Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1194 conjugacy classes of subgroups.
The subgroup lattice has 742 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11724624 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11724620 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#64125 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#64124 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11723711 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11723710 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11723707 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11723705 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11723652 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11723650 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #11723649 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #10594756 | — | 3 | 2 | no | maximal |
| 13 | #10594752 | — | 3 | 1 | no | maximal |
| 14 | C3×#3832 | C22 | 1 | 1 | yes | characteristic |
| 15 | C3×Q8×C3⋊D3 | C22 | 1 | 2 | yes | — |
| 16 | C3×#3830 | C22 | 1 | 2 | yes | — |
| 17 | C3×#3830 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#6296 | — | 2 | 1 | no | — |
| 19 | #89046 | — | 2 | 2 | no | — |
| 20 | #89046 | — | 2 | 1 | no | — |
| 21 | #89042 | — | 2 | 1 | no | — |
| 22 | #89042 | C22 | 1 | 1 | yes | characteristic |
| 23 | #89041 | — | 2 | 2 | no | — |
| 24 | #89041 | C22 | 1 | 2 | yes | — |
| 25 | #89040 | — | 2 | 1 | no | — |
| 26 | #89040 | C22 | 1 | 1 | yes | characteristic |
| 27 | #89040 | C22 | 1 | 2 | yes | — |
| 28 | #89040 | C22 | 1 | 1 | yes | characteristic |
| 29 | C33×SD16 | C22 | 1 | 1 | yes | characteristic |
| 30 | C3×#3756 | C22 | 1 | 2 | yes | — |
| 31 | C3×#3756 | C22 | 1 | 1 | yes | characteristic |
| 32 | C3×#3754 | C22 | 1 | 2 | yes | — |
| 33 | C3×#3753 | C22 | 1 | 1 | yes | characteristic |
| 34 | C3×#3746 | C22 | 1 | 2 | yes | — |
| 35 | C3×#3744 | C22 | 1 | 1 | yes | characteristic |
| 36 | C3×#3743 | C22 | 1 | 2 | yes | — |
| 37 | C3×C8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 38 | #88812 | C22 | 1 | 2 | yes | — |
| 39 | #88812 | C22 | 1 | 2 | yes | — |
| 40 | #88811 | C22 | 1 | 2 | yes | — |
| 41 | #88809 | C22 | 1 | 1 | yes | characteristic |
| 42 | #88808 | C22 | 1 | 2 | yes | — |
| 43 | #64316 | — | 3 | 1 | no | — |
| 44 | #64315 | — | 3 | 2 | no | — |
| 45 | #64309 | — | 3 | 1 | no | — |
| 46 | #64309 | — | 3 | 2 | no | — |
| 47 | #64125 | D3 | 1 | 1 | yes | characteristic, complemented |
| 48 | #64124 | D3 | 1 | 2 | yes | complemented |
| 49 | C3×#916 | — | 3 | 2 | no | — |
| 50 | C3×#916 | — | 6 | 1 | no | — |
| 51 | C3×#915 | — | 3 | 2 | no | — |
| 52 | C3×#915 | — | 3 | 2 | no | — |
| 53 | C3×#915 | — | 6 | 2 | no | — |
| 54 | #63945 | — | 3 | 1 | no | — |
| 55 | #63944 | — | 3 | 2 | no | — |
| 56 | #63943 | — | 3 | 2 | no | — |
| 57 | D3×#216 | — | 3 | 2 | no | — |
| 58 | D3×#216 | — | 3 | 2 | no | — |
| 59 | #63936 | — | 3 | 2 | no | — |
| 60 | #63935 | — | 3 | 2 | no | — |
| 61 | #63933 | — | 3 | 2 | no | — |
| 62 | #63931 | — | 3 | 1 | no | — |
| 63 | #63929 | — | 3 | 2 | no | — |
| 64 | #63811 | — | 3 | 2 | no | — |
| 65 | #63805 | — | 3 | 1 | no | — |
| 66 | #63804 | — | 3 | 2 | no | — |
| 67 | #63802 | — | 3 | 1 | no | — |
| 68 | #63801 | — | 3 | 2 | no | — |
| 69 | #63800 | — | 3 | 2 | no | — |
| 70 | D3×Dic12 | — | 3 | 2 | no | — |
| 71 | C33×Q8 | C23 | 1 | 1 | yes | characteristic |
| 72 | C33×D4 | C23 | 1 | 1 | yes | characteristic |
| 73 | C3×#638 | — | 2 | 1 | no | — |
| 74 | C3×#638 | — | 2 | 2 | no | — |
| 75 | C2×C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 76 | C2×C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 77 | C3×C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 78 | C3×C4⋊(C3⋊D3) | C23 | 1 | 1 | yes | characteristic |
| 79 | C3×C4×C3⋊D3 | — | 2 | 2 | no | — |
| 80 | C3×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 81 | C3×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 82 | C3×C4×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 83 | C3×#634 | — | 2 | 2 | no | — |
