Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1862 conjugacy classes of subgroups.
The subgroup lattice has 866 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#89049 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×C3⋊D3×#67 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11723632 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C3×#63978 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C2×C3×#3722 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11722999 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11722998 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11722997 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11722952 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11722951 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11722950 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #10595308 | — | 3 | 1 | no | maximal |
| 13 | #10595072 | — | 3 | 2 | no | maximal |
| 14 | C23×C3×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 15 | C22×#1113 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C22×D3×C3⋊D3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C2×#6312 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C2×C3×#638 | C22 | 1 | 2 | yes | complemented |
| 19 | C2×C32×#67 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C22×C32×Dic3 | C22 | 1 | 2 | yes | complemented |
| 21 | #89049 | — | 2 | 4 | no | — |
| 22 | C2×#6295 | C22 | 1 | 2 | yes | — |
| 23 | C2×#6294 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | C3⋊D3×#67 | — | 2 | 4 | no | — |
| 25 | C2×#6292 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#6292 | C22 | 1 | 2 | yes | complemented |
| 27 | C2×#6290 | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×Dic3×C3⋊D3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | C2×C3×#626 | C22 | 1 | 2 | yes | complemented |
| 30 | Dic3⋊(C3⋊Dic3) | C22 | 1 | 2 | yes | complemented |
| 31 | #88804 | C22 | 1 | 2 | yes | complemented |
| 32 | #88803 | C22 | 1 | 2 | yes | complemented |
| 33 | C3×Dic3⋊Dic3 | C22 | 1 | 2 | yes | complemented |
| 34 | C3×#3722 | C22 | 1 | 2 | yes | complemented |
| 35 | C3×#3722 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | C3×#3722 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | C3×#3722 | C22 | 1 | 2 | yes | complemented |
| 38 | C3×(C2×D3)⋊Dic3 | C22 | 1 | 2 | yes | complemented |
| 39 | C2×D4×C3⋊D3 | — | 3 | 1 | no | — |
| 40 | C2×#3811 | — | 3 | 1 | no | — |
| 41 | C2×D3×#67 | — | 3 | 2 | no | — |
| 42 | C2×D3×#67 | — | 3 | 2 | no | — |
| 43 | C2×D3×#67 | — | 6 | 1 | no | — |
| 44 | #64139 | — | 3 | 2 | no | — |
| 45 | C3×#939 | — | 3 | 2 | no | — |
| 46 | C3×#930 | — | 3 | 2 | no | — |
| 47 | C2×C3×(C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 48 | #63983 | — | 3 | 1 | no | — |
| 49 | #63981 | — | 3 | 2 | no | — |
| 50 | #63978 | — | 3 | 2 | no | — |
| 51 | #63978 | — | 3 | 2 | no | — |
| 52 | #63978 | — | 6 | 2 | no | — |
| 53 | #63978 | D3 | 1 | 2 | yes | complemented |
| 54 | #63975 | — | 3 | 1 | no | — |
| 55 | C2×#3722 | D3 | 1 | 1 | yes | characteristic, complemented |
| 56 | #63923 | — | 3 | 2 | no | — |
| 57 | #63923 | — | 3 | 2 | no | — |
| 58 | #63923 | — | 3 | 1 | no | — |
| 59 | #63922 | — | 3 | 2 | no | — |
| 60 | #63922 | — | 3 | 2 | no | — |
| 61 | #63897 | — | 3 | 1 | no | — |
| 62 | #63891 | — | 3 | 2 | no | — |
| 63 | #63891 | — | 3 | 2 | no | — |
| 64 | #63890 | — | 3 | 2 | no | — |
| 65 | #63890 | — | 3 | 2 | no | — |
| 66 | #63853 | — | 3 | 2 | no | — |
| 67 | C23×C33 | C23 | 1 | 1 | yes | characteristic |
| 68 | C22×C3⋊(C3⋊D3) | C23 | 1 | 1 | yes | characteristic |
| 69 | C22×C3×C3⋊D3 | — | 4 | 2 | no | — |
| 70 | C22×C3×C3⋊D3 | D4 | 1 | 4 | yes | complemented |
| 71 | C22×C3×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 72 | C22×C3×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 73 | C22×C3×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 74 | C22×C32×D3 | C23 | 1 | 1 | yes | characteristic |
| 75 | C2×#1113 | — | 2 | 2 | no | — |
| 76 | C2×#1113 | — | 4 | 2 | no | — |
| 77 | C2×D3×C3⋊D3 | — | 2 | 2 | no | — |
| 78 | C2×D3×C3⋊D3 | — | 4 | 2 | no | — |
| 79 | #6312 | — | 2 | 2 | no | — |
| 80 | C2×C3⋊(C3⋊Dic3) | C23 | 1 | 1 | yes | characteristic |
| 81 | C3×#638 | — | 2 | 4 | no | — |
| 82 | C2×C3×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 83 | C32×#67 | — | 2 | 2 | no | — |
| 84 | C2×C32×Dic3 | — | 4 | 2 | no | — |
| 85 | C2×C32×Dic3 | C23 | 1 | 2 | yes | — |
| 86 | C2×C32×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 87 | C2×C32×Dic3 | C23 | 1 | 2 | yes | — |
| 88 | #6295 | — | 2 | 4 | no | — |
| 89 | #6294 | — | 2 | 2 | no | — |
| 90 | #6292 | — | 2 | 2 | no | — |
| 91 | #6292 | — | 4 | 2 | no | — |
| 92 | #6290 | — | 2 | 2 | no | — |
| 93 | Dic3×C3⋊D3 | — | 2 | 2 | no | — |
| 94 | C3×#626 | — | 4 | 2 | no | — |
| 95 | #5605 | — | 9 | 2 | no | — |
