Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
6184 conjugacy classes of subgroups.
The subgroup lattice has 366 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×#3531 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D3×#564 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #87136 | C2 | 1 | 20 | yes | maximal, complemented |
| 4 | #87112 | C2 | 1 | 10 | yes | maximal, complemented |
| 5 | #86282 | C2 | 1 | 5 | yes | maximal, complemented |
| 6 | #86270 | C2 | 1 | 5 | yes | maximal, complemented |
| 7 | #86165 | C2 | 1 | 10 | yes | maximal, complemented |
| 8 | #86142 | C2 | 1 | 10 | yes | maximal, complemented |
| 9 | #63067 | — | 3 | 1 | no | maximal, Sylow |
| 10 | C3×#564 | C22 | 1 | 1 | yes | characteristic |
| 11 | C3×#563 | C22 | 1 | 10 | yes | — |
| 12 | C3×#562 | C22 | 1 | 5 | yes | — |
| 13 | C3×#533 | C22 | 1 | 5 | yes | — |
| 14 | C3×#529 | C22 | 1 | 10 | yes | — |
| 15 | #5729 | C22 | 1 | 20 | yes | — |
| 16 | #5721 | C22 | 1 | 20 | yes | — |
| 17 | #5708 | C22 | 1 | 40 | yes | — |
| 18 | #5701 | C22 | 1 | 40 | yes | — |
| 19 | #5688 | C22 | 1 | 10 | yes | — |
| 20 | D3×#125 | C22 | 1 | 10 | yes | — |
| 21 | D3×#125 | C22 | 1 | 20 | yes | — |
| 22 | C3⋊#564 | C22 | 1 | 10 | yes | — |
| 23 | C3⋊#564 | C22 | 1 | 10 | yes | — |
| 24 | C3⋊#564 | C22 | 1 | 20 | yes | — |
| 25 | #5680 | C22 | 1 | 20 | yes | — |
| 26 | #5672 | C22 | 1 | 20 | yes | — |
| 27 | #5660 | C22 | 1 | 40 | yes | — |
| 28 | #5650 | C22 | 1 | 40 | yes | — |
| 29 | #5639 | C22 | 1 | 20 | yes | — |
| 30 | #5636 | C22 | 1 | 40 | yes | — |
| 31 | #5625 | C22 | 1 | 40 | yes | — |
| 32 | #5623 | C22 | 1 | 20 | yes | — |
| 33 | #5614 | C22 | 1 | 20 | yes | — |
| 34 | #5602 | C22 | 1 | 20 | yes | — |
| 35 | #5579 | C22 | 1 | 10 | yes | — |
| 36 | #5570 | C22 | 1 | 10 | yes | — |
| 37 | #5567 | C22 | 1 | 20 | yes | — |
| 38 | #5551 | C22 | 1 | 10 | yes | — |
| 39 | #5543 | C22 | 1 | 10 | yes | — |
| 40 | #5541 | C22 | 1 | 20 | yes | — |
| 41 | #5523 | C22 | 1 | 10 | yes | — |
| 42 | #5519 | C22 | 1 | 10 | yes | — |
| 43 | #5518 | C22 | 1 | 20 | yes | — |
| 44 | C4×#235 | C22 | 1 | 5 | yes | — |
| 45 | #5470 | C22 | 1 | 10 | yes | — |
| 46 | C2×#870 | C22 | 1 | 5 | yes | — |
| 47 | #3563 | — | 3 | 20 | no | — |
| 48 | #3563 | — | 3 | 10 | no | — |
| 49 | #3556 | — | 3 | 5 | no | — |
| 50 | #3553 | — | 3 | 10 | no | — |
| 51 | #3531 | D3 | 1 | 1 | yes | characteristic, complemented |
| 52 | C2×#564 | — | 3 | 2 | no | — |
| 53 | #3515 | — | 3 | 10 | no | — |
| 54 | #3504 | — | 3 | 5 | no | — |
| 55 | C2×#235 | C23 | 1 | 5 | yes | — |
| 56 | C3×C4⋊Q8 | C23 | 1 | 10 | yes | — |
| 57 | C3×#126 | C23 | 1 | 20 | yes | — |
