Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
977 conjugacy classes of subgroups.
The subgroup lattice has 963 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11722520 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11722519 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11721807 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #64128⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #64127⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11721239 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11721238 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11721235 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11721233 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11721231 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11721229 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #11720854 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #11720849 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #11720839 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #11720835 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #10594763 | — | 3 | 1 | no | maximal |
| 17 | #10594762 | — | 3 | 1 | no | maximal |
| 18 | #88748 | C22 | 1 | 1 | yes | characteristic |
| 19 | Q8×#272 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #88722 | C22 | 1 | 1 | yes | characteristic |
| 21 | #88722 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #88722 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | Q8×(C3⋊D3)⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #88655 | — | 2 | 1 | no | — |
| 25 | #88655 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #88654 | — | 2 | 1 | no | — |
| 27 | #88654 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | C4×((C3⋊D3)⋊C3)⋊C2 | — | 2 | 1 | no | — |
| 29 | C4×((C3⋊D3)⋊C3)⋊C2 | — | 2 | 1 | no | — |
| 30 | C4×((C3⋊D3)⋊C3)⋊C2 | C22 | 1 | 1 | yes | characteristic |
| 31 | #88652 | — | 2 | 1 | no | — |
| 32 | #88652 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #88649 | — | 2 | 1 | no | — |
| 34 | #88649 | C22 | 1 | 1 | yes | characteristic |
| 35 | #88648 | — | 2 | 1 | no | — |
| 36 | #88648 | — | 2 | 1 | no | — |
| 37 | #88648 | C22 | 1 | 1 | yes | characteristic |
| 38 | #88648 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | Q16×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | #88550 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #88549 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #88528 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | #88527 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | #3755⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | #3755⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #3755⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | #3756⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | #3745⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | #3744⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | #3743⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | C8×(C3⋊D3)⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 52 | #88439 | C22 | 1 | 1 | yes | characteristic, complemented |
| 53 | #88438 | C22 | 1 | 1 | yes | characteristic, complemented |
| 54 | #88436 | C22 | 1 | 1 | yes | characteristic, complemented |
| 55 | #88436 | C22 | 1 | 1 | yes | characteristic, complemented |
| 56 | #88435 | C22 | 1 | 1 | yes | characteristic, complemented |
| 57 | #88432 | C22 | 1 | 1 | yes | characteristic, complemented |
| 58 | #88431 | C22 | 1 | 1 | yes | characteristic, complemented |
| 59 | #88430 | C22 | 1 | 1 | yes | characteristic, complemented |
| 60 | ((C3⋊D3)⋊C3)⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | #64319 | — | 3 | 1 | no | — |
| 62 | D3×#239 | — | 3 | 1 | no | — |
| 63 | D3×#239 | — | 3 | 1 | no | — |
| 64 | D3×#239 | — | 3 | 1 | no | — |
| 65 | #64128 | D3 | 1 | 1 | yes | characteristic, complemented |
| 66 | #64127 | D3 | 1 | 1 | yes | characteristic, complemented |
| 67 | C3×#919 | — | 3 | 1 | no | — |
| 68 | C3×#918 | — | 3 | 1 | no | — |
| 69 | C3×#918 | — | 3 | 1 | no | — |
| 70 | C3×#918 | — | 3 | 1 | no | — |
| 71 | C3×#918 | — | 6 | 1 | no | — |
| 72 | #63951 | — | 3 | 1 | no | — |
| 73 | #63950 | — | 3 | 1 | no | — |
| 74 | #63950 | — | 3 | 1 | no | — |
| 75 | #63949 | — | 3 | 1 | no | — |
| 76 | #63948 | — | 3 | 1 | no | — |
| 77 | #63948 | — | 3 | 1 | no | — |
| 78 | #63947 | — | 3 | 1 | no | — |
| 79 | #63946 | — | 3 | 1 | no | — |
| 80 | #63941 | — | 3 | 1 | no | — |
| 81 | #63939 | — | 3 | 1 | no | — |
| 82 | #63939 | — | 3 | 1 | no | — |
| 83 | #63939 | — | 3 | 1 | no | — |
| 84 | #63809 | — | 3 | 1 | no | — |
| 85 | #63806 | — | 3 | 1 | no | — |
| 86 | #63798 | — | 3 | 1 | no | — |
| 87 | #63795 | — | 3 | 1 | no | — |
| 88 | #63794 | — | 3 | 1 | no | — |
| 89 | #63794 | — | 3 | 1 | no | — |
| 90 | #63791 | — | 3 | 1 | no | — |
| 91 | D3×ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 92 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 2 | 1 | no | — |
| 93 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 2 | 1 | no | — |
| 94 | C2×((C3⋊D3)⋊C3)⋊C2 | D4 | 1 | 1 | yes | characteristic |