| 96 | #5493 | — | 9 | 1 | no | — |
| 97 | C23×C3⋊D3 | — | 3 | 1 | no | — |
| 98 | C23×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 99 | C23×C3×D3 | — | 3 | 2 | no | — |
| 100 | C23×C3×D3 | — | 6 | 1 | no | — |
| 101 | C22×D32 | — | 3 | 2 | no | — |
| 102 | C22×D32 | — | 3 | 1 | no | — |
| 103 | C22×D32 | — | 3 | 2 | no | — |
| 104 | C22×D32 | — | 6 | 1 | no | — |
| 105 | C2×C32×D4 | — | 3 | 1 | no | — |
| 106 | C22×C32×C4 | — | 3 | 2 | no | — |
| 107 | C2×#638 | — | 3 | 2 | no | — |
| 108 | C2×#638 | — | 3 | 1 | no | — |
| 109 | C2×#638 | — | 3 | 1 | no | — |
| 110 | C2×#638 | — | 6 | 1 | no | — |
| 111 | C2×#638 | — | 6 | 2 | no | — |
| 112 | C2×#638 | — | 12 | 1 | no | — |
| 113 | C2×#638 | C2×D3 | 1 | 2 | yes | complemented |
| 114 | D4×C3⋊D3 | — | 6 | 4 | no | — |
| 115 | C2×C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 116 | C2×C4⋊(C3⋊D3) | — | 3 | 2 | no | — |
| 117 | C2×C4×C3⋊D3 | — | 3 | 1 | no | — |
| 118 | C2×C3×#67 | — | 2 | 1 | no | — |
| 119 | C2×C3×#67 | — | 3 | 2 | no | — |
| 120 | C2×C3×#67 | — | 3 | 2 | no | — |
| 121 | C2×C3×#67 | — | 3 | 2 | no | — |
| 122 | C2×C3×#67 | — | 6 | 2 | no | — |
| 123 | C2×C3×#67 | C2×D3 | 1 | 2 | yes | complemented |
| 124 | C22×C3×Dic3 | — | 2 | 2 | no | — |
| 125 | C22×C3×Dic3 | C2×D3 | 1 | 2 | yes | complemented |
| 126 | C22×C3×Dic3 | C2×D3 | 1 | 2 | yes | complemented |
| 127 | C2×C3×D12 | — | 3 | 2 | no | — |
| 128 | #3811 | — | 6 | 4 | no | — |
| 129 | D3×#67 | — | 6 | 8 | no | — |
| 130 | D3×#67 | — | 6 | 8 | no | — |
| 131 | D3×#67 | — | 6 | 8 | no | — |
| 132 | C2×#626 | — | 3 | 2 | no | — |
| 133 | C2×#626 | — | 3 | 2 | no | — |
| 134 | C2×#626 | — | 3 | 2 | no | — |
| 135 | C2×#626 | — | 3 | 2 | no | — |
| 136 | C2×#626 | — | 3 | 2 | no | — |
| 137 | C2×#626 | — | 6 | 1 | no | — |
| 138 | C2×#626 | — | 6 | 2 | no | — |
| 139 | C2×#626 | C2×D3 | 1 | 2 | yes | complemented |
| 140 | C2×#625 | — | 3 | 2 | no | — |
| 141 | C2×#625 | — | 3 | 2 | no | — |
| 142 | C2×#625 | — | 6 | 1 | no | — |
| 143 | C2×#624 | — | 3 | 1 | no | — |
| 144 | C2×D3×Dic3 | — | 3 | 2 | no | — |
| 145 | C2×D3×Dic3 | — | 3 | 2 | no | — |
| 146 | C2×D3×Dic3 | — | 6 | 1 | no | — |
| 147 | #3752 | — | 3 | 2 | no | — |
| 148 | #3752 | — | 3 | 2 | no | — |
| 149 | C4⋊(C3⋊Dic3) | — | 3 | 2 | no | — |
| 150 | C3×#217 | — | 3 | 2 | no | — |
| 151 | C3×(C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 152 | C3×(C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 153 | C3×(C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 154 | C3×(C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 155 | C3×(C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 156 | C3×(C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 157 | C3×(C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 158 | C3×C4⋊Dic3 | — | 3 | 2 | no | — |
| 159 | C3×Dic3⋊C4 | — | 3 | 2 | no | — |
| 160 | Dic3⋊Dic3 | — | 3 | 2 | no | — |
| 161 | Dic3⋊Dic3 | — | 3 | 2 | no | — |
| 162 | Dic3⋊Dic3 | — | 6 | 2 | no | — |
| 163 | Dic3⋊Dic3 | C2×D3 | 1 | 2 | yes | complemented |
| 164 | #3722 | — | 3 | 2 | no | — |
| 165 | #3722 | — | 3 | 2 | no | — |
| 166 | #3722 | — | 6 | 2 | no | — |
| 167 | #3722 | C2×D3 | 1 | 2 | yes | complemented |
| 168 | #3722 | C2×D3 | 1 | 2 | yes | complemented |
| 169 | #3722 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 170 | #3722 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 171 | (C2×D3)⋊Dic3 | — | 3 | 2 | no | — |
| 172 | (C2×D3)⋊Dic3 | — | 3 | 2 | no | — |
| 173 | (C2×D3)⋊Dic3 | — | 6 | 2 | no | — |
| 174 | (C2×D3)⋊Dic3 | C2×D3 | 1 | 2 | yes | complemented |
| 175 | C22×C33 | — | 2 | 2 | no | — |
| 176 | C22×C33 | C2×D4 | 1 | 2 | yes | — |
| 177 | C22×C33 | C24 | 1 | 1 | yes | characteristic |
| 178 | C2×C3⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 179 | C2×C3⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 180 | C2×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 181 | C2×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 182 | C2×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 183 | C2×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 184 | C2×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 185 | C2×C3×C3⋊D3 | — | 4 | 4 | no | — |
| 186 | C2×C3×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 187 | C2×C3×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 188 | C2×C32×D3 | — | 2 | 1 | no | — |
| 189 | C2×C32×D3 | — | 2 | 2 | no | — |
| 190 | #1113 | — | 4 | 4 | no | — |
| 191 | D3×C3⋊D3 | — | 4 | 4 | no | — |
| 192 | C3⋊(C3⋊Dic3) | — | 2 | 1 | no | — |
| 193 | C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 194 | C32×Dic3 | — | 2 | 1 | no | — |
| 195 | C32×Dic3 | — | 2 | 2 | no | — |
| 196 | C32×Dic3 | — | 2 | 2 | no | — |
| 197 | C22×#67 | — | 9 | 1 | no | — |
| 198 | C22×#67 | — | 9 | 1 | no | — |
| 199 | C2×D3×D4 | — | 9 | 2 | no | — |
