Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1950 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 1950 conjugacy classes of subgroups — too many to draw. Only its 200 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 | C2×#89046 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C22×#6289 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11723639 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C3×#63966 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C3×#63957 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11722982 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11722968 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11722937 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #10594920 | — | 3 | 1 | no | maximal |
| 10 | #10594079 | — | 3 | 2 | no | maximal |
| 11 | C23×C3⋊(C3⋊D3) | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C3×#638 | C22 | 1 | 2 | yes | — |
| 13 | C22×C3×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 14 | C22×C32×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#6296 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C2×#6295 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | #89046 | — | 2 | 4 | no | — |
| 18 | C2×#6294 | C22 | 1 | 2 | yes | complemented |
| 19 | C2×#6292 | C22 | 1 | 4 | yes | — |
| 20 | C2×#6289 | — | 2 | 4 | no | — |
| 21 | C2×#6289 | C22 | 1 | 2 | yes | — |
| 22 | C2×#6289 | C22 | 1 | 2 | yes | — |
| 23 | C32×#217 | C22 | 1 | 2 | yes | — |
| 24 | #88804 | C22 | 1 | 4 | yes | — |
| 25 | C3×#3724 | C22 | 1 | 2 | yes | complemented |
| 26 | C3×Dic3⋊Dic3 | C22 | 1 | 4 | yes | complemented |
| 27 | C3×#3722 | C22 | 1 | 4 | yes | complemented |
| 28 | C3×Dic32 | C22 | 1 | 2 | yes | complemented |
| 29 | C22×C4×C3⋊D3 | — | 3 | 1 | no | — |
| 30 | C22×#624 | — | 3 | 2 | no | — |
| 31 | C22×#624 | — | 6 | 1 | no | — |
| 32 | C2×#3805 | — | 3 | 1 | no | — |
| 33 | C2×#3804 | — | 3 | 2 | no | — |
| 34 | #64091 | — | 3 | 2 | no | — |
| 35 | C3×#929 | — | 3 | 2 | no | — |
| 36 | C3×#886 | — | 3 | 2 | no | — |
| 37 | C3×#877 | — | 3 | 2 | no | — |
| 38 | #63981 | — | 3 | 2 | no | — |
| 39 | #63981 | — | 3 | 2 | no | — |
| 40 | #63981 | — | 6 | 2 | no | — |
| 41 | #63966 | D3 | 1 | 2 | yes | complemented |
| 42 | #63957 | D3 | 1 | 1 | yes | characteristic, complemented |
| 43 | #63912 | — | 3 | 2 | no | — |
| 44 | #63910 | — | 3 | 4 | no | — |
| 45 | #63895 | — | 3 | 4 | no | — |
| 46 | #63894 | — | 3 | 4 | no | — |
| 47 | #63881 | — | 3 | 4 | no | — |
| 48 | #63880 | — | 3 | 4 | no | — |
| 49 | #63865 | — | 3 | 2 | no | — |
| 50 | C23×C33 | C23 | 1 | 1 | yes | characteristic |
| 51 | C22×C3⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 52 | C22×C3⋊(C3⋊D3) | — | 2 | 4 | no | — |
| 53 | C22×C3⋊(C3⋊D3) | C23 | 1 | 2 | yes | — |
| 54 | C22×C3×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 55 | C3×#638 | — | 2 | 4 | no | — |
| 56 | C2×C3×C3⋊Dic3 | D4 | 1 | 4 | yes | complemented |
| 57 | C2×C3×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 58 | C2×C3×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 59 | C2×C3×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×C32×Dic3 | — | 2 | 2 | no | — |
| 61 | C2×C32×Dic3 | C23 | 1 | 4 | yes | — |
| 62 | C2×C32×Dic3 | C23 | 1 | 2 | yes | — |
| 63 | #6296 | — | 2 | 2 | no | — |
| 64 | #6295 | — | 2 | 2 | no | — |
