Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1154 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11724407 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×D32×Dic3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11724346 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11724331 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11724319 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#64241 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11724261 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11724119 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11724117 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | (D32⋊D3)⋊C4 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | Dic3×GO+(4,𝔽2) | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #10596510 | — | 3 | 1 | no | maximal |
| 13 | C22×C3×D32 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×D32⋊D3 | C22 | 1 | 2 | yes | — |
| 15 | C2×C3×GO+(4,𝔽2) | C22 | 1 | 2 | yes | — |
| 16 | #89049 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#6294 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×Dic3×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 19 | #89029 | — | 2 | 1 | no | — |
| 20 | C2×D3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 21 | C3×#3811 | C22 | 1 | 1 | yes | characteristic |
| 22 | C3×#3804 | — | 2 | 1 | no | — |
| 23 | C2×C3×D3×Dic3 | — | 2 | 1 | no | — |
| 24 | #88994 | C22 | 1 | 1 | yes | characteristic |
| 25 | C3×C22⋊#157 | C22 | 1 | 1 | yes | characteristic |
| 26 | #88964 | — | 2 | 1 | no | — |
| 27 | #88960 | — | 2 | 1 | no | — |
| 28 | #88957 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #88953 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | #88949 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | D32×Dic3 | — | 2 | 1 | no | — |
| 32 | D32×Dic3 | — | 2 | 1 | no | — |
| 33 | D32×Dic3 | C22 | 1 | 2 | yes | — |
| 34 | D32×Dic3 | C22 | 1 | 2 | yes | — |
| 35 | D32×Dic3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #88940 | C22 | 1 | 2 | yes | complemented |
| 37 | #88939 | C22 | 1 | 2 | yes | complemented |
| 38 | #88934 | C22 | 1 | 2 | yes | complemented |
| 39 | D32⋊Dic3 | C22 | 1 | 2 | yes | — |
| 40 | D32⋊Dic3 | C22 | 1 | 2 | yes | complemented |
| 41 | C3×D32⋊C4 | C22 | 1 | 2 | yes | — |
| 42 | Dic3⋊#157 | C22 | 1 | 2 | yes | complemented |
| 43 | Dic3×#157 | C22 | 1 | 2 | yes | complemented |
| 44 | C22×D3×Dic3 | — | 6 | 1 | no | — |
| 45 | D3×#237 | — | 6 | 1 | no | — |
| 46 | #64306 | — | 3 | 1 | no | — |
| 47 | C2×C4×D32 | — | 3 | 1 | no | — |
| 48 | #64286 | — | 3 | 1 | no | — |
| 49 | #64241 | — | 3 | 1 | no | — |
| 50 | #64241 | D3 | 1 | 1 | yes | characteristic, complemented |
| 51 | #64233 | — | 3 | 1 | no | — |
| 52 | #64233 | — | 3 | 1 | no | — |
| 53 | #64230 | — | 3 | 2 | no | — |
| 54 | C4×GO+(4,𝔽2) | — | 3 | 2 | no | — |
| 55 | C4×GO+(4,𝔽2) | — | 3 | 2 | no | — |
| 56 | D32⋊Q8 | — | 3 | 2 | no | — |
| 57 | C22×C3×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 58 | C22×C32×D3 | — | 2 | 1 | no | — |
| 59 | C2×#1113 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×C3×D32 | — | 2 | 1 | no | — |
| 61 | C2×C3×D32 | — | 2 | 4 | no | — |
| 62 | C2×C3×D32 | C23 | 1 | 1 | yes | characteristic |
| 63 | C2×C3×D32 | C23 | 1 | 2 | yes | — |
| 64 | C2×C3⋊#157 | C23 | 1 | 2 | yes | — |
| 65 | C2×C3×#157 | C23 | 1 | 2 | yes | — |
| 66 | D32⋊D3 | — | 2 | 4 | no | — |
| 67 | C3×GO+(4,𝔽2) | — | 2 | 4 | no | — |
| 68 | C2×C3⋊(C3⋊Dic3) | D4 | 1 | 1 | yes | characteristic, complemented |
| 69 | C3×#638 | — | 2 | 1 | no | — |
| 70 | C2×C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 71 | C32×#67 | — | 2 | 1 | no | — |
| 72 | C2×C32×Dic3 | D4 | 1 | 1 | yes | characteristic, complemented |
| 73 | #6295 | — | 2 | 1 | no | — |
| 74 | #6294 | — | 2 | 1 | no | — |
| 75 | #6294 | C23 | 1 | 1 | yes | characteristic |
| 76 | #6294 | C23 | 1 | 2 | yes | — |
| 77 | #6293 | — | 2 | 1 | no | — |
| 78 | #6290 | — | 2 | 1 | no | — |
| 79 | Dic3×C3⋊D3 | — | 2 | 1 | no | — |
| 80 | Dic3×C3⋊D3 | D4 | 1 | 1 | yes | characteristic, complemented |
| 81 | Dic3×C3⋊D3 | D4 | 1 | 1 | yes | characteristic, complemented |