| 200 | C2×D3×D4 | — | 9 | 2 | no | — |
| 201 | C2×D3×D4 | — | 18 | 1 | no | — |
| 202 | C3×#121 | — | 9 | 2 | no | — |
| 203 | C2×C3×C22⋊C4 | — | 9 | 1 | no | — |
| 204 | #939 | — | 3 | 2 | no | — |
| 205 | #939 | — | 9 | 2 | no | — |
| 206 | #937 | — | 9 | 2 | no | — |
| 207 | #937 | — | 9 | 2 | no | — |
| 208 | #930 | — | 3 | 2 | no | — |
| 209 | #930 | — | 9 | 2 | no | — |
| 210 | #930 | — | 9 | 2 | no | — |
| 211 | #930 | — | 18 | 2 | no | — |
| 212 | C2×(C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 213 | #894 | — | 9 | 2 | no | — |
| 214 | #894 | — | 9 | 2 | no | — |
| 215 | #886 | — | 9 | 1 | no | — |
| 216 | #886 | — | 9 | 2 | no | — |
| 217 | #886 | — | 9 | 1 | no | — |
| 218 | #883 | — | 9 | 2 | no | — |
| 219 | #883 | — | 9 | 2 | no | — |
| 220 | #882 | — | 9 | 1 | no | — |
| 221 | #882 | — | 9 | 2 | no | — |
| 222 | #882 | — | 9 | 2 | no | — |
| 223 | #882 | — | 9 | 2 | no | — |
| 224 | #882 | — | 9 | 1 | no | — |
| 225 | C23×C32 | — | 2 | 1 | no | — |
| 226 | C23×C32 | — | 2 | 2 | no | — |
| 227 | C23×C32 | — | 3 | 1 | no | — |
| 228 | C23×C32 | — | 4 | 1 | no | — |
| 229 | C23×C32 | C22×D3 | 1 | 1 | yes | characteristic |
| 230 | C23×C32 | C22×D3 | 1 | 2 | yes | — |
| 231 | C22×C3⋊D3 | — | 3 | 2 | no | — |
| 232 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 233 | C22×C3⋊D3 | — | 4 | 2 | no | — |
| 234 | C22×C3⋊D3 | — | 6 | 1 | no | — |
| 235 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 236 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 237 | C22×C3⋊D3 | — | 12 | 1 | no | — |
| 238 | C22×C3⋊D3 | — | 12 | 2 | no | — |
| 239 | C22×C3⋊D3 | D12 | 1 | 4 | yes | complemented |
| 240 | C22×C3⋊D3 | C22×D3 | 1 | 2 | yes | — |
| 241 | C22×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 242 | C22×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 243 | C22×C3×D3 | — | 2 | 1 | no | — |
| 244 | C22×C3×D3 | — | 3 | 2 | no | — |
| 245 | C22×C3×D3 | — | 3 | 2 | no | — |
| 246 | C22×C3×D3 | — | 3 | 8 | no | — |
| 247 | C22×C3×D3 | — | 3 | 2 | no | — |
| 248 | C22×C3×D3 | — | 3 | 2 | no | — |
| 249 | C22×C3×D3 | — | 6 | 1 | no | — |
| 250 | C22×C3×D3 | — | 6 | 4 | no | — |
| 251 | C22×C3×D3 | — | 6 | 1 | no | — |
| 252 | C22×C3×D3 | — | 6 | 2 | no | — |
| 253 | C22×C3×D3 | — | 12 | 2 | no | — |
| 254 | C22×C3×D3 | — | 12 | 2 | no | — |
| 255 | C22×C3×D3 | — | 12 | 4 | no | — |
| 256 | C22×C3×D3 | C22×D3 | 1 | 2 | yes | — |
| 257 | C2×D32 | — | 6 | 4 | no | — |
| 258 | C2×D32 | — | 6 | 4 | no | — |
| 259 | C2×D32 | — | 6 | 4 | no | — |
| 260 | C2×D32 | — | 6 | 2 | no | — |
| 261 | C2×D32 | — | 12 | 2 | no | — |
| 262 | C2×D32 | — | 12 | 2 | no | — |
| 263 | C2×D32 | — | 12 | 4 | no | — |
| 264 | C2×D32 | — | 12 | 2 | no | — |
| 265 | C2×D32 | — | 12 | 2 | no | — |
| 266 | C2×D32 | — | 12 | 2 | no | — |
| 267 | C32×D4 | — | 6 | 2 | no | — |
| 268 | C2×C32×C4 | — | 3 | 1 | no | — |
| 269 | C2×C32×C4 | — | 3 | 2 | no | — |
| 270 | C2×C32×C4 | — | 3 | 2 | no | — |
| 271 | C2×C32×C4 | — | 12 | 2 | no | — |
| 272 | #638 | — | 2 | 4 | no | — |
| 273 | #638 | — | 6 | 2 | no | — |
| 274 | #638 | — | 6 | 2 | no | — |
| 275 | #638 | — | 6 | 4 | no | — |
| 276 | #638 | — | 6 | 4 | no | — |
| 277 | #638 | — | 12 | 4 | no | — |
| 278 | #638 | — | 12 | 4 | no | — |
| 279 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 280 | C2×C3⋊Dic3 | — | 3 | 2 | no | — |
| 281 | C2×C3⋊Dic3 | — | 6 | 1 | no | — |
| 282 | C2×C3⋊Dic3 | — | 6 | 2 | no | — |
| 283 | C2×C3⋊Dic3 | — | 12 | 1 | no | — |
| 284 | C2×C3⋊Dic3 | C22×D3 | 1 | 2 | yes | — |
| 285 | C4⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 286 | C4⋊(C3⋊D3) | — | 12 | 2 | no | — |
| 287 | C4×C3⋊D3 | — | 6 | 2 | no | — |
| 288 | C3×#67 | — | 2 | 4 | no | — |
| 289 | C3×#67 | — | 2 | 4 | no | — |
| 290 | C3×#67 | — | 6 | 4 | no | — |
| 291 | C3×#67 | — | 6 | 4 | no | — |
| 292 | C3×#67 | — | 12 | 4 | no | — |
| 293 | C3×#67 | — | 12 | 2 | no | — |
| 294 | C2×C3×Dic3 | — | 2 | 2 | no | — |
| 295 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 296 | C2×C3×Dic3 | — | 2 | 2 | no | — |
| 297 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 298 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 299 | C2×C3×Dic3 | — | 4 | 2 | no | — |
| 300 | C2×C3×Dic3 | — | 4 | 2 | no | — |
| 301 | C2×C3×Dic3 | — | 4 | 4 | no | — |
| 302 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 303 | C2×C3×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 304 | C2×C3×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 305 | C2×C3×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 306 | C2×C3×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 307 | C2×C3×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 308 | C3×D12 | — | 12 | 2 | no | — |
| 309 | #626 | — | 4 | 2 | no | — |
| 310 | #626 | — | 6 | 4 | no | — |
| 311 | #626 | — | 6 | 4 | no | — |
| 312 | #626 | — | 6 | 4 | no | — |
