Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
806 conjugacy classes of subgroups.
The subgroup lattice has 542 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11722509 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #11721805 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | D3×C9×Q16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×Q16×D9 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11721222 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11721221 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11721208 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11720830 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11720829 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11720812 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11720806 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #10594765 | — | 3 | 1 | no | maximal |
| 13 | #10589868 | — | 3 | 1 | no | maximal |
| 14 | #88746 | C22 | 1 | 2 | yes | — |
| 15 | D3×Q8×C9 | C22 | 1 | 2 | yes | — |
| 16 | C3×Q8×D9 | C22 | 1 | 2 | yes | — |
| 17 | #88642 | — | 2 | 2 | no | — |
| 18 | #88642 | C22 | 1 | 2 | yes | — |
| 19 | #88640 | — | 2 | 2 | no | — |
| 20 | #88640 | C22 | 1 | 1 | yes | characteristic |
| 21 | (C3⋊D9)⋊Q8 | — | 2 | 2 | no | — |
| 22 | (C3⋊D9)⋊Q8 | C22 | 1 | 2 | yes | — |
| 23 | #88635 | — | 2 | 2 | no | — |
| 24 | #88635 | C22 | 1 | 2 | yes | — |
| 25 | C3×C9×Q16 | C22 | 1 | 1 | yes | characteristic |
| 26 | #88548 | C22 | 1 | 2 | yes | — |
| 27 | #88525 | C22 | 1 | 1 | yes | characteristic |
| 28 | C8×C3⋊D9 | C22 | 1 | 1 | yes | characteristic |
| 29 | C9×#216 | C22 | 1 | 2 | yes | — |
| 30 | C3×#3674 | C22 | 1 | 2 | yes | — |
| 31 | C9×Dic12 | C22 | 1 | 1 | yes | characteristic |
| 32 | D3×C8×C9 | C22 | 1 | 1 | yes | characteristic |
| 33 | C3×C8×D9 | C22 | 1 | 1 | yes | characteristic |
| 34 | C3×Dic36 | C22 | 1 | 1 | yes | characteristic |
| 35 | #88427 | C22 | 1 | 2 | yes | — |
| 36 | #88426 | C22 | 1 | 2 | yes | — |
| 37 | #88420 | C22 | 1 | 1 | yes | characteristic |
| 38 | #88416 | C22 | 1 | 2 | yes | — |
| 39 | #88414 | C22 | 1 | 1 | yes | characteristic |
| 40 | #88413 | C22 | 1 | 1 | yes | characteristic |
| 41 | #64316 | — | 3 | 2 | no | — |
| 42 | #64128 | — | 3 | 1 | no | — |
| 43 | C3×D3×Q16 | — | 3 | 1 | no | — |
| 44 | C3×D3×Q16 | D3 | 1 | 1 | yes | characteristic |
| 45 | #63948 | — | 3 | 2 | no | — |
| 46 | #63948 | — | 3 | 2 | no | — |
| 47 | #63945 | — | 3 | 2 | no | — |
| 48 | #63808 | — | 3 | 1 | no | — |
| 49 | #63808 | — | 3 | 1 | no | — |
| 50 | #63803 | — | 3 | 1 | no | — |
| 51 | #63802 | — | 3 | 1 | no | — |
| 52 | #63713 | — | 3 | 2 | no | — |
| 53 | C2×C9×Q16 | — | 3 | 1 | no | — |
| 54 | #63505 | — | 3 | 2 | no | — |
| 55 | #63481 | — | 3 | 1 | no | — |
| 56 | #63481 | — | 3 | 1 | no | — |
| 57 | #63481 | — | 6 | 1 | no | — |
| 58 | #63480 | — | 3 | 2 | no | — |
| 59 | #63480 | — | 3 | 2 | no | — |