| 82 | Dic3×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 83 | Dic3×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 84 | D3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 85 | D3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 86 | D3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 87 | C3×#627 | — | 2 | 1 | no | — |
| 88 | C3×#626 | — | 2 | 1 | no | — |
| 89 | C3×#626 | — | 2 | 1 | no | — |
| 90 | C3×#624 | — | 2 | 1 | no | — |
| 91 | C3×#624 | C23 | 1 | 1 | yes | characteristic |
| 92 | C3×D3×Dic3 | — | 2 | 2 | no | — |
| 93 | C3×D3×Dic3 | — | 2 | 2 | no | — |
| 94 | C3×D3×Dic3 | — | 2 | 1 | no | — |
| 95 | #5586 | — | 9 | 1 | no | maximal |
| 96 | C23×C3×D3 | — | 6 | 1 | no | — |
| 97 | C22×D32 | C2×D3 | 1 | 1 | yes | characteristic |
| 98 | C2×GO+(4,𝔽2) | — | 3 | 2 | no | — |
| 99 | C2×GO+(4,𝔽2) | C2×D3 | 1 | 2 | yes | — |
| 100 | C22×C3⋊Dic3 | — | 6 | 1 | no | — |
| 101 | #3830 | — | 6 | 1 | no | — |
| 102 | C2×C4×C3⋊D3 | — | 3 | 1 | no | — |
| 103 | C22×C3×Dic3 | — | 6 | 1 | no | — |
| 104 | C3×#237 | — | 6 | 1 | no | — |
| 105 | C3×D3×D4 | — | 6 | 1 | no | — |
| 106 | C3×#235 | — | 6 | 1 | no | — |
| 107 | C2×C3×C4×D3 | — | 6 | 1 | no | — |
| 108 | #3811 | — | 3 | 1 | no | — |
| 109 | #3811 | C2×D3 | 1 | 1 | yes | characteristic |
| 110 | D3×#67 | — | 6 | 1 | no | — |
| 111 | D3×#67 | — | 6 | 1 | no | — |
| 112 | C2×#624 | — | 3 | 1 | no | — |
| 113 | #3805 | — | 6 | 1 | no | — |
| 114 | #3805 | — | 6 | 1 | no | — |
| 115 | #3805 | — | 6 | 1 | no | — |
| 116 | #3805 | — | 12 | 1 | no | — |
| 117 | #3804 | — | 2 | 1 | no | — |
| 118 | #3804 | — | 6 | 1 | no | — |
| 119 | C2×D3×Dic3 | — | 2 | 1 | no | — |
| 120 | C2×D3×Dic3 | — | 6 | 1 | no | — |
| 121 | C2×D3×Dic3 | — | 6 | 2 | no | — |
| 122 | C2×D3×Dic3 | — | 6 | 2 | no | — |
| 123 | C2×D3×Dic3 | — | 6 | 2 | no | — |
| 124 | C2×D3×Dic3 | — | 6 | 2 | no | — |
| 125 | C2×D3×Dic3 | — | 6 | 1 | no | — |
| 126 | C2×D3×Dic3 | — | 6 | 1 | no | — |
| 127 | C2×D3×Dic3 | — | 6 | 1 | no | — |
| 128 | C2×D3×Dic3 | — | 6 | 1 | no | — |
| 129 | C2×D3×Dic3 | — | 6 | 1 | no | — |
| 130 | C2×D3×Dic3 | — | 12 | 1 | no | — |
| 131 | #3802 | — | 3 | 1 | no | — |
| 132 | C4×D32 | — | 3 | 2 | no | — |
| 133 | C4×D32 | — | 3 | 2 | no | — |
| 134 | C4×D32 | — | 3 | 1 | no | — |
| 135 | C4×D32 | — | 3 | 1 | no | — |
| 136 | C4×D32 | — | 6 | 1 | no | — |
| 137 | C4×D32 | — | 6 | 1 | no | — |
| 138 | C4×D32 | — | 6 | 1 | no | — |
| 139 | #3798 | — | 6 | 1 | no | — |
| 140 | #3797 | — | 3 | 1 | no | — |
| 141 | #3796 | — | 6 | 1 | no | — |
| 142 | #3796 | — | 6 | 1 | no | — |
| 143 | #3795 | — | 6 | 1 | no | — |
| 144 | D3×Dic6 | — | 6 | 1 | no | — |
| 145 | C22⋊#157 | — | 3 | 1 | no | — |
| 146 | C22⋊#157 | C2×D3 | 1 | 1 | yes | characteristic |
| 147 | C4⋊#157 | — | 3 | 2 | no | — |
| 148 | C4×#157 | — | 3 | 2 | no | — |
| 149 | #3773 | — | 3 | 2 | no | — |
| 150 | #3773 | — | 3 | 2 | no | — |
| 151 | D32⋊C4 | — | 3 | 2 | no | — |
| 152 | D32⋊C4 | — | 3 | 2 | no | — |
| 153 | D32⋊C4 | — | 3 | 2 | no | — |
| 154 | D32⋊C4 | C2×D3 | 1 | 2 | yes | — |
| 155 | C22×C33 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | C2×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 157 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 158 | C2×C3×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 159 | C2×C3×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 160 | C2×C32×D3 | — | 2 | 4 | no | — |
| 161 | C2×C32×D3 | — | 2 | 2 | no | — |
| 162 | C2×C32×D3 | — | 2 | 1 | no | — |
| 163 | #1113 | — | 2 | 2 | no | — |
| 164 | C3×D32 | — | 2 | 4 | no | — |
| 165 | C3×D32 | — | 2 | 2 | no | — |
| 166 | C3×D32 | — | 2 | 2 | no | — |
| 167 | C3×D32 | #41 | 1 | 4 | yes | complemented |
| 168 | C3⋊#157 | — | 2 | 2 | no | — |
| 169 | C3×#157 | — | 2 | 2 | no | — |
| 170 | C3⋊(C3⋊Dic3) | C2×D4 | 1 | 1 | yes | characteristic |
| 171 | C3⋊(C3⋊Dic3) | C2×D4 | 1 | 1 | yes | characteristic |
| 172 | C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 173 | C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 174 | C32×Dic3 | — | 2 | 1 | no | — |
| 175 | C32×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | C32×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 177 | C23×Dic3 | — | 9 | 1 | no | — |
| 178 | D3×#41 | — | 18 | 1 | no | — |
| 179 | C2×#237 | — | 9 | 1 | no | — |
| 180 | C22×C4×D3 | — | 18 | 1 | no | — |
| 181 | C3×#120 | — | 9 | 1 | no | — |
| 182 | #953 | — | 9 | 1 | no | — |