| 313 | #626 | — | 6 | 4 | no | — |
| 314 | #626 | — | 12 | 2 | no | — |
| 315 | #626 | — | 12 | 2 | no | — |
| 316 | #626 | — | 12 | 4 | no | — |
| 317 | #625 | — | 6 | 4 | no | — |
| 318 | #625 | — | 6 | 4 | no | — |
| 319 | #625 | — | 6 | 4 | no | — |
| 320 | #624 | — | 6 | 2 | no | — |
| 321 | D3×Dic3 | — | 6 | 4 | no | — |
| 322 | D3×Dic3 | — | 6 | 4 | no | — |
| 323 | D3×Dic3 | — | 6 | 4 | no | — |
| 324 | #534 | — | 27 | 1 | no | Sylow |
| 325 | C2×C33 | — | 2 | 2 | no | — |
| 326 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 327 | C2×C33 | H(5,𝔽2) | 1 | 2 | yes | — |
| 328 | C3⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 329 | C3×C3⋊D3 | — | 2 | 2 | no | — |
| 330 | C3×C3⋊D3 | — | 2 | 2 | no | — |
| 331 | C3×C3⋊D3 | — | 4 | 2 | no | — |
| 332 | C32×D3 | — | 4 | 1 | no | — |
| 333 | C24×C3 | — | 9 | 1 | no | — |
| 334 | C23×D3 | — | 3 | 2 | no | — |
| 335 | C23×D3 | — | 6 | 1 | no | — |
| 336 | C23×D3 | — | 9 | 1 | no | — |
| 337 | C23×D3 | — | 9 | 2 | no | — |
| 338 | C23×D3 | — | 9 | 2 | no | — |
| 339 | C23×D3 | — | 9 | 1 | no | — |
| 340 | C23×D3 | — | 18 | 1 | no | — |
| 341 | C2×C3×D4 | — | 3 | 2 | no | — |
| 342 | C2×C3×D4 | — | 6 | 1 | no | — |
| 343 | C2×C3×D4 | — | 9 | 2 | no | — |
| 344 | C2×C3×D4 | — | 9 | 2 | no | — |
| 345 | C22×C3×C4 | — | 3 | 2 | no | — |
| 346 | C22×C3×C4 | — | 3 | 2 | no | — |
| 347 | C22×C3×C4 | — | 6 | 2 | no | — |
| 348 | C2×#67 | — | 3 | 2 | no | — |
| 349 | C2×#67 | — | 3 | 2 | no | — |
| 350 | C2×#67 | — | 3 | 2 | no | — |
| 351 | C2×#67 | — | 6 | 2 | no | — |
| 352 | C2×#67 | — | 9 | 2 | no | — |
| 353 | C2×#67 | — | 9 | 2 | no | — |
| 354 | C2×#67 | — | 9 | 2 | no | — |
| 355 | C2×#67 | — | 9 | 1 | no | — |
| 356 | C2×#67 | — | 9 | 2 | no | — |
| 357 | C2×#67 | — | 9 | 1 | no | — |
| 358 | C2×#67 | — | 9 | 1 | no | — |
| 359 | C2×#67 | — | 9 | 2 | no | — |
| 360 | C2×#67 | — | 18 | 1 | no | — |
| 361 | C2×#67 | — | 18 | 1 | no | — |
| 362 | C2×#67 | — | 18 | 2 | no | — |
| 363 | C2×#67 | — | 18 | 4 | no | — |
| 364 | C2×#67 | — | 18 | 4 | no | — |
| 365 | C2×#67 | — | 36 | 1 | no | — |
| 366 | C2×#67 | D32 | 1 | 1 | yes | characteristic, complemented |
| 367 | C22×Dic3 | — | 9 | 1 | no | — |
| 368 | C22×Dic3 | — | 9 | 1 | no | — |
| 369 | C22×Dic3 | D32 | 1 | 2 | yes | complemented |
| 370 | D3×D4 | — | 18 | 8 | no | — |
| 371 | D3×D4 | — | 18 | 8 | no | — |
| 372 | D3×D4 | — | 18 | 8 | no | — |
| 373 | C2×D12 | — | 3 | 2 | no | — |
| 374 | C2×D12 | — | 9 | 2 | no | — |
| 375 | C2×D12 | — | 9 | 2 | no | — |
| 376 | C2×D12 | — | 9 | 2 | no | — |
| 377 | C2×D12 | — | 9 | 2 | no | — |
| 378 | C2×D12 | — | 18 | 1 | no | — |
| 379 | C2×D12 | — | 18 | 2 | no | — |
| 380 | C2×C4×D3 | — | 9 | 2 | no | — |
| 381 | C2×C4×D3 | — | 9 | 2 | no | — |
| 382 | C2×C4×D3 | — | 18 | 1 | no | — |
| 383 | C3×C4⋊C4 | — | 9 | 2 | no | — |
| 384 | C3×C22⋊C4 | — | 9 | 2 | no | — |
| 385 | C3×C22⋊C4 | — | 9 | 1 | no | — |
| 386 | C3×C22⋊C4 | — | 9 | 2 | no | — |
| 387 | C3×C22⋊C4 | — | 9 | 1 | no | — |
| 388 | C3×C22⋊C4 | — | 9 | 2 | no | — |
| 389 | #217 | — | 3 | 2 | no | — |
| 390 | #217 | — | 9 | 2 | no | — |
| 391 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 392 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 393 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 394 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 395 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 396 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 397 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 398 | (C2×D3)⋊C4 | — | 9 | 2 | no | — |
| 399 | (C2×D3)⋊C4 | — | 9 | 2 | no | — |
| 400 | (C2×D3)⋊C4 | — | 9 | 2 | no | — |
| 401 | (C2×D3)⋊C4 | — | 9 | 2 | no | — |
| 402 | (C2×D3)⋊C4 | — | 9 | 2 | no | — |
| 403 | (C2×D3)⋊C4 | — | 18 | 2 | no | — |
| 404 | (C2×D3)⋊C4 | — | 18 | 2 | no | — |
| 405 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 406 | C4⋊Dic3 | — | 9 | 2 | no | — |
| 407 | C4⋊Dic3 | — | 9 | 2 | no | — |
| 408 | C4⋊Dic3 | — | 18 | 2 | no | — |
| 409 | Dic3⋊C4 | — | 3 | 2 | no | — |
| 410 | Dic3⋊C4 | — | 9 | 2 | no | — |
| 411 | C22×C32 | — | 2 | 2 | no | — |
| 412 | C22×C32 | — | 2 | 2 | no | — |
| 413 | C22×C32 | — | 2 | 2 | no | — |
| 414 | C22×C32 | — | 2 | 2 | no | — |
| 415 | C22×C32 | — | 2 | 1 | no | — |
| 416 | C22×C32 | — | 2 | 4 | no | — |
| 417 | C22×C32 | — | 2 | 2 | no | — |
| 418 | C22×C32 | — | 4 | 1 | no | — |
| 419 | C22×C32 | — | 4 | 2 | no | — |
| 420 | C22×C32 | — | 4 | 2 | no | — |
| 421 | C22×C32 | — | 4 | 2 | no | — |
| 422 | C22×C32 | — | 4 | 2 | no | — |
| 423 | C22×C32 | — | 6 | 1 | no | — |
| 424 | C22×C32 | — | 6 | 2 | no | — |
| 425 | C22×C32 | — | 8 | 2 | no | — |
| 426 | C22×C32 | C2×D12 | 1 | 2 | yes | — |
| 427 | C22×C32 | D3×D4 | 1 | 4 | yes | — |
| 428 | C22×C32 | C23×D3 | 1 | 1 | yes | characteristic |
| 429 | C22×C32 | C23×D3 | 1 | 2 | yes | — |
