Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1356 conjugacy classes of subgroups.
The subgroup lattice has 708 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11723718 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11723629 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11723600 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C3×#63983 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#63976 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11723009 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11723006 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11723004 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11722946 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10595529 | — | 3 | 1 | no | maximal |
| 11 | #10595256 | — | 3 | 2 | no | maximal |
| 12 | C23×C32×D3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C22×C3×D32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C2×C3×#638 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C32×#67 | C22 | 1 | 2 | yes | — |
| 16 | C2×#6296 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C2×#6293 | C22 | 1 | 2 | yes | complemented |
| 18 | C2×#6290 | C22 | 1 | 2 | yes | — |
| 19 | C2×C3×#625 | C22 | 1 | 2 | yes | — |
| 20 | C2×C3×#625 | C22 | 1 | 2 | yes | — |
| 21 | #88864 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C3×#3757 | C22 | 1 | 2 | yes | complemented |
| 23 | #88814 | C22 | 1 | 2 | yes | complemented |
| 24 | #88813 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | (C2×D3)⋊(C3⋊Dic3) | C22 | 1 | 2 | yes | complemented |
| 26 | (C2×D3)⋊(C3⋊Dic3) | C22 | 1 | 2 | yes | complemented |
| 27 | (C2×D3)⋊(C3⋊Dic3) | C22 | 1 | 2 | yes | complemented |
| 28 | Dic3×C3⋊Dic3 | C22 | 1 | 2 | yes | complemented |
| 29 | C3×#3722 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | C3×(C2×D3)⋊Dic3 | C22 | 1 | 2 | yes | complemented |
| 31 | C3×(C2×D3)⋊Dic3 | C22 | 1 | 2 | yes | complemented |
| 32 | C3×(C2×D3)⋊Dic3 | C22 | 1 | 2 | yes | complemented |
| 33 | #64162 | — | 3 | 1 | no | — |
| 34 | #64145 | — | 3 | 2 | no | — |
| 35 | C3×#953 | — | 3 | 2 | no | — |
| 36 | C3×#937 | — | 3 | 2 | no | — |
| 37 | C3×#937 | — | 3 | 2 | no | — |
| 38 | #63983 | — | 3 | 2 | no | — |
| 39 | #63983 | D3 | 1 | 1 | yes | characteristic, complemented |
| 40 | #63976 | — | 3 | 2 | no | — |
| 41 | #63976 | — | 3 | 2 | no | — |
| 42 | #63976 | — | 3 | 2 | no | — |
| 43 | #63976 | — | 6 | 1 | no | — |
| 44 | #63976 | D3 | 1 | 2 | yes | complemented |
| 45 | #63959 | — | 3 | 2 | no | — |
| 46 | #63959 | — | 3 | 2 | no | — |
| 47 | #63959 | — | 3 | 2 | no | — |
| 48 | #63959 | — | 3 | 2 | no | — |
| 49 | #63959 | — | 3 | 2 | no | — |
| 50 | #63959 | — | 3 | 2 | no | — |
| 51 | #63959 | — | 3 | 2 | no | — |
| 52 | #63959 | — | 6 | 2 | no | — |
| 53 | #63953 | — | 3 | 1 | no | — |
| 54 | #63953 | — | 3 | 2 | no | — |
| 55 | #63915 | — | 3 | 2 | no | — |
| 56 | #63915 | — | 3 | 2 | no | — |
| 57 | #63913 | — | 3 | 2 | no | — |
| 58 | #63913 | — | 3 | 2 | no | — |
| 59 | C23×C33 | C23 | 1 | 1 | yes | characteristic |
| 60 | C22×C3×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 61 | C22×C32×D3 | — | 4 | 2 | no | — |
| 62 | C22×C32×D3 | — | 4 | 1 | no | — |
| 63 | C22×C32×D3 | C23 | 1 | 2 | yes | — |
| 64 | C22×C32×D3 | C23 | 1 | 2 | yes | — |
| 65 | C2×C3×D32 | — | 4 | 1 | no | — |
| 66 | C2×C3×D32 | — | 4 | 2 | no | — |
| 67 | C2×C3⋊(C3⋊Dic3) | C23 | 1 | 2 | yes | — |
| 68 | C3×#638 | — | 4 | 1 | no | — |
| 69 | C2×C3×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 70 | C2×C3×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 71 | C2×C3×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 72 | C32×#67 | — | 4 | 2 | no | — |
