Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2112 conjugacy classes of subgroups.
The subgroup lattice has 492 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D9×2−1+4 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C9×#578 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10589940 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10589881 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | D9×#137 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #10589873 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | D9×#135 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #10589868 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | C2×Q16×D9 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #10589855 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | D9×#131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | D3×#578 | — | 3 | 1 | no | maximal |
| 13 | C9×2−1+4 | C22 | 1 | 2 | yes | complemented |
| 14 | #63716 | — | 2 | 6 | no | — |
| 15 | #63716 | C22 | 1 | 6 | yes | complemented |
| 16 | #63716 | C22 | 1 | 2 | yes | complemented |
| 17 | #41×D9 | — | 2 | 6 | no | — |
| 18 | #41×D9 | C22 | 1 | 6 | yes | — |
| 19 | #41×D9 | C22 | 1 | 1 | yes | characteristic |
| 20 | #63713 | — | 2 | 2 | no | — |
| 21 | #63713 | C22 | 1 | 6 | yes | complemented |
| 22 | C2×Q8×D9 | — | 2 | 2 | no | — |
| 23 | C2×Q8×D9 | C22 | 1 | 6 | yes | — |
| 24 | C9×#137 | C22 | 1 | 6 | yes | complemented |
| 25 | C9×#135 | C22 | 1 | 3 | yes | complemented |
| 26 | C2×C9×Q16 | C22 | 1 | 3 | yes | complemented |
| 27 | C9×#131 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #63513 | C22 | 1 | 6 | yes | complemented |
| 29 | #63511 | C22 | 1 | 6 | yes | complemented |
| 30 | #63510 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #63505 | C22 | 1 | 6 | yes | complemented |
| 32 | C2×#3674 | C22 | 1 | 6 | yes | complemented |
| 33 | #63481 | C22 | 1 | 3 | yes | complemented |
| 34 | #63480 | C22 | 1 | 12 | yes | complemented |
| 35 | Q16×D9 | C22 | 1 | 3 | yes | — |
| 36 | Q16×D9 | C22 | 1 | 6 | yes | — |
| 37 | Q16×D9 | C22 | 1 | 6 | yes | complemented |
| 38 | Q16×D9 | C22 | 1 | 6 | yes | complemented |
| 39 | #63478 | C22 | 1 | 6 | yes | complemented |
| 40 | #63477 | C22 | 1 | 12 | yes | complemented |
| 41 | SD16×D9 | C22 | 1 | 6 | yes | — |
| 42 | #63474 | C22 | 1 | 3 | yes | complemented |
| 43 | D8×D9 | C22 | 1 | 1 | yes | characteristic |
| 44 | #63471 | C22 | 1 | 6 | yes | complemented |
| 45 | #63469 | C22 | 1 | 3 | yes | complemented |
| 46 | M16×D9 | C22 | 1 | 3 | yes | — |
| 47 | #63467 | C22 | 1 | 3 | yes | complemented |
| 48 | #63464 | C22 | 1 | 3 | yes | complemented |
| 49 | C2×C8×D9 | C22 | 1 | 3 | yes | — |
| 50 | C2×Dic36 | C22 | 1 | 3 | yes | complemented |
| 51 | D3×2−1+4 | — | 3 | 2 | no | — |