| 430 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 431 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 432 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 433 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 434 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 435 | C2×C3⋊D3 | — | 4 | 4 | no | — |
| 436 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 437 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 438 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 439 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 440 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 441 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 442 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 443 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 444 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 445 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 446 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 447 | C2×C3⋊D3 | — | 12 | 4 | no | — |
| 448 | C2×C3⋊D3 | — | 24 | 2 | no | — |
| 449 | C2×C3⋊D3 | C2×D12 | 1 | 2 | yes | — |
| 450 | C2×C3⋊D3 | C2×D12 | 1 | 2 | yes | — |
| 451 | C2×C3×D3 | — | 2 | 2 | no | — |
| 452 | C2×C3×D3 | — | 2 | 2 | no | — |
| 453 | C2×C3×D3 | — | 2 | 2 | no | — |
| 454 | C2×C3×D3 | — | 2 | 2 | no | — |
| 455 | C2×C3×D3 | — | 3 | 4 | no | — |
| 456 | C2×C3×D3 | — | 3 | 4 | no | — |
| 457 | C2×C3×D3 | — | 4 | 2 | no | — |
| 458 | C2×C3×D3 | — | 6 | 2 | no | — |
| 459 | C2×C3×D3 | — | 6 | 2 | no | — |
| 460 | C2×C3×D3 | — | 6 | 4 | no | — |
| 461 | C2×C3×D3 | — | 6 | 2 | no | — |
| 462 | C2×C3×D3 | — | 6 | 2 | no | — |
| 463 | C2×C3×D3 | — | 6 | 2 | no | — |
| 464 | C2×C3×D3 | — | 6 | 2 | no | — |
| 465 | C2×C3×D3 | — | 6 | 2 | no | — |
| 466 | C2×C3×D3 | — | 6 | 2 | no | — |
| 467 | C2×C3×D3 | — | 6 | 2 | no | — |
| 468 | C2×C3×D3 | — | 6 | 2 | no | — |
| 469 | C2×C3×D3 | — | 6 | 2 | no | — |
| 470 | C2×C3×D3 | — | 6 | 2 | no | — |
| 471 | C2×C3×D3 | — | 12 | 2 | no | — |
| 472 | C2×C3×D3 | — | 12 | 2 | no | — |
| 473 | C2×C3×D3 | — | 12 | 2 | no | — |
| 474 | C2×C3×D3 | — | 12 | 2 | no | — |
| 475 | C2×C3×D3 | — | 12 | 8 | no | — |
| 476 | C2×C3×D3 | — | 12 | 8 | no | — |
| 477 | D32 | — | 12 | 8 | no | — |
| 478 | D32 | — | 12 | 8 | no | — |
| 479 | D32 | — | 12 | 8 | no | — |
| 480 | D32 | — | 12 | 4 | no | — |
| 481 | C32×C4 | — | 6 | 1 | no | — |
| 482 | C32×C4 | — | 6 | 2 | no | — |
| 483 | C32×C4 | — | 6 | 2 | no | — |
| 484 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 485 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 486 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 487 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 488 | C3⋊Dic3 | — | 12 | 2 | no | — |
| 489 | C3⋊Dic3 | — | 12 | 2 | no | — |
| 490 | C3×Dic3 | — | 2 | 2 | no | — |
| 491 | C3×Dic3 | — | 2 | 4 | no | — |
| 492 | C3×Dic3 | — | 2 | 2 | no | — |
| 493 | C3×Dic3 | — | 2 | 2 | no | — |
| 494 | C3×Dic3 | — | 2 | 2 | no | — |
| 495 | C3×Dic3 | — | 2 | 2 | no | — |
| 496 | C3×Dic3 | — | 2 | 2 | no | — |
| 497 | C3×Dic3 | — | 4 | 2 | no | — |
| 498 | C3×Dic3 | — | 6 | 2 | no | — |
| 499 | C3×Dic3 | — | 6 | 2 | no | — |
| 500 | C3×Dic3 | — | 12 | 2 | no | — |
| 501 | C22×D4 | — | 27 | 1 | no | — |
| 502 | C22×D4 | — | 27 | 1 | no | — |
| 503 | #123 | — | 27 | 1 | no | — |
| 504 | #123 | — | 27 | 2 | no | — |
| 505 | #123 | — | 27 | 1 | no | — |
| 506 | #121 | — | 9 | 2 | no | — |
| 507 | #121 | — | 27 | 2 | no | — |
| 508 | #120 | — | 27 | 1 | no | — |
| 509 | #120 | — | 27 | 2 | no | — |
| 510 | #120 | — | 27 | 1 | no | — |
| 511 | C2×C22⋊C4 | — | 9 | 1 | no | — |
| 512 | C33 | #534 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 513 | C23×C3 | — | 2 | 2 | no | — |
| 514 | C23×C3 | — | 2 | 1 | no | — |
| 515 | C23×C3 | — | 3 | 2 | no | — |
| 516 | C23×C3 | — | 4 | 1 | no | — |
| 517 | C23×C3 | — | 6 | 1 | no | — |
| 518 | C23×C3 | — | 9 | 1 | no | — |
| 519 | C23×C3 | — | 9 | 1 | no | — |
| 520 | C23×C3 | — | 9 | 4 | no | — |
| 521 | C23×C3 | — | 9 | 2 | no | — |
| 522 | C23×C3 | — | 36 | 2 | no | — |
| 523 | C23×C3 | C2×D32 | 1 | 2 | yes | — |
| 524 | C23×C3 | C2×D32 | 1 | 1 | yes | characteristic |
| 525 | C22×D3 | — | 3 | 2 | no | — |
| 526 | C22×D3 | — | 3 | 2 | no | — |
| 527 | C22×D3 | — | 3 | 8 | no | — |
| 528 | C22×D3 | — | 3 | 2 | no | — |
| 529 | C22×D3 | — | 3 | 2 | no | — |
| 530 | C22×D3 | — | 6 | 1 | no | — |
| 531 | C22×D3 | — | 6 | 4 | no | — |
| 532 | C22×D3 | — | 6 | 1 | no | — |
| 533 | C22×D3 | — | 6 | 2 | no | — |
| 534 | C22×D3 | — | 9 | 2 | no | — |
| 535 | C22×D3 | — | 9 | 1 | no | — |
| 536 | C22×D3 | — | 12 | 2 | no | — |
| 537 | C22×D3 | — | 12 | 2 | no | — |
| 538 | C22×D3 | — | 12 | 4 | no | — |
| 539 | C22×D3 | — | 18 | 1 | no | — |
| 540 | C22×D3 | — | 18 | 2 | no | — |
| 541 | C22×D3 | — | 18 | 2 | no | — |
| 542 | C22×D3 | — | 18 | 4 | no | — |