| 58 | C3×#125 | C23 | 1 | 5 | yes | — |
| 59 | C3×#125 | C23 | 1 | 5 | yes | — |
| 60 | C3×#125 | C23 | 1 | 10 | yes | — |
| 61 | C3×#124 | C23 | 1 | 10 | yes | — |
| 62 | C3×#123 | C23 | 1 | 20 | yes | — |
| 63 | C3×C22⋊Q8 | C23 | 1 | 20 | yes | — |
| 64 | C3×C22⋊Q8 | C23 | 1 | 10 | yes | — |
| 65 | C3×#121 | C23 | 1 | 10 | yes | — |
| 66 | C3×C4×Q8 | C23 | 1 | 10 | yes | — |
| 67 | C3×C4×D4 | C23 | 1 | 10 | yes | — |
| 68 | C3×#117 | C23 | 1 | 10 | yes | — |
| 69 | C2×C3×C42 | C23 | 1 | 5 | yes | — |
| 70 | #946 | C23 | 1 | 20 | yes | — |
| 71 | Q8×Dic3 | C23 | 1 | 20 | yes | — |
| 72 | #944 | C23 | 1 | 40 | yes | — |
| 73 | #938 | C23 | 1 | 20 | yes | — |
| 74 | #935 | C23 | 1 | 40 | yes | — |
| 75 | D4×Dic3 | C23 | 1 | 20 | yes | — |
| 76 | C4×#67 | C23 | 1 | 20 | yes | — |
| 77 | #926 | C23 | 1 | 20 | yes | — |
| 78 | #926 | C23 | 1 | 5 | yes | — |
| 79 | C2×C4⋊Dic3 | C23 | 1 | 10 | yes | — |
| 80 | #924 | C23 | 1 | 20 | yes | — |
| 81 | #924 | C23 | 1 | 20 | yes | — |
| 82 | C2×Dic3⋊C4 | C23 | 1 | 20 | yes | — |
| 83 | #896 | C23 | 1 | 40 | yes | — |
| 84 | #892 | C23 | 1 | 20 | yes | — |
| 85 | D3×C4⋊C4 | C23 | 1 | 20 | yes | — |
| 86 | D3×C4⋊C4 | C23 | 1 | 20 | yes | — |
| 87 | D3×C4⋊C4 | C23 | 1 | 20 | yes | — |
| 88 | #890 | C23 | 1 | 20 | yes | — |
| 89 | #890 | C23 | 1 | 20 | yes | — |
| 90 | #890 | C23 | 1 | 40 | yes | — |
| 91 | #890 | C23 | 1 | 20 | yes | — |
| 92 | #889 | C23 | 1 | 40 | yes | — |
| 93 | #889 | C23 | 1 | 40 | yes | — |
| 94 | #889 | C23 | 1 | 40 | yes | — |
| 95 | #889 | C23 | 1 | 40 | yes | — |
| 96 | #889 | C23 | 1 | 40 | yes | — |
| 97 | #888 | C23 | 1 | 20 | yes | — |
| 98 | #887 | C23 | 1 | 40 | yes | — |
| 99 | #883 | C23 | 1 | 40 | yes | — |
| 100 | #67⋊C4 | C23 | 1 | 40 | yes | — |
| 101 | #879 | C23 | 1 | 40 | yes | — |
| 102 | #879 | C23 | 1 | 40 | yes | — |
| 103 | #879 | C23 | 1 | 40 | yes | — |
| 104 | #878 | C23 | 1 | 40 | yes | — |
| 105 | #878 | C23 | 1 | 40 | yes | — |
| 106 | #877 | C23 | 1 | 40 | yes | — |
| 107 | C4×D12 | C23 | 1 | 10 | yes | — |
| 108 | #872 | C23 | 1 | 10 | yes | — |
| 109 | C42×D3 | C23 | 1 | 10 | yes | — |
| 110 | #870 | C23 | 1 | 10 | yes | — |
| 111 | #870 | C23 | 1 | 20 | yes | — |
| 112 | #870 | C23 | 1 | 10 | yes | — |
| 113 | #870 | C23 | 1 | 20 | yes | — |
| 114 | #869 | C23 | 1 | 10 | yes | — |
| 115 | #869 | C23 | 1 | 10 | yes | — |
| 116 | C4×Dic6 | C23 | 1 | 20 | yes | — |
| 117 | C4×Dic6 | C23 | 1 | 20 | yes | — |
| 118 | C4×Dic6 | C23 | 1 | 10 | yes | — |
| 119 | #564 | — | 3 | 10 | no | — |
| 120 | #564 | — | 3 | 20 | no | — |
| 121 | #564 | — | 3 | 10 | no | — |
| 122 | #564 | C2×D3 | 1 | 1 | yes | characteristic |