| 73 | C2×C32×Dic3 | C23 | 1 | 2 | yes | — |
| 74 | #6296 | — | 4 | 1 | no | — |
| 75 | #6293 | — | 4 | 2 | no | — |
| 76 | #6290 | — | 4 | 2 | no | — |
| 77 | C3×#625 | — | 4 | 2 | no | — |
| 78 | C3×#625 | — | 4 | 2 | no | — |
| 79 | #5594 | — | 9 | 1 | no | — |
| 80 | #5594 | — | 9 | 2 | no | — |
| 81 | C24×C32 | — | 3 | 1 | no | — |
| 82 | C23×C3×D3 | — | 2 | 1 | no | — |
| 83 | C23×C3×D3 | — | 3 | 2 | no | — |
| 84 | C23×C3×D3 | C2×D3 | 1 | 2 | yes | complemented |
| 85 | C22×D32 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 86 | C2×C32×D4 | — | 3 | 2 | no | — |
| 87 | C2×#638 | — | 3 | 2 | no | — |
| 88 | C2×#638 | C2×D3 | 1 | 1 | yes | characteristic |
| 89 | C2×#634 | — | 3 | 2 | no | — |
| 90 | C2×C3×#67 | — | 2 | 2 | no | — |
| 91 | C2×C3×#67 | — | 3 | 2 | no | — |
| 92 | C2×C3×#67 | — | 3 | 2 | no | — |
| 93 | C2×C3×#67 | — | 3 | 2 | no | — |
| 94 | C2×C3×#67 | — | 3 | 2 | no | — |
| 95 | C2×C3×#67 | — | 3 | 2 | no | — |
| 96 | C2×C3×#67 | — | 6 | 1 | no | — |
| 97 | C2×C3×#67 | C2×D3 | 1 | 2 | yes | — |
| 98 | C2×C3×#67 | C2×D3 | 1 | 2 | yes | — |
| 99 | C2×#627 | — | 3 | 2 | no | — |
| 100 | C2×#627 | — | 3 | 1 | no | — |
| 101 | C2×#627 | — | 3 | 2 | no | — |
| 102 | C2×#627 | — | 3 | 2 | no | — |
| 103 | C2×#627 | — | 6 | 2 | no | — |
| 104 | C2×#625 | — | 3 | 2 | no | — |
| 105 | C2×#625 | — | 3 | 2 | no | — |
| 106 | C2×#625 | — | 6 | 2 | no | — |
| 107 | C2×#625 | C2×D3 | 1 | 2 | yes | — |
| 108 | C2×#625 | C2×D3 | 1 | 2 | yes | — |
| 109 | #3757 | — | 3 | 2 | no | — |
| 110 | #3757 | — | 3 | 1 | no | — |
| 111 | #3757 | — | 3 | 2 | no | — |
| 112 | #3757 | — | 3 | 2 | no | — |
| 113 | #3757 | — | 3 | 2 | no | — |
| 114 | #3757 | — | 6 | 2 | no | — |
| 115 | #3757 | — | 6 | 1 | no | — |
| 116 | #3757 | — | 12 | 1 | no | — |
| 117 | #3757 | C2×D3 | 1 | 2 | yes | complemented |
| 118 | C4×C3⋊Dic3 | — | 3 | 2 | no | — |
| 119 | C3×#217 | — | 3 | 2 | no | — |
| 120 | C3×#217 | — | 3 | 2 | no | — |
| 121 | C3×#217 | — | 3 | 2 | no | — |
| 122 | C3×#217 | — | 3 | 2 | no | — |
| 123 | C3×#217 | — | 3 | 2 | no | — |
| 124 | C3×#217 | — | 6 | 2 | no | — |
| 125 | C3×(C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 126 | C3×(C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 127 | C3×(C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 128 | C3×(C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 129 | #3722 | — | 3 | 2 | no | — |
| 130 | #3722 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 131 | (C2×D3)⋊Dic3 | — | 3 | 2 | no | — |
| 132 | (C2×D3)⋊Dic3 | — | 3 | 2 | no | — |
| 133 | (C2×D3)⋊Dic3 | — | 3 | 2 | no | — |
| 134 | (C2×D3)⋊Dic3 | — | 3 | 2 | no | — |
| 135 | (C2×D3)⋊Dic3 | — | 3 | 2 | no | — |
| 136 | (C2×D3)⋊Dic3 | — | 3 | 2 | no | — |
| 137 | (C2×D3)⋊Dic3 | — | 3 | 2 | no | — |
| 138 | (C2×D3)⋊Dic3 | — | 3 | 2 | no | — |
| 139 | (C2×D3)⋊Dic3 | — | 6 | 2 | no | — |
| 140 | (C2×D3)⋊Dic3 | — | 6 | 2 | no | — |
| 141 | (C2×D3)⋊Dic3 | — | 6 | 2 | no | — |
| 142 | (C2×D3)⋊Dic3 | C2×D3 | 1 | 2 | yes | complemented |
| 143 | (C2×D3)⋊Dic3 | C2×D3 | 1 | 2 | yes | complemented |
| 144 | (C2×D3)⋊Dic3 | C2×D3 | 1 | 2 | yes | complemented |
| 145 | Dic32 | — | 3 | 2 | no | — |
| 146 | Dic32 | — | 3 | 1 | no | — |
| 147 | Dic32 | — | 3 | 2 | no | — |
| 148 | Dic32 | — | 3 | 2 | no | — |
| 149 | Dic32 | — | 6 | 2 | no | — |
| 150 | C22×C33 | — | 2 | 1 | no | — |
| 151 | C22×C33 | — | 2 | 2 | no | — |
| 152 | C22×C33 | C24 | 1 | 1 | yes | characteristic |
| 153 | C2×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 154 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 155 | C2×C32×D3 | — | 2 | 2 | no | — |
