Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2594 conjugacy classes of subgroups.
The subgroup lattice has 930 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #41×C3⋊D9 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D3×C9×#41 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#41×D9 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11722515 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11722510 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11722509 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11722508 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11722501 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #11722500 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #11722499 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #11722494 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #11722475 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | D9×#235 | C2 | 1 | 3 | yes | maximal, complemented |
| 14 | D3×#3697 | C2 | 1 | 3 | yes | maximal, complemented |
| 15 | C2×#88640 | C2 | 1 | 3 | yes | maximal, complemented |
| 16 | #10596695 | — | 3 | 1 | no | maximal |
| 17 | #10593139 | — | 3 | 1 | no | maximal |
| 18 | C3×C9×#41 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #88746 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | Q8×C3⋊D9 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #88742 | C22 | 1 | 3 | yes | complemented |
| 22 | D4×C3⋊D9 | C22 | 1 | 3 | yes | complemented |
| 23 | #88736 | C22 | 1 | 3 | yes | complemented |
| 24 | C2×C4×C3⋊D9 | C22 | 1 | 3 | yes | complemented |
| 25 | C9×#239 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | D3×Q8×C9 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C3×#3701 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | C3×Q8×D9 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | C9×#237 | C22 | 1 | 3 | yes | complemented |
| 30 | D3×D4×C9 | C22 | 1 | 3 | yes | complemented |
| 31 | C3×#3699 | C22 | 1 | 3 | yes | complemented |
| 32 | C3×D4×D9 | C22 | 1 | 3 | yes | complemented |
| 33 | C9×#235 | C22 | 1 | 3 | yes | complemented |
| 34 | C2×C4×D3×C9 | C22 | 1 | 3 | yes | complemented |
| 35 | C3×#3697 | C22 | 1 | 3 | yes | complemented |
| 36 | C2×C3×C4×D9 | C22 | 1 | 3 | yes | complemented |
| 37 | #88668 | C22 | 1 | 6 | yes | complemented |
| 38 | D9×#67 | C22 | 1 | 6 | yes | complemented |
| 39 | D3×#611 | C22 | 1 | 6 | yes | complemented |
| 40 | C2×#6195 | C22 | 1 | 3 | yes | complemented |
| 41 | C2×#6194 | C22 | 1 | 3 | yes | complemented |
| 42 | #88663 | C22 | 1 | 6 | yes | complemented |
| 43 | #88662 | C22 | 1 | 6 | yes | complemented |
| 44 | C2×#6192 | C22 | 1 | 3 | yes | complemented |
| 45 | #88658 | C22 | 1 | 6 | yes | complemented |
| 46 | C2×#6189 | C22 | 1 | 3 | yes | complemented |
| 47 | #88646 | C22 | 1 | 3 | yes | complemented |
| 48 | D9×D12 | C22 | 1 | 3 | yes | complemented |
| 49 | D3×D36 | C22 | 1 | 3 | yes | complemented |
| 50 | C4×D3×D9 | C22 | 1 | 6 | yes | complemented |
| 51 | #88642 | C22 | 1 | 3 | yes | complemented |
| 52 | #88641 | C22 | 1 | 3 | yes | complemented |
| 53 | #88640 | C22 | 1 | 3 | yes | complemented |
| 54 | #88640 | C22 | 1 | 3 | yes | complemented |
| 55 | #88640 | C22 | 1 | 3 | yes | complemented |
| 56 | #88640 | C22 | 1 | 3 | yes | complemented |
| 57 | #88640 | C22 | 1 | 1 | yes | characteristic, complemented |
| 58 | #88640 | C22 | 1 | 3 | yes | complemented |
| 59 | #88640 | C22 | 1 | 3 | yes | complemented |
| 60 | #88640 | C22 | 1 | 3 | yes | complemented |
| 61 | #88639 | C22 | 1 | 3 | yes | complemented |
| 62 | #88638 | C22 | 1 | 3 | yes | complemented |
| 63 | D3×Dic18 | C22 | 1 | 3 | yes | complemented |
| 64 | (C3⋊D9)⋊Q8 | C22 | 1 | 3 | yes | complemented |
| 65 | #88635 | C22 | 1 | 3 | yes | complemented |
| 66 | #88634 | C22 | 1 | 3 | yes | complemented |
| 67 | D9×Dic6 | C22 | 1 | 3 | yes | complemented |
| 68 | #41×C3⋊D3 | — | 3 | 1 | no | — |
| 69 | C3×D3×#41 | — | 3 | 1 | no | — |
| 70 | C3×D3×#41 | D3 | 1 | 1 | yes | characteristic |
| 71 | #64320 | — | 3 | 1 | no | — |
| 72 | #64316 | — | 3 | 1 | no | — |
| 73 | #64315 | — | 3 | 1 | no | — |
| 74 | #64315 | — | 3 | 1 | no | — |
| 75 | #64314 | — | 3 | 3 | no | — |
| 76 | #64314 | — | 3 | 3 | no | — |
| 77 | #64313 | — | 3 | 3 | no | — |
| 78 | #64309 | — | 3 | 3 | no | — |
| 79 | #64306 | — | 3 | 3 | no | — |
| 80 | D3×#235 | — | 3 | 3 | no | — |
| 81 | D3×#235 | — | 3 | 3 | no | — |
| 82 | C2×#3798 | — | 3 | 3 | no | — |
| 83 | C2×C9×#41 | — | 3 | 1 | no | — |
| 84 | #63716 | — | 3 | 1 | no | — |
| 85 | #63716 | — | 3 | 3 | no | — |
| 86 | #63715 | — | 3 | 1 | no | — |
| 87 | #63715 | — | 3 | 3 | no | — |
| 88 | #41×D9 | — | 3 | 1 | no | — |
| 89 | #41×D9 | — | 3 | 3 | no | — |
| 90 | #41×D9 | — | 3 | 3 | no | — |
| 91 | #41×D9 | — | 6 | 1 | no | — |
| 92 | #41×D9 | D3 | 1 | 1 | yes | characteristic, complemented |
| 93 | #63713 | — | 3 | 1 | no | — |
| 94 | #63713 | — | 3 | 1 | no | — |
| 95 | #63710 | — | 3 | 3 | no | — |
| 96 | #63710 | — | 3 | 3 | no | — |
| 97 | C2×#3697 | — | 3 | 3 | no | — |
| 98 | C2×#3697 | — | 3 | 3 | no | — |
| 99 | C22×C3⋊D9 | C23 | 1 | 3 | yes | — |
| 100 | C22×D3×C9 | C23 | 1 | 3 | yes | — |
| 101 | C22×C3×D9 | C23 | 1 | 3 | yes | — |
