Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1432 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 1432 conjugacy classes of subgroups — too many to draw. Only its 132 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 | C22×D3×#157 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×D3×GO+(4,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | D3×#3811 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11724355 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11724332 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C3×#64242 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11724116 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11724115 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11724114 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | D3×#3773 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | D3×D32⋊C4 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×#64242 | — | 3 | 1 | no | maximal |
| 13 | C22×D3×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 14 | C22×C3⋊#157 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C22×C3×#157 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C2×D33 | C22 | 1 | 2 | yes | — |
| 17 | C2×#157⋊D3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C2×D32⋊D3 | C22 | 1 | 2 | yes | complemented |
| 19 | C2×C3×GO+(4,𝔽2) | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C2×D3×#157 | — | 2 | 4 | no | — |
| 21 | C2×D3×#157 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×D3×#157 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×D3×#157 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | C2×D3×#157 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | D3×GO+(4,𝔽2) | — | 2 | 4 | no | — |
| 26 | #89049 | C22 | 1 | 2 | yes | complemented |
| 27 | #89039 | — | 2 | 2 | no | — |
| 28 | C3×#3811 | C22 | 1 | 2 | yes | complemented |
| 29 | C3×D3×#67 | — | 2 | 2 | no | — |
| 30 | #88955 | C22 | 1 | 2 | yes | complemented |
| 31 | #88954 | — | 2 | 2 | no | — |
| 32 | #88952 | C22 | 1 | 2 | yes | complemented |
| 33 | D3×#626 | — | 2 | 2 | no | — |
| 34 | D3×#624 | C22 | 1 | 2 | yes | — |
| 35 | #88940 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #88939 | C22 | 1 | 2 | yes | complemented |
| 37 | #88934 | C22 | 1 | 2 | yes | complemented |
| 38 | D32⋊Dic3 | C22 | 1 | 2 | yes | complemented |
| 39 | #88932 | C22 | 1 | 2 | yes | complemented |
| 40 | C3×#3773 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | C3×D32⋊C4 | C22 | 1 | 2 | yes | complemented |
| 42 | C23×#157 | — | 3 | 1 | no | — |
| 43 | C22×GO+(4,𝔽2) | — | 3 | 1 | no | — |
| 44 | C2×#3811 | — | 3 | 2 | no | — |
| 45 | D32×D4 | — | 6 | 2 | no | — |
| 46 | #64242 | — | 3 | 2 | no | — |
| 47 | #64242 | — | 3 | 1 | no | — |
| 48 | #64242 | — | 3 | 2 | no | — |
| 49 | #64242 | — | 3 | 1 | no | — |
| 50 | #64242 | — | 3 | 1 | no | — |
| 51 | #64242 | D3 | 1 | 1 | yes | characteristic, direct product factor |
| 52 | C2×#3773 | — | 3 | 1 | no | — |
| 53 | C2×D32⋊C4 | — | 3 | 2 | no | — |
| 54 | C22×C3⋊(C3⋊D3) | D4 | 1 | 1 | yes | characteristic, complemented |
| 55 | C22×C3×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 56 | C22×C32×D3 | D4 | 1 | 1 | yes | characteristic, complemented |
| 57 | C2×#1113 | C23 | 1 | 2 | yes | — |
| 58 | C2×D3×C3⋊D3 | — | 2 | 2 | no | — |
| 59 | C2×D3×C3⋊D3 | — | 2 | 2 | no | — |
| 60 | C2×D3×C3⋊D3 | — | 2 | 2 | no | — |
| 61 | C2×D3×C3⋊D3 | D4 | 1 | 1 | yes | characteristic, complemented |
| 62 | C2×D3×C3⋊D3 | D4 | 1 | 1 | yes | characteristic, complemented |
| 63 | C2×D3×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 64 | C2×D3×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 65 | C2×C3×D32 | — | 2 | 2 | no | — |
| 66 | C2×C3×D32 | C23 | 1 | 2 | yes | — |
| 67 | C2×C3⋊#157 | — | 2 | 2 | no | — |
| 68 | C2×C3⋊#157 | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×C3⋊#157 | C23 | 1 | 1 | yes | characteristic |
| 70 | C2×C3×#157 | — | 2 | 2 | no | — |
| 71 | C2×C3×#157 | C23 | 1 | 1 | yes | characteristic |
| 72 | C2×C3×#157 | C23 | 1 | 1 | yes | characteristic |
| 73 | D33 | — | 2 | 4 | no | — |
| 74 | D33 | — | 2 | 4 | no | — |
| 75 | #157⋊D3 | — | 2 | 2 | no | — |
| 76 | D32⋊D3 | — | 2 | 4 | no | — |
| 77 | C3×GO+(4,𝔽2) | — | 2 | 2 | no | — |
