Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1436 conjugacy classes of subgroups.
The subgroup lattice has 970 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11724581 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#64307 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11723657 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11723367 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#88790 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#63823 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C3×#63822 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11722874 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11722873 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #11722858 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #11722830 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #10595461 | — | 3 | 1 | no | maximal |
| 13 | #10595456 | — | 3 | 1 | no | maximal |
| 14 | #10595097 | — | 3 | 1 | no | maximal |
| 15 | C2×C4⋊(C3⋊(C3⋊D3)) | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C3×#3828 | C22 | 1 | 1 | yes | characteristic |
| 17 | C32×#235 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C32×#235 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C2×C32×D12 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #89039 | — | 2 | 2 | no | — |
| 21 | C3⋊D3×D12 | C22 | 1 | 2 | yes | complemented |
| 22 | D3×C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 23 | #89022 | — | 2 | 1 | no | — |
| 24 | #89018 | C22 | 1 | 2 | yes | complemented |
| 25 | C3×D3×#67 | — | 2 | 2 | no | — |
| 26 | C3×#3802 | C22 | 1 | 2 | yes | complemented |
| 27 | C3×D3×D12 | — | 2 | 1 | no | — |
| 28 | C3×#3796 | C22 | 1 | 2 | yes | complemented |
| 29 | C3×#3795 | — | 2 | 1 | no | — |
| 30 | C3×#3748 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | C2×C3×C3⋊(C3⋊C8) | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | #88809 | C22 | 1 | 2 | yes | complemented |
| 33 | #88808 | C22 | 1 | 2 | yes | complemented |
| 34 | #88795 | C22 | 1 | 2 | yes | complemented |
| 35 | #88790 | C22 | 1 | 2 | yes | complemented |
| 36 | #88790 | C22 | 1 | 2 | yes | complemented |
| 37 | #88790 | C22 | 1 | 2 | yes | complemented |
| 38 | C3×#3718 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | C3×#3715 | C22 | 1 | 2 | yes | complemented |
| 40 | C3×#3715 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | C3×#3715 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | C3×#3713 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | C3×#3713 | C22 | 1 | 2 | yes | complemented |
| 44 | #64366 | — | 3 | 1 | no | — |
| 45 | C3×#1009 | — | 3 | 1 | no | — |
| 46 | C3×#1004 | — | 3 | 1 | no | — |
| 47 | #64308 | — | 3 | 1 | no | — |
| 48 | #64308 | — | 3 | 1 | no | — |
| 49 | #64308 | — | 6 | 1 | no | — |
| 50 | #64307 | D3 | 1 | 1 | yes | characteristic, complemented |
| 51 | #64158 | — | 3 | 1 | no | — |
| 52 | C2×#3753 | — | 3 | 1 | no | — |
| 53 | C3×#950 | — | 3 | 1 | no | — |
| 54 | C3×#950 | — | 3 | 1 | no | — |
| 55 | C3×#949 | — | 3 | 1 | no | — |
| 56 | C3×#932 | — | 3 | 1 | no | — |
| 57 | #63950 | — | 3 | 2 | no | — |
| 58 | #63949 | — | 3 | 2 | no | — |
| 59 | #63941 | — | 3 | 2 | no | — |
| 60 | #63939 | — | 3 | 2 | no | — |
| 61 | #63937 | — | 3 | 2 | no | — |
| 62 | #63935 | — | 3 | 2 | no | — |
| 63 | #63934 | — | 3 | 2 | no | — |
| 64 | #63934 | — | 3 | 2 | no | — |
| 65 | #63926 | — | 3 | 2 | no | — |
| 66 | #63925 | — | 3 | 2 | no | — |
| 67 | D3×#213 | — | 3 | 2 | no | — |
| 68 | D3×#213 | — | 3 | 2 | no | — |
| 69 | #63825 | — | 3 | 1 | no | — |
| 70 | #63825 | — | 3 | 1 | no | — |
| 71 | #63825 | — | 6 | 1 | no | — |
| 72 | C2×#3714 | — | 3 | 1 | no | — |
| 73 | C2×#3714 | — | 3 | 1 | no | — |
| 74 | C2×#3714 | — | 6 | 1 | no | — |
| 75 | #63823 | D3 | 1 | 1 | yes | characteristic, complemented |
| 76 | #63822 | D3 | 1 | 1 | yes | characteristic, complemented |
| 77 | #63817 | — | 3 | 1 | no | — |
| 78 | #63815 | — | 3 | 1 | no | — |
| 79 | #63814 | — | 3 | 1 | no | — |
| 80 | C22×C3⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 81 | C22×C32×D3 | — | 2 | 1 | no | — |
| 82 | C2×D3×C3⋊D3 | — | 2 | 2 | no | — |
| 83 | C2×C3×D32 | — | 2 | 2 | no | — |
| 84 | C2×C33×C4 | C23 | 1 | 1 | yes | characteristic |
| 85 | C4⋊(C3⋊(C3⋊D3)) | — | 2 | 1 | no | — |
| 86 | C4⋊(C3⋊(C3⋊D3)) | C23 | 1 | 2 | yes | — |
| 87 | C3×#638 | D4 | 1 | 2 | yes | — |
| 88 | C3×C4⋊(C3⋊D3) | D4 | 1 | 1 | yes | characteristic |
| 89 | C3×C4×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 90 | C3×#634 | D4 | 1 | 1 | yes | characteristic |
| 91 | C32×#67 | — | 2 | 1 | no | — |
| 92 | C32×#67 | — | 2 | 1 | no | — |
| 93 | C32×D12 | — | 2 | 1 | no | — |
| 94 | C32×D12 | C23 | 1 | 2 | yes | — |
| 95 | C32×D12 | C23 | 1 | 1 | yes | characteristic |
| 96 | C32×D12 | C23 | 1 | 1 | yes | characteristic |
| 97 | C32×C4×D3 | — | 2 | 1 | no | — |
| 98 | C32×C4×D3 | — | 2 | 1 | no | — |
| 99 | C32×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 100 | C32×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 101 | #6292 | — | 2 | 2 | no | — |
| 102 | #6291 | — | 2 | 2 | no | — |
| 103 | #6289 | — | 2 | 2 | no | — |
| 104 | C3×#626 | — | 2 | 2 | no | — |
| 105 | C3×#625 | — | 2 | 2 | no | — |
| 106 | C3×D3×Dic3 | — | 2 | 2 | no | — |
| 107 | C3×C3⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 108 | C3×C3⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 109 | C3×C3⋊(C3⋊C8) | C23 | 1 | 2 | yes | — |
