Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
970 conjugacy classes of subgroups.
The subgroup lattice has 646 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11722661 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11722477 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C9×#932 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×C3×#3673 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11721187 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11721186 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11721175 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11721174 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11720889 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11720868 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11720861 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #10595102 | — | 3 | 1 | no | maximal |
| 13 | #10589876 | — | 3 | 1 | no | maximal |
| 14 | C2×C3×D4×C9 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C2×#6233 | — | 2 | 2 | no | — |
| 16 | #88742 | — | 2 | 1 | no | — |
| 17 | #88742 | C22 | 1 | 2 | yes | complemented |
| 18 | D4×C3⋊D9 | — | 2 | 1 | no | — |
| 19 | D4×C3⋊D9 | C22 | 1 | 2 | yes | complemented |
| 20 | #88736 | C22 | 1 | 1 | yes | characteristic |
| 21 | #88736 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C9×#235 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C2×C3×D36 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | D9×#67 | — | 2 | 2 | no | — |
| 25 | #88646 | C22 | 1 | 2 | yes | complemented |
| 26 | D3×D36 | — | 2 | 1 | no | — |
| 27 | #88641 | — | 2 | 1 | no | — |
| 28 | #88634 | C22 | 1 | 2 | yes | complemented |
| 29 | C9×#214 | C22 | 1 | 2 | yes | complemented |
| 30 | C9×#213 | C22 | 1 | 2 | yes | complemented |
| 31 | C3×#3673 | C22 | 1 | 2 | yes | complemented |
| 32 | C3×#3673 | C22 | 1 | 2 | yes | complemented |
| 33 | C9×#208 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | C2×C3×C9⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | #88428 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #88426 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #88424 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | #88422 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #88417 | C22 | 1 | 2 | yes | complemented |
| 40 | #88415 | C22 | 1 | 2 | yes | complemented |
| 41 | #88414 | C22 | 1 | 2 | yes | complemented |
| 42 | (C3⋊D9)⋊C8 | C22 | 1 | 2 | yes | complemented |
| 43 | #64361 | — | 3 | 1 | no | — |
| 44 | #64307 | — | 3 | 1 | no | — |
| 45 | C3×#932 | D3 | 1 | 1 | yes | characteristic |
| 46 | C2×C3×#213 | — | 3 | 1 | no | — |
| 47 | #63937 | — | 3 | 2 | no | — |
| 48 | #63936 | — | 3 | 2 | no | — |
| 49 | #63927 | — | 3 | 2 | no | — |
| 50 | #63926 | — | 3 | 2 | no | — |
| 51 | #63830 | — | 3 | 1 | no | — |
| 52 | #63829 | — | 3 | 1 | no | — |
| 53 | #63817 | — | 3 | 1 | no | — |
| 54 | #63715 | — | 3 | 1 | no | — |
| 55 | #63710 | — | 3 | 1 | no | — |
| 56 | #63710 | — | 6 | 1 | no | — |
| 57 | C9×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 58 | #63513 | — | 3 | 1 | no | — |
| 59 | C2×#3673 | D3 | 1 | 1 | yes | characteristic, complemented |
| 60 | #63478 | — | 3 | 2 | no | — |
| 61 | #63476 | — | 3 | 2 | no | — |
| 62 | #63473 | — | 3 | 2 | no | — |
| 63 | D8×D9 | — | 3 | 2 | no | — |
| 64 | #63470 | — | 3 | 1 | no | — |
| 65 | #63469 | — | 3 | 1 | no | — |
| 66 | C23×C3×C9 | — | 2 | 1 | no | — |
| 67 | C22×C3⋊D9 | — | 2 | 2 | no | — |
| 68 | C22×C3×D9 | — | 2 | 1 | no | — |
| 69 | C2×D3×D9 | — | 2 | 2 | no | — |
| 70 | C3×D4×C9 | — | 2 | 1 | no | — |