| 156 | C2×C32×D3 | — | 2 | 2 | no | — |
| 157 | C2×C32×D3 | — | 2 | 2 | no | — |
| 158 | C2×C32×D3 | — | 2 | 2 | no | — |
| 159 | C2×C32×D3 | — | 2 | 2 | no | — |
| 160 | C2×C32×D3 | — | 2 | 2 | no | — |
| 161 | C2×C32×D3 | — | 4 | 4 | no | — |
| 162 | C3×D32 | — | 4 | 4 | no | — |
| 163 | C3⋊(C3⋊Dic3) | — | 2 | 2 | no | — |
| 164 | C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 165 | C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 166 | C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 167 | C32×Dic3 | — | 2 | 2 | no | — |
| 168 | C3×#120 | — | 9 | 1 | no | — |
| 169 | C3×#120 | — | 9 | 2 | no | — |
| 170 | #953 | — | 3 | 2 | no | — |
| 171 | #953 | — | 9 | 2 | no | — |
| 172 | #953 | — | 9 | 2 | no | — |
| 173 | #953 | — | 18 | 1 | no | — |
| 174 | #937 | — | 3 | 2 | no | — |
| 175 | #937 | — | 3 | 2 | no | — |
| 176 | #937 | — | 9 | 2 | no | — |
| 177 | #937 | — | 9 | 2 | no | — |
| 178 | #937 | — | 9 | 1 | no | — |
| 179 | #936 | — | 9 | 1 | no | — |
| 180 | #936 | — | 9 | 2 | no | — |
| 181 | #936 | — | 9 | 2 | no | — |
| 182 | #936 | — | 9 | 2 | no | — |
| 183 | #936 | — | 9 | 2 | no | — |
| 184 | #936 | — | 18 | 2 | no | — |
| 185 | #885 | — | 9 | 2 | no | — |
| 186 | #885 | — | 9 | 2 | no | — |
| 187 | #885 | — | 9 | 2 | no | — |
| 188 | #885 | — | 9 | 2 | no | — |
| 189 | #885 | — | 9 | 2 | no | — |
| 190 | #885 | — | 9 | 2 | no | — |
| 191 | #885 | — | 9 | 2 | no | — |
| 192 | #885 | — | 9 | 2 | no | — |
| 193 | #885 | — | 9 | 2 | no | — |
| 194 | C23×C32 | — | 2 | 1 | no | — |
| 195 | C23×C32 | — | 2 | 2 | no | — |
| 196 | C23×C32 | — | 3 | 2 | no | — |
| 197 | C23×C32 | — | 3 | 2 | no | — |
| 198 | C23×C32 | — | 4 | 1 | no | — |
| 199 | C23×C32 | — | 12 | 1 | no | — |
| 200 | C23×C32 | — | 12 | 2 | no | — |
| 201 | C23×C32 | C22×D3 | 1 | 2 | yes | — |
| 202 | C23×C32 | C22×D3 | 1 | 1 | yes | characteristic |
| 203 | C22×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 204 | C22×C3×D3 | — | 2 | 2 | no | — |
| 205 | C22×C3×D3 | — | 2 | 2 | no | — |
| 206 | C22×C3×D3 | — | 3 | 2 | no | — |
| 207 | C22×C3×D3 | — | 4 | 2 | no | — |
| 208 | C22×C3×D3 | — | 4 | 2 | no | — |
| 209 | C22×C3×D3 | — | 4 | 2 | no | — |
| 210 | C22×C3×D3 | — | 4 | 4 | no | — |
| 211 | C22×C3×D3 | — | 4 | 2 | no | — |
| 212 | C22×C3×D3 | — | 6 | 1 | no | — |
| 213 | C22×C3×D3 | — | 12 | 2 | no | — |
| 214 | C22×C3×D3 | — | 12 | 2 | no | — |
| 215 | C22×C3×D3 | — | 12 | 2 | no | — |
| 216 | C22×C3×D3 | C22×D3 | 1 | 2 | yes | — |
| 217 | C22×C3×D3 | C22×D3 | 1 | 2 | yes | — |
| 218 | C22×C3×D3 | C22×D3 | 1 | 2 | yes | — |
| 219 | C22×C3×D3 | C22×D3 | 1 | 2 | yes | — |
| 220 | C2×D32 | — | 4 | 2 | no | — |
| 221 | C2×D32 | — | 4 | 1 | no | — |
| 222 | C32×D4 | — | 12 | 2 | no | — |
| 223 | C2×C32×C4 | — | 3 | 2 | no | — |
| 224 | #638 | — | 4 | 1 | no | — |
| 225 | #638 | — | 12 | 2 | no | — |
| 226 | C2×C3⋊Dic3 | — | 3 | 2 | no | — |
| 227 | C2×C3⋊Dic3 | — | 3 | 2 | no | — |
| 228 | C2×C3⋊Dic3 | — | 3 | 2 | no | — |
| 229 | C2×C3⋊Dic3 | — | 6 | 2 | no | — |
| 230 | C2×C3⋊Dic3 | — | 6 | 2 | no | — |
| 231 | C2×C3⋊Dic3 | — | 6 | 2 | no | — |
| 232 | C2×C3⋊Dic3 | — | 12 | 2 | no | — |
| 233 | C2×C3⋊Dic3 | C22×D3 | 1 | 2 | yes | — |
| 234 | C2×C3⋊Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 235 | C2×C3⋊Dic3 | C22×D3 | 1 | 2 | yes | — |
| 236 | #634 | — | 12 | 2 | no | — |
| 237 | C3×#67 | — | 4 | 2 | no | — |
| 238 | C3×#67 | — | 4 | 2 | no | — |
| 239 | C3×#67 | — | 4 | 4 | no | — |
| 240 | C3×#67 | — | 12 | 2 | no | — |
| 241 | C3×#67 | — | 12 | 2 | no | — |
| 242 | C3×#67 | — | 12 | 2 | no | — |
| 243 | C3×#67 | — | 12 | 2 | no | — |