| 183 | #939 | — | 9 | 2 | no | — |
| 184 | #935 | — | 9 | 1 | no | — |
| 185 | D4×Dic3 | — | 9 | 2 | no | — |
| 186 | #886 | — | 9 | 1 | no | — |
| 187 | #67⋊C4 | — | 9 | 2 | no | — |
| 188 | #878 | — | 9 | 2 | no | — |
| 189 | #877 | — | 9 | 1 | no | — |
| 190 | C23×C32 | — | 6 | 1 | no | — |
| 191 | C22×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 192 | C22×C3×D3 | — | 2 | 1 | no | — |
| 193 | C22×C3×D3 | — | 2 | 1 | no | — |
| 194 | C22×C3×D3 | — | 4 | 1 | no | — |
| 195 | C22×C3×D3 | — | 6 | 2 | no | — |
| 196 | C22×C3×D3 | — | 6 | 1 | no | — |
| 197 | C22×C3×D3 | — | 6 | 1 | no | — |
| 198 | C22×C3×D3 | — | 6 | 1 | no | — |
| 199 | C22×C3×D3 | — | 6 | 8 | no | — |
| 200 | C22×C3×D3 | — | 6 | 2 | no | — |
| 201 | C2×D32 | — | 2 | 1 | no | — |
| 202 | C2×D32 | — | 2 | 4 | no | — |
| 203 | C2×D32 | — | 3 | 1 | no | — |
| 204 | C2×D32 | — | 6 | 1 | no | — |
| 205 | C2×D32 | C22×D3 | 1 | 1 | yes | characteristic |
| 206 | C2×D32 | C22×D3 | 1 | 2 | yes | — |
| 207 | C2×#157 | — | 3 | 2 | no | — |
| 208 | C2×#157 | C22×D3 | 1 | 2 | yes | — |
| 209 | GO+(4,𝔽2) | — | 2 | 4 | no | — |
| 210 | GO+(4,𝔽2) | — | 6 | 4 | no | — |
| 211 | C32×D4 | — | 6 | 1 | no | — |
| 212 | C2×C32×C4 | — | 3 | 1 | no | — |
| 213 | #638 | — | 2 | 1 | no | — |
| 214 | #638 | — | 6 | 1 | no | — |
| 215 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 216 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 217 | C2×C3⋊Dic3 | — | 6 | 1 | no | — |
| 218 | C2×C3⋊Dic3 | — | 6 | 1 | no | — |
| 219 | C2×C3⋊Dic3 | — | 6 | 2 | no | — |
| 220 | C2×C3⋊Dic3 | — | 6 | 2 | no | — |
| 221 | C2×C3⋊Dic3 | — | 6 | 1 | no | — |
| 222 | C2×C3⋊Dic3 | — | 12 | 1 | no | — |
| 223 | C2×C3⋊Dic3 | — | 12 | 1 | no | — |
| 224 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 225 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 226 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 227 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 228 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 229 | #634 | — | 6 | 1 | no | — |
| 230 | C3×#67 | — | 2 | 1 | no | — |
| 231 | C3×#67 | — | 2 | 1 | no | — |
| 232 | C3×#67 | — | 4 | 1 | no | — |
| 233 | C3×#67 | — | 6 | 1 | no | — |
| 234 | C3×#67 | — | 6 | 1 | no | — |
| 235 | C3×#67 | — | 6 | 1 | no | — |
| 236 | C3×#67 | — | 6 | 1 | no | — |
| 237 | C3×#67 | — | 12 | 1 | no | — |
| 238 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 239 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 240 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 241 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 242 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 243 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 244 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 245 | C2×C3×Dic3 | — | 12 | 1 | no | — |
| 246 | C3×D12 | — | 6 | 1 | no | — |
| 247 | C3×D12 | — | 6 | 1 | no | — |
| 248 | C3×C4×D3 | — | 6 | 1 | no | — |
| 249 | C3×C4×D3 | — | 6 | 1 | no | — |
| 250 | C3×C4×D3 | — | 6 | 1 | no | — |
| 251 | C3×C4×D3 | — | 6 | 1 | no | — |
| 252 | C3×C4×D3 | — | 6 | 2 | no | — |
| 253 | C3×C4×D3 | — | 6 | 2 | no | — |
| 254 | C3×Dic6 | — | 6 | 1 | no | — |
| 255 | C3×Dic6 | — | 6 | 1 | no | — |
| 256 | #627 | — | 2 | 1 | no | — |
| 257 | #627 | — | 6 | 1 | no | — |
| 258 | #627 | — | 6 | 1 | no | — |
| 259 | #627 | — | 12 | 1 | no | — |
| 260 | #626 | — | 2 | 1 | no | — |
| 261 | #626 | — | 2 | 1 | no | — |
| 262 | #626 | — | 6 | 1 | no | — |
| 263 | #626 | — | 6 | 1 | no | — |
| 264 | #625 | — | 6 | 1 | no | — |
| 265 | #625 | — | 6 | 1 | no | — |
| 266 | #625 | — | 6 | 1 | no | — |
| 267 | #625 | — | 12 | 1 | no | — |
| 268 | #624 | — | 2 | 1 | no | — |
| 269 | #624 | — | 3 | 1 | no | — |
| 270 | #624 | — | 3 | 2 | no | — |
| 271 | #624 | — | 6 | 1 | no | — |
| 272 | #624 | C22×D3 | 1 | 1 | yes | characteristic |
| 273 | D3×Dic3 | — | 2 | 1 | no | — |
| 274 | D3×Dic3 | — | 2 | 2 | no | — |
| 275 | D3×Dic3 | — | 2 | 2 | no | — |
| 276 | D3×Dic3 | — | 6 | 1 | no | — |
| 277 | D3×Dic3 | — | 6 | 1 | no | — |
| 278 | D3×Dic3 | — | 6 | 1 | no | — |
| 279 | D3×Dic3 | — | 6 | 1 | no | — |
| 280 | D3×Dic3 | — | 6 | 1 | no | — |
| 281 | D3×Dic3 | — | 6 | 1 | no | — |
| 282 | D3×Dic3 | — | 6 | 1 | no | — |
| 283 | D3×Dic3 | — | 6 | 1 | no | — |
| 284 | D3×Dic3 | — | 6 | 1 | no | — |
| 285 | D3×Dic3 | — | 6 | 2 | no | — |