| 71 | C3×D4×C9 | C23 | 1 | 2 | yes | — |
| 72 | C2×C3×C4×C9 | C23 | 1 | 1 | yes | characteristic |
| 73 | #6233 | — | 2 | 1 | no | — |
| 74 | #6233 | — | 2 | 2 | no | — |
| 75 | #6233 | — | 2 | 2 | no | — |
| 76 | #6233 | D4 | 1 | 2 | yes | — |
| 77 | C2×C3⋊Dic9 | — | 2 | 2 | no | — |
| 78 | C4⋊(C3⋊D9) | D4 | 1 | 1 | yes | characteristic |
| 79 | C4⋊(C3⋊D9) | C23 | 1 | 1 | yes | characteristic |
| 80 | C4×C3⋊D9 | — | 2 | 1 | no | — |
| 81 | C4×C3⋊D9 | C23 | 1 | 2 | yes | — |
| 82 | #6226 | D4 | 1 | 1 | yes | characteristic |
| 83 | #6226 | C23 | 1 | 1 | yes | characteristic |
| 84 | C9×#67 | — | 2 | 1 | no | — |
| 85 | C9×D12 | C23 | 1 | 1 | yes | characteristic |
| 86 | C4×D3×C9 | — | 2 | 1 | no | — |
| 87 | C3×D36 | — | 2 | 1 | no | — |
| 88 | C3×D36 | C23 | 1 | 2 | yes | — |
| 89 | C9×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 90 | #6194 | — | 2 | 2 | no | — |
| 91 | #6192 | — | 2 | 2 | no | — |
| 92 | Dic3×D9 | — | 2 | 2 | no | — |
| 93 | C9×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 94 | C3×C9⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 95 | C3×C9⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 96 | #5774 | — | 9 | 1 | no | — |
| 97 | #5757 | — | 9 | 1 | no | — |
| 98 | C2×C32×D4 | C2×D3 | 1 | 1 | yes | characteristic |
| 99 | C2×#638 | — | 6 | 2 | no | — |
| 100 | #3830 | — | 3 | 2 | no | — |
| 101 | #3830 | — | 6 | 1 | no | — |
| 102 | D4×C3⋊D3 | — | 3 | 2 | no | — |
| 103 | D4×C3⋊D3 | — | 6 | 1 | no | — |
| 104 | #3828 | — | 3 | 1 | no | — |
| 105 | #3828 | — | 3 | 1 | no | — |
| 106 | C3×#235 | C2×D3 | 1 | 1 | yes | characteristic |
| 107 | C2×C3×D12 | — | 3 | 1 | no | — |
| 108 | D3×#67 | — | 6 | 2 | no | — |
| 109 | #3802 | — | 3 | 2 | no | — |
| 110 | D3×D12 | — | 6 | 1 | no | — |
| 111 | #3796 | — | 3 | 2 | no | — |
| 112 | #3795 | — | 6 | 1 | no | — |
| 113 | C3×#214 | C2×D3 | 1 | 2 | yes | — |
| 114 | C3×#213 | — | 3 | 2 | no | — |
| 115 | C3×#213 | — | 3 | 2 | no | — |
| 116 | C3×#213 | C2×D3 | 1 | 2 | yes | — |
| 117 | C3×#208 | C2×D3 | 1 | 1 | yes | characteristic |
| 118 | C2×C3×C3⋊C8 | — | 3 | 1 | no | — |
| 119 | #3719 | — | 3 | 1 | no | — |
| 120 | #3717 | — | 3 | 1 | no | — |
| 121 | #3716 | — | 3 | 1 | no | — |
| 122 | #3716 | — | 3 | 2 | no | — |
| 123 | #3714 | — | 3 | 1 | no | — |
| 124 | #3714 | — | 3 | 2 | no | — |
| 125 | #3712 | — | 3 | 2 | no | — |
| 126 | #3710 | — | 3 | 2 | no | — |
| 127 | C9×#41 | — | 3 | 1 | no | — |
| 128 | C2×D4×C9 | — | 2 | 1 | no | — |
| 129 | C2×D4×C9 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 130 | C2×#611 | — | 6 | 2 | no | — |
| 131 | C2×#611 | — | 6 | 4 | no | — |
| 132 | #3701 | — | 3 | 2 | no | — |
| 133 | #3699 | — | 3 | 2 | no | — |
| 134 | #3699 | — | 6 | 1 | no | — |
| 135 | #3699 | — | 6 | 2 | no | — |
| 136 | #3699 | — | 6 | 2 | no | — |
| 137 | D4×D9 | — | 3 | 2 | no | — |
| 138 | D4×D9 | — | 3 | 2 | no | — |
| 139 | D4×D9 | — | 6 | 1 | no | — |
| 140 | D4×D9 | — | 6 | 2 | no | — |
| 141 | D4×D9 | — | 6 | 2 | no | — |
| 142 | D4×D9 | — | 6 | 2 | no | — |
| 143 | #3697 | — | 3 | 1 | no | — |
| 144 | #3697 | — | 3 | 1 | no | — |
| 145 | #3697 | — | 6 | 1 | no | — |
| 146 | #3697 | — | 6 | 1 | no | — |
| 147 | #3697 | — | 6 | 1 | no | — |
| 148 | C2×D36 | — | 6 | 1 | no | — |
| 149 | C2×D36 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 150 | C9×SD16 | — | 3 | 2 | no | — |
| 151 | C9×D8 | — | 3 | 2 | no | — |
| 152 | C9×M16 | — | 3 | 1 | no | — |
| 153 | #3675 | — | 3 | 1 | no | — |
| 154 | #3674 | — | 3 | 1 | no | — |
| 155 | #3673 | — | 3 | 1 | no | — |
| 156 | #3673 | C2×D3 | 1 | 2 | yes | complemented |
