Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1294 conjugacy classes of subgroups.
The subgroup lattice has 878 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11724381 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #11723654 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11723343 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11723331 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11723322 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#63807 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C3×#63797 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C3×D3×D24 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11722877 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #11722875 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #11722866 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #10594734 | — | 3 | 1 | no | maximal |
| 13 | #10594731 | — | 3 | 1 | no | maximal |
| 14 | #10594687 | — | 3 | 1 | no | maximal |
| 15 | #89041 | C22 | 1 | 2 | yes | complemented |
| 16 | #89026 | C22 | 1 | 2 | yes | complemented |
| 17 | #89020 | C22 | 1 | 1 | yes | characteristic |
| 18 | #89015 | C22 | 1 | 2 | yes | complemented |
| 19 | C3×#3802 | C22 | 1 | 2 | yes | complemented |
| 20 | C3×D3×D12 | C22 | 1 | 2 | yes | complemented |
| 21 | C3×#3795 | C22 | 1 | 2 | yes | complemented |
| 22 | #88961 | — | 2 | 2 | no | — |
| 23 | #88952 | — | 2 | 2 | no | — |
| 24 | D3×#626 | — | 2 | 2 | no | — |
| 25 | D3×#625 | — | 2 | 2 | no | — |
| 26 | C8×C3⋊(C3⋊D3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C3×#3746 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | C3×#3745 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | C3×C8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | C32×D24 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | C32×D24 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | C32×D3×C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #88811 | C22 | 1 | 2 | yes | complemented |
| 34 | #88792 | C22 | 1 | 2 | yes | complemented |
| 35 | #88789 | C22 | 1 | 2 | yes | complemented |
| 36 | #88788 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #88787 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | #88786 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | C3×#3716 | C22 | 1 | 2 | yes | complemented |
| 40 | C3×#3714 | C22 | 1 | 2 | yes | complemented |
| 41 | C3×#3713 | C22 | 1 | 2 | yes | complemented |
| 42 | #64314 | — | 3 | 2 | no | — |
| 43 | #64313 | — | 3 | 2 | no | — |
| 44 | #64307 | — | 3 | 2 | no | — |
| 45 | #64121 | — | 3 | 1 | no | — |
| 46 | D8×C3⋊D3 | — | 3 | 1 | no | — |
| 47 | #64110 | — | 3 | 1 | no | — |
| 48 | C3×#912 | — | 3 | 1 | no | — |
| 49 | C3×D3×D8 | — | 3 | 1 | no | — |
| 50 | C3×D3×D8 | — | 3 | 1 | no | — |
| 51 | C3×D3×D8 | — | 3 | 1 | no | — |
| 52 | C3×#904 | — | 3 | 1 | no | — |
| 53 | C2×C3×D24 | — | 3 | 1 | no | — |
| 54 | #63937 | — | 3 | 2 | no | — |
| 55 | #63934 | — | 3 | 2 | no | — |
| 56 | #63932 | — | 3 | 2 | no | — |
| 57 | #63932 | — | 3 | 2 | no | — |
| 58 | #63927 | — | 3 | 2 | no | — |
| 59 | #63925 | — | 3 | 2 | no | — |
| 60 | #63823 | — | 3 | 2 | no | — |
| 61 | #63810 | — | 3 | 1 | no | — |
| 62 | #63810 | — | 3 | 1 | no | — |
| 63 | #63810 | — | 3 | 1 | no | — |
| 64 | #63810 | — | 6 | 1 | no | — |
| 65 | #63808 | — | 3 | 1 | no | — |
| 66 | #63807 | — | 3 | 1 | no | — |
| 67 | #63807 | D3 | 1 | 1 | yes | characteristic, complemented |
| 68 | #63803 | — | 3 | 1 | no | — |
| 69 | #63803 | — | 3 | 1 | no | — |
| 70 | #63803 | — | 6 | 1 | no | — |
| 71 | #63798 | — | 3 | 2 | no | — |
| 72 | #63798 | — | 3 | 2 | no | — |
| 73 | #63797 | — | 3 | 1 | no | — |
| 74 | #63797 | — | 3 | 1 | no | — |
| 75 | #63797 | — | 6 | 1 | no | — |
| 76 | #63797 | D3 | 1 | 1 | yes | characteristic, complemented |
| 77 | D3×D24 | D3 | 1 | 1 | yes | characteristic, complemented |
| 78 | C2×D3×C3⋊D3 | — | 2 | 2 | no | — |
| 79 | C2×C3×D32 | — | 2 | 2 | no | — |
| 80 | C2×C3×D32 | — | 2 | 2 | no | — |
| 81 | C4×C3⋊(C3⋊D3) | C23 | 1 | 1 | yes | characteristic |
| 82 | C3×C4⋊(C3⋊D3) | C23 | 1 | 2 | yes | — |
| 83 | C3×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 84 | C3×#634 | C23 | 1 | 2 | yes | — |
| 85 | C32×D12 | C23 | 1 | 2 | yes | — |
| 86 | C32×D12 | C23 | 1 | 2 | yes | — |
| 87 | C32×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 88 | #6295 | — | 2 | 2 | no | — |
| 89 | #6294 | — | 2 | 2 | no | — |
| 90 | #6293 | D4 | 1 | 1 | yes | characteristic |
| 91 | #6292 | D4 | 1 | 1 | yes | characteristic |
| 92 | #6291 | — | 2 | 2 | no | — |
| 93 | #6291 | D4 | 1 | 1 | yes | characteristic |
| 94 | #6290 | — | 2 | 2 | no | — |
| 95 | #6290 | D4 | 1 | 1 | yes | characteristic |
| 96 | D3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 97 | C3×#626 | — | 2 | 2 | no | — |
| 98 | C3×#625 | — | 2 | 2 | no | — |
| 99 | C3×#625 | — | 2 | 2 | no | — |