| 84 | C3×#634 | C23 | 1 | 1 | yes | characteristic |
| 85 | C3×#634 | C23 | 1 | 2 | yes | — |
| 86 | C3×#634 | C23 | 1 | 2 | yes | — |
| 87 | #6296 | — | 2 | 1 | no | — |
| 88 | #6296 | — | 2 | 2 | no | — |
| 89 | #6296 | — | 2 | 1 | no | — |
| 90 | #6296 | D4 | 1 | 1 | yes | characteristic |
| 91 | #6295 | — | 2 | 2 | no | — |
| 92 | #6295 | D4 | 1 | 2 | yes | — |
| 93 | #6295 | D4 | 1 | 1 | yes | characteristic |
| 94 | #6294 | — | 2 | 1 | no | — |
| 95 | #6294 | — | 2 | 1 | no | — |
| 96 | #6294 | — | 2 | 2 | no | — |
| 97 | #6294 | — | 2 | 2 | no | — |
| 98 | C33×C8 | C23 | 1 | 1 | yes | characteristic |
| 99 | C3×C3⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 100 | C3×C3⋊(C3⋊C8) | C23 | 1 | 2 | yes | — |
| 101 | #5779 | — | 9 | 2 | no | — |
| 102 | #5771 | — | 9 | 1 | no | — |
| 103 | #3832 | C2×D3 | 1 | 1 | yes | characteristic |
| 104 | Q8×C3⋊D3 | C2×D3 | 1 | 2 | yes | — |
| 105 | #3830 | C2×D3 | 1 | 2 | yes | — |
| 106 | #3830 | C2×D3 | 1 | 1 | yes | characteristic |
| 107 | C3×#239 | — | 3 | 2 | no | — |
| 108 | C3×#239 | — | 6 | 1 | no | — |
| 109 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 110 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 111 | C3×D3×Q8 | — | 6 | 2 | no | — |
| 112 | C3×#237 | — | 3 | 2 | no | — |
| 113 | C3×#237 | — | 3 | 2 | no | — |
| 114 | C3×#237 | — | 3 | 2 | no | — |
| 115 | C3×#237 | — | 6 | 2 | no | — |
| 116 | C3×#237 | — | 6 | 1 | no | — |
| 117 | C2×#627 | — | 6 | 2 | no | — |
| 118 | C2×#627 | — | 6 | 1 | no | — |
| 119 | #3805 | — | 6 | 2 | no | — |
| 120 | #3805 | — | 6 | 1 | no | — |
| 121 | #3804 | — | 6 | 2 | no | — |
| 122 | #3804 | — | 6 | 2 | no | — |
| 123 | #3804 | — | 6 | 2 | no | — |
| 124 | #3799 | — | 3 | 2 | no | — |
| 125 | #3799 | — | 6 | 2 | no | — |
| 126 | #3798 | — | 3 | 2 | no | — |
| 127 | #3798 | — | 3 | 1 | no | — |
| 128 | #3798 | — | 6 | 1 | no | — |
| 129 | #3798 | — | 6 | 2 | no | — |
| 130 | #3797 | — | 3 | 1 | no | — |
| 131 | #3797 | — | 3 | 2 | no | — |
| 132 | #3797 | — | 3 | 1 | no | — |
| 133 | #3797 | — | 6 | 1 | no | — |
| 134 | #3796 | — | 3 | 2 | no | — |
| 135 | #3796 | — | 6 | 2 | no | — |
| 136 | #3795 | — | 3 | 2 | no | — |
| 137 | #3795 | — | 6 | 2 | no | — |
| 138 | D3×Dic6 | — | 3 | 2 | no | — |
| 139 | D3×Dic6 | — | 3 | 2 | no | — |
| 140 | D3×Dic6 | — | 3 | 2 | no | — |
| 141 | D3×Dic6 | — | 3 | 2 | no | — |
| 142 | D3×Dic6 | — | 6 | 2 | no | — |
| 143 | C32×SD16 | — | 2 | 2 | no | — |
| 144 | C32×SD16 | — | 2 | 1 | no | — |
| 145 | C32×SD16 | — | 4 | 1 | no | — |
| 146 | C32×SD16 | C2×D3 | 1 | 1 | yes | characteristic |
| 147 | C32×SD16 | C2×D3 | 1 | 2 | yes | — |
| 148 | #3756 | C2×D3 | 1 | 2 | yes | — |
| 149 | #3756 | C2×D3 | 1 | 1 | yes | characteristic |
| 150 | #3754 | C2×D3 | 1 | 2 | yes | — |
| 151 | #3753 | C2×D3 | 1 | 1 | yes | characteristic |
| 152 | #3746 | C2×D3 | 1 | 2 | yes | — |
| 153 | #3744 | C2×D3 | 1 | 1 | yes | characteristic |
| 154 | #3743 | C2×D3 | 1 | 2 | yes | — |
| 155 | C8×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 156 | C3×#216 | — | 3 | 2 | no | — |
| 157 | C3×#216 | — | 3 | 2 | no | — |
| 158 | C3×#216 | — | 3 | 2 | no | — |
| 159 | C3×#216 | — | 6 | 2 | no | — |
| 160 | C3×#216 | — | 6 | 1 | no | — |
| 161 | C3×#214 | — | 3 | 2 | no | — |
| 162 | C3×#214 | — | 3 | 2 | no | — |
| 163 | C3×#214 | — | 6 | 2 | no | — |
| 164 | C3×#213 | — | 3 | 2 | no | — |
| 165 | C3×#213 | — | 6 | 1 | no | — |
| 166 | C3×Dic12 | — | 3 | 2 | no | — |
| 167 | C3×Dic12 | — | 3 | 2 | no | — |
| 168 | C3×Dic12 | — | 6 | 2 | no | — |
| 169 | C3×#204 | — | 3 | 2 | no | — |
| 170 | C3×#204 | — | 6 | 1 | no | — |
| 171 | C3×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 172 | C3×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 173 | C3×ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 174 | C3×D3×C8 | — | 3 | 2 | no | — |