| 102 | C2×D3×D9 | C23 | 1 | 6 | yes | — |
| 103 | C3×Q8×C9 | C23 | 1 | 1 | yes | characteristic |
| 104 | C3×D4×C9 | C23 | 1 | 3 | yes | — |
| 105 | C2×C3×C4×C9 | C23 | 1 | 3 | yes | — |
| 106 | #6233 | C23 | 1 | 6 | yes | — |
| 107 | C2×C3⋊Dic9 | C23 | 1 | 3 | yes | — |
| 108 | C4⋊(C3⋊D9) | C23 | 1 | 3 | yes | — |
| 109 | C4×C3⋊D9 | C23 | 1 | 3 | yes | — |
| 110 | C4×C3⋊D9 | C23 | 1 | 3 | yes | — |
| 111 | C4×C3⋊D9 | C23 | 1 | 1 | yes | characteristic |
| 112 | C4×C3⋊D9 | C23 | 1 | 3 | yes | — |
| 113 | #6226 | C23 | 1 | 3 | yes | — |
| 114 | C9×#67 | C23 | 1 | 6 | yes | — |
| 115 | C3×#611 | C23 | 1 | 6 | yes | — |
| 116 | C2×C9×Dic3 | C23 | 1 | 3 | yes | — |
| 117 | C2×C3×Dic9 | C23 | 1 | 3 | yes | — |
| 118 | C9×D12 | C23 | 1 | 3 | yes | — |
| 119 | C4×D3×C9 | C23 | 1 | 3 | yes | — |
| 120 | C4×D3×C9 | C23 | 1 | 1 | yes | characteristic |
| 121 | C4×D3×C9 | C23 | 1 | 3 | yes | — |
| 122 | C4×D3×C9 | C23 | 1 | 3 | yes | — |
| 123 | C3×D36 | C23 | 1 | 3 | yes | — |
| 124 | C3×C4×D9 | C23 | 1 | 3 | yes | — |
| 125 | C3×C4×D9 | C23 | 1 | 3 | yes | — |
| 126 | C3×C4×D9 | C23 | 1 | 1 | yes | characteristic |
| 127 | C3×C4×D9 | C23 | 1 | 3 | yes | — |
| 128 | C9×Dic6 | C23 | 1 | 3 | yes | — |
| 129 | C3×Dic18 | C23 | 1 | 3 | yes | — |
| 130 | #6195 | C23 | 1 | 3 | yes | — |
| 131 | #6195 | C23 | 1 | 1 | yes | characteristic |
| 132 | #6195 | C23 | 1 | 3 | yes | — |
| 133 | #6195 | C23 | 1 | 3 | yes | — |
| 134 | #6194 | C23 | 1 | 3 | yes | — |
| 135 | #6194 | C23 | 1 | 1 | yes | characteristic |
| 136 | #6194 | C23 | 1 | 3 | yes | — |
| 137 | #6194 | C23 | 1 | 3 | yes | — |
| 138 | D3×Dic9 | C23 | 1 | 6 | yes | — |
| 139 | #6192 | C23 | 1 | 3 | yes | — |
| 140 | #6192 | C23 | 1 | 3 | yes | — |
| 141 | #6192 | C23 | 1 | 1 | yes | characteristic |
| 142 | #6192 | C23 | 1 | 3 | yes | — |
| 143 | (C3⋊D9)⋊C4 | C23 | 1 | 6 | yes | — |
| 144 | Dic3×D9 | C23 | 1 | 6 | yes | — |
| 145 | #6189 | C23 | 1 | 3 | yes | — |
| 146 | #6189 | C23 | 1 | 3 | yes | — |
| 147 | #6189 | C23 | 1 | 3 | yes | — |
| 148 | #6189 | C23 | 1 | 1 | yes | characteristic |
| 149 | #5964 | — | 9 | 1 | no | — |
| 150 | #5964 | — | 9 | 1 | no | — |
| 151 | C32×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 152 | #3832 | — | 3 | 1 | no | — |
| 153 | Q8×C3⋊D3 | — | 3 | 1 | no | — |
| 154 | #3830 | — | 3 | 3 | no | — |
| 155 | D4×C3⋊D3 | — | 3 | 3 | no | — |
| 156 | #3828 | — | 3 | 3 | no | — |
| 157 | C2×C4×C3⋊D3 | — | 3 | 3 | no | — |
| 158 | C3×#239 | — | 3 | 1 | no | — |
| 159 | C3×#239 | C2×D3 | 1 | 1 | yes | characteristic |
| 160 | C3×D3×Q8 | — | 3 | 1 | no | — |
| 161 | C3×D3×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 162 | C3×#237 | — | 3 | 3 | no | — |
| 163 | C3×#237 | C2×D3 | 1 | 3 | yes | — |
| 164 | C3×D3×D4 | — | 3 | 3 | no | — |
| 165 | C3×D3×D4 | C2×D3 | 1 | 3 | yes | — |
| 166 | C3×#235 | — | 3 | 3 | no | — |
| 167 | C3×#235 | C2×D3 | 1 | 3 | yes | — |
| 168 | C2×C3×C4×D3 | — | 3 | 3 | no | — |
| 169 | C2×C3×C4×D3 | C2×D3 | 1 | 3 | yes | — |
| 170 | #3811 | — | 3 | 6 | no | — |
| 171 | D3×#67 | — | 3 | 6 | no | — |
| 172 | D3×#67 | — | 3 | 6 | no | — |
| 173 | C2×#627 | — | 3 | 3 | no | — |
| 174 | C2×#626 | — | 3 | 3 | no | — |
| 175 | C2×#626 | — | 3 | 3 | no | — |
| 176 | C2×#625 | — | 3 | 3 | no | — |
| 177 | #3805 | — | 3 | 6 | no | — |
| 178 | #3804 | — | 3 | 6 | no | — |
| 179 | #3804 | — | 3 | 6 | no | — |
| 180 | #3802 | — | 3 | 3 | no | — |
| 181 | D3×D12 | — | 3 | 3 | no | — |
| 182 | D3×D12 | — | 3 | 3 | no | — |
| 183 | C4×D32 | — | 3 | 6 | no | — |
| 184 | #3799 | — | 3 | 3 | no | — |
| 185 | #3799 | — | 3 | 3 | no | — |
| 186 | #3798 | — | 3 | 1 | no | — |
| 187 | #3798 | — | 3 | 3 | no | — |
| 188 | #3798 | — | 3 | 3 | no | — |
| 189 | #3798 | — | 3 | 3 | no | — |
| 190 | #3798 | — | 3 | 3 | no | — |
| 191 | #3798 | — | 3 | 3 | no | — |
| 192 | #3798 | — | 3 | 3 | no | — |
| 193 | #3798 | — | 3 | 3 | no | — |
| 194 | #3797 | — | 3 | 3 | no | — |
| 195 | #3796 | — | 3 | 3 | no | — |
| 196 | #3796 | — | 3 | 3 | no | — |
| 197 | #3795 | — | 3 | 3 | no | — |
| 198 | #3795 | — | 3 | 3 | no | — |
| 199 | D3×Dic6 | — | 3 | 3 | no | — |
| 200 | D3×Dic6 | — | 3 | 3 | no | — |
| 201 | C9×#41 | — | 2 | 1 | no | — |
| 202 | C9×#41 | — | 3 | 1 | no | — |
| 203 | C9×#41 | — | 3 | 3 | no | — |
| 204 | C9×#41 | — | 3 | 3 | no | — |
| 205 | C9×#41 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 206 | C2×Q8×C9 | — | 3 | 1 | no | — |
| 207 | C2×D4×C9 | — | 3 | 3 | no | — |
| 208 | C22×C4×C9 | — | 3 | 3 | no | — |
| 209 | C2×#611 | — | 3 | 3 | no | — |
| 210 | C2×#611 | — | 3 | 6 | no | — |
| 211 | C2×#611 | — | 3 | 3 | no | — |
| 212 | #3701 | — | 3 | 1 | no | — |
| 213 | #3701 | — | 3 | 3 | no | — |
| 214 | #3701 | — | 3 | 3 | no | — |
| 215 | #3701 | — | 6 | 1 | no | — |
| 216 | #3701 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 217 | Q8×D9 | — | 3 | 1 | no | — |
| 218 | Q8×D9 | — | 3 | 3 | no | — |
| 219 | Q8×D9 | — | 3 | 3 | no | — |
| 220 | Q8×D9 | — | 6 | 1 | no | — |
| 221 | Q8×D9 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 222 | #3699 | — | 3 | 3 | no | — |
| 223 | #3699 | — | 3 | 6 | no | — |
| 224 | #3699 | — | 3 | 6 | no | — |
| 225 | #3699 | — | 3 | 3 | no | — |