| 110 | #5835 | — | 9 | 1 | no | — |
| 111 | #5774 | — | 9 | 1 | no | — |
| 112 | #5769 | — | 9 | 1 | no | — |
| 113 | C32×#41 | — | 3 | 1 | no | — |
| 114 | C32×#41 | — | 3 | 1 | no | — |
| 115 | C2×C32×D4 | — | 3 | 1 | no | — |
| 116 | #3832 | — | 3 | 2 | no | — |
| 117 | D4×C3⋊D3 | — | 3 | 2 | no | — |
| 118 | D4×C3⋊D3 | — | 6 | 2 | no | — |
| 119 | #3828 | — | 6 | 1 | no | — |
| 120 | #3828 | C2×D3 | 1 | 1 | yes | characteristic |
| 121 | C2×C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 122 | C2×C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 123 | C2×C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 124 | C2×C4⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 125 | C2×C4⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 126 | C2×C4⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 127 | C2×C4⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 128 | C2×C4⋊(C3⋊D3) | — | 12 | 1 | no | — |
| 129 | C2×C3×#67 | — | 6 | 2 | no | — |
| 130 | C3×#239 | — | 3 | 2 | no | — |
| 131 | C3×#237 | — | 3 | 2 | no | — |
| 132 | C3×#237 | — | 6 | 1 | no | — |
| 133 | C3×D3×D4 | — | 3 | 2 | no | — |
| 134 | C3×D3×D4 | — | 3 | 2 | no | — |
| 135 | C3×D3×D4 | — | 6 | 1 | no | — |
| 136 | C3×D3×D4 | — | 6 | 2 | no | — |
| 137 | C3×#235 | — | 2 | 1 | no | — |
| 138 | C3×#235 | — | 2 | 1 | no | — |
| 139 | C3×#235 | — | 3 | 1 | no | — |
| 140 | C3×#235 | — | 3 | 1 | no | — |
| 141 | C3×#235 | — | 6 | 1 | no | — |
| 142 | C3×#235 | — | 6 | 1 | no | — |
| 143 | C3×#235 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 144 | C3×#235 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 145 | C3×#235 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 146 | C3×#235 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 147 | C2×C3×D12 | — | 2 | 1 | no | — |
| 148 | C2×C3×D12 | — | 6 | 1 | no | — |
| 149 | C2×C3×D12 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 150 | C2×C3×D12 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 151 | #3811 | — | 6 | 2 | no | — |
| 152 | #3811 | — | 6 | 2 | no | — |
| 153 | #3811 | — | 6 | 4 | no | — |
| 154 | D3×#67 | — | 2 | 2 | no | — |
| 155 | #3802 | C2×D3 | 1 | 2 | yes | complemented |
| 156 | D3×D12 | — | 2 | 1 | no | — |
| 157 | D3×D12 | — | 3 | 2 | no | — |
| 158 | D3×D12 | — | 3 | 2 | no | — |
| 159 | D3×D12 | — | 6 | 1 | no | — |
| 160 | D3×D12 | — | 6 | 1 | no | — |
| 161 | D3×D12 | — | 6 | 2 | no | — |
| 162 | D3×D12 | — | 6 | 2 | no | — |
| 163 | #3799 | — | 3 | 2 | no | — |
| 164 | #3799 | — | 3 | 2 | no | — |
| 165 | #3799 | — | 6 | 2 | no | — |
| 166 | #3799 | — | 6 | 1 | no | — |
| 167 | #3799 | — | 6 | 1 | no | — |
| 168 | #3799 | — | 6 | 2 | no | — |
| 169 | #3796 | C2×D3 | 1 | 2 | yes | complemented |
| 170 | #3795 | — | 2 | 1 | no | — |
| 171 | #3755 | — | 3 | 2 | no | — |
| 172 | #3753 | — | 3 | 2 | no | — |
| 173 | #3753 | — | 3 | 2 | no | — |
| 174 | #3753 | — | 3 | 2 | no | — |
| 175 | #3748 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 176 | C2×C3⋊(C3⋊C8) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 177 | C3×#216 | — | 3 | 1 | no | — |
| 178 | C3×#216 | — | 3 | 1 | no | — |
| 179 | C3×#215 | — | 3 | 2 | no | — |
| 180 | C3×#215 | — | 3 | 1 | no | — |
| 181 | C3×#215 | — | 3 | 1 | no | — |
| 182 | C3×#214 | — | 3 | 2 | no | — |
| 183 | C3×#214 | — | 3 | 1 | no | — |
| 184 | C3×#214 | — | 3 | 1 | no | — |
| 185 | C3×#213 | — | 3 | 2 | no | — |
| 186 | C3×#213 | — | 3 | 2 | no | — |
| 187 | C3×#213 | — | 3 | 1 | no | — |
| 188 | C3×#213 | — | 3 | 1 | no | — |
| 189 | C3×#208 | — | 3 | 1 | no | — |
| 190 | C3×#208 | — | 3 | 1 | no | — |
| 191 | C3×#208 | — | 6 | 1 | no | — |
| 192 | C2×C3×C3⋊C8 | — | 3 | 1 | no | — |
| 193 | C2×C3×C3⋊C8 | — | 3 | 1 | no | — |
| 194 | C2×C3×C3⋊C8 | — | 6 | 1 | no | — |
| 195 | #3718 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 196 | #3717 | — | 3 | 2 | no | — |
| 197 | #3717 | — | 3 | 2 | no | — |
| 198 | #3717 | — | 6 | 2 | no | — |
| 199 | #3715 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 200 | #3715 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 201 | #3715 | C2×D3 | 1 | 2 | yes | complemented |
| 202 | #3714 | — | 3 | 2 | no | — |
| 203 | #3714 | — | 3 | 2 | no | — |
| 204 | #3714 | — | 3 | 2 | no | — |
| 205 | #3714 | — | 3 | 2 | no | — |
| 206 | #3714 | — | 3 | 2 | no | — |
| 207 | #3714 | — | 3 | 2 | no | — |
| 208 | #3714 | — | 6 | 2 | no | — |
| 209 | #3714 | — | 6 | 2 | no | — |
| 210 | #3714 | — | 6 | 2 | no | — |
| 211 | #3713 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 212 | #3713 | C2×D3 | 1 | 2 | yes | complemented |
| 213 | #3712 | — | 3 | 2 | no | — |
| 214 | #3711 | — | 3 | 2 | no | — |
| 215 | #3711 | — | 3 | 2 | no | — |
| 216 | #3710 | — | 3 | 2 | no | — |
| 217 | D3×C3⋊C8 | — | 3 | 2 | no | — |
| 218 | D3×C3⋊C8 | — | 3 | 2 | no | — |
| 219 | C22×C33 | C2×D4 | 1 | 1 | yes | characteristic |
| 220 | C2×C3⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 221 | C2×C3⋊(C3⋊D3) | — | 8 | 1 | no | — |
| 222 | C2×C3×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 223 | C2×C32×D3 | — | 2 | 1 | no | — |
| 224 | C2×C32×D3 | — | 2 | 2 | no | — |
| 225 | C2×C32×D3 | — | 2 | 1 | no | — |
| 226 | C2×C32×D3 | — | 8 | 1 | no | — |
| 227 | D3×C3⋊D3 | — | 8 | 2 | no | — |
| 228 | C3×D32 | — | 8 | 2 | no | — |
| 229 | C33×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 230 | C33×C4 | C24 | 1 | 1 | yes | characteristic |
