Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2594 conjugacy classes of subgroups.
The subgroup lattice has 484 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#88746 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C9×#1007 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#63713 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11722515 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | D9×#239 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | D3×#3701 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11722509 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #11722478 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | #11722475 | C2 | 1 | 6 | yes | maximal, complemented |
| 10 | #10596689 | — | 3 | 1 | no | maximal |
| 11 | #10593143 | — | 3 | 1 | no | maximal |
| 12 | C2×C3×Q8×C9 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | #88746 | C22 | 1 | 4 | yes | complemented |
| 14 | #88746 | C22 | 1 | 4 | yes | complemented |
| 15 | C2×C4⋊(C3⋊D9) | C22 | 1 | 3 | yes | complemented |
| 16 | C2×C4×C3⋊D9 | C22 | 1 | 3 | yes | complemented |
| 17 | C9×#239 | C22 | 1 | 4 | yes | complemented |
| 18 | D3×Q8×C9 | C22 | 1 | 4 | yes | complemented |
| 19 | C3×#3701 | C22 | 1 | 4 | yes | complemented |
| 20 | C3×Q8×D9 | C22 | 1 | 4 | yes | complemented |
| 21 | C9×#235 | C22 | 1 | 6 | yes | complemented |
| 22 | C3×#3697 | C22 | 1 | 6 | yes | complemented |
| 23 | #88668 | C22 | 1 | 12 | yes | complemented |
| 24 | #88663 | C22 | 1 | 4 | yes | complemented |
| 25 | #88646 | C22 | 1 | 6 | yes | complemented |
| 26 | D9×D12 | C22 | 1 | 12 | yes | complemented |
| 27 | D3×D36 | C22 | 1 | 12 | yes | complemented |
| 28 | C4×D3×D9 | C22 | 1 | 12 | yes | complemented |
| 29 | #88642 | C22 | 1 | 12 | yes | complemented |
| 30 | #88640 | C22 | 1 | 12 | yes | complemented |
| 31 | #88639 | C22 | 1 | 6 | yes | complemented |
| 32 | (C3⋊D9)⋊Q8 | C22 | 1 | 6 | yes | complemented |
| 33 | #88635 | C22 | 1 | 12 | yes | complemented |
| 34 | #88634 | C22 | 1 | 6 | yes | complemented |
| 35 | C2×#3832 | — | 3 | 1 | no | — |
| 36 | C3×#1007 | — | 3 | 1 | no | — |
| 37 | C3×#1007 | D3 | 1 | 1 | yes | characteristic |
| 38 | #64320 | — | 3 | 4 | no | — |
| 39 | D3×#239 | — | 3 | 4 | no | — |
| 40 | D3×#239 | — | 3 | 4 | no | — |
| 41 | #64316 | — | 3 | 4 | no | — |
| 42 | #64308 | — | 3 | 6 | no | — |
| 43 | #64306 | — | 3 | 6 | no | — |
| 44 | C9×2−1+4 | — | 3 | 1 | no | — |
| 45 | #63715 | — | 3 | 4 | no | — |
| 46 | #63715 | — | 3 | 6 | no | — |
| 47 | #41×D9 | — | 3 | 4 | no | — |
| 48 | #41×D9 | — | 3 | 6 | no | — |
| 49 | #63713 | — | 3 | 4 | no | — |
| 50 | #63713 | D3 | 1 | 1 | yes | characteristic, complemented |
| 51 | C2×#3701 | — | 3 | 1 | no | — |
| 52 | C2×#3701 | — | 3 | 4 | no | — |
