Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
928 conjugacy classes of subgroups.
The subgroup lattice has 928 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11722517 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11722516 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11721807 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #64127⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | Q16×(C3⋊D3)⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11721238 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11721236 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11721235 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11721234 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11721230 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11721226 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #11720854 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #11720853 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #11720845 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #11720841 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #10594769 | — | 3 | 1 | no | maximal |
| 17 | #10594766 | — | 3 | 1 | no | maximal |
| 18 | #88748 | C22 | 1 | 1 | yes | characteristic |
| 19 | Q8×#272 | C22 | 1 | 1 | yes | characteristic |
| 20 | #88722 | C22 | 1 | 1 | yes | characteristic |
| 21 | Q8×(C3⋊D3)⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 22 | Q8×(C3⋊D3)⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 23 | Q8×(C3⋊D3)⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 24 | #88652 | — | 2 | 1 | no | — |
| 25 | #88652 | — | 2 | 1 | no | — |
| 26 | #88652 | C22 | 1 | 1 | yes | characteristic |
| 27 | #88652 | C22 | 1 | 1 | yes | characteristic |
| 28 | #88651 | — | 2 | 1 | no | — |
| 29 | #88651 | C22 | 1 | 1 | yes | characteristic |
| 30 | #88650 | — | 2 | 1 | no | — |
| 31 | #88650 | — | 2 | 1 | no | — |
| 32 | #88650 | C22 | 1 | 1 | yes | characteristic |
| 33 | #88649 | — | 2 | 1 | no | — |
| 34 | #88649 | C22 | 1 | 1 | yes | characteristic |
| 35 | #88648 | — | 2 | 1 | no | — |
| 36 | #88648 | C22 | 1 | 1 | yes | characteristic |
| 37 | ((C3⋊D3)⋊C3)⋊Q8 | — | 2 | 1 | no | — |
| 38 | ((C3⋊D3)⋊C3)⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 39 | Q16×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 40 | #88550 | C22 | 1 | 1 | yes | characteristic |
| 41 | #88549 | C22 | 1 | 1 | yes | characteristic |
| 42 | #88528 | C22 | 1 | 1 | yes | characteristic |
| 43 | #88527 | C22 | 1 | 1 | yes | characteristic |
| 44 | #3755⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 45 | #3756⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 46 | #3756⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 47 | #3756⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 48 | #3744⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 49 | #3743⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 50 | C8×(C3⋊D3)⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 51 | #3746⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 52 | #88439 | C22 | 1 | 1 | yes | characteristic |
| 53 | #88439 | C22 | 1 | 1 | yes | characteristic |
| 54 | #88437 | C22 | 1 | 1 | yes | characteristic |
| 55 | #88436 | C22 | 1 | 1 | yes | characteristic |
| 56 | #88434 | C22 | 1 | 1 | yes | characteristic |
| 57 | #88433 | C22 | 1 | 1 | yes | characteristic |
| 58 | #88431 | C22 | 1 | 1 | yes | characteristic |
| 59 | #88430 | C22 | 1 | 1 | yes | characteristic |
| 60 | ((C3⋊D3)⋊C3)⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 61 | #64316 | — | 3 | 1 | no | — |
| 62 | #64315 | — | 3 | 1 | no | — |
| 63 | #64315 | — | 3 | 1 | no | — |
| 64 | #64315 | — | 3 | 1 | no | — |
| 65 | #64127 | D3 | 1 | 1 | yes | characteristic, complemented |
| 66 | Q16×C3⋊D3 | D3 | 1 | 1 | yes | characteristic, complemented |
| 67 | C3×#918 | — | 3 | 1 | no | — |
| 68 | C3×#918 | — | 3 | 1 | no | — |
| 69 | C3×#918 | — | 3 | 1 | no | — |
| 70 | C3×#918 | — | 6 | 1 | no | — |
| 71 | C3×D3×Q16 | — | 3 | 1 | no | — |
| 72 | #63951 | — | 3 | 1 | no | — |
| 73 | #63951 | — | 3 | 1 | no | — |
| 74 | #63950 | — | 3 | 1 | no | — |
| 75 | #63949 | — | 3 | 1 | no | — |
| 76 | #63948 | — | 3 | 1 | no | — |
| 77 | #63947 | — | 3 | 1 | no | — |
| 78 | #63947 | — | 3 | 1 | no | — |
| 79 | #63946 | — | 3 | 1 | no | — |
| 80 | #63944 | — | 3 | 1 | no | — |
| 81 | D3×#216 | — | 3 | 1 | no | — |
| 82 | D3×#216 | — | 3 | 1 | no | — |
| 83 | D3×#216 | — | 3 | 1 | no | — |
| 84 | #63811 | — | 3 | 1 | no | — |
| 85 | #63809 | — | 3 | 1 | no | — |
| 86 | #63806 | — | 3 | 1 | no | — |
| 87 | #63805 | — | 3 | 1 | no | — |
| 88 | #63804 | — | 3 | 1 | no | — |
| 89 | #63801 | — | 3 | 1 | no | — |
| 90 | #63800 | — | 3 | 1 | no | — |
| 91 | #63800 | — | 3 | 1 | no | — |
| 92 | Q8×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 93 | Q8×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 94 | C4⋊#272 | — | 2 | 1 | no | — |