| 95 | Q8×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 96 | Q8×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 97 | C4⋊#272 | — | 2 | 1 | no | — |
| 98 | C4⋊#272 | C23 | 1 | 1 | yes | characteristic |
| 99 | C4×#272 | — | 2 | 1 | no | — |
| 100 | C4×#272 | — | 2 | 1 | no | — |
| 101 | C4×#272 | C23 | 1 | 1 | yes | characteristic |
| 102 | #6229 | — | 2 | 1 | no | — |
| 103 | #6229 | C23 | 1 | 1 | yes | characteristic |
| 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 | C4⋊((C3⋊D3)⋊C3) | C23 | 1 | 1 | yes | characteristic |
| 110 | C4×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 111 | C4×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 112 | C4×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 113 | C4×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 114 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 115 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 116 | #634⋊C3 | — | 2 | 1 | no | — |
| 117 | #634⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 118 | #6200 | — | 2 | 1 | no | — |
| 119 | #6200 | — | 2 | 1 | no | — |
| 120 | #6200 | — | 2 | 1 | no | — |
| 121 | #6199 | — | 2 | 1 | no | — |
| 122 | #6199 | D4 | 1 | 1 | yes | characteristic |
| 123 | #6198 | — | 2 | 1 | no | — |
| 124 | #6198 | — | 2 | 1 | no | — |
| 125 | #6198 | — | 2 | 1 | no | — |
| 126 | ((C3⋊D3)⋊C3)⋊C4 | — | 2 | 1 | no | — |
| 127 | ((C3⋊D3)⋊C3)⋊C4 | — | 2 | 1 | no | — |
| 128 | ((C3⋊D3)⋊C3)⋊C4 | — | 2 | 1 | no | — |
| 129 | ((C3⋊D3)⋊C3)⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 130 | ((C3⋊D3)⋊C3)⋊C4 | 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 | #5777 | — | 9 | 1 | no | — |
| 136 | #5777 | — | 9 | 1 | no | — |
| 137 | #5768 | — | 9 | 1 | no | — |
| 138 | #3832 | C2×D3 | 1 | 1 | yes | characteristic |
| 139 | #3832 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 140 | #3832 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 141 | Q8×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 142 | C3×#239 | — | 3 | 1 | no | — |
| 143 | C3×#239 | — | 3 | 1 | no | — |
| 144 | C3×#239 | — | 3 | 1 | no | — |
| 145 | C3×#239 | — | 3 | 1 | no | — |
| 146 | C3×#239 | — | 3 | 1 | no | — |
| 147 | C3×#239 | — | 6 | 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 | #3802 | — | 3 | 1 | no | — |
| 153 | #3802 | — | 6 | 1 | no | — |
| 154 | D3×D12 | — | 3 | 1 | no | — |
| 155 | D3×D12 | — | 3 | 1 | no | — |
| 156 | D3×D12 | — | 3 | 1 | no | — |
| 157 | D3×D12 | — | 6 | 1 | no | — |
| 158 | D3×D12 | — | 6 | 1 | no | — |
| 159 | D3×D12 | — | 6 | 1 | no | — |
| 160 | C4×D32 | — | 3 | 1 | no | — |
| 161 | C4×D32 | — | 3 | 1 | no | — |
| 162 | C4×D32 | — | 6 | 1 | no | — |
| 163 | C4×D32 | — | 6 | 1 | no | — |
| 164 | C4×D32 | — | 6 | 1 | no | — |
| 165 | C4×D32 | — | 6 | 1 | no | — |
| 166 | #3799 | — | 3 | 1 | no | — |
| 167 | #3799 | — | 3 | 1 | no | — |
| 168 | #3799 | — | 3 | 1 | no | — |
| 169 | #3799 | — | 6 | 1 | no | — |
| 170 | #3799 | — | 6 | 1 | no | — |
| 171 | #3799 | — | 6 | 1 | no | — |
| 172 | #3796 | — | 3 | 1 | no | — |
| 173 | #3796 | — | 3 | 1 | no | — |
| 174 | #3796 | — | 3 | 1 | no | — |
| 175 | #3796 | — | 6 | 1 | no | — |
| 176 | #3796 | — | 6 | 1 | no | — |
| 177 | #3796 | — | 6 | 1 | no | — |
| 178 | #3795 | — | 3 | 1 | no | — |
| 179 | #3795 | — | 3 | 1 | no | — |
| 180 | #3795 | — | 6 | 1 | no | — |
| 181 | #3795 | — | 6 | 1 | no | — |
| 182 | C32×Q16 | — | 2 | 1 | no | — |
| 183 | C32×Q16 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 184 | C32×Q16 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 185 | #3756 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 186 | #3755 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 187 | #3755 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 188 | #3755 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 189 | #3745 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 190 | #3744 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 191 | #3743 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 192 | C8×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 193 | C3×#216 | — | 3 | 1 | no | — |
| 194 | C3×#216 | — | 3 | 1 | no | — |
| 195 | C3×#216 | — | 3 | 1 | no | — |
| 196 | C3×#216 | — | 6 | 1 | no | — |
| 197 | C3×#215 | — | 3 | 1 | no | — |
| 198 | C3×#215 | — | 3 | 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×D24 | — | 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 | #3718 | — | 3 | 1 | no | — |
| 215 | #3717 | — | 3 | 1 | no | — |
| 216 | #3717 | — | 3 | 1 | no | — |
| 217 | #3716 | — | 3 | 1 | no | — |
| 218 | #3715 | — | 3 | 1 | no | — |
| 219 | #3714 | — | 3 | 1 | no | — |
| 220 | #3714 | — | 3 | 1 | no | — |
| 221 | #3714 | — | 3 | 1 | no | — |
| 222 | #3714 | — | 3 | 1 | no | — |
| 223 | #3713 | — | 3 | 1 | no | — |
| 224 | #3713 | — | 3 | 1 | no | — |
| 225 | #3712 | — | 3 | 1 | no | — |
| 226 | #3711 | — | 3 | 1 | no | — |
| 227 | #3711 | — | 3 | 1 | no | — |
| 228 | #3711 | — | 3 | 1 | no | — |
| 229 | #3710 | — | 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 | — | 2 | 1 | no | — |
| 235 | C2×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 236 | C2×(C3⋊D3)⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 237 | C2×(C3⋊D3)⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 238 | ((C3⋊D3)⋊C3)⋊C2 | — | 4 | 1 | no | — |