| 157 | #3673 | C2×D3 | 1 | 2 | yes | complemented |
| 158 | #3672 | — | 3 | 1 | no | — |
| 159 | C2×C9⋊C8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 160 | D72 | — | 3 | 2 | no | — |
| 161 | #3664 | — | 3 | 2 | no | — |
| 162 | #3663 | — | 3 | 2 | no | — |
| 163 | C8×D9 | — | 3 | 2 | no | — |
| 164 | C22×C3×C9 | — | 2 | 2 | no | — |
| 165 | C22×C3×C9 | — | 8 | 1 | no | — |
| 166 | C22×C3×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C2×C3⋊D9 | — | 2 | 1 | no | — |
| 168 | C2×C3⋊D9 | — | 8 | 2 | no | — |
| 169 | C2×C3⋊D9 | C2×D4 | 1 | 2 | yes | — |
| 170 | C2×D3×C9 | — | 2 | 1 | no | — |
| 171 | C2×C3×D9 | — | 2 | 2 | no | — |
| 172 | C2×C3×D9 | — | 8 | 1 | no | — |
| 173 | D3×D9 | — | 8 | 2 | no | — |
| 174 | C3×C4×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | C3×C4×C9 | C24 | 1 | 1 | yes | characteristic |
| 176 | C3⋊Dic9 | — | 2 | 1 | no | — |
| 177 | C3⋊Dic9 | C2×D4 | 1 | 2 | yes | — |
| 178 | C9×Dic3 | — | 2 | 1 | no | — |
| 179 | #1009 | — | 9 | 1 | no | — |
| 180 | #1004 | — | 9 | 1 | no | — |
| 181 | #1004 | — | 9 | 1 | no | — |
| 182 | #1004 | — | 9 | 1 | no | — |
| 183 | #1004 | — | 18 | 1 | no | — |
| 184 | C3×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 185 | C2×C3×D8 | — | 9 | 1 | no | — |
| 186 | #950 | — | 9 | 1 | no | — |
| 187 | #932 | — | 9 | 1 | no | — |
| 188 | #932 | D9 | 1 | 1 | yes | characteristic, complemented |
| 189 | C2×#213 | — | 3 | 1 | no | — |
| 190 | #916 | — | 9 | 2 | no | — |
| 191 | #914 | — | 9 | 2 | no | — |
| 192 | #912 | — | 9 | 2 | no | — |
| 193 | #911 | — | 9 | 2 | no | — |
| 194 | #911 | — | 9 | 2 | no | — |
| 195 | #911 | — | 9 | 2 | no | — |
| 196 | D3×D8 | — | 9 | 2 | no | — |
| 197 | D3×D8 | — | 9 | 2 | no | — |
| 198 | #908 | — | 9 | 1 | no | — |
| 199 | #907 | — | 9 | 1 | no | — |
| 200 | #904 | — | 9 | 1 | no | — |
| 201 | #901 | — | 9 | 1 | no | — |
| 202 | C23×C32 | — | 2 | 1 | no | — |
| 203 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 204 | C22×C3×D3 | — | 6 | 1 | no | — |
| 205 | C2×D32 | — | 6 | 2 | no | — |
| 206 | C32×D4 | — | 2 | 1 | no | — |
| 207 | C32×D4 | C22×D3 | 1 | 2 | yes | — |
| 208 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 209 | #638 | — | 3 | 2 | no | — |
| 210 | #638 | — | 6 | 2 | no | — |
| 211 | #638 | — | 6 | 2 | no | — |
| 212 | #638 | — | 6 | 1 | no | — |
| 213 | C2×C3⋊Dic3 | — | 6 | 2 | no | — |
| 214 | C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 215 | C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 216 | C4×C3⋊D3 | — | 3 | 2 | no | — |
| 217 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 218 | #634 | — | 3 | 1 | no | — |
| 219 | #634 | — | 3 | 1 | no | — |
| 220 | C3×#67 | — | 2 | 1 | no | — |
| 221 | C3×D12 | — | 3 | 2 | no | — |
| 222 | C3×D12 | — | 6 | 1 | no | — |
| 223 | C3×D12 | C22×D3 | 1 | 1 | yes | characteristic |
| 224 | C3×C4×D3 | — | 2 | 1 | no | — |
| 225 | C3×Dic6 | C22×D3 | 1 | 1 | yes | characteristic |
| 226 | #626 | — | 6 | 2 | no | — |
| 227 | #625 | — | 6 | 2 | no | — |
| 228 | D3×Dic3 | — | 6 | 2 | no | — |
| 229 | C23×C9 | — | 2 | 2 | no | — |
| 230 | C23×C9 | — | 2 | 1 | no | — |
| 231 | C22×D9 | — | 2 | 1 | no | — |
| 232 | C22×D9 | — | 6 | 2 | no | — |
| 233 | C22×D9 | — | 6 | 2 | no | — |
| 234 | C22×D9 | — | 6 | 4 | no | — |
| 235 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 236 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 237 | C3×C3⋊C8 | C22×D3 | 1 | 2 | yes | — |
| 238 | Q8×C9 | — | 3 | 1 | no | — |
| 239 | D4×C9 | — | 2 | 2 | no | — |
| 240 | D4×C9 | — | 2 | 1 | no | — |
| 241 | D4×C9 | — | 2 | 2 | no | — |