| 52 | C3×#578 | D3 | 1 | 1 | yes | characteristic |
| 53 | #5838 | — | 3 | 2 | no | — |
| 54 | #5779 | — | 3 | 6 | no | — |
| 55 | D3×#137 | — | 3 | 6 | no | — |
| 56 | #5771 | — | 3 | 3 | no | — |
| 57 | D3×#135 | — | 3 | 3 | no | — |
| 58 | #5766 | — | 3 | 3 | no | — |
| 59 | C2×D3×Q16 | — | 3 | 3 | no | — |
| 60 | #5753 | — | 3 | 1 | no | — |
| 61 | D3×#131 | — | 3 | 1 | no | — |
| 62 | C9×#41 | — | 2 | 6 | no | — |
| 63 | C9×#41 | C23 | 1 | 6 | yes | — |
| 64 | C9×#41 | C23 | 1 | 1 | yes | characteristic |
| 65 | C2×Q8×C9 | — | 2 | 2 | no | — |
| 66 | C2×Q8×C9 | C23 | 1 | 6 | yes | — |
| 67 | #3701 | — | 2 | 6 | no | — |
| 68 | #3701 | D4 | 1 | 1 | yes | characteristic |
| 69 | #3701 | C23 | 1 | 6 | yes | — |
| 70 | Q8×D9 | — | 2 | 2 | no | — |
| 71 | Q8×D9 | — | 2 | 6 | no | — |
| 72 | Q8×D9 | — | 2 | 6 | no | — |
| 73 | Q8×D9 | — | 2 | 6 | no | — |
| 74 | Q8×D9 | D4 | 1 | 1 | yes | characteristic |
| 75 | Q8×D9 | C23 | 1 | 6 | yes | — |
| 76 | Q8×D9 | C23 | 1 | 12 | yes | — |
| 77 | #3699 | — | 2 | 6 | no | — |
| 78 | #3699 | — | 2 | 12 | no | — |
| 79 | #3699 | — | 2 | 6 | no | — |
| 80 | #3699 | D4 | 1 | 3 | yes | — |
| 81 | #3699 | C23 | 1 | 6 | yes | — |
| 82 | D4×D9 | — | 2 | 6 | no | — |
| 83 | D4×D9 | D4 | 1 | 3 | yes | — |
| 84 | D4×D9 | C23 | 1 | 2 | yes | — |
| 85 | #3697 | — | 2 | 12 | no | — |
| 86 | #3697 | — | 2 | 6 | no | — |
| 87 | #3697 | — | 2 | 6 | no | — |
| 88 | #3697 | C23 | 1 | 3 | yes | — |
| 89 | #3697 | C23 | 1 | 6 | yes | — |
| 90 | C2×C4×D9 | — | 2 | 6 | no | — |
| 91 | C2×C4×D9 | — | 2 | 6 | no | — |
| 92 | C2×C4×D9 | C23 | 1 | 3 | yes | — |
| 93 | C2×Dic18 | — | 2 | 6 | no | — |
| 94 | C2×Dic18 | — | 2 | 6 | no | — |
| 95 | C2×Dic18 | C23 | 1 | 6 | yes | — |
| 96 | C9×Q16 | C23 | 1 | 3 | yes | — |
| 97 | C9×Q16 | C23 | 1 | 6 | yes | — |
| 98 | C9×SD16 | C23 | 1 | 6 | yes | — |
| 99 | C9×D8 | C23 | 1 | 1 | yes | characteristic |
| 100 | C9×M16 | C23 | 1 | 3 | yes | — |
| 101 | C2×C8×C9 | C23 | 1 | 3 | yes | — |
| 102 | #3675 | C23 | 1 | 6 | yes | — |
| 103 | #3674 | C23 | 1 | 6 | yes | — |
| 104 | #3674 | C23 | 1 | 12 | yes | — |
| 105 | #3673 | C23 | 1 | 2 | yes | — |
| 106 | #3672 | C23 | 1 | 6 | yes | — |
| 107 | #3667 | C23 | 1 | 3 | yes | — |
| 108 | C2×C9⋊C8 | C23 | 1 | 3 | yes | — |
| 109 | D72 | C23 | 1 | 1 | yes | characteristic |
| 110 | #3664 | C23 | 1 | 6 | yes | — |
| 111 | #3663 | C23 | 1 | 6 | yes | — |
| 112 | C8×D9 | C23 | 1 | 1 | yes | characteristic |
| 113 | C8×D9 | C23 | 1 | 3 | yes | — |
| 114 | C8×D9 | C23 | 1 | 3 | yes | — |
| 115 | C8×D9 | C23 | 1 | 3 | yes | — |
| 116 | Dic36 | C23 | 1 | 3 | yes | — |
| 117 | Dic36 | C23 | 1 | 6 | yes | — |
| 118 | C2×#578 | — | 9 | 1 | no | Sylow |
| 119 | C3×2−1+4 | C2×D3 | 1 | 2 | yes | — |
| 120 | #1010 | — | 3 | 2 | no | — |