| 78 | D3×#157 | — | 2 | 2 | no | — |
| 79 | D3×#157 | — | 2 | 2 | no | — |
| 80 | D3×#157 | — | 2 | 2 | no | — |
| 81 | D3×#157 | D4 | 1 | 4 | yes | complemented |
| 82 | C3×#638 | — | 2 | 2 | no | — |
| 83 | C32×#67 | — | 2 | 2 | no | — |
| 84 | #6295 | — | 2 | 2 | no | — |
| 85 | #6294 | C23 | 1 | 2 | yes | — |
| 86 | #6292 | — | 2 | 2 | no | — |
| 87 | #6291 | — | 2 | 2 | no | — |
| 88 | #6289 | — | 2 | 2 | no | — |
| 89 | C3×#626 | — | 2 | 2 | no | — |
| 90 | C3×#626 | — | 2 | 2 | no | — |
| 91 | C3×#625 | — | 2 | 2 | no | — |
| 92 | C3×#624 | C23 | 1 | 2 | yes | — |
| 93 | C3×D3×Dic3 | — | 2 | 2 | no | — |
| 94 | D3×#121 | — | 9 | 1 | no | maximal |
| 95 | C23×C3⋊D3 | — | 3 | 1 | no | — |
| 96 | C22×D32 | — | 3 | 2 | no | — |
| 97 | C22×D32 | — | 6 | 2 | no | — |
| 98 | C22×D32 | — | 6 | 2 | no | — |
| 99 | C22×#157 | — | 3 | 1 | no | — |
| 100 | C22×#157 | — | 3 | 1 | no | — |
| 101 | C22×#157 | — | 3 | 1 | no | — |
| 102 | C22×#157 | — | 3 | 1 | no | — |
| 103 | C22×#157 | — | 3 | 1 | no | — |
| 104 | C22×#157 | — | 6 | 4 | no | — |
| 105 | C22×#157 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 106 | C2×GO+(4,𝔽2) | — | 3 | 2 | no | — |
| 107 | C2×GO+(4,𝔽2) | — | 3 | 1 | no | — |
| 108 | C2×GO+(4,𝔽2) | — | 6 | 4 | no | — |
| 109 | C2×GO+(4,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 110 | D4×C3⋊D3 | — | 6 | 2 | no | — |
| 111 | C2×C3×#67 | — | 6 | 2 | no | — |
| 112 | C3×D3×D4 | — | 6 | 2 | no | — |
| 113 | C3×D3×D4 | — | 6 | 2 | no | — |
| 114 | #3811 | — | 3 | 2 | no | — |
| 115 | #3811 | — | 3 | 2 | no | — |
| 116 | #3811 | — | 3 | 2 | no | — |
| 117 | #3811 | — | 6 | 2 | no | — |
| 118 | #3811 | — | 6 | 2 | no | — |
| 119 | #3811 | — | 6 | 2 | no | — |
| 120 | #3811 | — | 6 | 2 | no | — |
| 121 | #3811 | — | 12 | 2 | no | — |
| 122 | #3811 | C2×D3 | 1 | 2 | yes | complemented |
| 123 | D3×#67 | — | 2 | 2 | no | — |
| 124 | D3×#67 | — | 6 | 2 | no | — |
| 125 | D3×#67 | — | 6 | 2 | no | — |
| 126 | D3×#67 | — | 6 | 2 | no | — |
| 127 | C2×#626 | — | 6 | 2 | no | — |
| 128 | C2×#624 | — | 3 | 2 | no | — |
| 129 | #3802 | — | 6 | 2 | no | — |
| 130 | D3×D12 | — | 6 | 2 | no | — |
| 131 | D3×D12 | — | 6 | 2 | no | — |
| 132 | C4×D32 | — | 6 | 2 | no | — |
| 133 | #3773 | — | 3 | 1 | no | — |
| 134 | #3773 | — | 3 | 2 | no | — |
| 135 | #3773 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 136 | D32⋊C4 | — | 3 | 2 | no | — |
| 137 | D32⋊C4 | — | 3 | 2 | no | — |
| 138 | D32⋊C4 | — | 3 | 2 | no | — |
| 139 | D32⋊C4 | C2×D3 | 1 | 2 | yes | complemented |
| 140 | C22×C33 | C2×D4 | 1 | 1 | yes | characteristic, complemented |
| 141 | C2×C3⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 142 | C2×C3⋊(C3⋊D3) | C2×D4 | 1 | 1 | yes | characteristic |
| 143 | C2×C3⋊(C3⋊D3) | C2×D4 | 1 | 1 | yes | characteristic, complemented |
| 144 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 145 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 146 | C2×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 147 | C2×C3×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic, complemented |
| 148 | C2×C3×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 149 | C2×C32×D3 | — | 2 | 2 | no | — |
| 150 | C2×C32×D3 | — | 2 | 2 | no | — |
| 151 | C2×C32×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 152 | C2×C32×D3 | C2×D4 | 1 | 1 | yes | characteristic, complemented |
| 153 | #1113 | — | 2 | 2 | no | — |
| 154 | #1113 | — | 2 | 2 | no | — |
| 155 | D3×C3⋊D3 | — | 2 | 2 | no | — |
| 156 | D3×C3⋊D3 | — | 2 | 1 | no | — |
| 157 | D3×C3⋊D3 | — | 2 | 1 | no | — |
| 158 | D3×C3⋊D3 | — | 2 | 2 | no | — |
| 159 | D3×C3⋊D3 | — | 4 | 4 | no | — |
| 160 | D3×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 161 | D3×C3⋊D3 | #41 | 1 | 2 | yes | — |
| 162 | C3×D32 | — | 2 | 2 | no | — |
| 163 | C3×D32 | — | 2 | 2 | no | — |
| 164 | C3×D32 | — | 4 | 4 | no | — |
| 165 | C3⋊#157 | — | 2 | 1 | no | — |
| 166 | C3⋊#157 | C2×D4 | 1 | 2 | yes | complemented |
| 167 | C3×#157 | — | 2 | 1 | no | — |
| 168 | C3×#157 | C2×D4 | 1 | 2 | yes | complemented |
| 169 | C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 170 | C32×Dic3 | — | 2 | 2 | no | — |
| 171 | C2×D3×D4 | — | 9 | 2 | no | — |
| 172 | C2×D3×D4 | — | 9 | 1 | no | — |