| 95 | C4⋊#272 | C23 | 1 | 1 | yes | characteristic |
| 96 | C4×#272 | — | 2 | 1 | no | — |
| 97 | C4×#272 | — | 2 | 1 | no | — |
| 98 | C4×#272 | C23 | 1 | 1 | yes | characteristic |
| 99 | #6229 | — | 2 | 1 | no | — |
| 100 | #6229 | C23 | 1 | 1 | yes | characteristic |
| 101 | C4⋊((C3⋊D3)⋊C3) | — | 2 | 1 | no | — |
| 102 | C4⋊((C3⋊D3)⋊C3) | C23 | 1 | 1 | yes | characteristic |
| 103 | C4×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 104 | C4×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 105 | C4×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 106 | C4×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 107 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 108 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 109 | #634⋊C3 | — | 2 | 1 | no | — |
| 110 | #634⋊C3 | — | 2 | 1 | no | — |
| 111 | #634⋊C3 | — | 2 | 1 | no | — |
| 112 | #634⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 113 | #634⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 114 | #634⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 115 | #6200 | — | 2 | 1 | no | — |
| 116 | #6200 | — | 2 | 1 | no | — |
| 117 | #6200 | — | 2 | 1 | no | — |
| 118 | #6200 | D4 | 1 | 1 | yes | characteristic |
| 119 | #6200 | D4 | 1 | 1 | yes | characteristic |
| 120 | #6199 | — | 2 | 1 | no | — |
| 121 | #6199 | — | 2 | 1 | no | — |
| 122 | #6199 | — | 2 | 1 | no | — |
| 123 | #6198 | — | 2 | 1 | no | — |
| 124 | #6198 | D4 | 1 | 1 | yes | characteristic |
| 125 | ((C3⋊D3)⋊C3)⋊C4 | — | 2 | 1 | no | — |
| 126 | ((C3⋊D3)⋊C3)⋊C4 | — | 2 | 1 | no | — |
| 127 | ((C3⋊D3)⋊C3)⋊C4 | — | 2 | 1 | no | — |
| 128 | #6196 | — | 2 | 1 | no | — |
| 129 | #6196 | — | 2 | 1 | no | — |
| 130 | #6196 | D4 | 1 | 1 | yes | characteristic |
| 131 | C8×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 132 | #6180 | C23 | 1 | 1 | yes | characteristic |
| 133 | (C3⋊(C3⋊C8))⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 134 | (C3⋊(C3⋊C8))⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 135 | #5779 | — | 9 | 1 | no | — |
| 136 | #5779 | — | 9 | 1 | no | — |
| 137 | #5766 | — | 9 | 1 | no | — |
| 138 | #3832 | C2×D3 | 1 | 1 | yes | characteristic |
| 139 | Q8×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 140 | Q8×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 141 | Q8×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 142 | C3×#239 | — | 3 | 1 | no | — |
| 143 | C3×#239 | — | 3 | 1 | no | — |
| 144 | C3×#239 | — | 3 | 1 | no | — |
| 145 | C3×#239 | — | 6 | 1 | no | — |
| 146 | C3×D3×Q8 | — | 3 | 1 | no | — |
| 147 | C3×D3×Q8 | — | 3 | 1 | no | — |
| 148 | C3×D3×Q8 | — | 3 | 1 | no | — |
| 149 | C3×D3×Q8 | — | 3 | 1 | no | — |
| 150 | C3×D3×Q8 | — | 3 | 1 | no | — |
| 151 | C3×D3×Q8 | — | 6 | 1 | no | — |
| 152 | #3799 | — | 3 | 1 | no | — |
| 153 | #3799 | — | 3 | 1 | no | — |
| 154 | #3799 | — | 6 | 1 | no | — |
| 155 | #3799 | — | 6 | 1 | no | — |
| 156 | #3798 | — | 3 | 1 | no | — |
| 157 | #3798 | — | 3 | 1 | no | — |
| 158 | #3798 | — | 6 | 1 | no | — |
| 159 | #3798 | — | 6 | 1 | no | — |
| 160 | #3798 | — | 6 | 1 | no | — |
| 161 | #3798 | — | 6 | 1 | no | — |
| 162 | #3797 | — | 3 | 1 | no | — |
| 163 | #3797 | — | 6 | 1 | no | — |
| 164 | #3796 | — | 3 | 1 | no | — |
| 165 | #3796 | — | 3 | 1 | no | — |
| 166 | #3796 | — | 3 | 1 | no | — |
| 167 | #3796 | — | 6 | 1 | no | — |
| 168 | #3796 | — | 6 | 1 | no | — |
| 169 | #3796 | — | 6 | 1 | no | — |
| 170 | #3795 | — | 3 | 1 | no | — |
| 171 | #3795 | — | 3 | 1 | no | — |
| 172 | #3795 | — | 3 | 1 | no | — |
| 173 | #3795 | — | 6 | 1 | no | — |
| 174 | #3795 | — | 6 | 1 | no | — |
| 175 | #3795 | — | 6 | 1 | no | — |
| 176 | D3×Dic6 | — | 3 | 1 | no | — |
| 177 | D3×Dic6 | — | 3 | 1 | no | — |
| 178 | D3×Dic6 | — | 3 | 1 | no | — |
| 179 | D3×Dic6 | — | 6 | 1 | no | — |
| 180 | D3×Dic6 | — | 6 | 1 | no | — |
| 181 | D3×Dic6 | — | 6 | 1 | no | — |
| 182 | C32×Q16 | — | 2 | 1 | no | — |
| 183 | C32×Q16 | C2×D3 | 1 | 1 | yes | characteristic |
| 184 | C32×Q16 | C2×D3 | 1 | 1 | yes | characteristic |
| 185 | #3756 | C2×D3 | 1 | 1 | yes | characteristic |
| 186 | #3756 | C2×D3 | 1 | 1 | yes | characteristic |
| 187 | #3756 | C2×D3 | 1 | 1 | yes | characteristic |
| 188 | #3755 | C2×D3 | 1 | 1 | yes | characteristic |
| 189 | #3746 | C2×D3 | 1 | 1 | yes | characteristic |
| 190 | #3744 | C2×D3 | 1 | 1 | yes | characteristic |
| 191 | #3743 | C2×D3 | 1 | 1 | yes | characteristic |
| 192 | C8×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 193 | C3×#216 | — | 3 | 1 | no | — |
| 194 | C3×#216 | — | 3 | 1 | no | — |
| 195 | C3×#216 | — | 3 | 1 | no | — |
| 196 | C3×#216 | — | 3 | 1 | no | — |
| 197 | C3×#216 | — | 3 | 1 | no | — |
| 198 | C3×#216 | — | 6 | 1 | no | — |
| 199 | C3×#215 | — | 3 | 1 | no | — |
| 200 | C3×#215 | — | 3 | 1 | no | — |
| 201 | C3×#215 | — | 3 | 1 | no | — |
| 202 | C3×#215 | — | 6 | 1 | no | — |
| 203 | C3×Dic12 | — | 3 | 1 | no | — |
| 204 | C3×#204 | — | 3 | 1 | no | — |