| 175 | C3×D3×C8 | — | 6 | 1 | no | — |
| 176 | #3719 | — | 3 | 2 | no | — |
| 177 | #3719 | — | 3 | 2 | no | — |
| 178 | #3719 | — | 3 | 2 | no | — |
| 179 | #3719 | — | 3 | 2 | no | — |
| 180 | #3718 | — | 3 | 2 | no | — |
| 181 | #3718 | — | 3 | 2 | no | — |
| 182 | #3717 | — | 3 | 2 | no | — |
| 183 | #3716 | — | 3 | 2 | no | — |
| 184 | #3715 | — | 3 | 2 | no | — |
| 185 | #3712 | — | 3 | 1 | no | — |
| 186 | #3711 | — | 3 | 2 | no | — |
| 187 | #3710 | — | 3 | 2 | no | — |
| 188 | D3×C3⋊C8 | — | 3 | 2 | no | — |
| 189 | D3×C3⋊C8 | — | 3 | 2 | no | — |
| 190 | C22×C33 | — | 2 | 1 | no | — |
| 191 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 192 | C2×C3×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C2×C3×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 194 | C33×C4 | — | 2 | 1 | no | — |
| 195 | C33×C4 | C24 | 1 | 1 | yes | characteristic |
| 196 | C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 197 | C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 198 | C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 199 | C3×C3⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 200 | C3×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 201 | #1010 | — | 9 | 1 | no | — |
| 202 | #1010 | — | 9 | 2 | no | — |
| 203 | #1010 | — | 9 | 1 | no | — |
| 204 | #1007 | — | 9 | 2 | no | — |
| 205 | C3×#137 | — | 9 | 2 | no | — |
| 206 | C3×#135 | — | 9 | 1 | no | — |
| 207 | #951 | — | 9 | 1 | no | — |
| 208 | #951 | — | 9 | 1 | no | — |
| 209 | #950 | — | 9 | 2 | no | — |
| 210 | C2×#216 | — | 9 | 2 | no | — |
| 211 | #918 | — | 9 | 2 | no | — |
| 212 | #918 | — | 9 | 2 | no | — |
| 213 | D3×Q16 | — | 9 | 2 | no | — |
| 214 | D3×Q16 | — | 9 | 2 | no | — |
| 215 | D3×Q16 | — | 9 | 2 | no | — |
| 216 | #916 | — | 3 | 2 | no | — |
| 217 | #916 | — | 6 | 1 | no | — |
| 218 | #916 | — | 9 | 2 | no | — |
| 219 | #915 | — | 3 | 2 | no | — |
| 220 | #915 | — | 3 | 2 | no | — |
| 221 | #915 | — | 6 | 2 | no | — |
| 222 | #915 | — | 9 | 2 | no | — |
| 223 | #915 | — | 9 | 2 | no | — |
| 224 | #912 | — | 9 | 2 | no | — |
| 225 | #909 | — | 9 | 2 | no | — |
| 226 | #907 | — | 9 | 2 | no | — |
| 227 | C2×Dic12 | — | 9 | 1 | no | — |
| 228 | #901 | — | 9 | 1 | no | — |
| 229 | C32×Q8 | — | 2 | 2 | no | — |
| 230 | C32×Q8 | — | 2 | 1 | no | — |
| 231 | C32×Q8 | — | 4 | 1 | no | — |
| 232 | C32×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 233 | C32×Q8 | C22×D3 | 1 | 2 | yes | — |
| 234 | C32×D4 | — | 2 | 1 | no | — |
| 235 | C32×D4 | — | 2 | 2 | no | — |
| 236 | C32×D4 | — | 4 | 1 | no | — |
| 237 | C32×D4 | C22×D3 | 1 | 2 | yes | — |
| 238 | C32×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 239 | #638 | — | 2 | 1 | no | — |
| 240 | #638 | — | 2 | 2 | no | — |
| 241 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 242 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 243 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 244 | C4⋊(C3⋊D3) | C22×D3 | 1 | 1 | yes | characteristic |
| 245 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 246 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 247 | C4×C3⋊D3 | C22×D3 | 1 | 2 | yes | — |
| 248 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 249 | #634 | — | 2 | 2 | no | — |
| 250 | #634 | C22×D3 | 1 | 2 | yes | — |
| 251 | #634 | C22×D3 | 1 | 1 | yes | characteristic |
| 252 | #634 | C22×D3 | 1 | 2 | yes | — |
| 253 | C3×#67 | — | 6 | 2 | no | — |
| 254 | C3×#67 | — | 6 | 2 | no | — |
| 255 | C3×#67 | — | 6 | 2 | no | — |
| 256 | C3×#67 | — | 12 | 2 | no | — |
| 257 | C3×#67 | — | 12 | 1 | no | — |
| 258 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 259 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 260 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 261 | C2×C3×Dic3 | — | 12 | 2 | no | — |
| 262 | C2×C3×Dic3 | — | 12 | 1 | no | — |
| 263 | C3×D12 | — | 3 | 2 | no | — |
| 264 | C3×D12 | — | 6 | 1 | no | — |
| 265 | C3×D12 | — | 6 | 2 | no | — |