| 226 | #3699 | — | 3 | 3 | no | — |
| 227 | #3699 | — | 6 | 3 | no | — |
| 228 | #3699 | C2×D3 | 1 | 3 | yes | complemented |
| 229 | D4×D9 | — | 3 | 6 | no | — |
| 230 | D4×D9 | — | 3 | 3 | no | — |
| 231 | D4×D9 | — | 3 | 6 | no | — |
| 232 | D4×D9 | — | 3 | 3 | no | — |
| 233 | D4×D9 | — | 3 | 3 | no | — |
| 234 | D4×D9 | — | 6 | 3 | no | — |
| 235 | D4×D9 | C2×D3 | 1 | 3 | yes | complemented |
| 236 | #3697 | — | 3 | 3 | no | — |
| 237 | #3697 | — | 3 | 6 | no | — |
| 238 | #3697 | — | 3 | 3 | no | — |
| 239 | #3697 | — | 3 | 3 | no | — |
| 240 | #3697 | — | 3 | 1 | no | — |
| 241 | #3697 | — | 3 | 3 | no | — |
| 242 | #3697 | — | 3 | 3 | no | — |
| 243 | #3697 | — | 3 | 3 | no | — |
| 244 | #3697 | — | 3 | 3 | no | — |
| 245 | #3697 | — | 3 | 3 | no | — |
| 246 | #3697 | — | 3 | 3 | no | — |
| 247 | #3697 | — | 3 | 3 | no | — |
| 248 | #3697 | — | 6 | 3 | no | — |
| 249 | #3697 | C2×D3 | 1 | 3 | yes | complemented |
| 250 | C2×D36 | — | 3 | 3 | no | — |
| 251 | C2×D36 | — | 3 | 3 | no | — |
| 252 | C2×C4×D9 | — | 3 | 3 | no | — |
| 253 | C2×C4×D9 | — | 3 | 6 | no | — |
| 254 | C2×C4×D9 | — | 6 | 3 | no | — |
| 255 | C2×C4×D9 | C2×D3 | 1 | 3 | yes | complemented |
| 256 | C2×Dic18 | — | 3 | 3 | no | — |
| 257 | C2×Dic18 | — | 3 | 3 | no | — |
| 258 | C22×C3×C9 | C24 | 1 | 3 | yes | — |
| 259 | C2×C3⋊D9 | — | 4 | 3 | no | — |
| 260 | C2×C3⋊D9 | C24 | 1 | 3 | yes | — |
| 261 | C2×C3⋊D9 | C24 | 1 | 1 | yes | characteristic |
| 262 | C2×D3×C9 | — | 4 | 3 | no | — |
| 263 | C2×D3×C9 | C24 | 1 | 3 | yes | — |
| 264 | C2×D3×C9 | C24 | 1 | 1 | yes | characteristic |
| 265 | C2×C3×D9 | — | 4 | 3 | no | — |
| 266 | C2×C3×D9 | C24 | 1 | 3 | yes | — |
| 267 | C2×C3×D9 | C24 | 1 | 1 | yes | characteristic |
| 268 | D3×D9 | — | 4 | 6 | no | — |
| 269 | C3×C4×C9 | C24 | 1 | 3 | yes | — |
| 270 | C3×C4×C9 | C24 | 1 | 1 | yes | characteristic |
| 271 | C3⋊Dic9 | C24 | 1 | 1 | yes | characteristic |
| 272 | C3⋊Dic9 | C24 | 1 | 3 | yes | — |
| 273 | C9×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 274 | C9×Dic3 | C24 | 1 | 3 | yes | — |
| 275 | C3×Dic9 | C24 | 1 | 1 | yes | characteristic |
| 276 | C3×Dic9 | C24 | 1 | 3 | yes | — |
| 277 | C2×C3×#41 | — | 3 | 1 | no | — |
| 278 | C2×C3×#41 | — | 9 | 1 | no | — |
| 279 | #1010 | — | 9 | 3 | no | — |
| 280 | #1010 | — | 9 | 1 | no | — |
| 281 | #1010 | — | 9 | 1 | no | — |
| 282 | #1010 | — | 9 | 3 | no | — |
| 283 | #1009 | — | 9 | 3 | no | — |
| 284 | #1009 | — | 9 | 1 | no | — |
| 285 | #1009 | — | 9 | 1 | no | — |
| 286 | #1009 | — | 9 | 3 | no | — |
| 287 | D3×#41 | — | 3 | 1 | no | — |
| 288 | D3×#41 | — | 9 | 3 | no | — |
| 289 | D3×#41 | — | 9 | 3 | no | — |
| 290 | D3×#41 | — | 9 | 1 | no | — |
| 291 | D3×#41 | — | 9 | 1 | no | — |
| 292 | D3×#41 | — | 9 | 3 | no | — |
| 293 | D3×#41 | — | 9 | 3 | no | — |
| 294 | D3×#41 | — | 18 | 1 | no | — |
| 295 | D3×#41 | D9 | 1 | 1 | yes | characteristic, complemented |
| 296 | #1007 | — | 9 | 1 | no | — |
| 297 | #1007 | — | 9 | 1 | no | — |
| 298 | #1007 | — | 9 | 1 | no | — |
| 299 | #1007 | — | 9 | 1 | no | — |
| 300 | #1004 | — | 9 | 3 | no | — |
| 301 | #1004 | — | 9 | 3 | no | — |
| 302 | #1004 | — | 9 | 3 | no | — |
| 303 | #1004 | — | 9 | 3 | no | — |
| 304 | C2×#235 | — | 9 | 3 | no | — |
| 305 | C2×#235 | — | 9 | 3 | no | — |
| 306 | C2×#235 | — | 9 | 3 | no | — |
| 307 | C2×#235 | — | 9 | 3 | no | — |
| 308 | C22×C3⋊D3 | — | 3 | 3 | no | — |
| 309 | C22×C3×D3 | — | 3 | 3 | no | — |
| 310 | C22×C3×D3 | C22×D3 | 1 | 3 | yes | — |
| 311 | C2×D32 | — | 3 | 6 | no | — |
| 312 | C32×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 313 | C32×D4 | C22×D3 | 1 | 3 | yes | — |
| 314 | C2×C32×C4 | C22×D3 | 1 | 3 | yes | — |
| 315 | #638 | — | 3 | 6 | no | — |
| 316 | C2×C3⋊Dic3 | — | 3 | 3 | no | — |
| 317 | C4⋊(C3⋊D3) | — | 3 | 3 | no | — |
| 318 | C4×C3⋊D3 | — | 3 | 3 | no | — |
| 319 | C4×C3⋊D3 | — | 3 | 3 | no | — |
| 320 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 321 | C4×C3⋊D3 | — | 3 | 3 | no | — |
| 322 | #634 | — | 3 | 3 | no | — |
| 323 | C3×#67 | — | 3 | 6 | no | — |
| 324 | C3×#67 | C22×D3 | 1 | 6 | yes | — |
| 325 | C2×C3×Dic3 | — | 3 | 3 | no | — |
| 326 | C2×C3×Dic3 | C22×D3 | 1 | 3 | yes | — |
| 327 | C3×D12 | — | 3 | 3 | no | — |
| 328 | C3×D12 | C22×D3 | 1 | 3 | yes | — |
| 329 | C3×C4×D3 | — | 3 | 3 | no | — |
| 330 | C3×C4×D3 | — | 3 | 3 | no | — |
| 331 | C3×C4×D3 | — | 3 | 1 | no | — |
| 332 | C3×C4×D3 | — | 3 | 3 | no | — |
| 333 | C3×C4×D3 | C22×D3 | 1 | 3 | yes | — |
| 334 | C3×C4×D3 | C22×D3 | 1 | 3 | yes | — |
| 335 | C3×C4×D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 336 | C3×C4×D3 | C22×D3 | 1 | 3 | yes | — |
| 337 | C3×Dic6 | — | 3 | 3 | no | — |
| 338 | C3×Dic6 | C22×D3 | 1 | 3 | yes | — |
| 339 | #627 | — | 3 | 3 | no | — |
| 340 | #627 | — | 3 | 3 | no | — |
| 341 | #627 | — | 3 | 3 | no | — |
| 342 | #627 | — | 3 | 1 | no | — |
| 343 | #626 | — | 3 | 3 | no | — |
| 344 | #626 | — | 3 | 1 | no | — |
| 345 | #626 | — | 3 | 3 | no | — |
| 346 | #626 | — | 3 | 3 | no | — |
| 347 | #626 | — | 3 | 3 | no | — |
| 348 | #626 | — | 3 | 1 | no | — |
| 349 | #626 | — | 3 | 3 | no | — |
| 350 | #626 | — | 3 | 3 | no | — |
| 351 | #625 | — | 3 | 3 | no | — |