| 60 | Q16×D9 | — | 3 | 1 | no | — |
| 61 | Q16×D9 | D3 | 1 | 1 | yes | characteristic, complemented |
| 62 | #63467 | — | 3 | 1 | no | — |
| 63 | #63464 | — | 3 | 1 | no | — |
| 64 | C3×Q8×C9 | C23 | 1 | 2 | yes | — |
| 65 | C4⋊(C3⋊D9) | — | 2 | 2 | no | — |
| 66 | C4⋊(C3⋊D9) | C23 | 1 | 2 | yes | — |
| 67 | C4×C3⋊D9 | — | 2 | 2 | no | — |
| 68 | C4×C3⋊D9 | C23 | 1 | 1 | yes | characteristic |
| 69 | C4×D3×C9 | — | 2 | 2 | no | — |
| 70 | C4×D3×C9 | C23 | 1 | 1 | yes | characteristic |
| 71 | C3×C4×D9 | — | 2 | 2 | no | — |
| 72 | C3×C4×D9 | C23 | 1 | 1 | yes | characteristic |
| 73 | C9×Dic6 | — | 2 | 2 | no | — |
| 74 | C9×Dic6 | C23 | 1 | 2 | yes | — |
| 75 | C3×Dic18 | — | 2 | 2 | no | — |
| 76 | C3×Dic18 | C23 | 1 | 2 | yes | — |
| 77 | #6195 | — | 2 | 2 | no | — |
| 78 | #6195 | D4 | 1 | 1 | yes | characteristic |
| 79 | #6194 | D4 | 1 | 1 | yes | characteristic |
| 80 | #6192 | — | 2 | 2 | no | — |
| 81 | #6192 | D4 | 1 | 1 | yes | characteristic |
| 82 | (C3⋊D9)⋊C4 | — | 2 | 2 | no | — |
| 83 | (C3⋊D9)⋊C4 | — | 2 | 2 | no | — |
| 84 | (C3⋊D9)⋊C4 | — | 2 | 2 | no | — |
| 85 | #6189 | — | 2 | 2 | no | — |
| 86 | #6189 | D4 | 1 | 1 | yes | characteristic |
| 87 | C3×C8×C9 | C23 | 1 | 1 | yes | characteristic |
| 88 | C3⋊(C9⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 89 | C9×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 90 | C3×C9⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 91 | #5766 | — | 9 | 1 | no | — |
| 92 | #5766 | — | 9 | 1 | no | — |
| 93 | #3832 | — | 3 | 2 | no | — |
| 94 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 95 | C3×D3×Q8 | C2×D3 | 1 | 2 | yes | — |
| 96 | #3799 | — | 3 | 2 | no | — |
| 97 | #3799 | — | 3 | 2 | no | — |
| 98 | #3799 | — | 6 | 2 | no | — |
| 99 | #3799 | — | 6 | 2 | no | — |
| 100 | #3798 | — | 3 | 1 | no | — |
| 101 | #3798 | — | 6 | 2 | no | — |
| 102 | #3797 | — | 3 | 2 | no | — |
| 103 | #3797 | — | 6 | 2 | no | — |
| 104 | C32×Q16 | C2×D3 | 1 | 1 | yes | characteristic |
| 105 | #3755 | — | 3 | 2 | no | — |
| 106 | #3745 | — | 3 | 1 | no | — |
| 107 | C8×C3⋊D3 | — | 3 | 1 | no | — |
| 108 | C3×#216 | — | 3 | 2 | no | — |
| 109 | C3×#216 | C2×D3 | 1 | 2 | yes | — |
| 110 | C3×Dic12 | — | 3 | 1 | no | — |
| 111 | C3×Dic12 | C2×D3 | 1 | 1 | yes | characteristic |
| 112 | C3×D3×C8 | — | 3 | 1 | no | — |
| 113 | C3×D3×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 114 | #3718 | — | 3 | 2 | no | — |
| 115 | #3717 | — | 3 | 2 | no | — |
| 116 | #3717 | — | 3 | 2 | no | — |
| 117 | #3712 | — | 3 | 1 | no | — |
| 118 | #3711 | — | 3 | 1 | no | — |
| 119 | #3711 | — | 3 | 1 | no | — |
| 120 | C2×Q8×C9 | — | 3 | 2 | no | — |
| 121 | #3701 | — | 3 | 2 | no | — |
| 122 | #3701 | — | 3 | 2 | no | — |
| 123 | #3701 | — | 6 | 2 | no | — |
| 124 | #3701 | — | 6 | 2 | no | — |
| 125 | Q8×D9 | — | 3 | 2 | no | — |
| 126 | Q8×D9 | — | 6 | 2 | no | — |
| 127 | Q8×D9 | C2×D3 | 1 | 2 | yes | — |