| 53 | C2×#3701 | — | 6 | 1 | no | — |
| 54 | C22×C3⋊D9 | C23 | 1 | 3 | yes | — |
| 55 | C2×D3×D9 | C23 | 1 | 12 | yes | — |
| 56 | C3×Q8×C9 | C23 | 1 | 4 | yes | — |
| 57 | C2×C3×C4×C9 | C23 | 1 | 3 | yes | — |
| 58 | C2×C3⋊Dic9 | C23 | 1 | 1 | yes | characteristic |
| 59 | C4⋊(C3⋊D9) | C23 | 1 | 12 | yes | — |
| 60 | C4×C3⋊D9 | C23 | 1 | 6 | yes | — |
| 61 | C4×C3⋊D9 | C23 | 1 | 6 | yes | — |
| 62 | C9×#67 | C23 | 1 | 4 | yes | — |
| 63 | C3×#611 | C23 | 1 | 4 | yes | — |
| 64 | C9×D12 | C23 | 1 | 6 | yes | — |
| 65 | C4×D3×C9 | C23 | 1 | 12 | yes | — |
| 66 | C3×D36 | C23 | 1 | 6 | yes | — |
| 67 | C3×C4×D9 | C23 | 1 | 12 | yes | — |
| 68 | C9×Dic6 | C23 | 1 | 6 | yes | — |
| 69 | C3×Dic18 | C23 | 1 | 6 | yes | — |
| 70 | #6195 | C23 | 1 | 12 | yes | — |
| 71 | #6194 | C23 | 1 | 4 | yes | — |
| 72 | D3×Dic9 | C23 | 1 | 4 | yes | — |
| 73 | #6192 | C23 | 1 | 12 | yes | — |
| 74 | (C3⋊D9)⋊C4 | C23 | 1 | 12 | yes | — |
| 75 | Dic3×D9 | C23 | 1 | 4 | yes | — |
| 76 | #6189 | C23 | 1 | 4 | yes | — |
| 77 | #5968 | — | 9 | 1 | no | — |
| 78 | #5968 | — | 9 | 1 | no | — |
| 79 | C2×C32×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 80 | #3832 | — | 3 | 4 | no | — |
| 81 | #3832 | — | 3 | 4 | no | — |
| 82 | C2×C4⋊(C3⋊D3) | — | 3 | 3 | no | — |
| 83 | C2×C4×C3⋊D3 | — | 3 | 3 | no | — |
| 84 | C3×#239 | — | 3 | 4 | no | — |
| 85 | C3×#239 | C2×D3 | 1 | 4 | yes | — |
| 86 | C3×D3×Q8 | — | 3 | 4 | no | — |
| 87 | C3×D3×Q8 | C2×D3 | 1 | 4 | yes | — |
| 88 | C3×#235 | — | 3 | 6 | no | — |
| 89 | C3×#235 | C2×D3 | 1 | 6 | yes | — |
| 90 | #3811 | — | 3 | 12 | no | — |
| 91 | #3805 | — | 3 | 4 | no | — |
| 92 | #3802 | — | 3 | 6 | no | — |
| 93 | D3×D12 | — | 3 | 12 | no | — |
| 94 | D3×D12 | — | 3 | 12 | no | — |
| 95 | C4×D32 | — | 3 | 12 | no | — |
| 96 | #3799 | — | 3 | 12 | no | — |
| 97 | #3799 | — | 3 | 12 | no | — |
| 98 | #3798 | — | 3 | 12 | no | — |
| 99 | #3797 | — | 3 | 6 | no | — |
| 100 | #3796 | — | 3 | 6 | no | — |
| 101 | #3796 | — | 3 | 6 | no | — |
| 102 | C9×#41 | — | 3 | 4 | no | — |
| 103 | C9×#41 | — | 3 | 6 | no | — |
| 104 | C2×Q8×C9 | — | 2 | 1 | no | — |
| 105 | C2×Q8×C9 | — | 3 | 4 | no | — |
| 106 | C2×Q8×C9 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 107 | #3701 | — | 3 | 4 | no | — |
| 108 | #3701 | — | 3 | 4 | no | — |
| 109 | #3701 | — | 3 | 6 | no | — |
| 110 | #3701 | — | 3 | 12 | no | — |
| 111 | #3701 | — | 6 | 4 | no | — |
| 112 | #3701 | — | 6 | 4 | no | — |
| 113 | #3701 | C2×D3 | 1 | 4 | yes | complemented |
| 114 | Q8×D9 | — | 3 | 6 | no | — |
| 115 | Q8×D9 | C2×D3 | 1 | 4 | yes | complemented |
| 116 | #3699 | — | 3 | 4 | no | — |
| 117 | #3699 | — | 3 | 6 | no | — |
| 118 | D4×D9 | — | 3 | 12 | no | — |
| 119 | D4×D9 | — | 3 | 6 | no | — |
| 120 | D4×D9 | — | 3 | 12 | no | — |