| 352 | #625 | — | 3 | 3 | no | — |
| 353 | #625 | — | 3 | 1 | no | — |
| 354 | #625 | — | 3 | 3 | no | — |
| 355 | #624 | — | 3 | 6 | no | — |
| 356 | D3×Dic3 | — | 3 | 6 | no | — |
| 357 | D3×Dic3 | — | 3 | 6 | no | — |
| 358 | C23×C9 | — | 3 | 3 | no | — |
| 359 | C22×D9 | — | 3 | 3 | no | — |
| 360 | C22×D9 | — | 3 | 6 | no | — |
| 361 | C22×D9 | — | 6 | 3 | no | — |
| 362 | C22×D9 | C22×D3 | 1 | 3 | yes | — |
| 363 | Q8×C9 | — | 2 | 1 | no | — |
| 364 | Q8×C9 | — | 3 | 3 | no | — |
| 365 | Q8×C9 | C22×D3 | 1 | 1 | yes | characteristic |
| 366 | D4×C9 | — | 2 | 3 | no | — |
| 367 | D4×C9 | — | 3 | 6 | no | — |
| 368 | D4×C9 | — | 3 | 3 | no | — |
| 369 | D4×C9 | C22×D3 | 1 | 3 | yes | — |
| 370 | C2×C4×C9 | — | 2 | 3 | no | — |
| 371 | C2×C4×C9 | — | 3 | 3 | no | — |
| 372 | C2×C4×C9 | — | 3 | 3 | no | — |
| 373 | C2×C4×C9 | — | 3 | 3 | no | — |
| 374 | C2×C4×C9 | — | 3 | 1 | no | — |
| 375 | C2×C4×C9 | — | 3 | 3 | no | — |
| 376 | C2×C4×C9 | C22×D3 | 1 | 3 | yes | — |
| 377 | #611 | — | 3 | 6 | no | — |
| 378 | #611 | — | 3 | 3 | no | — |
| 379 | #611 | — | 3 | 1 | no | — |
| 380 | #611 | — | 3 | 3 | no | — |
| 381 | #611 | — | 3 | 3 | no | — |
| 382 | #611 | — | 3 | 1 | no | — |
| 383 | #611 | — | 3 | 3 | no | — |
| 384 | #611 | — | 3 | 3 | no | — |
| 385 | #611 | — | 3 | 3 | no | — |
| 386 | #611 | — | 6 | 6 | no | — |
| 387 | #611 | C22×D3 | 1 | 6 | yes | — |
| 388 | C2×Dic9 | — | 3 | 3 | no | — |
| 389 | C2×Dic9 | — | 3 | 6 | no | — |
| 390 | C2×Dic9 | — | 6 | 3 | no | — |
| 391 | C2×Dic9 | C22×D3 | 1 | 3 | yes | — |
| 392 | D36 | — | 3 | 3 | no | — |
| 393 | D36 | — | 3 | 1 | no | — |
| 394 | D36 | — | 3 | 3 | no | — |
| 395 | D36 | — | 3 | 3 | no | — |
| 396 | D36 | — | 3 | 3 | no | — |
| 397 | D36 | — | 6 | 3 | no | — |
| 398 | D36 | C22×D3 | 1 | 3 | yes | — |
| 399 | C4×D9 | — | 3 | 6 | no | — |
| 400 | C4×D9 | — | 3 | 1 | no | — |
| 401 | C4×D9 | — | 3 | 3 | no | — |
| 402 | C4×D9 | — | 3 | 3 | no | — |
| 403 | C4×D9 | — | 3 | 3 | no | — |
| 404 | C4×D9 | — | 3 | 6 | no | — |
| 405 | C4×D9 | — | 6 | 1 | no | — |
| 406 | C4×D9 | — | 6 | 3 | no | — |
| 407 | C4×D9 | — | 6 | 3 | no | — |
| 408 | C4×D9 | — | 6 | 3 | no | — |
| 409 | C4×D9 | C22×D3 | 1 | 3 | yes | — |
| 410 | C4×D9 | C22×D3 | 1 | 1 | yes | characteristic |
| 411 | C4×D9 | C22×D3 | 1 | 3 | yes | — |
| 412 | C4×D9 | C22×D3 | 1 | 3 | yes | — |
| 413 | Dic18 | — | 3 | 3 | no | — |
| 414 | Dic18 | — | 3 | 1 | no | — |
| 415 | Dic18 | — | 3 | 3 | no | — |
| 416 | Dic18 | — | 3 | 3 | no | — |
| 417 | Dic18 | — | 3 | 3 | no | — |
| 418 | Dic18 | — | 6 | 3 | no | — |
| 419 | Dic18 | C22×D3 | 1 | 3 | yes | — |
| 420 | #585 | — | 27 | 1 | no | Sylow |
| 421 | C2×C3×C9 | — | 2 | 3 | no | — |
| 422 | C2×C3×C9 | C25 | 1 | 1 | yes | characteristic |
| 423 | C3⋊D9 | — | 2 | 1 | no | — |
| 424 | C3⋊D9 | — | 2 | 3 | no | — |
| 425 | D3×C9 | — | 2 | 3 | no | — |
| 426 | D3×C9 | — | 2 | 1 | no | — |
| 427 | C3×D9 | — | 2 | 3 | no | — |
| 428 | C3×D9 | — | 2 | 1 | no | — |
| 429 | C3×#41 | — | 2 | 1 | no | — |
| 430 | C3×#41 | — | 3 | 1 | no | — |
| 431 | C3×#41 | — | 3 | 3 | no | — |
| 432 | C3×#41 | — | 3 | 3 | no | — |
| 433 | C3×#41 | — | 9 | 1 | no | — |
| 434 | C3×#41 | — | 9 | 3 | no | — |
| 435 | C3×#41 | — | 9 | 3 | no | — |
| 436 | C3×#41 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 437 | C3×#41 | D32 | 1 | 1 | yes | characteristic |
| 438 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 439 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 440 | C2×C3×D4 | — | 3 | 3 | no | — |
| 441 | C2×C3×D4 | — | 9 | 3 | no | — |
| 442 | C22×C3×C4 | — | 3 | 3 | no | — |
| 443 | C22×C3×C4 | — | 9 | 3 | no | — |
| 444 | C2×#67 | — | 9 | 3 | no | — |
| 445 | C2×#67 | — | 9 | 6 | no | — |
| 446 | C2×#67 | — | 9 | 3 | no | — |
| 447 | C2×#67 | — | 9 | 3 | no | — |
| 448 | C2×#67 | — | 9 | 6 | no | — |
| 449 | C2×#67 | — | 9 | 3 | no | — |
| 450 | #239 | — | 3 | 1 | no | — |
| 451 | #239 | — | 9 | 3 | no | — |
| 452 | #239 | — | 9 | 3 | no | — |
| 453 | #239 | — | 9 | 1 | no | — |
| 454 | #239 | — | 9 | 1 | no | — |
| 455 | #239 | — | 9 | 3 | no | — |
| 456 | #239 | — | 9 | 3 | no | — |
| 457 | #239 | — | 18 | 1 | no | — |
| 458 | #239 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 459 | D3×Q8 | — | 3 | 1 | no | — |
| 460 | D3×Q8 | — | 9 | 3 | no | — |
| 461 | D3×Q8 | — | 9 | 3 | no | — |
| 462 | D3×Q8 | — | 9 | 1 | no | — |
| 463 | D3×Q8 | — | 9 | 1 | no | — |
| 464 | D3×Q8 | — | 9 | 3 | no | — |
| 465 | D3×Q8 | — | 9 | 3 | no | — |
| 466 | D3×Q8 | — | 18 | 1 | no | — |
| 467 | D3×Q8 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 468 | #237 | — | 3 | 3 | no | — |
| 469 | #237 | — | 9 | 3 | no | — |
| 470 | #237 | — | 9 | 3 | no | — |
| 471 | #237 | — | 9 | 6 | no | — |
| 472 | #237 | — | 9 | 6 | no | — |
| 473 | #237 | — | 9 | 3 | no | — |
| 474 | #237 | — | 9 | 3 | no | — |
| 475 | #237 | — | 9 | 6 | no | — |
| 476 | #237 | — | 9 | 6 | no | — |
| 477 | #237 | — | 9 | 3 | no | — |
| 478 | #237 | — | 9 | 3 | no | — |
| 479 | #237 | — | 18 | 3 | no | — |
| 480 | #237 | C2×D9 | 1 | 3 | yes | complemented |
| 481 | D3×D4 | — | 3 | 3 | no | — |
| 482 | D3×D4 | — | 9 | 3 | no | — |
| 483 | D3×D4 | — | 9 | 3 | no | — |
| 484 | D3×D4 | — | 9 | 6 | no | — |