| 244 | C3×#67 | — | 12 | 2 | no | — |
| 245 | C3×#67 | — | 12 | 2 | no | — |
| 246 | C2×C3×Dic3 | — | 2 | 2 | no | — |
| 247 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 248 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 249 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 250 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 251 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 252 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 253 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 254 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 255 | C2×C3×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 256 | C2×C3×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 257 | #627 | — | 12 | 2 | no | — |
| 258 | #627 | — | 12 | 2 | no | — |
| 259 | #627 | — | 12 | 4 | no | — |
| 260 | #627 | — | 12 | 2 | no | — |
| 261 | #627 | — | 12 | 1 | no | — |
| 262 | #625 | — | 4 | 2 | no | — |
| 263 | #625 | — | 4 | 2 | no | — |
| 264 | #625 | — | 12 | 2 | no | — |
| 265 | #625 | — | 12 | 2 | no | — |
| 266 | #625 | — | 12 | 4 | no | — |
| 267 | H(3,𝔽4) | — | 27 | 1 | no | Sylow |
| 268 | C2×C33 | — | 4 | 1 | no | — |
| 269 | C2×C33 | H(5,𝔽2) | 1 | 2 | yes | — |
| 270 | C2×C33 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 271 | C3×C3⋊D3 | — | 4 | 1 | no | — |
| 272 | C32×D3 | — | 4 | 2 | no | — |
| 273 | C32×D3 | — | 4 | 2 | no | — |
| 274 | C24×C3 | — | 3 | 2 | no | — |
| 275 | C24×C3 | — | 6 | 1 | no | — |
| 276 | C24×C3 | — | 9 | 1 | no | — |
| 277 | C23×D3 | — | 3 | 2 | no | — |
| 278 | C23×D3 | D32 | 1 | 1 | yes | characteristic, complemented |
| 279 | C2×C3×D4 | — | 3 | 2 | no | — |
| 280 | C2×C3×D4 | — | 3 | 2 | no | — |
| 281 | C2×C3×D4 | — | 6 | 2 | no | — |
| 282 | C2×C3×D4 | — | 9 | 2 | no | — |
| 283 | C2×C3×D4 | — | 9 | 2 | no | — |
| 284 | C2×C3×D4 | — | 9 | 1 | no | — |
| 285 | C2×#67 | — | 3 | 2 | no | — |
| 286 | C2×#67 | — | 3 | 2 | no | — |
| 287 | C2×#67 | — | 3 | 2 | no | — |
| 288 | C2×#67 | — | 3 | 2 | no | — |
| 289 | C2×#67 | — | 3 | 2 | no | — |
| 290 | C2×#67 | — | 6 | 1 | no | — |
| 291 | C2×#67 | — | 9 | 2 | no | — |
| 292 | C2×#67 | — | 9 | 2 | no | — |
| 293 | C2×#67 | — | 9 | 2 | no | — |
| 294 | C2×#67 | — | 18 | 2 | no | — |
| 295 | C2×#67 | D32 | 1 | 2 | yes | — |
| 296 | C2×Dic6 | — | 9 | 1 | no | — |
| 297 | C2×Dic6 | — | 9 | 2 | no | — |
| 298 | C2×Dic6 | — | 9 | 2 | no | — |
| 299 | C2×Dic6 | — | 9 | 2 | no | — |
| 300 | C2×Dic6 | — | 9 | 2 | no | — |
| 301 | C2×Dic6 | — | 18 | 2 | no | — |
| 302 | C3×C22⋊C4 | — | 9 | 1 | no | — |
| 303 | C3×C22⋊C4 | — | 9 | 2 | no | — |
| 304 | C3×C22⋊C4 | — | 9 | 2 | no | — |
| 305 | C3×C22⋊C4 | — | 9 | 2 | no | — |
| 306 | C3×C22⋊C4 | — | 9 | 2 | no | — |
| 307 | #217 | — | 3 | 2 | no | — |
| 308 | #217 | — | 3 | 2 | no | — |
| 309 | #217 | — | 3 | 2 | no | — |
| 310 | #217 | — | 3 | 2 | no | — |
| 311 | #217 | — | 3 | 2 | no | — |
| 312 | #217 | — | 6 | 2 | no | — |
| 313 | #217 | — | 9 | 2 | no | — |
| 314 | #217 | — | 9 | 2 | no | — |
| 315 | #217 | — | 9 | 2 | no | — |
| 316 | #217 | — | 9 | 2 | no | — |
| 317 | #217 | — | 9 | 2 | no | — |
| 318 | #217 | — | 9 | 2 | no | — |
| 319 | #217 | — | 9 | 2 | no | — |
| 320 | #217 | — | 9 | 2 | no | — |
| 321 | #217 | — | 9 | 1 | no | — |
| 322 | #217 | — | 18 | 2 | no | — |
| 323 | #217 | — | 18 | 2 | no | — |
| 324 | #217 | — | 18 | 2 | no | — |
| 325 | #217 | — | 18 | 2 | no | — |
| 326 | #217 | — | 18 | 1 | no | — |
| 327 | #217 | — | 36 | 1 | no | — |
| 328 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 329 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 330 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 331 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 332 | (C2×D3)⋊C4 | — | 9 | 2 | no | — |