| 123 | #563 | — | 3 | 20 | no | — |
| 124 | #563 | C2×D3 | 1 | 10 | yes | — |
| 125 | #562 | C2×D3 | 1 | 5 | yes | — |
| 126 | #557 | — | 3 | 20 | no | — |
| 127 | #557 | — | 3 | 20 | no | — |
| 128 | #557 | — | 3 | 10 | no | — |
| 129 | #554 | — | 3 | 40 | no | — |
| 130 | #554 | — | 3 | 10 | no | — |
| 131 | #554 | — | 3 | 10 | no | — |
| 132 | #553 | — | 3 | 20 | no | — |
| 133 | #552 | — | 3 | 40 | no | — |
| 134 | #552 | — | 3 | 40 | no | — |
| 135 | #552 | — | 3 | 20 | no | — |
| 136 | #552 | — | 3 | 20 | no | — |
| 137 | #547 | — | 3 | 10 | no | — |
| 138 | #544 | — | 3 | 20 | no | — |
| 139 | #544 | — | 3 | 20 | no | — |
| 140 | #544 | — | 3 | 10 | no | — |
| 141 | #541 | — | 3 | 40 | no | — |
| 142 | #541 | — | 3 | 40 | no | — |
| 143 | #541 | — | 3 | 20 | no | — |
| 144 | #539 | — | 3 | 40 | no | — |
| 145 | #539 | — | 3 | 20 | no | — |
| 146 | #533 | — | 3 | 10 | no | — |
| 147 | #533 | — | 3 | 10 | no | — |
| 148 | #533 | C2×D3 | 1 | 5 | yes | — |
| 149 | #529 | — | 3 | 20 | no | — |
| 150 | #529 | C2×D3 | 1 | 10 | yes | — |
| 151 | C2×#125 | — | 3 | 10 | no | — |
| 152 | C2×#125 | — | 3 | 20 | no | — |
| 153 | C2×#125 | — | 3 | 5 | no | — |
| 154 | #520 | — | 3 | 10 | no | — |
| 155 | C4×#41 | — | 3 | 5 | no | — |
| 156 | C2×C3×Q8 | C24 | 1 | 10 | yes | — |
| 157 | C2×C3×D4 | C24 | 1 | 10 | yes | — |
| 158 | C22×C3×C4 | C24 | 1 | 5 | yes | — |
| 159 | C22×C3×C4 | C24 | 1 | 10 | yes | — |
| 160 | C2×#67 | C24 | 1 | 10 | yes | — |
| 161 | C22×Dic3 | C24 | 1 | 20 | yes | — |
| 162 | #235 | — | 2 | 20 | no | — |
| 163 | C2×D12 | C24 | 1 | 1 | yes | characteristic |
| 164 | C2×C4×D3 | C24 | 1 | 10 | yes | — |
| 165 | C2×C4×D3 | C24 | 1 | 20 | yes | — |
| 166 | C2×Dic6 | C24 | 1 | 5 | yes | — |
| 167 | C2×Dic6 | C24 | 1 | 20 | yes | — |
| 168 | C3×C4⋊C4 | C24 | 1 | 20 | yes | — |
| 169 | C3×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 170 | C3×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 171 | C3×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 172 | C3×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 173 | C3×C22⋊C4 | C24 | 1 | 20 | yes | — |
| 174 | C3×C22⋊C4 | C24 | 1 | 20 | yes | — |
| 175 | C3×C42 | C24 | 1 | 5 | yes | — |
| 176 | C3×C42 | C24 | 1 | 10 | yes | — |
| 177 | C3×C42 | C24 | 1 | 5 | yes | — |
| 178 | #217 | C24 | 1 | 40 | yes | — |
| 179 | #217 | C24 | 1 | 10 | yes | — |
| 180 | (C2×D3)⋊C4 | C24 | 1 | 20 | yes | — |
| 181 | C4⋊Dic3 | C24 | 1 | 10 | yes | — |
| 182 | C4⋊Dic3 | C24 | 1 | 20 | yes | — |
| 183 | C4⋊Dic3 | C24 | 1 | 20 | yes | — |
| 184 | C4⋊Dic3 | C24 | 1 | 20 | yes | — |
| 185 | C4⋊Dic3 | C24 | 1 | 20 | yes | — |