| 173 | C2×D3×D4 | — | 18 | 2 | no | — |
| 174 | C22×C4×D3 | — | 9 | 1 | no | — |
| 175 | C3×#121 | — | 9 | 1 | no | — |
| 176 | #939 | — | 9 | 2 | no | — |
| 177 | #938 | — | 9 | 1 | no | — |
| 178 | #930 | — | 9 | 1 | no | — |
| 179 | #895 | — | 9 | 1 | no | — |
| 180 | D3×C4⋊C4 | — | 9 | 1 | no | — |
| 181 | #884 | — | 9 | 2 | no | — |
| 182 | D3×C22⋊C4 | — | 9 | 2 | no | — |
| 183 | C23×C32 | — | 3 | 1 | no | — |
| 184 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 185 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 186 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 187 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 188 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 189 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 190 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 191 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 192 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 193 | C22×C3⋊D3 | — | 12 | 2 | no | — |
| 194 | C22×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 195 | C22×C3×D3 | — | 2 | 2 | no | — |
| 196 | C22×C3×D3 | — | 6 | 2 | no | — |
| 197 | C22×C3×D3 | — | 6 | 2 | no | — |
| 198 | C22×C3×D3 | — | 6 | 2 | no | — |
| 199 | C22×C3×D3 | — | 6 | 2 | no | — |
| 200 | C2×D32 | — | 2 | 2 | no | — |
| 201 | C2×D32 | — | 3 | 2 | no | — |
| 202 | C2×D32 | — | 6 | 2 | no | — |
| 203 | C2×D32 | — | 6 | 2 | no | — |
| 204 | C2×D32 | — | 6 | 2 | no | — |
| 205 | C2×D32 | — | 6 | 2 | no | — |
| 206 | C2×D32 | — | 6 | 2 | no | — |
| 207 | C2×D32 | — | 6 | 2 | no | — |
| 208 | C2×D32 | — | 6 | 2 | no | — |
| 209 | C2×D32 | — | 6 | 4 | no | — |
| 210 | C2×D32 | — | 6 | 4 | no | — |
| 211 | C2×D32 | — | 12 | 4 | no | — |
| 212 | C2×D32 | — | 12 | 4 | no | — |
| 213 | C2×D32 | — | 12 | 4 | no | — |
| 214 | C2×D32 | — | 12 | 4 | no | — |
| 215 | C2×D32 | — | 12 | 2 | no | — |
| 216 | C2×D32 | C22×D3 | 1 | 2 | yes | — |
| 217 | C2×#157 | — | 2 | 2 | no | — |
| 218 | C2×#157 | — | 3 | 1 | no | — |
| 219 | C2×#157 | — | 3 | 4 | no | — |
| 220 | C2×#157 | — | 3 | 1 | no | — |
| 221 | C2×#157 | — | 6 | 2 | no | — |
| 222 | C2×#157 | — | 6 | 2 | no | — |
| 223 | C2×#157 | — | 6 | 2 | no | — |
| 224 | C2×#157 | — | 6 | 2 | no | — |
| 225 | C2×#157 | C22×D3 | 1 | 1 | yes | characteristic |
| 226 | C2×#157 | C22×D3 | 1 | 1 | yes | characteristic |
| 227 | GO+(4,𝔽2) | — | 2 | 2 | no | — |
| 228 | GO+(4,𝔽2) | — | 6 | 4 | no | — |
| 229 | GO+(4,𝔽2) | — | 6 | 2 | no | — |
| 230 | C32×D4 | — | 6 | 2 | no | — |
| 231 | #638 | — | 2 | 2 | no | — |
| 232 | #638 | — | 6 | 2 | no | — |
| 233 | C4⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 234 | C4×C3⋊D3 | — | 6 | 2 | no | — |
| 235 | C3×#67 | — | 2 | 2 | no | — |
| 236 | C3×#67 | — | 2 | 2 | no | — |
| 237 | C3×#67 | — | 4 | 2 | no | — |
| 238 | C3×#67 | — | 6 | 2 | no | — |
| 239 | C3×#67 | — | 6 | 2 | no | — |
| 240 | C3×#67 | — | 6 | 2 | no | — |
| 241 | C3×#67 | — | 6 | 2 | no | — |
| 242 | C3×#67 | — | 6 | 2 | no | — |
| 243 | C3×#67 | — | 6 | 2 | no | — |
| 244 | C3×#67 | — | 12 | 2 | no | — |
| 245 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 246 | C3×D12 | — | 6 | 2 | no | — |
| 247 | C3×D12 | — | 6 | 2 | no | — |
| 248 | C3×C4×D3 | — | 6 | 2 | no | — |
| 249 | C3×C4×D3 | — | 6 | 2 | no | — |
| 250 | #626 | — | 2 | 2 | no | — |
| 251 | #626 | — | 2 | 2 | no | — |
| 252 | #626 | — | 6 | 2 | no | — |
| 253 | #626 | — | 6 | 2 | no | — |
| 254 | #626 | — | 6 | 2 | no | — |
| 255 | #626 | — | 6 | 2 | no | — |
| 256 | #626 | — | 6 | 2 | no | — |
| 257 | #626 | — | 6 | 2 | no | — |
| 258 | #626 | — | 12 | 2 | no | — |
| 259 | #626 | — | 12 | 2 | no | — |
| 260 | #625 | — | 2 | 2 | no | — |
| 261 | #625 | — | 6 | 2 | no | — |
| 262 | #624 | — | 3 | 2 | no | — |
| 263 | #624 | — | 6 | 2 | no | — |
| 264 | #624 | — | 6 | 2 | no | — |
| 265 | #624 | — | 12 | 2 | no | — |
| 266 | #624 | C22×D3 | 1 | 2 | yes | — |
| 267 | D3×Dic3 | — | 2 | 2 | no | — |
| 268 | D3×Dic3 | — | 6 | 2 | no | — |
| 269 | C2×#121 | — | 27 | 1 | no | Sylow |
| 270 | C2×C33 | — | 2 | 1 | no | — |
| 271 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 272 | C3⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 273 | C3⋊(C3⋊D3) | #121 | 1 | 2 | yes | complemented |