| 239 | ((C3⋊D3)⋊C3)⋊C2 | — | 4 | 2 | no | — |
| 240 | ((C3⋊D3)⋊C3)⋊C2 | — | 4 | 2 | no | — |
| 241 | C4×H(3,𝔽3) | — | 2 | 1 | no | — |
| 242 | C4×H(3,𝔽3) | — | 2 | 1 | no | — |
| 243 | C4×H(3,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 244 | #1084 | — | 2 | 1 | no | — |
| 245 | #1084 | C2×D4 | 1 | 1 | yes | characteristic |
| 246 | (C3⋊Dic3)⋊C3 | — | 2 | 1 | no | — |
| 247 | (C3⋊Dic3)⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 248 | (C3⋊Dic3)⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 249 | D3×#41 | — | 9 | 1 | no | — |
| 250 | D3×#41 | — | 9 | 1 | no | — |
| 251 | D3×#41 | — | 9 | 1 | no | — |
| 252 | D3×#41 | — | 9 | 1 | no | — |
| 253 | C2×#239 | — | 9 | 1 | no | — |
| 254 | C2×#239 | — | 9 | 1 | no | — |
| 255 | C3×#137 | — | 9 | 1 | no | — |
| 256 | C3×#137 | — | 9 | 1 | no | — |
| 257 | C3×#135 | — | 9 | 1 | no | — |
| 258 | #950 | — | 9 | 1 | no | — |
| 259 | #950 | — | 9 | 1 | no | — |
| 260 | #949 | — | 9 | 1 | no | — |
| 261 | #949 | — | 9 | 1 | no | — |
| 262 | #942 | — | 9 | 1 | no | — |
| 263 | #942 | — | 9 | 1 | no | — |
| 264 | #919 | — | 3 | 1 | no | — |
| 265 | #919 | — | 9 | 1 | no | — |
| 266 | #919 | — | 9 | 1 | no | — |
| 267 | #919 | — | 9 | 1 | no | — |
| 268 | #918 | — | 3 | 1 | no | — |
| 269 | #918 | — | 3 | 1 | no | — |
| 270 | #918 | — | 3 | 1 | no | — |
| 271 | #918 | — | 6 | 1 | no | — |
| 272 | #918 | — | 9 | 1 | no | — |
| 273 | #918 | — | 9 | 1 | no | — |
| 274 | #918 | — | 9 | 1 | no | — |
| 275 | #916 | — | 9 | 1 | no | — |
| 276 | #916 | — | 9 | 1 | no | — |
| 277 | #916 | — | 9 | 1 | no | — |
| 278 | #916 | — | 9 | 1 | no | — |
| 279 | #915 | — | 9 | 1 | no | — |
| 280 | #915 | — | 9 | 1 | no | — |
| 281 | #914 | — | 9 | 1 | no | — |
| 282 | #914 | — | 9 | 1 | no | — |
| 283 | #914 | — | 9 | 1 | no | — |
| 284 | #914 | — | 9 | 1 | no | — |
| 285 | #914 | — | 9 | 1 | no | — |
| 286 | #914 | — | 9 | 1 | no | — |
| 287 | #911 | — | 9 | 1 | no | — |
| 288 | #911 | — | 9 | 1 | no | — |
| 289 | #908 | — | 9 | 1 | no | — |
| 290 | #908 | — | 9 | 1 | no | — |
| 291 | D3×M16 | — | 9 | 1 | no | — |
| 292 | D3×M16 | — | 9 | 1 | no | — |
| 293 | #904 | — | 9 | 1 | no | — |
| 294 | C2×ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 295 | C2×D32 | — | 3 | 1 | no | — |
| 296 | C2×D32 | — | 3 | 1 | no | — |
| 297 | C2×D32 | — | 6 | 1 | no | — |
| 298 | C2×D32 | — | 6 | 1 | no | — |
| 299 | C2×D32 | — | 6 | 1 | no | — |
| 300 | C2×D32 | — | 6 | 1 | no | — |
| 301 | C32×Q8 | — | 2 | 1 | no | — |
| 302 | C32×Q8 | — | 2 | 1 | no | — |
| 303 | C32×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 304 | C32×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 305 | C32×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 306 | C32×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 307 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 308 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 309 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 310 | C4⋊(C3⋊D3) | C22×D3 | 1 | 1 | yes | characteristic |
| 311 | C4⋊(C3⋊D3) | C22×D3 | 1 | 1 | yes | characteristic |
| 312 | C4⋊(C3⋊D3) | C22×D3 | 1 | 1 | yes | characteristic |
| 313 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 314 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 315 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 316 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 317 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 318 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 319 | #634 | — | 2 | 1 | no | — |
| 320 | #634 | C22×D3 | 1 | 1 | yes | characteristic |
| 321 | C3×D12 | — | 3 | 1 | no | — |
| 322 | C3×D12 | — | 3 | 1 | no | — |
| 323 | C3×D12 | — | 3 | 1 | no | — |
| 324 | C3×D12 | — | 3 | 1 | no | — |
| 325 | C3×D12 | — | 3 | 1 | no | — |
| 326 | C3×D12 | — | 6 | 1 | no | — |
| 327 | C3×D12 | — | 6 | 1 | no | — |
| 328 | C3×D12 | — | 6 | 1 | no | — |
| 329 | C3×D12 | — | 6 | 1 | no | — |
| 330 | C3×D12 | — | 6 | 1 | no | — |
| 331 | C3×D12 | — | 6 | 1 | no | — |
| 332 | C3×D12 | — | 12 | 1 | no | — |
| 333 | C3×C4×D3 | — | 3 | 1 | no | — |
| 334 | C3×C4×D3 | — | 3 | 1 | no | — |
| 335 | C3×C4×D3 | — | 3 | 1 | no | — |
| 336 | C3×C4×D3 | — | 3 | 1 | no | — |
| 337 | C3×C4×D3 | — | 6 | 1 | no | — |
| 338 | C3×C4×D3 | — | 6 | 1 | no | — |
| 339 | C3×C4×D3 | — | 6 | 1 | no | — |
| 340 | C3×C4×D3 | — | 6 | 1 | no | — |
| 341 | C3×C4×D3 | — | 6 | 1 | no | — |
| 342 | C3×C4×D3 | — | 6 | 1 | no | — |
| 343 | C3×C4×D3 | — | 6 | 1 | no | — |
| 344 | C3×C4×D3 | — | 6 | 1 | no | — |
| 345 | C3×C4×D3 | — | 6 | 1 | no | — |
| 346 | C3×C4×D3 | — | 12 | 1 | no | — |
| 347 | C3×C4×D3 | — | 12 | 1 | no | — |
| 348 | C3×Dic6 | — | 3 | 1 | no | — |
| 349 | C3×Dic6 | — | 3 | 1 | no | — |
| 350 | C3×Dic6 | — | 3 | 1 | no | — |
| 351 | C3×Dic6 | — | 6 | 1 | no | — |
| 352 | C3×Dic6 | — | 6 | 1 | no | — |
| 353 | C3×Dic6 | — | 6 | 1 | no | — |
| 354 | C3×Dic6 | — | 6 | 1 | no | — |
| 355 | C3×Dic6 | — | 12 | 1 | no | — |
| 356 | #626 | — | 6 | 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 | #626 | — | 6 | 1 | no | — |
| 363 | #626 | — | 6 | 1 | no | — |
| 364 | #626 | — | 6 | 1 | no | — |
| 365 | #625 | — | 6 | 1 | no | — |