| 333 | (C2×D3)⋊C4 | — | 9 | 2 | no | — |
| 334 | (C2×D3)⋊C4 | — | 9 | 2 | no | — |
| 335 | (C2×D3)⋊C4 | — | 9 | 2 | no | — |
| 336 | (C2×D3)⋊C4 | — | 9 | 2 | no | — |
| 337 | C4×Dic3 | — | 9 | 1 | no | — |
| 338 | C4×Dic3 | — | 9 | 2 | no | — |
| 339 | C4×Dic3 | — | 9 | 2 | no | — |
| 340 | C4×Dic3 | — | 9 | 2 | no | — |
| 341 | C4×Dic3 | — | 9 | 2 | no | — |
| 342 | C4×Dic3 | — | 18 | 2 | no | — |
| 343 | C22×C32 | — | 2 | 1 | no | — |
| 344 | C22×C32 | — | 2 | 2 | no | — |
| 345 | C22×C32 | — | 2 | 2 | no | — |
| 346 | C22×C32 | — | 2 | 2 | no | — |
| 347 | C22×C32 | — | 2 | 2 | no | — |
| 348 | C22×C32 | — | 2 | 2 | no | — |
| 349 | C22×C32 | — | 2 | 2 | no | — |
| 350 | C22×C32 | — | 2 | 1 | no | — |
| 351 | C22×C32 | — | 4 | 1 | no | — |
| 352 | C22×C32 | — | 4 | 2 | no | — |
| 353 | C22×C32 | — | 4 | 2 | no | — |
| 354 | C22×C32 | — | 4 | 2 | no | — |
| 355 | C22×C32 | — | 4 | 2 | no | — |
| 356 | C22×C32 | — | 4 | 2 | no | — |
| 357 | C22×C32 | — | 6 | 2 | no | — |
| 358 | C22×C32 | — | 6 | 2 | no | — |
| 359 | C22×C32 | — | 6 | 2 | no | — |
| 360 | C22×C32 | — | 6 | 2 | no | — |
| 361 | C22×C32 | — | 6 | 2 | no | — |
| 362 | C22×C32 | — | 6 | 2 | no | — |
| 363 | C22×C32 | — | 8 | 2 | no | — |
| 364 | C22×C32 | — | 12 | 4 | no | — |
| 365 | C22×C32 | C23×D3 | 1 | 1 | yes | characteristic |
| 366 | C22×C32 | C23×D3 | 1 | 2 | yes | — |
| 367 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 368 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 369 | C2×C3×D3 | — | 2 | 4 | no | — |
| 370 | C2×C3×D3 | — | 2 | 2 | no | — |
| 371 | C2×C3×D3 | — | 2 | 2 | no | — |
| 372 | C2×C3×D3 | — | 2 | 2 | no | — |
| 373 | C2×C3×D3 | — | 2 | 2 | no | — |
| 374 | C2×C3×D3 | — | 2 | 2 | no | — |
| 375 | C2×C3×D3 | — | 2 | 2 | no | — |
| 376 | C2×C3×D3 | — | 2 | 2 | no | — |
| 377 | C2×C3×D3 | — | 2 | 2 | no | — |
| 378 | C2×C3×D3 | — | 2 | 2 | no | — |
| 379 | C2×C3×D3 | — | 2 | 2 | no | — |
| 380 | C2×C3×D3 | — | 2 | 2 | no | — |
| 381 | C2×C3×D3 | — | 2 | 2 | no | — |
| 382 | C2×C3×D3 | — | 4 | 2 | no | — |
| 383 | C2×C3×D3 | — | 4 | 2 | no | — |
| 384 | C2×C3×D3 | — | 4 | 2 | no | — |
| 385 | C2×C3×D3 | — | 4 | 2 | no | — |
| 386 | C2×C3×D3 | — | 4 | 2 | no | — |
| 387 | C2×C3×D3 | — | 4 | 8 | no | — |
| 388 | C2×C3×D3 | — | 4 | 8 | no | — |
| 389 | C2×C3×D3 | — | 6 | 2 | no | — |
| 390 | C2×C3×D3 | — | 6 | 2 | no | — |
| 391 | C2×C3×D3 | — | 6 | 2 | no | — |
| 392 | C2×C3×D3 | — | 12 | 2 | no | — |
| 393 | C2×C3×D3 | — | 12 | 1 | no | — |
| 394 | C2×C3×D3 | — | 12 | 8 | no | — |
| 395 | D32 | — | 4 | 4 | no | — |
| 396 | C32×C4 | — | 6 | 2 | no | — |
| 397 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 398 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 399 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 400 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 401 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 402 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 403 | C3⋊Dic3 | — | 12 | 2 | no | — |
| 404 | C3⋊Dic3 | — | 12 | 2 | no | — |
| 405 | C3⋊Dic3 | — | 12 | 2 | no | — |
| 406 | C3⋊Dic3 | — | 24 | 2 | no | — |
| 407 | C3×Dic3 | — | 2 | 4 | no | — |
| 408 | C3×Dic3 | — | 2 | 2 | no | — |
| 409 | C3×Dic3 | — | 2 | 2 | no | — |
| 410 | C3×Dic3 | — | 6 | 2 | no | — |
| 411 | C3×Dic3 | — | 6 | 2 | no | — |
| 412 | C3×Dic3 | — | 6 | 2 | no | — |
| 413 | C3×Dic3 | — | 6 | 2 | no | — |
| 414 | C3×Dic3 | — | 6 | 2 | no | — |
| 415 | C3×Dic3 | — | 12 | 2 | no | — |
| 416 | C3×Dic3 | — | 12 | 2 | no | — |
| 417 | C3×Dic3 | — | 12 | 1 | no | — |