| 128 | #3697 | — | 3 | 1 | no | — |
| 129 | #3697 | — | 3 | 2 | no | — |
| 130 | #3697 | — | 6 | 2 | no | — |
| 131 | #3697 | — | 6 | 2 | no | — |
| 132 | C9×Q16 | — | 2 | 1 | no | — |
| 133 | C9×Q16 | — | 3 | 2 | no | — |
| 134 | C9×Q16 | — | 3 | 1 | no | — |
| 135 | C9×Q16 | C2×D3 | 1 | 1 | yes | characteristic |
| 136 | C2×C8×C9 | — | 3 | 1 | no | — |
| 137 | #3675 | — | 3 | 2 | no | — |
| 138 | #3675 | — | 3 | 2 | no | — |
| 139 | #3675 | — | 6 | 2 | no | — |
| 140 | #3674 | — | 3 | 2 | no | — |
| 141 | #3674 | C2×D3 | 1 | 2 | yes | — |
| 142 | #3667 | — | 3 | 1 | no | — |
| 143 | D72 | — | 3 | 1 | no | — |
| 144 | D72 | — | 6 | 1 | no | — |
| 145 | #3664 | — | 3 | 2 | no | — |
| 146 | #3663 | — | 3 | 1 | no | — |
| 147 | #3663 | — | 3 | 1 | no | — |
| 148 | C8×D9 | — | 3 | 1 | no | — |
| 149 | C8×D9 | — | 6 | 1 | no | — |
| 150 | C8×D9 | C2×D3 | 1 | 1 | yes | characteristic |
| 151 | Dic36 | C2×D3 | 1 | 1 | yes | characteristic |
| 152 | C2×C3⋊D9 | — | 2 | 2 | no | — |
| 153 | C2×C3⋊D9 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C2×D3×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C2×C3×D9 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | C3×C4×C9 | — | 2 | 2 | no | — |
| 157 | C3×C4×C9 | C24 | 1 | 1 | yes | characteristic |
| 158 | C3⋊Dic9 | C2×D4 | 1 | 1 | yes | characteristic |
| 159 | C9×Dic3 | — | 2 | 2 | no | — |
| 160 | C9×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 161 | C3×Dic9 | — | 2 | 2 | no | — |
| 162 | C3×Dic9 | C2×D4 | 1 | 1 | yes | characteristic |
| 163 | #1007 | — | 9 | 2 | no | — |
| 164 | #1007 | — | 9 | 2 | no | — |
| 165 | C2×C3×Q16 | — | 3 | 1 | no | — |
| 166 | C2×C3×Q16 | — | 9 | 1 | no | — |
| 167 | #942 | — | 9 | 2 | no | — |
| 168 | #942 | — | 9 | 2 | no | — |
| 169 | #919 | — | 9 | 1 | no | — |
| 170 | #919 | — | 9 | 1 | no | — |
| 171 | #919 | — | 9 | 1 | no | — |
| 172 | #919 | — | 9 | 1 | no | — |
| 173 | #919 | — | 18 | 1 | no | — |
| 174 | #918 | — | 9 | 2 | no | — |
| 175 | #918 | — | 9 | 2 | no | — |
| 176 | #918 | — | 9 | 2 | no | — |
| 177 | #918 | — | 9 | 2 | no | — |
| 178 | D3×Q16 | — | 3 | 1 | no | — |
| 179 | D3×Q16 | — | 9 | 1 | no | — |
| 180 | D3×Q16 | — | 9 | 1 | no | — |
| 181 | D3×Q16 | D9 | 1 | 1 | yes | characteristic, complemented |
| 182 | #904 | — | 9 | 1 | no | — |
| 183 | #904 | — | 9 | 1 | no | — |
| 184 | #901 | — | 9 | 1 | no | — |
| 185 | #901 | — | 9 | 1 | no | — |
| 186 | C32×Q8 | C22×D3 | 1 | 2 | yes | — |
| 187 | C4⋊(C3⋊D3) | — | 3 | 2 | no | — |
| 188 | C4⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 189 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 190 | C4×C3⋊D3 | — | 6 | 2 | no | — |
| 191 | C3×C4×D3 | — | 2 | 2 | no | — |
| 192 | C3×C4×D3 | — | 3 | 1 | no | — |
| 193 | C3×C4×D3 | — | 6 | 2 | no | — |
| 194 | C3×C4×D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 195 | C3×Dic6 | — | 2 | 2 | no | — |