| 65 | #6294 | — | 2 | 4 | no | — |
| 66 | #6292 | — | 2 | 8 | no | — |
| 67 | #6289 | — | 2 | 4 | no | — |
| 68 | #6289 | — | 2 | 4 | no | — |
| 69 | #5656 | — | 9 | 2 | no | — |
| 70 | #5524 | — | 9 | 1 | no | — |
| 71 | C23×C3⋊D3 | — | 3 | 2 | no | — |
| 72 | C23×C3⋊D3 | — | 3 | 1 | no | — |
| 73 | C23×C3⋊D3 | — | 6 | 1 | no | — |
| 74 | C23×C3⋊D3 | — | 6 | 2 | no | — |
| 75 | C23×C3⋊D3 | — | 12 | 1 | no | — |
| 76 | C22×C32×C4 | — | 3 | 1 | no | — |
| 77 | C2×#638 | C2×D3 | 1 | 2 | yes | — |
| 78 | C22×C3⋊Dic3 | C2×D3 | 1 | 1 | yes | characteristic |
| 79 | C2×C4⋊(C3⋊D3) | — | 3 | 4 | no | — |
| 80 | C2×C4×C3⋊D3 | — | 3 | 2 | no | — |
| 81 | C2×C4×C3⋊D3 | — | 3 | 2 | no | — |
| 82 | C2×C4×C3⋊D3 | — | 6 | 4 | no | — |
| 83 | C2×C3×#67 | — | 3 | 2 | no | — |
| 84 | C2×C3×#67 | — | 3 | 2 | no | — |
| 85 | C2×C3×#67 | — | 6 | 2 | no | — |
| 86 | C22×C3×Dic3 | — | 2 | 1 | no | — |
| 87 | C22×C3×Dic3 | — | 3 | 2 | no | — |
| 88 | C22×C3×Dic3 | — | 6 | 1 | no | — |
| 89 | C22×C3×Dic3 | C2×D3 | 1 | 2 | yes | — |
| 90 | C2×#627 | — | 3 | 2 | no | — |
| 91 | C2×#627 | — | 3 | 1 | no | — |
| 92 | C2×#626 | — | 3 | 2 | no | — |
| 93 | C2×#626 | — | 3 | 4 | no | — |
| 94 | C2×#626 | — | 3 | 4 | no | — |
| 95 | C2×#626 | — | 6 | 4 | no | — |
| 96 | C2×#625 | — | 3 | 1 | no | — |
| 97 | C2×#624 | — | 3 | 2 | no | — |
| 98 | C2×#624 | — | 3 | 4 | no | — |
| 99 | C2×#624 | — | 3 | 4 | no | — |
| 100 | C2×#624 | — | 6 | 8 | no | — |
| 101 | C2×#624 | — | 6 | 2 | no | — |
| 102 | C2×#624 | — | 6 | 2 | no | — |
| 103 | C2×#624 | — | 6 | 8 | no | — |
| 104 | #3805 | — | 6 | 4 | no | — |
| 105 | #3804 | — | 6 | 8 | no | — |
| 106 | C2×D3×Dic3 | — | 3 | 2 | no | — |
| 107 | C2×D3×Dic3 | — | 3 | 2 | no | — |
| 108 | C32×C22⋊C4 | — | 3 | 2 | no | — |
| 109 | #3752 | — | 3 | 4 | no | — |
| 110 | C3×#217 | — | 2 | 2 | no | — |
| 111 | C3×#217 | C2×D3 | 1 | 2 | yes | — |
| 112 | C3×#217 | C2×D3 | 1 | 2 | yes | — |
| 113 | C3×(C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 114 | C3×(C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 115 | C3×C4⋊Dic3 | — | 3 | 4 | no | — |
| 116 | C3×Dic3⋊C4 | — | 3 | 4 | no | — |
| 117 | C3×Dic3⋊C4 | — | 3 | 4 | no | — |
| 118 | C3×C4×Dic3 | — | 3 | 4 | no | — |
| 119 | #3724 | C2×D3 | 1 | 2 | yes | complemented |
| 120 | Dic3⋊Dic3 | C2×D3 | 1 | 4 | yes | complemented |
| 121 | #3722 | — | 3 | 4 | no | — |
| 122 | #3722 | — | 3 | 4 | no | — |
| 123 | #3722 | — | 6 | 4 | no | — |
| 124 | #3722 | C2×D3 | 1 | 4 | yes | complemented |
| 125 | Dic32 | C2×D3 | 1 | 2 | yes | complemented |
| 126 | C22×C33 | — | 2 | 2 | no | — |
| 127 | C22×C33 | C2×D4 | 1 | 2 | yes | — |
| 128 | C22×C33 | C24 | 1 | 1 | yes | characteristic |
| 129 | C2×C3⋊(C3⋊D3) | — | 2 | 8 | no | — |
| 130 | C2×C3⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 131 | C2×C3⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 132 | C2×C3⋊(C3⋊D3) | #41 | 1 | 4 | yes | complemented |
| 133 | C2×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 134 | C2×C3×C3⋊D3 | — | 2 | 4 | no | — |
| 135 | C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 136 | C3×C3⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 137 | C3×C3⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 138 | C32×Dic3 | — | 2 | 2 | no | — |
| 139 | C32×Dic3 | — | 2 | 4 | no | — |
| 140 | C2×#237 | — | 9 | 2 | no | — |