| 121 | #1010 | — | 3 | 6 | no | — |
| 122 | #1010 | — | 6 | 6 | no | — |
| 123 | D3×#41 | — | 3 | 1 | no | — |
| 124 | D3×#41 | — | 3 | 6 | no | — |
| 125 | D3×#41 | — | 6 | 6 | no | — |
| 126 | #1007 | — | 3 | 6 | no | — |
| 127 | #1007 | — | 6 | 2 | no | — |
| 128 | C2×D3×Q8 | — | 3 | 6 | no | — |
| 129 | C2×D3×Q8 | — | 6 | 2 | no | — |
| 130 | C3×#137 | C2×D3 | 1 | 6 | yes | — |
| 131 | C3×#135 | C2×D3 | 1 | 3 | yes | — |
| 132 | C2×C3×Q16 | C2×D3 | 1 | 3 | yes | — |
| 133 | C3×#131 | C2×D3 | 1 | 1 | yes | characteristic |
| 134 | #951 | — | 3 | 6 | no | — |
| 135 | #950 | — | 3 | 6 | no | — |
| 136 | #948 | — | 3 | 1 | no | — |
| 137 | C2×#216 | — | 3 | 6 | no | — |
| 138 | #942 | — | 3 | 6 | no | — |
| 139 | #919 | — | 3 | 3 | no | — |
| 140 | #918 | — | 3 | 12 | no | — |
| 141 | D3×Q16 | — | 3 | 3 | no | — |
| 142 | D3×Q16 | — | 3 | 6 | no | — |
| 143 | D3×Q16 | — | 3 | 6 | no | — |
| 144 | D3×Q16 | — | 3 | 6 | no | — |
| 145 | #916 | — | 3 | 6 | no | — |
| 146 | #915 | — | 3 | 12 | no | — |
| 147 | D3×SD16 | — | 3 | 6 | no | — |
| 148 | #912 | — | 3 | 3 | no | — |
| 149 | D3×D8 | — | 3 | 1 | no | — |
| 150 | #909 | — | 3 | 6 | no | — |
| 151 | #907 | — | 3 | 3 | no | — |
| 152 | D3×M16 | — | 3 | 3 | no | — |
| 153 | C2×Dic12 | — | 3 | 3 | no | — |
| 154 | #904 | — | 3 | 3 | no | — |
| 155 | #901 | — | 3 | 3 | no | — |
| 156 | C2×D3×C8 | — | 3 | 3 | no | — |
| 157 | C22×D9 | — | 2 | 2 | no | — |
| 158 | C22×D9 | C2×D4 | 1 | 3 | yes | — |
| 159 | Q8×C9 | — | 2 | 6 | no | — |
| 160 | Q8×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 161 | Q8×C9 | C24 | 1 | 6 | yes | — |
| 162 | D4×C9 | — | 2 | 6 | no | — |
| 163 | D4×C9 | C2×D4 | 1 | 3 | yes | — |
| 164 | D4×C9 | C24 | 1 | 2 | yes | — |
| 165 | C2×C4×C9 | — | 2 | 6 | no | — |
| 166 | C2×C4×C9 | — | 2 | 6 | no | — |
| 167 | C2×C4×C9 | C24 | 1 | 3 | yes | — |
| 168 | #611 | — | 2 | 6 | no | — |
| 169 | #611 | — | 2 | 6 | no | — |
| 170 | #611 | — | 2 | 2 | no | — |
| 171 | #611 | C2×D4 | 1 | 6 | yes | — |
| 172 | C2×Dic9 | — | 2 | 6 | no | — |
| 173 | C2×Dic9 | — | 2 | 6 | no | — |
| 174 | C2×Dic9 | C2×D4 | 1 | 3 | yes | — |
| 175 | D36 | — | 2 | 6 | no | — |
| 176 | D36 | C2×D4 | 1 | 3 | yes | — |
| 177 | D36 | C24 | 1 | 2 | yes | — |
| 178 | C4×D9 | — | 2 | 6 | no | — |
| 179 | C4×D9 | — | 2 | 12 | no | — |
| 180 | C4×D9 | — | 2 | 6 | no | — |
| 181 | C4×D9 | — | 2 | 6 | no | — |
| 182 | C4×D9 | C2×D4 | 1 | 3 | yes | — |
| 183 | C4×D9 | C2×D4 | 1 | 3 | yes | — |
| 184 | C4×D9 | C24 | 1 | 1 | yes | characteristic |
| 185 | C4×D9 | C24 | 1 | 3 | yes | — |
| 186 | Dic18 | — | 2 | 6 | no | — |
| 187 | Dic18 | — | 2 | 6 | no | — |
| 188 | Dic18 | — | 2 | 12 | no | — |
| 189 | Dic18 | C2×D4 | 1 | 3 | yes | — |
| 190 | Dic18 | C24 | 1 | 6 | yes | — |