| 286 | D3×Dic3 | — | 6 | 1 | no | — |
| 287 | D3×Dic3 | — | 6 | 1 | no | — |
| 288 | D3×Dic3 | — | 6 | 2 | no | — |
| 289 | D3×Dic3 | — | 6 | 1 | no | — |
| 290 | D3×Dic3 | — | 6 | 2 | no | — |
| 291 | D3×Dic3 | — | 6 | 2 | no | — |
| 292 | D3×Dic3 | — | 6 | 1 | no | — |
| 293 | D3×Dic3 | — | 6 | 2 | no | — |
| 294 | D3×Dic3 | — | 6 | 2 | no | — |
| 295 | D3×Dic3 | — | 12 | 2 | no | — |
| 296 | D3×Dic3 | — | 12 | 2 | no | — |
| 297 | D3×Dic3 | — | 12 | 1 | no | — |
| 298 | D3×Dic3 | — | 12 | 1 | no | — |
| 299 | #525 | — | 27 | 1 | no | Sylow |
| 300 | C2×C33 | — | 2 | 1 | no | — |
| 301 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 302 | C3×C3⋊D3 | — | 2 | 1 | no | — |
| 303 | C3×C3⋊D3 | — | 4 | 1 | no | — |
| 304 | C3×C3⋊D3 | C2×#41 | 1 | 2 | yes | — |
| 305 | C32×D3 | — | 2 | 4 | no | — |
| 306 | C32×D3 | — | 4 | 1 | no | — |
| 307 | C24×C3 | — | 9 | 1 | no | — |
| 308 | C23×D3 | — | 6 | 1 | no | — |
| 309 | C3×#41 | — | 18 | 1 | no | — |
| 310 | C2×C3×D4 | — | 9 | 1 | no | — |
| 311 | C2×C3×D4 | — | 9 | 2 | no | — |
| 312 | C22×C3×C4 | — | 18 | 1 | no | — |
| 313 | C2×#67 | — | 9 | 1 | no | — |
| 314 | C2×#67 | — | 9 | 1 | no | — |
| 315 | C2×#67 | — | 9 | 2 | no | — |
| 316 | C22×Dic3 | — | 6 | 1 | no | — |
| 317 | C22×Dic3 | — | 9 | 2 | no | — |
| 318 | C22×Dic3 | — | 9 | 2 | no | — |
| 319 | C22×Dic3 | — | 9 | 1 | no | — |
| 320 | C22×Dic3 | — | 9 | 1 | no | — |
| 321 | C22×Dic3 | — | 9 | 1 | no | — |
| 322 | C22×Dic3 | — | 18 | 1 | no | — |
| 323 | C22×Dic3 | — | 18 | 1 | no | — |
| 324 | C22×Dic3 | — | 18 | 1 | no | — |
| 325 | C22×Dic3 | — | 18 | 1 | no | — |
| 326 | C22×Dic3 | — | 36 | 1 | no | — |
| 327 | #239 | — | 18 | 1 | no | — |
| 328 | D3×Q8 | — | 18 | 1 | no | — |
| 329 | #237 | — | 6 | 1 | no | — |
| 330 | #237 | — | 18 | 1 | no | — |
| 331 | #237 | — | 18 | 1 | no | — |
| 332 | #237 | — | 18 | 1 | no | — |
| 333 | #237 | — | 18 | 1 | no | — |
| 334 | #237 | — | 18 | 1 | no | — |
| 335 | #237 | — | 18 | 1 | no | — |
| 336 | #237 | — | 36 | 1 | no | — |
| 337 | D3×D4 | — | 6 | 1 | no | — |
| 338 | D3×D4 | — | 18 | 1 | no | — |
| 339 | D3×D4 | — | 18 | 1 | no | — |
| 340 | #235 | — | 6 | 1 | no | — |
| 341 | #235 | — | 18 | 1 | no | — |
| 342 | #235 | — | 18 | 1 | no | — |
| 343 | C2×C4×D3 | — | 6 | 1 | no | — |
| 344 | C2×C4×D3 | — | 9 | 1 | no | — |
| 345 | C2×C4×D3 | — | 18 | 1 | no | — |
| 346 | C2×C4×D3 | — | 18 | 2 | no | — |
| 347 | C2×C4×D3 | — | 18 | 2 | no | — |
| 348 | C2×C4×D3 | — | 18 | 1 | no | — |
| 349 | C2×C4×D3 | — | 18 | 1 | no | — |
| 350 | C2×C4×D3 | — | 18 | 1 | no | — |
| 351 | C2×C4×D3 | — | 18 | 1 | no | — |
| 352 | C2×C4×D3 | — | 18 | 2 | no | — |
| 353 | C2×C4×D3 | — | 18 | 2 | no | — |
| 354 | C2×C4×D3 | — | 18 | 1 | no | — |
| 355 | C2×Dic6 | — | 9 | 1 | no | — |
| 356 | C3×C22⋊C4 | — | 9 | 2 | no | — |
| 357 | C3×C22⋊C4 | — | 9 | 1 | no | — |
| 358 | #217 | — | 9 | 2 | no | — |
| 359 | #217 | — | 9 | 2 | no | — |
| 360 | #217 | — | 9 | 1 | no | — |
| 361 | (C2×D3)⋊C4 | — | 9 | 2 | no | — |
| 362 | C4⋊Dic3 | — | 9 | 2 | no | — |
| 363 | Dic3⋊C4 | — | 9 | 2 | no | — |
| 364 | Dic3⋊C4 | — | 9 | 2 | no | — |
| 365 | C4×Dic3 | — | 9 | 2 | no | — |
| 366 | C22×C32 | — | 2 | 1 | no | — |
| 367 | C22×C32 | — | 2 | 1 | no | — |
| 368 | C22×C32 | — | 4 | 1 | no | — |
| 369 | C22×C32 | — | 4 | 1 | no | — |
| 370 | C22×C32 | — | 6 | 2 | no | — |
| 371 | C22×C32 | — | 6 | 4 | no | — |
| 372 | C22×C32 | — | 6 | 1 | no | — |
| 373 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic |
| 374 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 375 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 376 | C2×C3⋊D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 377 | C2×C3⋊D3 | C23×D3 | 1 | 1 | yes | characteristic |
| 378 | C2×C3×D3 | — | 2 | 2 | no | — |
| 379 | C2×C3×D3 | — | 2 | 4 | no | — |
| 380 | C2×C3×D3 | — | 2 | 4 | no | — |
| 381 | C2×C3×D3 | — | 2 | 2 | no | — |
| 382 | C2×C3×D3 | — | 2 | 1 | no | — |
| 383 | C2×C3×D3 | — | 2 | 1 | no | — |
| 384 | C2×C3×D3 | — | 4 | 2 | no | — |
| 385 | C2×C3×D3 | — | 4 | 4 | no | — |
| 386 | C2×C3×D3 | — | 4 | 1 | no | — |
| 387 | C2×C3×D3 | — | 6 | 4 | no | — |
| 388 | C2×C3×D3 | — | 6 | 1 | no | — |
| 389 | C2×C3×D3 | — | 6 | 1 | no | — |
| 390 | C2×C3×D3 | — | 6 | 1 | no | — |
| 391 | C2×C3×D3 | — | 6 | 1 | no | — |