| 485 | D3×D4 | — | 9 | 6 | no | — |
| 486 | D3×D4 | — | 9 | 6 | no | — |
| 487 | D3×D4 | — | 9 | 3 | no | — |
| 488 | D3×D4 | — | 9 | 3 | no | — |
| 489 | D3×D4 | — | 9 | 6 | no | — |
| 490 | D3×D4 | — | 9 | 3 | no | — |
| 491 | D3×D4 | — | 9 | 3 | no | — |
| 492 | D3×D4 | — | 18 | 3 | no | — |
| 493 | D3×D4 | C2×D9 | 1 | 3 | yes | complemented |
| 494 | #235 | — | 3 | 3 | no | — |
| 495 | #235 | — | 9 | 3 | no | — |
| 496 | #235 | — | 9 | 1 | no | — |
| 497 | #235 | — | 9 | 3 | no | — |
| 498 | #235 | — | 9 | 3 | no | — |
| 499 | #235 | — | 9 | 3 | no | — |
| 500 | #235 | — | 9 | 3 | no | — |
| 501 | #235 | — | 9 | 3 | no | — |
| 502 | #235 | — | 9 | 3 | no | — |
| 503 | #235 | — | 9 | 3 | no | — |
| 504 | #235 | — | 9 | 3 | no | — |
| 505 | #235 | — | 9 | 6 | no | — |
| 506 | #235 | — | 9 | 3 | no | — |
| 507 | #235 | — | 9 | 3 | no | — |
| 508 | #235 | — | 9 | 6 | no | — |
| 509 | #235 | — | 9 | 3 | no | — |
| 510 | #235 | — | 9 | 3 | no | — |
| 511 | #235 | — | 9 | 1 | no | — |
| 512 | #235 | — | 9 | 3 | no | — |
| 513 | #235 | — | 9 | 3 | no | — |
| 514 | #235 | — | 9 | 3 | no | — |
| 515 | #235 | — | 9 | 3 | no | — |
| 516 | #235 | — | 9 | 3 | no | — |
| 517 | #235 | — | 9 | 3 | no | — |
| 518 | #235 | — | 9 | 3 | no | — |
| 519 | #235 | — | 18 | 3 | no | — |
| 520 | #235 | C2×D9 | 1 | 3 | yes | complemented |
| 521 | C2×D12 | — | 9 | 3 | no | — |
| 522 | C2×D12 | — | 9 | 3 | no | — |
| 523 | C2×D12 | — | 9 | 3 | no | — |
| 524 | C2×D12 | — | 9 | 3 | no | — |
| 525 | C2×C4×D3 | — | 3 | 3 | no | — |
| 526 | C2×C4×D3 | — | 9 | 6 | no | — |
| 527 | C2×C4×D3 | — | 9 | 3 | no | — |
| 528 | C2×C4×D3 | — | 9 | 3 | no | — |
| 529 | C2×C4×D3 | — | 9 | 6 | no | — |
| 530 | C2×C4×D3 | — | 18 | 3 | no | — |
| 531 | C2×C4×D3 | C2×D9 | 1 | 3 | yes | complemented |
| 532 | C2×Dic6 | — | 9 | 3 | no | — |
| 533 | C2×Dic6 | — | 9 | 3 | no | — |
| 534 | C2×Dic6 | — | 9 | 3 | no | — |
| 535 | C2×Dic6 | — | 9 | 3 | no | — |
| 536 | C22×C32 | C23×D3 | 1 | 3 | yes | — |
| 537 | C2×C3⋊D3 | — | 3 | 3 | no | — |
| 538 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 539 | C2×C3⋊D3 | — | 12 | 3 | no | — |
| 540 | C2×C3×D3 | — | 3 | 3 | no | — |
| 541 | C2×C3×D3 | — | 3 | 1 | no | — |
| 542 | C2×C3×D3 | — | 4 | 3 | no | — |
| 543 | C2×C3×D3 | — | 12 | 3 | no | — |
| 544 | C2×C3×D3 | C23×D3 | 1 | 3 | yes | — |
| 545 | C2×C3×D3 | C23×D3 | 1 | 1 | yes | characteristic |
| 546 | D32 | — | 12 | 6 | no | — |
| 547 | C32×C4 | C23×D3 | 1 | 3 | yes | — |
| 548 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 549 | C3⋊Dic3 | — | 3 | 3 | no | — |
| 550 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 551 | C3×Dic3 | — | 3 | 3 | no | — |
| 552 | C3×Dic3 | — | 3 | 1 | no | — |
| 553 | C3×Dic3 | C23×D3 | 1 | 3 | yes | — |
| 554 | C3×Dic3 | C23×D3 | 1 | 1 | yes | characteristic |
| 555 | C22×C9 | — | 2 | 3 | no | — |
| 556 | C22×C9 | — | 3 | 3 | no | — |
| 557 | C22×C9 | — | 3 | 1 | no | — |
| 558 | C22×C9 | — | 12 | 3 | no | — |
| 559 | C22×C9 | C23×D3 | 1 | 3 | yes | — |
| 560 | C2×D9 | — | 3 | 3 | no | — |
| 561 | C2×D9 | — | 3 | 1 | no | — |
| 562 | C2×D9 | — | 4 | 3 | no | — |
| 563 | C2×D9 | — | 6 | 1 | no | — |
| 564 | C2×D9 | — | 6 | 3 | no | — |
| 565 | C2×D9 | — | 12 | 6 | no | — |
| 566 | C2×D9 | — | 12 | 3 | no | — |
| 567 | C2×D9 | — | 12 | 6 | no | — |
| 568 | C2×D9 | C23×D3 | 1 | 3 | yes | — |
| 569 | C2×D9 | C23×D3 | 1 | 1 | yes | characteristic |
| 570 | C4×C9 | — | 2 | 3 | no | — |
| 571 | C4×C9 | — | 2 | 1 | no | — |
| 572 | C4×C9 | — | 3 | 1 | no | — |
| 573 | C4×C9 | — | 3 | 3 | no | — |
| 574 | C4×C9 | C23×D3 | 1 | 3 | yes | — |
| 575 | C4×C9 | C23×D3 | 1 | 1 | yes | characteristic |
| 576 | Dic9 | — | 3 | 1 | no | — |
| 577 | Dic9 | — | 3 | 3 | no | — |
| 578 | Dic9 | — | 6 | 3 | no | — |
| 579 | Dic9 | — | 6 | 1 | no | — |
| 580 | Dic9 | C23×D3 | 1 | 1 | yes | characteristic |
| 581 | Dic9 | C23×D3 | 1 | 3 | yes | — |
| 582 | 2−1+4 | — | 27 | 1 | no | — |
| 583 | 2−1+4 | — | 27 | 1 | no | — |
| 584 | 2−1+4 | — | 27 | 1 | no | — |
| 585 | 2−1+4 | — | 27 | 3 | no | — |
| 586 | H(5,𝔽2) | — | 27 | 3 | no | — |
| 587 | H(5,𝔽2) | — | 27 | 3 | no | — |
| 588 | H(5,𝔽2) | — | 27 | 3 | no | — |
| 589 | H(5,𝔽2) | — | 27 | 1 | no | — |
| 590 | C2×#41 | — | 3 | 1 | no | — |
| 591 | C2×#41 | — | 9 | 1 | no | — |
| 592 | C2×#41 | — | 27 | 3 | no | — |
| 593 | C2×#41 | — | 27 | 3 | no | — |
| 594 | C2×#41 | — | 27 | 3 | no | — |
| 595 | C2×#41 | — | 27 | 3 | no | — |
| 596 | C2×#41 | — | 27 | 1 | no | — |
| 597 | C3×C9 | #585 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 598 | C23×C3 | — | 3 | 3 | no | — |
| 599 | C23×C3 | — | 9 | 3 | no | — |
| 600 | C22×D3 | — | 3 | 3 | no | — |
| 601 | C22×D3 | — | 9 | 6 | no | — |
| 602 | C22×D3 | — | 9 | 3 | no | — |
| 603 | C22×D3 | — | 9 | 3 | no | — |
| 604 | C22×D3 | — | 9 | 6 | no | — |
| 605 | C22×D3 | — | 18 | 3 | no | — |
| 606 | C22×D3 | C22×D9 | 1 | 3 | yes | — |
| 607 | C3×Q8 | — | 2 | 1 | no | — |
| 608 | C3×Q8 | — | 3 | 3 | no | — |
| 609 | C3×Q8 | — | 9 | 3 | no | — |
| 610 | C3×Q8 | C22×D9 | 1 | 1 | yes | characteristic |
| 611 | C3×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 612 | C3×D4 | — | 2 | 3 | no | — |
| 613 | C3×D4 | — | 3 | 6 | no | — |