| 366 | #625 | — | 6 | 1 | no | — |
| 367 | #625 | — | 6 | 1 | no | — |
| 368 | #624 | — | 3 | 1 | no | — |
| 369 | #624 | — | 3 | 1 | no | — |
| 370 | #624 | — | 6 | 1 | no | — |
| 371 | #624 | — | 6 | 1 | no | — |
| 372 | #624 | — | 6 | 1 | no | — |
| 373 | D3×Dic3 | — | 3 | 1 | no | — |
| 374 | D3×Dic3 | — | 3 | 1 | no | — |
| 375 | D3×Dic3 | — | 3 | 1 | no | — |
| 376 | D3×Dic3 | — | 3 | 1 | no | — |
| 377 | D3×Dic3 | — | 6 | 1 | no | — |
| 378 | D3×Dic3 | — | 6 | 1 | no | — |
| 379 | D3×Dic3 | — | 6 | 1 | no | — |
| 380 | D3×Dic3 | — | 6 | 1 | no | — |
| 381 | D3×Dic3 | — | 6 | 1 | no | — |
| 382 | C32×C8 | — | 2 | 1 | no | — |
| 383 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 384 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 385 | C3⋊(C3⋊C8) | C22×D3 | 1 | 1 | yes | characteristic |
| 386 | C3⋊(C3⋊C8) | C22×D3 | 1 | 1 | yes | characteristic |
| 387 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 388 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 389 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 390 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 391 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 392 | #575 | — | 27 | 1 | no | Sylow |
| 393 | C2×H(3,𝔽3) | C22×D4 | 1 | 1 | yes | characteristic |
| 394 | #272 | — | 2 | 1 | no | — |
| 395 | #272 | — | 4 | 1 | no | — |
| 396 | (C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 397 | (C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 398 | (C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 399 | (C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 400 | (C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 401 | C3×#41 | — | 9 | 1 | no | — |
| 402 | C3×#41 | — | 9 | 1 | no | — |
| 403 | C3×#41 | — | 9 | 1 | no | — |
| 404 | C3×#41 | — | 9 | 1 | no | — |
| 405 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 406 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 407 | #239 | — | 3 | 1 | no | — |
| 408 | #239 | — | 3 | 1 | no | — |
| 409 | #239 | — | 3 | 1 | no | — |
| 410 | #239 | — | 3 | 1 | no | — |
| 411 | #239 | — | 3 | 1 | no | — |
| 412 | #239 | — | 6 | 1 | no | — |
| 413 | #239 | — | 9 | 1 | no | — |
| 414 | #239 | — | 9 | 1 | no | — |
| 415 | #239 | — | 9 | 1 | no | — |
| 416 | #239 | — | 9 | 1 | no | — |
| 417 | #239 | — | 9 | 1 | no | — |
| 418 | #239 | — | 9 | 1 | no | — |
| 419 | #239 | — | 9 | 1 | no | — |
| 420 | #239 | — | 18 | 1 | no | — |
| 421 | #239 | — | 18 | 1 | no | — |
| 422 | #239 | — | 18 | 1 | no | — |
| 423 | #239 | — | 18 | 1 | no | — |
| 424 | D3×Q8 | — | 3 | 1 | no | — |
| 425 | D3×Q8 | — | 3 | 1 | no | — |
| 426 | D3×Q8 | — | 3 | 1 | no | — |
| 427 | D3×Q8 | — | 6 | 1 | no | — |
| 428 | D3×Q8 | — | 9 | 1 | no | — |
| 429 | #237 | — | 9 | 1 | no | — |
| 430 | #237 | — | 9 | 1 | no | — |
| 431 | #237 | — | 9 | 1 | no | — |
| 432 | #237 | — | 9 | 1 | no | — |
| 433 | #237 | — | 18 | 1 | no | — |
| 434 | #237 | — | 18 | 1 | no | — |
| 435 | #237 | — | 18 | 1 | no | — |
| 436 | #237 | — | 18 | 1 | no | — |
| 437 | D3×D4 | — | 9 | 1 | no | — |
| 438 | D3×D4 | — | 9 | 1 | no | — |
| 439 | D3×D4 | — | 9 | 1 | no | — |
| 440 | D3×D4 | — | 9 | 1 | no | — |
| 441 | D3×D4 | — | 18 | 1 | no | — |
| 442 | D3×D4 | — | 18 | 1 | no | — |
| 443 | D3×D4 | — | 18 | 1 | no | — |
| 444 | D3×D4 | — | 18 | 1 | no | — |
| 445 | #235 | — | 9 | 1 | no | — |
| 446 | #235 | — | 9 | 1 | no | — |
| 447 | #235 | — | 9 | 1 | no | — |
| 448 | #235 | — | 9 | 1 | no | — |
| 449 | #235 | — | 18 | 1 | no | — |
| 450 | #235 | — | 18 | 1 | no | — |
| 451 | #235 | — | 18 | 1 | no | — |
| 452 | #235 | — | 18 | 1 | no | — |
| 453 | C2×D12 | — | 9 | 1 | no | — |
| 454 | C2×D12 | — | 9 | 1 | no | — |
| 455 | C2×D12 | — | 18 | 1 | no | — |
| 456 | C2×D12 | — | 18 | 1 | no | — |
| 457 | C2×C4×D3 | — | 9 | 1 | no | — |
| 458 | C2×C4×D3 | — | 9 | 1 | no | — |
| 459 | C2×C4×D3 | — | 9 | 1 | no | — |
| 460 | C2×C4×D3 | — | 18 | 1 | no | — |
| 461 | C2×C4×D3 | — | 18 | 1 | no | — |
| 462 | C2×C4×D3 | — | 18 | 1 | no | — |
| 463 | C2×C4×D3 | — | 18 | 1 | no | — |
| 464 | C2×C4×D3 | — | 18 | 1 | no | — |
| 465 | C2×C4×D3 | — | 18 | 1 | no | — |
| 466 | C3×Q16 | — | 3 | 1 | no | — |
| 467 | C3×Q16 | — | 3 | 1 | no | — |
| 468 | C3×Q16 | — | 6 | 1 | no | — |
| 469 | C3×Q16 | — | 9 | 1 | no | — |
| 470 | C3×Q16 | — | 9 | 1 | no | — |
| 471 | C3×Q16 | D32 | 1 | 1 | yes | characteristic |
| 472 | C3×SD16 | — | 9 | 1 | no | — |
| 473 | C3×SD16 | — | 9 | 1 | no | — |
| 474 | C3×SD16 | — | 9 | 1 | no | — |
| 475 | C3×SD16 | — | 9 | 1 | no | — |
| 476 | C3×SD16 | — | 9 | 1 | no | — |
| 477 | C3×SD16 | — | 9 | 1 | no | — |
| 478 | C3×D8 | — | 9 | 1 | no | — |
| 479 | C3×M16 | — | 9 | 1 | no | — |
| 480 | C3×M16 | — | 9 | 1 | no | — |
| 481 | C2×C3×C8 | — | 9 | 1 | no | — |
| 482 | #216 | — | 3 | 1 | no | — |
| 483 | #216 | — | 3 | 1 | no | — |
| 484 | #216 | — | 3 | 1 | no | — |
| 485 | #216 | — | 6 | 1 | no | — |
| 486 | #216 | — | 9 | 1 | no | — |
| 487 | #216 | — | 9 | 1 | no | — |
| 488 | #216 | — | 9 | 1 | no | — |
| 489 | #215 | — | 3 | 1 | no | — |
| 490 | #215 | — | 3 | 1 | no | — |
| 491 | #215 | — | 3 | 1 | no | — |
| 492 | #215 | — | 3 | 1 | no | — |
| 493 | #215 | — | 3 | 1 | no | — |