| 231 | C3×C3⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 232 | C32×Dic3 | — | 2 | 1 | no | — |
| 233 | C32×Dic3 | — | 2 | 1 | no | — |
| 234 | C3×H(5,𝔽2) | — | 9 | 1 | no | — |
| 235 | #1009 | — | 3 | 1 | no | — |
| 236 | #1009 | — | 9 | 1 | no | — |
| 237 | #1009 | — | 9 | 1 | no | — |
| 238 | #1009 | — | 9 | 1 | no | — |
| 239 | #1009 | — | 18 | 1 | no | — |
| 240 | #1004 | — | 3 | 1 | no | — |
| 241 | C3×AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 242 | C3×#135 | — | 9 | 1 | no | — |
| 243 | #950 | — | 3 | 1 | no | — |
| 244 | #950 | — | 3 | 1 | no | — |
| 245 | #950 | — | 9 | 2 | no | — |
| 246 | #949 | — | 3 | 1 | no | — |
| 247 | #949 | — | 9 | 1 | no | — |
| 248 | #949 | — | 9 | 1 | no | — |
| 249 | #949 | — | 9 | 2 | no | — |
| 250 | #949 | — | 18 | 1 | no | — |
| 251 | #948 | — | 9 | 1 | no | — |
| 252 | #932 | — | 3 | 1 | no | — |
| 253 | #932 | — | 9 | 2 | no | — |
| 254 | C2×#213 | — | 9 | 1 | no | — |
| 255 | C2×#213 | — | 9 | 1 | no | — |
| 256 | C2×#213 | — | 9 | 2 | no | — |
| 257 | C2×#213 | — | 18 | 1 | no | — |
| 258 | #919 | — | 9 | 2 | no | — |
| 259 | #916 | — | 9 | 2 | no | — |
| 260 | #914 | — | 9 | 2 | no | — |
| 261 | #914 | — | 9 | 2 | no | — |
| 262 | #914 | — | 9 | 2 | no | — |
| 263 | #911 | — | 9 | 2 | no | — |
| 264 | D3×D8 | — | 9 | 2 | no | — |
| 265 | D3×D8 | — | 9 | 2 | no | — |
| 266 | #908 | — | 9 | 1 | no | — |
| 267 | #907 | — | 9 | 1 | no | — |
| 268 | C2×D24 | — | 9 | 1 | no | — |
| 269 | #901 | — | 9 | 1 | no | — |
| 270 | C23×C32 | — | 6 | 1 | no | — |
| 271 | C22×C3⋊D3 | — | 6 | 1 | no | — |
| 272 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 273 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 274 | C22×C3⋊D3 | — | 6 | 1 | no | — |
| 275 | C22×C3⋊D3 | — | 6 | 1 | no | — |
| 276 | C22×C3⋊D3 | — | 12 | 1 | no | — |
| 277 | C22×C3⋊D3 | — | 12 | 1 | no | — |
| 278 | C22×C3⋊D3 | — | 12 | 2 | no | — |
| 279 | C22×C3×D3 | — | 2 | 1 | no | — |
| 280 | C22×C3×D3 | — | 2 | 1 | no | — |
| 281 | C22×C3×D3 | — | 4 | 1 | no | — |
| 282 | C22×C3×D3 | — | 6 | 2 | no | — |
| 283 | C22×C3×D3 | — | 6 | 2 | no | — |
| 284 | C2×D32 | — | 2 | 2 | no | — |
| 285 | C2×D32 | — | 6 | 2 | no | — |
| 286 | C2×D32 | — | 6 | 2 | no | — |
| 287 | C2×D32 | — | 6 | 4 | no | — |
| 288 | C32×Q8 | — | 3 | 1 | no | — |
| 289 | C32×Q8 | — | 3 | 1 | no | — |
| 290 | C32×D4 | — | 3 | 1 | no | — |
| 291 | C32×D4 | — | 3 | 1 | no | — |
| 292 | C32×D4 | — | 3 | 2 | no | — |
| 293 | C32×D4 | — | 6 | 1 | no | — |
| 294 | C32×D4 | — | 6 | 1 | no | — |
| 295 | C32×D4 | — | 6 | 1 | no | — |
| 296 | C2×C32×C4 | — | 2 | 1 | no | — |
| 297 | C2×C32×C4 | — | 2 | 1 | no | — |
| 298 | C2×C32×C4 | — | 2 | 1 | no | — |
| 299 | C2×C32×C4 | — | 4 | 1 | no | — |
| 300 | C2×C32×C4 | — | 6 | 1 | no | — |
| 301 | C2×C32×C4 | — | 6 | 1 | no | — |
| 302 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 303 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 304 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 305 | #638 | — | 6 | 2 | no | — |
| 306 | #638 | #67 | 1 | 2 | yes | — |
| 307 | C4⋊(C3⋊D3) | — | 3 | 2 | no | — |
| 308 | C4⋊(C3⋊D3) | — | 3 | 2 | no | — |
| 309 | C4⋊(C3⋊D3) | — | 3 | 2 | no | — |
| 310 | C4⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 311 | C4⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 312 | C4⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 313 | C4⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 314 | C4⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 315 | C4⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 316 | C4⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 317 | C4⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 318 | C4⋊(C3⋊D3) | — | 12 | 2 | no | — |
| 319 | C4⋊(C3⋊D3) | — | 12 | 1 | no | — |
| 320 | C4⋊(C3⋊D3) | — | 12 | 1 | no | — |
| 321 | C4⋊(C3⋊D3) | — | 12 | 2 | no | — |
| 322 | C4⋊(C3⋊D3) | #67 | 1 | 1 | yes | characteristic |
| 323 | C4×C3⋊D3 | — | 6 | 2 | no | — |
| 324 | C4×C3⋊D3 | C22×D3 | 1 | 2 | yes | — |
| 325 | #634 | #67 | 1 | 1 | yes | characteristic |
| 326 | C3×#67 | — | 2 | 2 | no | — |
| 327 | C3×#67 | — | 2 | 1 | no | — |
| 328 | C3×#67 | — | 2 | 1 | no | — |
| 329 | C3×#67 | — | 2 | 1 | no | — |
| 330 | C3×#67 | — | 2 | 1 | no | — |
| 331 | C3×#67 | — | 3 | 2 | no | — |
| 332 | C3×#67 | — | 3 | 2 | no | — |
| 333 | C3×#67 | — | 4 | 1 | no | — |
| 334 | C3×#67 | — | 6 | 2 | no | — |
| 335 | C3×#67 | — | 6 | 2 | no | — |
| 336 | C3×#67 | — | 6 | 2 | no | — |
| 337 | C3×#67 | — | 6 | 2 | no | — |
| 338 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 339 | C3×D12 | — | 2 | 1 | no | — |
| 340 | C3×D12 | — | 2 | 1 | no | — |
| 341 | C3×D12 | — | 2 | 1 | no | — |
| 342 | C3×D12 | — | 2 | 2 | no | — |
| 343 | C3×D12 | — | 2 | 1 | no | — |
| 344 | C3×D12 | — | 3 | 1 | no | — |
| 345 | C3×D12 | — | 3 | 1 | no | — |
| 346 | C3×D12 | — | 4 | 1 | no | — |
| 347 | C3×D12 | — | 6 | 1 | no | — |
| 348 | C3×D12 | — | 6 | 2 | no | — |
| 349 | C3×D12 | C22×D3 | 1 | 1 | yes | characteristic |
| 350 | C3×D12 | C22×D3 | 1 | 2 | yes | — |
| 351 | C3×D12 | C22×D3 | 1 | 1 | yes | characteristic |
| 352 | C3×D12 | C22×D3 | 1 | 1 | yes | characteristic |
| 353 | C3×D12 | C22×D3 | 1 | 2 | yes | — |
| 354 | C3×D12 | C22×D3 | 1 | 1 | yes | characteristic |
| 355 | C3×C4×D3 | — | 2 | 2 | no | — |
| 356 | C3×C4×D3 | — | 2 | 1 | no | — |
| 357 | C3×C4×D3 | — | 2 | 1 | no | — |
| 358 | C3×C4×D3 | — | 2 | 1 | no | — |