| 418 | #124 | — | 27 | 2 | no | — |
| 419 | #124 | — | 27 | 2 | no | — |
| 420 | #124 | — | 27 | 2 | no | — |
| 421 | #124 | — | 27 | 1 | no | — |
| 422 | #124 | — | 27 | 2 | no | — |
| 423 | #120 | — | 9 | 1 | no | — |
| 424 | #120 | — | 9 | 2 | no | — |
| 425 | #120 | — | 27 | 2 | no | — |
| 426 | #120 | — | 27 | 1 | no | — |
| 427 | C33 | H(3,𝔽4) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 428 | C23×C3 | — | 2 | 1 | no | — |
| 429 | C23×C3 | — | 2 | 2 | no | — |
| 430 | C23×C3 | — | 3 | 2 | no | — |
| 431 | C23×C3 | — | 3 | 2 | no | — |
| 432 | C23×C3 | — | 3 | 2 | no | — |
| 433 | C23×C3 | — | 3 | 2 | no | — |
| 434 | C23×C3 | — | 4 | 1 | no | — |
| 435 | C23×C3 | — | 6 | 2 | no | — |
| 436 | C23×C3 | — | 6 | 2 | no | — |
| 437 | C23×C3 | — | 9 | 1 | no | — |
| 438 | C23×C3 | — | 12 | 2 | no | — |
| 439 | C23×C3 | — | 12 | 2 | no | — |
| 440 | C23×C3 | — | 12 | 2 | no | — |
| 441 | C23×C3 | — | 12 | 2 | no | — |
| 442 | C23×C3 | — | 12 | 4 | no | — |
| 443 | C23×C3 | — | 36 | 1 | no | — |
| 444 | C23×C3 | — | 36 | 2 | no | — |
| 445 | C23×C3 | C2×D32 | 1 | 1 | yes | characteristic |
| 446 | C23×C3 | C2×D32 | 1 | 2 | yes | — |
| 447 | C22×D3 | — | 3 | 2 | no | — |
| 448 | C22×D3 | — | 4 | 1 | no | — |
| 449 | C22×D3 | — | 4 | 2 | no | — |
| 450 | C22×D3 | — | 6 | 1 | no | — |
| 451 | C22×D3 | — | 12 | 2 | no | — |
| 452 | C22×D3 | — | 12 | 2 | no | — |
| 453 | C22×D3 | — | 12 | 2 | no | — |
| 454 | C22×D3 | C2×D32 | 1 | 2 | yes | — |
| 455 | C22×D3 | C2×D32 | 1 | 2 | yes | — |
| 456 | C3×D4 | — | 12 | 2 | no | — |
| 457 | C3×D4 | — | 12 | 2 | no | — |
| 458 | C3×D4 | — | 12 | 4 | no | — |
| 459 | C3×D4 | — | 36 | 1 | no | — |
| 460 | C3×D4 | — | 36 | 2 | no | — |
| 461 | C3×D4 | — | 36 | 2 | no | — |
| 462 | C2×C3×C4 | — | 3 | 2 | no | — |
| 463 | C2×C3×C4 | — | 3 | 2 | no | — |
| 464 | C2×C3×C4 | — | 6 | 2 | no | — |
| 465 | C2×C3×C4 | — | 9 | 2 | no | — |
| 466 | C2×C3×C4 | — | 9 | 2 | no | — |
| 467 | C2×C3×C4 | — | 9 | 1 | no | — |
| 468 | #67 | — | 4 | 2 | no | — |
| 469 | #67 | — | 12 | 2 | no | — |
| 470 | #67 | — | 12 | 2 | no | — |
| 471 | #67 | — | 12 | 2 | no | — |
| 472 | #67 | — | 12 | 2 | no | — |
| 473 | #67 | — | 12 | 2 | no | — |
| 474 | #67 | — | 12 | 2 | no | — |
| 475 | #67 | — | 36 | 2 | no | — |
| 476 | #67 | — | 36 | 2 | no | — |
| 477 | #67 | — | 36 | 2 | no | — |
| 478 | #67 | — | 36 | 4 | no | — |
| 479 | C2×Dic3 | — | 3 | 2 | no | — |
| 480 | C2×Dic3 | — | 3 | 2 | no | — |
| 481 | C2×Dic3 | — | 3 | 2 | no | — |
| 482 | C2×Dic3 | — | 3 | 2 | no | — |
| 483 | C2×Dic3 | — | 3 | 2 | no | — |
| 484 | C2×Dic3 | — | 6 | 2 | no | — |
| 485 | C2×Dic3 | — | 6 | 2 | no | — |
| 486 | C2×Dic3 | — | 6 | 1 | no | — |
| 487 | C2×Dic3 | — | 9 | 2 | no | — |
| 488 | C2×Dic3 | — | 9 | 2 | no | — |
| 489 | C2×Dic3 | — | 9 | 2 | no | — |
| 490 | C2×Dic3 | — | 18 | 2 | no | — |
| 491 | C2×Dic3 | — | 18 | 2 | no | — |
| 492 | C2×Dic3 | — | 18 | 2 | no | — |
| 493 | C2×Dic3 | — | 36 | 2 | no | — |
| 494 | C2×Dic3 | C2×D32 | 1 | 2 | yes | — |
| 495 | Dic6 | — | 36 | 2 | no | — |
| 496 | Dic6 | — | 36 | 2 | no | — |
| 497 | Dic6 | — | 36 | 1 | no | — |
| 498 | Dic6 | — | 36 | 2 | no | — |
| 499 | Dic6 | — | 36 | 2 | no | — |
| 500 | Dic6 | — | 36 | 4 | no | — |
| 501 | C2×C32 | — | 2 | 2 | no | — |
| 502 | C2×C32 | — | 2 | 2 | no | — |
| 503 | C2×C32 | — | 2 | 2 | no | — |
| 504 | C2×C32 | — | 2 | 1 | no | — |
| 505 | C2×C32 | — | 2 | 2 | no | — |
| 506 | C2×C32 | — | 4 | 2 | no | — |
| 507 | C2×C32 | — | 4 | 1 | no | — |
| 508 | C2×C32 | — | 4 | 1 | no | — |
| 509 | C2×C32 | — | 4 | 2 | no | — |
| 510 | C2×C32 | — | 4 | 2 | no | — |