| 614 | C3×D4 | — | 3 | 3 | no | — |
| 615 | C3×D4 | — | 9 | 6 | no | — |
| 616 | C3×D4 | — | 9 | 3 | no | — |
| 617 | C3×D4 | C22×D9 | 1 | 3 | yes | — |
| 618 | C3×D4 | C2×D32 | 1 | 3 | yes | — |
| 619 | C2×C3×C4 | — | 2 | 3 | no | — |
| 620 | C2×C3×C4 | — | 3 | 3 | no | — |
| 621 | C2×C3×C4 | — | 3 | 3 | no | — |
| 622 | C2×C3×C4 | — | 3 | 3 | no | — |
| 623 | C2×C3×C4 | — | 3 | 1 | no | — |
| 624 | C2×C3×C4 | — | 3 | 3 | no | — |
| 625 | C2×C3×C4 | — | 9 | 3 | no | — |
| 626 | C2×C3×C4 | — | 9 | 3 | no | — |
| 627 | C2×C3×C4 | — | 9 | 3 | no | — |
| 628 | C2×C3×C4 | — | 9 | 1 | no | — |
| 629 | C2×C3×C4 | — | 9 | 3 | no | — |
| 630 | C2×C3×C4 | C22×D9 | 1 | 3 | yes | — |
| 631 | C2×C3×C4 | C2×D32 | 1 | 3 | yes | — |
| 632 | #67 | — | 3 | 6 | no | — |
| 633 | #67 | — | 9 | 3 | no | — |
| 634 | #67 | — | 9 | 1 | no | — |
| 635 | #67 | — | 9 | 3 | no | — |
| 636 | #67 | — | 9 | 3 | no | — |
| 637 | #67 | — | 9 | 1 | no | — |
| 638 | #67 | — | 9 | 3 | no | — |
| 639 | #67 | — | 9 | 3 | no | — |
| 640 | #67 | — | 9 | 3 | no | — |
| 641 | #67 | — | 9 | 6 | no | — |
| 642 | #67 | — | 9 | 6 | no | — |
| 643 | #67 | — | 9 | 3 | no | — |
| 644 | #67 | — | 9 | 1 | no | — |
| 645 | #67 | — | 9 | 3 | no | — |
| 646 | #67 | — | 9 | 3 | no | — |
| 647 | #67 | — | 9 | 1 | no | — |
| 648 | #67 | — | 9 | 3 | no | — |
| 649 | #67 | — | 9 | 3 | no | — |
| 650 | #67 | — | 9 | 3 | no | — |
| 651 | #67 | — | 18 | 6 | no | — |
| 652 | #67 | C22×D9 | 1 | 6 | yes | — |
| 653 | C2×Dic3 | — | 3 | 3 | no | — |
| 654 | C2×Dic3 | — | 9 | 6 | no | — |
| 655 | C2×Dic3 | — | 9 | 3 | no | — |
| 656 | C2×Dic3 | — | 9 | 3 | no | — |
| 657 | C2×Dic3 | — | 9 | 6 | no | — |
| 658 | C2×Dic3 | — | 18 | 3 | no | — |
| 659 | C2×Dic3 | C22×D9 | 1 | 3 | yes | — |
| 660 | D12 | — | 3 | 3 | no | — |
| 661 | D12 | — | 9 | 1 | no | — |
| 662 | D12 | — | 9 | 3 | no | — |
| 663 | D12 | — | 9 | 3 | no | — |
| 664 | D12 | — | 9 | 3 | no | — |
| 665 | D12 | — | 9 | 3 | no | — |
| 666 | D12 | — | 9 | 1 | no | — |
| 667 | D12 | — | 9 | 3 | no | — |
| 668 | D12 | — | 9 | 3 | no | — |
| 669 | D12 | — | 9 | 3 | no | — |
| 670 | D12 | — | 9 | 3 | no | — |
| 671 | D12 | — | 18 | 3 | no | — |
| 672 | D12 | C22×D9 | 1 | 3 | yes | — |
| 673 | C4×D3 | — | 3 | 1 | no | — |
| 674 | C4×D3 | — | 3 | 3 | no | — |
| 675 | C4×D3 | — | 3 | 3 | no | — |
| 676 | C4×D3 | — | 3 | 3 | no | — |
| 677 | C4×D3 | — | 9 | 6 | no | — |
| 678 | C4×D3 | — | 9 | 6 | no | — |
| 679 | C4×D3 | — | 9 | 6 | no | — |
| 680 | C4×D3 | — | 9 | 1 | no | — |
| 681 | C4×D3 | — | 9 | 3 | no | — |
| 682 | C4×D3 | — | 9 | 3 | no | — |
| 683 | C4×D3 | — | 9 | 3 | no | — |
| 684 | C4×D3 | — | 9 | 1 | no | — |
| 685 | C4×D3 | — | 9 | 3 | no | — |
| 686 | C4×D3 | — | 9 | 3 | no | — |
| 687 | C4×D3 | — | 9 | 3 | no | — |
| 688 | C4×D3 | — | 9 | 6 | no | — |
| 689 | C4×D3 | — | 18 | 1 | no | — |
| 690 | C4×D3 | — | 18 | 3 | no | — |
| 691 | C4×D3 | — | 18 | 3 | no | — |
| 692 | C4×D3 | — | 18 | 3 | no | — |
| 693 | C4×D3 | C22×D9 | 1 | 3 | yes | — |
| 694 | C4×D3 | C22×D9 | 1 | 1 | yes | characteristic |
| 695 | C4×D3 | C22×D9 | 1 | 3 | yes | — |
| 696 | C4×D3 | C22×D9 | 1 | 3 | yes | — |
| 697 | Dic6 | — | 3 | 3 | no | — |
| 698 | Dic6 | — | 9 | 3 | no | — |
| 699 | Dic6 | — | 9 | 1 | no | — |
| 700 | Dic6 | — | 9 | 3 | no | — |
| 701 | Dic6 | — | 9 | 3 | no | — |
| 702 | Dic6 | — | 9 | 3 | no | — |
| 703 | Dic6 | — | 9 | 3 | no | — |
| 704 | Dic6 | — | 9 | 1 | no | — |
| 705 | Dic6 | — | 9 | 3 | no | — |
| 706 | Dic6 | — | 9 | 3 | no | — |
| 707 | Dic6 | — | 9 | 3 | no | — |
| 708 | Dic6 | — | 18 | 3 | no | — |
| 709 | Dic6 | C22×D9 | 1 | 3 | yes | — |
| 710 | C2×C32 | — | 2 | 3 | no | — |
| 711 | C2×C32 | C24×D3 | 1 | 1 | yes | characteristic |
| 712 | C3⋊D3 | — | 6 | 1 | no | — |
| 713 | C3⋊D3 | — | 6 | 3 | no | — |
| 714 | C3×D3 | — | 2 | 3 | no | — |
| 715 | C3×D3 | — | 2 | 1 | no | — |
| 716 | C3×D3 | — | 6 | 3 | no | — |
| 717 | C3×D3 | — | 6 | 1 | no | — |
| 718 | C2×C9 | — | 2 | 3 | no | — |
| 719 | C2×C9 | — | 2 | 1 | no | — |
| 720 | C2×C9 | — | 4 | 3 | no | — |
| 721 | C2×C9 | — | 6 | 3 | no | — |
| 722 | C2×C9 | — | 6 | 1 | no | — |
| 723 | C2×C9 | C24×D3 | 1 | 1 | yes | characteristic |
| 724 | D9 | — | 2 | 1 | no | — |
| 725 | D9 | — | 2 | 3 | no | — |
| 726 | D9 | — | 6 | 2 | no | — |
| 727 | D9 | — | 6 | 1 | no | — |
| 728 | D9 | — | 6 | 3 | no | — |
| 729 | D9 | — | 12 | 3 | no | — |
| 730 | #41 | — | 3 | 1 | no | — |
| 731 | #41 | — | 3 | 3 | no | — |
| 732 | #41 | — | 3 | 3 | no | — |
| 733 | #41 | — | 9 | 1 | no | — |
| 734 | #41 | — | 9 | 3 | no | — |
| 735 | #41 | — | 9 | 3 | no | — |
| 736 | #41 | — | 27 | 1 | no | — |
| 737 | #41 | — | 27 | 3 | no | — |
| 738 | #41 | — | 27 | 3 | no | — |
| 739 | #41 | — | 27 | 3 | no | — |
| 740 | #41 | — | 27 | 3 | no | — |
| 741 | #41 | — | 27 | 3 | no | — |
| 742 | #41 | — | 27 | 3 | no | — |
| 743 | #41 | — | 27 | 3 | no | — |
| 744 | #41 | — | 27 | 6 | no | — |
| 745 | #41 | — | 27 | 3 | no | — |
| 746 | #41 | — | 27 | 3 | no | — |
| 747 | #41 | — | 27 | 6 | no | — |
| 748 | #41 | — | 27 | 3 | no | — |
| 749 | #41 | — | 27 | 3 | no | — |
| 750 | #41 | — | 27 | 6 | no | — |
| 751 | #41 | — | 27 | 3 | no | — |
| 752 | #41 | — | 27 | 3 | no | — |