| 274 | C3×C3⋊D3 | — | 2 | 1 | no | — |
| 275 | C3×C3⋊D3 | — | 4 | 2 | no | — |
| 276 | C3×C3⋊D3 | C22×D4 | 1 | 1 | yes | characteristic |
| 277 | C3×C3⋊D3 | C2×#41 | 1 | 1 | yes | characteristic |
| 278 | C32×D3 | — | 2 | 1 | no | — |
| 279 | C32×D3 | — | 4 | 2 | no | — |
| 280 | C32×D3 | #121 | 1 | 2 | yes | complemented |
| 281 | C23×D3 | — | 9 | 2 | no | — |
| 282 | C23×D3 | — | 9 | 1 | no | — |
| 283 | C23×D3 | — | 18 | 2 | no | — |
| 284 | C23×D3 | — | 18 | 2 | no | — |
| 285 | C2×C3×D4 | — | 9 | 2 | no | — |
| 286 | C2×C3×D4 | — | 9 | 1 | no | — |
| 287 | C2×C3×D4 | — | 18 | 2 | no | — |
| 288 | C22×C3×C4 | — | 9 | 1 | no | — |
| 289 | C2×#67 | — | 6 | 2 | no | — |
| 290 | C2×#67 | — | 9 | 2 | no | — |
| 291 | C2×#67 | — | 9 | 2 | no | — |
| 292 | C2×#67 | — | 9 | 2 | no | — |
| 293 | C2×#67 | — | 18 | 2 | no | — |
| 294 | C22×Dic3 | — | 9 | 1 | no | — |
| 295 | D3×D4 | — | 6 | 2 | no | — |
| 296 | D3×D4 | — | 6 | 2 | no | — |
| 297 | D3×D4 | — | 18 | 2 | no | — |
| 298 | D3×D4 | — | 18 | 2 | no | — |
| 299 | D3×D4 | — | 18 | 2 | no | — |
| 300 | D3×D4 | — | 18 | 2 | no | — |
| 301 | D3×D4 | — | 18 | 4 | no | — |
| 302 | D3×D4 | — | 18 | 2 | no | — |
| 303 | D3×D4 | — | 18 | 2 | no | — |
| 304 | D3×D4 | — | 18 | 2 | no | — |
| 305 | D3×D4 | — | 18 | 2 | no | — |
| 306 | D3×D4 | — | 18 | 2 | no | — |
| 307 | D3×D4 | — | 18 | 2 | no | — |
| 308 | D3×D4 | — | 36 | 2 | no | — |
| 309 | C2×D12 | — | 9 | 2 | no | — |
| 310 | C2×D12 | — | 9 | 1 | no | — |
| 311 | C2×D12 | — | 18 | 2 | no | — |
| 312 | C2×C4×D3 | — | 9 | 2 | no | — |
| 313 | C2×C4×D3 | — | 9 | 1 | no | — |
| 314 | C2×C4×D3 | — | 9 | 1 | no | — |
| 315 | C2×C4×D3 | — | 9 | 1 | no | — |
| 316 | C2×C4×D3 | — | 9 | 1 | no | — |
| 317 | C2×C4×D3 | — | 18 | 2 | no | — |
| 318 | C2×C4×D3 | — | 18 | 4 | no | — |
| 319 | C3×C4⋊C4 | — | 9 | 1 | no | — |
| 320 | C3×C22⋊C4 | — | 9 | 2 | no | — |
| 321 | #217 | — | 9 | 2 | no | — |
| 322 | (C2×D3)⋊C4 | — | 9 | 2 | no | — |
| 323 | (C2×D3)⋊C4 | — | 9 | 2 | no | — |
| 324 | C4⋊Dic3 | — | 9 | 1 | no | — |
| 325 | Dic3⋊C4 | — | 9 | 2 | no | — |
| 326 | C22×C32 | — | 2 | 2 | no | — |
| 327 | C22×C32 | — | 3 | 1 | no | — |
| 328 | C22×C32 | — | 3 | 1 | no | — |
| 329 | C22×C32 | — | 4 | 2 | no | — |
| 330 | C22×C32 | — | 6 | 2 | no | — |
| 331 | C22×C32 | — | 6 | 2 | no | — |
| 332 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic, complemented |
| 333 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 334 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 335 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 336 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 337 | C2×C3⋊D3 | — | 3 | 2 | no | — |
| 338 | C2×C3⋊D3 | — | 3 | 2 | no | — |
| 339 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 340 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 341 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 342 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 343 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 344 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 345 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 346 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 347 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 348 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 349 | C2×C3⋊D3 | — | 12 | 4 | no | — |
| 350 | C2×C3⋊D3 | — | 12 | 4 | no | — |
| 351 | C2×C3⋊D3 | — | 24 | 4 | no | — |
| 352 | C2×C3⋊D3 | D3×D4 | 1 | 1 | yes | characteristic, complemented |
| 353 | C2×C3⋊D3 | C23×D3 | 1 | 1 | yes | characteristic |
| 354 | C2×C3×D3 | — | 2 | 2 | no | — |
| 355 | C2×C3×D3 | — | 2 | 2 | no | — |
| 356 | C2×C3×D3 | — | 2 | 2 | no | — |
| 357 | C2×C3×D3 | — | 2 | 2 | no | — |
| 358 | C2×C3×D3 | — | 4 | 4 | no | — |
| 359 | C2×C3×D3 | — | 4 | 2 | no | — |
| 360 | C2×C3×D3 | — | 6 | 2 | no | — |
| 361 | C2×C3×D3 | — | 6 | 2 | no | — |
| 362 | C2×C3×D3 | — | 6 | 2 | no | — |
| 363 | C2×C3×D3 | — | 6 | 2 | no | — |
| 364 | C2×C3×D3 | — | 12 | 2 | no | — |
| 365 | C2×C3×D3 | — | 12 | 2 | no | — |
| 366 | C2×C3×D3 | — | 12 | 2 | no | — |
| 367 | C2×C3×D3 | — | 12 | 2 | no | — |
| 368 | C2×C3×D3 | — | 12 | 2 | no | — |
| 369 | C2×C3×D3 | — | 12 | 4 | no | — |
| 370 | C2×C3×D3 | — | 12 | 4 | no | — |