| 242 | D4×C9 | — | 3 | 1 | no | — |
| 243 | D4×C9 | — | 6 | 1 | no | — |
| 244 | D4×C9 | C22×D3 | 1 | 2 | yes | — |
| 245 | C2×C4×C9 | — | 2 | 1 | no | — |
| 246 | C2×C4×C9 | — | 6 | 1 | no | — |
| 247 | C2×C4×C9 | C22×D3 | 1 | 1 | yes | characteristic |
| 248 | #611 | — | 3 | 2 | no | — |
| 249 | #611 | — | 6 | 2 | no | — |
| 250 | #611 | — | 6 | 2 | no | — |
| 251 | #611 | — | 6 | 2 | no | — |
| 252 | #611 | — | 6 | 2 | no | — |
| 253 | #611 | — | 6 | 2 | no | — |
| 254 | #611 | — | 6 | 4 | no | — |
| 255 | #611 | — | 6 | 4 | no | — |
| 256 | #611 | — | 6 | 1 | no | — |
| 257 | C2×Dic9 | — | 6 | 2 | no | — |
| 258 | C2×Dic9 | — | 6 | 4 | no | — |
| 259 | D36 | — | 2 | 1 | no | — |
| 260 | D36 | — | 3 | 1 | no | — |
| 261 | D36 | — | 3 | 1 | no | — |
| 262 | D36 | — | 6 | 1 | no | — |
| 263 | D36 | — | 6 | 1 | no | — |
| 264 | D36 | — | 6 | 2 | no | — |
| 265 | D36 | C22×D3 | 1 | 2 | yes | — |
| 266 | C4×D9 | — | 3 | 2 | no | — |
| 267 | C4×D9 | — | 6 | 2 | no | — |
| 268 | C4×D9 | — | 6 | 2 | no | — |
| 269 | C4×D9 | — | 6 | 2 | no | — |
| 270 | C4×D9 | — | 6 | 1 | no | — |
| 271 | Dic18 | — | 3 | 1 | no | — |
| 272 | Dic18 | — | 3 | 1 | no | — |
| 273 | Dic18 | — | 6 | 1 | no | — |
| 274 | Dic18 | — | 6 | 1 | no | — |
| 275 | C8×C9 | — | 3 | 2 | no | — |
| 276 | C9⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 277 | C9⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 278 | #576 | — | 27 | 1 | no | Sylow |
| 279 | C2×C3×C9 | — | 2 | 1 | no | — |
| 280 | C2×C3×C9 | — | 4 | 2 | no | — |
| 281 | C2×C3×C9 | C22×D4 | 1 | 1 | yes | characteristic |
| 282 | C3⋊D9 | — | 2 | 2 | no | — |
| 283 | C3⋊D9 | — | 4 | 1 | no | — |
| 284 | D3×C9 | — | 4 | 1 | no | — |
| 285 | C3×D9 | — | 4 | 2 | no | — |
| 286 | C3×#41 | — | 3 | 1 | no | — |
| 287 | C2×C3×D4 | — | 2 | 1 | no | — |
| 288 | C2×C3×D4 | — | 9 | 1 | no | — |
| 289 | C2×C3×D4 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 290 | C2×C3×D4 | D32 | 1 | 1 | yes | characteristic |
| 291 | C2×#67 | — | 18 | 2 | no | — |
| 292 | C2×#67 | — | 18 | 2 | no | — |
| 293 | C2×#67 | — | 18 | 2 | no | — |
| 294 | C2×#67 | — | 18 | 4 | no | — |
| 295 | #239 | — | 9 | 2 | no | — |
| 296 | #237 | — | 9 | 2 | no | — |
| 297 | #237 | — | 9 | 2 | no | — |
| 298 | #237 | — | 9 | 2 | no | — |
| 299 | #237 | — | 18 | 2 | no | — |
| 300 | #237 | — | 18 | 1 | no | — |
| 301 | #237 | — | 18 | 1 | no | — |
| 302 | #237 | — | 18 | 1 | no | — |
| 303 | #237 | — | 18 | 2 | no | — |
| 304 | D3×D4 | — | 9 | 2 | no | — |
| 305 | D3×D4 | — | 9 | 2 | no | — |
| 306 | D3×D4 | — | 9 | 2 | no | — |
| 307 | D3×D4 | — | 9 | 2 | no | — |
| 308 | D3×D4 | — | 18 | 2 | no | — |
| 309 | D3×D4 | — | 18 | 1 | no | — |
| 310 | D3×D4 | — | 18 | 1 | no | — |
| 311 | D3×D4 | — | 18 | 1 | no | — |
| 312 | D3×D4 | — | 18 | 2 | no | — |
| 313 | D3×D4 | — | 18 | 2 | no | — |
| 314 | #235 | — | 9 | 1 | no | — |
| 315 | #235 | — | 9 | 1 | no | — |
| 316 | #235 | — | 9 | 1 | no | — |
| 317 | #235 | — | 9 | 1 | no | — |
| 318 | #235 | — | 18 | 1 | no | — |
| 319 | #235 | — | 18 | 1 | no | — |
| 320 | #235 | — | 18 | 1 | no | — |
| 321 | #235 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 322 | C2×D12 | — | 3 | 1 | no | — |
| 323 | C2×D12 | — | 18 | 1 | no | — |
| 324 | C3×SD16 | — | 3 | 2 | no | — |
| 325 | C3×D8 | — | 3 | 2 | no | — |
| 326 | C3×D8 | — | 9 | 2 | no | — |
| 327 | C3×D8 | — | 9 | 2 | no | — |
| 328 | C3×M16 | — | 3 | 1 | no | — |
| 329 | C2×C3×C8 | — | 9 | 1 | no | — |
| 330 | #216 | — | 9 | 1 | no | — |
| 331 | #215 | — | 9 | 1 | no | — |
| 332 | #214 | — | 9 | 1 | no | — |
| 333 | #214 | — | 9 | 2 | no | — |