| 186 | Dic3⋊C4 | C24 | 1 | 40 | yes | — |
| 187 | Dic3⋊C4 | C24 | 1 | 40 | yes | — |
| 188 | Dic3⋊C4 | C24 | 1 | 20 | yes | — |
| 189 | Dic3⋊C4 | C24 | 1 | 40 | yes | — |
| 190 | Dic3⋊C4 | C24 | 1 | 40 | yes | — |
| 191 | C4×Dic3 | C24 | 1 | 40 | yes | — |
| 192 | C4×Dic3 | C24 | 1 | 20 | yes | — |
| 193 | C4×Dic3 | C24 | 1 | 10 | yes | — |
| 194 | C2×#41 | — | 3 | 5 | no | — |
| 195 | C4⋊Q8 | — | 3 | 40 | no | — |
| 196 | C4⋊Q8 | — | 3 | 20 | no | — |
| 197 | C4⋊Q8 | — | 3 | 10 | no | — |
| 198 | C4⋊Q8 | — | 3 | 10 | no | — |
| 199 | C4⋊Q8 | C22×D3 | 1 | 10 | yes | — |
| 200 | #126 | — | 3 | 40 | no | — |
| 201 | #126 | — | 3 | 40 | no | — |
| 202 | #126 | — | 3 | 40 | no | — |
| 203 | #126 | C22×D3 | 1 | 20 | yes | — |
| 204 | #125 | — | 3 | 40 | no | — |
| 205 | #125 | — | 3 | 40 | no | — |
| 206 | #125 | — | 3 | 20 | no | — |
| 207 | #125 | — | 3 | 20 | no | — |
| 208 | #125 | — | 3 | 40 | no | — |
| 209 | #125 | — | 3 | 20 | no | — |
| 210 | #125 | — | 3 | 40 | no | — |
| 211 | #125 | — | 3 | 40 | no | — |
| 212 | #125 | — | 3 | 40 | no | — |
| 213 | #125 | — | 3 | 10 | no | — |
| 214 | #125 | — | 3 | 20 | no | — |
| 215 | #125 | — | 3 | 10 | no | — |
| 216 | #125 | — | 3 | 20 | no | — |
| 217 | #125 | C22×D3 | 1 | 10 | yes | — |
| 218 | #125 | C22×D3 | 1 | 5 | yes | — |
| 219 | #125 | C22×D3 | 1 | 5 | yes | — |
| 220 | #124 | C22×D3 | 1 | 10 | yes | — |
| 221 | #123 | — | 3 | 40 | no | — |
| 222 | #123 | — | 3 | 40 | no | — |
| 223 | #123 | C22×D3 | 1 | 20 | yes | — |
| 224 | C22⋊Q8 | — | 3 | 20 | no | — |
| 225 | C22⋊Q8 | — | 3 | 20 | no | — |
| 226 | C22⋊Q8 | — | 3 | 20 | no | — |
| 227 | C22⋊Q8 | — | 3 | 40 | no | — |
| 228 | C22⋊Q8 | — | 3 | 40 | no | — |
| 229 | C22⋊Q8 | — | 3 | 40 | no | — |
| 230 | C22⋊Q8 | C22×D3 | 1 | 10 | yes | — |
| 231 | C22⋊Q8 | C22×D3 | 1 | 20 | yes | — |
| 232 | #121 | — | 3 | 20 | no | — |
| 233 | #121 | C22×D3 | 1 | 10 | yes | — |
| 234 | C4×Q8 | — | 3 | 20 | no | — |
| 235 | C4×Q8 | — | 3 | 40 | no | — |
| 236 | C4×Q8 | — | 3 | 10 | no | — |
| 237 | C4×Q8 | — | 3 | 20 | no | — |
| 238 | C4×Q8 | — | 3 | 20 | no | — |
| 239 | C4×Q8 | C22×D3 | 1 | 10 | yes | — |
| 240 | C4×D4 | — | 3 | 20 | no | — |
| 241 | C4×D4 | — | 3 | 20 | no | — |
| 242 | C4×D4 | — | 3 | 40 | no | — |
| 243 | C4×D4 | — | 3 | 10 | no | — |
| 244 | C4×D4 | C22×D3 | 1 | 10 | yes | — |
| 245 | #117 | — | 3 | 5 | no | — |
| 246 | #117 | — | 3 | 20 | no | — |
| 247 | #117 | — | 3 | 20 | no | — |
| 248 | #117 | — | 3 | 40 | no | — |
| 249 | #117 | — | 3 | 10 | no | — |
| 250 | #117 | C22×D3 | 1 | 10 | yes | — |
| 251 | C2×C4⋊C4 | — | 3 | 10 | no | — |
| 252 | C2×C4⋊C4 | — | 3 | 20 | no | — |