| 371 | D32 | — | 2 | 2 | no | — |
| 372 | D32 | — | 2 | 2 | no | — |
| 373 | D32 | — | 4 | 4 | no | — |
| 374 | D32 | — | 6 | 4 | no | — |
| 375 | D32 | — | 6 | 4 | no | — |
| 376 | D32 | — | 6 | 2 | no | — |
| 377 | D32 | — | 6 | 2 | no | — |
| 378 | D32 | — | 12 | 4 | no | — |
| 379 | D32 | — | 12 | 2 | no | — |
| 380 | D32 | — | 12 | 2 | no | — |
| 381 | D32 | — | 12 | 4 | no | — |
| 382 | D32 | — | 12 | 2 | no | — |
| 383 | D32 | — | 12 | 2 | no | — |
| 384 | D32 | — | 12 | 4 | no | — |
| 385 | D32 | — | 12 | 4 | no | — |
| 386 | D32 | — | 24 | 4 | no | — |
| 387 | #157 | — | 2 | 1 | no | — |
| 388 | #157 | — | 3 | 2 | no | — |
| 389 | #157 | — | 6 | 1 | no | — |
| 390 | #157 | D3×D4 | 1 | 2 | yes | complemented |
| 391 | C32×C4 | — | 6 | 2 | no | — |
| 392 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 393 | C3×Dic3 | — | 2 | 2 | no | — |
| 394 | C3×Dic3 | — | 2 | 2 | no | — |
| 395 | C3×Dic3 | — | 4 | 2 | no | — |
| 396 | C3×Dic3 | — | 6 | 2 | no | — |
| 397 | C3×Dic3 | — | 6 | 2 | no | — |
| 398 | C3×Dic3 | — | 12 | 2 | no | — |
| 399 | C22×D4 | — | 27 | 2 | no | — |
| 400 | C22×D4 | — | 27 | 1 | no | — |
| 401 | C23×C4 | — | 27 | 1 | no | — |
| 402 | #121 | — | 9 | 1 | no | — |
| 403 | #121 | — | 27 | 2 | no | — |
| 404 | #121 | — | 27 | 1 | no | — |
| 405 | #121 | — | 27 | 1 | no | — |
| 406 | #121 | — | 27 | 1 | no | — |
| 407 | #121 | — | 27 | 2 | no | — |
| 408 | C2×C4⋊C4 | — | 27 | 1 | no | — |
| 409 | C2×C22⋊C4 | — | 27 | 2 | no | — |
| 410 | C33 | C2×#121 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 411 | C23×C3 | — | 6 | 2 | no | — |
| 412 | C23×C3 | — | 9 | 2 | no | — |
| 413 | C23×C3 | — | 9 | 1 | no | — |
| 414 | C23×C3 | — | 18 | 2 | no | — |
| 415 | C22×D3 | — | 6 | 2 | no | — |
| 416 | C22×D3 | — | 6 | 2 | no | — |
| 417 | C22×D3 | — | 6 | 2 | no | — |
| 418 | C22×D3 | — | 6 | 2 | no | — |
| 419 | C22×D3 | — | 9 | 2 | no | — |
| 420 | C22×D3 | — | 9 | 1 | no | — |
| 421 | C22×D3 | — | 9 | 1 | no | — |
| 422 | C22×D3 | — | 9 | 1 | no | — |
| 423 | C22×D3 | — | 9 | 1 | no | — |
| 424 | C22×D3 | — | 9 | 1 | no | — |
| 425 | C22×D3 | — | 18 | 2 | no | — |
| 426 | C22×D3 | — | 18 | 2 | no | — |
| 427 | C22×D3 | — | 18 | 2 | no | — |
| 428 | C22×D3 | — | 18 | 2 | no | — |
| 429 | C22×D3 | — | 18 | 2 | no | — |
| 430 | C22×D3 | — | 18 | 2 | no | — |
| 431 | C22×D3 | — | 18 | 2 | no | — |
| 432 | C22×D3 | — | 18 | 2 | no | — |
| 433 | C22×D3 | — | 18 | 2 | no | — |
| 434 | C22×D3 | — | 18 | 2 | no | — |
| 435 | C22×D3 | — | 18 | 2 | no | — |
| 436 | C22×D3 | — | 18 | 4 | no | — |
| 437 | C22×D3 | — | 18 | 4 | no | — |
| 438 | C22×D3 | — | 36 | 2 | no | — |
| 439 | C22×D3 | — | 36 | 4 | no | — |
| 440 | C22×D3 | — | 36 | 4 | no | — |
| 441 | C22×D3 | — | 36 | 4 | no | — |
| 442 | C22×D3 | — | 36 | 4 | no | — |
| 443 | C22×D3 | — | 36 | 2 | no | — |
| 444 | C22×D3 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 445 | C3×D4 | — | 6 | 2 | no | — |
| 446 | C3×D4 | — | 6 | 2 | no | — |
| 447 | C3×D4 | — | 12 | 2 | no | — |
| 448 | C3×D4 | — | 18 | 2 | no | — |
| 449 | C3×D4 | — | 18 | 2 | no | — |
| 450 | C3×D4 | — | 18 | 2 | no | — |
| 451 | C3×D4 | — | 18 | 2 | no | — |
| 452 | C3×D4 | — | 18 | 2 | no | — |
| 453 | C2×C3×C4 | — | 9 | 2 | no | — |
| 454 | C2×C3×C4 | — | 9 | 1 | no | — |
| 455 | C2×C3×C4 | — | 9 | 1 | no | — |
| 456 | C2×C3×C4 | — | 18 | 2 | no | — |
| 457 | C2×C3×C4 | — | 18 | 2 | no | — |
| 458 | #67 | — | 2 | 2 | no | — |
| 459 | #67 | — | 6 | 2 | no | — |
| 460 | #67 | — | 6 | 2 | no | — |
| 461 | #67 | — | 6 | 2 | no | — |
| 462 | #67 | — | 6 | 2 | no | — |
| 463 | #67 | — | 6 | 2 | no | — |
| 464 | #67 | — | 6 | 2 | no | — |
| 465 | #67 | — | 12 | 2 | no | — |
| 466 | #67 | — | 18 | 2 | no | — |
| 467 | #67 | — | 18 | 2 | no | — |
| 468 | #67 | — | 18 | 2 | no | — |
| 469 | #67 | — | 18 | 2 | no | — |
| 470 | #67 | — | 18 | 2 | no | — |
| 471 | #67 | — | 18 | 4 | no | — |
| 472 | #67 | — | 36 | 2 | no | — |
| 473 | C2×Dic3 | — | 6 | 2 | no | — |
| 474 | C2×Dic3 | — | 9 | 2 | no | — |
| 475 | C2×Dic3 | — | 9 | 1 | no | — |
| 476 | C2×Dic3 | — | 9 | 1 | no | — |
| 477 | C2×Dic3 | — | 18 | 2 | no | — |
| 478 | D12 | — | 6 | 2 | no | — |
| 479 | D12 | — | 6 | 2 | no | — |
| 480 | D12 | — | 18 | 2 | no | — |