| 753 | #41 | — | 27 | 1 | no | — |
| 754 | #41 | — | 27 | 3 | no | — |
| 755 | #41 | — | 27 | 3 | no | — |
| 756 | #41 | D3×D9 | 1 | 1 | yes | characteristic, complemented |
| 757 | C2×Q8 | — | 3 | 1 | no | — |
| 758 | C2×Q8 | — | 9 | 1 | no | — |
| 759 | C2×Q8 | — | 27 | 3 | no | — |
| 760 | C2×Q8 | — | 27 | 3 | no | — |
| 761 | C2×Q8 | — | 27 | 3 | no | — |
| 762 | C2×Q8 | — | 27 | 3 | no | — |
| 763 | C2×Q8 | — | 27 | 1 | no | — |
| 764 | C2×D4 | — | 3 | 3 | no | — |
| 765 | C2×D4 | — | 9 | 3 | no | — |
| 766 | C2×D4 | — | 27 | 3 | no | — |
| 767 | C2×D4 | — | 27 | 3 | no | — |
| 768 | C2×D4 | — | 27 | 3 | no | — |
| 769 | C2×D4 | — | 27 | 3 | no | — |
| 770 | C2×D4 | — | 27 | 6 | no | — |
| 771 | C2×D4 | — | 27 | 3 | no | — |
| 772 | C2×D4 | — | 27 | 6 | no | — |
| 773 | C2×D4 | — | 27 | 6 | no | — |
| 774 | C2×D4 | — | 27 | 3 | no | — |
| 775 | C2×D4 | — | 27 | 3 | no | — |
| 776 | C22×C4 | — | 3 | 3 | no | — |
| 777 | C22×C4 | — | 9 | 3 | no | — |
| 778 | C22×C4 | — | 27 | 6 | no | — |
| 779 | C22×C4 | — | 27 | 3 | no | — |
| 780 | C22×C3 | — | 2 | 3 | no | — |
| 781 | C22×C3 | — | 3 | 3 | no | — |
| 782 | C22×C3 | — | 3 | 1 | no | — |
| 783 | C22×C3 | — | 9 | 3 | no | — |
| 784 | C22×C3 | — | 9 | 1 | no | — |
| 785 | C22×C3 | — | 12 | 3 | no | — |
| 786 | C22×C3 | — | 36 | 3 | no | — |
| 787 | C22×C3 | C23×D9 | 1 | 3 | yes | — |
| 788 | C22×C3 | C22×D32 | 1 | 3 | yes | — |
| 789 | C2×D3 | — | 3 | 1 | no | — |
| 790 | C2×D3 | — | 3 | 3 | no | — |
| 791 | C2×D3 | — | 4 | 3 | no | — |
| 792 | C2×D3 | — | 9 | 1 | no | — |
| 793 | C2×D3 | — | 9 | 3 | no | — |
| 794 | C2×D3 | — | 9 | 1 | no | — |
| 795 | C2×D3 | — | 9 | 3 | no | — |
| 796 | C2×D3 | — | 12 | 3 | no | — |
| 797 | C2×D3 | — | 18 | 1 | no | — |
| 798 | C2×D3 | — | 18 | 3 | no | — |
| 799 | C2×D3 | — | 36 | 6 | no | — |
| 800 | C2×D3 | — | 36 | 6 | no | — |
| 801 | C2×D3 | — | 36 | 3 | no | — |
| 802 | C2×D3 | — | 36 | 3 | no | — |
| 803 | C2×D3 | — | 36 | 6 | no | — |
| 804 | C2×D3 | C23×D9 | 1 | 3 | yes | — |
| 805 | C2×D3 | C23×D9 | 1 | 1 | yes | characteristic |
| 806 | C3×C4 | — | 2 | 3 | no | — |
| 807 | C3×C4 | — | 2 | 1 | no | — |
| 808 | C3×C4 | — | 3 | 1 | no | — |
| 809 | C3×C4 | — | 3 | 3 | no | — |
| 810 | C3×C4 | — | 9 | 1 | no | — |
| 811 | C3×C4 | — | 9 | 3 | no | — |
| 812 | C3×C4 | C23×D9 | 1 | 3 | yes | — |
| 813 | C3×C4 | C23×D9 | 1 | 1 | yes | characteristic |
| 814 | C3×C4 | C22×D32 | 1 | 3 | yes | — |
| 815 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 816 | Dic3 | — | 3 | 3 | no | — |
| 817 | Dic3 | — | 3 | 1 | no | — |
| 818 | Dic3 | — | 9 | 1 | no | — |
| 819 | Dic3 | — | 9 | 3 | no | — |
| 820 | Dic3 | — | 9 | 3 | no | — |
| 821 | Dic3 | — | 9 | 1 | no | — |
| 822 | Dic3 | — | 18 | 3 | no | — |
| 823 | Dic3 | — | 18 | 1 | no | — |
| 824 | Dic3 | C23×D9 | 1 | 1 | yes | characteristic |
| 825 | Dic3 | C23×D9 | 1 | 3 | yes | — |
| 826 | C32 | #5964 | 1 | 1 | yes | characteristic |
| 827 | C9 | — | 2 | 1 | no | — |
| 828 | C9 | #5964 | 1 | 1 | yes | characteristic, complemented |
| 829 | C23 | — | 3 | 3 | no | — |
| 830 | C23 | — | 9 | 3 | no | — |
| 831 | C23 | — | 27 | 6 | no | — |
| 832 | C23 | — | 27 | 3 | no | — |
| 833 | Q8 | — | 3 | 3 | no | — |
| 834 | Q8 | — | 9 | 3 | no | — |
| 835 | Q8 | — | 27 | 1 | no | — |
| 836 | Q8 | — | 27 | 3 | no | — |
| 837 | Q8 | — | 27 | 3 | no | — |
| 838 | Q8 | — | 27 | 3 | no | — |
| 839 | Q8 | — | 27 | 3 | no | — |
| 840 | Q8 | C2×D3×D9 | 1 | 1 | yes | characteristic |
| 841 | D4 | — | 3 | 6 | no | — |
| 842 | D4 | — | 3 | 3 | no | — |
| 843 | D4 | — | 9 | 6 | no | — |
| 844 | D4 | — | 9 | 3 | no | — |
| 845 | D4 | — | 27 | 1 | no | — |
| 846 | D4 | — | 27 | 3 | no | — |
| 847 | D4 | — | 27 | 3 | no | — |
| 848 | D4 | — | 27 | 3 | no | — |
| 849 | D4 | — | 27 | 1 | no | — |
| 850 | D4 | — | 27 | 3 | no | — |
| 851 | D4 | — | 27 | 3 | no | — |
| 852 | D4 | — | 27 | 3 | no | — |
| 853 | D4 | — | 27 | 1 | no | — |
| 854 | D4 | — | 27 | 3 | no | — |
| 855 | D4 | — | 27 | 3 | no | — |
| 856 | D4 | — | 27 | 3 | no | — |
| 857 | D4 | — | 27 | 6 | no | — |
| 858 | D4 | — | 27 | 3 | no | — |
| 859 | D4 | C2×D3×D9 | 1 | 3 | yes | — |
| 860 | C2×C4 | — | 3 | 3 | no | — |
| 861 | C2×C4 | — | 3 | 3 | no | — |
| 862 | C2×C4 | — | 3 | 3 | no | — |
| 863 | C2×C4 | — | 3 | 1 | no | — |
| 864 | C2×C4 | — | 3 | 3 | no | — |
| 865 | C2×C4 | — | 9 | 3 | no | — |
| 866 | C2×C4 | — | 9 | 3 | no | — |
| 867 | C2×C4 | — | 9 | 3 | no | — |
| 868 | C2×C4 | — | 9 | 1 | no | — |
| 869 | C2×C4 | — | 9 | 3 | no | — |
| 870 | C2×C4 | — | 27 | 6 | no | — |
| 871 | C2×C4 | — | 27 | 6 | no | — |
| 872 | C2×C4 | — | 27 | 6 | no | — |
| 873 | C2×C4 | — | 27 | 3 | no | — |
| 874 | C2×C4 | — | 27 | 3 | no | — |
| 875 | C2×C4 | — | 27 | 3 | no | — |
| 876 | C2×C4 | — | 27 | 3 | no | — |
| 877 | C2×C4 | — | 27 | 1 | no | — |
| 878 | C2×C4 | C2×D3×D9 | 1 | 3 | yes | — |
| 879 | C2×C3 | — | 2 | 3 | no | — |
| 880 | C2×C3 | — | 2 | 3 | no | — |
| 881 | C2×C3 | — | 2 | 1 | no | — |
| 882 | C2×C3 | — | 4 | 3 | no | — |
| 883 | C2×C3 | — | 6 | 3 | no | — |
| 884 | C2×C3 | — | 6 | 1 | no | — |
| 885 | C2×C3 | — | 18 | 3 | no | — |
| 886 | C2×C3 | — | 18 | 1 | no | — |
| 887 | C2×C3 | C24×D9 | 1 | 1 | yes | characteristic |