| 141 | C2×#235 | — | 9 | 1 | no | — |
| 142 | C22×C4×D3 | — | 9 | 2 | no | — |
| 143 | C22×C4×D3 | — | 9 | 1 | no | — |
| 144 | C22×C4×D3 | — | 18 | 1 | no | — |
| 145 | C3×#123 | — | 9 | 2 | no | — |
| 146 | C3×#117 | — | 9 | 1 | no | — |
| 147 | #937 | — | 9 | 2 | no | — |
| 148 | #929 | — | 3 | 2 | no | — |
| 149 | #897 | — | 9 | 2 | no | — |
| 150 | #896 | — | 9 | 4 | no | — |
| 151 | #895 | — | 9 | 2 | no | — |
| 152 | #893 | — | 9 | 4 | no | — |
| 153 | #886 | — | 3 | 2 | no | — |
| 154 | #884 | — | 9 | 4 | no | — |
| 155 | #882 | — | 9 | 2 | no | — |
| 156 | #882 | — | 9 | 2 | no | — |
| 157 | #882 | — | 18 | 2 | no | — |
| 158 | #67⋊C4 | — | 9 | 4 | no | — |
| 159 | #877 | — | 3 | 2 | no | — |
| 160 | C4×D12 | — | 9 | 4 | no | — |
| 161 | C23×C32 | — | 2 | 1 | no | — |
| 162 | C23×C32 | — | 2 | 2 | no | — |
| 163 | C23×C32 | — | 4 | 1 | no | — |
| 164 | C23×C32 | C22×D3 | 1 | 1 | yes | characteristic |
| 165 | C23×C32 | C22×D3 | 1 | 2 | yes | — |
| 166 | C22×C3⋊D3 | — | 3 | 2 | no | — |
| 167 | C22×C3⋊D3 | — | 3 | 4 | no | — |
| 168 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 169 | C22×C3⋊D3 | — | 6 | 4 | no | — |
| 170 | C22×C3⋊D3 | — | 6 | 4 | no | — |
| 171 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 172 | C22×C3⋊D3 | — | 6 | 8 | no | — |
| 173 | C22×C3⋊D3 | — | 6 | 8 | no | — |
| 174 | C22×C3⋊D3 | — | 6 | 4 | no | — |
| 175 | C22×C3⋊D3 | — | 6 | 4 | no | — |
| 176 | C22×C3⋊D3 | — | 12 | 2 | no | — |
| 177 | C22×C3⋊D3 | — | 12 | 8 | no | — |
| 178 | C22×C3⋊D3 | — | 12 | 4 | no | — |
| 179 | C22×C3⋊D3 | — | 12 | 4 | no | — |
| 180 | C22×C3⋊D3 | — | 12 | 8 | no | — |
| 181 | C22×C3⋊D3 | C22×D3 | 1 | 2 | yes | — |
| 182 | C22×C3×D3 | — | 3 | 2 | no | — |
| 183 | C22×C3×D3 | — | 3 | 2 | no | — |
| 184 | C22×C3×D3 | — | 6 | 2 | no | — |
| 185 | C2×C32×C4 | — | 3 | 4 | no | — |
| 186 | C2×C32×C4 | — | 3 | 2 | no | — |
| 187 | C2×C32×C4 | — | 6 | 2 | no | — |
| 188 | #638 | — | 2 | 4 | no | — |
| 189 | C2×C3⋊Dic3 | D12 | 1 | 4 | yes | complemented |
| 190 | C2×C3⋊Dic3 | C22×D3 | 1 | 2 | yes | — |
| 191 | C2×C3⋊Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 192 | C2×C3⋊Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 193 | C4⋊(C3⋊D3) | — | 6 | 8 | no | — |
| 194 | C4×C3⋊D3 | — | 6 | 4 | no | — |
| 195 | C4×C3⋊D3 | — | 6 | 4 | no | — |
| 196 | C3×#67 | — | 6 | 4 | no | — |
| 197 | C3×#67 | — | 6 | 4 | no | — |
| 198 | C3×#67 | — | 12 | 4 | no | — |
| 199 | C2×C3×Dic3 | — | 2 | 4 | no | — |
| 200 | C2×C3×Dic3 | — | 2 | 4 | no | — |
| 201 | C2×C3×Dic3 | — | 2 | 2 | no | — |
| 202 | C2×C3×Dic3 | — | 2 | 4 | no | — |
| 203 | C2×C3×Dic3 | — | 3 | 8 | no | — |
| 204 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 205 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 206 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 207 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 208 | C2×C3×Dic3 | — | 6 | 4 | no | — |
| 209 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 210 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 211 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 212 | C2×C3×Dic3 | C22×D3 | 1 | 4 | yes | — |
| 213 | C2×C3×Dic3 | C22×D3 | 1 | 4 | yes | — |
| 214 | C2×C3×Dic3 | C22×D3 | 1 | 4 | yes | — |
| 215 | #627 | — | 6 | 4 | no | — |
| 216 | #627 | — | 6 | 2 | no | — |
| 217 | #626 | — | 6 | 8 | no | — |