| 253 | C2×C4⋊C4 | — | 3 | 20 | no | — |
| 254 | C2×C4⋊C4 | — | 3 | 20 | no | — |
| 255 | C2×C4⋊C4 | — | 3 | 20 | no | — |
| 256 | C2×C42 | — | 3 | 10 | no | — |
| 257 | C2×C42 | C22×D3 | 1 | 5 | yes | — |
| 258 | C23×C3 | C25 | 1 | 5 | yes | — |
| 259 | C22×D3 | C25 | 1 | 2 | yes | — |
| 260 | C3×Q8 | — | 4 | 10 | no | — |
| 261 | C3×D4 | — | 4 | 10 | no | — |
| 262 | C2×C3×C4 | — | 2 | 10 | no | — |
| 263 | C2×C3×C4 | — | 4 | 10 | no | — |
| 264 | C2×C3×C4 | C25 | 1 | 10 | yes | — |
| 265 | C2×C3×C4 | C25 | 1 | 5 | yes | — |
| 266 | C2×C3×C4 | C25 | 1 | 10 | yes | — |
| 267 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 268 | #67 | — | 2 | 20 | no | — |
| 269 | C2×Dic3 | — | 4 | 20 | no | — |
| 270 | C2×Dic3 | C25 | 1 | 10 | yes | — |
| 271 | C2×Dic3 | C25 | 1 | 20 | yes | — |
| 272 | D12 | 2−1+4 | 1 | 4 | yes | — |
| 273 | C4×D3 | — | 2 | 20 | no | — |
| 274 | C4×D3 | — | 4 | 20 | no | — |
| 275 | Dic6 | — | 2 | 10 | no | — |
| 276 | Dic6 | — | 4 | 20 | no | — |
| 277 | #41 | — | 6 | 20 | no | — |
| 278 | C2×Q8 | — | 3 | 5 | no | — |
| 279 | C2×Q8 | — | 3 | 20 | no | — |
| 280 | C2×Q8 | C23×D3 | 1 | 10 | yes | — |
| 281 | C2×D4 | — | 3 | 10 | no | — |
| 282 | C2×D4 | — | 3 | 1 | no | — |
| 283 | C2×D4 | C23×D3 | 1 | 10 | yes | — |
| 284 | C22×C4 | — | 3 | 20 | no | — |
| 285 | C22×C4 | — | 3 | 10 | no | — |
| 286 | C22×C4 | — | 3 | 20 | no | — |
| 287 | C22×C4 | C23×D3 | 1 | 5 | yes | — |
| 288 | C22×C4 | C23×D3 | 1 | 10 | yes | — |
| 289 | C4⋊C4 | — | 3 | 10 | no | — |
| 290 | C4⋊C4 | — | 3 | 20 | no | — |
| 291 | C4⋊C4 | — | 3 | 40 | no | — |
| 292 | C4⋊C4 | — | 3 | 20 | no | — |
| 293 | C4⋊C4 | — | 3 | 20 | no | — |
| 294 | C4⋊C4 | — | 3 | 40 | no | — |
| 295 | C4⋊C4 | — | 3 | 40 | no | — |
| 296 | C4⋊C4 | — | 3 | 40 | no | — |
| 297 | C4⋊C4 | — | 3 | 20 | no | — |
| 298 | C4⋊C4 | — | 3 | 20 | no | — |
| 299 | C4⋊C4 | C23×D3 | 1 | 10 | yes | — |
| 300 | C4⋊C4 | C23×D3 | 1 | 10 | yes | — |
| 301 | C4⋊C4 | C23×D3 | 1 | 10 | yes | — |
| 302 | C4⋊C4 | C23×D3 | 1 | 10 | yes | — |
| 303 | C4⋊C4 | C23×D3 | 1 | 20 | yes | — |
| 304 | C22⋊C4 | — | 3 | 40 | no | — |
| 305 | C22⋊C4 | — | 3 | 10 | no | — |
| 306 | C22⋊C4 | — | 3 | 20 | no | — |
| 307 | C22⋊C4 | C23×D3 | 1 | 20 | yes | — |
| 308 | C22⋊C4 | C23×D3 | 1 | 20 | yes | — |
| 309 | C42 | — | 3 | 10 | no | — |
| 310 | C42 | — | 3 | 20 | no | — |
| 311 | C42 | — | 3 | 40 | no | — |
| 312 | C42 | C23×D3 | 1 | 5 | yes | — |
| 313 | C42 | C23×D3 | 1 | 5 | yes | — |
| 314 | C42 | C23×D3 | 1 | 10 | yes | — |
| 315 | C22×C3 | — | 2 | 5 | no | — |
| 316 | C22×C3 | — | 2 | 10 | no | — |
| 317 | C22×C3 | C26 | 1 | 1 | yes | characteristic |