| 888 | C2×C3 | C23×D32 | 1 | 1 | yes | characteristic |
| 889 | D3 | — | 2 | 1 | no | — |
| 890 | D3 | — | 2 | 3 | no | — |
| 891 | D3 | — | 6 | 1 | no | — |
| 892 | D3 | — | 6 | 3 | no | — |
| 893 | D3 | — | 18 | 2 | no | — |
| 894 | D3 | — | 18 | 1 | no | — |
| 895 | D3 | — | 18 | 3 | no | — |
| 896 | D3 | — | 18 | 1 | no | — |
| 897 | D3 | — | 18 | 3 | no | — |
| 898 | D3 | — | 36 | 3 | no | — |
| 899 | C22 | — | 3 | 1 | no | — |
| 900 | C22 | — | 3 | 3 | no | — |
| 901 | C22 | — | 9 | 1 | no | — |
| 902 | C22 | — | 9 | 3 | no | — |
| 903 | C22 | — | 12 | 3 | no | — |
| 904 | C22 | — | 27 | 1 | no | — |
| 905 | C22 | — | 27 | 3 | no | — |
| 906 | C22 | — | 36 | 3 | no | — |
| 907 | C22 | — | 108 | 3 | no | — |
| 908 | C22 | — | 108 | 6 | no | — |
| 909 | C22 | C22×D3×D9 | 1 | 3 | yes | — |
| 910 | C4 | — | 3 | 1 | no | — |
| 911 | C4 | — | 3 | 3 | no | — |
| 912 | C4 | — | 9 | 1 | no | — |
| 913 | C4 | — | 9 | 3 | no | — |
| 914 | C4 | — | 27 | 3 | no | — |
| 915 | C4 | — | 27 | 1 | no | — |
| 916 | C4 | C22×D3×D9 | 1 | 3 | yes | — |
| 917 | C4 | C22×D3×D9 | 1 | 1 | yes | characteristic |
| 918 | C3 | — | 2 | 1 | no | — |
| 919 | C3 | #10593139 | 1 | 1 | yes | characteristic, complemented |
| 920 | C3 | #10596695 | 1 | 1 | yes | characteristic |
| 921 | C2 | — | 2 | 3 | no | — |
| 922 | C2 | — | 6 | 1 | no | — |
| 923 | C2 | — | 6 | 3 | no | — |
| 924 | C2 | — | 18 | 1 | no | — |
| 925 | C2 | — | 18 | 3 | no | — |
| 926 | C2 | — | 54 | 1 | no | — |
| 927 | C2 | — | 54 | 3 | no | — |
| 928 | C2 | C23×D3×D9 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×D3×D9 |
| commutator, cosocle | C2×C3×C9 | C25 |
| Frattini | C2×C3 | C23×D32 |
| Fitting | C3×C9×#41 | C22 |
| socle | C2×C32 | C24×D3 |
| hypercenter | #41 | D3×D9 |
| hypocenter | C3×C9 | #585 |
| LCS | G ▷ C2×C3×C9 ▷ C3×C9 | |
| UCS | C1 ◁ C4 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #41×C3⋊D9 | C2 | semidirect |
| 2. D3×C9×#41 | C2 | semidirect |
| 3. C3×#41×D9 | C2 | semidirect |
| 4. #11722515 | C2 | semidirect |
| 5. #11722510 | C2 | semidirect |
| 6. #11722509 | C2 | semidirect |
| 7. #11722508 | C2 | semidirect |
| 8. #11722501 | C2 | semidirect |
| 9. #11722500 | C2 | semidirect |
| 10. #11722499 | C2 | semidirect |
| 11. #11722494 | C2 | semidirect |
| 12. #11722475 | C2 | semidirect |
| 13. D9×#235 | C2 | semidirect |
| 14. D3×#3697 | C2 | semidirect |
| 15. C2×#88640 | C2 | semidirect |
| 18. C3×C9×#41 | C22 | semidirect |
| 19. #88746 | C22 | semidirect |
| 20. Q8×C3⋊D9 | C22 | semidirect |
| 21. #88742 | C22 | semidirect |
| 22. D4×C3⋊D9 | C22 | semidirect |
| 23. #88736 | C22 | semidirect |
| 24. C2×C4×C3⋊D9 | C22 | semidirect |
| 25. C9×#239 | C22 | semidirect |
| 26. D3×Q8×C9 | C22 | semidirect |
| 27. C3×#3701 | C22 | semidirect |
| 28. C3×Q8×D9 | C22 | semidirect |
| 29. C9×#237 | C22 | semidirect |
| 30. D3×D4×C9 | C22 | semidirect |
| 31. C3×#3699 | C22 | semidirect |
| 32. C3×D4×D9 | C22 | semidirect |
| 33. C9×#235 | C22 | semidirect |
| 34. C2×C4×D3×C9 | C22 | semidirect |
| 35. C3×#3697 | C22 | semidirect |
| 36. C2×C3×C4×D9 | C22 | semidirect |
| 37. #88668 | C22 | semidirect |
| 38. D9×#67 | C22 | semidirect |
| 39. D3×#611 | C22 | semidirect |
| 40. C2×#6195 | C22 | semidirect |
| 41. C2×#6194 | C22 | semidirect |
| 42. #88663 | C22 | semidirect |
| 43. #88662 | C22 | semidirect |
| 44. C2×#6192 | C22 | semidirect |
| 45. #88658 | C22 | semidirect |
| 46. C2×#6189 | C22 | semidirect |
| 47. #88646 | C22 | semidirect |
| 48. D9×D12 | C22 | semidirect |
| 49. D3×D36 | C22 | semidirect |
| 50. C4×D3×D9 | C22 | semidirect |
| 51. #88642 | C22 | semidirect |
| 52. #88641 | C22 | semidirect |
| 53. #88640 | C22 | semidirect |
| 54. #88640 | C22 | semidirect |
| 55. #88640 | C22 | semidirect |
| 56. #88640 | C22 | semidirect |
| 57. #88640 | C22 | semidirect |
| 58. #88640 | C22 | semidirect |
| 59. #88640 | C22 | semidirect |
| 60. #88640 | C22 | semidirect |
| 61. #88639 | C22 | semidirect |
| 62. #88638 | C22 | semidirect |
| 63. D3×Dic18 | C22 | semidirect |
| 64. (C3⋊D9)⋊Q8 | C22 | semidirect |
| 65. #88635 | C22 | semidirect |
| 66. #88634 | C22 | semidirect |
| 67. D9×Dic6 | C22 | semidirect |
| 92. #41×D9 | D3 | semidirect |
| 205. C9×#41 | C2×D3 | semidirect |
| 216. #3701 | C2×D3 | semidirect |
| 221. Q8×D9 | C2×D3 | semidirect |
| 228. #3699 | C2×D3 | semidirect |
| 235. D4×D9 | C2×D3 | semidirect |
| 249. #3697 | C2×D3 | semidirect |
| 255. C2×C4×D9 | C2×D3 | semidirect |
| 295. D3×#41 | D9 | semidirect |
| 436. C3×#41 | C2×D9 | semidirect |
| 458. #239 | C2×D9 | semidirect |
| 467. D3×Q8 | C2×D9 | semidirect |
| 480. #237 | C2×D9 | semidirect |
| 493. D3×D4 | C2×D9 | semidirect |
| 520. #235 | C2×D9 | semidirect |
| 531. C2×C4×D3 | C2×D9 | semidirect |
| 597. C3×C9 | #585 | semidirect |
| 756. #41 | D3×D9 | semidirect |
| 828. C9 | #5964 | semidirect |
| 919. C3 | #10593139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×C3⋊D9 | 2 |
| D3×C9×#41 | 2 |
| C3×#41×D9 | 2 |
| #11722515 | 2 |
| #11722510 | 2 |
| #11722509 | 2 |
| #11722508 | 2 |
| #11722501 | 2 |
| #11722500 | 2 |
| #11722499 | 2 |
| #11722494 | 2 |
| #11722475 | 2 |
| D9×#235 | 2 |
| D3×#3697 | 2 |
| C2×#88640 | 2 |
| #10596695 | 3 |
| #10593139 | 3 |