| 121 | #3697 | — | 3 | 12 | no | — |
| 122 | #3697 | — | 3 | 12 | no | — |
| 123 | #3697 | C2×D3 | 1 | 6 | yes | complemented |
| 124 | C2×D36 | — | 3 | 3 | no | — |
| 125 | C2×D36 | — | 3 | 12 | no | — |
| 126 | C2×D36 | — | 6 | 3 | no | — |
| 127 | C2×C4×D9 | — | 3 | 3 | no | — |
| 128 | C2×C4×D9 | — | 3 | 12 | no | — |
| 129 | C2×C4×D9 | — | 6 | 3 | no | — |
| 130 | C22×C3×C9 | C24 | 1 | 1 | yes | characteristic |
| 131 | C2×C3⋊D9 | — | 4 | 3 | no | — |
| 132 | C2×C3⋊D9 | C24 | 1 | 6 | yes | — |
| 133 | C2×D3×C9 | C24 | 1 | 4 | yes | — |
| 134 | C2×C3×D9 | C24 | 1 | 4 | yes | — |
| 135 | D3×D9 | — | 4 | 12 | no | — |
| 136 | C3×C4×C9 | C24 | 1 | 6 | yes | — |
| 137 | C3⋊Dic9 | C24 | 1 | 1 | yes | characteristic |
| 138 | C3⋊Dic9 | C24 | 1 | 1 | yes | characteristic |
| 139 | C9×Dic3 | C24 | 1 | 4 | yes | — |
| 140 | C3×Dic9 | C24 | 1 | 4 | yes | — |
| 141 | C3×2−1+4 | — | 3 | 1 | no | — |
| 142 | C3×2−1+4 | — | 9 | 1 | no | — |
| 143 | #1009 | — | 9 | 6 | no | — |
| 144 | #1009 | — | 9 | 4 | no | — |
| 145 | #1009 | — | 9 | 4 | no | — |
| 146 | #1009 | — | 9 | 6 | no | — |
| 147 | D3×#41 | — | 9 | 6 | no | — |
| 148 | D3×#41 | — | 9 | 4 | no | — |
| 149 | D3×#41 | — | 9 | 4 | no | — |
| 150 | D3×#41 | — | 9 | 6 | no | — |
| 151 | #1007 | — | 3 | 1 | no | — |
| 152 | #1007 | — | 9 | 4 | no | — |
| 153 | #1007 | — | 9 | 4 | no | — |
| 154 | #1007 | D9 | 1 | 1 | yes | characteristic, complemented |
| 155 | C2×#239 | — | 9 | 4 | no | — |
| 156 | C2×#239 | — | 9 | 1 | no | — |
| 157 | C2×#239 | — | 9 | 1 | no | — |
| 158 | C2×#239 | — | 9 | 4 | no | — |
| 159 | C2×#239 | — | 18 | 1 | no | — |
| 160 | C22×C3⋊D3 | — | 3 | 3 | no | — |
| 161 | C2×D32 | — | 3 | 12 | no | — |
| 162 | C32×Q8 | C22×D3 | 1 | 4 | yes | — |
| 163 | C2×C32×C4 | C22×D3 | 1 | 3 | yes | — |
| 164 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 165 | C4⋊(C3⋊D3) | — | 3 | 12 | no | — |
| 166 | C4×C3⋊D3 | — | 3 | 6 | no | — |
| 167 | C4×C3⋊D3 | — | 3 | 6 | no | — |
| 168 | C3×#67 | — | 3 | 4 | no | — |
| 169 | C3×#67 | C22×D3 | 1 | 4 | yes | — |
| 170 | C3×D12 | — | 3 | 6 | no | — |
| 171 | C3×D12 | C22×D3 | 1 | 6 | yes | — |
| 172 | C3×C4×D3 | — | 3 | 12 | no | — |
| 173 | C3×C4×D3 | C22×D3 | 1 | 12 | yes | — |
| 174 | C3×Dic6 | — | 3 | 6 | no | — |
| 175 | C3×Dic6 | C22×D3 | 1 | 6 | yes | — |
| 176 | #627 | — | 3 | 4 | no | — |
| 177 | #626 | — | 3 | 12 | no | — |
| 178 | #626 | — | 3 | 12 | no | — |
| 179 | #625 | — | 3 | 4 | no | — |
| 180 | #624 | — | 3 | 12 | no | — |
| 181 | D3×Dic3 | — | 3 | 4 | no | — |
| 182 | D3×Dic3 | — | 3 | 4 | no | — |
| 183 | C22×D9 | — | 3 | 3 | no | — |
| 184 | C22×D9 | — | 3 | 12 | no | — |
| 185 | C22×D9 | — | 6 | 3 | no | — |
| 186 | Q8×C9 | — | 2 | 4 | no | — |
| 187 | Q8×C9 | — | 3 | 6 | no | — |