| 218 | #626 | — | 6 | 8 | no | — |
| 219 | #626 | — | 6 | 4 | no | — |
| 220 | #626 | — | 12 | 8 | no | — |
| 221 | #625 | — | 6 | 2 | no | — |
| 222 | #624 | — | 6 | 8 | no | — |
| 223 | #624 | — | 6 | 8 | no | — |
| 224 | #624 | — | 6 | 8 | no | — |
| 225 | #624 | — | 6 | 8 | no | — |
| 226 | #624 | — | 6 | 4 | no | — |
| 227 | D3×Dic3 | — | 6 | 4 | no | — |
| 228 | D3×Dic3 | — | 6 | 4 | no | — |
| 229 | #525 | — | 27 | 1 | no | Sylow |
| 230 | C2×C33 | — | 2 | 2 | no | — |
| 231 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 232 | C2×C33 | C2×#41 | 1 | 2 | yes | — |
| 233 | C3⋊(C3⋊D3) | — | 2 | 4 | no | — |
| 234 | C3×C3⋊D3 | — | 4 | 2 | no | — |
| 235 | C23×D3 | — | 9 | 1 | no | — |
| 236 | C23×D3 | — | 9 | 2 | no | — |
| 237 | C23×D3 | — | 18 | 1 | no | — |
| 238 | C23×D3 | — | 18 | 2 | no | — |
| 239 | C23×D3 | — | 36 | 1 | no | — |
| 240 | C2×C3×D4 | — | 9 | 2 | no | — |
| 241 | C22×C3×C4 | — | 3 | 2 | no | — |
| 242 | C22×C3×C4 | — | 6 | 1 | no | — |
| 243 | C22×C3×C4 | — | 9 | 1 | no | — |
| 244 | C2×#67 | — | 3 | 2 | no | — |
| 245 | C2×#67 | — | 3 | 2 | no | — |
| 246 | C2×#67 | — | 6 | 2 | no | — |
| 247 | C2×#67 | — | 9 | 2 | no | — |
| 248 | C2×#67 | — | 9 | 4 | no | — |
| 249 | C22×Dic3 | — | 3 | 2 | no | — |
| 250 | C22×Dic3 | — | 6 | 1 | no | — |
| 251 | C22×Dic3 | — | 9 | 2 | no | — |
| 252 | C22×Dic3 | D32 | 1 | 1 | yes | characteristic |
| 253 | #237 | — | 18 | 8 | no | — |
| 254 | #235 | — | 18 | 4 | no | — |
| 255 | C2×D12 | — | 9 | 4 | no | — |
| 256 | C2×D12 | — | 9 | 4 | no | — |
| 257 | C2×D12 | — | 9 | 1 | no | — |
| 258 | C2×D12 | — | 18 | 4 | no | — |
| 259 | C2×C4×D3 | — | 9 | 4 | no | — |
| 260 | C2×C4×D3 | — | 9 | 4 | no | — |
| 261 | C2×C4×D3 | — | 9 | 2 | no | — |
| 262 | C2×C4×D3 | — | 9 | 2 | no | — |
| 263 | C2×C4×D3 | — | 9 | 2 | no | — |
| 264 | C2×C4×D3 | — | 9 | 2 | no | — |
| 265 | C2×C4×D3 | — | 18 | 2 | no | — |
| 266 | C2×C4×D3 | — | 18 | 2 | no | — |
| 267 | C2×C4×D3 | — | 18 | 4 | no | — |
| 268 | C2×C4×D3 | — | 18 | 8 | no | — |
| 269 | C2×C4×D3 | — | 18 | 8 | no | — |
| 270 | C2×Dic6 | — | 9 | 2 | no | — |
| 271 | C2×Dic6 | — | 9 | 1 | no | — |
| 272 | C3×C4⋊C4 | — | 9 | 4 | no | — |
| 273 | C3×C4⋊C4 | — | 9 | 2 | no | — |
| 274 | C3×C22⋊C4 | — | 3 | 2 | no | — |
| 275 | C3×C22⋊C4 | — | 3 | 2 | no | — |
| 276 | C3×C22⋊C4 | — | 6 | 2 | no | — |
| 277 | C3×C22⋊C4 | — | 9 | 4 | no | — |
| 278 | C3×C42 | — | 9 | 2 | no | — |
| 279 | #217 | D32 | 1 | 2 | yes | — |
| 280 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 281 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 282 | (C2×D3)⋊C4 | — | 9 | 4 | no | — |
| 283 | (C2×D3)⋊C4 | — | 9 | 4 | no | — |
| 284 | (C2×D3)⋊C4 | — | 9 | 4 | no | — |
| 285 | (C2×D3)⋊C4 | — | 18 | 4 | no | — |
| 286 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 287 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 288 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 289 | C4×Dic3 | — | 3 | 4 | no | — |
| 290 | C22×C32 | — | 2 | 2 | no | — |
| 291 | C22×C32 | — | 2 | 4 | no | — |
| 292 | C22×C32 | — | 2 | 4 | no | — |
| 293 | C22×C32 | — | 2 | 1 | no | — |
| 294 | C22×C32 | — | 2 | 2 | no | — |
| 295 | C22×C32 | — | 2 | 4 | no | — |
| 296 | C22×C32 | — | 2 | 2 | no | — |
| 297 | C22×C32 | — | 4 | 2 | no | — |
| 298 | C22×C32 | — | 4 | 1 | no | — |
| 299 | C22×C32 | — | 4 | 4 | no | — |