| 266 | C3×D12 | — | 12 | 1 | no | — |
| 267 | C3×C4×D3 | — | 3 | 2 | no | — |
| 268 | C3×C4×D3 | — | 3 | 2 | no | — |
| 269 | C3×C4×D3 | — | 3 | 2 | no | — |
| 270 | C3×C4×D3 | — | 6 | 1 | no | — |
| 271 | C3×C4×D3 | — | 6 | 2 | no | — |
| 272 | C3×C4×D3 | — | 6 | 2 | no | — |
| 273 | C3×C4×D3 | — | 6 | 2 | no | — |
| 274 | C3×C4×D3 | — | 6 | 2 | no | — |
| 275 | C3×C4×D3 | — | 12 | 1 | no | — |
| 276 | C3×C4×D3 | — | 12 | 2 | no | — |
| 277 | C3×Dic6 | — | 3 | 2 | no | — |
| 278 | C3×Dic6 | — | 3 | 2 | no | — |
| 279 | C3×Dic6 | — | 3 | 2 | no | — |
| 280 | C3×Dic6 | — | 3 | 2 | no | — |
| 281 | C3×Dic6 | — | 3 | 2 | no | — |
| 282 | C3×Dic6 | — | 6 | 1 | no | — |
| 283 | C3×Dic6 | — | 6 | 2 | no | — |
| 284 | C3×Dic6 | — | 6 | 2 | no | — |
| 285 | C3×Dic6 | — | 6 | 2 | no | — |
| 286 | C3×Dic6 | — | 6 | 2 | no | — |
| 287 | C3×Dic6 | — | 12 | 2 | no | — |
| 288 | #627 | — | 3 | 2 | no | — |
| 289 | #627 | — | 3 | 1 | no | — |
| 290 | #627 | — | 6 | 2 | no | — |
| 291 | #627 | — | 6 | 2 | no | — |
| 292 | #627 | — | 6 | 2 | no | — |
| 293 | #627 | — | 6 | 2 | no | — |
| 294 | #627 | — | 6 | 1 | no | — |
| 295 | #627 | — | 6 | 2 | no | — |
| 296 | #627 | — | 6 | 1 | no | — |
| 297 | #626 | — | 3 | 2 | no | — |
| 298 | #626 | — | 3 | 2 | no | — |
| 299 | #626 | — | 3 | 2 | no | — |
| 300 | #626 | — | 6 | 2 | no | — |
| 301 | #626 | — | 6 | 2 | no | — |
| 302 | #625 | — | 3 | 2 | no | — |
| 303 | #625 | — | 3 | 1 | no | — |
| 304 | #625 | — | 6 | 2 | no | — |
| 305 | #624 | — | 6 | 2 | no | — |
| 306 | #624 | — | 6 | 1 | no | — |
| 307 | #624 | — | 6 | 1 | no | — |
| 308 | #624 | — | 6 | 2 | no | — |
| 309 | D3×Dic3 | — | 6 | 2 | no | — |
| 310 | D3×Dic3 | — | 6 | 2 | no | — |
| 311 | D3×Dic3 | — | 6 | 2 | no | — |
| 312 | D3×Dic3 | — | 6 | 2 | no | — |
| 313 | D3×Dic3 | — | 6 | 2 | no | — |
| 314 | D3×Dic3 | — | 6 | 2 | no | — |
| 315 | C32×C8 | — | 2 | 1 | no | — |
| 316 | C32×C8 | — | 2 | 2 | no | — |
| 317 | C32×C8 | — | 4 | 1 | no | — |
| 318 | C32×C8 | C22×D3 | 1 | 2 | yes | — |
| 319 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 320 | C3⋊(C3⋊C8) | C22×D3 | 1 | 1 | yes | characteristic |
| 321 | C3⋊(C3⋊C8) | C22×D3 | 1 | 2 | yes | — |
| 322 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 323 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 324 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 325 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 326 | C3×C3⋊C8 | — | 6 | 2 | no | — |
| 327 | #578 | — | 27 | 1 | no | Sylow |
| 328 | C2×C33 | — | 4 | 1 | no | — |
| 329 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 330 | C3×C3⋊D3 | — | 2 | 2 | no | — |
| 331 | C3×C3⋊D3 | — | 2 | 1 | no | — |
| 332 | C3×C3⋊D3 | — | 4 | 1 | no | — |
| 333 | C3×#41 | — | 9 | 1 | no | — |
| 334 | C3×#41 | — | 9 | 2 | no | — |
| 335 | C3×#41 | — | 9 | 1 | no | — |
| 336 | C2×C3×Q8 | — | 9 | 2 | no | — |
| 337 | #239 | — | 3 | 2 | no | — |
| 338 | #239 | — | 6 | 1 | no | — |
| 339 | #239 | — | 9 | 2 | no | — |
| 340 | #239 | — | 18 | 2 | no | — |
| 341 | D3×Q8 | — | 3 | 2 | no | — |
| 342 | D3×Q8 | — | 3 | 2 | no | — |
| 343 | D3×Q8 | — | 6 | 2 | no | — |
| 344 | D3×Q8 | — | 9 | 2 | no | — |
| 345 | D3×Q8 | — | 9 | 2 | no | — |
| 346 | D3×Q8 | — | 9 | 2 | no | — |
| 347 | D3×Q8 | — | 9 | 2 | no | — |
| 348 | D3×Q8 | — | 18 | 2 | no | — |
| 349 | #237 | — | 3 | 2 | no | — |
| 350 | #237 | — | 3 | 2 | no | — |
| 351 | #237 | — | 3 | 2 | no | — |
| 352 | #237 | — | 6 | 2 | no | — |
| 353 | #237 | — | 6 | 1 | no | — |
| 354 | #237 | — | 9 | 2 | no | — |
| 355 | #237 | — | 18 | 2 | no | — |
| 356 | #237 | — | 18 | 2 | no | — |
| 357 | #237 | — | 18 | 2 | no | — |
| 358 | #237 | — | 18 | 2 | no | — |
| 359 | #235 | — | 9 | 2 | no | — |
| 360 | #235 | — | 9 | 1 | no | — |
| 361 | #235 | — | 9 | 2 | no | — |
| 362 | #235 | — | 18 | 2 | no | — |
| 363 | #235 | — | 18 | 1 | no | — |
| 364 | #235 | — | 18 | 2 | no | — |
| 365 | #235 | — | 18 | 1 | no | — |
| 366 | #235 | — | 18 | 2 | no | — |