| 188 | Q8×C9 | C22×D3 | 1 | 4 | yes | — |
| 189 | D4×C9 | — | 3 | 4 | no | — |
| 190 | D4×C9 | — | 3 | 6 | no | — |
| 191 | C2×C4×C9 | — | 2 | 3 | no | — |
| 192 | C2×C4×C9 | — | 3 | 12 | no | — |
| 193 | C2×C4×C9 | C22×D3 | 1 | 3 | yes | — |
| 194 | #611 | — | 3 | 4 | no | — |
| 195 | #611 | — | 3 | 12 | no | — |
| 196 | #611 | C22×D3 | 1 | 4 | yes | — |
| 197 | C2×Dic9 | — | 3 | 1 | no | — |
| 198 | C2×Dic9 | — | 3 | 4 | no | — |
| 199 | C2×Dic9 | — | 6 | 1 | no | — |
| 200 | D36 | — | 3 | 12 | no | — |
| 201 | D36 | — | 3 | 12 | no | — |
| 202 | D36 | — | 6 | 12 | no | — |
| 203 | D36 | C22×D3 | 1 | 6 | yes | — |
| 204 | C4×D9 | — | 3 | 4 | no | — |
| 205 | C4×D9 | — | 3 | 6 | no | — |
| 206 | C4×D9 | — | 3 | 6 | no | — |
| 207 | C4×D9 | — | 3 | 12 | no | — |
| 208 | C4×D9 | — | 6 | 6 | no | — |
| 209 | C4×D9 | — | 6 | 6 | no | — |
| 210 | C4×D9 | C22×D3 | 1 | 12 | yes | — |
| 211 | Dic18 | — | 3 | 4 | no | — |
| 212 | Dic18 | C22×D3 | 1 | 6 | yes | — |
| 213 | #585 | — | 27 | 1 | no | Sylow |
| 214 | C2×C3×C9 | — | 2 | 1 | no | — |
| 215 | C2×C3×C9 | C25 | 1 | 1 | yes | characteristic |
| 216 | C3⋊D9 | — | 2 | 6 | no | — |
| 217 | D3×C9 | — | 2 | 4 | no | — |
| 218 | C3×D9 | — | 2 | 4 | no | — |
| 219 | C3×#41 | — | 3 | 4 | no | — |
| 220 | C3×#41 | — | 3 | 6 | no | — |
| 221 | C3×#41 | — | 9 | 4 | no | — |
| 222 | C3×#41 | — | 9 | 6 | no | — |
| 223 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 224 | C2×C3×Q8 | — | 3 | 4 | no | — |
| 225 | C2×C3×Q8 | — | 9 | 4 | no | — |
| 226 | C2×C3×Q8 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 227 | C2×C3×Q8 | D32 | 1 | 1 | yes | characteristic |
| 228 | #239 | — | 3 | 4 | no | — |
| 229 | #239 | — | 9 | 12 | no | — |
| 230 | #239 | — | 9 | 6 | no | — |
| 231 | #239 | — | 9 | 4 | no | — |
| 232 | #239 | — | 9 | 4 | no | — |
| 233 | #239 | — | 9 | 4 | no | — |
| 234 | #239 | — | 9 | 4 | no | — |
| 235 | #239 | — | 9 | 6 | no | — |
| 236 | #239 | — | 9 | 12 | no | — |
| 237 | #239 | — | 18 | 4 | no | — |
| 238 | #239 | — | 18 | 4 | no | — |
| 239 | #239 | C2×D9 | 1 | 4 | yes | complemented |
| 240 | D3×Q8 | — | 3 | 4 | no | — |
| 241 | D3×Q8 | — | 9 | 6 | no | — |
| 242 | D3×Q8 | — | 9 | 6 | no | — |
| 243 | D3×Q8 | C2×D9 | 1 | 4 | yes | complemented |
| 244 | #237 | — | 9 | 6 | no | — |
| 245 | #237 | — | 9 | 4 | no | — |
| 246 | #237 | — | 9 | 4 | no | — |
| 247 | #237 | — | 9 | 6 | no | — |
| 248 | D3×D4 | — | 9 | 12 | no | — |
| 249 | D3×D4 | — | 9 | 6 | no | — |
| 250 | D3×D4 | — | 9 | 12 | no | — |
| 251 | D3×D4 | — | 9 | 12 | no | — |
| 252 | D3×D4 | — | 9 | 6 | no | — |
| 253 | D3×D4 | — | 9 | 12 | no | — |
| 254 | #235 | — | 3 | 6 | no | — |
| 255 | #235 | — | 9 | 12 | no | — |
| 256 | #235 | — | 9 | 12 | no | — |
| 257 | #235 | — | 9 | 12 | no | — |