| 300 | C22×C32 | — | 4 | 4 | no | — |
| 301 | C22×C32 | C2×D12 | 1 | 2 | yes | — |
| 302 | C22×C32 | D3×D4 | 1 | 4 | yes | — |
| 303 | C22×C32 | C23×D3 | 1 | 1 | yes | characteristic |
| 304 | C22×C32 | C23×D3 | 1 | 2 | yes | — |
| 305 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 306 | C2×C3⋊D3 | — | 2 | 4 | no | — |
| 307 | C2×C3⋊D3 | — | 3 | 4 | no | — |
| 308 | C2×C3⋊D3 | — | 3 | 8 | no | — |
| 309 | C2×C3⋊D3 | — | 6 | 4 | no | — |
| 310 | C2×C3⋊D3 | — | 6 | 8 | no | — |
| 311 | C2×C3⋊D3 | — | 6 | 8 | no | — |
| 312 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 313 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 314 | C2×C3⋊D3 | — | 6 | 4 | no | — |
| 315 | C2×C3⋊D3 | — | 6 | 16 | no | — |
| 316 | C2×C3⋊D3 | — | 6 | 16 | no | — |
| 317 | C2×C3⋊D3 | — | 6 | 4 | no | — |
| 318 | C2×C3⋊D3 | — | 6 | 4 | no | — |
| 319 | C2×C3⋊D3 | — | 6 | 4 | no | — |
| 320 | C2×C3⋊D3 | — | 12 | 4 | no | — |
| 321 | C2×C3⋊D3 | — | 12 | 4 | no | — |
| 322 | C2×C3⋊D3 | — | 12 | 4 | no | — |
| 323 | C2×C3⋊D3 | — | 12 | 4 | no | — |
| 324 | C2×C3⋊D3 | — | 12 | 4 | no | — |
| 325 | C2×C3⋊D3 | — | 12 | 16 | no | — |
| 326 | C2×C3⋊D3 | — | 12 | 16 | no | — |
| 327 | C2×C3×D3 | — | 6 | 2 | no | — |
| 328 | C2×C3×D3 | — | 6 | 2 | no | — |
| 329 | C2×C3×D3 | — | 6 | 4 | no | — |
| 330 | C2×C3×D3 | — | 6 | 4 | no | — |
| 331 | C2×C3×D3 | — | 12 | 4 | no | — |
| 332 | C2×C3×D3 | — | 12 | 2 | no | — |
| 333 | C32×C4 | — | 6 | 2 | no | — |
| 334 | C32×C4 | — | 6 | 4 | no | — |
| 335 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 336 | C3⋊Dic3 | C2×D12 | 1 | 2 | yes | — |
| 337 | C3⋊Dic3 | C2×D12 | 1 | 2 | yes | — |
| 338 | C3×Dic3 | — | 2 | 4 | no | — |
| 339 | C3×Dic3 | — | 2 | 4 | no | — |
| 340 | C3×Dic3 | — | 2 | 4 | no | — |
| 341 | C3×Dic3 | — | 2 | 4 | no | — |
| 342 | C3×Dic3 | — | 3 | 4 | no | — |
| 343 | C3×Dic3 | — | 3 | 4 | no | — |
| 344 | C3×Dic3 | — | 4 | 4 | no | — |
| 345 | C3×Dic3 | — | 6 | 2 | no | — |
| 346 | C3×Dic3 | — | 6 | 2 | no | — |
| 347 | C3×Dic3 | — | 6 | 2 | no | — |
| 348 | C3×Dic3 | — | 6 | 2 | no | — |
| 349 | C3×Dic3 | — | 12 | 2 | no | — |
| 350 | C2×#41 | — | 27 | 1 | no | — |
| 351 | C23×C4 | — | 27 | 1 | no | — |
| 352 | #123 | — | 9 | 2 | no | — |
| 353 | C22⋊Q8 | — | 27 | 2 | no | — |
| 354 | #121 | — | 27 | 2 | no | — |
| 355 | #120 | — | 27 | 2 | no | — |
| 356 | C4×D4 | — | 27 | 4 | no | — |
| 357 | #117 | — | 9 | 1 | no | — |
| 358 | C33 | #525 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 359 | C23×C3 | — | 2 | 1 | no | — |
| 360 | C23×C3 | — | 2 | 2 | no | — |
| 361 | C23×C3 | — | 4 | 1 | no | — |
| 362 | C23×C3 | — | 9 | 2 | no | — |
| 363 | C23×C3 | C2×D32 | 1 | 2 | yes | — |
| 364 | C23×C3 | C2×D32 | 1 | 1 | yes | characteristic |
| 365 | C22×D3 | — | 3 | 2 | no | — |
| 366 | C22×D3 | — | 3 | 2 | no | — |
| 367 | C22×D3 | — | 6 | 2 | no | — |
| 368 | C22×D3 | — | 9 | 2 | no | — |
| 369 | C22×D3 | — | 9 | 4 | no | — |
| 370 | C22×D3 | — | 18 | 2 | no | — |
| 371 | C22×D3 | — | 18 | 4 | no | — |
| 372 | C22×D3 | — | 18 | 4 | no | — |
| 373 | C22×D3 | — | 18 | 8 | no | — |
| 374 | C22×D3 | — | 18 | 4 | no | — |
| 375 | C22×D3 | — | 18 | 8 | no | — |
| 376 | C22×D3 | — | 18 | 4 | no | — |
| 377 | C22×D3 | — | 18 | 2 | no | — |
| 378 | C22×D3 | — | 36 | 2 | no | — |
| 379 | C22×D3 | — | 36 | 8 | no | — |