| 100 | C3×D3×Dic3 | — | 2 | 2 | no | — |
| 101 | C33×C8 | C23 | 1 | 1 | yes | characteristic |
| 102 | C3⋊(C3⋊(C3⋊C8)) | C23 | 1 | 1 | yes | characteristic |
| 103 | C3×C3⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 104 | C32×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 105 | #5769 | — | 9 | 1 | no | — |
| 106 | #5757 | — | 9 | 1 | no | — |
| 107 | #5757 | — | 9 | 1 | no | — |
| 108 | #3830 | — | 3 | 2 | no | — |
| 109 | D4×C3⋊D3 | — | 3 | 2 | no | — |
| 110 | #3828 | — | 3 | 1 | 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×#235 | — | 3 | 2 | no | — |
| 116 | C2×C3×D12 | — | 3 | 2 | no | — |
| 117 | #3811 | — | 6 | 2 | no | — |
| 118 | D3×#67 | — | 6 | 2 | no | — |
| 119 | D3×#67 | — | 6 | 2 | no | — |
| 120 | D3×#67 | — | 6 | 2 | no | — |
| 121 | D3×#67 | — | 6 | 2 | no | — |
| 122 | D3×#67 | — | 6 | 2 | no | — |
| 123 | C2×#626 | — | 6 | 2 | no | — |
| 124 | C2×#625 | — | 6 | 2 | no | — |
| 125 | #3805 | — | 6 | 2 | no | — |
| 126 | #3804 | — | 6 | 2 | no | — |
| 127 | #3802 | — | 3 | 2 | no | — |
| 128 | #3802 | — | 3 | 2 | no | — |
| 129 | #3802 | — | 6 | 2 | no | — |
| 130 | #3802 | C2×D3 | 1 | 2 | yes | complemented |
| 131 | D3×D12 | — | 6 | 2 | no | — |
| 132 | D3×D12 | C2×D3 | 1 | 2 | yes | complemented |
| 133 | #3799 | — | 3 | 2 | no | — |
| 134 | #3798 | — | 3 | 1 | no | — |
| 135 | #3798 | — | 3 | 1 | no | — |
| 136 | #3798 | — | 6 | 1 | no | — |
| 137 | #3796 | — | 3 | 2 | no | — |
| 138 | #3796 | — | 3 | 2 | no | — |
| 139 | #3796 | — | 3 | 2 | no | — |
| 140 | #3796 | — | 6 | 2 | no | — |
| 141 | #3795 | — | 3 | 2 | no | — |
| 142 | #3795 | — | 6 | 2 | no | — |
| 143 | #3795 | C2×D3 | 1 | 2 | yes | complemented |
| 144 | C32×D8 | — | 3 | 1 | no | — |
| 145 | C32×D8 | — | 3 | 1 | no | — |
| 146 | C2×C32×C8 | — | 3 | 1 | no | — |
| 147 | #3754 | — | 3 | 2 | no | — |
| 148 | #3753 | — | 3 | 2 | no | — |
| 149 | #3748 | — | 3 | 1 | no | — |
| 150 | #3746 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 151 | #3745 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 152 | #3743 | — | 3 | 1 | no | — |
| 153 | #3743 | — | 3 | 1 | no | — |
| 154 | C8×C3⋊D3 | — | 3 | 1 | no | — |
| 155 | C8×C3⋊D3 | — | 3 | 1 | no | — |
| 156 | C8×C3⋊D3 | — | 3 | 1 | no | — |
| 157 | C8×C3⋊D3 | — | 6 | 1 | no | — |
| 158 | C8×C3⋊D3 | — | 6 | 1 | no | — |
| 159 | C8×C3⋊D3 | — | 6 | 1 | no | — |
| 160 | C8×C3⋊D3 | — | 12 | 1 | no | — |
| 161 | C8×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 162 | C3×#214 | — | 3 | 2 | no | — |
| 163 | C3×#213 | — | 3 | 2 | no | — |
| 164 | C3×#213 | — | 3 | 2 | no | — |
| 165 | C3×#213 | — | 3 | 2 | no | — |
| 166 | C3×Dic12 | — | 3 | 1 | no | — |
| 167 | C3×Dic12 | — | 3 | 1 | no | — |
| 168 | C3×Dic12 | — | 6 | 1 | no | — |
| 169 | C3×D24 | — | 2 | 1 | no | — |
| 170 | C3×D24 | — | 2 | 1 | no | — |
| 171 | C3×D24 | — | 3 | 2 | no | — |
| 172 | C3×D24 | — | 3 | 1 | no | — |
| 173 | C3×D24 | — | 3 | 1 | no | — |
| 174 | C3×D24 | — | 6 | 1 | no | — |
| 175 | C3×D24 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 176 | C3×D24 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 177 | C3×D24 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 178 | C3×D24 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 179 | C3×#204 | — | 3 | 2 | no | — |
| 180 | C3×D3×C8 | — | 2 | 1 | no | — |
| 181 | C3×D3×C8 | — | 3 | 1 | no | — |
| 182 | C3×D3×C8 | — | 3 | 1 | no | — |
| 183 | C3×D3×C8 | — | 6 | 1 | no | — |
| 184 | C3×D3×C8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 185 | C3×D3×C8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 186 | #3717 | — | 3 | 2 | no | — |
| 187 | #3716 | — | 3 | 2 | no | — |
| 188 | #3716 | C2×D3 | 1 | 2 | yes | complemented |
| 189 | #3715 | — | 3 | 2 | no | — |
| 190 | #3715 | — | 3 | 2 | no | — |
| 191 | #3715 | — | 3 | 2 | no | — |
| 192 | #3715 | — | 6 | 2 | no | — |
| 193 | #3714 | C2×D3 | 1 | 2 | yes | complemented |
| 194 | #3713 | — | 3 | 2 | no | — |
| 195 | #3713 | — | 3 | 2 | no | — |
| 196 | #3713 | — | 6 | 2 | no | — |
| 197 | #3713 | C2×D3 | 1 | 2 | yes | complemented |
| 198 | #3712 | — | 3 | 1 | no | — |
| 199 | #3712 | — | 3 | 1 | no | — |
| 200 | #3712 | — | 6 | 1 | no | — |
| 201 | #3711 | — | 3 | 1 | no | — |
| 202 | #3711 | — | 3 | 1 | no | — |
| 203 | #3711 | — | 3 | 1 | no | — |
| 204 | #3711 | — | 3 | 1 | no | — |
| 205 | #3711 | — | 6 | 1 | no | — |
| 206 | #3711 | — | 6 | 1 | no | — |
| 207 | C2×C3⋊(C3⋊D3) | C2×D4 | 1 | 1 | yes | characteristic |
| 208 | C2×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 209 | C2×C3×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 210 | C2×C32×D3 | — | 2 | 2 | no | — |
| 211 | C2×C32×D3 | — | 2 | 2 | no | — |
| 212 | C2×C32×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 213 | D3×C3⋊D3 | — | 8 | 2 | no | — |
| 214 | C3×D32 | — | 8 | 2 | no | — |
| 215 | C3×D32 | — | 8 | 2 | no | — |
| 216 | C33×C4 | C24 | 1 | 1 | yes | characteristic |