| 359 | C3×C4×D3 | — | 2 | 1 | no | — |
| 360 | C3×C4×D3 | — | 3 | 2 | no | — |
| 361 | C3×C4×D3 | — | 3 | 2 | no | — |
| 362 | C3×C4×D3 | — | 4 | 1 | no | — |
| 363 | C3×C4×D3 | — | 6 | 2 | no | — |
| 364 | C3×C4×D3 | — | 6 | 2 | no | — |
| 365 | C3×Dic6 | — | 2 | 1 | no | — |
| 366 | C3×Dic6 | — | 2 | 1 | no | — |
| 367 | C3×Dic6 | — | 3 | 1 | no | — |
| 368 | C3×Dic6 | — | 3 | 1 | no | — |
| 369 | C3×Dic6 | — | 6 | 1 | no | — |
| 370 | C3×Dic6 | C22×D3 | 1 | 1 | yes | characteristic |
| 371 | C3×Dic6 | C22×D3 | 1 | 1 | yes | characteristic |
| 372 | C3×Dic6 | C22×D3 | 1 | 1 | yes | characteristic |
| 373 | C3×Dic6 | C22×D3 | 1 | 1 | yes | characteristic |
| 374 | #626 | — | 2 | 2 | no | — |
| 375 | #626 | — | 6 | 2 | no | — |
| 376 | #626 | — | 6 | 2 | no | — |
| 377 | #626 | — | 6 | 4 | no | — |
| 378 | #626 | — | 6 | 2 | no | — |
| 379 | #626 | — | 6 | 2 | no | — |
| 380 | #626 | — | 6 | 4 | no | — |
| 381 | #625 | — | 2 | 2 | no | — |
| 382 | #624 | — | 6 | 2 | no | — |
| 383 | #624 | — | 6 | 2 | no | — |
| 384 | #624 | — | 6 | 4 | no | — |
| 385 | D3×Dic3 | — | 2 | 2 | no | — |
| 386 | C3⋊(C3⋊C8) | C22×D3 | 1 | 1 | yes | characteristic |
| 387 | C3⋊(C3⋊C8) | C22×D3 | 1 | 2 | yes | — |
| 388 | C3⋊(C3⋊C8) | C22×D3 | 1 | 1 | yes | characteristic |
| 389 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 390 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 391 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 392 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 393 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 394 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 395 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 396 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 397 | C3×C3⋊C8 | — | 6 | 2 | no | — |
| 398 | #576 | — | 27 | 1 | no | Sylow |
| 399 | C2×C33 | — | 2 | 1 | no | — |
| 400 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 401 | C3⋊(C3⋊D3) | — | 4 | 2 | no | — |
| 402 | C3×C3⋊D3 | — | 2 | 2 | no | — |
| 403 | C32×D3 | — | 4 | 1 | no | — |
| 404 | C32×D3 | — | 4 | 1 | no | — |
| 405 | C32×D3 | — | 4 | 2 | no | — |
| 406 | C3×#41 | — | 3 | 1 | no | — |
| 407 | C3×#41 | — | 3 | 1 | no | — |
| 408 | C3×#41 | — | 3 | 1 | no | — |
| 409 | C3×#41 | — | 3 | 1 | no | — |
| 410 | C3×#41 | — | 6 | 1 | no | — |
| 411 | C3×#41 | — | 6 | 1 | no | — |
| 412 | C3×#41 | — | 9 | 1 | no | — |
| 413 | C3×#41 | — | 9 | 2 | no | — |
| 414 | C3×#41 | — | 18 | 1 | no | — |
| 415 | C2×C3×D4 | — | 3 | 1 | no | — |
| 416 | C2×C3×D4 | — | 3 | 1 | no | — |
| 417 | C2×C3×D4 | — | 6 | 1 | no | — |
| 418 | C2×C3×D4 | — | 9 | 2 | no | — |
| 419 | C2×C3×D4 | — | 18 | 1 | no | — |
| 420 | C2×C3×D4 | — | 18 | 2 | no | — |
| 421 | C2×#67 | — | 6 | 2 | no | — |
| 422 | #239 | — | 3 | 2 | no | — |
| 423 | #239 | — | 9 | 2 | no | — |
| 424 | #239 | — | 9 | 2 | no | — |
| 425 | #239 | — | 18 | 2 | no | — |
| 426 | #239 | — | 18 | 1 | no | — |
| 427 | #237 | — | 3 | 2 | no | — |
| 428 | #237 | — | 6 | 1 | no | — |
| 429 | D3×D4 | — | 3 | 2 | no | — |
| 430 | D3×D4 | — | 3 | 2 | no | — |
| 431 | D3×D4 | — | 6 | 1 | no | — |
| 432 | D3×D4 | — | 6 | 2 | no | — |
| 433 | D3×D4 | — | 9 | 2 | no | — |
| 434 | D3×D4 | — | 9 | 2 | no | — |
| 435 | D3×D4 | — | 18 | 2 | no | — |
| 436 | D3×D4 | — | 18 | 1 | no | — |
| 437 | D3×D4 | — | 18 | 2 | no | — |
| 438 | D3×D4 | — | 18 | 2 | no | — |
| 439 | D3×D4 | — | 18 | 2 | no | — |
| 440 | D3×D4 | — | 18 | 4 | no | — |
| 441 | #235 | — | 3 | 1 | no | — |
| 442 | #235 | — | 3 | 1 | no | — |
| 443 | #235 | — | 6 | 1 | no | — |
| 444 | #235 | — | 6 | 1 | no | — |
| 445 | #235 | — | 9 | 2 | no | — |
| 446 | #235 | — | 18 | 1 | no | — |
| 447 | #235 | — | 18 | 1 | no | — |
| 448 | #235 | — | 18 | 2 | no | — |
| 449 | #235 | D32 | 1 | 1 | yes | characteristic, complemented |
| 450 | #235 | D32 | 1 | 1 | yes | characteristic, complemented |
| 451 | C2×D12 | — | 6 | 1 | no | — |
| 452 | C2×D12 | — | 9 | 1 | no | — |
| 453 | C2×D12 | — | 9 | 1 | no | — |
| 454 | C2×D12 | — | 9 | 1 | no | — |
| 455 | C2×D12 | — | 9 | 2 | no | — |
| 456 | C2×D12 | — | 18 | 1 | no | — |
| 457 | C2×D12 | — | 18 | 1 | no | — |
| 458 | C2×D12 | — | 18 | 1 | no | — |
| 459 | C2×D12 | — | 18 | 1 | no | — |
| 460 | C2×D12 | — | 18 | 1 | no | — |
| 461 | C2×D12 | — | 18 | 2 | no | — |
| 462 | C2×D12 | — | 36 | 1 | no | — |
| 463 | C2×D12 | D32 | 1 | 1 | yes | characteristic, complemented |
| 464 | C3×Q16 | — | 9 | 1 | no | — |
| 465 | C3×SD16 | — | 9 | 1 | no | — |
| 466 | C3×SD16 | — | 9 | 1 | no | — |
| 467 | C3×SD16 | — | 9 | 2 | no | — |
| 468 | C3×D8 | — | 9 | 1 | no | — |
| 469 | C3×D8 | — | 9 | 2 | no | — |
| 470 | C3×M16 | — | 9 | 1 | no | — |
| 471 | C2×C3×C8 | — | 9 | 1 | no | — |
| 472 | #216 | — | 3 | 1 | no | — |
| 473 | #216 | — | 3 | 1 | no | — |
| 474 | #215 | — | 3 | 1 | no | — |
| 475 | #215 | — | 3 | 2 | no | — |
| 476 | #215 | — | 3 | 1 | no | — |
| 477 | #215 | — | 9 | 2 | no | — |
| 478 | #215 | — | 9 | 2 | no | — |
| 479 | #215 | — | 18 | 2 | no | — |
| 480 | #214 | — | 3 | 1 | no | — |
| 481 | #214 | — | 3 | 2 | no | — |
| 482 | #214 | — | 3 | 1 | no | — |
| 483 | #213 | — | 3 | 1 | no | — |
| 484 | #213 | — | 3 | 2 | no | — |
| 485 | #213 | — | 3 | 1 | no | — |
| 486 | #213 | — | 3 | 2 | no | — |
| 487 | #213 | — | 9 | 2 | no | — |
| 488 | #213 | — | 9 | 2 | no | — |
| 489 | #213 | — | 9 | 2 | no | — |
| 490 | #213 | — | 9 | 2 | no | — |
| 491 | #213 | — | 9 | 2 | no | — |
| 492 | #213 | — | 9 | 2 | no | — |