| 481 | D12 | — | 18 | 2 | no | — |
| 482 | D12 | — | 18 | 2 | no | — |
| 483 | D12 | — | 18 | 2 | no | — |
| 484 | D12 | — | 18 | 2 | no | — |
| 485 | D12 | — | 36 | 2 | no | — |
| 486 | C4×D3 | — | 6 | 2 | no | — |
| 487 | C4×D3 | — | 6 | 2 | no | — |
| 488 | C4×D3 | — | 9 | 4 | no | — |
| 489 | C4×D3 | — | 18 | 2 | no | — |
| 490 | C4×D3 | — | 18 | 2 | no | — |
| 491 | C4×D3 | — | 18 | 2 | no | — |
| 492 | C4×D3 | — | 18 | 2 | no | — |
| 493 | C4×D3 | — | 18 | 2 | no | — |
| 494 | C4×D3 | — | 18 | 2 | no | — |
| 495 | C4×D3 | — | 18 | 2 | no | — |
| 496 | C4×D3 | — | 36 | 2 | no | — |
| 497 | C2×C32 | — | 2 | 2 | no | — |
| 498 | C2×C32 | — | 2 | 1 | no | — |
| 499 | C2×C32 | — | 3 | 2 | no | — |
| 500 | C2×C32 | — | 4 | 2 | no | — |
| 501 | C2×C32 | — | 4 | 2 | no | — |
| 502 | C2×C32 | — | 6 | 1 | no | — |
| 503 | C2×C32 | — | 8 | 2 | no | — |
| 504 | C2×C32 | — | 12 | 2 | no | — |
| 505 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 506 | C3⋊D3 | — | 2 | 1 | no | — |
| 507 | C3⋊D3 | — | 3 | 2 | no | — |
| 508 | C3⋊D3 | — | 4 | 2 | no | — |
| 509 | C3⋊D3 | — | 6 | 4 | no | — |
| 510 | C3⋊D3 | — | 6 | 1 | no | — |
| 511 | C3⋊D3 | — | 12 | 4 | no | — |
| 512 | C3⋊D3 | — | 12 | 2 | no | — |
| 513 | C3⋊D3 | — | 24 | 2 | no | — |
| 514 | C3⋊D3 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 515 | C3⋊D3 | D3×#41 | 1 | 1 | yes | characteristic |
| 516 | C3×D3 | — | 2 | 4 | no | — |
| 517 | C3×D3 | — | 4 | 2 | no | — |
| 518 | C3×D3 | — | 4 | 2 | no | — |
| 519 | C3×D3 | — | 4 | 2 | no | — |
| 520 | C3×D3 | — | 6 | 2 | no | — |
| 521 | C3×D3 | — | 6 | 2 | no | — |
| 522 | C3×D3 | — | 8 | 2 | no | — |
| 523 | C3×D3 | — | 12 | 2 | no | — |
| 524 | C3×D3 | — | 12 | 2 | no | — |
| 525 | C3×D3 | — | 12 | 2 | no | — |
| 526 | C3×D3 | — | 24 | 2 | no | — |
| 527 | C24 | — | 27 | 1 | no | — |
| 528 | C24 | — | 27 | 2 | no | — |
| 529 | C2×D4 | — | 9 | 2 | no | — |
| 530 | C2×D4 | — | 9 | 1 | no | — |
| 531 | C2×D4 | — | 18 | 2 | no | — |
| 532 | C2×D4 | — | 27 | 2 | no | — |
| 533 | C2×D4 | — | 27 | 1 | no | — |
| 534 | C2×D4 | — | 27 | 2 | no | — |
| 535 | C2×D4 | — | 27 | 2 | no | — |
| 536 | C2×D4 | — | 27 | 2 | no | — |
| 537 | C2×D4 | — | 54 | 2 | no | — |
| 538 | C2×D4 | — | 54 | 4 | no | — |
| 539 | C2×D4 | — | 54 | 2 | no | — |
| 540 | C2×D4 | — | 54 | 2 | no | — |
| 541 | C22×C4 | — | 9 | 1 | no | — |
| 542 | C22×C4 | — | 27 | 2 | no | — |
| 543 | C22×C4 | — | 27 | 1 | no | — |
| 544 | C22×C4 | — | 27 | 1 | no | — |
| 545 | C22×C4 | — | 27 | 1 | no | — |
| 546 | C22×C4 | — | 27 | 1 | no | — |
| 547 | C22×C4 | — | 27 | 1 | no | — |
| 548 | C22×C4 | — | 54 | 4 | no | — |
| 549 | C4⋊C4 | — | 9 | 1 | no | — |
| 550 | C4⋊C4 | — | 27 | 2 | no | — |
| 551 | C4⋊C4 | — | 27 | 1 | no | — |
| 552 | C22⋊C4 | — | 9 | 2 | no | — |
| 553 | C22⋊C4 | — | 27 | 2 | no | — |
| 554 | C22⋊C4 | — | 27 | 2 | no | — |
| 555 | C22⋊C4 | — | 27 | 2 | no | — |
| 556 | C22×C3 | — | 2 | 2 | no | — |
| 557 | C22×C3 | — | 4 | 2 | no | — |
| 558 | C22×C3 | — | 6 | 2 | no | — |
| 559 | C22×C3 | — | 6 | 2 | no | — |
| 560 | C22×C3 | — | 6 | 2 | no | — |
| 561 | C22×C3 | — | 6 | 2 | no | — |
| 562 | C22×C3 | — | 9 | 1 | no | — |
| 563 | C22×C3 | — | 9 | 1 | no | — |
| 564 | C22×C3 | — | 12 | 4 | no | — |
| 565 | C22×C3 | — | 12 | 2 | no | — |
| 566 | C22×C3 | — | 18 | 1 | no | — |
| 567 | C22×C3 | — | 18 | 1 | no | — |
| 568 | C22×C3 | — | 18 | 2 | no | — |
| 569 | C22×C3 | — | 18 | 2 | no | — |
| 570 | C22×C3 | — | 18 | 2 | no | — |
| 571 | C22×C3 | — | 36 | 4 | no | — |
| 572 | C22×C3 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 573 | C2×D3 | — | 2 | 2 | no | — |
| 574 | C2×D3 | — | 2 | 2 | no | — |
| 575 | C2×D3 | — | 6 | 2 | no | — |
| 576 | C2×D3 | — | 6 | 2 | no | — |
| 577 | C2×D3 | — | 6 | 2 | no | — |
| 578 | C2×D3 | — | 6 | 2 | no | — |
| 579 | C2×D3 | — | 9 | 1 | no | — |
| 580 | C2×D3 | — | 9 | 2 | no | — |
| 581 | C2×D3 | — | 9 | 2 | no | — |
| 582 | C2×D3 | — | 9 | 1 | no | — |
| 583 | C2×D3 | — | 12 | 2 | no | — |
| 584 | C2×D3 | — | 12 | 2 | no | — |
| 585 | C2×D3 | — | 12 | 2 | no | — |
| 586 | C2×D3 | — | 12 | 2 | no | — |
| 587 | C2×D3 | — | 12 | 2 | no | — |
| 588 | C2×D3 | — | 12 | 4 | no | — |
| 589 | C2×D3 | — | 12 | 4 | no | — |