| 380 | C22×D3 | — | 36 | 4 | no | — |
| 381 | C22×D3 | — | 36 | 8 | no | — |
| 382 | C22×D3 | — | 36 | 4 | no | — |
| 383 | C3×D4 | — | 18 | 4 | no | — |
| 384 | C2×C3×C4 | — | 3 | 4 | no | — |
| 385 | C2×C3×C4 | — | 3 | 4 | no | — |
| 386 | C2×C3×C4 | — | 3 | 4 | no | — |
| 387 | C2×C3×C4 | — | 6 | 2 | no | — |
| 388 | C2×C3×C4 | — | 6 | 4 | no | — |
| 389 | C2×C3×C4 | — | 6 | 4 | no | — |
| 390 | C2×C3×C4 | — | 6 | 4 | no | — |
| 391 | C2×C3×C4 | — | 9 | 1 | no | — |
| 392 | C2×C3×C4 | — | 9 | 1 | no | — |
| 393 | C2×C3×C4 | — | 9 | 4 | no | — |
| 394 | C2×C3×C4 | — | 9 | 2 | no | — |
| 395 | #67 | — | 6 | 4 | no | — |
| 396 | #67 | — | 6 | 4 | no | — |
| 397 | #67 | — | 12 | 4 | no | — |
| 398 | #67 | — | 18 | 8 | no | — |
| 399 | #67 | — | 18 | 4 | no | — |
| 400 | C2×Dic3 | — | 2 | 2 | no | — |
| 401 | C2×Dic3 | — | 3 | 2 | no | — |
| 402 | C2×Dic3 | — | 3 | 2 | no | — |
| 403 | C2×Dic3 | — | 3 | 8 | no | — |
| 404 | C2×Dic3 | — | 3 | 2 | no | — |
| 405 | C2×Dic3 | — | 3 | 2 | no | — |
| 406 | C2×Dic3 | — | 6 | 4 | no | — |
| 407 | C2×Dic3 | — | 6 | 1 | no | — |
| 408 | C2×Dic3 | — | 6 | 1 | no | — |
| 409 | C2×Dic3 | — | 6 | 2 | no | — |
| 410 | C2×Dic3 | — | 18 | 4 | no | — |
| 411 | C2×Dic3 | C2×D32 | 1 | 4 | yes | — |
| 412 | C2×Dic3 | C2×D32 | 1 | 2 | yes | — |
| 413 | D12 | — | 18 | 8 | no | — |
| 414 | D12 | — | 18 | 8 | no | — |
| 415 | D12 | — | 18 | 2 | no | — |
| 416 | D12 | — | 36 | 8 | no | — |
| 417 | C4×D3 | — | 18 | 4 | no | — |
| 418 | C4×D3 | — | 18 | 4 | no | — |
| 419 | C4×D3 | — | 18 | 8 | no | — |
| 420 | C4×D3 | — | 18 | 8 | no | — |
| 421 | C4×D3 | — | 18 | 4 | no | — |
| 422 | C4×D3 | — | 18 | 8 | no | — |
| 423 | C4×D3 | — | 18 | 8 | no | — |
| 424 | C4×D3 | — | 18 | 4 | no | — |
| 425 | Dic6 | — | 18 | 4 | no | — |
| 426 | Dic6 | — | 18 | 2 | no | — |
| 427 | C2×C32 | — | 2 | 2 | no | — |
| 428 | C2×C32 | — | 2 | 4 | no | — |
| 429 | C2×C32 | — | 2 | 4 | no | — |
| 430 | C2×C32 | — | 2 | 2 | no | — |
| 431 | C2×C32 | — | 2 | 2 | no | — |
| 432 | C2×C32 | — | 2 | 4 | no | — |
| 433 | C2×C32 | — | 2 | 1 | no | — |
| 434 | C2×C32 | — | 4 | 1 | no | — |
| 435 | C2×C32 | — | 4 | 2 | no | — |
| 436 | C2×C32 | — | 4 | 4 | no | — |
| 437 | C2×C32 | — | 4 | 4 | no | — |
| 438 | C2×C32 | C22×D12 | 1 | 1 | yes | characteristic |
| 439 | C2×C32 | C2×D3×D4 | 1 | 2 | yes | — |
| 440 | C2×C32 | D3×#41 | 1 | 4 | yes | — |
| 441 | C2×C32 | D3×#41 | 1 | 2 | yes | — |
| 442 | C3⋊D3 | — | 4 | 2 | no | — |
| 443 | C3⋊D3 | — | 6 | 4 | no | — |
| 444 | C3⋊D3 | — | 6 | 8 | no | — |
| 445 | C3⋊D3 | — | 6 | 8 | no | — |
| 446 | C3⋊D3 | — | 12 | 8 | no | — |
| 447 | C3⋊D3 | — | 12 | 8 | no | — |
| 448 | C3×D3 | — | 12 | 2 | no | — |
| 449 | C3×D3 | — | 12 | 2 | no | — |
| 450 | C3×D3 | — | 24 | 2 | no | — |
| 451 | C24 | — | 27 | 1 | no | — |
| 452 | #41 | — | 54 | 4 | no | — |
| 453 | C2×Q8 | — | 27 | 1 | no | — |
| 454 | C2×D4 | — | 9 | 2 | no | — |
| 455 | C2×D4 | — | 27 | 4 | no | — |
| 456 | C2×D4 | — | 27 | 1 | no | — |
| 457 | C22×C4 | — | 3 | 1 | no | — |
| 458 | C22×C4 | — | 9 | 1 | no | — |
| 459 | C22×C4 | — | 27 | 2 | no | — |
| 460 | C22×C4 | — | 27 | 2 | no | — |
| 461 | C22×C4 | — | 27 | 2 | no | — |
| 462 | C22×C4 | — | 54 | 4 | no | — |
| 463 | C4⋊C4 | — | 9 | 2 | no | — |
| 464 | C4⋊C4 | — | 9 | 4 | no | — |
| 465 | C22⋊C4 | — | 3 | 2 | no | — |
| 466 | C22⋊C4 | — | 9 | 4 | no | — |