| 191 | C8×C9 | C24 | 1 | 1 | yes | characteristic |
| 192 | C8×C9 | C24 | 1 | 3 | yes | — |
| 193 | C9⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 194 | C9⋊C8 | C24 | 1 | 3 | yes | — |
| 195 | C2×2−1+4 | — | 9 | 2 | no | — |
| 196 | #578 | — | 9 | 2 | no | — |
| 197 | #578 | — | 9 | 6 | no | — |
| 198 | #578 | — | 9 | 3 | no | — |
| 199 | #578 | — | 9 | 3 | no | — |
| 200 | #578 | — | 9 | 1 | no | — |
| 201 | #578 | D9 | 1 | 1 | yes | characteristic, direct product factor |
| 202 | C2×#137 | — | 9 | 6 | no | — |
| 203 | C2×#135 | — | 9 | 3 | no | — |
| 204 | C22×Q16 | — | 9 | 3 | no | — |
| 205 | C2×#131 | — | 9 | 1 | no | — |
| 206 | C3×#41 | — | 2 | 6 | no | — |
| 207 | C3×#41 | C22×D3 | 1 | 6 | yes | — |
| 208 | C3×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 209 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 210 | C2×C3×Q8 | C22×D3 | 1 | 6 | yes | — |
| 211 | #239 | — | 3 | 1 | no | — |
| 212 | #239 | — | 3 | 6 | no | — |
| 213 | #239 | — | 6 | 6 | no | — |
| 214 | D3×Q8 | — | 3 | 1 | no | — |
| 215 | D3×Q8 | — | 3 | 6 | no | — |
| 216 | D3×Q8 | — | 3 | 12 | no | — |
| 217 | D3×Q8 | — | 6 | 6 | no | — |
| 218 | D3×Q8 | — | 6 | 6 | no | — |
| 219 | D3×Q8 | — | 6 | 6 | no | — |
| 220 | D3×Q8 | — | 6 | 2 | no | — |
| 221 | #237 | — | 3 | 3 | no | — |
| 222 | #237 | — | 3 | 6 | no | — |
| 223 | #237 | — | 6 | 6 | no | — |
| 224 | #237 | — | 6 | 12 | no | — |
| 225 | #237 | — | 6 | 6 | no | — |
| 226 | D3×D4 | — | 3 | 3 | no | — |
| 227 | D3×D4 | — | 3 | 2 | no | — |
| 228 | D3×D4 | — | 6 | 6 | no | — |
| 229 | #235 | — | 3 | 3 | no | — |
| 230 | #235 | — | 3 | 6 | no | — |
| 231 | #235 | — | 6 | 6 | no | — |
| 232 | #235 | — | 6 | 6 | no | — |
| 233 | #235 | — | 6 | 12 | no | — |
| 234 | C2×C4×D3 | — | 3 | 3 | no | — |
| 235 | C2×C4×D3 | — | 6 | 6 | no | — |
| 236 | C2×C4×D3 | — | 6 | 6 | no | — |
| 237 | C2×Dic6 | — | 3 | 6 | no | — |
| 238 | C2×Dic6 | — | 6 | 6 | no | — |
| 239 | C2×Dic6 | — | 6 | 6 | no | — |
| 240 | C3×Q16 | C22×D3 | 1 | 3 | yes | — |
| 241 | C3×Q16 | C22×D3 | 1 | 6 | yes | — |
| 242 | C3×SD16 | C22×D3 | 1 | 6 | yes | — |
| 243 | C3×D8 | C22×D3 | 1 | 1 | yes | characteristic |
| 244 | C3×M16 | C22×D3 | 1 | 3 | yes | — |
| 245 | C2×C3×C8 | C22×D3 | 1 | 3 | yes | — |
| 246 | #216 | — | 3 | 12 | no | — |
| 247 | #216 | — | 3 | 6 | no | — |
| 248 | #215 | — | 3 | 6 | no | — |
| 249 | #214 | — | 3 | 6 | no | — |
| 250 | #213 | — | 3 | 2 | no | — |
| 251 | #208 | — | 3 | 3 | no | — |
| 252 | C2×C3⋊C8 | — | 3 | 3 | no | — |
| 253 | Dic12 | — | 3 | 3 | no | — |
| 254 | Dic12 | — | 3 | 6 | no | — |
| 255 | D24 | — | 3 | 1 | no | — |
| 256 | #204 | — | 3 | 6 | no | — |
| 257 | ΓL(1,𝔽25) | — | 3 | 6 | no | — |
| 258 | D3×C8 | — | 3 | 1 | no | — |
| 259 | D3×C8 | — | 3 | 3 | no | — |