| 392 | C2×C3×D3 | — | 6 | 4 | no | — |
| 393 | C2×C3×D3 | — | 6 | 8 | no | — |
| 394 | C2×C3×D3 | — | 6 | 4 | no | — |
| 395 | C2×C3×D3 | — | 6 | 1 | no | — |
| 396 | C2×C3×D3 | — | 6 | 1 | no | — |
| 397 | C2×C3×D3 | — | 12 | 2 | no | — |
| 398 | C2×C3×D3 | — | 12 | 2 | no | — |
| 399 | C2×C3×D3 | — | 12 | 1 | no | — |
| 400 | D32 | — | 2 | 4 | no | — |
| 401 | D32 | — | 2 | 2 | no | — |
| 402 | D32 | — | 2 | 2 | no | — |
| 403 | D32 | — | 6 | 2 | no | — |
| 404 | D32 | — | 12 | 2 | no | — |
| 405 | D32 | #237 | 1 | 4 | yes | complemented |
| 406 | #157 | — | 2 | 2 | no | — |
| 407 | #157 | — | 6 | 2 | no | — |
| 408 | C32×C4 | — | 3 | 1 | no | — |
| 409 | C32×C4 | — | 3 | 1 | no | — |
| 410 | C32×C4 | — | 6 | 1 | no | — |
| 411 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 412 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 413 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 414 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 415 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 416 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 417 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 418 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 419 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 420 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 421 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 422 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 423 | C3×Dic3 | — | 2 | 1 | no | — |
| 424 | C3×Dic3 | — | 2 | 1 | no | — |
| 425 | C3×Dic3 | — | 2 | 1 | no | — |
| 426 | C3×Dic3 | — | 2 | 1 | no | — |
| 427 | C3×Dic3 | — | 2 | 1 | no | — |
| 428 | C3×Dic3 | — | 2 | 1 | no | — |
| 429 | C3×Dic3 | — | 4 | 1 | no | — |
| 430 | C3×Dic3 | — | 6 | 2 | no | — |
| 431 | C3×Dic3 | — | 6 | 1 | no | — |
| 432 | C3×Dic3 | — | 6 | 2 | no | — |
| 433 | C3×Dic3 | — | 6 | 1 | no | — |
| 434 | C3×Dic3 | — | 12 | 2 | no | — |
| 435 | C3×Dic3 | — | 12 | 1 | no | — |
| 436 | C2×#41 | — | 27 | 1 | no | — |
| 437 | C23×C4 | — | 27 | 1 | no | — |
| 438 | #123 | — | 27 | 1 | no | — |
| 439 | #123 | — | 27 | 1 | no | — |
| 440 | C22⋊Q8 | — | 27 | 2 | no | — |
| 441 | #121 | — | 27 | 2 | no | — |
| 442 | #120 | — | 9 | 1 | no | — |
| 443 | #120 | — | 27 | 1 | no | — |
| 444 | C4×D4 | — | 27 | 2 | no | — |
| 445 | C4×D4 | — | 27 | 2 | no | — |
| 446 | #117 | — | 27 | 1 | no | — |
| 447 | C33 | #525 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 448 | C23×C3 | — | 6 | 1 | no | — |
| 449 | C23×C3 | — | 6 | 1 | no | — |
| 450 | C23×C3 | — | 9 | 2 | no | — |
| 451 | C23×C3 | — | 9 | 1 | no | — |
| 452 | C23×C3 | — | 9 | 1 | no | — |
| 453 | C23×C3 | — | 12 | 1 | no | — |
| 454 | C23×C3 | — | 18 | 1 | no | — |
| 455 | C23×C3 | — | 18 | 4 | no | — |
| 456 | C22×D3 | — | 2 | 1 | no | — |
| 457 | C22×D3 | — | 6 | 2 | no | — |
| 458 | C22×D3 | — | 6 | 1 | no | — |
| 459 | C22×D3 | — | 6 | 1 | no | — |
| 460 | C22×D3 | — | 6 | 1 | no | — |
| 461 | C22×D3 | — | 6 | 2 | no | — |
| 462 | C22×D3 | — | 6 | 8 | no | — |
| 463 | C22×D3 | — | 9 | 1 | no | — |
| 464 | C22×D3 | — | 18 | 1 | no | — |
| 465 | C3×Q8 | — | 18 | 1 | no | — |
| 466 | C3×D4 | — | 6 | 1 | no | — |
| 467 | C3×D4 | — | 6 | 1 | no | — |
| 468 | C3×D4 | — | 12 | 1 | no | — |
| 469 | C3×D4 | — | 18 | 1 | no | — |
| 470 | C3×D4 | — | 18 | 1 | no | — |
| 471 | C3×D4 | — | 18 | 1 | no | — |
| 472 | C3×D4 | — | 18 | 4 | no | — |
| 473 | C2×C3×C4 | — | 6 | 1 | no | — |
| 474 | C2×C3×C4 | — | 6 | 1 | no | — |
| 475 | C2×C3×C4 | — | 9 | 1 | no | — |
| 476 | C2×C3×C4 | — | 9 | 2 | no | — |
| 477 | C2×C3×C4 | — | 18 | 1 | no | — |
| 478 | C2×C3×C4 | — | 18 | 2 | no | — |
| 479 | C2×C3×C4 | — | 18 | 2 | no | — |
| 480 | C2×C3×C4 | — | 18 | 1 | no | — |
| 481 | C2×C3×C4 | — | 18 | 1 | no | — |
| 482 | #67 | — | 2 | 1 | no | — |
| 483 | #67 | — | 6 | 1 | no | — |
| 484 | #67 | — | 6 | 1 | no | — |
| 485 | #67 | — | 6 | 1 | no | — |
| 486 | #67 | — | 6 | 1 | no | — |
| 487 | #67 | — | 12 | 1 | no | — |
| 488 | #67 | — | 18 | 1 | no | — |
| 489 | #67 | — | 18 | 1 | no | — |
| 490 | #67 | — | 18 | 1 | no | — |
| 491 | #67 | — | 18 | 1 | no | — |
| 492 | #67 | — | 18 | 1 | no | — |
| 493 | #67 | — | 18 | 4 | no | — |
| 494 | #67 | — | 36 | 1 | no | — |
| 495 | C2×Dic3 | — | 6 | 1 | no | — |
| 496 | C2×Dic3 | — | 6 | 1 | no | — |