| 205 | C3×#204 | — | 3 | 1 | no | — |
| 206 | C3×#204 | — | 3 | 1 | no | — |
| 207 | C3×#204 | — | 6 | 1 | no | — |
| 208 | C3×ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 209 | C3×ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 210 | C3×ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 211 | C3×ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 212 | C3×D3×C8 | — | 3 | 1 | no | — |
| 213 | #3719 | — | 3 | 1 | no | — |
| 214 | #3719 | — | 3 | 1 | no | — |
| 215 | #3719 | — | 3 | 1 | no | — |
| 216 | #3719 | — | 3 | 1 | no | — |
| 217 | #3718 | — | 3 | 1 | no | — |
| 218 | #3718 | — | 3 | 1 | no | — |
| 219 | #3717 | — | 3 | 1 | no | — |
| 220 | #3716 | — | 3 | 1 | no | — |
| 221 | #3716 | — | 3 | 1 | no | — |
| 222 | #3715 | — | 3 | 1 | no | — |
| 223 | #3714 | — | 3 | 1 | no | — |
| 224 | #3713 | — | 3 | 1 | no | — |
| 225 | #3712 | — | 3 | 1 | no | — |
| 226 | #3711 | — | 3 | 1 | no | — |
| 227 | #3710 | — | 3 | 1 | no | — |
| 228 | D3×C3⋊C8 | — | 3 | 1 | no | — |
| 229 | D3×C3⋊C8 | — | 3 | 1 | no | — |
| 230 | D3×C3⋊C8 | — | 3 | 1 | no | — |
| 231 | C2×#272 | — | 2 | 1 | no | — |
| 232 | C2×#272 | C2×D4 | 1 | 1 | yes | characteristic |
| 233 | C2×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 234 | C2×(C3⋊D3)⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 235 | C2×(C3⋊D3)⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 236 | C4×H(3,𝔽3) | — | 2 | 1 | no | — |
| 237 | C4×H(3,𝔽3) | — | 2 | 1 | no | — |
| 238 | C4×H(3,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 239 | #1084 | — | 2 | 1 | no | — |
| 240 | #1084 | C2×D4 | 1 | 1 | yes | characteristic |
| 241 | (C3⋊Dic3)⋊C3 | — | 2 | 1 | no | — |
| 242 | (C3⋊Dic3)⋊C3 | — | 2 | 1 | no | — |
| 243 | (C3⋊Dic3)⋊C3 | — | 2 | 1 | no | — |
| 244 | (C3⋊Dic3)⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 245 | (C3⋊Dic3)⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 246 | #1010 | — | 9 | 1 | no | — |
| 247 | #1010 | — | 9 | 1 | no | — |
| 248 | #1007 | — | 9 | 1 | no | — |
| 249 | #1007 | — | 9 | 1 | no | — |
| 250 | #1007 | — | 9 | 1 | no | — |
| 251 | #1007 | — | 9 | 1 | no | — |
| 252 | C3×#137 | — | 9 | 1 | no | — |
| 253 | C3×#137 | — | 9 | 1 | no | — |
| 254 | C2×C3×Q16 | — | 9 | 1 | no | — |
| 255 | #950 | — | 9 | 1 | no | — |
| 256 | #950 | — | 9 | 1 | no | — |
| 257 | C2×#216 | — | 9 | 1 | no | — |
| 258 | C2×#216 | — | 9 | 1 | no | — |
| 259 | #942 | — | 9 | 1 | no | — |
| 260 | #942 | — | 9 | 1 | no | — |
| 261 | #919 | — | 9 | 1 | no | — |
| 262 | #919 | — | 9 | 1 | no | — |
| 263 | #918 | — | 3 | 1 | no | — |
| 264 | #918 | — | 3 | 1 | no | — |
| 265 | #918 | — | 3 | 1 | no | — |
| 266 | #918 | — | 6 | 1 | no | — |
| 267 | #918 | — | 9 | 1 | no | — |
| 268 | #918 | — | 9 | 1 | no | — |
| 269 | #918 | — | 9 | 1 | no | — |
| 270 | #918 | — | 9 | 1 | no | — |
| 271 | #918 | — | 9 | 1 | no | — |
| 272 | D3×Q16 | — | 3 | 1 | no | — |
| 273 | D3×Q16 | — | 9 | 1 | no | — |
| 274 | D3×Q16 | — | 9 | 1 | no | — |
| 275 | D3×Q16 | — | 9 | 1 | no | — |
| 276 | D3×Q16 | — | 9 | 1 | no | — |
| 277 | D3×Q16 | — | 9 | 1 | no | — |
| 278 | #916 | — | 9 | 1 | no | — |
| 279 | #916 | — | 9 | 1 | no | — |
| 280 | #916 | — | 9 | 1 | no | — |
| 281 | #916 | — | 9 | 1 | no | — |
| 282 | #915 | — | 9 | 1 | no | — |
| 283 | #915 | — | 9 | 1 | no | — |
| 284 | #915 | — | 9 | 1 | no | — |
| 285 | #915 | — | 9 | 1 | no | — |
| 286 | #909 | — | 9 | 1 | no | — |
| 287 | #909 | — | 9 | 1 | no | — |
| 288 | #907 | — | 9 | 1 | no | — |
| 289 | #907 | — | 9 | 1 | no | — |
| 290 | #904 | — | 9 | 1 | no | — |
| 291 | #901 | — | 9 | 1 | no | — |
| 292 | C32×Q8 | — | 2 | 1 | no | — |
| 293 | C32×Q8 | — | 2 | 1 | no | — |
| 294 | C32×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 295 | C32×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 296 | C32×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 297 | C32×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 298 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 299 | C4⋊(C3⋊D3) | C22×D3 | 1 | 1 | yes | characteristic |
| 300 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 301 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 302 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 303 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 304 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 305 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 306 | #634 | — | 2 | 1 | no | — |
| 307 | #634 | — | 2 | 1 | no | — |
| 308 | #634 | — | 2 | 1 | no | — |
| 309 | #634 | C22×D3 | 1 | 1 | yes | characteristic |
| 310 | #634 | C22×D3 | 1 | 1 | yes | characteristic |
| 311 | #634 | C22×D3 | 1 | 1 | yes | characteristic |
| 312 | C3×D12 | — | 3 | 1 | no | — |
| 313 | C3×D12 | — | 3 | 1 | no | — |
| 314 | C3×D12 | — | 3 | 1 | no | — |
| 315 | C3×D12 | — | 6 | 1 | no | — |
| 316 | C3×D12 | — | 6 | 1 | no | — |
| 317 | C3×D12 | — | 6 | 1 | no | — |
| 318 | C3×D12 | — | 6 | 1 | no | — |
| 319 | C3×D12 | — | 12 | 1 | no | — |