| 260 | D3×C8 | — | 3 | 3 | no | — |
| 261 | D3×C8 | — | 3 | 3 | no | — |
| 262 | C22×C9 | — | 2 | 2 | no | — |
| 263 | C22×C9 | C22×D4 | 1 | 3 | yes | — |
| 264 | C2×D9 | — | 2 | 6 | no | — |
| 265 | C2×D9 | — | 2 | 2 | no | — |
| 266 | C2×D9 | — | 4 | 4 | no | — |
| 267 | C2×D9 | C22×D4 | 1 | 3 | yes | — |
| 268 | C2×D9 | C22×D4 | 1 | 1 | yes | characteristic |
| 269 | C4×C9 | — | 2 | 6 | no | — |
| 270 | C4×C9 | C22×D4 | 1 | 3 | yes | — |
| 271 | C4×C9 | C25 | 1 | 1 | yes | characteristic |
| 272 | Dic9 | — | 2 | 6 | no | — |
| 273 | Dic9 | C22×D4 | 1 | 1 | yes | characteristic |
| 274 | Dic9 | C22×D4 | 1 | 3 | yes | — |
| 275 | 2−1+4 | — | 9 | 6 | no | — |
| 276 | 2−1+4 | — | 9 | 2 | no | — |
| 277 | 2−1+4 | — | 9 | 6 | no | — |
| 278 | 2−1+4 | — | 18 | 2 | no | — |
| 279 | 2−1+4 | — | 18 | 6 | no | — |
| 280 | 2−1+4 | C2×D9 | 1 | 2 | yes | complemented |
| 281 | C2×#41 | — | 9 | 1 | no | — |
| 282 | C2×#41 | — | 9 | 6 | no | — |
| 283 | C2×#41 | — | 18 | 6 | no | — |
| 284 | C22×Q8 | — | 9 | 6 | no | — |
| 285 | C22×Q8 | — | 18 | 2 | no | — |
| 286 | #137 | — | 9 | 6 | no | — |
| 287 | #137 | — | 9 | 6 | no | — |
| 288 | #137 | — | 9 | 12 | no | — |
| 289 | #137 | — | 9 | 12 | no | — |
| 290 | #137 | — | 9 | 6 | no | — |
| 291 | #137 | C2×D9 | 1 | 6 | yes | complemented |
| 292 | #135 | — | 9 | 6 | no | — |
| 293 | #135 | — | 9 | 3 | no | — |
| 294 | #135 | — | 9 | 6 | no | — |
| 295 | #135 | — | 9 | 3 | no | — |
| 296 | #135 | — | 9 | 3 | no | — |
| 297 | #135 | C2×D9 | 1 | 3 | yes | complemented |
| 298 | C2×Q16 | — | 9 | 6 | no | — |
| 299 | C2×Q16 | — | 9 | 3 | no | — |
| 300 | C2×Q16 | — | 9 | 6 | no | — |
| 301 | C2×Q16 | — | 9 | 6 | no | — |
| 302 | C2×Q16 | — | 9 | 6 | no | — |
| 303 | C2×Q16 | — | 9 | 3 | no | — |
| 304 | C2×Q16 | C2×D9 | 1 | 3 | yes | complemented |
| 305 | C2×SD16 | — | 9 | 6 | no | — |
| 306 | C2×D8 | — | 9 | 1 | no | — |
| 307 | #131 | — | 9 | 1 | no | — |
| 308 | #131 | — | 9 | 3 | no | — |
| 309 | #131 | — | 9 | 3 | no | — |
| 310 | #131 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 311 | C2×M16 | — | 9 | 3 | no | — |
| 312 | C22×C8 | — | 9 | 3 | no | — |
| 313 | C22×D3 | — | 3 | 3 | no | — |
| 314 | C22×D3 | — | 6 | 2 | no | — |
| 315 | C3×Q8 | — | 2 | 6 | no | — |
| 316 | C3×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 317 | C3×Q8 | C23×D3 | 1 | 6 | yes | — |
| 318 | C3×D4 | — | 2 | 6 | no | — |
| 319 | C3×D4 | D3×D4 | 1 | 3 | yes | — |
| 320 | C3×D4 | C23×D3 | 1 | 2 | yes | — |
| 321 | C2×C3×C4 | — | 2 | 6 | no | — |
| 322 | C2×C3×C4 | — | 2 | 6 | no | — |
| 323 | C2×C3×C4 | C23×D3 | 1 | 3 | yes | — |
| 324 | #67 | — | 3 | 6 | no | — |
| 325 | #67 | — | 6 | 2 | no | — |
| 326 | #67 | — | 6 | 6 | no | — |
| 327 | #67 | — | 6 | 6 | no | — |
| 328 | C2×Dic3 | — | 3 | 3 | no | — |