| 497 | C2×Dic3 | — | 6 | 1 | no | — |
| 498 | C2×Dic3 | — | 6 | 2 | no | — |
| 499 | C2×Dic3 | — | 6 | 2 | no | — |
| 500 | C2×Dic3 | — | 9 | 2 | no | — |
| 501 | C2×Dic3 | — | 9 | 1 | no | — |
| 502 | C2×Dic3 | — | 9 | 1 | no | — |
| 503 | C2×Dic3 | — | 9 | 1 | no | — |
| 504 | C2×Dic3 | — | 9 | 1 | no | — |
| 505 | C2×Dic3 | — | 9 | 1 | no | — |
| 506 | C2×Dic3 | — | 9 | 1 | no | — |
| 507 | C2×Dic3 | — | 9 | 2 | no | — |
| 508 | C2×Dic3 | — | 12 | 1 | no | — |
| 509 | C2×Dic3 | — | 18 | 1 | no | — |
| 510 | C2×Dic3 | — | 18 | 1 | no | — |
| 511 | C2×Dic3 | — | 18 | 1 | no | — |
| 512 | C2×Dic3 | — | 18 | 1 | no | — |
| 513 | C2×Dic3 | — | 18 | 1 | no | — |
| 514 | C2×Dic3 | — | 18 | 2 | no | — |
| 515 | C2×Dic3 | — | 18 | 2 | no | — |
| 516 | C2×Dic3 | — | 18 | 2 | no | — |
| 517 | C2×Dic3 | — | 18 | 2 | no | — |
| 518 | C2×Dic3 | — | 18 | 1 | no | — |
| 519 | C2×Dic3 | — | 36 | 1 | no | — |
| 520 | C2×Dic3 | — | 36 | 1 | no | — |
| 521 | C2×Dic3 | — | 36 | 1 | no | — |
| 522 | C2×Dic3 | — | 36 | 2 | no | — |
| 523 | C2×Dic3 | — | 36 | 2 | no | — |
| 524 | C2×Dic3 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 525 | D12 | — | 6 | 1 | no | — |
| 526 | D12 | — | 6 | 1 | no | — |
| 527 | D12 | — | 18 | 1 | no | — |
| 528 | C4×D3 | — | 6 | 1 | no | — |
| 529 | C4×D3 | — | 6 | 1 | no | — |
| 530 | C4×D3 | — | 6 | 2 | no | — |
| 531 | C4×D3 | — | 6 | 2 | no | — |
| 532 | C4×D3 | — | 6 | 1 | no | — |
| 533 | C4×D3 | — | 6 | 1 | no | — |
| 534 | C4×D3 | — | 18 | 2 | no | — |
| 535 | C4×D3 | — | 18 | 1 | no | — |
| 536 | C4×D3 | — | 18 | 1 | no | — |
| 537 | C4×D3 | — | 18 | 1 | no | — |
| 538 | C4×D3 | — | 18 | 1 | no | — |
| 539 | C4×D3 | — | 18 | 1 | no | — |
| 540 | C4×D3 | — | 18 | 1 | no | — |
| 541 | C4×D3 | — | 18 | 1 | no | — |
| 542 | C4×D3 | — | 18 | 1 | no | — |
| 543 | C4×D3 | — | 18 | 1 | no | — |
| 544 | C4×D3 | — | 18 | 2 | no | — |
| 545 | C4×D3 | — | 18 | 1 | no | — |
| 546 | C4×D3 | — | 18 | 1 | no | — |
| 547 | C4×D3 | — | 18 | 2 | no | — |
| 548 | C4×D3 | — | 18 | 2 | no | — |
| 549 | C4×D3 | — | 18 | 1 | no | — |
| 550 | C4×D3 | — | 36 | 1 | no | — |
| 551 | Dic6 | — | 6 | 1 | no | — |
| 552 | Dic6 | — | 6 | 1 | no | — |
| 553 | Dic6 | — | 18 | 1 | no | — |
| 554 | Dic6 | — | 18 | 1 | no | — |
| 555 | Dic6 | — | 18 | 1 | no | — |
| 556 | Dic6 | — | 36 | 1 | no | — |
| 557 | C2×C32 | — | 2 | 2 | no | — |
| 558 | C2×C32 | — | 2 | 1 | no | — |
| 559 | C2×C32 | — | 2 | 1 | no | — |
| 560 | C2×C32 | — | 2 | 1 | no | — |
| 561 | C2×C32 | — | 4 | 1 | no | — |
| 562 | C2×C32 | — | 4 | 1 | no | — |
| 563 | C2×C32 | — | 4 | 1 | no | — |
| 564 | C2×C32 | — | 4 | 2 | no | — |
| 565 | C2×C32 | — | 6 | 4 | no | — |
| 566 | C2×C32 | — | 8 | 1 | no | — |
| 567 | C2×C32 | — | 12 | 1 | no | — |
| 568 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 569 | C3⋊D3 | — | 2 | 1 | no | — |
| 570 | C3⋊D3 | — | 4 | 1 | no | — |
| 571 | C3⋊D3 | C2×#237 | 1 | 2 | yes | — |
| 572 | C3×D3 | — | 2 | 4 | no | — |
| 573 | C3×D3 | — | 2 | 4 | no | — |
| 574 | C3×D3 | — | 4 | 4 | no | — |
| 575 | C3×D3 | — | 4 | 1 | no | — |
| 576 | C3×D3 | — | 4 | 1 | no | — |
| 577 | C3×D3 | — | 6 | 2 | no | — |
| 578 | C3×D3 | — | 6 | 2 | no | — |
| 579 | C3×D3 | — | 6 | 2 | no | — |
| 580 | C3×D3 | — | 8 | 1 | no | — |
| 581 | C3×D3 | — | 12 | 1 | no | — |
| 582 | C3×D3 | — | 12 | 1 | no | — |
| 583 | C3×D3 | — | 12 | 1 | no | — |
| 584 | C3×D3 | — | 24 | 1 | no | — |
| 585 | C24 | — | 9 | 1 | no | — |
| 586 | #41 | — | 18 | 1 | no | — |
| 587 | #41 | — | 54 | 1 | no | — |
| 588 | #41 | — | 54 | 1 | no | — |
| 589 | #41 | — | 54 | 1 | no | — |
| 590 | C2×Q8 | — | 27 | 1 | no | — |
| 591 | C2×D4 | — | 9 | 1 | no | — |
| 592 | C2×D4 | — | 9 | 2 | no | — |
| 593 | C2×D4 | — | 27 | 1 | no | — |
| 594 | C2×D4 | — | 27 | 1 | no | — |
| 595 | C2×D4 | — | 27 | 2 | no | — |
| 596 | C22×C4 | — | 18 | 1 | no | — |
| 597 | C22×C4 | — | 27 | 1 | no | — |
| 598 | C22×C4 | — | 27 | 1 | no | — |
| 599 | C22×C4 | — | 27 | 2 | no | — |
| 600 | C22×C4 | — | 27 | 1 | no | — |
| 601 | C22×C4 | — | 27 | 2 | no | — |
| 602 | C22×C4 | — | 27 | 1 | no | — |
| 603 | C22×C4 | — | 54 | 1 | no | — |
| 604 | C22×C4 | — | 54 | 1 | no | — |
| 605 | C22×C4 | — | 54 | 1 | no | — |
| 606 | C4⋊C4 | — | 27 | 2 | no | — |
| 607 | C4⋊C4 | — | 27 | 2 | no | — |
| 608 | C4⋊C4 | — | 27 | 2 | no | — |