| 217 | C3⋊(C3⋊Dic3) | C2×D4 | 1 | 1 | yes | characteristic |
| 218 | C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 219 | C3×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 220 | C32×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 221 | #1009 | — | 9 | 2 | no | — |
| 222 | #1004 | — | 9 | 2 | no | — |
| 223 | #1004 | — | 9 | 2 | no | — |
| 224 | C3×#135 | — | 9 | 1 | no | — |
| 225 | C2×C3×D8 | — | 9 | 1 | no | — |
| 226 | C2×C3×D8 | — | 9 | 1 | no | — |
| 227 | #949 | — | 9 | 2 | no | — |
| 228 | #932 | — | 9 | 2 | no | — |
| 229 | #932 | — | 9 | 2 | no | — |
| 230 | #919 | — | 9 | 1 | no | — |
| 231 | #919 | — | 9 | 1 | no | — |
| 232 | #914 | — | 9 | 2 | no | — |
| 233 | #914 | — | 9 | 2 | no | — |
| 234 | #912 | — | 3 | 1 | no | — |
| 235 | #912 | — | 9 | 1 | no | — |
| 236 | #912 | — | 9 | 1 | no | — |
| 237 | #912 | — | 9 | 1 | no | — |
| 238 | #912 | — | 18 | 1 | no | — |
| 239 | #911 | — | 9 | 2 | no | — |
| 240 | #911 | — | 9 | 2 | no | — |
| 241 | #911 | — | 9 | 2 | no | — |
| 242 | #911 | — | 9 | 2 | no | — |
| 243 | D3×D8 | — | 3 | 1 | no | — |
| 244 | D3×D8 | — | 3 | 1 | no | — |
| 245 | D3×D8 | — | 3 | 1 | no | — |
| 246 | D3×D8 | — | 9 | 1 | no | — |
| 247 | D3×D8 | — | 9 | 1 | no | — |
| 248 | D3×D8 | — | 9 | 1 | no | — |
| 249 | D3×D8 | — | 18 | 1 | no | — |
| 250 | #904 | — | 3 | 1 | no | — |
| 251 | #904 | — | 9 | 1 | no | — |
| 252 | C2×D24 | — | 3 | 1 | no | — |
| 253 | #901 | — | 9 | 1 | no | — |
| 254 | #901 | — | 9 | 1 | no | — |
| 255 | #901 | — | 9 | 1 | no | — |
| 256 | #901 | — | 18 | 1 | no | — |
| 257 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 258 | C22×C3×D3 | — | 6 | 2 | no | — |
| 259 | C22×C3×D3 | — | 6 | 2 | no | — |
| 260 | C22×C3×D3 | — | 6 | 2 | no | — |
| 261 | C22×C3×D3 | — | 6 | 2 | no | — |
| 262 | C2×D32 | — | 2 | 2 | no | — |
| 263 | C2×D32 | — | 2 | 2 | no | — |
| 264 | C2×D32 | — | 6 | 2 | no | — |
| 265 | C2×D32 | — | 6 | 2 | no | — |
| 266 | C2×D32 | — | 12 | 2 | no | — |
| 267 | C32×D4 | — | 3 | 2 | no | — |
| 268 | C32×D4 | — | 3 | 2 | no | — |
| 269 | C2×C32×C4 | — | 3 | 1 | no | — |
| 270 | #638 | — | 3 | 1 | no | — |
| 271 | #638 | — | 3 | 1 | no | — |
| 272 | #638 | — | 6 | 2 | no | — |
| 273 | #638 | — | 6 | 2 | no | — |
| 274 | C2×C3⋊Dic3 | — | 6 | 2 | no | — |
| 275 | C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 276 | C4⋊(C3⋊D3) | C22×D3 | 1 | 2 | yes | — |
| 277 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 278 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 279 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 280 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 281 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 282 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 283 | C4×C3⋊D3 | — | 12 | 1 | no | — |
| 284 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 285 | #634 | — | 3 | 1 | no | — |
| 286 | #634 | C22×D3 | 1 | 2 | yes | — |
| 287 | C3×#67 | — | 6 | 2 | no | — |
| 288 | C3×#67 | — | 6 | 2 | no | — |
| 289 | C3×#67 | — | 6 | 2 | no | — |
| 290 | C3×#67 | — | 6 | 2 | no | — |
| 291 | C3×#67 | — | 6 | 2 | no | — |
| 292 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 293 | C3×D12 | — | 2 | 2 | no | — |
| 294 | C3×D12 | — | 2 | 2 | no | — |
| 295 | C3×D12 | — | 3 | 2 | no | — |
| 296 | C3×D12 | — | 3 | 2 | no | — |
| 297 | C3×D12 | — | 6 | 2 | no | — |
| 298 | C3×D12 | — | 6 | 2 | no | — |
| 299 | C3×D12 | C22×D3 | 1 | 2 | yes | — |
| 300 | C3×D12 | C22×D3 | 1 | 2 | yes | — |
| 301 | C3×D12 | C22×D3 | 1 | 2 | yes | — |
| 302 | C3×D12 | C22×D3 | 1 | 2 | yes | — |
| 303 | C3×C4×D3 | — | 2 | 1 | no | — |
| 304 | C3×C4×D3 | — | 3 | 1 | no | — |
| 305 | C3×C4×D3 | — | 3 | 1 | no | — |
| 306 | C3×C4×D3 | — | 6 | 1 | no | — |
| 307 | C3×C4×D3 | — | 6 | 2 | no | — |
| 308 | C3×C4×D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 309 | C3×C4×D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 310 | C3×Dic6 | — | 3 | 2 | no | — |
| 311 | C3×Dic6 | — | 3 | 2 | no | — |
| 312 | C3×Dic6 | — | 6 | 2 | no | — |
| 313 | #627 | — | 3 | 1 | no | — |
| 314 | #627 | — | 3 | 1 | no | — |
| 315 | #627 | — | 6 | 1 | no | — |
| 316 | #626 | — | 2 | 2 | no | — |
| 317 | #626 | — | 3 | 1 | no | — |
| 318 | #626 | — | 3 | 1 | no | — |
| 319 | #626 | — | 3 | 1 | no | — |
| 320 | #626 | — | 3 | 1 | no | — |
| 321 | #626 | — | 6 | 1 | no | — |
| 322 | #626 | — | 6 | 1 | no | — |
| 323 | #626 | — | 6 | 2 | no | — |
| 324 | #626 | — | 6 | 2 | no | — |
| 325 | #626 | — | 6 | 2 | no | — |
| 326 | #626 | — | 6 | 2 | no | — |
| 327 | #626 | — | 12 | 2 | no | — |
| 328 | #625 | — | 2 | 2 | no | — |
| 329 | #625 | — | 2 | 2 | no | — |
| 330 | #625 | — | 3 | 1 | no | — |
| 331 | #625 | — | 3 | 1 | no | — |
| 332 | #625 | — | 6 | 1 | no | — |
| 333 | #625 | — | 6 | 2 | no | — |
| 334 | #625 | — | 6 | 2 | no | — |
| 335 | #625 | — | 6 | 2 | no | — |
| 336 | #625 | — | 12 | 2 | no | — |
