1 | no | — |
| 802 | C3 | D3×#911 | 1 | 2 | yes | complemented |
| 803 | C3 | #10594740 | 1 | 1 | yes | characteristic, complemented |
| 804 | C2 | — | 4 | 1 | no | — |
| 805 | C2 | — | 9 | 2 | no | — |
| 806 | C2 | — | 12 | 2 | no | — |
| 807 | C2 | — | 18 | 2 | no | — |
| 808 | C2 | — | 36 | 1 | no | — |
| 809 | C2 | — | 36 | 2 | no | — |
| 810 | C2 | #11724440 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #11724440 |
| commutator, cosocle | C33×C4 | C24 |
| Frattini | C4 | C2×D33 |
| Fitting | C33×D4 | C23 |
| socle | C2×C33 | C22×D4 |
| hypercenter | D4 | D33 |
| hypocenter | C33 | C2×AGL(1,ℤ/8) |
| LCS | G ▷ C33×C4 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D4×#1113 | C2 | semidirect |
| 2. #11724374 | C2 | semidirect |
| 3. #11723560 | C2 | semidirect |
| 4. C3⋊D3×#214 | C2 | semidirect |
| 5. C3×#63937 | C2 | semidirect |
| 6. C3×#63926 | C2 | semidirect |
| 7. #11722880 | C2 | semidirect |
| 8. #11722876 | C2 | semidirect |
| 9. #11722843 | C2 | semidirect |
| 10. #11722831 | C2 | semidirect |
| 11. #11722820 | C2 | semidirect |
| 16. C3×D4×C3⋊D3 | C22 | semidirect |
| 20. C4⋊#1113 | C22 | semidirect |
| 22. C3⋊D3×Dic6 | C22 | semidirect |
| 23. #89014 | C22 | semidirect |
| 24. C3×#3802 | C22 | semidirect |
| 25. C3×#3796 | C22 | semidirect |
| 29. #88861 | C22 | semidirect |
| 30. C32×#214 | C22 | semidirect |
| 31. C32×#213 | C22 | semidirect |
| 32. #88796 | C22 | semidirect |
| 33. #88796 | C22 | semidirect |
| 34. #88793 | C22 | semidirect |
| 35. #88789 | C22 | semidirect |
| 36. #88787 | C22 | semidirect |
| 37. C3⋊D3×C3⋊C8 | C22 | semidirect |
| 38. C3×#3717 | C22 | semidirect |
| 39. C3×#3714 | C22 | semidirect |
| 40. C3×#3714 | C22 | semidirect |
| 41. C3×#3712 | C22 | semidirect |
| 42. C3×#3710 | C22 | semidirect |
| 54. #63937 | D3 | semidirect |
| 61. #63926 | D3 | semidirect |
| 79. #6308 | C23 | semidirect |
| 86. C32×D12 | C23 | semidirect |
| 87. C32×Dic6 | C23 | semidirect |
| 99. C3⋊(C3⋊(C3⋊C8)) | C23 | semidirect |
| 100. C32×C3⋊C8 | C23 | semidirect |
| 101. C32×C3⋊C8 | C23 | semidirect |
| 109. D4×C3⋊D3 | C2×D3 | semidirect |
| 130. #3802 | C2×D3 | semidirect |
| 137. #3796 | C2×D3 | semidirect |
| 159. C3×#214 | C2×D3 | semidirect |
| 163. C3×#213 | C2×D3 | semidirect |
| 164. C3×#213 | C2×D3 | semidirect |
| 171. #3717 | C2×D3 | semidirect |
| 179. #3714 | C2×D3 | semidirect |
| 180. #3714 | C2×D3 | semidirect |
| 184. #3712 | C2×D3 | semidirect |
| 188. #3710 | C2×D3 | semidirect |
| 291. C3×D12 | C22×D3 | semidirect |
| 292. C3×D12 | C22×D3 | semidirect |
| 300. C3×Dic6 | C22×D3 | semidirect |
| 333. C3×C3⋊C8 | C22×D3 | semidirect |
| 334. C3×C3⋊C8 | C22×D3 | semidirect |
| 335. C3×C3⋊C8 | C22×D3 | semidirect |
| 342. C3×C3⋊D3 | AGL(1,ℤ/8) | semidirect |
| 405. #214 | D32 | semidirect |
| 412. #213 | D32 | semidirect |
| 501. C33 | C2×AGL(1,ℤ/8) | semidirect |
| 568. D12 | C2×D32 | semidirect |
| 589. Dic6 | C2×D32 | semidirect |
| 600. C3⋊C8 | C2×D32 | semidirect |
| 601. C3⋊C8 | C2×D32 | semidirect |
| 616. C3⋊D3 | #911 | semidirect |
| 721. C32 | C2×#911 | semidirect |
| 722. C32 | D3×AGL(1,ℤ/8) | semidirect |
| 802. C3 | D3×#911 | semidirect |
| 803. C3 | #10594740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#1113 | 2 |
| #11724374 | 2 |
| #11723560 | 2 |
| C3⋊D3×#214 | 2 |
| C3×#63937 | 2 |
| C3×#63926 | 2 |
| #11722880 | 2 |
| #11722876 | 2 |
| #11722843 | 2 |
| #11722831 | 2 |
| #11722820 | 2 |
| #10594740 | 3 |
| D3×#911 | 3 |