| 494 | #215 | — | 6 | 1 | no | — |
| 495 | #215 | — | 9 | 1 | no | — |
| 496 | #215 | — | 9 | 1 | no | — |
| 497 | #215 | — | 9 | 1 | no | — |
| 498 | #215 | — | 9 | 1 | no | — |
| 499 | #215 | — | 9 | 1 | no | — |
| 500 | #214 | — | 9 | 1 | no | — |
| 501 | #214 | — | 9 | 1 | no | — |
| 502 | #213 | — | 9 | 1 | no | — |
| 503 | #213 | — | 9 | 1 | no | — |
| 504 | #213 | — | 9 | 1 | no | — |
| 505 | #213 | — | 9 | 1 | no | — |
| 506 | #213 | — | 9 | 1 | no | — |
| 507 | #213 | — | 9 | 1 | no | — |
| 508 | #208 | — | 9 | 1 | no | — |
| 509 | #208 | — | 9 | 1 | no | — |
| 510 | C2×C3⋊C8 | — | 9 | 1 | no | — |
| 511 | Dic12 | — | 9 | 1 | no | — |
| 512 | D24 | — | 3 | 1 | no | — |
| 513 | D24 | — | 9 | 1 | no | — |
| 514 | D24 | — | 9 | 1 | no | — |
| 515 | D24 | — | 9 | 1 | no | — |
| 516 | D24 | — | 9 | 1 | no | — |
| 517 | #204 | — | 3 | 1 | no | — |
| 518 | #204 | — | 3 | 1 | no | — |
| 519 | #204 | — | 3 | 1 | no | — |
| 520 | #204 | — | 6 | 1 | no | — |
| 521 | #204 | — | 9 | 1 | no | — |
| 522 | #204 | — | 9 | 1 | no | — |
| 523 | #204 | — | 9 | 1 | no | — |
| 524 | ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 525 | ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 526 | ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 527 | ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 528 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 529 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 530 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 531 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 532 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 533 | D3×C8 | — | 3 | 1 | no | — |
| 534 | D3×C8 | — | 9 | 1 | no | — |
| 535 | D3×C8 | — | 9 | 1 | no | — |
| 536 | D3×C8 | — | 9 | 1 | no | — |
| 537 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 538 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 539 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 540 | C2×C3⋊D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 541 | C2×C3⋊D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 542 | C2×C3×D3 | — | 3 | 1 | no | — |
| 543 | C2×C3×D3 | — | 3 | 1 | no | — |
| 544 | C2×C3×D3 | — | 3 | 1 | no | — |
| 545 | C2×C3×D3 | — | 3 | 1 | no | — |
| 546 | C2×C3×D3 | — | 6 | 1 | no | — |
| 547 | C2×C3×D3 | — | 6 | 1 | no | — |
| 548 | C2×C3×D3 | — | 6 | 1 | no | — |
| 549 | C2×C3×D3 | — | 6 | 1 | no | — |
| 550 | C2×C3×D3 | — | 6 | 1 | no | — |
| 551 | C2×C3×D3 | — | 6 | 1 | no | — |
| 552 | C2×C3×D3 | — | 12 | 1 | no | — |
| 553 | D32 | — | 12 | 1 | no | — |
| 554 | D32 | — | 12 | 1 | no | — |
| 555 | D32 | — | 12 | 2 | no | — |
| 556 | D32 | — | 12 | 2 | no | — |
| 557 | D32 | — | 12 | 2 | no | — |
| 558 | D32 | — | 12 | 2 | no | — |
| 559 | C32×C4 | — | 2 | 1 | no | — |
| 560 | C32×C4 | — | 2 | 1 | no | — |
| 561 | C32×C4 | — | 2 | 1 | no | — |
| 562 | C32×C4 | — | 2 | 1 | no | — |
| 563 | C32×C4 | — | 2 | 1 | no | — |
| 564 | C32×C4 | — | 4 | 1 | no | — |
| 565 | C32×C4 | — | 4 | 1 | no | — |
| 566 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 567 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 568 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 569 | C3⋊Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 570 | C3⋊Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 571 | C3×Dic3 | — | 3 | 1 | no | — |
| 572 | C3×Dic3 | — | 3 | 1 | no | — |
| 573 | C3×Dic3 | — | 3 | 1 | no | — |
| 574 | C3×Dic3 | — | 3 | 1 | no | — |
| 575 | C3×Dic3 | — | 6 | 1 | no | — |
| 576 | C3×Dic3 | — | 6 | 1 | no | — |
| 577 | C3×Dic3 | — | 6 | 1 | no | — |
| 578 | C3×Dic3 | — | 6 | 1 | no | — |
| 579 | C3×Dic3 | — | 12 | 1 | no | — |
| 580 | C2×#41 | — | 27 | 1 | no | — |
| 581 | C2×#41 | — | 27 | 1 | no | — |
| 582 | #137 | — | 9 | 1 | no | — |
| 583 | #137 | — | 9 | 1 | no | — |
| 584 | #137 | — | 27 | 1 | no | — |
| 585 | #137 | — | 27 | 1 | no | — |
| 586 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 587 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 588 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 589 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 590 | #135 | — | 9 | 1 | no | — |
| 591 | #135 | — | 27 | 1 | no | — |
| 592 | #135 | — | 27 | 1 | no | — |
| 593 | #135 | — | 27 | 1 | no | — |
| 594 | C2×M16 | — | 27 | 1 | no | — |
| 595 | H(3,𝔽3) | #575 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 596 | C22×D3 | — | 9 | 1 | no | — |
| 597 | C22×D3 | — | 9 | 1 | no | — |
| 598 | C22×D3 | — | 9 | 1 | no | — |
| 599 | C22×D3 | — | 18 | 1 | no | — |
| 600 | C22×D3 | — | 18 | 1 | no | — |
| 601 | C22×D3 | — | 18 | 1 | no | — |
| 602 | C22×D3 | — | 18 | 1 | no | — |
| 603 | C22×D3 | — | 18 | 1 | no | — |
| 604 | C22×D3 | — | 18 | 1 | no | — |
| 605 | C3×Q8 | — | 3 | 1 | no | — |
| 606 | C3×Q8 | — | 3 | 1 | no | — |
| 607 | C3×Q8 | — | 3 | 1 | no | — |
| 608 | C3×Q8 | — | 3 | 1 | no | — |
| 609 | C3×Q8 | — | 6 | 1 | no | — |
| 610 | C3×Q8 | — | 6 | 1 | no | — |
| 611 | C3×Q8 | — | 9 | 1 | no | — |
| 612 | C3×Q8 | — | 9 | 1 | no | — |
| 613 | C3×Q8 | — | 18 | 1 | no | — |
| 614 | C3×Q8 | — | 18 | 1 | no | — |
| 615 | C3×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 616 | C3×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 617 | C3×D4 | — | 9 | 1 | no | — |