| 609 | C22⋊C4 | — | 9 | 1 | no | — |
| 610 | C22⋊C4 | — | 9 | 2 | no | — |
| 611 | C22⋊C4 | — | 27 | 2 | no | — |
| 612 | C22⋊C4 | — | 27 | 1 | no | — |
| 613 | C22⋊C4 | — | 27 | 2 | no | — |
| 614 | C22⋊C4 | — | 27 | 2 | no | — |
| 615 | C42 | — | 27 | 2 | no | — |
| 616 | C22×C3 | — | 2 | 1 | no | — |
| 617 | C22×C3 | — | 2 | 1 | no | — |
| 618 | C22×C3 | — | 4 | 1 | no | — |
| 619 | C22×C3 | — | 4 | 1 | no | — |
| 620 | C22×C3 | — | 6 | 2 | no | — |
| 621 | C22×C3 | — | 6 | 4 | no | — |
| 622 | C22×C3 | — | 6 | 4 | no | — |
| 623 | C22×C3 | — | 6 | 1 | no | — |
| 624 | C22×C3 | — | 6 | 2 | no | — |
| 625 | C22×C3 | — | 6 | 1 | no | — |
| 626 | C22×C3 | — | 9 | 4 | no | — |
| 627 | C22×C3 | — | 9 | 1 | no | — |
| 628 | C22×C3 | — | 9 | 1 | no | — |
| 629 | C22×C3 | — | 12 | 2 | no | — |
| 630 | C22×C3 | — | 12 | 4 | no | — |
| 631 | C22×C3 | — | 12 | 1 | no | — |
| 632 | C22×C3 | — | 18 | 2 | no | — |
| 633 | C22×C3 | — | 18 | 1 | no | — |
| 634 | C22×C3 | — | 18 | 2 | no | — |
| 635 | C22×C3 | — | 18 | 4 | no | — |
| 636 | C22×C3 | — | 18 | 2 | no | — |
| 637 | C22×C3 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 638 | C2×D3 | — | 2 | 2 | no | — |
| 639 | C2×D3 | — | 2 | 4 | no | — |
| 640 | C2×D3 | — | 2 | 1 | no | — |
| 641 | C2×D3 | — | 6 | 4 | no | — |
| 642 | C2×D3 | — | 6 | 1 | no | — |
| 643 | C2×D3 | — | 6 | 1 | no | — |
| 644 | C2×D3 | — | 6 | 1 | no | — |
| 645 | C2×D3 | — | 6 | 1 | no | — |
| 646 | C2×D3 | — | 6 | 4 | no | — |
| 647 | C2×D3 | — | 6 | 8 | no | — |
| 648 | C2×D3 | — | 6 | 4 | no | — |
| 649 | C2×D3 | — | 6 | 1 | no | — |
| 650 | C2×D3 | — | 6 | 1 | no | — |
| 651 | C2×D3 | — | 12 | 2 | no | — |
| 652 | C2×D3 | — | 12 | 2 | no | — |
| 653 | C2×D3 | — | 12 | 1 | no | — |
| 654 | C2×D3 | — | 18 | 2 | no | — |
| 655 | C2×D3 | — | 36 | 2 | no | — |
| 656 | C3×C4 | — | 6 | 1 | no | — |
| 657 | C3×C4 | — | 6 | 1 | no | — |
| 658 | C3×C4 | — | 6 | 1 | no | — |
| 659 | C3×C4 | — | 6 | 1 | no | — |
| 660 | C3×C4 | — | 6 | 1 | no | — |
| 661 | C3×C4 | — | 6 | 1 | no | — |
| 662 | C3×C4 | — | 12 | 1 | no | — |
| 663 | C3×C4 | — | 18 | 1 | no | — |
| 664 | C3×C4 | — | 18 | 2 | no | — |
| 665 | C3×C4 | — | 18 | 2 | no | — |
| 666 | Dic3 | — | 2 | 1 | no | — |
| 667 | Dic3 | — | 6 | 1 | no | — |
| 668 | Dic3 | — | 6 | 2 | no | — |
| 669 | Dic3 | — | 6 | 1 | no | — |
| 670 | Dic3 | — | 6 | 2 | no | — |
| 671 | Dic3 | — | 9 | 1 | no | — |
| 672 | Dic3 | — | 9 | 1 | no | — |
| 673 | Dic3 | — | 12 | 1 | no | — |
| 674 | Dic3 | — | 12 | 2 | no | — |
| 675 | Dic3 | — | 18 | 1 | no | — |
| 676 | Dic3 | — | 18 | 1 | no | — |
| 677 | Dic3 | — | 18 | 1 | no | — |
| 678 | Dic3 | — | 18 | 1 | no | — |
| 679 | Dic3 | — | 18 | 2 | no | — |
| 680 | Dic3 | — | 36 | 1 | no | — |
| 681 | Dic3 | — | 36 | 1 | no | — |
| 682 | Dic3 | — | 36 | 1 | no | — |
| 683 | Dic3 | — | 36 | 1 | no | — |
| 684 | Dic3 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 685 | Dic3 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 686 | C32 | — | 2 | 1 | no | — |
| 687 | C32 | — | 2 | 1 | no | — |
| 688 | C32 | — | 4 | 1 | no | — |
| 689 | C32 | — | 4 | 1 | no | — |
| 690 | C32 | #5586 | 1 | 1 | yes | characteristic, complemented |
| 691 | C23 | — | 6 | 1 | no | — |
| 692 | C23 | — | 9 | 2 | no | — |
| 693 | C23 | — | 9 | 1 | no | — |
| 694 | C23 | — | 9 | 1 | no | — |
| 695 | C23 | — | 18 | 1 | no | — |
| 696 | C23 | — | 18 | 4 | no | — |
| 697 | C23 | — | 27 | 1 | no | — |
| 698 | Q8 | — | 18 | 1 | no | — |
| 699 | Q8 | — | 54 | 1 | no | — |
| 700 | D4 | — | 6 | 1 | no | — |
| 701 | D4 | — | 18 | 1 | no | — |
| 702 | D4 | — | 18 | 1 | no | — |
| 703 | D4 | — | 18 | 4 | no | — |
| 704 | D4 | — | 18 | 1 | no | — |
| 705 | D4 | — | 54 | 1 | no | — |
| 706 | D4 | — | 54 | 1 | no | — |
| 707 | D4 | — | 54 | 4 | no | — |
| 708 | C2×C4 | — | 3 | 1 | no | — |
| 709 | C2×C4 | — | 9 | 1 | no | — |
| 710 | C2×C4 | — | 9 | 2 | no | — |
| 711 | C2×C4 | — | 18 | 1 | no | — |
| 712 | C2×C4 | — | 18 | 2 | no | — |
| 713 | C2×C4 | — | 18 | 2 | no | — |
| 714 | C2×C4 | — | 18 | 1 | no | — |
| 715 | C2×C4 | — | 18 | 1 | no | — |
| 716 | C2×C4 | — | 27 | 1 | no | — |
| 717 | C2×C4 | — | 27 | 1 | no | — |
| 718 | C2×C4 | — | 27 | 1 | no | — |
| 719 | C2×C4 | — | 27 | 1 | no | — |
| 720 | C2×C4 | — | 27 | 2 | no | — |
| 721 | C2×C4 | — | 27 | 1 | no | — |