| 334 | #214 | C2×D9 | 1 | 2 | yes | complemented |
| 335 | #213 | — | 3 | 2 | no | — |
| 336 | #213 | — | 3 | 2 | no | — |
| 337 | #213 | — | 9 | 1 | no | — |
| 338 | #213 | — | 9 | 2 | no | — |
| 339 | #213 | C2×D9 | 1 | 2 | yes | complemented |
| 340 | #208 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 341 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 342 | Dic12 | — | 9 | 1 | no | — |
| 343 | D24 | — | 9 | 2 | no | — |
| 344 | D24 | — | 9 | 1 | no | — |
| 345 | #204 | — | 9 | 2 | no | — |
| 346 | #204 | — | 9 | 1 | no | — |
| 347 | #204 | — | 9 | 1 | no | — |
| 348 | ΓL(1,𝔽25) | — | 9 | 2 | no | — |
| 349 | ΓL(1,𝔽25) | — | 9 | 2 | no | — |
| 350 | D3×C8 | — | 9 | 2 | no | — |
| 351 | D3×C8 | — | 9 | 2 | no | — |
| 352 | C22×C32 | — | 2 | 2 | no | — |
| 353 | C22×C32 | — | 8 | 1 | no | — |
| 354 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic |
| 355 | C2×C3⋊D3 | — | 3 | 2 | no | — |
| 356 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 357 | C2×C3⋊D3 | — | 24 | 2 | no | — |
| 358 | C2×C3×D3 | — | 2 | 1 | no | — |
| 359 | C2×C3×D3 | — | 6 | 2 | no | — |
| 360 | C2×C3×D3 | — | 24 | 1 | no | — |
| 361 | D32 | — | 24 | 2 | no | — |
| 362 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 363 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 364 | C3⋊Dic3 | — | 3 | 2 | no | — |
| 365 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 366 | C3×Dic3 | — | 2 | 1 | no | — |
| 367 | C22×C9 | — | 2 | 4 | no | — |
| 368 | C22×C9 | — | 2 | 2 | no | — |
| 369 | C22×C9 | — | 2 | 1 | no | — |
| 370 | C22×C9 | — | 6 | 1 | no | — |
| 371 | C22×C9 | — | 8 | 1 | no | — |
| 372 | C22×C9 | — | 8 | 2 | no | — |
| 373 | C22×C9 | D3×D4 | 1 | 1 | yes | characteristic |
| 374 | C2×D9 | — | 2 | 2 | no | — |
| 375 | C2×D9 | — | 3 | 2 | no | — |
| 376 | C2×D9 | — | 6 | 2 | no | — |
| 377 | C2×D9 | — | 6 | 2 | no | — |
| 378 | C2×D9 | — | 6 | 1 | no | — |
| 379 | C2×D9 | — | 8 | 1 | no | — |
| 380 | C2×D9 | — | 24 | 2 | no | — |
| 381 | C2×D9 | — | 24 | 2 | no | — |
| 382 | C2×D9 | — | 24 | 4 | no | — |
| 383 | C4×C9 | — | 2 | 1 | no | — |
| 384 | C4×C9 | — | 2 | 1 | no | — |
| 385 | C4×C9 | — | 6 | 1 | no | — |
| 386 | C4×C9 | D3×D4 | 1 | 1 | yes | characteristic |
| 387 | C4×C9 | C23×D3 | 1 | 1 | yes | characteristic |
| 388 | Dic9 | — | 3 | 2 | no | — |
| 389 | Dic9 | — | 6 | 2 | no | — |
| 390 | Dic9 | — | 6 | 2 | no | — |
| 391 | Dic9 | — | 6 | 1 | no | — |
| 392 | H(5,𝔽2) | — | 27 | 1 | no | — |
| 393 | H(5,𝔽2) | — | 27 | 1 | no | — |
| 394 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 395 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 396 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 397 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 398 | #135 | — | 27 | 1 | no | — |
| 399 | #135 | — | 27 | 2 | no | — |
| 400 | C2×D8 | — | 9 | 1 | no | — |
| 401 | C2×D8 | — | 27 | 2 | no | — |
| 402 | #131 | — | 27 | 1 | no | — |
| 403 | C3×C9 | #576 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 404 | C23×C3 | — | 2 | 2 | no | — |
| 405 | C23×C3 | — | 2 | 1 | no | — |
| 406 | C23×C3 | — | 2 | 1 | no | — |
| 407 | C23×C3 | — | 18 | 1 | no | — |
| 408 | C22×D3 | — | 6 | 1 | no | — |
| 409 | C22×D3 | — | 18 | 2 | no | — |
| 410 | C22×D3 | — | 18 | 2 | no | — |
| 411 | C22×D3 | — | 18 | 2 | no | — |
| 412 | C22×D3 | — | 18 | 2 | no | — |
| 413 | C22×D3 | — | 18 | 4 | no | — |
| 414 | C3×Q8 | — | 3 | 1 | no | — |
| 415 | C3×D4 | — | 2 | 2 | no | — |
| 416 | C3×D4 | — | 2 | 1 | no | — |
| 417 | C3×D4 | — | 2 | 1 | no | — |
| 418 | C3×D4 | — | 2 | 2 | no | — |
| 419 | C3×D4 | — | 3 | 1 | no | — |