| 196 | C3×Dic6 | — | 3 | 2 | no | — |
| 197 | C3×Dic6 | — | 6 | 2 | no | — |
| 198 | C3×Dic6 | C22×D3 | 1 | 2 | yes | — |
| 199 | #627 | — | 3 | 1 | no | — |
| 200 | #627 | — | 6 | 2 | no | — |
| 201 | #626 | — | 3 | 1 | no | — |
| 202 | #626 | — | 3 | 1 | no | — |
| 203 | #626 | — | 6 | 2 | no | — |
| 204 | #626 | — | 6 | 2 | no | — |
| 205 | #625 | — | 3 | 1 | no | — |
| 206 | #624 | — | 6 | 2 | no | — |
| 207 | #624 | — | 6 | 2 | no | — |
| 208 | #624 | — | 6 | 2 | no | — |
| 209 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 210 | C3⋊(C3⋊C8) | — | 3 | 1 | no | — |
| 211 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 212 | C3×C3⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 213 | Q8×C9 | — | 2 | 2 | no | — |
| 214 | Q8×C9 | — | 3 | 2 | no | — |
| 215 | Q8×C9 | — | 6 | 2 | no | — |
| 216 | Q8×C9 | C22×D3 | 1 | 2 | yes | — |
| 217 | C2×C4×C9 | — | 3 | 1 | no | — |
| 218 | C2×C4×C9 | — | 6 | 2 | no | — |
| 219 | #611 | — | 3 | 1 | no | — |
| 220 | #611 | — | 3 | 1 | no | — |
| 221 | #611 | — | 6 | 2 | no | — |
| 222 | D36 | — | 3 | 1 | no | — |
| 223 | D36 | — | 3 | 2 | no | — |
| 224 | D36 | — | 6 | 2 | no | — |
| 225 | D36 | — | 6 | 2 | no | — |
| 226 | D36 | — | 6 | 2 | no | — |
| 227 | D36 | — | 12 | 2 | no | — |
| 228 | C4×D9 | — | 2 | 2 | no | — |
| 229 | C4×D9 | — | 3 | 1 | no | — |
| 230 | C4×D9 | — | 6 | 1 | no | — |
| 231 | C4×D9 | — | 6 | 2 | no | — |
| 232 | C4×D9 | — | 6 | 2 | no | — |
| 233 | C4×D9 | — | 6 | 2 | no | — |
| 234 | C4×D9 | — | 6 | 2 | no | — |
| 235 | C4×D9 | — | 12 | 2 | no | — |
| 236 | C4×D9 | C22×D3 | 1 | 1 | yes | characteristic |
| 237 | Dic18 | — | 2 | 2 | no | — |
| 238 | Dic18 | — | 3 | 1 | no | — |
| 239 | Dic18 | — | 6 | 2 | no | — |
| 240 | Dic18 | C22×D3 | 1 | 2 | yes | — |
| 241 | C8×C9 | — | 2 | 1 | no | — |
| 242 | C8×C9 | — | 3 | 1 | no | — |
| 243 | C8×C9 | C22×D3 | 1 | 1 | yes | characteristic |
| 244 | C9⋊C8 | — | 3 | 1 | no | — |
| 245 | C9⋊C8 | — | 6 | 1 | no | — |
| 246 | C9⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 247 | #578 | — | 27 | 1 | no | Sylow |
| 248 | C2×C3×C9 | C22×D4 | 1 | 1 | yes | characteristic |
| 249 | C3⋊D9 | — | 2 | 1 | no | — |
| 250 | C3⋊D9 | — | 4 | 2 | no | — |
| 251 | D3×C9 | — | 2 | 1 | no | — |
| 252 | C3×D9 | — | 2 | 1 | no | — |
| 253 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 254 | C2×C3×Q8 | — | 9 | 2 | no | — |
| 255 | #239 | — | 9 | 2 | no | — |
| 256 | #239 | — | 9 | 2 | no | — |
| 257 | #239 | — | 9 | 2 | no | — |
| 258 | #239 | — | 9 | 2 | no | — |
| 259 | #239 | — | 18 | 2 | no | — |
| 260 | #239 | — | 18 | 2 | no | — |
| 261 | #239 | — | 18 | 2 | no | — |
| 262 | D3×Q8 | — | 3 | 2 | no | — |
| 263 | D3×Q8 | — | 9 | 2 | no | — |
| 264 | D3×Q8 | — | 9 | 2 | no | — |
| 265 | D3×Q8 | — | 18 | 2 | no | — |
| 266 | D3×Q8 | — | 18 | 2 | no | — |
| 267 | D3×Q8 | C2×D9 | 1 | 2 | yes | — |
| 268 | #235 | — | 9 | 2 | no | — |