| 320 | C3×C4×D3 | — | 3 | 1 | no | — |
| 321 | C3×C4×D3 | — | 3 | 1 | no | — |
| 322 | C3×C4×D3 | — | 3 | 1 | no | — |
| 323 | C3×C4×D3 | — | 3 | 1 | no | — |
| 324 | C3×C4×D3 | — | 6 | 1 | no | — |
| 325 | C3×C4×D3 | — | 6 | 1 | no | — |
| 326 | C3×C4×D3 | — | 6 | 1 | no | — |
| 327 | C3×C4×D3 | — | 6 | 1 | no | — |
| 328 | C3×C4×D3 | — | 6 | 1 | no | — |
| 329 | C3×C4×D3 | — | 6 | 1 | no | — |
| 330 | C3×C4×D3 | — | 6 | 1 | no | — |
| 331 | C3×C4×D3 | — | 6 | 1 | no | — |
| 332 | C3×C4×D3 | — | 6 | 1 | no | — |
| 333 | C3×C4×D3 | — | 12 | 1 | no | — |
| 334 | C3×C4×D3 | — | 12 | 1 | no | — |
| 335 | C3×Dic6 | — | 3 | 1 | no | — |
| 336 | C3×Dic6 | — | 3 | 1 | no | — |
| 337 | C3×Dic6 | — | 3 | 1 | no | — |
| 338 | C3×Dic6 | — | 3 | 1 | no | — |
| 339 | C3×Dic6 | — | 3 | 1 | no | — |
| 340 | C3×Dic6 | — | 6 | 1 | no | — |
| 341 | C3×Dic6 | — | 6 | 1 | no | — |
| 342 | C3×Dic6 | — | 6 | 1 | no | — |
| 343 | C3×Dic6 | — | 6 | 1 | no | — |
| 344 | C3×Dic6 | — | 6 | 1 | no | — |
| 345 | C3×Dic6 | — | 6 | 1 | no | — |
| 346 | C3×Dic6 | — | 12 | 1 | no | — |
| 347 | #627 | — | 3 | 1 | no | — |
| 348 | #627 | — | 3 | 1 | no | — |
| 349 | #627 | — | 6 | 1 | no | — |
| 350 | #627 | — | 6 | 1 | no | — |
| 351 | #627 | — | 6 | 1 | no | — |
| 352 | #627 | — | 6 | 1 | no | — |
| 353 | #626 | — | 3 | 1 | no | — |
| 354 | #626 | — | 3 | 1 | no | — |
| 355 | #626 | — | 3 | 1 | no | — |
| 356 | #626 | — | 3 | 1 | no | — |
| 357 | #626 | — | 6 | 1 | no | — |
| 358 | #626 | — | 6 | 1 | no | — |
| 359 | #626 | — | 6 | 1 | no | — |
| 360 | #626 | — | 6 | 1 | no | — |
| 361 | #626 | — | 6 | 1 | no | — |
| 362 | #625 | — | 3 | 1 | no | — |
| 363 | #625 | — | 3 | 1 | no | — |
| 364 | #625 | — | 6 | 1 | no | — |
| 365 | #625 | — | 6 | 1 | no | — |
| 366 | #625 | — | 6 | 1 | no | — |
| 367 | #624 | — | 6 | 1 | no | — |
| 368 | #624 | — | 6 | 1 | no | — |
| 369 | #624 | — | 6 | 1 | no | — |
| 370 | D3×Dic3 | — | 6 | 1 | no | — |
| 371 | D3×Dic3 | — | 6 | 1 | no | — |
| 372 | D3×Dic3 | — | 6 | 1 | no | — |
| 373 | D3×Dic3 | — | 6 | 1 | no | — |
| 374 | D3×Dic3 | — | 6 | 1 | no | — |
| 375 | D3×Dic3 | — | 6 | 1 | no | — |
| 376 | D3×Dic3 | — | 6 | 1 | no | — |
| 377 | D3×Dic3 | — | 6 | 1 | no | — |
| 378 | D3×Dic3 | — | 6 | 1 | no | — |
| 379 | C32×C8 | — | 2 | 1 | no | — |
| 380 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 381 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 382 | C3⋊(C3⋊C8) | C22×D3 | 1 | 1 | yes | characteristic |
| 383 | C3⋊(C3⋊C8) | C22×D3 | 1 | 1 | yes | characteristic |
| 384 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 385 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 386 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 387 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 388 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 389 | #578 | — | 27 | 1 | no | Sylow |
| 390 | C2×H(3,𝔽3) | C22×D4 | 1 | 1 | yes | characteristic |
| 391 | #272 | — | 2 | 1 | no | — |
| 392 | #272 | — | 4 | 1 | no | — |
| 393 | (C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 394 | (C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 395 | (C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 396 | C3×#41 | — | 9 | 1 | no | — |
| 397 | C3×#41 | — | 9 | 1 | no | — |
| 398 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 399 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 400 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 401 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 402 | #239 | — | 3 | 1 | no | — |
| 403 | #239 | — | 3 | 1 | no | — |
| 404 | #239 | — | 3 | 1 | no | — |
| 405 | #239 | — | 6 | 1 | no | — |
| 406 | #239 | — | 9 | 1 | no | — |
| 407 | #239 | — | 9 | 1 | no | — |
| 408 | #239 | — | 9 | 1 | no | — |
| 409 | #239 | — | 9 | 1 | no | — |
| 410 | #239 | — | 9 | 1 | no | — |
| 411 | #239 | — | 18 | 1 | no | — |
| 412 | #239 | — | 18 | 1 | no | — |
| 413 | #239 | — | 18 | 1 | no | — |
| 414 | #239 | — | 18 | 1 | no | — |
| 415 | D3×Q8 | — | 3 | 1 | no | — |
| 416 | D3×Q8 | — | 3 | 1 | no | — |
| 417 | D3×Q8 | — | 3 | 1 | no | — |
| 418 | D3×Q8 | — | 3 | 1 | no | — |
| 419 | D3×Q8 | — | 3 | 1 | no | — |
| 420 | D3×Q8 | — | 6 | 1 | no | — |
| 421 | D3×Q8 | — | 9 | 1 | no | — |
| 422 | D3×Q8 | — | 9 | 1 | no | — |
| 423 | D3×Q8 | — | 9 | 1 | no | — |
| 424 | D3×Q8 | — | 9 | 1 | no | — |
| 425 | D3×Q8 | — | 9 | 1 | no | — |
| 426 | D3×Q8 | — | 9 | 1 | no | — |
| 427 | D3×Q8 | — | 9 | 1 | no | — |
| 428 | D3×Q8 | — | 18 | 1 | no | — |
| 429 | D3×Q8 | — | 18 | 1 | no | — |
| 430 | D3×Q8 | — | 18 | 1 | no | — |
| 431 | D3×Q8 | — | 18 | 1 | no | — |
| 432 | #237 | — | 9 | 1 | no | — |
| 433 | #237 | — | 9 | 1 | no | — |
| 434 | #237 | — | 9 | 1 | no | — |
| 435 | #237 | — | 9 | 1 | no | — |
| 436 | #237 | — | 18 | 1 | no | — |
| 437 | #237 | — | 18 | 1 | no | — |
| 438 | #237 | — | 18 | 1 | no | — |
| 439 | #237 | — | 18 | 1 | no | — |
| 440 | #235 | — | 9 | 1 | no | — |