| 511 | C2×C32 | — | 8 | 2 | no | — |
| 512 | C2×C32 | — | 8 | 2 | no | — |
| 513 | C2×C32 | — | 12 | 2 | no | — |
| 514 | C2×C32 | — | 12 | 2 | no | — |
| 515 | C2×C32 | #1004 | 1 | 1 | yes | characteristic |
| 516 | C2×C32 | #1004 | 1 | 2 | yes | — |
| 517 | C2×C32 | #1004 | 1 | 2 | yes | — |
| 518 | C2×C32 | #1004 | 1 | 2 | yes | — |
| 519 | C2×C32 | #1004 | 1 | 2 | yes | — |
| 520 | C3⋊D3 | — | 4 | 1 | no | — |
| 521 | C3×D3 | — | 4 | 4 | no | — |
| 522 | C3×D3 | — | 4 | 2 | no | — |
| 523 | C3×D3 | — | 4 | 2 | no | — |
| 524 | C3×D3 | — | 4 | 2 | no | — |
| 525 | C3×D3 | — | 4 | 2 | no | — |
| 526 | C3×D3 | — | 8 | 2 | no | — |
| 527 | C3×D3 | — | 12 | 2 | no | — |
| 528 | C3×D3 | — | 24 | 1 | no | — |
| 529 | C24 | — | 3 | 1 | no | — |
| 530 | C24 | — | 9 | 1 | no | — |
| 531 | C2×Q8 | — | 27 | 2 | no | — |
| 532 | C2×Q8 | — | 27 | 1 | no | — |
| 533 | C2×D4 | — | 3 | 2 | no | — |
| 534 | C2×D4 | — | 9 | 2 | no | — |
| 535 | C2×D4 | — | 9 | 2 | no | — |
| 536 | C2×D4 | — | 9 | 1 | no | — |
| 537 | C2×D4 | — | 27 | 2 | no | — |
| 538 | C22⋊C4 | — | 9 | 1 | no | — |
| 539 | C22⋊C4 | — | 9 | 2 | no | — |
| 540 | C22⋊C4 | — | 9 | 2 | no | — |
| 541 | C22⋊C4 | — | 9 | 2 | no | — |
| 542 | C22⋊C4 | — | 9 | 2 | no | — |
| 543 | C22⋊C4 | — | 27 | 2 | no | — |
| 544 | C22⋊C4 | — | 27 | 2 | no | — |
| 545 | C22⋊C4 | — | 27 | 2 | no | — |
| 546 | C22⋊C4 | — | 27 | 2 | no | — |
| 547 | C22⋊C4 | — | 27 | 1 | no | — |
| 548 | C42 | — | 27 | 2 | no | — |
| 549 | C42 | — | 27 | 1 | no | — |
| 550 | C22×C3 | — | 2 | 2 | no | — |
| 551 | C22×C3 | — | 2 | 2 | no | — |
| 552 | C22×C3 | — | 2 | 2 | no | — |
| 553 | C22×C3 | — | 2 | 2 | no | — |
| 554 | C22×C3 | — | 2 | 2 | no | — |
| 555 | C22×C3 | — | 2 | 1 | no | — |
| 556 | C22×C3 | — | 2 | 2 | no | — |
| 557 | C22×C3 | — | 2 | 1 | no | — |
| 558 | C22×C3 | — | 4 | 2 | no | — |
| 559 | C22×C3 | — | 4 | 2 | no | — |
| 560 | C22×C3 | — | 4 | 2 | no | — |
| 561 | C22×C3 | — | 4 | 2 | no | — |
| 562 | C22×C3 | — | 4 | 2 | no | — |
| 563 | C22×C3 | — | 4 | 1 | no | — |
| 564 | C22×C3 | — | 6 | 4 | no | — |
| 565 | C22×C3 | — | 6 | 2 | no | — |
| 566 | C22×C3 | — | 6 | 2 | no | — |
| 567 | C22×C3 | — | 6 | 2 | no | — |
| 568 | C22×C3 | — | 6 | 2 | no | — |
| 569 | C22×C3 | — | 6 | 2 | no | — |
| 570 | C22×C3 | — | 6 | 2 | no | — |
| 571 | C22×C3 | — | 6 | 2 | no | — |
| 572 | C22×C3 | — | 6 | 2 | no | — |
| 573 | C22×C3 | — | 6 | 2 | no | — |
| 574 | C22×C3 | — | 6 | 2 | no | — |
| 575 | C22×C3 | — | 6 | 2 | no | — |
| 576 | C22×C3 | — | 6 | 2 | no | — |
| 577 | C22×C3 | — | 8 | 2 | no | — |
| 578 | C22×C3 | — | 12 | 2 | no | — |
| 579 | C22×C3 | — | 12 | 2 | no | — |
| 580 | C22×C3 | — | 12 | 2 | no | — |
| 581 | C22×C3 | — | 12 | 2 | no | — |
| 582 | C22×C3 | — | 12 | 2 | no | — |
| 583 | C22×C3 | — | 12 | 8 | no | — |
| 584 | C22×C3 | — | 12 | 8 | no | — |
| 585 | C22×C3 | — | 18 | 2 | no | — |
| 586 | C22×C3 | — | 18 | 1 | no | — |
| 587 | C22×C3 | — | 36 | 4 | no | — |
| 588 | C22×C3 | C22×D32 | 1 | 2 | yes | — |
| 589 | C22×C3 | C22×D32 | 1 | 1 | yes | characteristic |
| 590 | C2×D3 | — | 2 | 2 | no | — |
| 591 | C2×D3 | — | 2 | 2 | no | — |
| 592 | C2×D3 | — | 2 | 2 | no | — |
| 593 | C2×D3 | — | 2 | 2 | no | — |
| 594 | C2×D3 | — | 2 | 2 | no | — |
| 595 | C2×D3 | — | 2 | 2 | no | — |
| 596 | C2×D3 | — | 4 | 4 | no | — |
| 597 | C2×D3 | — | 6 | 2 | no | — |
| 598 | C2×D3 | — | 6 | 2 | no | — |
| 599 | C2×D3 | — | 6 | 2 | no | — |
| 600 | C2×D3 | — | 12 | 1 | no | — |
| 601 | C2×D3 | — | 12 | 2 | no | — |
| 602 | C2×D3 | — | 12 | 8 | no | — |
| 603 | C3×C4 | — | 6 | 4 | no | — |
| 604 | C3×C4 | — | 6 | 2 | no | — |
| 605 | C3×C4 | — | 6 | 2 | no | — |