| 329 | C2×Dic3 | — | 6 | 6 | no | — |
| 330 | C2×Dic3 | — | 6 | 6 | no | — |
| 331 | D12 | — | 3 | 3 | no | — |
| 332 | D12 | — | 3 | 2 | no | — |
| 333 | D12 | — | 6 | 6 | no | — |
| 334 | C4×D3 | — | 3 | 3 | no | — |
| 335 | C4×D3 | — | 3 | 3 | no | — |
| 336 | C4×D3 | — | 3 | 1 | no | — |
| 337 | C4×D3 | — | 3 | 3 | no | — |
| 338 | C4×D3 | — | 6 | 6 | no | — |
| 339 | C4×D3 | — | 6 | 6 | no | — |
| 340 | C4×D3 | — | 6 | 12 | no | — |
| 341 | C4×D3 | — | 6 | 6 | no | — |
| 342 | Dic6 | — | 3 | 3 | no | — |
| 343 | Dic6 | — | 3 | 6 | no | — |
| 344 | Dic6 | — | 6 | 12 | no | — |
| 345 | Dic6 | — | 6 | 6 | no | — |
| 346 | Dic6 | — | 6 | 6 | no | — |
| 347 | C3×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 348 | C3×C8 | C23×D3 | 1 | 3 | yes | — |
| 349 | C3⋊C8 | — | 3 | 1 | no | — |
| 350 | C3⋊C8 | — | 3 | 3 | no | — |
| 351 | C2×C9 | — | 2 | 3 | no | — |
| 352 | C2×C9 | — | 4 | 2 | no | — |
| 353 | C2×C9 | C23×D4 | 1 | 1 | yes | characteristic |
| 354 | D9 | — | 2 | 3 | no | — |
| 355 | D9 | — | 4 | 2 | no | — |
| 356 | D9 | #578 | 1 | 2 | yes | direct product factor |
| 357 | #41 | — | 2 | 6 | no | — |
| 358 | #41 | — | 9 | 1 | no | — |
| 359 | #41 | — | 9 | 3 | no | — |
| 360 | #41 | — | 9 | 3 | no | — |
| 361 | #41 | — | 9 | 6 | no | — |
| 362 | #41 | — | 9 | 6 | no | — |
| 363 | #41 | — | 9 | 6 | no | — |
| 364 | #41 | — | 18 | 6 | no | — |
| 365 | #41 | — | 18 | 12 | no | — |
| 366 | #41 | — | 18 | 6 | no | — |
| 367 | #41 | — | 18 | 6 | no | — |
| 368 | #41 | — | 18 | 12 | no | — |
| 369 | #41 | — | 18 | 6 | no | — |
| 370 | #41 | — | 18 | 6 | no | — |
| 371 | #41 | C22×D9 | 1 | 6 | yes | — |
| 372 | #41 | C22×D9 | 1 | 1 | yes | characteristic |
| 373 | C2×Q8 | — | 2 | 2 | no | — |
| 374 | C2×Q8 | — | 9 | 1 | no | — |
| 375 | C2×Q8 | — | 9 | 6 | no | — |
| 376 | C2×Q8 | — | 9 | 12 | no | — |
| 377 | C2×Q8 | — | 9 | 6 | no | — |
| 378 | C2×Q8 | — | 18 | 6 | no | — |
| 379 | C2×Q8 | — | 18 | 6 | no | — |
| 380 | C2×Q8 | — | 18 | 6 | no | — |
| 381 | C2×Q8 | — | 18 | 6 | no | — |
| 382 | C2×Q8 | — | 18 | 6 | no | — |
| 383 | C2×Q8 | — | 18 | 2 | no | — |
| 384 | C2×Q8 | C22×D9 | 1 | 6 | yes | — |
| 385 | C2×D4 | — | 9 | 3 | no | — |
| 386 | C2×D4 | — | 9 | 2 | no | — |
| 387 | C2×D4 | — | 18 | 6 | no | — |
| 388 | C22×C4 | — | 9 | 3 | no | — |
| 389 | C22×C4 | — | 18 | 6 | no | — |
| 390 | C22×C4 | — | 18 | 6 | no | — |
| 391 | Q16 | — | 9 | 6 | no | — |
| 392 | Q16 | — | 9 | 12 | no | — |
| 393 | Q16 | — | 9 | 3 | no | — |
| 394 | Q16 | — | 9 | 6 | no | — |
| 395 | Q16 | C22×D9 | 1 | 3 | yes | — |
| 396 | Q16 | C22×D9 | 1 | 6 | yes | — |
| 397 | SD16 | — | 9 | 6 | no | — |
| 398 | SD16 | — | 9 | 6 | no | — |
| 399 | SD16 | — | 9 | 6 | no | — |
| 400 | SD16 | C22×D9 | 1 | 6 | yes | — |
| 401 | D8 | — | 9 | 2 | no | — |