| 441 | #235 | — | 9 | 1 | no | — |
| 442 | #235 | — | 9 | 1 | no | — |
| 443 | #235 | — | 9 | 1 | no | — |
| 444 | #235 | — | 9 | 1 | no | — |
| 445 | #235 | — | 9 | 1 | no | — |
| 446 | #235 | — | 9 | 1 | no | — |
| 447 | #235 | — | 18 | 1 | no | — |
| 448 | #235 | — | 18 | 1 | no | — |
| 449 | #235 | — | 18 | 1 | no | — |
| 450 | #235 | — | 18 | 1 | no | — |
| 451 | #235 | — | 18 | 1 | no | — |
| 452 | #235 | — | 18 | 1 | no | — |
| 453 | #235 | — | 18 | 1 | no | — |
| 454 | #235 | — | 18 | 1 | no | — |
| 455 | #235 | — | 18 | 1 | no | — |
| 456 | #235 | — | 18 | 1 | no | — |
| 457 | C2×Dic6 | — | 9 | 1 | no | — |
| 458 | C2×Dic6 | — | 9 | 1 | no | — |
| 459 | C2×Dic6 | — | 18 | 1 | no | — |
| 460 | C2×Dic6 | — | 18 | 1 | no | — |
| 461 | C3×Q16 | — | 3 | 1 | no | — |
| 462 | C3×Q16 | — | 3 | 1 | no | — |
| 463 | C3×Q16 | — | 6 | 1 | no | — |
| 464 | C3×Q16 | — | 9 | 1 | no | — |
| 465 | C3×Q16 | — | 9 | 1 | no | — |
| 466 | C3×Q16 | — | 9 | 1 | no | — |
| 467 | C3×Q16 | — | 9 | 1 | no | — |
| 468 | C3×Q16 | — | 9 | 1 | no | — |
| 469 | C3×Q16 | D32 | 1 | 1 | yes | characteristic |
| 470 | C3×SD16 | — | 9 | 1 | no | — |
| 471 | C3×SD16 | — | 9 | 1 | no | — |
| 472 | C3×SD16 | — | 9 | 1 | no | — |
| 473 | C3×SD16 | — | 9 | 1 | no | — |
| 474 | C3×M16 | — | 9 | 1 | no | — |
| 475 | C3×M16 | — | 9 | 1 | no | — |
| 476 | C2×C3×C8 | — | 9 | 1 | no | — |
| 477 | #216 | — | 3 | 1 | no | — |
| 478 | #216 | — | 3 | 1 | no | — |
| 479 | #216 | — | 3 | 1 | no | — |
| 480 | #216 | — | 3 | 1 | no | — |
| 481 | #216 | — | 3 | 1 | no | — |
| 482 | #216 | — | 6 | 1 | no | — |
| 483 | #216 | — | 9 | 1 | no | — |
| 484 | #216 | — | 9 | 1 | no | — |
| 485 | #216 | — | 9 | 1 | no | — |
| 486 | #216 | — | 9 | 1 | no | — |
| 487 | #216 | — | 9 | 1 | no | — |
| 488 | #216 | — | 9 | 1 | no | — |
| 489 | #216 | — | 9 | 1 | no | — |
| 490 | #216 | — | 9 | 1 | no | — |
| 491 | #216 | — | 9 | 1 | no | — |
| 492 | #215 | — | 3 | 1 | no | — |
| 493 | #215 | — | 3 | 1 | no | — |
| 494 | #215 | — | 3 | 1 | no | — |
| 495 | #215 | — | 6 | 1 | no | — |
| 496 | #215 | — | 9 | 1 | no | — |
| 497 | #215 | — | 9 | 1 | no | — |
| 498 | #215 | — | 9 | 1 | no | — |
| 499 | #214 | — | 9 | 1 | no | — |
| 500 | #214 | — | 9 | 1 | no | — |
| 501 | #213 | — | 9 | 1 | no | — |
| 502 | #213 | — | 9 | 1 | no | — |
| 503 | #208 | — | 9 | 1 | no | — |
| 504 | C2×C3⋊C8 | — | 9 | 1 | no | — |
| 505 | C2×C3⋊C8 | — | 9 | 1 | no | — |
| 506 | Dic12 | — | 3 | 1 | no | — |
| 507 | Dic12 | — | 9 | 1 | no | — |
| 508 | Dic12 | — | 9 | 1 | no | — |
| 509 | Dic12 | — | 9 | 1 | no | — |
| 510 | Dic12 | — | 9 | 1 | no | — |
| 511 | D24 | — | 9 | 1 | no | — |
| 512 | #204 | — | 3 | 1 | no | — |
| 513 | #204 | — | 3 | 1 | no | — |
| 514 | #204 | — | 3 | 1 | no | — |
| 515 | #204 | — | 6 | 1 | no | — |
| 516 | #204 | — | 9 | 1 | no | — |
| 517 | #204 | — | 9 | 1 | no | — |
| 518 | #204 | — | 9 | 1 | no | — |
| 519 | ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 520 | ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 521 | ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 522 | ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 523 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 524 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 525 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 526 | D3×C8 | — | 3 | 1 | no | — |
| 527 | D3×C8 | — | 9 | 1 | no | — |
| 528 | D3×C8 | — | 9 | 1 | no | — |
| 529 | D3×C8 | — | 9 | 1 | no | — |
| 530 | D3×C8 | — | 9 | 1 | no | — |
| 531 | D3×C8 | — | 9 | 1 | no | — |
| 532 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 533 | C2×C3⋊D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 534 | C2×C3⋊D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 535 | C2×C3×D3 | — | 3 | 1 | no | — |
| 536 | C2×C3×D3 | — | 3 | 1 | no | — |
| 537 | C2×C3×D3 | — | 3 | 1 | no | — |
| 538 | C2×C3×D3 | — | 3 | 1 | no | — |
| 539 | C2×C3×D3 | — | 6 | 1 | no | — |
| 540 | C2×C3×D3 | — | 6 | 1 | no | — |
| 541 | C2×C3×D3 | — | 6 | 1 | no | — |
| 542 | C2×C3×D3 | — | 6 | 1 | no | — |
| 543 | C2×C3×D3 | — | 12 | 1 | no | — |
| 544 | C32×C4 | — | 2 | 1 | no | — |
| 545 | C32×C4 | — | 2 | 1 | no | — |
| 546 | C32×C4 | — | 2 | 1 | no | — |
| 547 | C32×C4 | — | 2 | 1 | no | — |
| 548 | C32×C4 | — | 2 | 1 | no | — |
| 549 | C32×C4 | — | 4 | 1 | no | — |
| 550 | C32×C4 | — | 4 | 1 | no | — |
| 551 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 552 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 553 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 554 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 555 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 556 | C3⋊Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 557 | C3⋊Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 558 | C3×Dic3 | — | 3 | 1 | no | — |
| 559 | C3×Dic3 | — | 3 | 1 | no | — |
| 560 | C3×Dic3 | — | 3 | 1 | no | — |
| 561 | C3×Dic3 | — | 3 | 1 | no | — |
| 562 | C3×Dic3 | — | 6 | 1 | no | — |