| 367 | C2×Dic6 | — | 9 | 1 | no | — |
| 368 | C2×Dic6 | — | 9 | 1 | no | — |
| 369 | C2×Dic6 | — | 9 | 2 | no | — |
| 370 | C2×Dic6 | — | 18 | 1 | no | — |
| 371 | C2×Dic6 | — | 18 | 1 | no | — |
| 372 | C2×Dic6 | — | 18 | 2 | no | — |
| 373 | C3×Q16 | — | 9 | 1 | no | — |
| 374 | C3×Q16 | — | 9 | 2 | no | — |
| 375 | C3×Q16 | — | 9 | 2 | no | — |
| 376 | C3×SD16 | — | 2 | 2 | no | — |
| 377 | C3×SD16 | — | 2 | 1 | no | — |
| 378 | C3×SD16 | — | 4 | 1 | no | — |
| 379 | C3×SD16 | — | 9 | 2 | no | — |
| 380 | C3×SD16 | — | 9 | 1 | no | — |
| 381 | C3×SD16 | D32 | 1 | 1 | yes | characteristic |
| 382 | C3×SD16 | D32 | 1 | 2 | yes | — |
| 383 | C3×D8 | — | 9 | 1 | no | — |
| 384 | C3×M16 | — | 9 | 2 | no | — |
| 385 | C2×C3×C8 | — | 9 | 1 | no | — |
| 386 | #216 | — | 3 | 2 | no | — |
| 387 | #216 | — | 3 | 2 | no | — |
| 388 | #216 | — | 3 | 2 | no | — |
| 389 | #216 | — | 6 | 2 | no | — |
| 390 | #216 | — | 6 | 1 | no | — |
| 391 | #216 | — | 9 | 2 | no | — |
| 392 | #216 | — | 9 | 2 | no | — |
| 393 | #216 | — | 9 | 2 | no | — |
| 394 | #216 | — | 9 | 2 | no | — |
| 395 | #215 | — | 9 | 2 | no | — |
| 396 | #214 | — | 3 | 2 | no | — |
| 397 | #214 | — | 3 | 2 | no | — |
| 398 | #214 | — | 6 | 2 | no | — |
| 399 | #214 | — | 9 | 2 | no | — |
| 400 | #213 | — | 3 | 2 | no | — |
| 401 | #213 | — | 6 | 1 | no | — |
| 402 | #208 | — | 9 | 1 | no | — |
| 403 | C2×C3⋊C8 | — | 9 | 2 | no | — |
| 404 | Dic12 | — | 3 | 2 | no | — |
| 405 | Dic12 | — | 3 | 2 | no | — |
| 406 | Dic12 | — | 6 | 2 | no | — |
| 407 | Dic12 | — | 9 | 2 | no | — |
| 408 | Dic12 | — | 9 | 2 | no | — |
| 409 | #204 | — | 3 | 2 | no | — |
| 410 | #204 | — | 6 | 1 | no | — |
| 411 | #204 | — | 9 | 2 | no | — |
| 412 | ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 413 | ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 414 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 415 | ΓL(1,𝔽25) | — | 9 | 2 | no | — |
| 416 | D3×C8 | — | 3 | 2 | no | — |
| 417 | D3×C8 | — | 6 | 1 | no | — |
| 418 | D3×C8 | — | 9 | 2 | no | — |
| 419 | D3×C8 | — | 9 | 2 | no | — |
| 420 | C22×C32 | — | 2 | 1 | no | — |
| 421 | C22×C32 | — | 2 | 2 | no | — |
| 422 | C22×C32 | — | 4 | 2 | no | — |
| 423 | C22×C32 | — | 4 | 1 | no | — |
| 424 | C22×C32 | — | 8 | 1 | no | — |
| 425 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 426 | C2×C3⋊D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 427 | C2×C3⋊D3 | D3×D4 | 1 | 2 | yes | — |
| 428 | C2×C3×D3 | — | 3 | 2 | no | — |
| 429 | C2×C3×D3 | — | 3 | 2 | no | — |
| 430 | C2×C3×D3 | — | 3 | 2 | no | — |
| 431 | C2×C3×D3 | — | 6 | 2 | no | — |
| 432 | C2×C3×D3 | — | 6 | 1 | no | — |
| 433 | C2×C3×D3 | — | 6 | 2 | no | — |
| 434 | C2×C3×D3 | — | 12 | 1 | no | — |
| 435 | C32×C4 | — | 2 | 1 | no | — |
| 436 | C32×C4 | — | 2 | 2 | no | — |
| 437 | C32×C4 | — | 2 | 2 | no | — |
| 438 | C32×C4 | — | 2 | 1 | no | — |
| 439 | C32×C4 | — | 4 | 1 | no | — |
| 440 | C32×C4 | — | 4 | 2 | no | — |
| 441 | C32×C4 | — | 4 | 1 | no | — |
| 442 | C32×C4 | — | 8 | 1 | no | — |
| 443 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 444 | C32×C4 | C23×D3 | 1 | 2 | yes | — |
| 445 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 446 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 447 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 448 | C3⋊Dic3 | D3×D4 | 1 | 2 | yes | — |
| 449 | C3⋊Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 450 | C3×Dic3 | — | 3 | 2 | no | — |
| 451 | C3×Dic3 | — | 3 | 2 | no | — |
| 452 | C3×Dic3 | — | 3 | 2 | no | — |
| 453 | C3×Dic3 | — | 6 | 2 | no | — |
| 454 | C3×Dic3 | — | 6 | 1 | no | — |
| 455 | C3×Dic3 | — | 6 | 2 | no | — |
| 456 | C3×Dic3 | — | 6 | 2 | no | — |
| 457 | C3×Dic3 | — | 6 | 2 | no | — |
| 458 | C3×Dic3 | — | 6 | 2 | no | — |
| 459 | C3×Dic3 | — | 6 | 2 | no | — |
| 460 | C3×Dic3 | — | 12 | 2 | no | — |
| 461 | C3×Dic3 | — | 12 | 2 | no | — |
| 462 | C3×Dic3 | — | 12 | 1 | no | — |