| 337 | #624 | — | 6 | 2 | no | — |
| 338 | D3×Dic3 | — | 2 | 2 | no | — |
| 339 | D3×Dic3 | — | 6 | 2 | no | — |
| 340 | D3×Dic3 | — | 6 | 2 | no | — |
| 341 | D3×Dic3 | — | 6 | 2 | no | — |
| 342 | D3×Dic3 | — | 6 | 2 | no | — |
| 343 | D3×Dic3 | — | 12 | 2 | no | — |
| 344 | C32×C8 | — | 2 | 1 | no | — |
| 345 | C32×C8 | — | 2 | 1 | no | — |
| 346 | C32×C8 | — | 2 | 1 | no | — |
| 347 | C32×C8 | — | 3 | 1 | no | — |
| 348 | C32×C8 | — | 4 | 1 | no | — |
| 349 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 350 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 351 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 352 | C3⋊(C3⋊C8) | — | 3 | 1 | no | — |
| 353 | C3⋊(C3⋊C8) | — | 3 | 1 | no | — |
| 354 | C3⋊(C3⋊C8) | — | 3 | 1 | no | — |
| 355 | C3⋊(C3⋊C8) | — | 6 | 1 | no | — |
| 356 | C3⋊(C3⋊C8) | — | 6 | 1 | no | — |
| 357 | C3⋊(C3⋊C8) | — | 6 | 1 | no | — |
| 358 | C3⋊(C3⋊C8) | — | 12 | 1 | no | — |
| 359 | C3⋊(C3⋊C8) | C22×D3 | 1 | 1 | yes | characteristic |
| 360 | C3×C3⋊C8 | — | 2 | 1 | no | — |
| 361 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 362 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 363 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 364 | C3×C3⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 365 | C3×C3⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 366 | #576 | — | 27 | 1 | no | Sylow |
| 367 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 368 | C3⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 369 | C3×C3⋊D3 | — | 2 | 1 | no | — |
| 370 | C3×C3⋊D3 | — | 4 | 2 | no | — |
| 371 | C32×D3 | — | 2 | 1 | no | — |
| 372 | C32×D3 | — | 4 | 2 | no | — |
| 373 | C32×D3 | — | 4 | 2 | no | — |
| 374 | C3×#41 | — | 9 | 2 | no | — |
| 375 | C2×C3×D4 | — | 9 | 2 | no | — |
| 376 | C2×C3×D4 | — | 9 | 2 | no | — |
| 377 | C2×#67 | — | 18 | 2 | no | — |
| 378 | C2×#67 | — | 18 | 2 | no | — |
| 379 | C2×#67 | — | 18 | 2 | no | — |
| 380 | C2×#67 | — | 18 | 2 | no | — |
| 381 | #239 | — | 9 | 2 | no | — |
| 382 | #239 | — | 9 | 2 | no | — |
| 383 | #237 | — | 3 | 2 | no | — |
| 384 | #237 | — | 9 | 2 | no | — |
| 385 | #237 | — | 9 | 2 | no | — |
| 386 | #237 | — | 9 | 2 | no | — |
| 387 | #237 | — | 18 | 2 | no | — |
| 388 | #237 | — | 18 | 2 | no | — |
| 389 | #237 | — | 18 | 2 | no | — |
| 390 | D3×D4 | — | 3 | 2 | no | — |
| 391 | D3×D4 | — | 3 | 2 | no | — |
| 392 | D3×D4 | — | 3 | 2 | no | — |
| 393 | D3×D4 | — | 9 | 2 | no | — |
| 394 | D3×D4 | — | 9 | 2 | no | — |
| 395 | D3×D4 | — | 9 | 2 | no | — |
| 396 | D3×D4 | — | 18 | 2 | no | — |
| 397 | D3×D4 | — | 18 | 2 | no | — |
| 398 | D3×D4 | — | 18 | 2 | no | — |
| 399 | D3×D4 | — | 18 | 2 | no | — |
| 400 | D3×D4 | — | 18 | 2 | no | — |
| 401 | #235 | — | 3 | 2 | no | — |
| 402 | #235 | — | 9 | 2 | no | — |
| 403 | #235 | — | 9 | 1 | no | — |
| 404 | #235 | — | 9 | 1 | no | — |
| 405 | #235 | — | 9 | 1 | no | — |
| 406 | #235 | — | 18 | 1 | no | — |
| 407 | #235 | — | 18 | 2 | no | — |
| 408 | C2×D12 | — | 3 | 2 | no | — |
| 409 | C2×D12 | — | 18 | 2 | no | — |
| 410 | C3×Q16 | — | 9 | 1 | no | — |
| 411 | C3×SD16 | — | 9 | 2 | no | — |
| 412 | C3×D8 | — | 3 | 1 | no | — |
| 413 | C3×D8 | — | 3 | 1 | no | — |
| 414 | C3×D8 | — | 3 | 1 | no | — |
| 415 | C3×D8 | — | 3 | 1 | no | — |
| 416 | C3×D8 | — | 6 | 1 | no | — |
| 417 | C3×D8 | — | 6 | 1 | no | — |
| 418 | C3×D8 | — | 9 | 2 | no | — |
| 419 | C3×D8 | — | 9 | 2 | no | — |
| 420 | C3×D8 | — | 9 | 1 | no | — |
| 421 | C2×C3×C8 | — | 3 | 1 | no | — |
| 422 | C2×C3×C8 | — | 3 | 1 | no | — |
| 423 | C2×C3×C8 | — | 6 | 1 | no | — |
| 424 | C2×C3×C8 | — | 9 | 1 | no | — |
| 425 | #215 | — | 9 | 2 | no | — |
| 426 | #215 | — | 9 | 2 | no | — |
| 427 | #214 | — | 3 | 2 | no | — |
| 428 | #214 | — | 9 | 2 | no | — |
| 429 | #214 | — | 9 | 2 | no | — |
| 430 | #214 | — | 9 | 2 | no | — |
| 431 | #214 | — | 18 | 2 | no | — |
| 432 | #213 | — | 3 | 2 | no | — |
| 433 | #213 | — | 3 | 2 | no | — |
| 434 | #213 | — | 3 | 2 | no | — |
| 435 | #213 | — | 9 | 2 | no | — |
| 436 | #213 | — | 9 | 2 | no | — |
| 437 | #213 | — | 9 | 2 | no | — |
| 438 | #213 | — | 18 | 2 | no | — |
| 439 | #208 | — | 9 | 1 | no | — |
| 440 | #208 | — | 9 | 1 | no | — |
| 441 | #208 | — | 9 | 1 | no | — |
| 442 | #208 | — | 18 | 1 | no | — |
| 443 | Dic12 | — | 3 | 1 | no | — |
| 444 | Dic12 | — | 3 | 1 | no | — |
| 445 | Dic12 | — | 6 | 1 | no | — |
| 446 | D24 | — | 3 | 2 | no | — |
| 447 | D24 | — | 3 | 1 | no | — |
| 448 | D24 | — | 3 | 1 | no | — |
| 449 | D24 | — | 6 | 1 | no | — |
| 450 | D24 | D32 | 1 | 1 | yes | characteristic, complemented |
| 451 | D24 | D32 | 1 | 1 | yes | characteristic, complemented |
| 452 | #204 | — | 3 | 2 | no | — |
| 453 | #204 | — | 9 | 2 | no | — |