| 563 | C3×Dic3 | — | 6 | 1 | no | — |
| 564 | C3×Dic3 | — | 6 | 1 | no | — |
| 565 | C3×Dic3 | — | 6 | 1 | no | — |
| 566 | C3×Dic3 | — | 6 | 1 | no | — |
| 567 | C3×Dic3 | — | 6 | 1 | no | — |
| 568 | C3×Dic3 | — | 12 | 1 | no | — |
| 569 | 2−1+4 | — | 27 | 1 | no | — |
| 570 | 2−1+4 | — | 27 | 1 | no | — |
| 571 | #137 | — | 9 | 1 | no | — |
| 572 | #137 | — | 9 | 1 | no | — |
| 573 | #137 | — | 27 | 1 | no | — |
| 574 | #137 | — | 27 | 1 | no | — |
| 575 | #137 | — | 27 | 1 | no | — |
| 576 | #137 | — | 27 | 1 | no | — |
| 577 | #135 | — | 27 | 1 | no | — |
| 578 | #135 | — | 27 | 1 | no | — |
| 579 | #135 | — | 27 | 1 | no | — |
| 580 | C2×Q16 | — | 9 | 1 | no | — |
| 581 | C2×Q16 | — | 27 | 1 | no | — |
| 582 | C2×Q16 | — | 27 | 1 | no | — |
| 583 | #131 | — | 27 | 1 | no | — |
| 584 | H(3,𝔽3) | #578 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 585 | C3×Q8 | — | 3 | 1 | no | — |
| 586 | C3×Q8 | — | 3 | 1 | no | — |
| 587 | C3×Q8 | — | 3 | 1 | no | — |
| 588 | C3×Q8 | — | 3 | 1 | no | — |
| 589 | C3×Q8 | — | 6 | 1 | no | — |
| 590 | C3×Q8 | — | 6 | 1 | no | — |
| 591 | C3×Q8 | — | 9 | 1 | no | — |
| 592 | C3×Q8 | — | 9 | 1 | no | — |
| 593 | C3×Q8 | — | 9 | 1 | no | — |
| 594 | C3×Q8 | — | 9 | 1 | no | — |
| 595 | C3×Q8 | — | 18 | 1 | no | — |
| 596 | C3×Q8 | — | 18 | 1 | no | — |
| 597 | C3×Q8 | — | 18 | 1 | no | — |
| 598 | C3×Q8 | — | 18 | 1 | no | — |
| 599 | C3×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 600 | C3×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 601 | C3×D4 | — | 9 | 1 | no | — |
| 602 | C3×D4 | — | 9 | 1 | no | — |
| 603 | C3×D4 | — | 18 | 1 | no | — |
| 604 | C3×D4 | — | 18 | 1 | no | — |
| 605 | C2×C3×C4 | — | 9 | 1 | no | — |
| 606 | C2×C3×C4 | — | 9 | 1 | no | — |
| 607 | C2×C3×C4 | — | 9 | 1 | no | — |
| 608 | C2×C3×C4 | — | 18 | 1 | no | — |
| 609 | C2×C3×C4 | — | 18 | 1 | no | — |
| 610 | C2×C3×C4 | — | 18 | 1 | no | — |
| 611 | C2×C3×C4 | — | 18 | 1 | no | — |
| 612 | C2×C3×C4 | — | 18 | 1 | no | — |
| 613 | C2×C3×C4 | — | 18 | 1 | no | — |
| 614 | #67 | — | 9 | 1 | no | — |
| 615 | #67 | — | 9 | 1 | no | — |
| 616 | #67 | — | 9 | 1 | no | — |
| 617 | #67 | — | 9 | 1 | no | — |
| 618 | #67 | — | 9 | 1 | no | — |
| 619 | #67 | — | 9 | 1 | no | — |
| 620 | #67 | — | 18 | 1 | no | — |
| 621 | #67 | — | 18 | 1 | no | — |
| 622 | #67 | — | 18 | 1 | no | — |
| 623 | #67 | — | 18 | 1 | no | — |
| 624 | #67 | — | 18 | 1 | no | — |
| 625 | #67 | — | 18 | 1 | no | — |
| 626 | #67 | — | 18 | 1 | no | — |
| 627 | #67 | — | 18 | 1 | no | — |
| 628 | C2×Dic3 | — | 18 | 1 | no | — |
| 629 | C2×Dic3 | — | 18 | 1 | no | — |
| 630 | C2×Dic3 | — | 18 | 1 | no | — |
| 631 | C2×Dic3 | — | 18 | 1 | no | — |
| 632 | C2×Dic3 | — | 18 | 1 | no | — |
| 633 | C2×Dic3 | — | 18 | 1 | no | — |
| 634 | D12 | — | 3 | 1 | no | — |
| 635 | D12 | — | 3 | 1 | no | — |
| 636 | D12 | — | 3 | 1 | no | — |
| 637 | D12 | — | 6 | 1 | no | — |
| 638 | D12 | — | 6 | 1 | no | — |
| 639 | D12 | — | 6 | 1 | no | — |
| 640 | D12 | — | 6 | 1 | no | — |
| 641 | D12 | — | 9 | 1 | no | — |
| 642 | D12 | — | 9 | 1 | no | — |
| 643 | D12 | — | 9 | 1 | no | — |
| 644 | D12 | — | 9 | 1 | no | — |
| 645 | D12 | — | 12 | 1 | no | — |
| 646 | D12 | — | 18 | 1 | no | — |
| 647 | D12 | — | 18 | 1 | no | — |
| 648 | D12 | — | 18 | 1 | no | — |
| 649 | D12 | — | 18 | 1 | no | — |
| 650 | D12 | — | 18 | 1 | no | — |
| 651 | C4×D3 | — | 3 | 1 | no | — |
| 652 | C4×D3 | — | 3 | 1 | no | — |
| 653 | C4×D3 | — | 3 | 1 | no | — |
| 654 | C4×D3 | — | 3 | 1 | no | — |
| 655 | C4×D3 | — | 6 | 1 | no | — |
| 656 | C4×D3 | — | 6 | 1 | no | — |
| 657 | C4×D3 | — | 6 | 1 | no | — |
| 658 | C4×D3 | — | 6 | 1 | no | — |
| 659 | C4×D3 | — | 6 | 1 | no | — |
| 660 | C4×D3 | — | 6 | 1 | no | — |
| 661 | C4×D3 | — | 6 | 1 | no | — |
| 662 | C4×D3 | — | 6 | 1 | no | — |
| 663 | C4×D3 | — | 6 | 1 | no | — |
| 664 | C4×D3 | — | 9 | 1 | no | — |
| 665 | C4×D3 | — | 9 | 1 | no | — |
| 666 | C4×D3 | — | 12 | 1 | no | — |
| 667 | C4×D3 | — | 12 | 1 | no | — |
| 668 | C4×D3 | — | 18 | 1 | no | — |
| 669 | C4×D3 | — | 18 | 1 | no | — |
| 670 | C4×D3 | — | 18 | 1 | no | — |
| 671 | C4×D3 | — | 18 | 1 | no | — |
| 672 | C4×D3 | — | 18 | 1 | no | — |
| 673 | C4×D3 | — | 18 | 1 | no | — |
| 674 | C4×D3 | — | 18 | 1 | no | — |
| 675 | C4×D3 | — | 18 | 1 | no | — |
| 676 | C4×D3 | — | 18 | 1 | no | — |
| 677 | C4×D3 | — | 18 | 1 | no | — |
| 678 | C4×D3 | — | 18 | 1 | no | — |
| 679 | C4×D3 | — | 18 | 1 | no | — |
| 680 | C4×D3 | — | 18 | 1 | no | — |
| 681 | C4×D3 | — | 18 | 1 | no | — |
| 682 | C4×D3 | — | 18 | 1 | no | — |
| 683 | C4×D3 | — | 18 | 1 | no | — |
| 684 | Dic6 | — | 3 | 1 | no | — |
| 685 | Dic6 | — | 3 | 1 | no | — |
| 686 | Dic6 | — | 3 | 1 | no | — |
| 687 | Dic6 | — | 3 | 1 | no | — |
| 688 | Dic6 | — | 3 | 1 | no | — |
| 689 | Dic6 | — | 6 | 1 | no | — |
| 690 | Dic6 | — | 6 | 1 | no | — |
| 691 | Dic6 | — | 6 | 1 | no | — |
| 692 | Dic6 | — | 6 | 1 | no | — |