| 258 | #235 | — | 9 | 12 | no | — |
| 259 | #235 | C2×D9 | 1 | 6 | yes | complemented |
| 260 | C2×D12 | — | 9 | 12 | no | — |
| 261 | C2×D12 | — | 9 | 3 | no | — |
| 262 | C2×D12 | — | 9 | 3 | no | — |
| 263 | C2×D12 | — | 9 | 12 | no | — |
| 264 | C2×D12 | — | 18 | 3 | no | — |
| 265 | C2×C4×D3 | — | 9 | 12 | no | — |
| 266 | C2×C4×D3 | — | 9 | 3 | no | — |
| 267 | C2×C4×D3 | — | 9 | 3 | no | — |
| 268 | C2×C4×D3 | — | 9 | 12 | no | — |
| 269 | C2×C4×D3 | — | 18 | 3 | no | — |
| 270 | C22×C32 | C23×D3 | 1 | 1 | yes | characteristic |
| 271 | C2×C3⋊D3 | — | 3 | 6 | no | — |
| 272 | C2×C3⋊D3 | — | 12 | 3 | no | — |
| 273 | C2×C3×D3 | — | 3 | 4 | no | — |
| 274 | C2×C3×D3 | C23×D3 | 1 | 4 | yes | — |
| 275 | D32 | — | 12 | 12 | no | — |
| 276 | C32×C4 | C23×D3 | 1 | 6 | yes | — |
| 277 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 278 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 279 | C3×Dic3 | — | 3 | 4 | no | — |
| 280 | C3×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 281 | C22×C9 | — | 2 | 1 | no | — |
| 282 | C22×C9 | — | 3 | 4 | no | — |
| 283 | C22×C9 | C23×D3 | 1 | 1 | yes | characteristic |
| 284 | C2×D9 | — | 3 | 6 | no | — |
| 285 | C2×D9 | — | 6 | 6 | no | — |
| 286 | C2×D9 | — | 12 | 12 | no | — |
| 287 | C2×D9 | — | 12 | 3 | no | — |
| 288 | C2×D9 | — | 12 | 6 | no | — |
| 289 | C2×D9 | C23×D3 | 1 | 4 | yes | — |
| 290 | C4×C9 | — | 2 | 6 | no | — |
| 291 | C4×C9 | — | 3 | 4 | no | — |
| 292 | C4×C9 | C23×D3 | 1 | 6 | yes | — |
| 293 | Dic9 | — | 3 | 1 | no | — |
| 294 | Dic9 | — | 3 | 1 | no | — |
| 295 | Dic9 | — | 6 | 1 | no | — |
| 296 | Dic9 | — | 6 | 1 | no | — |
| 297 | Dic9 | C23×D3 | 1 | 4 | yes | — |
| 298 | 2−1+4 | — | 3 | 1 | no | — |
| 299 | 2−1+4 | — | 9 | 1 | no | — |
| 300 | 2−1+4 | — | 27 | 4 | no | — |
| 301 | H(5,𝔽2) | — | 27 | 4 | no | — |
| 302 | H(5,𝔽2) | — | 27 | 6 | no | — |
| 303 | C2×#41 | — | 27 | 4 | no | — |
| 304 | C2×#41 | — | 27 | 4 | no | — |
| 305 | C2×#41 | — | 27 | 6 | no | — |
| 306 | C2×#41 | — | 27 | 1 | no | — |
| 307 | C3×C9 | #585 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 308 | C22×D3 | — | 9 | 12 | no | — |
| 309 | C22×D3 | — | 9 | 3 | no | — |
| 310 | C22×D3 | — | 9 | 3 | no | — |
| 311 | C22×D3 | — | 9 | 12 | no | — |
| 312 | C22×D3 | — | 18 | 3 | no | — |
| 313 | C3×Q8 | — | 2 | 4 | no | — |
| 314 | C3×Q8 | — | 3 | 6 | no | — |
| 315 | C3×Q8 | — | 9 | 6 | no | — |
| 316 | C3×Q8 | C22×D9 | 1 | 4 | yes | — |
| 317 | C3×Q8 | C2×D32 | 1 | 4 | yes | — |
| 318 | C3×D4 | — | 3 | 4 | no | — |
| 319 | C3×D4 | — | 3 | 6 | no | — |
| 320 | C3×D4 | — | 9 | 4 | no | — |
| 321 | C3×D4 | — | 9 | 6 | no | — |
| 322 | C2×C3×C4 | — | 2 | 3 | no | — |
| 323 | C2×C3×C4 | — | 3 | 12 | no | — |
| 324 | C2×C3×C4 | — | 9 | 12 | no | — |