| 454 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 455 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 456 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 457 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 458 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 459 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 460 | ΓL(1,𝔽25) | — | 18 | 1 | no | — |
| 461 | ΓL(1,𝔽25) | — | 18 | 1 | no | — |
| 462 | D3×C8 | — | 3 | 1 | no | — |
| 463 | D3×C8 | — | 3 | 1 | no | — |
| 464 | D3×C8 | — | 6 | 1 | no | — |
| 465 | D3×C8 | — | 9 | 1 | no | — |
| 466 | D3×C8 | — | 9 | 1 | no | — |
| 467 | D3×C8 | — | 9 | 1 | no | — |
| 468 | D3×C8 | — | 18 | 1 | no | — |
| 469 | D3×C8 | — | 18 | 1 | no | — |
| 470 | D3×C8 | — | 18 | 1 | no | — |
| 471 | D3×C8 | — | 36 | 1 | no | — |
| 472 | D3×C8 | D32 | 1 | 1 | yes | characteristic, complemented |
| 473 | C22×C32 | — | 3 | 1 | no | — |
| 474 | C22×C32 | — | 6 | 2 | no | — |
| 475 | C22×C32 | — | 6 | 2 | no | — |
| 476 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 477 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 478 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 479 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 480 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 481 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 482 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 483 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 484 | C2×C3⋊D3 | — | 24 | 2 | no | — |
| 485 | C2×C3⋊D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 486 | C2×C3×D3 | — | 2 | 2 | no | — |
| 487 | C2×C3×D3 | — | 2 | 2 | no | — |
| 488 | C2×C3×D3 | — | 2 | 2 | no | — |
| 489 | C2×C3×D3 | — | 2 | 2 | no | — |
| 490 | C2×C3×D3 | — | 2 | 1 | no | — |
| 491 | C2×C3×D3 | — | 3 | 1 | no | — |
| 492 | C2×C3×D3 | — | 3 | 1 | no | — |
| 493 | C2×C3×D3 | — | 4 | 2 | no | — |
| 494 | C2×C3×D3 | — | 4 | 2 | no | — |
| 495 | C2×C3×D3 | — | 6 | 1 | no | — |
| 496 | C2×C3×D3 | — | 6 | 2 | no | — |
| 497 | C2×C3×D3 | — | 6 | 2 | no | — |
| 498 | C2×C3×D3 | — | 12 | 2 | no | — |
| 499 | C2×C3×D3 | — | 24 | 2 | no | — |
| 500 | C2×C3×D3 | — | 24 | 2 | no | — |
| 501 | C2×C3×D3 | — | 24 | 2 | no | — |
| 502 | C2×C3×D3 | — | 24 | 2 | no | — |
| 503 | C2×C3×D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 504 | C2×C3×D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 505 | D32 | — | 8 | 2 | no | — |
| 506 | D32 | — | 8 | 2 | no | — |
| 507 | D32 | — | 24 | 2 | no | — |
| 508 | D32 | — | 24 | 2 | no | — |
| 509 | D32 | — | 24 | 4 | no | — |
| 510 | C32×C4 | — | 2 | 1 | no | — |
| 511 | C32×C4 | — | 2 | 1 | no | — |
| 512 | C32×C4 | — | 2 | 1 | no | — |
| 513 | C32×C4 | — | 3 | 1 | no | — |
| 514 | C32×C4 | — | 4 | 1 | no | — |
| 515 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 516 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 517 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 518 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 519 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 520 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 521 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 522 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 523 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 524 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 525 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 526 | C3⋊Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 527 | C3×Dic3 | — | 2 | 1 | no | — |
| 528 | C3×Dic3 | — | 3 | 1 | no | — |
| 529 | C3×Dic3 | — | 3 | 1 | no | — |
| 530 | C3×Dic3 | — | 6 | 1 | no | — |
| 531 | C3×Dic3 | — | 6 | 2 | no | — |
| 532 | C3×Dic3 | — | 6 | 2 | no | — |
| 533 | C3×Dic3 | — | 12 | 2 | no | — |
| 534 | C3×Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 535 | C3×Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 536 | H(5,𝔽2) | — | 27 | 2 | no | — |
| 537 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 538 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 539 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 540 | #135 | — | 9 | 1 | no | — |
| 541 | #135 | — | 27 | 1 | no | — |
| 542 | #135 | — | 27 | 1 | no | — |
| 543 | C2×D8 | — | 9 | 1 | no | — |
| 544 | C2×D8 | — | 9 | 1 | no | — |
| 545 | C2×D8 | — | 27 | 1 | no | — |
| 546 | #131 | — | 27 | 1 | no | — |
| 547 | C33 | #576 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 548 | C23×C3 | — | 18 | 2 | no | — |
| 549 | C23×C3 | — | 18 | 2 | no | — |
| 550 | C22×D3 | — | 6 | 2 | no | — |
| 551 | C22×D3 | — | 6 | 2 | no | — |
| 552 | C22×D3 | — | 6 | 2 | no | — |
| 553 | C22×D3 | — | 6 | 2 | no | — |
| 554 | C22×D3 | — | 18 | 2 | no | — |
| 555 | C22×D3 | — | 18 | 2 | no | — |
| 556 | C22×D3 | — | 18 | 2 | no | — |
| 557 | C22×D3 | — | 36 | 2 | no | — |
| 558 | C3×Q8 | — | 9 | 2 | no | — |
| 559 | C3×D4 | — | 3 | 2 | no | — |
| 560 | C3×D4 | — | 3 | 2 | no | — |
| 561 | C3×D4 | — | 3 | 2 | no | — |
| 562 | C3×D4 | — | 3 | 2 | no | — |
| 563 | C3×D4 | — | 6 | 2 | no | — |
| 564 | C3×D4 | — | 6 | 2 | no | — |
| 565 | C3×D4 | — | 9 | 2 | no | — |