| 463 | 2−1+4 | — | 27 | 1 | no | — |
| 464 | 2−1+4 | — | 27 | 1 | no | — |
| 465 | #137 | — | 9 | 2 | no | — |
| 466 | #137 | — | 27 | 2 | no | — |
| 467 | #137 | — | 27 | 1 | no | — |
| 468 | #137 | — | 27 | 1 | no | — |
| 469 | #135 | — | 9 | 1 | no | — |
| 470 | #135 | — | 27 | 2 | no | — |
| 471 | C2×Q16 | — | 27 | 1 | no | — |
| 472 | C2×Q16 | — | 27 | 2 | no | — |
| 473 | #131 | — | 27 | 1 | no | — |
| 474 | C33 | #578 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 475 | C3×Q8 | — | 2 | 2 | no | — |
| 476 | C3×Q8 | — | 2 | 1 | no | — |
| 477 | C3×Q8 | — | 4 | 1 | no | — |
| 478 | C3×Q8 | — | 9 | 2 | no | — |
| 479 | C3×Q8 | — | 9 | 1 | no | — |
| 480 | C3×Q8 | — | 9 | 2 | no | — |
| 481 | C3×Q8 | — | 18 | 2 | no | — |
| 482 | C3×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 483 | C3×Q8 | C2×D32 | 1 | 2 | yes | — |
| 484 | C3×D4 | — | 2 | 1 | no | — |
| 485 | C3×D4 | — | 2 | 2 | no | — |
| 486 | C3×D4 | — | 4 | 1 | no | — |
| 487 | C3×D4 | — | 9 | 1 | no | — |
| 488 | C3×D4 | — | 18 | 1 | no | — |
| 489 | C3×D4 | — | 18 | 1 | no | — |
| 490 | C3×D4 | — | 18 | 2 | no | — |
| 491 | C3×D4 | C2×D32 | 1 | 2 | yes | — |
| 492 | C3×D4 | C2×D32 | 1 | 1 | yes | characteristic |
| 493 | C2×C3×C4 | — | 9 | 2 | no | — |
| 494 | C2×C3×C4 | — | 9 | 1 | no | — |
| 495 | C2×C3×C4 | — | 18 | 1 | no | — |
| 496 | C2×C3×C4 | — | 18 | 2 | no | — |
| 497 | C2×C3×C4 | — | 18 | 1 | no | — |
| 498 | C2×C3×C4 | — | 18 | 2 | no | — |
| 499 | #67 | — | 6 | 2 | no | — |
| 500 | #67 | — | 6 | 2 | no | — |
| 501 | #67 | — | 6 | 2 | no | — |
| 502 | #67 | — | 9 | 2 | no | — |
| 503 | #67 | — | 9 | 2 | no | — |
| 504 | #67 | — | 9 | 2 | no | — |
| 505 | #67 | — | 12 | 2 | no | — |
| 506 | #67 | — | 12 | 1 | no | — |
| 507 | #67 | — | 18 | 2 | no | — |
| 508 | #67 | — | 18 | 2 | no | — |
| 509 | C2×Dic3 | — | 6 | 2 | no | — |
| 510 | C2×Dic3 | — | 6 | 2 | no | — |
| 511 | C2×Dic3 | — | 6 | 2 | no | — |
| 512 | C2×Dic3 | — | 12 | 2 | no | — |
| 513 | C2×Dic3 | — | 12 | 1 | no | — |
| 514 | C2×Dic3 | — | 18 | 2 | no | — |
| 515 | C2×Dic3 | — | 18 | 1 | no | — |
| 516 | C2×Dic3 | — | 18 | 1 | no | — |
| 517 | C2×Dic3 | — | 18 | 2 | no | — |
| 518 | D12 | — | 3 | 2 | no | — |
| 519 | D12 | — | 6 | 1 | no | — |
| 520 | D12 | — | 6 | 2 | no | — |
| 521 | D12 | — | 9 | 1 | no | — |
| 522 | D12 | — | 9 | 2 | no | — |
| 523 | D12 | — | 12 | 1 | no | — |
| 524 | D12 | — | 18 | 2 | no | — |
| 525 | C4×D3 | — | 3 | 2 | no | — |
| 526 | C4×D3 | — | 3 | 2 | no | — |
| 527 | C4×D3 | — | 3 | 2 | no | — |
| 528 | C4×D3 | — | 6 | 1 | no | — |
| 529 | C4×D3 | — | 6 | 2 | no | — |
| 530 | C4×D3 | — | 6 | 2 | no | — |
| 531 | C4×D3 | — | 6 | 2 | no | — |
| 532 | C4×D3 | — | 6 | 2 | no | — |
| 533 | C4×D3 | — | 12 | 1 | no | — |
| 534 | C4×D3 | — | 12 | 2 | no | — |
| 535 | C4×D3 | — | 18 | 2 | no | — |
| 536 | C4×D3 | — | 18 | 2 | no | — |
| 537 | C4×D3 | — | 18 | 2 | no | — |
| 538 | C4×D3 | — | 18 | 2 | no | — |
| 539 | C4×D3 | — | 18 | 2 | no | — |
| 540 | C4×D3 | — | 18 | 2 | no | — |
| 541 | Dic6 | — | 3 | 2 | no | — |
| 542 | Dic6 | — | 3 | 2 | no | — |
| 543 | Dic6 | — | 3 | 2 | no | — |
| 544 | Dic6 | — | 3 | 2 | no | — |
| 545 | Dic6 | — | 3 | 2 | no | — |
| 546 | Dic6 | — | 6 | 1 | no | — |
| 547 | Dic6 | — | 6 | 2 | no | — |
| 548 | Dic6 | — | 6 | 2 | no | — |
| 549 | Dic6 | — | 6 | 2 | no | — |
| 550 | Dic6 | — | 6 | 2 | no | — |
| 551 | Dic6 | — | 9 | 1 | no | — |
| 552 | Dic6 | — | 9 | 2 | no | — |
| 553 | Dic6 | — | 12 | 2 | no | — |
| 554 | Dic6 | — | 18 | 2 | no | — |
| 555 | Dic6 | — | 18 | 2 | no | — |
| 556 | Dic6 | — | 18 | 2 | no | — |
| 557 | Dic6 | — | 18 | 2 | no | — |
| 558 | Dic6 | — | 18 | 1 | no | — |
| 559 | Dic6 | — | 18 | 1 | no | — |
| 560 | Dic6 | — | 18 | 2 | no | — |
| 561 | C3×C8 | — | 2 | 1 | no | — |
| 562 | C3×C8 | — | 2 | 2 | no | — |
| 563 | C3×C8 | — | 4 | 1 | no | — |
| 564 | C3×C8 | — | 9 | 1 | no | — |
| 565 | C3×C8 | — | 9 | 2 | no | — |
| 566 | C3×C8 | C2×D32 | 1 | 2 | yes | — |