| 543 | C22×D3 | — | 18 | 4 | no | — |
| 544 | C22×D3 | — | 18 | 2 | no | — |
| 545 | C22×D3 | — | 18 | 4 | no | — |
| 546 | C22×D3 | — | 36 | 1 | no | — |
| 547 | C22×D3 | — | 36 | 2 | no | — |
| 548 | C22×D3 | — | 36 | 2 | no | — |
| 549 | C22×D3 | — | 36 | 2 | no | — |
| 550 | C22×D3 | — | 36 | 2 | no | — |
| 551 | C22×D3 | — | 36 | 2 | no | — |
| 552 | C22×D3 | — | 36 | 2 | no | — |
| 553 | C22×D3 | — | 36 | 4 | no | — |
| 554 | C22×D3 | C2×D32 | 1 | 1 | yes | characteristic |
| 555 | C3×D4 | — | 6 | 4 | no | — |
| 556 | C3×D4 | — | 6 | 4 | no | — |
| 557 | C3×D4 | — | 18 | 4 | no | — |
| 558 | C3×D4 | — | 36 | 2 | no | — |
| 559 | C2×C3×C4 | — | 3 | 2 | no | — |
| 560 | C2×C3×C4 | — | 3 | 2 | no | — |
| 561 | C2×C3×C4 | — | 3 | 2 | no | — |
| 562 | C2×C3×C4 | — | 3 | 2 | no | — |
| 563 | C2×C3×C4 | — | 3 | 2 | no | — |
| 564 | C2×C3×C4 | — | 6 | 2 | no | — |
| 565 | C2×C3×C4 | — | 6 | 1 | no | — |
| 566 | C2×C3×C4 | — | 6 | 2 | no | — |
| 567 | C2×C3×C4 | — | 9 | 2 | no | — |
| 568 | C2×C3×C4 | — | 12 | 2 | no | — |
| 569 | C2×C3×C4 | — | 12 | 2 | no | — |
| 570 | C2×C3×C4 | — | 12 | 4 | no | — |
| 571 | #67 | — | 2 | 2 | no | — |
| 572 | #67 | — | 6 | 4 | no | — |
| 573 | #67 | — | 6 | 4 | no | — |
| 574 | #67 | — | 12 | 4 | no | — |
| 575 | #67 | — | 12 | 2 | no | — |
| 576 | #67 | — | 18 | 2 | no | — |
| 577 | #67 | — | 18 | 4 | no | — |
| 578 | #67 | — | 18 | 4 | no | — |
| 579 | #67 | — | 18 | 2 | no | — |
| 580 | #67 | — | 18 | 4 | no | — |
| 581 | #67 | — | 18 | 4 | no | — |
| 582 | #67 | — | 18 | 4 | no | — |
| 583 | #67 | — | 18 | 4 | no | — |
| 584 | #67 | — | 18 | 2 | no | — |
| 585 | #67 | — | 36 | 4 | no | — |
| 586 | #67 | — | 36 | 4 | no | — |
| 587 | #67 | — | 36 | 2 | no | — |
| 588 | C2×Dic3 | — | 3 | 2 | no | — |
| 589 | C2×Dic3 | — | 3 | 2 | no | — |
| 590 | C2×Dic3 | — | 4 | 2 | no | — |
| 591 | C2×Dic3 | — | 6 | 2 | no | — |
| 592 | C2×Dic3 | — | 9 | 2 | no | — |
| 593 | C2×Dic3 | — | 9 | 1 | no | — |
| 594 | C2×Dic3 | — | 18 | 1 | no | — |
| 595 | C2×Dic3 | — | 18 | 2 | no | — |
| 596 | C2×Dic3 | — | 18 | 2 | no | — |
| 597 | C2×Dic3 | — | 18 | 2 | no | — |
| 598 | C2×Dic3 | — | 36 | 1 | no | — |
| 599 | C2×Dic3 | C2×D32 | 1 | 2 | yes | — |
| 600 | C2×Dic3 | C2×D32 | 1 | 2 | yes | — |
| 601 | C2×Dic3 | C2×D32 | 1 | 1 | yes | characteristic |
| 602 | D12 | — | 12 | 2 | no | — |
| 603 | D12 | — | 18 | 4 | no | — |
| 604 | D12 | — | 18 | 4 | no | — |
| 605 | D12 | — | 18 | 4 | no | — |
| 606 | D12 | — | 36 | 2 | no | — |
| 607 | D12 | — | 36 | 2 | no | — |
| 608 | D12 | — | 36 | 4 | no | — |
| 609 | C4×D3 | — | 18 | 4 | no | — |
| 610 | C4×D3 | — | 18 | 4 | no | — |
| 611 | C4×D3 | — | 18 | 4 | no | — |
| 612 | C2×C32 | — | 2 | 2 | no | — |
| 613 | C2×C32 | — | 2 | 4 | no | — |
| 614 | C2×C32 | — | 2 | 2 | no | — |
| 615 | C2×C32 | — | 2 | 2 | no | — |
| 616 | C2×C32 | — | 2 | 2 | no | — |
| 617 | C2×C32 | — | 2 | 1 | no | — |
| 618 | C2×C32 | — | 2 | 2 | no | — |
| 619 | C2×C32 | — | 4 | 1 | no | — |
| 620 | C2×C32 | — | 4 | 2 | no | — |
| 621 | C2×C32 | — | 4 | 2 | no | — |
| 622 | C2×C32 | — | 4 | 4 | no | — |
| 623 | C2×C32 | — | 8 | 2 | no | — |
| 624 | C2×C32 | — | 12 | 1 | no | — |
| 625 | C2×C32 | C22×D12 | 1 | 1 | yes | characteristic |
| 626 | C2×C32 | C2×D3×D4 | 1 | 2 | yes | — |
| 627 | C2×C32 | #1004 | 1 | 2 | yes | — |
| 628 | C2×C32 | #1004 | 1 | 2 | yes | — |
| 629 | C2×C32 | #1009 | 1 | 2 | yes | — |
| 630 | C3⋊D3 | — | 2 | 2 | no | — |
| 631 | C3⋊D3 | — | 2 | 2 | no | — |
| 632 | C3⋊D3 | — | 4 | 2 | no | — |
| 633 | C3⋊D3 | — | 12 | 1 | no | — |
| 634 | C3⋊D3 | — | 12 | 2 | no | — |
| 635 | C3⋊D3 | — | 12 | 2 | no | — |
| 636 | C3⋊D3 | — | 24 | 2 | no | — |
| 637 | C3⋊D3 | — | 24 | 2 | no | — |
| 638 | C3×D3 | — | 4 | 2 | no | — |
| 639 | C3×D3 | — | 4 | 2 | no | — |
| 640 | C3×D3 | — | 6 | 4 | no | — |
| 641 | C3×D3 | — | 6 | 4 | no | — |
| 642 | C3×D3 | — | 6 | 4 | no | — |
| 643 | C3×D3 | — | 12 | 2 | no | — |
| 644 | C3×D3 | — | 12 | 2 | no | — |
| 645 | C3×D3 | — | 12 | 2 | no | — |
| 646 | C3×D3 | — | 24 | 2 | no | — |
| 647 | C24 | — | 9 | 1 | no | — |
| 648 | C24 | — | 27 | 1 | no | — |
| 649 | C24 | — | 27 | 1 | no | — |
| 650 | C2×D4 | — | 3 | 1 | no | — |
| 651 | C2×D4 | — | 9 | 2 | no | — |
| 652 | C2×D4 | — | 9 | 2 | no | — |
| 653 | C2×D4 | — | 27 | 1 | no | — |
| 654 | C2×D4 | — | 27 | 2 | no | — |
| 655 | C2×D4 | — | 27 | 2 | no | — |
| 656 | C2×D4 | — | 27 | 1 | no | — |
| 657 | C2×D4 | — | 27 | 1 | no | — |
| 658 | C2×D4 | — | 54 | 4 | no | — |
| 659 | C2×D4 | — | 54 | 4 | no | — |
| 660 | C22×C4 | — | 3 | 2 | no | — |
| 661 | C22×C4 | — | 27 | 1 | no | — |
| 662 | C22×C4 | — | 27 | 1 | no | — |
| 663 | C4⋊C4 | — | 9 | 2 | no | — |
| 664 | C4⋊C4 | — | 27 | 2 | no | — |
| 665 | C22⋊C4 | — | 9 | 1 | no | — |
| 666 | C22⋊C4 | — | 9 | 2 | no | — |
| 667 | C22⋊C4 | — | 9 | 1 | no | — |
| 668 | C22⋊C4 | — | 9 | 2 | no | — |