| 325 | C2×C3×C4 | C22×D9 | 1 | 3 | yes | — |
| 326 | C2×C3×C4 | C2×D32 | 1 | 3 | yes | — |
| 327 | #67 | — | 3 | 4 | no | — |
| 328 | #67 | — | 9 | 12 | no | — |
| 329 | #67 | — | 9 | 4 | no | — |
| 330 | #67 | — | 9 | 4 | no | — |
| 331 | #67 | — | 9 | 12 | no | — |
| 332 | #67 | C22×D9 | 1 | 4 | yes | — |
| 333 | C2×Dic3 | — | 9 | 4 | no | — |
| 334 | C2×Dic3 | — | 9 | 1 | no | — |
| 335 | C2×Dic3 | — | 9 | 1 | no | — |
| 336 | C2×Dic3 | — | 9 | 4 | no | — |
| 337 | C2×Dic3 | — | 18 | 1 | no | — |
| 338 | D12 | — | 3 | 6 | no | — |
| 339 | D12 | — | 9 | 12 | no | — |
| 340 | D12 | — | 9 | 12 | no | — |
| 341 | D12 | — | 9 | 12 | no | — |
| 342 | D12 | — | 9 | 12 | no | — |
| 343 | D12 | — | 18 | 12 | no | — |
| 344 | D12 | C22×D9 | 1 | 6 | yes | — |
| 345 | C4×D3 | — | 3 | 12 | no | — |
| 346 | C4×D3 | — | 9 | 12 | no | — |
| 347 | C4×D3 | — | 9 | 4 | no | — |
| 348 | C4×D3 | — | 9 | 4 | no | — |
| 349 | C4×D3 | — | 9 | 6 | no | — |
| 350 | C4×D3 | — | 9 | 6 | no | — |
| 351 | C4×D3 | — | 9 | 6 | no | — |
| 352 | C4×D3 | — | 9 | 6 | no | — |
| 353 | C4×D3 | — | 9 | 12 | no | — |
| 354 | C4×D3 | — | 18 | 6 | no | — |
| 355 | C4×D3 | — | 18 | 6 | no | — |
| 356 | C4×D3 | C22×D9 | 1 | 12 | yes | — |
| 357 | Dic6 | — | 3 | 6 | no | — |
| 358 | Dic6 | — | 9 | 4 | no | — |
| 359 | Dic6 | — | 9 | 4 | no | — |
| 360 | Dic6 | C22×D9 | 1 | 6 | yes | — |
| 361 | C2×C32 | — | 2 | 1 | no | — |
| 362 | C2×C32 | C24×D3 | 1 | 1 | yes | characteristic |
| 363 | C3⋊D3 | — | 6 | 6 | no | — |
| 364 | C3×D3 | — | 2 | 4 | no | — |
| 365 | C3×D3 | — | 6 | 4 | no | — |
| 366 | C2×C9 | — | 2 | 2 | no | — |
| 367 | C2×C9 | — | 2 | 1 | no | — |
| 368 | C2×C9 | — | 2 | 1 | no | — |
| 369 | C2×C9 | — | 6 | 4 | no | — |
| 370 | C2×C9 | C24×D3 | 1 | 1 | yes | characteristic |
| 371 | D9 | — | 2 | 4 | no | — |
| 372 | D9 | — | 6 | 6 | no | — |
| 373 | D9 | — | 12 | 6 | no | — |
| 374 | #41 | — | 3 | 4 | no | — |
| 375 | #41 | — | 3 | 6 | no | — |
| 376 | #41 | — | 9 | 4 | no | — |
| 377 | #41 | — | 9 | 6 | no | — |
| 378 | #41 | — | 27 | 12 | no | — |
| 379 | #41 | — | 27 | 12 | no | — |
| 380 | #41 | — | 27 | 12 | no | — |
| 381 | #41 | — | 27 | 4 | no | — |
| 382 | #41 | — | 27 | 6 | no | — |
| 383 | #41 | — | 27 | 6 | no | — |
| 384 | #41 | — | 27 | 4 | no | — |
| 385 | #41 | — | 27 | 4 | no | — |
| 386 | C2×Q8 | — | 3 | 4 | no | — |
| 387 | C2×Q8 | — | 9 | 4 | no | — |
| 388 | C2×Q8 | — | 27 | 6 | no | — |
| 389 | C2×Q8 | D3×D9 | 1 | 1 | yes | characteristic, complemented |
| 390 | C2×D4 | — | 27 | 12 | no | — |
| 391 | C2×D4 | — | 27 | 12 | no | — |
| 392 | C2×D4 | — | 27 | 12 | no | — |
| 393 | C2×D4 | — | 27 | 6 | no | — |
| 394 | C2×D4 | — | 27 | 3 | no | — |
| 395 | C22×C4 | — | 27 | 12 | no | — |
| 396 | C22×C4 | — | 27 | 3 | no | — |