| 567 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 568 | C3⋊C8 | — | 3 | 2 | no | — |
| 569 | C3⋊C8 | — | 3 | 2 | no | — |
| 570 | C3⋊C8 | — | 3 | 2 | no | — |
| 571 | C3⋊C8 | — | 6 | 1 | no | — |
| 572 | C3⋊C8 | — | 6 | 2 | no | — |
| 573 | C2×C32 | — | 2 | 2 | no | — |
| 574 | C2×C32 | — | 2 | 1 | no | — |
| 575 | C2×C32 | — | 4 | 1 | no | — |
| 576 | C2×C32 | — | 4 | 1 | no | — |
| 577 | C2×C32 | — | 4 | 2 | no | — |
| 578 | C2×C32 | — | 8 | 1 | no | — |
| 579 | C2×C32 | — | 8 | 2 | no | — |
| 580 | C2×C32 | — | 16 | 1 | no | — |
| 581 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 582 | C2×C32 | C2×D3×D4 | 1 | 2 | yes | — |
| 583 | C3⋊D3 | — | 2 | 1 | no | — |
| 584 | C3⋊D3 | — | 2 | 2 | no | — |
| 585 | C3⋊D3 | — | 4 | 1 | no | — |
| 586 | C3×D3 | — | 6 | 2 | no | — |
| 587 | C3×D3 | — | 6 | 2 | no | — |
| 588 | C3×D3 | — | 6 | 2 | no | — |
| 589 | C3×D3 | — | 12 | 1 | no | — |
| 590 | C3×D3 | — | 12 | 2 | no | — |
| 591 | C3×D3 | — | 12 | 2 | no | — |
| 592 | C3×D3 | — | 24 | 1 | no | — |
| 593 | #41 | — | 9 | 1 | no | — |
| 594 | #41 | — | 9 | 1 | no | — |
| 595 | #41 | — | 9 | 2 | no | — |
| 596 | #41 | — | 27 | 1 | no | — |
| 597 | #41 | — | 27 | 2 | no | — |
| 598 | #41 | — | 54 | 1 | no | — |
| 599 | #41 | — | 54 | 1 | no | — |
| 600 | #41 | — | 54 | 2 | no | — |
| 601 | #41 | — | 54 | 2 | no | — |
| 602 | C2×Q8 | — | 9 | 2 | no | — |
| 603 | C2×Q8 | — | 27 | 1 | no | — |
| 604 | C2×Q8 | — | 27 | 1 | no | — |
| 605 | C2×Q8 | — | 27 | 2 | no | — |
| 606 | C2×Q8 | — | 54 | 1 | no | — |
| 607 | C2×Q8 | — | 54 | 1 | no | — |
| 608 | Q16 | — | 9 | 1 | no | — |
| 609 | Q16 | — | 9 | 2 | no | — |
| 610 | Q16 | — | 9 | 2 | no | — |
| 611 | Q16 | — | 27 | 2 | no | — |
| 612 | Q16 | — | 27 | 2 | no | — |
| 613 | SD16 | — | 9 | 2 | no | — |
| 614 | SD16 | — | 9 | 1 | no | — |
| 615 | SD16 | — | 27 | 2 | no | — |
| 616 | SD16 | #1113 | 1 | 1 | yes | characteristic |
| 617 | D8 | — | 9 | 1 | no | — |
| 618 | M16 | — | 9 | 2 | no | — |
| 619 | M16 | — | 27 | 1 | no | — |
| 620 | C2×C8 | — | 9 | 1 | no | — |
| 621 | C2×C8 | — | 27 | 2 | no | — |
| 622 | C22×C3 | — | 2 | 1 | no | — |
| 623 | C22×C3 | — | 2 | 2 | no | — |
| 624 | C22×C3 | — | 4 | 2 | no | — |
| 625 | C22×C3 | — | 4 | 1 | no | — |
| 626 | C22×C3 | — | 8 | 1 | no | — |
| 627 | C22×C3 | — | 9 | 1 | no | — |
| 628 | C22×C3 | — | 9 | 2 | no | — |
| 629 | C22×C3 | — | 18 | 1 | no | — |
| 630 | C2×D3 | — | 3 | 2 | no | — |
| 631 | C2×D3 | — | 3 | 2 | no | — |
| 632 | C2×D3 | — | 3 | 2 | no | — |
| 633 | C2×D3 | — | 6 | 2 | no | — |
| 634 | C2×D3 | — | 6 | 1 | no | — |
| 635 | C2×D3 | — | 6 | 2 | no | — |
| 636 | C2×D3 | — | 12 | 1 | no | — |
| 637 | C3×C4 | — | 2 | 1 | no | — |
| 638 | C3×C4 | — | 2 | 2 | no | — |
| 639 | C3×C4 | — | 2 | 2 | no | — |
| 640 | C3×C4 | — | 2 | 1 | no | — |
| 641 | C3×C4 | — | 4 | 2 | no | — |
| 642 | C3×C4 | — | 4 | 1 | no | — |
| 643 | C3×C4 | — | 4 | 1 | no | — |
| 644 | C3×C4 | — | 8 | 1 | no | — |
| 645 | C3×C4 | — | 9 | 1 | no | — |
| 646 | C3×C4 | — | 9 | 2 | no | — |
| 647 | C3×C4 | — | 18 | 1 | no | — |
| 648 | C3×C4 | — | 18 | 2 | no | — |
| 649 | C3×C4 | — | 18 | 2 | no | — |
| 650 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 651 | C3×C4 | C22×D32 | 1 | 2 | yes | — |
| 652 | Dic3 | — | 3 | 2 | no | — |
| 653 | Dic3 | — | 3 | 2 | no | — |
| 654 | Dic3 | — | 3 | 2 | no | — |
| 655 | Dic3 | — | 6 | 2 | no | — |
| 656 | Dic3 | — | 6 | 1 | no | — |
| 657 | Dic3 | — | 6 | 2 | no | — |
| 658 | Dic3 | — | 6 | 2 | no | — |
| 659 | Dic3 | — | 6 | 2 | no | — |
| 660 | Dic3 | — | 6 | 2 | no | — |
| 661 | Dic3 | — | 6 | 2 | no | — |
| 662 | Dic3 | — | 12 | 2 | no | — |
| 663 | Dic3 | — | 12 | 2 | no | — |
| 664 | Dic3 | — | 12 | 1 | no | — |
| 665 | C32 | — | 2 | 1 | no | — |
| 666 | C32 | — | 2 | 2 | no | — |
| 667 | C32 | — | 4 | 1 | no | — |
| 668 | C32 | #5771 | 1 | 1 | yes | characteristic, complemented |
| 669 | C32 | #5779 | 1 | 2 | yes | complemented |