| 566 | C3×D4 | — | 18 | 2 | no | — |
| 567 | C3×D4 | — | 18 | 2 | no | — |
| 568 | C3×D4 | — | 18 | 2 | no | — |
| 569 | C2×C3×C4 | — | 3 | 1 | no | — |
| 570 | C2×C3×C4 | — | 3 | 1 | no | — |
| 571 | C2×C3×C4 | — | 6 | 1 | no | — |
| 572 | C2×C3×C4 | — | 9 | 1 | no | — |
| 573 | C2×C3×C4 | — | 18 | 2 | no | — |
| 574 | #67 | — | 6 | 2 | no | — |
| 575 | #67 | — | 6 | 2 | no | — |
| 576 | #67 | — | 6 | 2 | no | — |
| 577 | #67 | — | 6 | 2 | no | — |
| 578 | #67 | — | 6 | 2 | no | — |
| 579 | #67 | — | 9 | 1 | no | — |
| 580 | #67 | — | 9 | 1 | no | — |
| 581 | #67 | — | 9 | 1 | no | — |
| 582 | #67 | — | 9 | 1 | no | — |
| 583 | #67 | — | 9 | 1 | no | — |
| 584 | #67 | — | 9 | 1 | no | — |
| 585 | #67 | — | 18 | 1 | no | — |
| 586 | #67 | — | 18 | 1 | no | — |
| 587 | #67 | — | 18 | 2 | no | — |
| 588 | #67 | — | 18 | 2 | no | — |
| 589 | #67 | — | 18 | 2 | no | — |
| 590 | #67 | — | 18 | 2 | no | — |
| 591 | #67 | — | 18 | 2 | no | — |
| 592 | #67 | — | 18 | 2 | no | — |
| 593 | #67 | — | 18 | 2 | no | — |
| 594 | #67 | — | 36 | 2 | no | — |
| 595 | #67 | — | 36 | 2 | no | — |
| 596 | C2×Dic3 | — | 6 | 2 | no | — |
| 597 | C2×Dic3 | — | 18 | 2 | no | — |
| 598 | C2×Dic3 | — | 18 | 2 | no | — |
| 599 | C2×Dic3 | — | 18 | 2 | no | — |
| 600 | C2×Dic3 | — | 36 | 2 | no | — |
| 601 | D12 | — | 3 | 2 | no | — |
| 602 | D12 | — | 3 | 2 | no | — |
| 603 | D12 | — | 6 | 2 | no | — |
| 604 | D12 | — | 6 | 2 | no | — |
| 605 | D12 | — | 9 | 1 | no | — |
| 606 | D12 | — | 9 | 1 | no | — |
| 607 | D12 | — | 9 | 1 | no | — |
| 608 | D12 | — | 18 | 1 | no | — |
| 609 | D12 | — | 18 | 2 | no | — |
| 610 | D12 | — | 18 | 2 | no | — |
| 611 | D12 | C2×D32 | 1 | 2 | yes | — |
| 612 | D12 | C2×D32 | 1 | 2 | yes | — |
| 613 | C4×D3 | — | 3 | 1 | no | — |
| 614 | C4×D3 | — | 3 | 1 | no | — |
| 615 | C4×D3 | — | 6 | 1 | no | — |
| 616 | C4×D3 | — | 6 | 2 | no | — |
| 617 | C4×D3 | — | 9 | 1 | no | — |
| 618 | C4×D3 | — | 9 | 1 | no | — |
| 619 | C4×D3 | — | 9 | 1 | no | — |
| 620 | C4×D3 | — | 18 | 1 | no | — |
| 621 | C4×D3 | — | 18 | 1 | no | — |
| 622 | C4×D3 | — | 18 | 1 | no | — |
| 623 | C4×D3 | — | 18 | 2 | no | — |
| 624 | C4×D3 | — | 18 | 2 | no | — |
| 625 | C4×D3 | — | 18 | 2 | no | — |
| 626 | C4×D3 | — | 36 | 1 | no | — |
| 627 | C4×D3 | C2×D32 | 1 | 1 | yes | characteristic |
| 628 | Dic6 | — | 3 | 2 | no | — |
| 629 | Dic6 | — | 3 | 2 | no | — |
| 630 | Dic6 | — | 6 | 2 | no | — |
| 631 | Dic6 | — | 9 | 1 | no | — |
| 632 | Dic6 | — | 9 | 1 | no | — |
| 633 | Dic6 | — | 9 | 1 | no | — |
| 634 | Dic6 | — | 18 | 1 | no | — |
| 635 | C3×C8 | — | 2 | 1 | no | — |
| 636 | C3×C8 | — | 2 | 1 | no | — |
| 637 | C3×C8 | — | 2 | 1 | no | — |
| 638 | C3×C8 | — | 3 | 1 | no | — |
| 639 | C3×C8 | — | 3 | 1 | no | — |
| 640 | C3×C8 | — | 4 | 1 | no | — |
| 641 | C3×C8 | — | 6 | 1 | no | — |
| 642 | C3×C8 | — | 9 | 1 | no | — |
| 643 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 644 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 645 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 646 | C3⋊C8 | — | 3 | 1 | no | — |
| 647 | C3⋊C8 | — | 3 | 1 | no | — |
| 648 | C3⋊C8 | — | 6 | 1 | no | — |
| 649 | C3⋊C8 | — | 9 | 1 | no | — |
| 650 | C3⋊C8 | — | 9 | 1 | no | — |
| 651 | C3⋊C8 | — | 9 | 1 | no | — |
| 652 | C3⋊C8 | — | 18 | 1 | no | — |
| 653 | C3⋊C8 | — | 18 | 1 | no | — |
| 654 | C3⋊C8 | — | 18 | 1 | no | — |
| 655 | C3⋊C8 | — | 36 | 1 | no | — |
| 656 | C3⋊C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 657 | C2×C32 | — | 2 | 1 | no | — |
| 658 | C2×C32 | — | 2 | 1 | no | — |
| 659 | C2×C32 | — | 2 | 1 | no | — |
| 660 | C2×C32 | — | 4 | 1 | no | — |
| 661 | C2×C32 | — | 6 | 1 | no | — |
| 662 | C2×C32 | — | 12 | 2 | no | — |
| 663 | C2×C32 | — | 12 | 2 | no | — |
| 664 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 665 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 666 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 667 | C3⋊D3 | — | 2 | 1 | no | — |
| 668 | C3⋊D3 | — | 4 | 2 | no | — |
| 669 | C3⋊D3 | — | 6 | 1 | no | — |
| 670 | C3⋊D3 | — | 6 | 2 | no | — |
| 671 | C3⋊D3 | — | 6 | 1 | no | — |
| 672 | C3⋊D3 | — | 6 | 1 | no | — |
| 673 | C3⋊D3 | — | 12 | 1 | no | — |
| 674 | C3⋊D3 | — | 12 | 1 | no | — |
| 675 | C3⋊D3 | — | 12 | 2 | no | — |
| 676 | C3×D3 | — | 2 | 1 | no | — |
| 677 | C3×D3 | — | 2 | 1 | no | — |
| 678 | C3×D3 | — | 4 | 1 | no | — |
| 679 | C3×D3 | — | 4 | 2 | no | — |
| 680 | C3×D3 | — | 4 | 2 | no | — |
| 681 | C3×D3 | — | 4 | 2 | no | — |
| 682 | C3×D3 | — | 4 | 2 | no | — |
| 683 | C3×D3 | — | 6 | 1 | no | — |
| 684 | C3×D3 | — | 6 | 1 | no | — |
| 685 | C3×D3 | — | 8 | 2 | no | — |
| 686 | C3×D3 | — | 8 | 2 | no | — |
| 687 | C3×D3 | — | 12 | 1 | no | — |
| 688 | C3×D3 | — | 12 | 2 | no | — |
| 689 | C3×D3 | — | 12 | 2 | no | — |
| 690 | C3×D3 | — | 24 | 2 | no | — |
| 691 | #41 | — | 9 | 2 | no | — |
| 692 | #41 | — | 27 | 1 | no | — |
| 693 | #41 | — | 27 | 2 | no | — |