| 397 | C22×C3 | — | 2 | 1 | no | — |
| 398 | C22×C3 | — | 3 | 4 | no | — |
| 399 | C22×C3 | — | 9 | 4 | no | — |
| 400 | C22×C3 | C23×D9 | 1 | 1 | yes | characteristic |
| 401 | C22×C3 | C22×D32 | 1 | 1 | yes | characteristic |
| 402 | C2×D3 | — | 3 | 4 | no | — |
| 403 | C2×D3 | — | 9 | 6 | no | — |
| 404 | C2×D3 | — | 9 | 6 | no | — |
| 405 | C2×D3 | — | 18 | 6 | no | — |
| 406 | C2×D3 | — | 36 | 12 | no | — |
| 407 | C2×D3 | — | 36 | 12 | no | — |
| 408 | C2×D3 | — | 36 | 3 | no | — |
| 409 | C2×D3 | — | 36 | 3 | no | — |
| 410 | C2×D3 | — | 36 | 6 | no | — |
| 411 | C2×D3 | C23×D9 | 1 | 4 | yes | — |
| 412 | C3×C4 | — | 2 | 6 | no | — |
| 413 | C3×C4 | — | 3 | 4 | no | — |
| 414 | C3×C4 | — | 9 | 4 | no | — |
| 415 | C3×C4 | C23×D9 | 1 | 6 | yes | — |
| 416 | C3×C4 | C22×D32 | 1 | 6 | yes | — |
| 417 | Dic3 | — | 3 | 4 | no | — |
| 418 | Dic3 | — | 9 | 1 | no | — |
| 419 | Dic3 | — | 9 | 1 | no | — |
| 420 | Dic3 | — | 9 | 1 | no | — |
| 421 | Dic3 | — | 9 | 1 | no | — |
| 422 | Dic3 | — | 18 | 1 | no | — |
| 423 | Dic3 | — | 18 | 1 | no | — |
| 424 | Dic3 | C23×D9 | 1 | 4 | yes | — |
| 425 | C32 | #5968 | 1 | 1 | yes | characteristic |
| 426 | C9 | — | 2 | 1 | no | — |
| 427 | C9 | #5968 | 1 | 1 | yes | characteristic, complemented |
| 428 | C23 | — | 27 | 12 | no | — |
| 429 | C23 | — | 27 | 3 | no | — |
| 430 | Q8 | — | 3 | 6 | no | — |
| 431 | Q8 | — | 9 | 6 | no | — |
| 432 | Q8 | — | 27 | 4 | no | — |
| 433 | Q8 | C2×D3×D9 | 1 | 4 | yes | — |
| 434 | D4 | — | 3 | 4 | no | — |
| 435 | D4 | — | 3 | 6 | no | — |
| 436 | D4 | — | 9 | 4 | no | — |
| 437 | D4 | — | 9 | 6 | no | — |
| 438 | D4 | — | 27 | 12 | no | — |
| 439 | D4 | — | 27 | 12 | no | — |
| 440 | D4 | — | 27 | 4 | no | — |
| 441 | D4 | — | 27 | 12 | no | — |
| 442 | C2×C4 | — | 3 | 12 | no | — |
| 443 | C2×C4 | — | 9 | 12 | no | — |
| 444 | C2×C4 | — | 27 | 12 | no | — |
| 445 | C2×C4 | — | 27 | 4 | no | — |
| 446 | C2×C4 | — | 27 | 4 | no | — |
| 447 | C2×C4 | — | 27 | 1 | no | — |
| 448 | C2×C4 | — | 27 | 6 | no | — |
| 449 | C2×C4 | — | 27 | 6 | no | — |
| 450 | C2×C4 | C2×D3×D9 | 1 | 3 | yes | — |
| 451 | C2×C3 | — | 2 | 2 | no | — |
| 452 | C2×C3 | — | 2 | 1 | no | — |
| 453 | C2×C3 | — | 2 | 1 | no | — |
| 454 | C2×C3 | — | 2 | 1 | no | — |
| 455 | C2×C3 | — | 6 | 4 | no | — |
| 456 | C2×C3 | — | 18 | 4 | no | — |
| 457 | C2×C3 | C24×D9 | 1 | 1 | yes | characteristic |
| 458 | C2×C3 | C23×D32 | 1 | 1 | yes | characteristic |
| 459 | D3 | — | 2 | 4 | no | — |
| 460 | D3 | — | 6 | 4 | no | — |
| 461 | D3 | — | 18 | 6 | no | — |
| 462 | D3 | — | 18 | 6 | no | — |
| 463 | D3 | — | 36 | 6 | no | — |
| 464 | C22 | — | 3 | 4 | no | — |
| 465 | C22 | — | 9 | 4 | no | — |
| 466 | C22 | — | 27 | 6 | no | — |
| 467 | C22 | — | 108 | 3 | no | — |
| 468 | C22 | — | 108 | 12 | no | — |