| 670 | Q8 | — | 9 | 2 | no | — |
| 671 | Q8 | — | 9 | 1 | no | — |
| 672 | Q8 | — | 9 | 2 | no | — |
| 673 | Q8 | — | 18 | 2 | no | — |
| 674 | Q8 | — | 27 | 1 | no | — |
| 675 | Q8 | — | 54 | 1 | no | — |
| 676 | Q8 | — | 54 | 1 | no | — |
| 677 | Q8 | — | 54 | 2 | no | — |
| 678 | Q8 | C2×#1113 | 1 | 1 | yes | characteristic |
| 679 | D4 | — | 9 | 1 | no | — |
| 680 | D4 | — | 18 | 1 | no | — |
| 681 | D4 | — | 18 | 2 | no | — |
| 682 | D4 | — | 18 | 1 | no | — |
| 683 | D4 | — | 27 | 1 | no | — |
| 684 | D4 | — | 27 | 2 | no | — |
| 685 | D4 | — | 54 | 2 | no | — |
| 686 | D4 | C2×#1113 | 1 | 1 | yes | characteristic |
| 687 | C2×C4 | — | 9 | 1 | no | — |
| 688 | C2×C4 | — | 9 | 2 | no | — |
| 689 | C2×C4 | — | 18 | 1 | no | — |
| 690 | C2×C4 | — | 18 | 2 | no | — |
| 691 | C2×C4 | — | 18 | 1 | no | — |
| 692 | C2×C4 | — | 18 | 2 | no | — |
| 693 | C2×C4 | — | 54 | 2 | no | — |
| 694 | C2×C4 | — | 54 | 2 | no | — |
| 695 | C2×C4 | — | 54 | 1 | no | — |
| 696 | C2×C4 | — | 54 | 1 | no | — |
| 697 | C8 | — | 9 | 1 | no | — |
| 698 | C8 | — | 9 | 2 | no | — |
| 699 | C8 | C2×#1113 | 1 | 1 | yes | characteristic |
| 700 | C2×C3 | — | 2 | 2 | no | — |
| 701 | C2×C3 | — | 2 | 1 | no | — |
| 702 | C2×C3 | — | 4 | 1 | no | — |
| 703 | C2×C3 | — | 4 | 2 | no | — |
| 704 | C2×C3 | — | 4 | 1 | no | — |
| 705 | C2×C3 | — | 8 | 1 | no | — |
| 706 | C2×C3 | — | 8 | 2 | no | — |
| 707 | C2×C3 | — | 16 | 1 | no | — |
| 708 | C2×C3 | — | 18 | 1 | no | — |
| 709 | C2×C3 | — | 18 | 2 | no | — |
| 710 | C2×C3 | — | 36 | 1 | no | — |
| 711 | C2×C3 | D32×D4 | 1 | 1 | yes | characteristic |
| 712 | C2×C3 | D32×D4 | 1 | 2 | yes | — |
| 713 | D3 | — | 6 | 2 | no | — |
| 714 | D3 | — | 6 | 2 | no | — |
| 715 | D3 | — | 6 | 2 | no | — |
| 716 | D3 | — | 12 | 1 | no | — |
| 717 | D3 | — | 12 | 2 | no | — |
| 718 | D3 | — | 12 | 2 | no | — |
| 719 | D3 | — | 24 | 1 | no | — |
| 720 | C22 | — | 2 | 1 | no | — |
| 721 | C22 | — | 9 | 2 | no | — |
| 722 | C22 | — | 9 | 1 | no | — |
| 723 | C22 | — | 18 | 1 | no | — |
| 724 | C4 | — | 2 | 1 | no | — |
| 725 | C4 | — | 9 | 1 | no | — |
| 726 | C4 | — | 9 | 2 | no | — |
| 727 | C4 | — | 18 | 1 | no | — |
| 728 | C4 | — | 18 | 2 | no | — |
| 729 | C4 | — | 18 | 2 | no | — |
| 730 | C4 | C22×#1113 | 1 | 1 | yes | characteristic |
| 731 | C3 | — | 2 | 1 | no | — |
| 732 | C3 | — | 2 | 2 | no | — |
| 733 | C3 | — | 4 | 1 | no | — |
| 734 | C3 | #10594752 | 1 | 1 | yes | characteristic, complemented |
| 735 | C3 | #10594756 | 1 | 2 | yes | complemented |
| 736 | C2 | — | 4 | 1 | no | — |
| 737 | C2 | — | 18 | 2 | no | — |
| 738 | C2 | — | 18 | 1 | no | — |
| 739 | C2 | — | 36 | 1 | no | — |
| 740 | C2 | D4×#1113 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×#1113 |
| commutator, cosocle | C33×C4 | C24 |
| Frattini | C4 | C22×#1113 |
| Fitting | C33×SD16 | C22 |
| socle | C2×C33 | C22×D4 |
| hypercenter | SD16 | #1113 |
| hypocenter | C33 | #578 |
| LCS | G ▷ C33×C4 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ SD16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11724624 | C2 | semidirect |
| 2. #11724620 | C2 | semidirect |
| 3. C3×#64125 | C2 | semidirect |
| 4. C3×#64124 | C2 | semidirect |
| 5. #11723711 | C2 | semidirect |
| 6. #11723710 | C2 | semidirect |
| 7. #11723707 | C2 | semidirect |
| 8. #11723705 | C2 | semidirect |
| 9. #11723652 | C2 | semidirect |
| 10. #11723650 | C2 | semidirect |
| 11. #11723649 | C2 | semidirect |
| 47. #64125 | D3 | semidirect |
| 48. #64124 | D3 | semidirect |
| 474. C33 | #578 | semidirect |
| 668. C32 | #5771 | semidirect |
| 669. C32 | #5779 | semidirect |
| 734. C3 | #10594752 | semidirect |
| 735. C3 | #10594756 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724624 | 2 |
| #11724620 | 2 |
| C3×#64125 | 2 |
| C3×#64124 | 2 |
| #11723711 | 2 |
| #11723710 | 2 |
| #11723707 | 2 |
| #11723705 | 2 |
| #11723652 | 2 |
| #11723650 | 2 |
| #11723649 | 2 |
| #10594756 | 3 |
| #10594752 | 3 |