| 694 | #41 | — | 27 | 2 | no | — |
| 695 | #41 | — | 54 | 2 | no | — |
| 696 | C2×D4 | — | 9 | 2 | no | — |
| 697 | C2×D4 | — | 9 | 2 | no | — |
| 698 | C2×D4 | — | 27 | 2 | no | — |
| 699 | C2×D4 | — | 54 | 2 | no | — |
| 700 | C2×D4 | — | 54 | 2 | no | — |
| 701 | C2×D4 | — | 54 | 2 | no | — |
| 702 | Q16 | — | 9 | 1 | no | — |
| 703 | SD16 | — | 9 | 2 | no | — |
| 704 | SD16 | — | 27 | 2 | no | — |
| 705 | SD16 | — | 27 | 2 | no | — |
| 706 | D8 | — | 3 | 1 | no | — |
| 707 | D8 | — | 3 | 1 | no | — |
| 708 | D8 | — | 9 | 2 | no | — |
| 709 | D8 | — | 9 | 2 | no | — |
| 710 | D8 | — | 9 | 1 | no | — |
| 711 | D8 | — | 27 | 2 | no | — |
| 712 | M16 | — | 27 | 1 | no | — |
| 713 | M16 | — | 27 | 1 | no | — |
| 714 | M16 | — | 27 | 1 | no | — |
| 715 | C2×C8 | — | 3 | 1 | no | — |
| 716 | C2×C8 | — | 9 | 1 | no | — |
| 717 | C2×C8 | — | 27 | 1 | no | — |
| 718 | C22×C3 | — | 3 | 1 | no | — |
| 719 | C22×C3 | — | 3 | 1 | no | — |
| 720 | C22×C3 | — | 6 | 1 | no | — |
| 721 | C22×C3 | — | 6 | 2 | no | — |
| 722 | C22×C3 | — | 6 | 2 | no | — |
| 723 | C22×C3 | — | 6 | 2 | no | — |
| 724 | C22×C3 | — | 6 | 2 | no | — |
| 725 | C22×C3 | — | 9 | 1 | no | — |
| 726 | C22×C3 | — | 12 | 2 | no | — |
| 727 | C22×C3 | — | 12 | 2 | no | — |
| 728 | C22×C3 | — | 18 | 2 | no | — |
| 729 | C22×C3 | — | 72 | 2 | no | — |
| 730 | C22×C3 | — | 72 | 2 | no | — |
| 731 | C2×D3 | — | 2 | 2 | no | — |
| 732 | C2×D3 | — | 2 | 2 | no | — |
| 733 | C2×D3 | — | 3 | 1 | no | — |
| 734 | C2×D3 | — | 3 | 1 | no | — |
| 735 | C2×D3 | — | 6 | 1 | no | — |
| 736 | C2×D3 | — | 6 | 2 | no | — |
| 737 | C2×D3 | — | 6 | 2 | no | — |
| 738 | C2×D3 | — | 9 | 1 | no | — |
| 739 | C2×D3 | — | 9 | 1 | no | — |
| 740 | C2×D3 | — | 9 | 1 | no | — |
| 741 | C2×D3 | — | 12 | 2 | no | — |
| 742 | C2×D3 | — | 18 | 1 | no | — |
| 743 | C2×D3 | — | 18 | 1 | no | — |
| 744 | C2×D3 | — | 18 | 1 | no | — |
| 745 | C2×D3 | — | 24 | 2 | no | — |
| 746 | C2×D3 | — | 24 | 2 | no | — |
| 747 | C2×D3 | — | 24 | 2 | no | — |
| 748 | C2×D3 | — | 24 | 2 | no | — |
| 749 | C2×D3 | — | 36 | 1 | no | — |
| 750 | C2×D3 | — | 72 | 2 | no | — |
| 751 | C2×D3 | — | 72 | 2 | no | — |
| 752 | C2×D3 | — | 72 | 2 | no | — |
| 753 | C2×D3 | — | 72 | 4 | no | — |
| 754 | C2×D3 | #3802 | 1 | 1 | yes | characteristic |
| 755 | C3×C4 | — | 2 | 1 | no | — |
| 756 | C3×C4 | — | 2 | 1 | no | — |
| 757 | C3×C4 | — | 2 | 1 | no | — |
| 758 | C3×C4 | — | 3 | 1 | no | — |
| 759 | C3×C4 | — | 3 | 1 | no | — |
| 760 | C3×C4 | — | 4 | 1 | no | — |
| 761 | C3×C4 | — | 6 | 1 | no | — |
| 762 | C3×C4 | — | 9 | 1 | no | — |
| 763 | C3×C4 | — | 18 | 2 | no | — |
| 764 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 765 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 766 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 767 | Dic3 | — | 3 | 1 | no | — |
| 768 | Dic3 | — | 3 | 1 | no | — |
| 769 | Dic3 | — | 6 | 1 | no | — |
| 770 | Dic3 | — | 6 | 2 | no | — |
| 771 | Dic3 | — | 6 | 2 | no | — |
| 772 | Dic3 | — | 9 | 1 | no | — |
| 773 | Dic3 | — | 9 | 1 | no | — |
| 774 | Dic3 | — | 9 | 1 | no | — |
| 775 | Dic3 | — | 12 | 2 | no | — |
| 776 | Dic3 | — | 18 | 1 | no | — |
| 777 | Dic3 | — | 18 | 1 | no | — |
| 778 | Dic3 | — | 18 | 1 | no | — |
| 779 | Dic3 | — | 36 | 1 | no | — |
| 780 | Dic3 | #3802 | 1 | 1 | yes | characteristic |
| 781 | C32 | — | 2 | 1 | no | — |
| 782 | C32 | — | 2 | 1 | no | — |
| 783 | C32 | — | 2 | 1 | no | — |
| 784 | C32 | — | 4 | 1 | no | — |
| 785 | C32 | #5757 | 1 | 1 | yes | characteristic, complemented |
| 786 | C32 | #5757 | 1 | 1 | yes | characteristic, complemented |
| 787 | C32 | #5769 | 1 | 1 | yes | characteristic, complemented |
| 788 | C23 | — | 18 | 2 | no | — |
| 789 | C23 | — | 18 | 2 | no | — |
| 790 | C23 | — | 54 | 2 | no | — |
| 791 | Q8 | — | 9 | 2 | no | — |
| 792 | Q8 | — | 27 | 1 | no | — |
| 793 | D4 | — | 3 | 2 | no | — |
| 794 | D4 | — | 3 | 2 | no | — |
| 795 | D4 | — | 9 | 2 | no | — |
| 796 | D4 | — | 18 | 2 | no | — |
| 797 | D4 | — | 18 | 2 | no | — |
| 798 | D4 | — | 18 | 2 | no | — |
| 799 | D4 | — | 27 | 1 | no | — |
| 800 | D4 | — | 27 | 1 | no | — |
| 801 | D4 | — | 27 | 1 | no | — |
| 802 | D4 | — | 54 | 2 | no | — |
| 803 | D4 | — | 54 | 2 | no | — |
| 804 | D4 | — | 54 | 2 | no | — |
| 805 | C2×C4 | — | 3 | 1 | no | — |
| 806 | C2×C4 | — | 9 | 1 | no | — |
| 807 | C2×C4 | — | 18 | 2 | no | — |
| 808 | C2×C4 | — | 27 | 1 | no | — |
| 809 | C2×C4 | — | 54 | 2 | no | — |
| 810 | C2×C4 | — | 54 | 2 | no | — |
| 811 | C8 | — | 3 | 1 | no | — |
| 812 | C8 | — | 9 | 1 | no | — |
| 813 | C8 | — | 27 | 1 | no | — |
| 814 | C8 | D33 | 1 | 1 | yes | characteristic |
| 815 | C2×C3 | — | 2 | 1 | no | — |
| 816 | C2×C3 | — | 2 | 1 | no | — |
| 817 | C2×C3 | — | 2 | 1 | no | — |
| 818 | C2×C3 | — | 4 | 1 | no | — |
| 819 | C2×C3 | — | 6 | 1 | no | — |
| 820 | C2×C3 | — | 6 | 1 | no | — |