| 669 | C22⋊C4 | — | 9 | 2 | no | — |
| 670 | C22⋊C4 | — | 27 | 2 | no | — |
| 671 | C22⋊C4 | — | 27 | 2 | no | — |
| 672 | C22×C3 | — | 2 | 2 | no | — |
| 673 | C22×C3 | — | 2 | 2 | no | — |
| 674 | C22×C3 | — | 2 | 2 | no | — |
| 675 | C22×C3 | — | 2 | 2 | no | — |
| 676 | C22×C3 | — | 2 | 1 | no | — |
| 677 | C22×C3 | — | 2 | 4 | no | — |
| 678 | C22×C3 | — | 2 | 2 | no | — |
| 679 | C22×C3 | — | 4 | 2 | no | — |
| 680 | C22×C3 | — | 4 | 2 | no | — |
| 681 | C22×C3 | — | 4 | 2 | no | — |
| 682 | C22×C3 | — | 4 | 1 | no | — |
| 683 | C22×C3 | — | 4 | 2 | no | — |
| 684 | C22×C3 | — | 6 | 2 | no | — |
| 685 | C22×C3 | — | 6 | 2 | no | — |
| 686 | C22×C3 | — | 6 | 2 | no | — |
| 687 | C22×C3 | — | 6 | 2 | no | — |
| 688 | C22×C3 | — | 8 | 2 | no | — |
| 689 | C22×C3 | — | 9 | 2 | no | — |
| 690 | C22×C3 | — | 9 | 2 | no | — |
| 691 | C22×C3 | — | 12 | 2 | no | — |
| 692 | C22×C3 | — | 18 | 2 | no | — |
| 693 | C22×C3 | — | 18 | 2 | no | — |
| 694 | C22×C3 | — | 18 | 2 | no | — |
| 695 | C22×C3 | — | 18 | 2 | no | — |
| 696 | C22×C3 | — | 18 | 2 | no | — |
| 697 | C22×C3 | — | 36 | 4 | no | — |
| 698 | C22×C3 | D3×D12 | 1 | 4 | yes | — |
| 699 | C22×C3 | #3811 | 1 | 2 | yes | — |
| 700 | C22×C3 | C22×D32 | 1 | 2 | yes | — |
| 701 | C22×C3 | C22×D32 | 1 | 1 | yes | characteristic |
| 702 | C2×D3 | — | 2 | 2 | no | — |
| 703 | C2×D3 | — | 2 | 1 | no | — |
| 704 | C2×D3 | — | 3 | 4 | no | — |
| 705 | C2×D3 | — | 3 | 4 | no | — |
| 706 | C2×D3 | — | 6 | 2 | no | — |
| 707 | C2×D3 | — | 6 | 2 | no | — |
| 708 | C2×D3 | — | 6 | 4 | no | — |
| 709 | C2×D3 | — | 6 | 2 | no | — |
| 710 | C2×D3 | — | 6 | 2 | no | — |
| 711 | C2×D3 | — | 6 | 2 | no | — |
| 712 | C2×D3 | — | 6 | 2 | no | — |
| 713 | C2×D3 | — | 6 | 2 | no | — |
| 714 | C2×D3 | — | 6 | 2 | no | — |
| 715 | C2×D3 | — | 6 | 2 | no | — |
| 716 | C2×D3 | — | 6 | 2 | no | — |
| 717 | C2×D3 | — | 6 | 2 | no | — |
| 718 | C2×D3 | — | 6 | 2 | no | — |
| 719 | C2×D3 | — | 12 | 2 | no | — |
| 720 | C2×D3 | — | 12 | 2 | no | — |
| 721 | C2×D3 | — | 12 | 2 | no | — |
| 722 | C2×D3 | — | 12 | 2 | no | — |
| 723 | C2×D3 | — | 12 | 8 | no | — |
| 724 | C2×D3 | — | 12 | 8 | no | — |
| 725 | C2×D3 | — | 18 | 2 | no | — |
| 726 | C2×D3 | — | 18 | 2 | no | — |
| 727 | C2×D3 | — | 18 | 2 | no | — |
| 728 | C2×D3 | — | 18 | 2 | no | — |
| 729 | C2×D3 | — | 18 | 1 | no | — |
| 730 | C2×D3 | — | 18 | 2 | no | — |
| 731 | C2×D3 | — | 36 | 2 | no | — |
| 732 | C2×D3 | — | 36 | 2 | no | — |
| 733 | C2×D3 | — | 36 | 2 | no | — |
| 734 | C2×D3 | — | 36 | 2 | no | — |
| 735 | C2×D3 | — | 36 | 2 | no | — |
| 736 | C2×D3 | — | 36 | 4 | no | — |
| 737 | C2×D3 | — | 36 | 8 | no | — |
| 738 | C2×D3 | — | 36 | 8 | no | — |
| 739 | C2×D3 | — | 36 | 8 | no | — |
| 740 | C2×D3 | — | 36 | 4 | no | — |
| 741 | C2×D3 | — | 72 | 2 | no | — |
| 742 | C3×C4 | — | 6 | 2 | no | — |
| 743 | C3×C4 | — | 6 | 4 | no | — |
| 744 | C3×C4 | — | 6 | 2 | no | — |
| 745 | C3×C4 | — | 6 | 2 | no | — |
| 746 | C3×C4 | — | 6 | 2 | no | — |
| 747 | C3×C4 | — | 6 | 2 | no | — |
| 748 | C3×C4 | — | 6 | 2 | no | — |
| 749 | C3×C4 | — | 12 | 2 | no | — |
| 750 | C3×C4 | — | 18 | 2 | no | — |
| 751 | Dic3 | — | 2 | 1 | no | — |
| 752 | Dic3 | — | 2 | 2 | no | — |
| 753 | Dic3 | — | 2 | 2 | no | — |
| 754 | Dic3 | — | 6 | 2 | no | — |
| 755 | Dic3 | — | 6 | 2 | no | — |
| 756 | Dic3 | — | 12 | 2 | no | — |
| 757 | Dic3 | — | 18 | 2 | no | — |
| 758 | Dic3 | — | 18 | 2 | no | — |
| 759 | Dic3 | — | 18 | 1 | no | — |
| 760 | Dic3 | — | 36 | 2 | no | — |
| 761 | Dic3 | — | 36 | 2 | no | — |
| 762 | C32 | — | 2 | 2 | no | — |
| 763 | C32 | — | 2 | 1 | no | — |
| 764 | C32 | — | 4 | 1 | no | — |
| 765 | C32 | #5493 | 1 | 1 | yes | characteristic, complemented |
| 766 | C32 | #5605 | 1 | 2 | yes | complemented |
| 767 | C23 | — | 3 | 1 | no | — |
| 768 | C23 | — | 9 | 1 | no | — |
| 769 | C23 | — | 9 | 1 | no | — |
| 770 | C23 | — | 9 | 4 | no | — |
| 771 | C23 | — | 9 | 2 | no | — |
| 772 | C23 | — | 27 | 1 | no | — |
| 773 | C23 | — | 36 | 2 | no | — |
| 774 | C23 | — | 54 | 2 | no | — |
| 775 | C23 | — | 54 | 2 | no | — |
| 776 | C23 | — | 108 | 2 | no | — |
| 777 | C23 | — | 108 | 2 | no | — |
| 778 | C23 | D33 | 1 | 1 | yes | characteristic |
| 779 | D4 | — | 6 | 2 | no | — |
| 780 | D4 | — | 18 | 4 | no | — |
| 781 | D4 | — | 36 | 2 | no | — |
| 782 | D4 | — | 54 | 2 | no | — |
| 783 | D4 | — | 54 | 4 | no | — |
| 784 | D4 | — | 54 | 2 | no | — |
| 785 | D4 | — | 54 | 2 | no | — |
| 786 | D4 | — | 108 | 2 | no | — |
| 787 | C2×C4 | — | 3 | 2 | no | — |
| 788 | C2×C4 | — | 3 | 2 | no | — |
| 789 | C2×C4 | — | 3 | 1 | no | — |
| 790 | C2×C4 | — | 9 | 2 | no | — |
| 791 | C2×C4 | — | 12 | 2 | no | — |
| 792 | C2×C4 | — | 27 | 1 | no | — |
| 793 | C2×C4 | — | 54 | 2 | no | — |
| 794 | C2×C4 | — | 54 | 2 | no | — |
| 795 | C2×C3 | — | 2 | 4 | no | — |
| 796 | C2×C3 | — | 2 | 2 | no | — |