| 467 | C22⋊C4 | — | 27 | 4 | no | — |
| 468 | C42 | — | 9 | 2 | no | — |
| 469 | C22×C3 | — | 2 | 4 | no | — |
| 470 | C22×C3 | — | 2 | 2 | no | — |
| 471 | C22×C3 | — | 2 | 4 | no | — |
| 472 | C22×C3 | — | 2 | 1 | no | — |
| 473 | C22×C3 | — | 2 | 2 | no | — |
| 474 | C22×C3 | — | 2 | 2 | no | — |
| 475 | C22×C3 | — | 2 | 4 | no | — |
| 476 | C22×C3 | — | 4 | 4 | no | — |
| 477 | C22×C3 | — | 4 | 4 | no | — |
| 478 | C22×C3 | — | 4 | 1 | no | — |
| 479 | C22×C3 | — | 4 | 2 | no | — |
| 480 | C22×C3 | — | 18 | 2 | no | — |
| 481 | C22×C3 | — | 18 | 4 | no | — |
| 482 | C22×C3 | D3×D12 | 1 | 4 | yes | — |
| 483 | C22×C3 | #3811 | 1 | 2 | yes | — |
| 484 | C22×C3 | C22×D32 | 1 | 2 | yes | — |
| 485 | C22×C3 | C22×D32 | 1 | 1 | yes | characteristic |
| 486 | C2×D3 | — | 6 | 2 | no | — |
| 487 | C2×D3 | — | 6 | 4 | no | — |
| 488 | C2×D3 | — | 6 | 4 | no | — |
| 489 | C2×D3 | — | 6 | 2 | no | — |
| 490 | C2×D3 | — | 9 | 4 | no | — |
| 491 | C2×D3 | — | 9 | 8 | no | — |
| 492 | C2×D3 | — | 12 | 4 | no | — |
| 493 | C2×D3 | — | 12 | 2 | no | — |
| 494 | C2×D3 | — | 18 | 4 | no | — |
| 495 | C2×D3 | — | 18 | 8 | no | — |
| 496 | C2×D3 | — | 18 | 4 | no | — |
| 497 | C2×D3 | — | 18 | 8 | no | — |
| 498 | C2×D3 | — | 18 | 16 | no | — |
| 499 | C2×D3 | — | 18 | 16 | no | — |
| 500 | C2×D3 | — | 18 | 4 | no | — |
| 501 | C2×D3 | — | 18 | 4 | no | — |
| 502 | C2×D3 | — | 18 | 2 | no | — |
| 503 | C2×D3 | — | 18 | 4 | no | — |
| 504 | C2×D3 | — | 18 | 2 | no | — |
| 505 | C2×D3 | — | 36 | 4 | no | — |
| 506 | C2×D3 | — | 36 | 4 | no | — |
| 507 | C2×D3 | — | 36 | 4 | no | — |
| 508 | C2×D3 | — | 36 | 16 | no | — |
| 509 | C2×D3 | — | 36 | 16 | no | — |
| 510 | C2×D3 | — | 36 | 4 | no | — |
| 511 | C2×D3 | — | 36 | 4 | no | — |
| 512 | C3×C4 | — | 6 | 4 | no | — |
| 513 | C3×C4 | — | 6 | 4 | no | — |
| 514 | C3×C4 | — | 6 | 4 | no | — |
| 515 | C3×C4 | — | 6 | 4 | no | — |
| 516 | C3×C4 | — | 9 | 2 | no | — |
| 517 | C3×C4 | — | 9 | 2 | no | — |
| 518 | C3×C4 | — | 12 | 4 | no | — |
| 519 | C3×C4 | — | 18 | 2 | no | — |
| 520 | Dic3 | — | 2 | 4 | no | — |
| 521 | Dic3 | — | 2 | 2 | no | — |
| 522 | Dic3 | — | 3 | 4 | no | — |
| 523 | Dic3 | — | 3 | 4 | no | — |
| 524 | Dic3 | — | 6 | 2 | no | — |
| 525 | Dic3 | — | 6 | 2 | no | — |
| 526 | Dic3 | — | 6 | 2 | no | — |
| 527 | Dic3 | — | 6 | 2 | no | — |
| 528 | Dic3 | — | 12 | 2 | no | — |
| 529 | C32 | — | 2 | 2 | no | — |
| 530 | C32 | — | 2 | 1 | no | — |
| 531 | C32 | — | 4 | 1 | no | — |
| 532 | C32 | #5524 | 1 | 1 | yes | characteristic, complemented |
| 533 | C32 | #5656 | 1 | 2 | yes | complemented |
| 534 | C23 | — | 9 | 2 | no | — |
| 535 | C23 | — | 27 | 2 | no | — |
| 536 | C23 | — | 54 | 4 | no | — |
| 537 | C23 | — | 54 | 2 | no | — |
| 538 | C23 | D33 | 1 | 1 | yes | characteristic |
| 539 | Q8 | — | 54 | 2 | no | — |
| 540 | D4 | — | 18 | 4 | no | — |
| 541 | D4 | — | 54 | 8 | no | — |
| 542 | D4 | — | 54 | 2 | no | — |
| 543 | C2×C4 | — | 3 | 4 | no | — |
| 544 | C2×C4 | — | 3 | 2 | no | — |
| 545 | C2×C4 | — | 6 | 2 | no | — |
| 546 | C2×C4 | — | 9 | 1 | no | — |
| 547 | C2×C4 | — | 9 | 1 | no | — |
| 548 | C2×C4 | — | 9 | 4 | no | — |
| 549 | C2×C4 | — | 9 | 2 | no | — |
| 550 | C2×C4 | — | 54 | 4 | no | — |
| 551 | C2×C4 | — | 54 | 4 | no | — |
| 552 | C2×C4 | — | 54 | 4 | no | — |
| 553 | C2×C3 | — | 2 | 4 | no | — |