| 821 | C2×C3 | — | 12 | 1 | no | — |
| 822 | C2×C3 | — | 12 | 2 | no | — |
| 823 | C2×C3 | — | 12 | 2 | no | — |
| 824 | C2×C3 | — | 12 | 2 | no | — |
| 825 | C2×C3 | — | 12 | 2 | no | — |
| 826 | C2×C3 | — | 18 | 1 | no | — |
| 827 | C2×C3 | — | 24 | 2 | no | — |
| 828 | C2×C3 | — | 24 | 2 | no | — |
| 829 | C2×C3 | — | 36 | 2 | no | — |
| 830 | C2×C3 | C2×#3802 | 1 | 1 | yes | characteristic |
| 831 | C2×C3 | D32×D4 | 1 | 1 | yes | characteristic |
| 832 | C2×C3 | D32×D4 | 1 | 1 | yes | characteristic |
| 833 | D3 | — | 2 | 1 | no | — |
| 834 | D3 | — | 4 | 2 | no | — |
| 835 | D3 | — | 4 | 2 | no | — |
| 836 | D3 | — | 6 | 1 | no | — |
| 837 | D3 | — | 6 | 1 | no | — |
| 838 | D3 | — | 12 | 1 | no | — |
| 839 | D3 | — | 12 | 2 | no | — |
| 840 | D3 | — | 12 | 2 | no | — |
| 841 | D3 | — | 18 | 2 | no | — |
| 842 | D3 | — | 18 | 1 | no | — |
| 843 | D3 | — | 18 | 1 | no | — |
| 844 | D3 | — | 18 | 1 | no | — |
| 845 | D3 | — | 24 | 2 | no | — |
| 846 | D3 | — | 36 | 1 | no | — |
| 847 | D3 | — | 36 | 1 | no | — |
| 848 | D3 | — | 36 | 2 | no | — |
| 849 | C22 | — | 3 | 1 | no | — |
| 850 | C22 | — | 6 | 2 | no | — |
| 851 | C22 | — | 6 | 2 | no | — |
| 852 | C22 | — | 9 | 1 | no | — |
| 853 | C22 | — | 18 | 2 | no | — |
| 854 | C22 | — | 27 | 1 | no | — |
| 855 | C22 | — | 72 | 2 | no | — |
| 856 | C22 | — | 72 | 2 | no | — |
| 857 | C22 | — | 216 | 2 | no | — |
| 858 | C4 | — | 3 | 1 | no | — |
| 859 | C4 | — | 9 | 1 | no | — |
| 860 | C4 | — | 18 | 2 | no | — |
| 861 | C4 | — | 27 | 1 | no | — |
| 862 | C4 | C2×D33 | 1 | 1 | yes | characteristic |
| 863 | C3 | — | 2 | 1 | no | — |
| 864 | C3 | — | 2 | 1 | no | — |
| 865 | C3 | — | 2 | 1 | no | — |
| 866 | C3 | — | 4 | 1 | no | — |
| 867 | C3 | #10594687 | 1 | 1 | yes | characteristic, complemented |
| 868 | C3 | #10594731 | 1 | 1 | yes | characteristic, complemented |
| 869 | C3 | #10594734 | 1 | 1 | yes | characteristic, complemented |
| 870 | C2 | — | 6 | 1 | no | — |
| 871 | C2 | — | 12 | 2 | no | — |
| 872 | C2 | — | 12 | 2 | no | — |
| 873 | C2 | — | 18 | 1 | no | — |
| 874 | C2 | — | 36 | 2 | no | — |
| 875 | C2 | — | 54 | 1 | no | — |
| 876 | C2 | D3×#3802 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D3×#3802 |
| commutator, cosocle | C33×C4 | C24 |
| Frattini | C4 | C2×D33 |
| Fitting | C33×C8 | C23 |
| socle | C2×C33 | C22×D4 |
| hypercenter | C8 | D33 |
| hypocenter | C33 | #576 |
| LCS | G ▷ C33×C4 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11724381 | C2 | semidirect |
| 2. #11723654 | C2 | semidirect |
| 3. #11723343 | C2 | semidirect |
| 4. #11723331 | C2 | semidirect |
| 5. #11723322 | C2 | semidirect |
| 6. C3×#63807 | C2 | semidirect |
| 7. C3×#63797 | C2 | semidirect |
| 8. C3×D3×D24 | C2 | semidirect |
| 9. #11722877 | C2 | semidirect |
| 10. #11722875 | C2 | semidirect |
| 11. #11722866 | C2 | semidirect |
| 15. #89041 | C22 | semidirect |
| 16. #89026 | C22 | semidirect |
| 18. #89015 | C22 | semidirect |
| 19. C3×#3802 | C22 | semidirect |
| 20. C3×D3×D12 | C22 | semidirect |
| 21. C3×#3795 | C22 | semidirect |
| 26. C8×C3⋊(C3⋊D3) | C22 | semidirect |
| 27. C3×#3746 | C22 | semidirect |
| 28. C3×#3745 | C22 | semidirect |
| 29. C3×C8×C3⋊D3 | C22 | semidirect |
| 30. C32×D24 | C22 | semidirect |
| 31. C32×D24 | C22 | semidirect |
| 32. C32×D3×C8 | C22 | semidirect |
| 33. #88811 | C22 | semidirect |
| 34. #88792 | C22 | semidirect |
| 35. #88789 | C22 | semidirect |
| 36. #88788 | C22 | semidirect |
| 37. #88787 | C22 | semidirect |
| 38. #88786 | C22 | semidirect |
| 39. C3×#3716 | C22 | semidirect |
| 40. C3×#3714 | C22 | semidirect |
| 41. C3×#3713 | C22 | semidirect |
| 67. #63807 | D3 | semidirect |
| 76. #63797 | D3 | semidirect |
| 77. D3×D24 | D3 | semidirect |
| 130. #3802 | C2×D3 | semidirect |
| 132. D3×D12 | C2×D3 | semidirect |
| 143. #3795 | C2×D3 | semidirect |
| 150. #3746 | C2×D3 | semidirect |
| 151. #3745 | C2×D3 | semidirect |
| 161. C8×C3⋊D3 | C2×D3 | semidirect |
| 175. C3×D24 | C2×D3 | semidirect |
| 176. C3×D24 | C2×D3 | semidirect |
| 177. C3×D24 | C2×D3 | semidirect |
| 178. C3×D24 | C2×D3 | semidirect |
| 184. C3×D3×C8 | C2×D3 | semidirect |
| 185. C3×D3×C8 | C2×D3 | semidirect |
| 188. #3716 | C2×D3 | semidirect |
| 193. #3714 | C2×D3 | semidirect |
| 197. #3713 | C2×D3 | semidirect |
| 450. D24 | D32 | semidirect |
| 451. D24 | D32 | semidirect |
| 472. D3×C8 | D32 | semidirect |
| 547. C33 | #576 | semidirect |
| 785. C32 | #5757 | semidirect |
| 786. C32 | #5757 | semidirect |
| 787. C32 | #5769 | semidirect |
| 867. C3 | #10594687 | semidirect |
| 868. C3 | #10594731 | semidirect |
| 869. C3 | #10594734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724381 | 2 |
| #11723654 | 2 |
| #11723343 | 2 |
| #11723331 | 2 |
| #11723322 | 2 |
| C3×#63807 | 2 |
| C3×#63797 | 2 |
| C3×D3×D24 | 2 |
| #11722877 | 2 |
| #11722875 | 2 |
| #11722866 | 2 |
| #10594734 | 3 |
| #10594731 | 3 |
| #10594687 | 3 |