| 693 | Dic6 | — | 6 | 1 | no | — |
| 694 | Dic6 | — | 6 | 1 | no | — |
| 695 | Dic6 | — | 9 | 1 | no | — |
| 696 | Dic6 | — | 9 | 1 | no | — |
| 697 | Dic6 | — | 9 | 1 | no | — |
| 698 | Dic6 | — | 9 | 1 | no | — |
| 699 | Dic6 | — | 9 | 1 | no | — |
| 700 | Dic6 | — | 9 | 1 | no | — |
| 701 | Dic6 | — | 12 | 1 | no | — |
| 702 | Dic6 | — | 18 | 1 | no | — |
| 703 | Dic6 | — | 18 | 1 | no | — |
| 704 | Dic6 | — | 18 | 1 | no | — |
| 705 | Dic6 | — | 18 | 1 | no | — |
| 706 | Dic6 | — | 18 | 1 | no | — |
| 707 | Dic6 | — | 18 | 1 | no | — |
| 708 | Dic6 | — | 18 | 1 | no | — |
| 709 | Dic6 | — | 18 | 1 | no | — |
| 710 | Dic6 | — | 18 | 1 | no | — |
| 711 | C3×C8 | — | 3 | 1 | no | — |
| 712 | C3×C8 | — | 3 | 1 | no | — |
| 713 | C3×C8 | — | 6 | 1 | no | — |
| 714 | C3×C8 | — | 9 | 1 | no | — |
| 715 | C3×C8 | — | 9 | 1 | no | — |
| 716 | C3×C8 | — | 9 | 1 | no | — |
| 717 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 718 | C3⋊C8 | — | 3 | 1 | no | — |
| 719 | C3⋊C8 | — | 3 | 1 | no | — |
| 720 | C3⋊C8 | — | 3 | 1 | no | — |
| 721 | C3⋊C8 | — | 3 | 1 | no | — |
| 722 | C3⋊C8 | — | 6 | 1 | no | — |
| 723 | C3⋊C8 | — | 9 | 1 | no | — |
| 724 | C3⋊C8 | — | 9 | 1 | no | — |
| 725 | C2×C32 | — | 2 | 1 | no | — |
| 726 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 727 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 728 | C3⋊D3 | — | 2 | 1 | no | — |
| 729 | C3⋊D3 | — | 2 | 1 | no | — |
| 730 | C3⋊D3 | — | 4 | 1 | no | — |
| 731 | C3×D3 | — | 6 | 1 | no | — |
| 732 | C3×D3 | — | 6 | 1 | no | — |
| 733 | C3×D3 | — | 6 | 1 | no | — |
| 734 | C3×D3 | — | 6 | 1 | no | — |
| 735 | C3×D3 | — | 12 | 1 | no | — |
| 736 | C3×D3 | — | 12 | 1 | no | — |
| 737 | C3×D3 | — | 12 | 1 | no | — |
| 738 | C3×D3 | — | 12 | 1 | no | — |
| 739 | C3×D3 | — | 24 | 1 | no | — |
| 740 | #41 | — | 9 | 1 | no | — |
| 741 | #41 | — | 9 | 1 | no | — |
| 742 | #41 | — | 27 | 1 | no | — |
| 743 | #41 | — | 27 | 1 | no | — |
| 744 | #41 | — | 27 | 1 | no | — |
| 745 | #41 | — | 27 | 1 | no | — |
| 746 | #41 | — | 27 | 1 | no | — |
| 747 | #41 | — | 54 | 1 | no | — |
| 748 | #41 | — | 54 | 1 | no | — |
| 749 | #41 | — | 54 | 1 | no | — |
| 750 | #41 | — | 54 | 1 | no | — |
| 751 | #41 | — | 54 | 1 | no | — |
| 752 | #41 | — | 54 | 1 | no | — |
| 753 | C2×Q8 | — | 9 | 1 | no | — |
| 754 | C2×Q8 | — | 9 | 1 | no | — |
| 755 | C2×Q8 | — | 9 | 1 | no | — |
| 756 | C2×Q8 | — | 9 | 1 | no | — |
| 757 | C2×Q8 | — | 27 | 1 | no | — |
| 758 | C2×Q8 | — | 27 | 1 | no | — |
| 759 | C2×Q8 | — | 54 | 1 | no | — |
| 760 | C2×Q8 | — | 54 | 1 | no | — |
| 761 | Q16 | — | 9 | 1 | no | — |
| 762 | Q16 | — | 9 | 1 | no | — |
| 763 | Q16 | — | 9 | 1 | no | — |
| 764 | Q16 | — | 9 | 1 | no | — |
| 765 | Q16 | — | 9 | 1 | no | — |
| 766 | Q16 | — | 27 | 1 | no | — |
| 767 | Q16 | — | 27 | 1 | no | — |
| 768 | Q16 | — | 27 | 1 | no | — |
| 769 | Q16 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 770 | SD16 | — | 9 | 1 | no | — |
| 771 | SD16 | — | 9 | 1 | no | — |
| 772 | SD16 | — | 9 | 1 | no | — |
| 773 | SD16 | — | 9 | 1 | no | — |
| 774 | SD16 | — | 27 | 1 | no | — |
| 775 | SD16 | — | 27 | 1 | no | — |
| 776 | D8 | — | 27 | 1 | no | — |
| 777 | M16 | — | 9 | 1 | no | — |
| 778 | M16 | — | 9 | 1 | no | — |
| 779 | M16 | — | 27 | 1 | no | — |
| 780 | C2×C8 | — | 9 | 1 | no | — |
| 781 | C2×C8 | — | 27 | 1 | no | — |
| 782 | C2×C8 | — | 27 | 1 | no | — |
| 783 | C22×C3 | — | 9 | 1 | no | — |
| 784 | C22×C3 | — | 9 | 1 | no | — |
| 785 | C22×C3 | — | 9 | 1 | no | — |
| 786 | C22×C3 | — | 18 | 1 | no | — |
| 787 | C22×C3 | — | 18 | 1 | no | — |
| 788 | C2×D3 | — | 3 | 1 | no | — |
| 789 | C2×D3 | — | 3 | 1 | no | — |
| 790 | C2×D3 | — | 3 | 1 | no | — |
| 791 | C2×D3 | — | 3 | 1 | no | — |
| 792 | C2×D3 | — | 6 | 1 | no | — |
| 793 | C2×D3 | — | 6 | 1 | no | — |
| 794 | C2×D3 | — | 6 | 1 | no | — |
| 795 | C2×D3 | — | 6 | 1 | no | — |
| 796 | C2×D3 | — | 9 | 1 | no | — |
| 797 | C2×D3 | — | 9 | 1 | no | — |
| 798 | C2×D3 | — | 12 | 1 | no | — |
| 799 | C2×D3 | — | 18 | 1 | no | — |
| 800 | C3×C4 | — | 2 | 1 | no | — |
| 801 | C3×C4 | — | 2 | 1 | no | — |
| 802 | C3×C4 | — | 3 | 1 | no | — |
| 803 | C3×C4 | — | 3 | 1 | no | — |
| 804 | C3×C4 | — | 6 | 1 | no | — |
| 805 | C3×C4 | — | 6 | 1 | no | — |
| 806 | C3×C4 | — | 6 | 1 | no | — |
| 807 | C3×C4 | — | 6 | 1 | no | — |
| 808 | C3×C4 | — | 6 | 1 | no | — |
| 809 | C3×C4 | — | 9 | 1 | no | — |
| 810 | C3×C4 | — | 9 | 1 | no | — |
| 811 | C3×C4 | — | 9 | 1 | no | — |
| 812 | C3×C4 | — | 12 | 1 | no | — |
| 813 | C3×C4 | — | 12 | 1 | no | — |
| 814 | C3×C4 | — | 18 | 1 | no | — |
| 815 | C3×C4 | — | 18 | 1 | no | — |
| 816 | C3×C4 | — | 18 | 1 | no | — |
| 817 | C3×C4 | — | 18 | 1 | no | — |
| 818 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 819 | Dic3 | — | 3 | 1 | no | — |
| 820 | Dic3 | — | 3 | 1 | no | — |
| 821 | Dic3 | — | 3 | 1 | no | — |
| 822 | Dic3 | — | 3 | 1 | no | — |
| 823 | Dic3 | — | 6 | 1 | no | — |