| 554 | C2×C3 | — | 2 | 4 | no | — |
| 555 | C2×C3 | — | 2 | 2 | no | — |
| 556 | C2×C3 | — | 2 | 4 | no | — |
| 557 | C2×C3 | — | 2 | 2 | no | — |
| 558 | C2×C3 | — | 2 | 1 | no | — |
| 559 | C2×C3 | — | 2 | 2 | no | — |
| 560 | C2×C3 | — | 4 | 4 | no | — |
| 561 | C2×C3 | — | 4 | 4 | no | — |
| 562 | C2×C3 | — | 4 | 2 | no | — |
| 563 | C2×C3 | — | 4 | 1 | no | — |
| 564 | C2×C3 | — | 36 | 2 | no | — |
| 565 | C2×C3 | C2×D3×D12 | 1 | 2 | yes | — |
| 566 | C2×C3 | #64306 | 1 | 2 | yes | — |
| 567 | C2×C3 | #64312 | 1 | 4 | yes | — |
| 568 | C2×C3 | C2×#3811 | 1 | 1 | yes | characteristic |
| 569 | D3 | — | 12 | 2 | no | — |
| 570 | D3 | — | 12 | 2 | no | — |
| 571 | D3 | — | 18 | 8 | no | — |
| 572 | D3 | — | 18 | 8 | no | — |
| 573 | D3 | — | 18 | 4 | no | — |
| 574 | D3 | — | 24 | 2 | no | — |
| 575 | D3 | — | 36 | 8 | no | — |
| 576 | D3 | — | 36 | 8 | no | — |
| 577 | C22 | — | 2 | 2 | no | — |
| 578 | C22 | — | 18 | 4 | no | — |
| 579 | C22 | — | 18 | 2 | no | — |
| 580 | C22 | — | 27 | 4 | no | — |
| 581 | C22 | — | 54 | 8 | no | — |
| 582 | C22 | — | 54 | 2 | no | — |
| 583 | C22 | — | 54 | 2 | no | — |
| 584 | C22 | #88955 | 1 | 2 | yes | — |
| 585 | C22 | C2×D33 | 1 | 1 | yes | characteristic |
| 586 | C4 | — | 6 | 4 | no | — |
| 587 | C4 | — | 6 | 2 | no | — |
| 588 | C4 | — | 9 | 2 | no | — |
| 589 | C4 | — | 9 | 2 | no | — |
| 590 | C4 | — | 18 | 2 | no | — |
| 591 | C3 | — | 2 | 1 | no | — |
| 592 | C3 | — | 2 | 2 | no | — |
| 593 | C3 | — | 4 | 1 | no | — |
| 594 | C3 | #10594079 | 1 | 2 | yes | complemented |
| 595 | C3 | #10594920 | 1 | 1 | yes | characteristic, complemented |
| 596 | C2 | — | 2 | 2 | no | — |
| 597 | C2 | — | 36 | 2 | no | — |
| 598 | C2 | — | 54 | 4 | no | — |
| 599 | C2 | #11724411 | 1 | 2 | yes | — |
| 600 | C2 | C2×#88955 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D33 |
| commutator, socle, cosocle | C22×C33 | C24 |
| Fitting | C23×C33 | C23 |
| hypercenter | C23 | D33 |
| hypocenter | C33 | #525 |
| LCS | G ▷ C22×C33 ▷ C33 | |
| UCS | C1 ◁ C22 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#89046 | C2 | semidirect |
| 2. C22×#6289 | C2 | semidirect |
| 3. #11723639 | C2 | semidirect |
| 4. C3×#63966 | C2 | semidirect |
| 5. C3×#63957 | C2 | semidirect |
| 6. #11722982 | C2 | semidirect |
| 7. #11722968 | C2 | semidirect |
| 8. #11722937 | C2 | semidirect |
| 15. C2×#6296 | C22 | semidirect |
| 16. C2×#6295 | C22 | semidirect |
| 18. C2×#6294 | C22 | semidirect |
| 25. C3×#3724 | C22 | semidirect |
| 26. C3×Dic3⋊Dic3 | C22 | semidirect |
| 27. C3×#3722 | C22 | semidirect |
| 28. C3×Dic32 | C22 | semidirect |
| 41. #63966 | D3 | semidirect |
| 42. #63957 | D3 | semidirect |
| 56. C2×C3×C3⋊Dic3 | D4 | semidirect |
| 119. #3724 | C2×D3 | semidirect |
| 120. Dic3⋊Dic3 | C2×D3 | semidirect |
| 124. #3722 | C2×D3 | semidirect |
| 125. Dic32 | C2×D3 | semidirect |
| 132. C2×C3⋊(C3⋊D3) | #41 | semidirect |
| 189. C2×C3⋊Dic3 | D12 | semidirect |
| 358. C33 | #525 | semidirect |
| 532. C32 | #5524 | semidirect |
| 533. C32 | #5656 | semidirect |
| 594. C3 | #10594079 | semidirect |
| 595. C3 | #10594920 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89046 | 2 |
| C22×#6289 | 2 |
| #11723639 | 2 |
| C3×#63966 | 2 |
| C3×#63957 | 2 |
| #11722982 | 2 |
| #11722968 | 2 |
| #11722937 | 2 |
| #10594920 | 3 |
| #10594079 | 3 |