| 493 | #213 | — | 18 | 2 | no | — |
| 494 | #213 | — | 18 | 2 | no | — |
| 495 | #213 | — | 18 | 2 | no | — |
| 496 | #208 | — | 3 | 1 | no | — |
| 497 | #208 | — | 3 | 1 | no | — |
| 498 | #208 | — | 6 | 1 | no | — |
| 499 | #208 | — | 9 | 2 | no | — |
| 500 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 501 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 502 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 503 | C2×C3⋊C8 | — | 9 | 2 | no | — |
| 504 | D24 | — | 9 | 2 | no | — |
| 505 | D24 | — | 9 | 2 | no | — |
| 506 | D24 | — | 9 | 2 | no | — |
| 507 | #204 | — | 9 | 2 | no | — |
| 508 | ΓL(1,𝔽25) | — | 9 | 2 | no | — |
| 509 | ΓL(1,𝔽25) | — | 9 | 2 | no | — |
| 510 | D3×C8 | — | 9 | 2 | no | — |
| 511 | D3×C8 | — | 9 | 2 | no | — |
| 512 | C22×C32 | — | 2 | 1 | no | — |
| 513 | C22×C32 | — | 2 | 1 | no | — |
| 514 | C22×C32 | — | 2 | 1 | no | — |
| 515 | C22×C32 | — | 4 | 1 | no | — |
| 516 | C22×C32 | — | 6 | 1 | no | — |
| 517 | C22×C32 | — | 6 | 2 | no | — |
| 518 | C22×C32 | — | 6 | 1 | no | — |
| 519 | C22×C32 | — | 24 | 1 | no | — |
| 520 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic |
| 521 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic |
| 522 | C22×C32 | C2×#67 | 1 | 1 | yes | characteristic |
| 523 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 524 | C2×C3⋊D3 | — | 6 | 4 | no | — |
| 525 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 526 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 527 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 528 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 529 | C2×C3⋊D3 | — | 12 | 4 | no | — |
| 530 | C2×C3⋊D3 | — | 24 | 2 | no | — |
| 531 | C2×C3⋊D3 | — | 24 | 1 | no | — |
| 532 | C2×C3⋊D3 | — | 24 | 1 | no | — |
| 533 | C2×C3⋊D3 | — | 24 | 1 | no | — |
| 534 | C2×C3⋊D3 | — | 24 | 2 | no | — |
| 535 | C2×C3⋊D3 | — | 24 | 2 | no | — |
| 536 | C2×C3⋊D3 | — | 24 | 2 | no | — |
| 537 | C2×C3⋊D3 | — | 24 | 4 | no | — |
| 538 | C2×C3⋊D3 | C2×#67 | 1 | 2 | yes | — |
| 539 | C2×C3×D3 | — | 2 | 2 | no | — |
| 540 | C2×C3×D3 | — | 2 | 1 | no | — |
| 541 | C2×C3×D3 | — | 2 | 1 | no | — |
| 542 | C2×C3×D3 | — | 2 | 1 | no | — |
| 543 | C2×C3×D3 | — | 2 | 2 | no | — |
| 544 | C2×C3×D3 | — | 2 | 2 | no | — |
| 545 | C2×C3×D3 | — | 2 | 1 | no | — |
| 546 | C2×C3×D3 | — | 3 | 2 | no | — |
| 547 | C2×C3×D3 | — | 3 | 2 | no | — |
| 548 | C2×C3×D3 | — | 4 | 1 | no | — |
| 549 | C2×C3×D3 | — | 4 | 2 | no | — |
| 550 | C2×C3×D3 | — | 6 | 2 | no | — |
| 551 | C2×C3×D3 | — | 8 | 1 | no | — |
| 552 | C2×C3×D3 | — | 8 | 1 | no | — |
| 553 | C2×C3×D3 | — | 8 | 2 | no | — |
| 554 | C2×C3×D3 | — | 24 | 2 | no | — |
| 555 | C2×C3×D3 | — | 24 | 2 | no | — |
| 556 | D32 | — | 8 | 2 | no | — |
| 557 | D32 | — | 24 | 2 | no | — |
| 558 | D32 | — | 24 | 2 | no | — |
| 559 | D32 | — | 24 | 4 | no | — |
| 560 | C32×C4 | — | 2 | 1 | no | — |
| 561 | C32×C4 | — | 2 | 1 | no | — |
| 562 | C32×C4 | — | 2 | 1 | no | — |
| 563 | C32×C4 | — | 2 | 1 | no | — |
| 564 | C32×C4 | — | 2 | 1 | no | — |
| 565 | C32×C4 | — | 2 | 1 | no | — |
| 566 | C32×C4 | — | 4 | 1 | no | — |
| 567 | C32×C4 | — | 4 | 1 | no | — |
| 568 | C32×C4 | — | 6 | 1 | no | — |
| 569 | C32×C4 | — | 6 | 1 | no | — |
| 570 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 571 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 572 | C32×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 573 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 574 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 575 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 576 | C3⋊Dic3 | C2×#67 | 1 | 2 | yes | — |
| 577 | C3×Dic3 | — | 2 | 2 | no | — |
| 578 | C3×Dic3 | — | 2 | 1 | no | — |
| 579 | C3×Dic3 | — | 2 | 1 | no | — |
| 580 | C3×Dic3 | — | 2 | 1 | no | — |
| 581 | C3×Dic3 | — | 2 | 1 | no | — |
| 582 | C3×Dic3 | — | 3 | 2 | no | — |
| 583 | C3×Dic3 | — | 3 | 2 | no | — |
| 584 | C3×Dic3 | — | 4 | 1 | no | — |
| 585 | C3×Dic3 | — | 6 | 2 | no | — |
| 586 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 587 | H(5,𝔽2) | — | 27 | 1 | no | — |
| 588 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 589 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 590 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 591 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 592 | #135 | — | 9 | 1 | no | — |
| 593 | #135 | — | 27 | 2 | no | — |
| 594 | C2×D8 | — | 27 | 1 | no | — |
| 595 | C2×D8 | — | 27 | 2 | no | — |
| 596 | #131 | — | 27 | 1 | no | — |
| 597 | C33 | #576 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 598 | C23×C3 | — | 6 | 1 | no | — |
| 599 | C23×C3 | — | 6 | 1 | no | — |
| 600 | C23×C3 | — | 12 | 1 | no | — |
| 601 | C23×C3 | — | 18 | 2 | no | — |
| 602 | C22×D3 | — | 2 | 1 | no | — |
| 603 | C22×D3 | — | 6 | 2 | no | — |
| 604 | C22×D3 | — | 6 | 2 | no | — |
| 605 | C22×D3 | — | 18 | 2 | no | — |
| 606 | C22×D3 | — | 18 | 2 | no | — |
| 607 | C22×D3 | — | 18 | 2 | no | — |
| 608 | C22×D3 | — | 18 | 4 | no | — |
| 609 | C22×D3 | — | 18 | 2 | no | — |
| 610 | C22×D3 | — | 18 | 1 | no | — |
| 611 | C22×D3 | — | 18 | 1 | no | — |
| 612 | C22×D3 | — | 18 | 1 | no | — |
| 613 | C22×D3 | — | 36 | 1 | no | — |
| 614 | C22×D3 | — | 36 | 1 | no | — |
| 615 | C22×D3 | — | 36 | 2 | no | — |
| 616 | C3×Q8 | — | 3 | 1 | no | — |
| 617 | C3×Q8 | — | 3 | 1 | no | — |
| 618 | C3×Q8 | — | 3 | 1 | no | — |
| 619 | C3×Q8 | — | 3 | 1 | no | — |
| 620 | C3×Q8 | — | 6 | 1 | no | — |