| 618 | C3×D4 | — | 9 | 1 | no | — |
| 619 | C3×D4 | — | 9 | 1 | no | — |
| 620 | C3×D4 | — | 9 | 1 | no | — |
| 621 | C3×D4 | — | 18 | 1 | no | — |
| 622 | C3×D4 | — | 18 | 1 | no | — |
| 623 | C3×D4 | — | 18 | 1 | no | — |
| 624 | C3×D4 | — | 18 | 1 | no | — |
| 625 | C2×C3×C4 | — | 9 | 1 | no | — |
| 626 | C2×C3×C4 | — | 9 | 1 | no | — |
| 627 | C2×C3×C4 | — | 9 | 1 | no | — |
| 628 | C2×C3×C4 | — | 18 | 1 | no | — |
| 629 | C2×C3×C4 | — | 18 | 1 | no | — |
| 630 | C2×C3×C4 | — | 18 | 1 | no | — |
| 631 | C2×C3×C4 | — | 18 | 1 | no | — |
| 632 | C2×C3×C4 | — | 18 | 1 | no | — |
| 633 | C2×C3×C4 | — | 18 | 1 | no | — |
| 634 | #67 | — | 18 | 1 | no | — |
| 635 | #67 | — | 18 | 1 | no | — |
| 636 | #67 | — | 18 | 1 | no | — |
| 637 | #67 | — | 18 | 1 | no | — |
| 638 | #67 | — | 18 | 1 | no | — |
| 639 | #67 | — | 18 | 1 | no | — |
| 640 | #67 | — | 18 | 1 | no | — |
| 641 | #67 | — | 18 | 1 | no | — |
| 642 | #67 | — | 18 | 1 | no | — |
| 643 | #67 | — | 18 | 1 | no | — |
| 644 | #67 | — | 18 | 1 | no | — |
| 645 | #67 | — | 18 | 1 | no | — |
| 646 | C2×Dic3 | — | 9 | 1 | no | — |
| 647 | C2×Dic3 | — | 9 | 1 | no | — |
| 648 | C2×Dic3 | — | 9 | 1 | no | — |
| 649 | C2×Dic3 | — | 18 | 1 | no | — |
| 650 | C2×Dic3 | — | 18 | 1 | no | — |
| 651 | C2×Dic3 | — | 18 | 1 | no | — |
| 652 | C2×Dic3 | — | 18 | 1 | no | — |
| 653 | D12 | — | 3 | 1 | no | — |
| 654 | D12 | — | 3 | 1 | no | — |
| 655 | D12 | — | 3 | 1 | no | — |
| 656 | D12 | — | 3 | 1 | no | — |
| 657 | D12 | — | 3 | 1 | no | — |
| 658 | D12 | — | 6 | 1 | no | — |
| 659 | D12 | — | 6 | 1 | no | — |
| 660 | D12 | — | 6 | 1 | no | — |
| 661 | D12 | — | 6 | 1 | no | — |
| 662 | D12 | — | 6 | 1 | no | — |
| 663 | D12 | — | 6 | 1 | no | — |
| 664 | D12 | — | 9 | 1 | no | — |
| 665 | D12 | — | 9 | 1 | no | — |
| 666 | D12 | — | 9 | 1 | no | — |
| 667 | D12 | — | 12 | 1 | no | — |
| 668 | D12 | — | 18 | 1 | no | — |
| 669 | D12 | — | 18 | 1 | no | — |
| 670 | D12 | — | 18 | 1 | no | — |
| 671 | D12 | — | 18 | 1 | no | — |
| 672 | D12 | — | 18 | 1 | no | — |
| 673 | D12 | — | 18 | 1 | no | — |
| 674 | D12 | — | 18 | 1 | no | — |
| 675 | D12 | — | 18 | 1 | no | — |
| 676 | D12 | — | 18 | 1 | no | — |
| 677 | C4×D3 | — | 3 | 1 | no | — |
| 678 | C4×D3 | — | 3 | 1 | no | — |
| 679 | C4×D3 | — | 3 | 1 | no | — |
| 680 | C4×D3 | — | 3 | 1 | no | — |
| 681 | C4×D3 | — | 6 | 1 | no | — |
| 682 | C4×D3 | — | 6 | 1 | no | — |
| 683 | C4×D3 | — | 6 | 1 | no | — |
| 684 | C4×D3 | — | 6 | 1 | no | — |
| 685 | C4×D3 | — | 6 | 1 | no | — |
| 686 | C4×D3 | — | 6 | 1 | no | — |
| 687 | C4×D3 | — | 6 | 1 | no | — |
| 688 | C4×D3 | — | 6 | 1 | no | — |
| 689 | C4×D3 | — | 6 | 1 | no | — |
| 690 | C4×D3 | — | 9 | 1 | no | — |
| 691 | C4×D3 | — | 9 | 1 | no | — |
| 692 | C4×D3 | — | 9 | 1 | no | — |
| 693 | C4×D3 | — | 9 | 1 | no | — |
| 694 | C4×D3 | — | 9 | 1 | no | — |
| 695 | C4×D3 | — | 9 | 1 | no | — |
| 696 | C4×D3 | — | 9 | 1 | no | — |
| 697 | C4×D3 | — | 9 | 1 | no | — |
| 698 | C4×D3 | — | 12 | 1 | no | — |
| 699 | C4×D3 | — | 12 | 1 | no | — |
| 700 | C4×D3 | — | 18 | 1 | no | — |
| 701 | C4×D3 | — | 18 | 1 | no | — |
| 702 | C4×D3 | — | 18 | 1 | no | — |
| 703 | C4×D3 | — | 18 | 1 | no | — |
| 704 | C4×D3 | — | 18 | 1 | no | — |
| 705 | C4×D3 | — | 18 | 1 | no | — |
| 706 | C4×D3 | — | 18 | 1 | no | — |
| 707 | C4×D3 | — | 18 | 1 | no | — |
| 708 | C4×D3 | — | 18 | 1 | no | — |
| 709 | C4×D3 | — | 18 | 1 | no | — |
| 710 | C4×D3 | — | 18 | 1 | no | — |
| 711 | C4×D3 | — | 18 | 1 | no | — |
| 712 | Dic6 | — | 3 | 1 | no | — |
| 713 | Dic6 | — | 3 | 1 | no | — |
| 714 | Dic6 | — | 3 | 1 | no | — |
| 715 | Dic6 | — | 6 | 1 | no | — |
| 716 | Dic6 | — | 6 | 1 | no | — |
| 717 | Dic6 | — | 6 | 1 | no | — |
| 718 | Dic6 | — | 6 | 1 | no | — |
| 719 | Dic6 | — | 9 | 1 | no | — |
| 720 | Dic6 | — | 12 | 1 | no | — |
| 721 | Dic6 | — | 18 | 1 | no | — |
| 722 | C3×C8 | — | 3 | 1 | no | — |
| 723 | C3×C8 | — | 3 | 1 | no | — |
| 724 | C3×C8 | — | 6 | 1 | no | — |
| 725 | C3×C8 | — | 9 | 1 | no | — |
| 726 | C3×C8 | — | 9 | 1 | no | — |
| 727 | C3×C8 | — | 9 | 1 | no | — |
| 728 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 729 | C3⋊C8 | — | 3 | 1 | no | — |
| 730 | C3⋊C8 | — | 3 | 1 | no | — |
| 731 | C3⋊C8 | — | 3 | 1 | no | — |
| 732 | C3⋊C8 | — | 3 | 1 | no | — |
| 733 | C3⋊C8 | — | 6 | 1 | no | — |
| 734 | C3⋊C8 | — | 9 | 1 | no | — |
| 735 | C3⋊C8 | — | 9 | 1 | no | — |
| 736 | C2×C32 | — | 2 | 1 | no | — |
| 737 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 738 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 739 | C3⋊D3 | — | 2 | 1 | no | — |
| 740 | C3⋊D3 | — | 2 | 1 | no | — |
| 741 | C3⋊D3 | — | 4 | 1 | no | — |
| 742 | C3⋊D3 | — | 4 | 1 | no | — |
| 743 | C3⋊D3 | — | 4 | 1 | no | — |
| 744 | C3×D3 | — | 6 | 1 | no | — |
| 745 | C3×D3 | — | 6 | 1 | no | — |
| 746 | C3×D3 | — | 6 | 1 | no | — |
| 747 | C3×D3 | — | 6 | 1 | no | — |
| 748 | C3×D3 | — | 12 | 1 | no | — |
| 749 | C3×D3 | — | 12 | 1 | no | — |
| 750 | C3×D3 | — | 12 | 1 | no | — |
| 751 | C3×D3 | — | 12 | 1 | no | — |
| 752 | C3×D3 | — | 12 | 1 | no | — |
| 753 | C3×D3 | — | 12 | 1 | no | — |
| 754 | C3×D3 | — | 24 | 1 | no | — |
| 755 | #41 | — | 9 | 1 | no | — |