| 420 | C3×D4 | — | 6 | 1 | no | — |
| 421 | C3×D4 | — | 9 | 2 | no | — |
| 422 | C3×D4 | — | 18 | 1 | no | — |
| 423 | C3×D4 | C22×D9 | 1 | 2 | yes | — |
| 424 | C3×D4 | C2×D32 | 1 | 2 | yes | — |
| 425 | C2×C3×C4 | — | 2 | 1 | no | — |
| 426 | C2×C3×C4 | — | 6 | 1 | no | — |
| 427 | C2×C3×C4 | C22×D9 | 1 | 1 | yes | characteristic |
| 428 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 429 | #67 | — | 2 | 1 | no | — |
| 430 | #67 | — | 9 | 2 | no | — |
| 431 | #67 | — | 9 | 2 | no | — |
| 432 | #67 | — | 18 | 2 | no | — |
| 433 | #67 | — | 18 | 2 | no | — |
| 434 | #67 | — | 18 | 2 | no | — |
| 435 | #67 | — | 18 | 2 | no | — |
| 436 | #67 | — | 18 | 2 | no | — |
| 437 | #67 | — | 18 | 2 | no | — |
| 438 | #67 | — | 18 | 2 | no | — |
| 439 | #67 | — | 18 | 2 | no | — |
| 440 | #67 | — | 18 | 2 | no | — |
| 441 | #67 | — | 18 | 4 | no | — |
| 442 | #67 | — | 18 | 4 | no | — |
| 443 | #67 | — | 18 | 1 | no | — |
| 444 | #67 | — | 18 | 1 | no | — |
| 445 | C2×Dic3 | — | 18 | 2 | no | — |
| 446 | C2×Dic3 | — | 18 | 2 | no | — |
| 447 | C2×Dic3 | — | 18 | 2 | no | — |
| 448 | C2×Dic3 | — | 18 | 4 | no | — |
| 449 | D12 | — | 3 | 2 | no | — |
| 450 | D12 | — | 6 | 1 | no | — |
| 451 | D12 | — | 9 | 1 | no | — |
| 452 | D12 | — | 9 | 1 | no | — |
| 453 | D12 | — | 9 | 1 | no | — |
| 454 | D12 | — | 9 | 1 | no | — |
| 455 | D12 | — | 18 | 1 | no | — |
| 456 | D12 | — | 18 | 1 | no | — |
| 457 | D12 | — | 18 | 2 | no | — |
| 458 | D12 | C22×D9 | 1 | 1 | yes | characteristic |
| 459 | C4×D3 | — | 2 | 1 | no | — |
| 460 | C4×D3 | — | 9 | 2 | no | — |
| 461 | C4×D3 | — | 9 | 2 | no | — |
| 462 | C4×D3 | — | 18 | 2 | no | — |
| 463 | C4×D3 | — | 18 | 2 | no | — |
| 464 | C4×D3 | — | 18 | 2 | no | — |
| 465 | C4×D3 | — | 18 | 1 | no | — |
| 466 | C4×D3 | — | 18 | 1 | no | — |
| 467 | Dic6 | — | 9 | 1 | no | — |
| 468 | Dic6 | — | 9 | 1 | no | — |
| 469 | Dic6 | — | 9 | 1 | no | — |
| 470 | Dic6 | — | 9 | 1 | no | — |
| 471 | Dic6 | — | 18 | 1 | no | — |
| 472 | Dic6 | — | 18 | 1 | no | — |
| 473 | Dic6 | C22×D9 | 1 | 1 | yes | characteristic |
| 474 | C3×C8 | — | 3 | 2 | no | — |
| 475 | C3×C8 | — | 9 | 1 | no | — |
| 476 | C3×C8 | — | 9 | 1 | no | — |
| 477 | C3⋊C8 | — | 3 | 1 | no | — |
| 478 | C3⋊C8 | — | 3 | 1 | no | — |
| 479 | C3⋊C8 | C22×D9 | 1 | 2 | yes | — |
| 480 | C2×C32 | — | 2 | 1 | no | — |
| 481 | C2×C32 | — | 4 | 2 | no | — |
| 482 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 483 | C3⋊D3 | — | 6 | 2 | no | — |
| 484 | C3⋊D3 | — | 12 | 1 | no | — |
| 485 | C3×D3 | — | 4 | 1 | no | — |
| 486 | C3×D3 | — | 12 | 2 | no | — |
| 487 | C2×C9 | — | 2 | 1 | no | — |
| 488 | C2×C9 | — | 2 | 1 | no | — |
| 489 | C2×C9 | — | 4 | 1 | no | — |
| 490 | C2×C9 | — | 4 | 4 | no | — |
| 491 | C2×C9 | — | 4 | 2 | no | — |
| 492 | C2×C9 | — | 12 | 1 | no | — |
| 493 | C2×C9 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 494 | D9 | — | 4 | 2 | no | — |
| 495 | D9 | — | 6 | 2 | no | — |
| 496 | D9 | — | 12 | 2 | no | — |
| 497 | D9 | — | 12 | 2 | no | — |
| 498 | D9 | — | 12 | 1 | no | — |
| 499 | #41 | — | 3 | 1 | no | — |
| 500 | #41 | — | 27 | 1 | no | — |
| 501 | #41 | — | 27 | 2 | no | — |
| 502 | #41 | — | 27 | 2 | no | — |
| 503 | #41 | — | 27 | 1 | no | — |
| 504 | #41 | — | 54 | 1 | no | — |
| 505 | #41 | — | 54 | 1 | no | — |
| 506 | C2×D4 | — | 9 | 1 | no | — |
| 507 | C2×D4 | — | 27 | 2 | no | — |
| 508 | C2×D4 | — | 27 | 2 | no | — |
| 509 | C2×D4 | — | 54 | 1 | no | — |
| 510 | C2×D4 | — | 54 | 1 | no | — |
| 511 | C2×D4 | — | 54 | 2 | no | — |
| 512 | C2×D4 | — | 54 | 2 | no | — |