| 621 | C3×Q8 | — | 6 | 1 | no | — |
| 622 | C3×Q8 | — | 9 | 1 | no | — |
| 623 | C3×D4 | — | 3 | 1 | no | — |
| 624 | C3×D4 | — | 3 | 2 | no | — |
| 625 | C3×D4 | — | 3 | 1 | no | — |
| 626 | C3×D4 | — | 3 | 1 | no | — |
| 627 | C3×D4 | — | 3 | 1 | no | — |
| 628 | C3×D4 | — | 3 | 2 | no | — |
| 629 | C3×D4 | — | 6 | 1 | no | — |
| 630 | C3×D4 | — | 6 | 2 | no | — |
| 631 | C3×D4 | — | 6 | 1 | no | — |
| 632 | C3×D4 | — | 6 | 2 | no | — |
| 633 | C3×D4 | — | 6 | 1 | no | — |
| 634 | C3×D4 | — | 6 | 1 | no | — |
| 635 | C3×D4 | — | 6 | 1 | no | — |
| 636 | C3×D4 | — | 6 | 1 | no | — |
| 637 | C3×D4 | — | 6 | 1 | no | — |
| 638 | C3×D4 | — | 6 | 1 | no | — |
| 639 | C3×D4 | — | 9 | 2 | no | — |
| 640 | C3×D4 | — | 9 | 1 | no | — |
| 641 | C3×D4 | — | 12 | 1 | no | — |
| 642 | C3×D4 | — | 12 | 1 | no | — |
| 643 | C3×D4 | — | 18 | 2 | no | — |
| 644 | C3×D4 | — | 18 | 2 | no | — |
| 645 | C2×C3×C4 | — | 2 | 1 | no | — |
| 646 | C2×C3×C4 | — | 2 | 1 | no | — |
| 647 | C2×C3×C4 | — | 2 | 1 | no | — |
| 648 | C2×C3×C4 | — | 4 | 1 | no | — |
| 649 | C2×C3×C4 | — | 6 | 2 | no | — |
| 650 | C2×C3×C4 | — | 6 | 1 | no | — |
| 651 | C2×C3×C4 | — | 6 | 1 | no | — |
| 652 | C2×C3×C4 | — | 6 | 1 | no | — |
| 653 | C2×C3×C4 | — | 6 | 1 | no | — |
| 654 | C2×C3×C4 | — | 9 | 2 | no | — |
| 655 | C2×C3×C4 | — | 12 | 1 | no | — |
| 656 | C2×C3×C4 | — | 18 | 2 | no | — |
| 657 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 658 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 659 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 660 | #67 | — | 2 | 1 | no | — |
| 661 | #67 | — | 2 | 1 | no | — |
| 662 | #67 | — | 3 | 2 | no | — |
| 663 | #67 | — | 3 | 2 | no | — |
| 664 | #67 | — | 6 | 2 | no | — |
| 665 | #67 | — | 6 | 2 | no | — |
| 666 | #67 | — | 6 | 2 | no | — |
| 667 | #67 | — | 6 | 2 | no | — |
| 668 | #67 | — | 18 | 2 | no | — |
| 669 | #67 | — | 18 | 2 | no | — |
| 670 | #67 | — | 18 | 2 | no | — |
| 671 | #67 | — | 18 | 4 | no | — |
| 672 | C2×Dic3 | — | 6 | 2 | no | — |
| 673 | D12 | — | 2 | 1 | no | — |
| 674 | D12 | — | 3 | 1 | no | — |
| 675 | D12 | — | 3 | 1 | no | — |
| 676 | D12 | — | 6 | 1 | no | — |
| 677 | D12 | — | 6 | 2 | no | — |
| 678 | D12 | — | 9 | 2 | no | — |
| 679 | D12 | — | 9 | 2 | no | — |
| 680 | D12 | — | 9 | 2 | no | — |
| 681 | D12 | — | 18 | 2 | no | — |
| 682 | D12 | — | 18 | 2 | no | — |
| 683 | D12 | — | 18 | 2 | no | — |
| 684 | D12 | — | 18 | 2 | no | — |
| 685 | D12 | — | 18 | 2 | no | — |
| 686 | D12 | — | 18 | 2 | no | — |
| 687 | D12 | — | 18 | 4 | no | — |
| 688 | D12 | — | 18 | 2 | no | — |
| 689 | D12 | — | 18 | 1 | no | — |
| 690 | D12 | — | 18 | 1 | no | — |
| 691 | D12 | — | 18 | 1 | no | — |
| 692 | D12 | — | 36 | 2 | no | — |
| 693 | D12 | — | 36 | 1 | no | — |
| 694 | D12 | — | 36 | 1 | no | — |
| 695 | D12 | — | 36 | 2 | no | — |
| 696 | D12 | C2×D32 | 1 | 2 | yes | — |
| 697 | D12 | C2×D32 | 1 | 1 | yes | characteristic |
| 698 | D12 | C2×D32 | 1 | 1 | yes | characteristic |
| 699 | C4×D3 | — | 2 | 1 | no | — |
| 700 | C4×D3 | — | 2 | 1 | no | — |
| 701 | C4×D3 | — | 3 | 2 | no | — |
| 702 | C4×D3 | — | 3 | 2 | no | — |
| 703 | C4×D3 | — | 6 | 2 | no | — |
| 704 | C4×D3 | — | 6 | 2 | no | — |
| 705 | C4×D3 | — | 18 | 2 | no | — |
| 706 | C4×D3 | — | 18 | 2 | no | — |
| 707 | C4×D3 | — | 18 | 2 | no | — |
| 708 | C4×D3 | — | 18 | 4 | no | — |
| 709 | Dic6 | — | 3 | 1 | no | — |
| 710 | Dic6 | — | 3 | 1 | no | — |
| 711 | Dic6 | — | 6 | 1 | no | — |
| 712 | Dic6 | C2×D32 | 1 | 1 | yes | characteristic |
| 713 | Dic6 | C2×D32 | 1 | 1 | yes | characteristic |
| 714 | C3×C8 | — | 9 | 1 | no | — |
| 715 | C3×C8 | — | 9 | 2 | no | — |
| 716 | C3×C8 | — | 9 | 1 | no | — |
| 717 | C3⋊C8 | — | 3 | 1 | no | — |
| 718 | C3⋊C8 | — | 3 | 2 | no | — |
| 719 | C3⋊C8 | — | 3 | 1 | no | — |
| 720 | C3⋊C8 | — | 3 | 1 | no | — |
| 721 | C3⋊C8 | — | 3 | 1 | no | — |
| 722 | C3⋊C8 | — | 3 | 2 | no | — |
| 723 | C3⋊C8 | — | 6 | 1 | no | — |
| 724 | C3⋊C8 | — | 6 | 1 | no | — |
| 725 | C3⋊C8 | — | 6 | 2 | no | — |
| 726 | C2×C32 | — | 2 | 1 | no | — |
| 727 | C2×C32 | — | 2 | 2 | no | — |
| 728 | C2×C32 | — | 2 | 1 | no | — |
| 729 | C2×C32 | — | 2 | 1 | no | — |
| 730 | C2×C32 | — | 2 | 1 | no | — |
| 731 | C2×C32 | — | 2 | 1 | no | — |
| 732 | C2×C32 | — | 2 | 1 | no | — |
| 733 | C2×C32 | — | 4 | 1 | no | — |
| 734 | C2×C32 | — | 4 | 1 | no | — |
| 735 | C2×C32 | — | 4 | 1 | no | — |
| 736 | C2×C32 | — | 4 | 2 | no | — |
| 737 | C2×C32 | — | 12 | 1 | no | — |
| 738 | C2×C32 | — | 12 | 2 | no | — |
| 739 | C2×C32 | — | 12 | 1 | no | — |
| 740 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 741 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 742 | C2×C32 | C22×#67 | 1 | 1 | yes | characteristic |
| 743 | C3⋊D3 | — | 2 | 2 | no | — |
| 744 | C3⋊D3 | — | 12 | 2 | no | — |
| 745 | C3⋊D3 | — | 12 | 4 | no | — |
| 746 | C3⋊D3 | — | 12 | 2 | no | — |
| 747 | C3⋊D3 | — | 12 | 2 | no | — |
| 748 | C3⋊D3 | — | 24 | 2 | no | — |
| 749 | C3⋊D3 | — | 24 | 2 | no | — |
| 750 | C3⋊D3 | — | 24 | 4 | no | — |
| 751 | C3×D3 | — | 4 | 2 | no | — |
| 752 | C3×D3 | — | 4 | 1 | no | — |
| 753 | C3×D3 | — | 4 | 1 | no | — |
| 754 | C3×D3 | — | 4 | 1 | no | — |
| 755 | C3×D3 | — | 4 | 2 | no | — |
| 756 | C3×D3 | — | 4 | 1 | no | — |
| 757 | C3×D3 | — | 4 | 2 | no | — |
| 758 | C3×D3 | — | 6 | 2 | no | — |
| 759 | C3×D3 | — | 6 | 2 | no | — |
| 760 | C3×D3 | — | 8 | 1 | no | — |
| 761 | C3×D3 | — | 8 | 2 | no | — |