| 756 | #41 | — | 9 | 1 | no | — |
| 757 | #41 | — | 9 | 1 | no | — |
| 758 | #41 | — | 9 | 1 | no | — |
| 759 | #41 | — | 27 | 1 | no | — |
| 760 | #41 | — | 27 | 1 | no | — |
| 761 | #41 | — | 27 | 1 | no | — |
| 762 | #41 | — | 27 | 1 | no | — |
| 763 | #41 | — | 54 | 1 | no | — |
| 764 | #41 | — | 54 | 1 | no | — |
| 765 | #41 | — | 54 | 1 | no | — |
| 766 | #41 | — | 54 | 1 | no | — |
| 767 | C2×Q8 | — | 9 | 1 | no | — |
| 768 | C2×Q8 | — | 9 | 1 | no | — |
| 769 | C2×D4 | — | 27 | 1 | no | — |
| 770 | C2×D4 | — | 27 | 1 | no | — |
| 771 | C2×D4 | — | 54 | 1 | no | — |
| 772 | C2×D4 | — | 54 | 1 | no | — |
| 773 | C22×C4 | — | 27 | 1 | no | — |
| 774 | C22×C4 | — | 54 | 1 | no | — |
| 775 | C22×C4 | — | 54 | 1 | no | — |
| 776 | Q16 | — | 9 | 1 | no | — |
| 777 | Q16 | — | 9 | 1 | no | — |
| 778 | Q16 | — | 27 | 1 | no | — |
| 779 | Q16 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 780 | SD16 | — | 9 | 1 | no | — |
| 781 | SD16 | — | 9 | 1 | no | — |
| 782 | SD16 | — | 9 | 1 | no | — |
| 783 | SD16 | — | 9 | 1 | no | — |
| 784 | SD16 | — | 9 | 1 | no | — |
| 785 | SD16 | — | 9 | 1 | no | — |
| 786 | SD16 | — | 27 | 1 | no | — |
| 787 | SD16 | — | 27 | 1 | no | — |
| 788 | D8 | — | 9 | 1 | no | — |
| 789 | D8 | — | 27 | 1 | no | — |
| 790 | D8 | — | 27 | 1 | no | — |
| 791 | D8 | — | 27 | 1 | no | — |
| 792 | M16 | — | 9 | 1 | no | — |
| 793 | M16 | — | 9 | 1 | no | — |
| 794 | M16 | — | 27 | 1 | no | — |
| 795 | M16 | — | 27 | 1 | no | — |
| 796 | C2×C8 | — | 9 | 1 | no | — |
| 797 | C2×C8 | — | 27 | 1 | no | — |
| 798 | C22×C3 | — | 9 | 1 | no | — |
| 799 | C22×C3 | — | 9 | 1 | no | — |
| 800 | C22×C3 | — | 9 | 1 | no | — |
| 801 | C22×C3 | — | 18 | 1 | no | — |
| 802 | C22×C3 | — | 18 | 1 | no | — |
| 803 | C22×C3 | — | 18 | 1 | no | — |
| 804 | C22×C3 | — | 18 | 1 | no | — |
| 805 | C2×D3 | — | 3 | 1 | no | — |
| 806 | C2×D3 | — | 3 | 1 | no | — |
| 807 | C2×D3 | — | 3 | 1 | no | — |
| 808 | C2×D3 | — | 3 | 1 | no | — |
| 809 | C2×D3 | — | 6 | 1 | no | — |
| 810 | C2×D3 | — | 6 | 1 | no | — |
| 811 | C2×D3 | — | 6 | 1 | no | — |
| 812 | C2×D3 | — | 6 | 1 | no | — |
| 813 | C2×D3 | — | 6 | 1 | no | — |
| 814 | C2×D3 | — | 6 | 1 | no | — |
| 815 | C2×D3 | — | 9 | 1 | no | — |
| 816 | C2×D3 | — | 9 | 1 | no | — |
| 817 | C2×D3 | — | 12 | 1 | no | — |
| 818 | C2×D3 | — | 18 | 1 | no | — |
| 819 | C2×D3 | — | 18 | 1 | no | — |
| 820 | C2×D3 | — | 18 | 1 | no | — |
| 821 | C2×D3 | — | 36 | 1 | no | — |
| 822 | C2×D3 | — | 36 | 2 | no | — |
| 823 | C2×D3 | — | 36 | 1 | no | — |
| 824 | C2×D3 | — | 36 | 1 | no | — |
| 825 | C2×D3 | — | 36 | 2 | no | — |
| 826 | C2×D3 | — | 36 | 2 | no | — |
| 827 | C2×D3 | — | 36 | 2 | no | — |
| 828 | C2×D3 | — | 36 | 2 | no | — |
| 829 | C2×D3 | — | 36 | 2 | no | — |
| 830 | C3×C4 | — | 2 | 1 | no | — |
| 831 | C3×C4 | — | 2 | 1 | no | — |
| 832 | C3×C4 | — | 3 | 1 | no | — |
| 833 | C3×C4 | — | 3 | 1 | no | — |
| 834 | C3×C4 | — | 6 | 1 | no | — |
| 835 | C3×C4 | — | 6 | 1 | no | — |
| 836 | C3×C4 | — | 6 | 1 | no | — |
| 837 | C3×C4 | — | 6 | 1 | no | — |
| 838 | C3×C4 | — | 6 | 1 | no | — |
| 839 | C3×C4 | — | 9 | 1 | no | — |
| 840 | C3×C4 | — | 9 | 1 | no | — |
| 841 | C3×C4 | — | 9 | 1 | no | — |
| 842 | C3×C4 | — | 12 | 1 | no | — |
| 843 | C3×C4 | — | 12 | 1 | no | — |
| 844 | C3×C4 | — | 18 | 1 | no | — |
| 845 | C3×C4 | — | 18 | 1 | no | — |
| 846 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 847 | Dic3 | — | 3 | 1 | no | — |
| 848 | Dic3 | — | 3 | 1 | no | — |
| 849 | Dic3 | — | 3 | 1 | no | — |
| 850 | Dic3 | — | 3 | 1 | no | — |
| 851 | Dic3 | — | 6 | 1 | no | — |
| 852 | Dic3 | — | 6 | 1 | no | — |
| 853 | Dic3 | — | 6 | 1 | no | — |
| 854 | Dic3 | — | 6 | 1 | no | — |
| 855 | Dic3 | — | 9 | 1 | no | — |
| 856 | Dic3 | — | 9 | 1 | no | — |
| 857 | Dic3 | — | 12 | 1 | no | — |
| 858 | Dic3 | — | 18 | 1 | no | — |
| 859 | C32 | — | 2 | 1 | no | — |
| 860 | C32 | #5768 | 1 | 1 | yes | characteristic, complemented |
| 861 | C32 | #5777 | 1 | 1 | yes | characteristic, complemented |
| 862 | C23 | — | 27 | 1 | no | — |
| 863 | C23 | — | 54 | 1 | no | — |
| 864 | C23 | — | 54 | 1 | no | — |
| 865 | Q8 | — | 9 | 1 | no | — |
| 866 | Q8 | — | 9 | 1 | no | — |
| 867 | Q8 | — | 18 | 1 | no | — |
| 868 | Q8 | — | 18 | 1 | no | — |
| 869 | Q8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 870 | Q8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 871 | D4 | — | 9 | 1 | no | — |
| 872 | D4 | — | 9 | 1 | no | — |
| 873 | D4 | — | 9 | 1 | no | — |
| 874 | D4 | — | 9 | 1 | no | — |
| 875 | D4 | — | 18 | 1 | no | — |
| 876 | D4 | — | 18 | 1 | no | — |
| 877 | D4 | — | 18 | 1 | no | — |
| 878 | D4 | — | 18 | 1 | no | — |
| 879 | D4 | — | 54 | 1 | no | — |
| 880 | D4 | — | 54 | 1 | no | — |
| 881 | D4 | — | 54 | 1 | no | — |
| 882 | D4 | — | 54 | 1 | no | — |
| 883 | D4 | — | 54 | 1 | no | — |
| 884 | D4 | — | 54 | 1 | no | — |
| 885 | C2×C4 | — | 9 | 1 | no | — |
| 886 | C2×C4 | — | 9 | 1 | no | — |
| 887 | C2×C4 | — | 9 | 1 | no | — |
| 888 | C2×C4 | — | 18 | 1 | no | — |
| 889 | C2×C4 | — | 18 | 1 | no | — |
| 890 | C2×C4 | — | 18 | 1 | no | — |
| 891 | C2×C4 | — | 18 | 1 | no | — |
| 892 | C2×C4 | — | 18 | 1 | no | — |