| 269 | #235 | — | 9 | 1 | no | — |
| 270 | #235 | — | 9 | 1 | no | — |
| 271 | #235 | — | 9 | 2 | no | — |
| 272 | #235 | — | 18 | 2 | no | — |
| 273 | #235 | — | 18 | 2 | no | — |
| 274 | #235 | — | 18 | 2 | no | — |
| 275 | #235 | — | 18 | 2 | no | — |
| 276 | C3×Q16 | — | 2 | 1 | no | — |
| 277 | C3×Q16 | — | 3 | 2 | no | — |
| 278 | C3×Q16 | — | 3 | 1 | no | — |
| 279 | C3×Q16 | — | 9 | 2 | no | — |
| 280 | C3×Q16 | — | 9 | 1 | no | — |
| 281 | C3×Q16 | C2×D9 | 1 | 1 | yes | characteristic |
| 282 | C3×Q16 | D32 | 1 | 1 | yes | characteristic |
| 283 | C2×C3×C8 | — | 3 | 1 | no | — |
| 284 | C2×C3×C8 | — | 9 | 1 | no | — |
| 285 | #216 | — | 3 | 2 | no | — |
| 286 | #216 | — | 9 | 2 | no | — |
| 287 | #216 | — | 9 | 2 | no | — |
| 288 | #216 | C2×D9 | 1 | 2 | yes | — |
| 289 | #215 | — | 9 | 2 | no | — |
| 290 | #215 | — | 9 | 2 | no | — |
| 291 | #215 | — | 9 | 2 | no | — |
| 292 | #215 | — | 9 | 2 | no | — |
| 293 | #215 | — | 18 | 2 | no | — |
| 294 | #208 | — | 9 | 1 | no | — |
| 295 | #208 | — | 9 | 1 | no | — |
| 296 | Dic12 | — | 3 | 1 | no | — |
| 297 | Dic12 | C2×D9 | 1 | 1 | yes | characteristic |
| 298 | D24 | — | 9 | 1 | no | — |
| 299 | D24 | — | 9 | 1 | no | — |
| 300 | D24 | — | 18 | 1 | no | — |
| 301 | #204 | — | 9 | 2 | no | — |
| 302 | #204 | — | 9 | 2 | no | — |
| 303 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 304 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 305 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 306 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 307 | D3×C8 | — | 3 | 1 | no | — |
| 308 | D3×C8 | — | 9 | 1 | no | — |
| 309 | D3×C8 | — | 9 | 1 | no | — |
| 310 | D3×C8 | — | 18 | 1 | no | — |
| 311 | D3×C8 | C2×D9 | 1 | 1 | yes | characteristic |
| 312 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 313 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 314 | C2×C3×D3 | — | 3 | 1 | no | — |
| 315 | C2×C3×D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 316 | C32×C4 | — | 2 | 2 | no | — |
| 317 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 318 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 319 | C3×Dic3 | — | 2 | 2 | no | — |
| 320 | C3×Dic3 | — | 3 | 1 | no | — |
| 321 | C3×Dic3 | — | 6 | 2 | no | — |
| 322 | C3×Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 323 | C22×C9 | — | 3 | 1 | no | — |
| 324 | C2×D9 | — | 3 | 1 | no | — |
| 325 | C2×D9 | — | 6 | 1 | no | — |
| 326 | C2×D9 | — | 6 | 2 | no | — |
| 327 | C2×D9 | — | 12 | 2 | no | — |
| 328 | C2×D9 | D3×D4 | 1 | 1 | yes | characteristic |
| 329 | C4×C9 | — | 2 | 2 | no | — |
| 330 | C4×C9 | — | 2 | 1 | no | — |
| 331 | C4×C9 | — | 3 | 1 | no | — |
| 332 | C4×C9 | — | 4 | 2 | no | — |
| 333 | C4×C9 | — | 6 | 2 | no | — |
| 334 | C4×C9 | C23×D3 | 1 | 1 | yes | characteristic |
| 335 | Dic9 | — | 2 | 2 | no | — |
| 336 | Dic9 | — | 3 | 1 | no | — |
| 337 | Dic9 | — | 6 | 1 | no | — |