| 797 | C2×C3 | — | 2 | 2 | no | — |
| 798 | C2×C3 | — | 2 | 2 | no | — |
| 799 | C2×C3 | — | 2 | 2 | no | — |
| 800 | C2×C3 | — | 2 | 2 | no | — |
| 801 | C2×C3 | — | 2 | 1 | no | — |
| 802 | C2×C3 | — | 4 | 2 | no | — |
| 803 | C2×C3 | — | 4 | 4 | no | — |
| 804 | C2×C3 | — | 4 | 2 | no | — |
| 805 | C2×C3 | — | 4 | 1 | no | — |
| 806 | C2×C3 | — | 8 | 2 | no | — |
| 807 | C2×C3 | — | 12 | 2 | no | — |
| 808 | C2×C3 | — | 12 | 2 | no | — |
| 809 | C2×C3 | — | 18 | 2 | no | — |
| 810 | C2×C3 | — | 18 | 2 | no | — |
| 811 | C2×C3 | — | 36 | 2 | no | — |
| 812 | C2×C3 | C2×D3×D12 | 1 | 2 | yes | — |
| 813 | C2×C3 | #64307 | 1 | 2 | yes | — |
| 814 | C2×C3 | #64314 | 1 | 2 | yes | — |
| 815 | C2×C3 | C2×#3811 | 1 | 1 | yes | characteristic |
| 816 | C2×C3 | #64330 | 1 | 2 | yes | — |
| 817 | D3 | — | 4 | 1 | no | — |
| 818 | D3 | — | 6 | 4 | no | — |
| 819 | D3 | — | 6 | 4 | no | — |
| 820 | D3 | — | 6 | 4 | no | — |
| 821 | D3 | — | 12 | 2 | no | — |
| 822 | D3 | — | 12 | 2 | no | — |
| 823 | D3 | — | 12 | 2 | no | — |
| 824 | D3 | — | 24 | 2 | no | — |
| 825 | D3 | — | 36 | 2 | no | — |
| 826 | D3 | — | 36 | 2 | no | — |
| 827 | D3 | — | 36 | 1 | no | — |
| 828 | D3 | — | 72 | 2 | no | — |
| 829 | D3 | — | 72 | 2 | no | — |
| 830 | C22 | — | 2 | 2 | no | — |
| 831 | C22 | — | 6 | 2 | no | — |
| 832 | C22 | — | 6 | 1 | no | — |
| 833 | C22 | — | 9 | 2 | no | — |
| 834 | C22 | — | 9 | 2 | no | — |
| 835 | C22 | — | 18 | 2 | no | — |
| 836 | C22 | — | 18 | 2 | no | — |
| 837 | C22 | — | 18 | 2 | no | — |
| 838 | C22 | — | 18 | 2 | no | — |
| 839 | C22 | — | 18 | 2 | no | — |
| 840 | C22 | — | 36 | 4 | no | — |
| 841 | C22 | — | 54 | 2 | no | — |
| 842 | C22 | — | 54 | 1 | no | — |
| 843 | C22 | — | 108 | 4 | no | — |
| 844 | C22 | — | 108 | 4 | no | — |
| 845 | C22 | #88955 | 1 | 2 | yes | — |
| 846 | C22 | C2×D33 | 1 | 1 | yes | characteristic |
| 847 | C4 | — | 6 | 2 | no | — |
| 848 | C4 | — | 6 | 2 | no | — |
| 849 | C4 | — | 6 | 1 | no | — |
| 850 | C4 | — | 18 | 2 | no | — |
| 851 | C4 | — | 54 | 1 | no | — |
| 852 | C3 | — | 2 | 1 | no | — |
| 853 | C3 | — | 2 | 2 | no | — |
| 854 | C3 | — | 4 | 1 | no | — |
| 855 | C3 | #10595072 | 1 | 2 | yes | complemented |
| 856 | C3 | #10595308 | 1 | 1 | yes | characteristic, complemented |
| 857 | C2 | — | 2 | 2 | no | — |
| 858 | C2 | — | 12 | 1 | no | — |
| 859 | C2 | — | 18 | 2 | no | — |
| 860 | C2 | — | 18 | 2 | no | — |
| 861 | C2 | — | 36 | 2 | no | — |
| 862 | C2 | — | 108 | 1 | no | — |
| 863 | C2 | #11724418 | 1 | 2 | yes | — |
| 864 | 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 | #534 |
| 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×#89049 | C2 | semidirect |
| 2. C2×C3⋊D3×#67 | C2 | semidirect |
| 3. #11723632 | C2 | semidirect |
| 4. C3×#63978 | C2 | semidirect |
| 5. C2×C3×#3722 | C2 | semidirect |
| 6. #11722999 | C2 | semidirect |
| 7. #11722998 | C2 | semidirect |
| 8. #11722997 | C2 | semidirect |
| 9. #11722952 | C2 | semidirect |
| 10. #11722951 | C2 | semidirect |
| 11. #11722950 | C2 | semidirect |
| 15. C22×#1113 | C22 | semidirect |
| 16. C22×D3×C3⋊D3 | C22 | semidirect |
| 17. C2×#6312 | C22 | semidirect |
| 18. C2×C3×#638 | C22 | semidirect |
| 19. C2×C32×#67 | C22 | semidirect |
| 20. C22×C32×Dic3 | C22 | semidirect |
| 23. C2×#6294 | C22 | semidirect |
| 26. C2×#6292 | C22 | semidirect |
| 28. C2×Dic3×C3⋊D3 | C22 | semidirect |
| 29. C2×C3×#626 | C22 | semidirect |
| 30. Dic3⋊(C3⋊Dic3) | C22 | semidirect |
| 31. #88804 | C22 | semidirect |
| 32. #88803 | C22 | semidirect |
| 33. C3×Dic3⋊Dic3 | C22 | semidirect |
| 34. C3×#3722 | C22 | semidirect |
| 35. C3×#3722 | C22 | semidirect |
| 36. C3×#3722 | C22 | semidirect |
| 37. C3×#3722 | C22 | semidirect |
| 38. C3×(C2×D3)⋊Dic3 | C22 | semidirect |
| 53. #63978 | D3 | semidirect |
| 55. C2×#3722 | D3 | semidirect |
| 70. C22×C3×C3⋊D3 | D4 | semidirect |
| 113. C2×#638 | C2×D3 | semidirect |
| 123. C2×C3×#67 | C2×D3 | semidirect |
| 125. C22×C3×Dic3 | C2×D3 | semidirect |
| 126. C22×C3×Dic3 | C2×D3 | semidirect |
| 139. C2×#626 | C2×D3 | semidirect |
| 163. Dic3⋊Dic3 | C2×D3 | semidirect |
| 167. #3722 | C2×D3 | semidirect |
| 168. #3722 | C2×D3 | semidirect |
| 169. #3722 | C2×D3 | semidirect |
| 170. #3722 | C2×D3 | semidirect |
| 174. (C2×D3)⋊Dic3 | C2×D3 | semidirect |
| 239. C22×C3⋊D3 | D12 | semidirect |
| 366. C2×#67 | D32 | semidirect |
| 369. C22×Dic3 | D32 | semidirect |
| 512. C33 | #534 | semidirect |
| 765. C32 | #5493 | semidirect |
| 766. C32 | #5605 | semidirect |
| 855. C3 | #10595072 | semidirect |
| 856. C3 | #10595308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89049 | 2 |
| C2×C3⋊D3×#67 | 2 |
| #11723632 | 2 |
| C3×#63978 | 2 |
| C2×C3×#3722 | 2 |
| #11722999 | 2 |
| #11722998 | 2 |
| #11722997 | 2 |
| #11722952 | 2 |
| #11722951 | 2 |
| #11722950 | 2 |
| #10595308 | 3 |
| #10595072 | 3 |