| 893 | C2×C4 | — | 18 | 1 | no | — |
| 894 | C2×C4 | — | 27 | 1 | no | — |
| 895 | C2×C4 | — | 27 | 1 | no | — |
| 896 | C2×C4 | — | 27 | 1 | no | — |
| 897 | C2×C4 | — | 54 | 1 | no | — |
| 898 | C2×C4 | — | 54 | 1 | no | — |
| 899 | C2×C4 | — | 54 | 1 | no | — |
| 900 | C2×C4 | — | 54 | 1 | no | — |
| 901 | C8 | — | 9 | 1 | no | — |
| 902 | C8 | — | 9 | 1 | no | — |
| 903 | C8 | — | 9 | 1 | no | — |
| 904 | C8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 905 | C2×C3 | — | 3 | 1 | no | — |
| 906 | C2×C3 | — | 3 | 1 | no | — |
| 907 | C2×C3 | — | 6 | 1 | no | — |
| 908 | C2×C3 | — | 18 | 1 | no | — |
| 909 | C2×C3 | — | 18 | 1 | no | — |
| 910 | C2×C3 | — | 18 | 1 | no | — |
| 911 | C2×C3 | — | 36 | 1 | no | — |
| 912 | C2×C3 | — | 36 | 1 | no | — |
| 913 | C2×C3 | — | 36 | 1 | no | — |
| 914 | C2×C3 | — | 36 | 1 | no | — |
| 915 | C2×C3 | D32×D4 | 1 | 1 | yes | characteristic |
| 916 | D3 | — | 6 | 1 | no | — |
| 917 | D3 | — | 6 | 1 | no | — |
| 918 | D3 | — | 6 | 1 | no | — |
| 919 | D3 | — | 6 | 1 | no | — |
| 920 | D3 | — | 12 | 1 | no | — |
| 921 | D3 | — | 12 | 1 | no | — |
| 922 | D3 | — | 12 | 1 | no | — |
| 923 | D3 | — | 12 | 1 | no | — |
| 924 | D3 | — | 12 | 1 | no | — |
| 925 | D3 | — | 12 | 1 | no | — |
| 926 | D3 | — | 18 | 1 | no | — |
| 927 | D3 | — | 18 | 1 | no | — |
| 928 | D3 | — | 24 | 1 | no | — |
| 929 | D3 | — | 36 | 1 | no | — |
| 930 | D3 | — | 36 | 1 | no | — |
| 931 | D3 | — | 36 | 1 | no | — |
| 932 | C22 | — | 9 | 1 | no | — |
| 933 | C22 | — | 9 | 1 | no | — |
| 934 | C22 | — | 9 | 1 | no | — |
| 935 | C22 | — | 18 | 1 | no | — |
| 936 | C22 | — | 18 | 1 | no | — |
| 937 | C22 | — | 18 | 1 | no | — |
| 938 | C22 | — | 18 | 1 | no | — |
| 939 | C22 | — | 108 | 1 | no | — |
| 940 | C22 | — | 108 | 2 | no | — |
| 941 | C22 | — | 108 | 2 | no | — |
| 942 | C4 | — | 2 | 1 | no | — |
| 943 | C4 | — | 2 | 1 | no | — |
| 944 | C4 | — | 9 | 1 | no | — |
| 945 | C4 | — | 9 | 1 | no | — |
| 946 | C4 | — | 9 | 1 | no | — |
| 947 | C4 | — | 18 | 1 | no | — |
| 948 | C4 | — | 18 | 1 | no | — |
| 949 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 950 | C3 | — | 3 | 1 | no | — |
| 951 | C3 | — | 3 | 1 | no | — |
| 952 | C3 | — | 6 | 1 | no | — |
| 953 | C3 | #10594763 | 1 | 1 | yes | characteristic |
| 954 | C2 | — | 18 | 1 | no | — |
| 955 | C2 | — | 18 | 1 | no | — |
| 956 | C2 | — | 18 | 1 | no | — |
| 957 | C2 | — | 36 | 1 | no | — |
| 958 | C2 | — | 36 | 1 | no | — |
| 959 | C2 | — | 36 | 1 | no | — |
| 960 | C2 | — | 36 | 1 | no | — |
| 961 | 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. #11722520 | C2 | semidirect |
| 2. #11722519 | C2 | semidirect |
| 3. #11721807 | C2 | semidirect |
| 4. #64128⋊C3 | C2 | semidirect |
| 5. #64127⋊C3 | C2 | semidirect |
| 6. #11721239 | C2 | semidirect |
| 7. #11721238 | C2 | semidirect |
| 8. #11721235 | C2 | semidirect |
| 9. #11721233 | C2 | semidirect |
| 10. #11721231 | C2 | semidirect |
| 11. #11721229 | C2 | semidirect |
| 12. #11720854 | C2 | semidirect |
| 13. #11720849 | C2 | semidirect |
| 14. #11720839 | C2 | semidirect |
| 15. #11720835 | C2 | semidirect |
| 19. Q8×#272 | C22 | semidirect |
| 21. #88722 | C22 | semidirect |
| 22. #88722 | C22 | semidirect |
| 23. Q8×(C3⋊D3)⋊C3 | C22 | semidirect |
| 25. #88655 | C22 | semidirect |
| 27. #88654 | C22 | semidirect |
| 32. #88652 | C22 | semidirect |
| 38. #88648 | C22 | semidirect |
| 39. Q16×H(3,𝔽3) | C22 | semidirect |
| 40. #88550 | C22 | semidirect |
| 41. #88549 | C22 | semidirect |
| 42. #88528 | C22 | semidirect |
| 43. #88527 | C22 | semidirect |
| 44. #3755⋊C3 | C22 | semidirect |
| 45. #3755⋊C3 | C22 | semidirect |
| 46. #3755⋊C3 | C22 | semidirect |
| 47. #3756⋊C3 | C22 | semidirect |
| 48. #3745⋊C3 | C22 | semidirect |
| 49. #3744⋊C3 | C22 | semidirect |
| 50. #3743⋊C3 | C22 | semidirect |
| 51. C8×(C3⋊D3)⋊C3 | C22 | semidirect |
| 52. #88439 | C22 | semidirect |
| 53. #88438 | C22 | semidirect |
| 54. #88436 | C22 | semidirect |
| 55. #88436 | C22 | semidirect |
| 56. #88435 | C22 | semidirect |
| 57. #88432 | C22 | semidirect |
| 58. #88431 | C22 | semidirect |
| 59. #88430 | C22 | semidirect |
| 60. ((C3⋊D3)⋊C3)⋊C8 | C22 | semidirect |
| 65. #64128 | D3 | semidirect |
| 66. #64127 | D3 | semidirect |
| 139. #3832 | C2×D3 | semidirect |
| 140. #3832 | C2×D3 | semidirect |
| 141. Q8×C3⋊D3 | C2×D3 | semidirect |
| 183. C32×Q16 | C2×D3 | semidirect |
| 184. C32×Q16 | C2×D3 | semidirect |
| 185. #3756 | C2×D3 | semidirect |
| 186. #3755 | C2×D3 | semidirect |
| 187. #3755 | C2×D3 | semidirect |
| 188. #3755 | C2×D3 | semidirect |
| 189. #3745 | C2×D3 | semidirect |
| 190. #3744 | C2×D3 | semidirect |
| 191. #3743 | C2×D3 | semidirect |
| 192. C8×C3⋊D3 | C2×D3 | semidirect |
| 595. H(3,𝔽3) | #575 | semidirect |
| 779. Q16 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 860. C32 | #5768 | semidirect |
| 861. C32 | #5777 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722520 | 2 |
| #11722519 | 2 |
| #11721807 | 2 |
| #64128⋊C3 | 2 |
| #64127⋊C3 | 2 |
| #11721239 | 2 |
| #11721238 | 2 |
| #11721235 | 2 |
| #11721233 | 2 |
| #11721231 | 2 |
| #11721229 | 2 |
| #11720854 | 2 |
| #11720849 | 2 |
| #11720839 | 2 |
| #11720835 | 2 |
| #10594763 | 3 |
| #10594762 | 3 |