| 762 | C3×D3 | — | 12 | 2 | no | — |
| 763 | #41 | — | 3 | 1 | no | — |
| 764 | #41 | — | 3 | 1 | no | — |
| 765 | #41 | — | 9 | 1 | no | — |
| 766 | #41 | — | 9 | 2 | no | — |
| 767 | #41 | — | 18 | 1 | no | — |
| 768 | #41 | — | 27 | 2 | no | — |
| 769 | #41 | — | 54 | 1 | no | — |
| 770 | C2×D4 | — | 3 | 1 | no | — |
| 771 | C2×D4 | — | 9 | 2 | no | — |
| 772 | C2×D4 | — | 18 | 1 | no | — |
| 773 | C2×D4 | — | 18 | 2 | no | — |
| 774 | C2×D4 | — | 27 | 2 | no | — |
| 775 | C2×D4 | — | 27 | 1 | no | — |
| 776 | C2×D4 | — | 54 | 1 | no | — |
| 777 | C2×D4 | — | 54 | 2 | no | — |
| 778 | Q16 | — | 9 | 1 | no | — |
| 779 | SD16 | — | 9 | 1 | no | — |
| 780 | SD16 | — | 9 | 1 | no | — |
| 781 | SD16 | — | 9 | 2 | no | — |
| 782 | SD16 | — | 27 | 2 | no | — |
| 783 | D8 | — | 9 | 1 | no | — |
| 784 | D8 | — | 9 | 2 | no | — |
| 785 | D8 | — | 27 | 2 | no | — |
| 786 | D8 | — | 27 | 2 | no | — |
| 787 | D8 | — | 27 | 2 | no | — |
| 788 | M16 | — | 9 | 1 | no | — |
| 789 | M16 | — | 27 | 2 | no | — |
| 790 | C2×C8 | — | 9 | 1 | no | — |
| 791 | C2×C8 | — | 27 | 2 | no | — |
| 792 | C22×C3 | — | 2 | 1 | no | — |
| 793 | C22×C3 | — | 2 | 1 | no | — |
| 794 | C22×C3 | — | 2 | 1 | no | — |
| 795 | C22×C3 | — | 4 | 1 | no | — |
| 796 | C22×C3 | — | 6 | 2 | no | — |
| 797 | C22×C3 | — | 6 | 2 | no | — |
| 798 | C22×C3 | — | 6 | 1 | no | — |
| 799 | C22×C3 | — | 6 | 1 | no | — |
| 800 | C22×C3 | — | 6 | 1 | no | — |
| 801 | C22×C3 | — | 6 | 1 | no | — |
| 802 | C22×C3 | — | 6 | 2 | no | — |
| 803 | C22×C3 | — | 9 | 2 | no | — |
| 804 | C22×C3 | — | 12 | 1 | no | — |
| 805 | C22×C3 | — | 12 | 2 | no | — |
| 806 | C22×C3 | — | 24 | 1 | no | — |
| 807 | C22×C3 | — | 24 | 1 | no | — |
| 808 | C22×C3 | — | 24 | 2 | no | — |
| 809 | C22×C3 | — | 72 | 2 | no | — |
| 810 | C22×C3 | D3×#67 | 1 | 1 | yes | characteristic |
| 811 | C22×C3 | D3×#67 | 1 | 1 | yes | characteristic |
| 812 | C22×C3 | #3811 | 1 | 1 | yes | characteristic |
| 813 | C2×D3 | — | 2 | 1 | no | — |
| 814 | C2×D3 | — | 2 | 2 | no | — |
| 815 | C2×D3 | — | 2 | 1 | no | — |
| 816 | C2×D3 | — | 3 | 2 | no | — |
| 817 | C2×D3 | — | 3 | 2 | no | — |
| 818 | C2×D3 | — | 6 | 2 | no | — |
| 819 | C2×D3 | — | 8 | 1 | no | — |
| 820 | C2×D3 | — | 18 | 4 | no | — |
| 821 | C2×D3 | — | 18 | 2 | no | — |
| 822 | C2×D3 | — | 18 | 2 | no | — |
| 823 | C2×D3 | — | 18 | 2 | no | — |
| 824 | C2×D3 | — | 24 | 2 | no | — |
| 825 | C2×D3 | — | 24 | 2 | no | — |
| 826 | C2×D3 | — | 36 | 2 | no | — |
| 827 | C2×D3 | — | 36 | 2 | no | — |
| 828 | C2×D3 | — | 36 | 4 | no | — |
| 829 | C2×D3 | — | 72 | 2 | no | — |
| 830 | C2×D3 | — | 72 | 2 | no | — |
| 831 | C2×D3 | — | 72 | 2 | no | — |
| 832 | C2×D3 | — | 72 | 4 | no | — |
| 833 | C2×D3 | — | 72 | 1 | no | — |
| 834 | C2×D3 | — | 72 | 1 | no | — |
| 835 | C2×D3 | — | 72 | 1 | no | — |
| 836 | C2×D3 | — | 72 | 2 | no | — |
| 837 | C2×D3 | — | 72 | 2 | no | — |
| 838 | C2×D3 | — | 72 | 2 | no | — |
| 839 | C2×D3 | — | 72 | 4 | no | — |
| 840 | C3×C4 | — | 2 | 1 | no | — |
| 841 | C3×C4 | — | 2 | 1 | no | — |
| 842 | C3×C4 | — | 2 | 1 | no | — |
| 843 | C3×C4 | — | 2 | 1 | no | — |
| 844 | C3×C4 | — | 2 | 1 | no | — |
| 845 | C3×C4 | — | 2 | 1 | no | — |
| 846 | C3×C4 | — | 4 | 1 | no | — |
| 847 | C3×C4 | — | 4 | 1 | no | — |
| 848 | C3×C4 | — | 6 | 2 | no | — |
| 849 | C3×C4 | — | 6 | 1 | no | — |
| 850 | C3×C4 | — | 6 | 1 | no | — |
| 851 | C3×C4 | — | 6 | 1 | no | — |
| 852 | C3×C4 | — | 6 | 1 | no | — |
| 853 | C3×C4 | — | 9 | 2 | no | — |
| 854 | C3×C4 | — | 12 | 1 | no | — |
| 855 | C3×C4 | D3×#67 | 1 | 1 | yes | characteristic |
| 856 | C3×C4 | D3×#67 | 1 | 1 | yes | characteristic |
| 857 | C3×C4 | #3811 | 1 | 1 | yes | characteristic |
| 858 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 859 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 860 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 861 | Dic3 | — | 2 | 1 | no | — |
| 862 | Dic3 | — | 2 | 1 | no | — |
| 863 | Dic3 | — | 3 | 2 | no | — |
| 864 | Dic3 | — | 3 | 2 | no | — |
| 865 | Dic3 | — | 6 | 2 | no | — |
| 866 | C32 | — | 2 | 1 | no | — |
| 867 | C32 | — | 2 | 1 | no | — |
| 868 | C32 | — | 2 | 1 | no | — |
| 869 | C32 | — | 4 | 1 | no | — |
| 870 | C32 | #5769 | 1 | 1 | yes | characteristic, complemented |
| 871 | C32 | #5774 | 1 | 1 | yes | characteristic, complemented |
| 872 | C32 | #5835 | 1 | 1 | yes | characteristic, complemented |
| 873 | C23 | — | 6 | 1 | no | — |
| 874 | C23 | — | 18 | 2 | no | — |
| 875 | C23 | — | 54 | 2 | no | — |
| 876 | C23 | — | 54 | 1 | no | — |
| 877 | Q8 | — | 3 | 1 | no | — |
| 878 | Q8 | — | 3 | 1 | no | — |
| 879 | Q8 | — | 9 | 1 | no | — |
| 880 | D4 | — | 3 | 1 | no | — |
| 881 | D4 | — | 3 | 2 | no | — |
| 882 | D4 | — | 3 | 1 | no | — |
| 883 | D4 | — | 6 | 1 | no | — |
| 884 | D4 | — | 6 | 1 | no | — |
| 885 | D4 | — | 6 | 1 | no | — |
| 886 | D4 | — | 9 | 2 | no | — |
| 887 | D4 | — | 9 | 1 | no | — |
| 888 | D4 | — | 18 | 2 | no | — |
| 889 | D4 | — | 18 | 2 | no | — |
| 890 | D4 | — | 27 | 2 | no | — |
| 891 | D4 | — | 54 | 2 | no | — |
| 892 | D4 | — | 54 | 2 | no | — |
| 893 | D4 | — | 54 | 1 | no | — |
| 894 | C2×C4 | — | 6 | 1 | no | — |
| 895 | C2×C4 | — | 6 | 1 | no | — |
| 896 | C2×C4 | — | 9 | 2 | no | — |
| 897 | C2×C4 | — | 18 | 2 | no | — |
| 898 | C2×C4 | — | 54 | 2 | no | — |
| 899 | C2×C4 | D33 | 1 | 1 | yes | characteristic |
| 900 | C8 | — | 9 | 1 | no | — |
| 901 | C8 | — | 9 | 1 | no | — |