| 513 | C2×D4 | D3×D9 | 1 | 1 | yes | characteristic, complemented |
| 514 | Q16 | — | 27 | 1 | no | — |
| 515 | SD16 | — | 3 | 2 | no | — |
| 516 | SD16 | — | 27 | 2 | no | — |
| 517 | SD16 | — | 27 | 1 | no | — |
| 518 | SD16 | — | 27 | 1 | no | — |
| 519 | D8 | — | 3 | 2 | no | — |
| 520 | D8 | — | 9 | 2 | no | — |
| 521 | D8 | — | 9 | 2 | no | — |
| 522 | D8 | — | 27 | 2 | no | — |
| 523 | D8 | — | 27 | 1 | no | — |
| 524 | M16 | — | 3 | 1 | no | — |
| 525 | M16 | — | 27 | 2 | no | — |
| 526 | C2×C8 | — | 9 | 1 | no | — |
| 527 | C2×C8 | — | 27 | 2 | no | — |
| 528 | C22×C3 | — | 2 | 4 | no | — |
| 529 | C22×C3 | — | 2 | 2 | no | — |
| 530 | C22×C3 | — | 2 | 2 | no | — |
| 531 | C22×C3 | — | 2 | 1 | no | — |
| 532 | C22×C3 | — | 6 | 1 | no | — |
| 533 | C22×C3 | — | 8 | 1 | no | — |
| 534 | C22×C3 | — | 8 | 1 | no | — |
| 535 | C22×C3 | — | 8 | 2 | no | — |
| 536 | C22×C3 | — | 18 | 2 | no | — |
| 537 | C22×C3 | — | 72 | 1 | no | — |
| 538 | C22×C3 | D4×D9 | 1 | 1 | yes | characteristic |
| 539 | C22×C3 | #3811 | 1 | 1 | yes | characteristic |
| 540 | C2×D3 | — | 2 | 1 | no | — |
| 541 | C2×D3 | — | 6 | 2 | no | — |
| 542 | C2×D3 | — | 9 | 2 | no | — |
| 543 | C2×D3 | — | 9 | 2 | no | — |
| 544 | C2×D3 | — | 18 | 2 | no | — |
| 545 | C2×D3 | — | 18 | 2 | no | — |
| 546 | C2×D3 | — | 18 | 1 | no | — |
| 547 | C2×D3 | — | 18 | 1 | no | — |
| 548 | C2×D3 | — | 24 | 1 | no | — |
| 549 | C2×D3 | — | 72 | 2 | no | — |
| 550 | C2×D3 | — | 72 | 2 | no | — |
| 551 | C2×D3 | — | 72 | 2 | no | — |
| 552 | C2×D3 | — | 72 | 2 | no | — |
| 553 | C2×D3 | — | 72 | 4 | no | — |
| 554 | C3×C4 | — | 2 | 1 | no | — |
| 555 | C3×C4 | — | 2 | 1 | no | — |
| 556 | C3×C4 | — | 6 | 1 | no | — |
| 557 | C3×C4 | D4×D9 | 1 | 1 | yes | characteristic |
| 558 | C3×C4 | C23×D9 | 1 | 1 | yes | characteristic |
| 559 | C3×C4 | #3811 | 1 | 1 | yes | characteristic |
| 560 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 561 | Dic3 | — | 2 | 1 | no | — |
| 562 | Dic3 | — | 9 | 2 | no | — |
| 563 | Dic3 | — | 9 | 2 | no | — |
| 564 | Dic3 | — | 18 | 2 | no | — |
| 565 | Dic3 | — | 18 | 2 | no | — |
| 566 | Dic3 | — | 18 | 1 | no | — |
| 567 | Dic3 | — | 18 | 1 | no | — |
| 568 | C32 | #5774 | 1 | 1 | yes | characteristic |
| 569 | C9 | — | 2 | 1 | no | — |
| 570 | C9 | #5757 | 1 | 1 | yes | characteristic, complemented |
| 571 | C23 | — | 2 | 1 | no | — |
| 572 | C23 | — | 18 | 1 | no | — |
| 573 | C23 | — | 54 | 2 | no | — |
| 574 | C23 | — | 54 | 2 | no | — |
| 575 | Q8 | — | 3 | 1 | no | — |
| 576 | Q8 | — | 27 | 1 | no | — |
| 577 | Q8 | — | 27 | 1 | no | — |
| 578 | D4 | — | 2 | 1 | no | — |
| 579 | D4 | — | 3 | 1 | no | — |
| 580 | D4 | — | 6 | 1 | no | — |
| 581 | D4 | — | 9 | 2 | no | — |
| 582 | D4 | — | 18 | 1 | no | — |
| 583 | D4 | — | 27 | 2 | no | — |
| 584 | D4 | — | 27 | 1 | no | — |
| 585 | D4 | — | 27 | 1 | no | — |
| 586 | D4 | — | 54 | 2 | no | — |
| 587 | D4 | — | 54 | 2 | no | — |
| 588 | D4 | — | 54 | 2 | no | — |
| 589 | D4 | — | 54 | 2 | no | — |
| 590 | D4 | — | 54 | 1 | no | — |
| 591 | D4 | C2×D3×D9 | 1 | 2 | yes | — |
| 592 | C2×C4 | — | 6 | 1 | no | — |
| 593 | C2×C4 | — | 27 | 2 | no | — |
| 594 | C2×C4 | — | 54 | 2 | no | — |
| 595 | C2×C4 | — | 54 | 2 | no | — |
| 596 | C2×C4 | — | 54 | 1 | no | — |
| 597 | C2×C4 | C2×D3×D9 | 1 | 1 | yes | characteristic |
| 598 | C8 | — | 3 | 2 | no | — |
| 599 | C8 | — | 9 | 1 | no | — |
| 600 | C8 | — | 9 | 1 | no | — |
| 601 | C2×C3 | — | 2 | 1 | no | — |
| 602 | C2×C3 | — | 2 | 1 | no | — |
| 603 | C2×C3 | — | 2 | 1 | no | — |
| 604 | C2×C3 | — | 4 | 1 | no | — |
| 605 | C2×C3 | — | 4 | 4 | no | — |