| 338 | Dic9 | D3×D4 | 1 | 1 | yes | characteristic |
| 339 | 2−1+4 | — | 27 | 2 | no | — |
| 340 | #137 | — | 27 | 2 | no | — |
| 341 | #137 | — | 27 | 2 | no | — |
| 342 | #137 | — | 27 | 2 | no | — |
| 343 | #135 | — | 27 | 1 | no | — |
| 344 | #135 | — | 27 | 1 | no | — |
| 345 | #135 | — | 27 | 1 | no | — |
| 346 | C2×Q16 | — | 3 | 1 | no | — |
| 347 | C2×Q16 | — | 9 | 1 | no | — |
| 348 | C2×Q16 | — | 27 | 1 | no | — |
| 349 | #131 | — | 27 | 1 | no | — |
| 350 | C3×C9 | #578 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 351 | C3×Q8 | — | 2 | 2 | no | — |
| 352 | C3×Q8 | — | 3 | 2 | no | — |
| 353 | C3×Q8 | — | 6 | 2 | no | — |
| 354 | C3×Q8 | — | 9 | 2 | no | — |
| 355 | C3×Q8 | — | 18 | 2 | no | — |
| 356 | C3×Q8 | C22×D9 | 1 | 2 | yes | — |
| 357 | C3×Q8 | C2×D32 | 1 | 2 | yes | — |
| 358 | C2×C3×C4 | — | 3 | 1 | no | — |
| 359 | C2×C3×C4 | — | 6 | 2 | no | — |
| 360 | C2×C3×C4 | — | 9 | 1 | no | — |
| 361 | C2×C3×C4 | — | 18 | 2 | no | — |
| 362 | #67 | — | 9 | 1 | no | — |
| 363 | #67 | — | 9 | 1 | no | — |
| 364 | #67 | — | 9 | 1 | no | — |
| 365 | #67 | — | 9 | 1 | no | — |
| 366 | #67 | — | 18 | 2 | no | — |
| 367 | #67 | — | 18 | 2 | no | — |
| 368 | D12 | — | 9 | 1 | no | — |
| 369 | D12 | — | 9 | 1 | no | — |
| 370 | D12 | — | 9 | 2 | no | — |
| 371 | D12 | — | 9 | 2 | no | — |
| 372 | D12 | — | 18 | 2 | no | — |
| 373 | D12 | — | 18 | 2 | no | — |
| 374 | D12 | — | 18 | 2 | no | — |
| 375 | D12 | — | 18 | 2 | no | — |
| 376 | D12 | — | 18 | 2 | no | — |
| 377 | D12 | — | 36 | 2 | no | — |
| 378 | C4×D3 | — | 2 | 2 | no | — |
| 379 | C4×D3 | — | 3 | 1 | no | — |
| 380 | C4×D3 | — | 6 | 2 | no | — |
| 381 | C4×D3 | — | 9 | 1 | no | — |
| 382 | C4×D3 | — | 9 | 1 | no | — |
| 383 | C4×D3 | — | 18 | 1 | no | — |
| 384 | C4×D3 | — | 18 | 2 | no | — |
| 385 | C4×D3 | — | 18 | 2 | no | — |
| 386 | C4×D3 | — | 18 | 2 | no | — |
| 387 | C4×D3 | — | 18 | 2 | no | — |
| 388 | C4×D3 | — | 18 | 2 | no | — |
| 389 | C4×D3 | — | 18 | 2 | no | — |
| 390 | C4×D3 | — | 18 | 2 | no | — |
| 391 | C4×D3 | — | 18 | 2 | no | — |
| 392 | C4×D3 | — | 36 | 2 | no | — |
| 393 | C4×D3 | C22×D9 | 1 | 1 | yes | characteristic |
| 394 | Dic6 | — | 2 | 2 | no | — |
| 395 | Dic6 | — | 3 | 2 | no | — |
| 396 | Dic6 | — | 6 | 2 | no | — |
| 397 | Dic6 | — | 9 | 1 | no | — |
| 398 | Dic6 | — | 9 | 1 | no | — |
| 399 | Dic6 | — | 18 | 2 | no | — |
| 400 | Dic6 | — | 18 | 2 | no | — |
| 401 | Dic6 | C22×D9 | 1 | 2 | yes | — |
| 402 | C3×C8 | — | 2 | 1 | no | — |
| 403 | C3×C8 | — | 3 | 1 | no | — |
| 404 | C3×C8 | — | 9 | 1 | no | — |
| 405 | C3×C8 | C22×D9 | 1 | 1 | yes | characteristic |
| 406 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 407 | C3⋊C8 | — | 3 | 1 | no | — |
| 408 | C3⋊C8 | — | 9 | 1 | no | — |
| 409 | C3⋊C8 | — | 9 | 1 | no | — |
| 410 | C3⋊C8 | — | 18 | 1 | no | — |
| 411 | C3⋊C8 | C22×D9 | 1 | 1 | yes | characteristic |