| 590 | C2×D3 | — | 18 | 4 | no | — |
| 591 | C2×D3 | — | 18 | 4 | no | — |
| 592 | C2×D3 | — | 18 | 2 | no | — |
| 593 | C2×D3 | — | 18 | 2 | no | — |
| 594 | C2×D3 | — | 18 | 2 | no | — |
| 595 | C2×D3 | — | 18 | 1 | no | — |
| 596 | C2×D3 | — | 18 | 1 | no | — |
| 597 | C2×D3 | — | 18 | 2 | no | — |
| 598 | C2×D3 | — | 18 | 2 | no | — |
| 599 | C2×D3 | — | 18 | 2 | no | — |
| 600 | C2×D3 | — | 18 | 2 | no | — |
| 601 | C2×D3 | — | 36 | 2 | no | — |
| 602 | C2×D3 | — | 36 | 2 | no | — |
| 603 | C2×D3 | — | 36 | 2 | no | — |
| 604 | C2×D3 | — | 36 | 2 | no | — |
| 605 | C2×D3 | — | 36 | 2 | no | — |
| 606 | C2×D3 | — | 36 | 2 | no | — |
| 607 | C2×D3 | — | 36 | 4 | no | — |
| 608 | C2×D3 | — | 36 | 4 | no | — |
| 609 | C2×D3 | — | 36 | 4 | no | — |
| 610 | C2×D3 | — | 36 | 4 | no | — |
| 611 | C2×D3 | — | 36 | 4 | no | — |
| 612 | C2×D3 | — | 36 | 4 | no | — |
| 613 | C2×D3 | — | 72 | 4 | no | — |
| 614 | C2×D3 | — | 72 | 4 | no | — |
| 615 | C2×D3 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 616 | C2×D3 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 617 | C3×C4 | — | 6 | 2 | no | — |
| 618 | C3×C4 | — | 6 | 2 | no | — |
| 619 | C3×C4 | — | 9 | 2 | no | — |
| 620 | C3×C4 | — | 12 | 2 | no | — |
| 621 | C3×C4 | — | 18 | 2 | no | — |
| 622 | C3×C4 | — | 18 | 1 | no | — |
| 623 | Dic3 | — | 2 | 2 | no | — |
| 624 | Dic3 | — | 6 | 2 | no | — |
| 625 | Dic3 | — | 6 | 2 | no | — |
| 626 | Dic3 | — | 9 | 2 | no | — |
| 627 | Dic3 | — | 12 | 2 | no | — |
| 628 | Dic3 | — | 18 | 1 | no | — |
| 629 | C32 | — | 2 | 2 | no | — |
| 630 | C32 | — | 4 | 2 | no | — |
| 631 | C32 | D3×#121 | 1 | 1 | yes | characteristic, complemented |
| 632 | C23 | — | 3 | 1 | no | — |
| 633 | C23 | — | 9 | 2 | no | — |
| 634 | C23 | — | 9 | 1 | no | — |
| 635 | C23 | — | 18 | 2 | no | — |
| 636 | C23 | — | 27 | 1 | no | — |
| 637 | C23 | — | 27 | 1 | no | — |
| 638 | C23 | — | 27 | 1 | no | — |
| 639 | C23 | — | 27 | 1 | no | — |
| 640 | C23 | — | 27 | 2 | no | — |
| 641 | C23 | — | 27 | 1 | no | — |
| 642 | C23 | — | 54 | 2 | no | — |
| 643 | C23 | — | 54 | 2 | no | — |
| 644 | C23 | — | 54 | 2 | no | — |
| 645 | C23 | — | 54 | 4 | no | — |
| 646 | C23 | — | 54 | 4 | no | — |
| 647 | D4 | — | 6 | 2 | no | — |
| 648 | D4 | — | 18 | 2 | no | — |
| 649 | D4 | — | 18 | 2 | no | — |
| 650 | D4 | — | 18 | 2 | no | — |
| 651 | D4 | — | 18 | 2 | no | — |
| 652 | D4 | — | 18 | 2 | no | — |
| 653 | D4 | — | 54 | 2 | no | — |
| 654 | D4 | — | 54 | 2 | no | — |
| 655 | D4 | — | 54 | 2 | no | — |
| 656 | D4 | — | 54 | 2 | no | — |
| 657 | D4 | — | 54 | 4 | no | — |
| 658 | C2×C4 | — | 9 | 2 | no | — |
| 659 | C2×C4 | — | 9 | 1 | no | — |
| 660 | C2×C4 | — | 9 | 1 | no | — |
| 661 | C2×C4 | — | 18 | 2 | no | — |
| 662 | C2×C4 | — | 18 | 2 | no | — |
| 663 | C2×C4 | — | 27 | 4 | no | — |
| 664 | C2×C4 | — | 27 | 2 | no | — |
| 665 | C2×C4 | — | 27 | 1 | no | — |
| 666 | C2×C4 | — | 27 | 1 | no | — |
| 667 | C2×C4 | — | 54 | 2 | no | — |
| 668 | C2×C4 | — | 54 | 2 | no | — |
| 669 | C2×C4 | — | 54 | 2 | no | — |
| 670 | C2×C4 | — | 54 | 2 | no | — |
| 671 | C2×C4 | — | 54 | 2 | no | — |
| 672 | C2×C3 | — | 2 | 1 | no | — |
| 673 | C2×C3 | — | 2 | 2 | no | — |
| 674 | C2×C3 | — | 4 | 2 | no | — |
| 675 | C2×C3 | — | 4 | 2 | no | — |
| 676 | C2×C3 | — | 6 | 4 | no | — |
| 677 | C2×C3 | — | 8 | 2 | no | — |
| 678 | C2×C3 | — | 9 | 1 | no | — |
| 679 | C2×C3 | — | 9 | 1 | no | — |
| 680 | C2×C3 | — | 12 | 2 | no | — |
| 681 | C2×C3 | — | 12 | 2 | no | — |
| 682 | C2×C3 | — | 12 | 2 | no | — |
| 683 | C2×C3 | — | 18 | 1 | no | — |
| 684 | C2×C3 | — | 24 | 2 | no | — |
| 685 | C2×C3 | — | 36 | 2 | no | — |
| 686 | C2×C3 | C22×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 687 | D3 | — | 2 | 1 | no | — |
| 688 | D3 | — | 4 | 2 | no | — |
| 689 | D3 | — | 6 | 2 | no | — |
| 690 | D3 | — | 6 | 2 | no | — |
| 691 | D3 | — | 9 | 2 | no | — |
| 692 | D3 | — | 12 | 2 | no | — |
| 693 | D3 | — | 12 | 2 | no | — |
| 694 | D3 | — | 12 | 2 | no | — |
| 695 | D3 | — | 18 | 4 | no | — |
| 696 | D3 | — | 18 | 1 | no | — |
| 697 | D3 | — | 24 | 2 | no | — |
| 698 | D3 | — | 36 | 4 | no | — |
| 699 | D3 | — | 36 | 2 | no | — |
| 700 | D3 | — | 72 | 2 | no | — |
| 701 | D3 | #64242 | 1 | 2 | yes | direct product factor |