| 606 | C2×C3 | — | 4 | 2 | no | — |
| 607 | C2×C3 | — | 4 | 2 | no | — |
| 608 | C2×C3 | — | 12 | 1 | no | — |
| 609 | C2×C3 | — | 36 | 2 | no | — |
| 610 | C2×C3 | C2×D4×D9 | 1 | 1 | yes | characteristic |
| 611 | C2×C3 | C2×#3811 | 1 | 1 | yes | characteristic |
| 612 | D3 | — | 4 | 1 | no | — |
| 613 | D3 | — | 12 | 2 | no | — |
| 614 | D3 | — | 18 | 2 | no | — |
| 615 | D3 | — | 18 | 2 | no | — |
| 616 | D3 | — | 36 | 2 | no | — |
| 617 | D3 | — | 36 | 2 | no | — |
| 618 | D3 | — | 36 | 1 | no | — |
| 619 | D3 | — | 36 | 1 | no | — |
| 620 | C22 | — | 2 | 2 | no | — |
| 621 | C22 | — | 6 | 1 | no | — |
| 622 | C22 | — | 8 | 1 | no | — |
| 623 | C22 | — | 18 | 2 | no | — |
| 624 | C22 | — | 27 | 2 | no | — |
| 625 | C22 | — | 54 | 1 | no | — |
| 626 | C22 | — | 72 | 1 | no | — |
| 627 | C22 | — | 216 | 2 | no | — |
| 628 | C22 | — | 216 | 2 | no | — |
| 629 | C22 | #88668 | 1 | 1 | yes | characteristic |
| 630 | C4 | — | 6 | 1 | no | — |
| 631 | C4 | — | 27 | 2 | no | — |
| 632 | C4 | — | 54 | 1 | no | — |
| 633 | C4 | #88668 | 1 | 1 | yes | characteristic |
| 634 | C4 | C22×D3×D9 | 1 | 1 | yes | characteristic |
| 635 | C3 | — | 2 | 1 | no | — |
| 636 | C3 | #10589876 | 1 | 1 | yes | characteristic, complemented |
| 637 | C3 | #10595102 | 1 | 1 | yes | characteristic |
| 638 | C2 | — | 2 | 1 | no | — |
| 639 | C2 | — | 4 | 2 | no | — |
| 640 | C2 | — | 12 | 1 | no | — |
| 641 | C2 | — | 36 | 2 | no | — |
| 642 | C2 | — | 54 | 2 | no | — |
| 643 | C2 | — | 108 | 1 | no | — |
| 644 | C2 | C2×#88668 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11722661 | C2 | semidirect |
| 2. #11722477 | C2 | semidirect |
| 3. C9×#932 | C2 | semidirect |
| 4. C2×C3×#3673 | C2 | semidirect |
| 5. #11721187 | C2 | semidirect |
| 6. #11721186 | C2 | semidirect |
| 7. #11721175 | C2 | semidirect |
| 8. #11721174 | C2 | semidirect |
| 9. #11720889 | C2 | semidirect |
| 10. #11720868 | C2 | semidirect |
| 11. #11720861 | C2 | semidirect |
| 14. C2×C3×D4×C9 | C22 | semidirect |
| 17. #88742 | C22 | semidirect |
| 19. D4×C3⋊D9 | C22 | semidirect |
| 21. #88736 | C22 | semidirect |
| 22. C9×#235 | C22 | semidirect |
| 23. C2×C3×D36 | C22 | semidirect |
| 25. #88646 | C22 | semidirect |
| 28. #88634 | C22 | semidirect |
| 29. C9×#214 | C22 | semidirect |
| 30. C9×#213 | C22 | semidirect |
| 31. C3×#3673 | C22 | semidirect |
| 32. C3×#3673 | C22 | semidirect |
| 33. C9×#208 | C22 | semidirect |
| 34. C2×C3×C9⋊C8 | C22 | semidirect |
| 35. #88428 | C22 | semidirect |
| 36. #88426 | C22 | semidirect |
| 37. #88424 | C22 | semidirect |
| 38. #88422 | C22 | semidirect |
| 39. #88417 | C22 | semidirect |
| 40. #88415 | C22 | semidirect |
| 41. #88414 | C22 | semidirect |
| 42. (C3⋊D9)⋊C8 | C22 | semidirect |
| 59. C2×#3673 | D3 | semidirect |
| 129. C2×D4×C9 | C2×D3 | semidirect |
| 149. C2×D36 | C2×D3 | semidirect |
| 156. #3673 | C2×D3 | semidirect |
| 157. #3673 | C2×D3 | semidirect |
| 159. C2×C9⋊C8 | C2×D3 | semidirect |
| 188. #932 | D9 | semidirect |
| 289. C2×C3×D4 | C2×D9 | semidirect |
| 321. #235 | C2×D9 | semidirect |
| 334. #214 | C2×D9 | semidirect |
| 339. #213 | C2×D9 | semidirect |
| 340. #208 | C2×D9 | semidirect |
| 403. C3×C9 | #576 | semidirect |
| 513. C2×D4 | D3×D9 | semidirect |
| 570. C9 | #5757 | semidirect |
| 636. C3 | #10589876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722661 | 2 |
| #11722477 | 2 |
| C9×#932 | 2 |
| C2×C3×#3673 | 2 |
| #11721187 | 2 |
| #11721186 | 2 |
| #11721175 | 2 |
| #11721174 | 2 |
| #11720889 | 2 |
| #11720868 | 2 |
| #11720861 | 2 |
| #10595102 | 3 |
| #10589876 | 3 |