| 402 | D8 | — | 9 | 1 | no | — |
| 403 | D8 | C22×D9 | 1 | 1 | yes | characteristic |
| 404 | M16 | — | 9 | 3 | no | — |
| 405 | M16 | — | 9 | 6 | no | — |
| 406 | M16 | C22×D9 | 1 | 3 | yes | — |
| 407 | C2×C8 | — | 9 | 3 | no | — |
| 408 | C2×C8 | — | 9 | 1 | no | — |
| 409 | C2×C8 | — | 9 | 3 | no | — |
| 410 | C2×C8 | — | 9 | 3 | no | — |
| 411 | C2×C8 | — | 9 | 3 | no | — |
| 412 | C2×C8 | C22×D9 | 1 | 3 | yes | — |
| 413 | C22×C3 | — | 2 | 2 | no | — |
| 414 | C22×C3 | C2×D3×D4 | 1 | 3 | yes | — |
| 415 | C2×D3 | — | 3 | 1 | no | — |
| 416 | C2×D3 | — | 3 | 3 | no | — |
| 417 | C2×D3 | — | 6 | 6 | no | — |
| 418 | C2×D3 | — | 6 | 2 | no | — |
| 419 | C2×D3 | — | 12 | 4 | no | — |
| 420 | C3×C4 | — | 2 | 6 | no | — |
| 421 | C3×C4 | C2×D3×D4 | 1 | 3 | yes | — |
| 422 | C3×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 423 | Dic3 | — | 3 | 3 | no | — |
| 424 | Dic3 | — | 3 | 1 | no | — |
| 425 | Dic3 | — | 6 | 6 | no | — |
| 426 | C9 | C2×#578 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 427 | C23 | — | 9 | 3 | no | — |
| 428 | C23 | — | 18 | 2 | no | — |
| 429 | Q8 | — | 2 | 6 | no | — |
| 430 | Q8 | — | 9 | 3 | no | — |
| 431 | Q8 | — | 9 | 6 | no | — |
| 432 | Q8 | — | 18 | 6 | no | — |
| 433 | Q8 | — | 18 | 12 | no | — |
| 434 | Q8 | — | 18 | 6 | no | — |
| 435 | Q8 | D4×D9 | 1 | 1 | yes | characteristic |
| 436 | Q8 | C23×D9 | 1 | 6 | yes | — |
| 437 | D4 | — | 2 | 6 | no | — |
| 438 | D4 | — | 9 | 6 | no | — |
| 439 | D4 | — | 9 | 2 | no | — |
| 440 | D4 | — | 9 | 3 | no | — |
| 441 | D4 | — | 18 | 6 | no | — |
| 442 | D4 | — | 18 | 2 | no | — |
| 443 | D4 | — | 18 | 6 | no | — |
| 444 | D4 | — | 18 | 6 | no | — |
| 445 | D4 | D4×D9 | 1 | 3 | yes | — |
| 446 | D4 | C23×D9 | 1 | 2 | yes | — |
| 447 | C2×C4 | — | 2 | 6 | no | — |
| 448 | C2×C4 | — | 2 | 6 | no | — |
| 449 | C2×C4 | — | 9 | 3 | no | — |
| 450 | C2×C4 | — | 9 | 1 | no | — |
| 451 | C2×C4 | — | 9 | 3 | no | — |
| 452 | C2×C4 | — | 9 | 3 | no | — |
| 453 | C2×C4 | — | 9 | 3 | no | — |
| 454 | C2×C4 | — | 18 | 6 | no | — |
| 455 | C2×C4 | — | 18 | 6 | no | — |
| 456 | C2×C4 | — | 18 | 12 | no | — |
| 457 | C2×C4 | — | 18 | 6 | no | — |
| 458 | C2×C4 | — | 18 | 6 | no | — |
| 459 | C2×C4 | — | 18 | 6 | no | — |
| 460 | C2×C4 | C23×D9 | 1 | 3 | yes | — |
| 461 | C8 | — | 9 | 1 | no | — |
| 462 | C8 | — | 9 | 3 | no | — |
| 463 | C8 | C23×D9 | 1 | 1 | yes | characteristic |
| 464 | C8 | C23×D9 | 1 | 3 | yes | — |
| 465 | C2×C3 | — | 2 | 3 | no | — |
| 466 | C2×C3 | — | 4 | 2 | no | — |
| 467 | C2×C3 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 468 | D3 | — | 3 | 2 | no | — |
| 469 | D3 | — | 6 | 3 | no | — |
| 470 | D3 | — | 12 | 2 | no | — |
| 471 | C22 | — | 2 | 2 | no | — |
| 472 | C22 | — | 9 | 1 | no | — |
| 473 | C22 | — | 9 | 3 | no | — |