| 318 | C2×D3 | — | 2 | 4 | no | — |
| 319 | C2×D3 | C2×2−1+4 | 1 | 4 | yes | — |
| 320 | C3×C4 | — | 2 | 5 | no | — |
| 321 | C3×C4 | — | 2 | 10 | no | — |
| 322 | C3×C4 | — | 2 | 10 | no | — |
| 323 | C3×C4 | C2×2−1+4 | 1 | 2 | yes | — |
| 324 | Dic3 | — | 2 | 10 | no | — |
| 325 | Dic3 | — | 2 | 20 | no | — |
| 326 | C23 | — | 3 | 2 | no | — |
| 327 | C23 | C24×D3 | 1 | 5 | yes | — |
| 328 | Q8 | — | 4 | 10 | no | — |
| 329 | Q8 | — | 6 | 10 | no | — |
| 330 | Q8 | — | 12 | 20 | no | — |
| 331 | D4 | — | 3 | 4 | no | — |
| 332 | D4 | — | 4 | 10 | no | — |
| 333 | D4 | — | 6 | 20 | no | — |
| 334 | C2×C4 | — | 2 | 10 | no | — |
| 335 | C2×C4 | — | 3 | 10 | no | — |
| 336 | C2×C4 | — | 3 | 20 | no | — |
| 337 | C2×C4 | — | 4 | 10 | no | — |
| 338 | C2×C4 | — | 6 | 20 | no | — |
| 339 | C2×C4 | — | 12 | 20 | no | — |
| 340 | C2×C4 | — | 12 | 20 | no | — |
| 341 | C2×C4 | C24×D3 | 1 | 10 | yes | — |
| 342 | C2×C4 | C24×D3 | 1 | 5 | yes | — |
| 343 | C2×C4 | C24×D3 | 1 | 10 | yes | — |
| 344 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 345 | C2×C3 | — | 4 | 5 | no | — |
| 346 | C2×C3 | C22×2−1+4 | 1 | 1 | yes | characteristic |
| 347 | C2×C3 | 2−1+6 | 1 | 2 | yes | — |
| 348 | D3 | — | 2 | 4 | no | — |
| 349 | C22 | — | 2 | 5 | no | — |
| 350 | C22 | — | 2 | 10 | no | — |
| 351 | C22 | — | 3 | 4 | no | — |
| 352 | C22 | — | 6 | 4 | no | — |
| 353 | C22 | C25×D3 | 1 | 1 | yes | characteristic |
| 354 | C4 | — | 2 | 5 | no | — |
| 355 | C4 | — | 2 | 10 | no | — |
| 356 | C4 | — | 2 | 10 | no | — |
| 357 | C4 | — | 6 | 10 | no | — |
| 358 | C4 | — | 6 | 20 | no | — |
| 359 | C4 | D3×2−1+4 | 1 | 2 | yes | — |
| 360 | C3 | #63067 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 361 | C2 | — | 4 | 5 | no | — |
| 362 | C2 | — | 6 | 4 | no | — |
| 363 | C2 | C2×D3×2−1+4 | 1 | 1 | yes | characteristic |
| 364 | C2 | #87572 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D3 |
| commutator, socle, cosocle | C22×C3 | C26 |
| Fitting | C3×#3531 | C2 |
| hypercenter | #3531 | D3 |
| hypocenter | C3 | #63067 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #3531 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#3531 | C2 | semidirect |
| 2. D3×#564 | C2 | semidirect |
| 3. #87136 | C2 | semidirect |
| 4. #87112 | C2 | semidirect |
| 5. #86282 | C2 | semidirect |
| 6. #86270 | C2 | semidirect |
| 7. #86165 | C2 | semidirect |
| 8. #86142 | C2 | semidirect |
| 51. #3531 | D3 | semidirect |
| 360. C3 | #63067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3531 | 2 |
| D3×#564 | 2 |
| #87136 | 2 |
| #87112 | 2 |
| #86282 | 2 |
| #86270 | 2 |
| #86165 | 2 |
| #86142 | 2 |
| #63067 | 3 |