| 469 | C22 | C22×D3×D9 | 1 | 1 | yes | characteristic |
| 470 | C4 | — | 3 | 4 | no | — |
| 471 | C4 | — | 9 | 4 | no | — |
| 472 | C4 | — | 27 | 1 | no | — |
| 473 | C4 | — | 27 | 1 | no | — |
| 474 | C4 | C22×D3×D9 | 1 | 6 | yes | — |
| 475 | C3 | — | 2 | 1 | no | — |
| 476 | C3 | #10593143 | 1 | 1 | yes | characteristic, complemented |
| 477 | C3 | #10596689 | 1 | 1 | yes | characteristic |
| 478 | C2 | — | 2 | 1 | no | — |
| 479 | C2 | — | 6 | 4 | no | — |
| 480 | C2 | — | 18 | 4 | no | — |
| 481 | C2 | — | 54 | 6 | no | — |
| 482 | C2 | C23×D3×D9 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×D3×D9 |
| commutator, cosocle | C2×C3×C9 | C25 |
| Frattini | C2×C3 | C23×D32 |
| Fitting | C2×C3×Q8×C9 | C22 |
| socle | C2×C32 | C24×D3 |
| hypercenter | C2×Q8 | D3×D9 |
| hypocenter | C3×C9 | #585 |
| LCS | G ▷ C2×C3×C9 ▷ C3×C9 | |
| UCS | C1 ◁ C2 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#88746 | C2 | semidirect |
| 2. C9×#1007 | C2 | semidirect |
| 3. C3×#63713 | C2 | semidirect |
| 4. #11722515 | C2 | semidirect |
| 5. D9×#239 | C2 | semidirect |
| 6. D3×#3701 | C2 | semidirect |
| 7. #11722509 | C2 | semidirect |
| 8. #11722478 | C2 | semidirect |
| 9. #11722475 | C2 | semidirect |
| 12. C2×C3×Q8×C9 | C22 | semidirect |
| 13. #88746 | C22 | semidirect |
| 14. #88746 | C22 | semidirect |
| 15. C2×C4⋊(C3⋊D9) | C22 | semidirect |
| 16. C2×C4×C3⋊D9 | C22 | semidirect |
| 17. C9×#239 | C22 | semidirect |
| 18. D3×Q8×C9 | C22 | semidirect |
| 19. C3×#3701 | C22 | semidirect |
| 20. C3×Q8×D9 | C22 | semidirect |
| 21. C9×#235 | C22 | semidirect |
| 22. C3×#3697 | C22 | semidirect |
| 23. #88668 | C22 | semidirect |
| 24. #88663 | C22 | semidirect |
| 25. #88646 | C22 | semidirect |
| 26. D9×D12 | C22 | semidirect |
| 27. D3×D36 | C22 | semidirect |
| 28. C4×D3×D9 | C22 | semidirect |
| 29. #88642 | C22 | semidirect |
| 30. #88640 | C22 | semidirect |
| 31. #88639 | C22 | semidirect |
| 32. (C3⋊D9)⋊Q8 | C22 | semidirect |
| 33. #88635 | C22 | semidirect |
| 34. #88634 | C22 | semidirect |
| 50. #63713 | D3 | semidirect |
| 106. C2×Q8×C9 | C2×D3 | semidirect |
| 113. #3701 | C2×D3 | semidirect |
| 115. Q8×D9 | C2×D3 | semidirect |
| 123. #3697 | C2×D3 | semidirect |
| 154. #1007 | D9 | semidirect |
| 226. C2×C3×Q8 | C2×D9 | semidirect |
| 239. #239 | C2×D9 | semidirect |
| 243. D3×Q8 | C2×D9 | semidirect |
| 259. #235 | C2×D9 | semidirect |
| 307. C3×C9 | #585 | semidirect |
| 389. C2×Q8 | D3×D9 | semidirect |
| 427. C9 | #5968 | semidirect |
| 476. C3 | #10593143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88746 | 2 |
| C9×#1007 | 2 |
| C3×#63713 | 2 |
| #11722515 | 2 |
| D9×#239 | 2 |
| D3×#3701 | 2 |
| #11722509 | 2 |
| #11722478 | 2 |
| #11722475 | 2 |
| #10596689 | 3 |
| #10593143 | 3 |