| 412 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 413 | C3⋊D3 | — | 6 | 1 | no | — |
| 414 | C3⋊D3 | — | 12 | 2 | no | — |
| 415 | C3×D3 | — | 2 | 1 | no | — |
| 416 | C3×D3 | — | 6 | 1 | no | — |
| 417 | C2×C9 | — | 2 | 1 | no | — |
| 418 | C2×C9 | — | 6 | 1 | no | — |
| 419 | C2×C9 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 420 | D9 | — | 2 | 1 | no | — |
| 421 | D9 | — | 6 | 1 | no | — |
| 422 | D9 | — | 12 | 1 | no | — |
| 423 | D9 | — | 12 | 2 | no | — |
| 424 | D9 | — | 24 | 2 | no | — |
| 425 | #41 | — | 27 | 1 | no | — |
| 426 | #41 | — | 27 | 2 | no | — |
| 427 | #41 | — | 27 | 2 | no | — |
| 428 | #41 | — | 27 | 2 | no | — |
| 429 | #41 | — | 54 | 2 | no | — |
| 430 | #41 | — | 54 | 2 | no | — |
| 431 | #41 | — | 54 | 2 | no | — |
| 432 | C2×Q8 | — | 3 | 2 | no | — |
| 433 | C2×Q8 | — | 9 | 2 | no | — |
| 434 | C2×Q8 | — | 27 | 2 | no | — |
| 435 | C2×Q8 | — | 54 | 2 | no | — |
| 436 | Q16 | — | 3 | 2 | no | — |
| 437 | Q16 | — | 3 | 1 | no | — |
| 438 | Q16 | — | 9 | 2 | no | — |
| 439 | Q16 | — | 9 | 1 | no | — |
| 440 | Q16 | — | 27 | 2 | no | — |
| 441 | Q16 | D3×D9 | 1 | 1 | yes | characteristic |
| 442 | SD16 | — | 27 | 2 | no | — |
| 443 | SD16 | — | 27 | 2 | no | — |
| 444 | SD16 | — | 27 | 2 | no | — |
| 445 | D8 | — | 27 | 1 | no | — |
| 446 | M16 | — | 27 | 1 | no | — |
| 447 | M16 | — | 27 | 1 | no | — |
| 448 | M16 | — | 27 | 1 | no | — |
| 449 | C2×C8 | — | 3 | 1 | no | — |
| 450 | C2×C8 | — | 9 | 1 | no | — |
| 451 | C2×C8 | — | 27 | 1 | no | — |
| 452 | C22×C3 | — | 3 | 1 | no | — |
| 453 | C22×C3 | — | 9 | 1 | no | — |
| 454 | C2×D3 | — | 3 | 1 | no | — |
| 455 | C2×D3 | — | 9 | 1 | no | — |
| 456 | C2×D3 | — | 9 | 1 | no | — |
| 457 | C2×D3 | — | 18 | 1 | no | — |
| 458 | C2×D3 | — | 18 | 2 | no | — |
| 459 | C2×D3 | — | 18 | 2 | no | — |
| 460 | C2×D3 | — | 36 | 2 | no | — |
| 461 | C2×D3 | D4×D9 | 1 | 1 | yes | characteristic |
| 462 | C3×C4 | — | 2 | 2 | no | — |
| 463 | C3×C4 | — | 2 | 2 | no | — |
| 464 | C3×C4 | — | 2 | 1 | no | — |
| 465 | C3×C4 | — | 3 | 1 | no | — |
| 466 | C3×C4 | — | 4 | 2 | no | — |
| 467 | C3×C4 | — | 6 | 2 | no | — |
| 468 | C3×C4 | — | 9 | 1 | no | — |
| 469 | C3×C4 | — | 18 | 2 | no | — |
| 470 | C3×C4 | C23×D9 | 1 | 1 | yes | characteristic |
| 471 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 472 | Dic3 | — | 2 | 2 | no | — |
| 473 | Dic3 | — | 3 | 1 | no | — |
| 474 | Dic3 | — | 6 | 2 | no | — |
| 475 | Dic3 | — | 9 | 1 | no | — |
| 476 | Dic3 | — | 9 | 1 | no | — |
| 477 | Dic3 | — | 18 | 1 | no | — |
| 478 | Dic3 | D4×D9 | 1 | 1 | yes | characteristic |
| 479 | C32 | #5766 | 1 | 1 | yes | characteristic |
| 480 | C9 | — | 2 | 1 | no | — |
| 481 | C9 | #5766 | 1 | 1 | yes | characteristic, complemented |
| 482 | Q8 | — | 3 | 2 | no | — |
| 483 | Q8 | — | 6 | 2 | no | — |
| 484 | Q8 | — | 9 | 2 | no | — |
| 485 | Q8 | — | 18 | 2 | no | — |
| 486 | Q8 | — | 27 | 1 | no | — |
| 487 | Q8 | — | 54 | 2 | no | — |