| 722 | C2×C4 | — | 27 | 1 | no | — |
| 723 | C2×C4 | — | 27 | 2 | no | — |
| 724 | C2×C4 | — | 54 | 1 | no | — |
| 725 | C2×C4 | — | 54 | 1 | no | — |
| 726 | C2×C4 | — | 54 | 2 | no | — |
| 727 | C2×C4 | — | 54 | 2 | no | — |
| 728 | C2×C4 | — | 54 | 1 | no | — |
| 729 | C2×C3 | — | 2 | 2 | no | — |
| 730 | C2×C3 | — | 2 | 1 | no | — |
| 731 | C2×C3 | — | 2 | 1 | no | — |
| 732 | C2×C3 | — | 2 | 1 | no | — |
| 733 | C2×C3 | — | 4 | 1 | no | — |
| 734 | C2×C3 | — | 4 | 2 | no | — |
| 735 | C2×C3 | — | 4 | 1 | no | — |
| 736 | C2×C3 | — | 4 | 1 | no | — |
| 737 | C2×C3 | — | 6 | 4 | no | — |
| 738 | C2×C3 | — | 6 | 4 | no | — |
| 739 | C2×C3 | — | 8 | 1 | no | — |
| 740 | C2×C3 | — | 9 | 2 | no | — |
| 741 | C2×C3 | — | 12 | 4 | no | — |
| 742 | C2×C3 | — | 12 | 1 | no | — |
| 743 | C2×C3 | — | 12 | 1 | no | — |
| 744 | C2×C3 | — | 18 | 1 | no | — |
| 745 | C2×C3 | — | 24 | 1 | no | — |
| 746 | C2×C3 | — | 36 | 1 | no | — |
| 747 | C2×C3 | C22×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 748 | D3 | — | 2 | 4 | no | — |
| 749 | D3 | — | 4 | 1 | no | — |
| 750 | D3 | — | 6 | 2 | no | — |
| 751 | D3 | — | 6 | 2 | no | — |
| 752 | D3 | — | 6 | 2 | no | — |
| 753 | D3 | — | 12 | 1 | no | — |
| 754 | D3 | — | 12 | 1 | no | — |
| 755 | D3 | — | 12 | 1 | no | — |
| 756 | D3 | — | 24 | 1 | no | — |
| 757 | C22 | — | 6 | 4 | no | — |
| 758 | C22 | — | 6 | 2 | no | — |
| 759 | C22 | — | 6 | 1 | no | — |
| 760 | C22 | — | 9 | 4 | no | — |
| 761 | C22 | — | 9 | 1 | no | — |
| 762 | C22 | — | 9 | 1 | no | — |
| 763 | C22 | — | 18 | 2 | no | — |
| 764 | C22 | — | 18 | 2 | no | — |
| 765 | C22 | — | 18 | 4 | no | — |
| 766 | C22 | — | 18 | 2 | no | — |
| 767 | C22 | — | 18 | 1 | no | — |
| 768 | C22 | — | 54 | 2 | no | — |
| 769 | C22 | D3×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 770 | C4 | — | 3 | 1 | no | — |
| 771 | C4 | — | 3 | 1 | no | — |
| 772 | C4 | — | 6 | 1 | no | — |
| 773 | C4 | — | 18 | 2 | no | — |
| 774 | C4 | — | 18 | 2 | no | — |
| 775 | C4 | — | 18 | 1 | no | — |
| 776 | C4 | — | 27 | 1 | no | — |
| 777 | C4 | — | 27 | 1 | no | — |
| 778 | C4 | — | 54 | 2 | no | — |
| 779 | C3 | — | 2 | 1 | no | — |
| 780 | C3 | — | 2 | 1 | no | — |
| 781 | C3 | — | 4 | 1 | no | — |
| 782 | C3 | — | 4 | 1 | no | — |
| 783 | C3 | #10596510 | 1 | 1 | yes | characteristic, complemented |
| 784 | C2 | — | 2 | 1 | no | — |
| 785 | C2 | — | 6 | 4 | no | — |
| 786 | C2 | — | 9 | 2 | no | — |
| 787 | C2 | — | 12 | 1 | no | — |
| 788 | C2 | — | 18 | 1 | no | — |
| 789 | C2 | — | 36 | 1 | no | — |
| 790 | C2 | C2×D3×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D3×GO+(4,𝔽2) |
| commutator, cosocle | C2×C3×C3⋊D3 | C24 |
| Fitting | C22×C33 | C2×D4 |
| socle | C2×C33 | C22×D4 |
| hypercenter | C22 | D3×GO+(4,𝔽2) |
| hypocenter | C33 | #525 |
| LCS | G ▷ C2×C3×C3⋊D3 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11724407 | C2 | semidirect |
| 2. C2×D32×Dic3 | C2 | semidirect |
| 3. #11724346 | C2 | semidirect |
| 4. #11724331 | C2 | semidirect |
| 5. #11724319 | C2 | semidirect |
| 6. C3×#64241 | C2 | semidirect |
| 7. #11724261 | C2 | semidirect |
| 8. #11724119 | C2 | semidirect |
| 9. #11724117 | C2 | semidirect |
| 10. (D32⋊D3)⋊C4 | C2 | semidirect |
| 11. Dic3×GO+(4,𝔽2) | C2 | semidirect |
| 28. #88957 | C22 | semidirect |
| 29. #88953 | C22 | semidirect |
| 30. #88949 | C22 | semidirect |
| 35. D32×Dic3 | C22 | semidirect |
| 36. #88940 | C22 | semidirect |
| 37. #88939 | C22 | semidirect |
| 38. #88934 | C22 | semidirect |
| 40. D32⋊Dic3 | C22 | semidirect |
| 42. Dic3⋊#157 | C22 | semidirect |
| 43. Dic3×#157 | C22 | semidirect |
| 50. #64241 | D3 | semidirect |
| 68. C2×C3⋊(C3⋊Dic3) | D4 | semidirect |
| 72. C2×C32×Dic3 | D4 | semidirect |
| 80. Dic3×C3⋊D3 | D4 | semidirect |
| 81. Dic3×C3⋊D3 | D4 | semidirect |
| 167. C3×D32 | #41 | semidirect |
| 405. D32 | #237 | semidirect |
| 447. C33 | #525 | semidirect |
| 524. C2×Dic3 | GO+(4,𝔽2) | semidirect |
| 690. C32 | #5586 | semidirect |
| 783. C3 | #10596510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724407 | 2 |
| C2×D32×Dic3 | 2 |
| #11724346 | 2 |
| #11724331 | 2 |
| #11724319 | 2 |
| C3×#64241 | 2 |
| #11724261 | 2 |
| #11724119 | 2 |
| #11724117 | 2 |
| (D32⋊D3)⋊C4 | 2 |
| Dic3×GO+(4,𝔽2) | 2 |
| #10596510 | 3 |
| #5586 | 9 |