| 902 | C8 | — | 9 | 2 | no | — |
| 903 | C2×C3 | — | 2 | 2 | no | — |
| 904 | C2×C3 | — | 2 | 1 | no | — |
| 905 | C2×C3 | — | 2 | 1 | no | — |
| 906 | C2×C3 | — | 2 | 1 | no | — |
| 907 | C2×C3 | — | 2 | 1 | no | — |
| 908 | C2×C3 | — | 2 | 1 | no | — |
| 909 | C2×C3 | — | 2 | 1 | no | — |
| 910 | C2×C3 | — | 4 | 1 | no | — |
| 911 | C2×C3 | — | 4 | 1 | no | — |
| 912 | C2×C3 | — | 4 | 2 | no | — |
| 913 | C2×C3 | — | 4 | 1 | no | — |
| 914 | C2×C3 | — | 12 | 2 | no | — |
| 915 | C2×C3 | — | 12 | 1 | no | — |
| 916 | C2×C3 | — | 12 | 1 | no | — |
| 917 | C2×C3 | — | 12 | 2 | no | — |
| 918 | C2×C3 | — | 12 | 1 | no | — |
| 919 | C2×C3 | — | 12 | 2 | no | — |
| 920 | C2×C3 | — | 12 | 1 | no | — |
| 921 | C2×C3 | — | 18 | 2 | no | — |
| 922 | C2×C3 | — | 24 | 2 | no | — |
| 923 | C2×C3 | — | 24 | 1 | no | — |
| 924 | C2×C3 | C2×D3×#67 | 1 | 1 | yes | characteristic |
| 925 | C2×C3 | C2×D3×#67 | 1 | 1 | yes | characteristic |
| 926 | C2×C3 | C2×#3811 | 1 | 1 | yes | characteristic |
| 927 | D3 | — | 4 | 2 | no | — |
| 928 | D3 | — | 4 | 1 | no | — |
| 929 | D3 | — | 4 | 1 | no | — |
| 930 | D3 | — | 6 | 2 | no | — |
| 931 | D3 | — | 6 | 2 | no | — |
| 932 | D3 | — | 12 | 2 | no | — |
| 933 | D3 | — | 36 | 4 | no | — |
| 934 | D3 | — | 36 | 2 | no | — |
| 935 | D3 | — | 36 | 2 | no | — |
| 936 | D3 | — | 36 | 2 | no | — |
| 937 | D3 | — | 72 | 2 | no | — |
| 938 | D3 | — | 72 | 2 | no | — |
| 939 | D3 | — | 72 | 4 | no | — |
| 940 | C22 | — | 6 | 1 | no | — |
| 941 | C22 | — | 6 | 1 | no | — |
| 942 | C22 | — | 6 | 2 | no | — |
| 943 | C22 | — | 9 | 2 | no | — |
| 944 | C22 | — | 24 | 1 | no | — |
| 945 | C22 | — | 54 | 2 | no | — |
| 946 | C22 | — | 72 | 2 | no | — |
| 947 | C22 | — | 216 | 1 | no | — |
| 948 | C22 | — | 216 | 2 | no | — |
| 949 | C22 | #88952 | 1 | 1 | yes | characteristic |
| 950 | C4 | — | 6 | 1 | no | — |
| 951 | C4 | — | 6 | 1 | no | — |
| 952 | C4 | — | 9 | 2 | no | — |
| 953 | C4 | #88952 | 1 | 1 | yes | characteristic |
| 954 | C4 | C2×D33 | 1 | 1 | yes | characteristic |
| 955 | C3 | — | 2 | 1 | no | — |
| 956 | C3 | — | 2 | 1 | no | — |
| 957 | C3 | — | 2 | 1 | no | — |
| 958 | C3 | — | 4 | 1 | no | — |
| 959 | C3 | #10595097 | 1 | 1 | yes | characteristic, complemented |
| 960 | C3 | #10595456 | 1 | 1 | yes | characteristic, complemented |
| 961 | C3 | #10595461 | 1 | 1 | yes | characteristic, complemented |
| 962 | C2 | — | 2 | 1 | no | — |
| 963 | C2 | — | 12 | 2 | no | — |
| 964 | C2 | — | 12 | 1 | no | — |
| 965 | C2 | — | 12 | 1 | no | — |
| 966 | C2 | — | 18 | 2 | no | — |
| 967 | C2 | — | 108 | 2 | no | — |
| 968 | C2 | C2×#88952 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#88952 |
| commutator, cosocle | C33×C4 | C24 |
| Frattini | C4 | C2×D33 |
| Fitting | C2×C33×C4 | C23 |
| socle | C2×C33 | C22×D4 |
| hypercenter | C2×C4 | D33 |
| hypocenter | C33 | #576 |
| LCS | G ▷ C33×C4 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11724581 | C2 | semidirect |
| 2. C3×#64307 | C2 | semidirect |
| 3. #11723657 | C2 | semidirect |
| 4. #11723367 | C2 | semidirect |
| 5. C2×#88790 | C2 | semidirect |
| 6. C3×#63823 | C2 | semidirect |
| 7. C3×#63822 | C2 | semidirect |
| 8. #11722874 | C2 | semidirect |
| 9. #11722873 | C2 | semidirect |
| 10. #11722858 | C2 | semidirect |
| 11. #11722830 | C2 | semidirect |
| 15. C2×C4⋊(C3⋊(C3⋊D3)) | C22 | semidirect |
| 17. C32×#235 | C22 | semidirect |
| 18. C32×#235 | C22 | semidirect |
| 19. C2×C32×D12 | C22 | semidirect |
| 21. C3⋊D3×D12 | C22 | semidirect |
| 24. #89018 | C22 | semidirect |
| 26. C3×#3802 | C22 | semidirect |
| 28. C3×#3796 | C22 | semidirect |
| 30. C3×#3748 | C22 | semidirect |
| 31. C2×C3×C3⋊(C3⋊C8) | C22 | semidirect |
| 32. #88809 | C22 | semidirect |
| 33. #88808 | C22 | semidirect |
| 34. #88795 | C22 | semidirect |
| 35. #88790 | C22 | semidirect |
| 36. #88790 | C22 | semidirect |
| 37. #88790 | C22 | semidirect |
| 38. C3×#3718 | C22 | semidirect |
| 39. C3×#3715 | C22 | semidirect |
| 40. C3×#3715 | C22 | semidirect |
| 41. C3×#3715 | C22 | semidirect |
| 42. C3×#3713 | C22 | semidirect |
| 43. C3×#3713 | C22 | semidirect |
| 50. #64307 | D3 | semidirect |
| 75. #63823 | D3 | semidirect |
| 76. #63822 | D3 | semidirect |
| 143. C3×#235 | C2×D3 | semidirect |
| 144. C3×#235 | C2×D3 | semidirect |
| 145. C3×#235 | C2×D3 | semidirect |
| 146. C3×#235 | C2×D3 | semidirect |
| 149. C2×C3×D12 | C2×D3 | semidirect |
| 150. C2×C3×D12 | C2×D3 | semidirect |
| 155. #3802 | C2×D3 | semidirect |
| 169. #3796 | C2×D3 | semidirect |
| 175. #3748 | C2×D3 | semidirect |
| 176. C2×C3⋊(C3⋊C8) | C2×D3 | semidirect |
| 195. #3718 | C2×D3 | semidirect |
| 199. #3715 | C2×D3 | semidirect |
| 200. #3715 | C2×D3 | semidirect |
| 201. #3715 | C2×D3 | semidirect |
| 211. #3713 | C2×D3 | semidirect |
| 212. #3713 | C2×D3 | semidirect |
| 449. #235 | D32 | semidirect |
| 450. #235 | D32 | semidirect |
| 463. C2×D12 | D32 | semidirect |
| 597. C33 | #576 | semidirect |
| 870. C32 | #5769 | semidirect |
| 871. C32 | #5774 | semidirect |
| 872. C32 | #5835 | semidirect |
| 959. C3 | #10595097 | semidirect |
| 960. C3 | #10595456 | semidirect |
| 961. C3 | #10595461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724581 | 2 |
| C3×#64307 | 2 |
| #11723657 | 2 |
| #11723367 | 2 |
| C2×#88790 | 2 |
| C3×#63823 | 2 |
| C3×#63822 | 2 |
| #11722874 | 2 |
| #11722873 | 2 |
| #11722858 | 2 |
| #11722830 | 2 |
| #10595461 | 3 |
| #10595456 | 3 |
| #10595097 | 3 |