| 824 | Dic3 | — | 6 | 1 | no | — |
| 825 | Dic3 | — | 6 | 1 | no | — |
| 826 | Dic3 | — | 6 | 1 | no | — |
| 827 | Dic3 | — | 6 | 1 | no | — |
| 828 | Dic3 | — | 6 | 1 | no | — |
| 829 | Dic3 | — | 9 | 1 | no | — |
| 830 | Dic3 | — | 9 | 1 | no | — |
| 831 | Dic3 | — | 12 | 1 | no | — |
| 832 | Dic3 | — | 18 | 1 | no | — |
| 833 | Dic3 | — | 18 | 1 | no | — |
| 834 | Dic3 | — | 18 | 1 | no | — |
| 835 | C32 | — | 2 | 1 | no | — |
| 836 | C32 | #5766 | 1 | 1 | yes | characteristic, complemented |
| 837 | C32 | #5779 | 1 | 1 | yes | characteristic, complemented |
| 838 | Q8 | — | 9 | 1 | no | — |
| 839 | Q8 | — | 9 | 1 | no | — |
| 840 | Q8 | — | 9 | 1 | no | — |
| 841 | Q8 | — | 9 | 1 | no | — |
| 842 | Q8 | — | 18 | 1 | no | — |
| 843 | Q8 | — | 18 | 1 | no | — |
| 844 | Q8 | — | 18 | 1 | no | — |
| 845 | Q8 | — | 18 | 1 | no | — |
| 846 | Q8 | — | 27 | 1 | no | — |
| 847 | Q8 | — | 54 | 1 | no | — |
| 848 | Q8 | — | 54 | 1 | no | — |
| 849 | Q8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 850 | Q8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 851 | D4 | — | 9 | 1 | no | — |
| 852 | D4 | — | 9 | 1 | no | — |
| 853 | D4 | — | 18 | 1 | no | — |
| 854 | D4 | — | 18 | 1 | no | — |
| 855 | D4 | — | 27 | 1 | no | — |
| 856 | D4 | — | 27 | 1 | no | — |
| 857 | D4 | — | 27 | 1 | no | — |
| 858 | D4 | — | 54 | 1 | no | — |
| 859 | D4 | — | 54 | 1 | no | — |
| 860 | D4 | — | 54 | 1 | no | — |
| 861 | D4 | — | 54 | 1 | no | — |
| 862 | C2×C4 | — | 9 | 1 | no | — |
| 863 | C2×C4 | — | 9 | 1 | no | — |
| 864 | C2×C4 | — | 9 | 1 | no | — |
| 865 | C2×C4 | — | 18 | 1 | no | — |
| 866 | C2×C4 | — | 18 | 1 | no | — |
| 867 | C2×C4 | — | 18 | 1 | no | — |
| 868 | C2×C4 | — | 18 | 1 | no | — |
| 869 | C2×C4 | — | 18 | 1 | no | — |
| 870 | C2×C4 | — | 18 | 1 | no | — |
| 871 | C2×C4 | — | 54 | 1 | no | — |
| 872 | C2×C4 | — | 54 | 1 | no | — |
| 873 | C2×C4 | — | 54 | 1 | no | — |
| 874 | C2×C4 | — | 54 | 1 | no | — |
| 875 | C2×C4 | — | 54 | 1 | no | — |
| 876 | C2×C4 | — | 54 | 1 | no | — |
| 877 | C8 | — | 9 | 1 | no | — |
| 878 | C8 | — | 9 | 1 | no | — |
| 879 | C8 | — | 9 | 1 | no | — |
| 880 | C8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 881 | C2×C3 | — | 3 | 1 | no | — |
| 882 | C2×C3 | — | 3 | 1 | no | — |
| 883 | C2×C3 | — | 6 | 1 | no | — |
| 884 | C2×C3 | — | 18 | 1 | no | — |
| 885 | C2×C3 | — | 18 | 1 | no | — |
| 886 | C2×C3 | — | 18 | 1 | no | — |
| 887 | C2×C3 | — | 36 | 1 | no | — |
| 888 | C2×C3 | — | 36 | 1 | no | — |
| 889 | C2×C3 | D32×D4 | 1 | 1 | yes | characteristic |
| 890 | D3 | — | 6 | 1 | no | — |
| 891 | D3 | — | 6 | 1 | no | — |
| 892 | D3 | — | 6 | 1 | no | — |
| 893 | D3 | — | 6 | 1 | no | — |
| 894 | D3 | — | 12 | 1 | no | — |
| 895 | D3 | — | 12 | 1 | no | — |
| 896 | D3 | — | 12 | 1 | no | — |
| 897 | D3 | — | 12 | 1 | no | — |
| 898 | D3 | — | 18 | 1 | no | — |
| 899 | D3 | — | 18 | 1 | no | — |
| 900 | D3 | — | 24 | 1 | no | — |
| 901 | D3 | — | 36 | 1 | no | — |
| 902 | C22 | — | 9 | 1 | no | — |
| 903 | C22 | — | 9 | 1 | no | — |
| 904 | C22 | — | 9 | 1 | no | — |
| 905 | C22 | — | 18 | 1 | no | — |
| 906 | C22 | — | 18 | 1 | no | — |
| 907 | C4 | — | 2 | 1 | no | — |
| 908 | C4 | — | 2 | 1 | no | — |
| 909 | C4 | — | 9 | 1 | no | — |
| 910 | C4 | — | 9 | 1 | no | — |
| 911 | C4 | — | 9 | 1 | no | — |
| 912 | C4 | — | 18 | 1 | no | — |
| 913 | C4 | — | 18 | 1 | no | — |
| 914 | C4 | — | 18 | 1 | no | — |
| 915 | C4 | — | 18 | 1 | no | — |
| 916 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 917 | C3 | — | 3 | 1 | no | — |
| 918 | C3 | — | 3 | 1 | no | — |
| 919 | C3 | — | 6 | 1 | no | — |
| 920 | C3 | #10594766 | 1 | 1 | yes | characteristic |
| 921 | C2 | — | 18 | 1 | no | — |
| 922 | C2 | — | 18 | 1 | no | — |
| 923 | C2 | — | 18 | 1 | no | — |
| 924 | C2 | — | 36 | 1 | no | — |
| 925 | C2 | — | 36 | 1 | no | — |
| 926 | C2 | D4×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11722517 | C2 | semidirect |
| 2. #11722516 | C2 | semidirect |
| 3. #11721807 | C2 | semidirect |
| 4. #64127⋊C3 | C2 | semidirect |
| 5. Q16×(C3⋊D3)⋊C3 | C2 | semidirect |
| 6. #11721238 | C2 | semidirect |
| 7. #11721236 | C2 | semidirect |
| 8. #11721235 | C2 | semidirect |
| 9. #11721234 | C2 | semidirect |
| 10. #11721230 | C2 | semidirect |
| 11. #11721226 | C2 | semidirect |
| 12. #11720854 | C2 | semidirect |
| 13. #11720853 | C2 | semidirect |
| 14. #11720845 | C2 | semidirect |
| 15. #11720841 | C2 | semidirect |
| 65. #64127 | D3 | semidirect |
| 66. Q16×C3⋊D3 | D3 | semidirect |
| 584. H(3,𝔽3) | #578 | semidirect |
| 836. C32 | #5766 | semidirect |
| 837. C32 | #5779 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722517 | 2 |
| #11722516 | 2 |
| #11721807 | 2 |
| #64127⋊C3 | 2 |
| Q16×(C3⋊D3)⋊C3 | 2 |
| #11721238 | 2 |
| #11721236 | 2 |
| #11721235 | 2 |
| #11721234 | 2 |
| #11721230 | 2 |
| #11721226 | 2 |
| #11720854 | 2 |
| #11720853 | 2 |
| #11720845 | 2 |
| #11720841 | 2 |
| #10594769 | 3 |
| #10594766 | 3 |