| 488 | Q8 | C2×D3×D9 | 1 | 2 | yes | — |
| 489 | D4 | — | 27 | 1 | no | — |
| 490 | D4 | — | 27 | 1 | no | — |
| 491 | D4 | — | 27 | 1 | no | — |
| 492 | D4 | — | 27 | 2 | no | — |
| 493 | D4 | — | 54 | 2 | no | — |
| 494 | D4 | — | 54 | 2 | no | — |
| 495 | D4 | — | 54 | 2 | no | — |
| 496 | C2×C4 | — | 3 | 1 | no | — |
| 497 | C2×C4 | — | 6 | 2 | no | — |
| 498 | C2×C4 | — | 9 | 1 | no | — |
| 499 | C2×C4 | — | 18 | 2 | no | — |
| 500 | C2×C4 | — | 27 | 1 | no | — |
| 501 | C2×C4 | — | 54 | 2 | no | — |
| 502 | C2×C4 | — | 54 | 2 | no | — |
| 503 | C2×C4 | — | 54 | 2 | no | — |
| 504 | C2×C4 | — | 54 | 2 | no | — |
| 505 | C8 | — | 3 | 1 | no | — |
| 506 | C8 | — | 9 | 1 | no | — |
| 507 | C8 | — | 27 | 1 | no | — |
| 508 | C8 | C2×D3×D9 | 1 | 1 | yes | characteristic |
| 509 | C2×C3 | — | 2 | 1 | no | — |
| 510 | C2×C3 | — | 6 | 1 | no | — |
| 511 | C2×C3 | — | 18 | 1 | no | — |
| 512 | C2×C3 | C2×D4×D9 | 1 | 1 | yes | characteristic |
| 513 | C2×C3 | D32×D4 | 1 | 1 | yes | characteristic |
| 514 | D3 | — | 2 | 1 | no | — |
| 515 | D3 | — | 6 | 1 | no | — |
| 516 | D3 | — | 18 | 1 | no | — |
| 517 | D3 | — | 18 | 1 | no | — |
| 518 | D3 | — | 36 | 1 | no | — |
| 519 | D3 | — | 36 | 2 | no | — |
| 520 | D3 | — | 36 | 2 | no | — |
| 521 | D3 | — | 72 | 2 | no | — |
| 522 | C22 | — | 3 | 1 | no | — |
| 523 | C22 | — | 9 | 1 | no | — |
| 524 | C22 | — | 27 | 1 | no | — |
| 525 | C22 | — | 54 | 2 | no | — |
| 526 | C4 | — | 2 | 2 | no | — |
| 527 | C4 | — | 3 | 1 | no | — |
| 528 | C4 | — | 6 | 2 | no | — |
| 529 | C4 | — | 9 | 1 | no | — |
| 530 | C4 | — | 18 | 2 | no | — |
| 531 | C4 | — | 27 | 1 | no | — |
| 532 | C4 | C22×D3×D9 | 1 | 1 | yes | characteristic |
| 533 | C3 | — | 2 | 1 | no | — |
| 534 | C3 | #10589868 | 1 | 1 | yes | characteristic, complemented |
| 535 | C3 | #10594765 | 1 | 1 | yes | characteristic |
| 536 | C2 | — | 6 | 1 | no | — |
| 537 | C2 | — | 18 | 1 | no | — |
| 538 | C2 | — | 54 | 1 | no | — |
| 539 | C2 | — | 108 | 2 | no | — |
| 540 | C2 | D3×D4×D9 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11722509 | C2 | semidirect |
| 2. #11721805 | C2 | semidirect |
| 3. D3×C9×Q16 | C2 | semidirect |
| 4. C3×Q16×D9 | C2 | semidirect |
| 5. #11721222 | C2 | semidirect |
| 6. #11721221 | C2 | semidirect |
| 7. #11721208 | C2 | semidirect |
| 8. #11720830 | C2 | semidirect |
| 9. #11720829 | C2 | semidirect |
| 10. #11720812 | C2 | semidirect |
| 11. #11720806 | C2 | semidirect |
| 61. Q16×D9 | D3 | semidirect |
| 181. D3×Q16 | D9 | semidirect |
| 350. C3×C9 | #578 | semidirect |
| 481. C9 | #5766 | semidirect |
| 534. C3 | #10589868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722509 | 2 |
| #11721805 | 2 |
| D3×C9×Q16 | 2 |
| C3×Q16×D9 | 2 |
| #11721222 | 2 |
| #11721221 | 2 |
| #11721208 | 2 |
| #11720830 | 2 |
| #11720829 | 2 |
| #11720812 | 2 |
| #11720806 | 2 |
| #10594765 | 3 |
| #10589868 | 3 |