| 474 | C22 | — | 18 | 6 | no | — |
| 475 | C22 | — | 18 | 2 | no | — |
| 476 | C22 | — | 36 | 4 | no | — |
| 477 | C22 | C2×D4×D9 | 1 | 3 | yes | — |
| 478 | C4 | — | 2 | 6 | no | — |
| 479 | C4 | — | 9 | 1 | no | — |
| 480 | C4 | — | 9 | 3 | no | — |
| 481 | C4 | — | 18 | 6 | no | — |
| 482 | C4 | C2×D4×D9 | 1 | 3 | yes | — |
| 483 | C4 | C24×D9 | 1 | 1 | yes | characteristic |
| 484 | C3 | D3×#578 | 1 | 1 | yes | characteristic |
| 485 | C2 | — | 2 | 3 | no | — |
| 486 | C2 | — | 4 | 2 | no | — |
| 487 | C2 | — | 9 | 2 | no | — |
| 488 | C2 | — | 18 | 3 | no | — |
| 489 | C2 | — | 36 | 2 | no | — |
| 490 | C2 | C22×D4×D9 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D4×D9 |
| commutator, cosocle | C4×C9 | C25 |
| Frattini | C3×C4 | C24×D3 |
| Fitting | C9×#578 | C2 |
| socle | C2×C3 | C22×D3×D4 |
| hypercenter | #578 | D9 |
| hypocenter | C9 | C2×#578 |
| LCS | G ▷ C4×C9 ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #578 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D9×2−1+4 | C2 | semidirect |
| 2. C9×#578 | C2 | semidirect |
| 3. #10589940 | C2 | semidirect |
| 4. #10589881 | C2 | semidirect |
| 5. D9×#137 | C2 | semidirect |
| 6. #10589873 | C2 | semidirect |
| 7. D9×#135 | C2 | semidirect |
| 8. #10589868 | C2 | semidirect |
| 9. C2×Q16×D9 | C2 | semidirect |
| 10. #10589855 | C2 | semidirect |
| 11. D9×#131 | C2 | semidirect |
| 13. C9×2−1+4 | C22 | semidirect |
| 15. #63716 | C22 | semidirect |
| 16. #63716 | C22 | semidirect |
| 21. #63713 | C22 | semidirect |
| 24. C9×#137 | C22 | semidirect |
| 25. C9×#135 | C22 | semidirect |
| 26. C2×C9×Q16 | C22 | semidirect |
| 27. C9×#131 | C22 | semidirect |
| 28. #63513 | C22 | semidirect |
| 29. #63511 | C22 | semidirect |
| 30. #63510 | C22 | semidirect |
| 31. #63505 | C22 | semidirect |
| 32. C2×#3674 | C22 | semidirect |
| 33. #63481 | C22 | semidirect |
| 34. #63480 | C22 | semidirect |
| 37. Q16×D9 | C22 | semidirect |
| 38. Q16×D9 | C22 | semidirect |
| 39. #63478 | C22 | semidirect |
| 40. #63477 | C22 | semidirect |
| 42. #63474 | C22 | semidirect |
| 44. #63471 | C22 | semidirect |
| 45. #63469 | C22 | semidirect |
| 47. #63467 | C22 | semidirect |
| 48. #63464 | C22 | semidirect |
| 50. C2×Dic36 | C22 | semidirect |
| 201. #578 | D9 | direct (N × H) |
| 280. 2−1+4 | C2×D9 | semidirect |
| 291. #137 | C2×D9 | semidirect |
| 297. #135 | C2×D9 | semidirect |
| 304. C2×Q16 | C2×D9 | semidirect |
| 310. #131 | C2×D9 | semidirect |
| 356. D9 | #578 | direct (N × H) |
| 426. C9 | C2×#578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D9×2−1+4 | 2 |
| C9×#578 | 2 |
| #10589940 | 2 |
| #10589881 | 2 |
| D9×#137 | 2 |
| #10589873 | 2 |
| D9×#135 | 2 |
| #10589868 | 2 |
| C2×Q16×D9 | 2 |
| #10589855 | 2 |
| D9×#131 | 2 |
| D3×#578 | 3 |