| 702 | C22 | — | 3 | 1 | no | — |
| 703 | C22 | — | 3 | 1 | no | — |
| 704 | C22 | — | 6 | 2 | no | — |
| 705 | C22 | — | 6 | 2 | no | — |
| 706 | C22 | — | 9 | 1 | no | — |
| 707 | C22 | — | 9 | 1 | no | — |
| 708 | C22 | — | 18 | 1 | no | — |
| 709 | C22 | — | 18 | 1 | no | — |
| 710 | C22 | — | 18 | 2 | no | — |
| 711 | C22 | — | 18 | 2 | no | — |
| 712 | C22 | — | 18 | 2 | no | — |
| 713 | C22 | — | 27 | 2 | no | — |
| 714 | C22 | — | 27 | 2 | no | — |
| 715 | C22 | — | 27 | 1 | no | — |
| 716 | C22 | — | 27 | 1 | no | — |
| 717 | C22 | — | 36 | 4 | no | — |
| 718 | C22 | — | 54 | 2 | no | — |
| 719 | C22 | — | 54 | 2 | no | — |
| 720 | C22 | — | 54 | 1 | no | — |
| 721 | C22 | — | 54 | 1 | no | — |
| 722 | C22 | — | 54 | 2 | no | — |
| 723 | C22 | — | 54 | 2 | no | — |
| 724 | C22 | — | 54 | 2 | no | — |
| 725 | C22 | — | 108 | 4 | no | — |
| 726 | C22 | D3×GO+(4,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 727 | C4 | — | 6 | 2 | no | — |
| 728 | C4 | — | 9 | 2 | no | — |
| 729 | C4 | — | 18 | 1 | no | — |
| 730 | C4 | — | 18 | 2 | no | — |
| 731 | C4 | — | 27 | 2 | no | — |
| 732 | C4 | — | 54 | 1 | no | — |
| 733 | C3 | — | 2 | 2 | no | — |
| 734 | C3 | — | 4 | 2 | no | — |
| 735 | C3 | C2×#64242 | 1 | 1 | yes | characteristic, complemented |
| 736 | C2 | — | 2 | 1 | no | — |
| 737 | C2 | — | 3 | 2 | no | — |
| 738 | C2 | — | 6 | 1 | no | — |
| 739 | C2 | — | 9 | 1 | no | — |
| 740 | C2 | — | 9 | 1 | no | — |
| 741 | C2 | — | 12 | 2 | no | — |
| 742 | C2 | — | 18 | 1 | no | — |
| 743 | C2 | — | 27 | 2 | no | — |
| 744 | C2 | — | 36 | 2 | no | — |
| 745 | C2 | — | 54 | 1 | no | — |
| 746 | 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 | C2×#121 |
| 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. C22×D3×#157 | C2 | semidirect |
| 2. C2×D3×GO+(4,𝔽2) | C2 | semidirect |
| 3. D3×#3811 | C2 | semidirect |
| 4. #11724355 | C2 | semidirect |
| 5. #11724332 | C2 | semidirect |
| 6. C3×#64242 | C2 | semidirect |
| 7. #11724116 | C2 | semidirect |
| 8. #11724115 | C2 | semidirect |
| 9. #11724114 | C2 | semidirect |
| 10. D3×#3773 | C2 | semidirect |
| 11. D3×D32⋊C4 | C2 | semidirect |
| 14. C22×C3⋊#157 | C22 | semidirect |
| 15. C22×C3×#157 | C22 | semidirect |
| 17. C2×#157⋊D3 | C22 | semidirect |
| 18. C2×D32⋊D3 | C22 | semidirect |
| 19. C2×C3×GO+(4,𝔽2) | C22 | semidirect |
| 23. C2×D3×#157 | C22 | semidirect |
| 24. C2×D3×#157 | C22 | semidirect |
| 26. #89049 | C22 | semidirect |
| 28. C3×#3811 | C22 | semidirect |
| 30. #88955 | C22 | semidirect |
| 32. #88952 | C22 | semidirect |
| 35. #88940 | C22 | semidirect |
| 36. #88939 | C22 | semidirect |
| 37. #88934 | C22 | semidirect |
| 38. D32⋊Dic3 | C22 | semidirect |
| 39. #88932 | C22 | semidirect |
| 40. C3×#3773 | C22 | semidirect |
| 41. C3×D32⋊C4 | C22 | semidirect |
| 51. #64242 | D3 | direct (N × H) |
| 54. C22×C3⋊(C3⋊D3) | D4 | semidirect |
| 56. C22×C32×D3 | D4 | semidirect |
| 61. C2×D3×C3⋊D3 | D4 | semidirect |
| 62. C2×D3×C3⋊D3 | D4 | semidirect |
| 81. D3×#157 | D4 | semidirect |
| 105. C22×#157 | C2×D3 | semidirect |
| 109. C2×GO+(4,𝔽2) | C2×D3 | semidirect |
| 122. #3811 | C2×D3 | semidirect |
| 135. #3773 | C2×D3 | semidirect |
| 139. D32⋊C4 | C2×D3 | semidirect |
| 140. C22×C33 | C2×D4 | semidirect |
| 143. C2×C3⋊(C3⋊D3) | C2×D4 | semidirect |
| 147. C2×C3×C3⋊D3 | C2×D4 | semidirect |
| 152. C2×C32×D3 | C2×D4 | semidirect |
| 166. C3⋊#157 | C2×D4 | semidirect |
| 168. C3×#157 | C2×D4 | semidirect |
| 273. C3⋊(C3⋊D3) | #121 | semidirect |
| 280. C32×D3 | #121 | semidirect |
| 332. C22×C32 | D3×D4 | semidirect |
| 352. C2×C3⋊D3 | D3×D4 | semidirect |
| 390. #157 | D3×D4 | semidirect |
| 410. C33 | C2×#121 | semidirect |
| 444. C22×D3 | GO+(4,𝔽2) | semidirect |
| 572. C22×C3 | C2×GO+(4,𝔽2) | semidirect |
| 616. C2×D3 | C2×GO+(4,𝔽2) | semidirect |
| 631. C32 | D3×#121 | semidirect |
| 701. D3 | #64242 | direct (N × H) |
| 726. C22 | D3×GO+(4,𝔽2) | semidirect |
| 735. C3 | C2×#64242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×#157 | 2 |
| C2×D3×GO+(4,𝔽2) | 2 |
| D3×#3811 | 2 |
| #11724355 | 2 |
| #11724332 | 2 |
| C3×#64242 | 2 |
| #11724116 | 2 |
| #11724115 | 2 |
| #11724114 | 2 |
| D3×#3773 | 2 |
| D3×D32⋊C4 | 2 |
| C2×#64242 | 3 |
| D3×#121 | 9 |