| 606 | C3×C4 | — | 18 | 2 | no | — |
| 607 | C3×C4 | — | 18 | 2 | no | — |
| 608 | C3×C4 | — | 18 | 1 | no | — |
| 609 | Dic3 | — | 2 | 2 | no | — |
| 610 | Dic3 | — | 6 | 2 | no | — |
| 611 | Dic3 | — | 6 | 2 | no | — |
| 612 | Dic3 | — | 6 | 2 | no | — |
| 613 | Dic3 | — | 6 | 2 | no | — |
| 614 | Dic3 | — | 6 | 2 | no | — |
| 615 | Dic3 | — | 12 | 2 | no | — |
| 616 | Dic3 | — | 12 | 1 | no | — |
| 617 | Dic3 | — | 12 | 2 | no | — |
| 618 | Dic3 | — | 18 | 2 | no | — |
| 619 | Dic3 | — | 18 | 2 | no | — |
| 620 | Dic3 | — | 18 | 2 | no | — |
| 621 | Dic3 | — | 36 | 2 | no | — |
| 622 | Dic3 | — | 36 | 2 | no | — |
| 623 | Dic3 | — | 36 | 2 | no | — |
| 624 | Dic3 | — | 72 | 2 | no | — |
| 625 | C32 | — | 2 | 2 | no | — |
| 626 | C32 | — | 2 | 1 | no | — |
| 627 | C32 | — | 4 | 1 | no | — |
| 628 | C32 | #5594 | 1 | 1 | yes | characteristic, complemented |
| 629 | C32 | #5594 | 1 | 2 | yes | complemented |
| 630 | C23 | — | 3 | 2 | no | — |
| 631 | C23 | — | 3 | 2 | no | — |
| 632 | C23 | — | 9 | 1 | no | — |
| 633 | C23 | — | 12 | 2 | no | — |
| 634 | C23 | — | 12 | 1 | no | — |
| 635 | C23 | — | 36 | 2 | no | — |
| 636 | C23 | — | 36 | 1 | no | — |
| 637 | C23 | D33 | 1 | 1 | yes | characteristic |
| 638 | Q8 | — | 108 | 2 | no | — |
| 639 | Q8 | — | 108 | 1 | no | — |
| 640 | D4 | — | 12 | 2 | no | — |
| 641 | D4 | — | 36 | 1 | no | — |
| 642 | D4 | — | 36 | 2 | no | — |
| 643 | D4 | — | 36 | 2 | no | — |
| 644 | D4 | — | 108 | 2 | no | — |
| 645 | C2×C4 | — | 3 | 2 | no | — |
| 646 | C2×C4 | — | 9 | 2 | no | — |
| 647 | C2×C4 | — | 9 | 2 | no | — |
| 648 | C2×C4 | — | 9 | 1 | no | — |
| 649 | C2×C4 | — | 27 | 2 | no | — |
| 650 | C2×C3 | — | 2 | 2 | no | — |
| 651 | C2×C3 | — | 2 | 2 | no | — |
| 652 | C2×C3 | — | 2 | 2 | no | — |
| 653 | C2×C3 | — | 2 | 1 | no | — |
| 654 | C2×C3 | — | 2 | 2 | no | — |
| 655 | C2×C3 | — | 4 | 2 | no | — |
| 656 | C2×C3 | — | 4 | 2 | no | — |
| 657 | C2×C3 | — | 4 | 1 | no | — |
| 658 | C2×C3 | — | 4 | 2 | no | — |
| 659 | C2×C3 | — | 4 | 1 | no | — |
| 660 | C2×C3 | — | 8 | 2 | no | — |
| 661 | C2×C3 | — | 8 | 2 | no | — |
| 662 | C2×C3 | — | 12 | 4 | no | — |
| 663 | C2×C3 | — | 12 | 2 | no | — |
| 664 | C2×C3 | — | 12 | 2 | no | — |
| 665 | C2×C3 | — | 12 | 2 | no | — |
| 666 | C2×C3 | — | 12 | 2 | no | — |
| 667 | C2×C3 | — | 24 | 2 | no | — |
| 668 | C2×C3 | — | 36 | 1 | no | — |
| 669 | C2×C3 | #64313 | 1 | 2 | yes | — |
| 670 | C2×C3 | #64313 | 1 | 2 | yes | — |
| 671 | C2×C3 | #64330 | 1 | 2 | yes | — |
| 672 | C2×C3 | #64330 | 1 | 2 | yes | — |
| 673 | C2×C3 | #64330 | 1 | 1 | yes | characteristic |
| 674 | D3 | — | 4 | 2 | no | — |
| 675 | D3 | — | 4 | 2 | no | — |
| 676 | D3 | — | 12 | 2 | no | — |
| 677 | D3 | — | 24 | 1 | no | — |
| 678 | C22 | — | 2 | 2 | no | — |
| 679 | C22 | — | 2 | 1 | no | — |
| 680 | C22 | — | 6 | 2 | no | — |
| 681 | C22 | — | 6 | 2 | no | — |
| 682 | C22 | — | 6 | 2 | no | — |
| 683 | C22 | — | 6 | 2 | no | — |
| 684 | C22 | — | 6 | 2 | no | — |
| 685 | C22 | — | 6 | 2 | no | — |
| 686 | C22 | — | 12 | 4 | no | — |
| 687 | C22 | — | 18 | 2 | no | — |
| 688 | C22 | — | 18 | 1 | no | — |
| 689 | C22 | — | 36 | 4 | no | — |
| 690 | C22 | C2×D33 | 1 | 1 | yes | characteristic |
| 691 | C4 | — | 6 | 2 | no | — |
| 692 | C4 | — | 18 | 2 | no | — |
| 693 | C4 | — | 18 | 1 | no | — |
| 694 | C4 | — | 18 | 2 | no | — |
| 695 | C4 | — | 54 | 2 | no | — |
| 696 | C3 | — | 2 | 1 | no | — |
| 697 | C3 | — | 2 | 2 | no | — |
| 698 | C3 | — | 4 | 1 | no | — |
| 699 | C3 | #10595256 | 1 | 2 | yes | complemented |
| 700 | C3 | #10595529 | 1 | 1 | yes | characteristic, complemented |
| 701 | C2 | — | 4 | 1 | no | — |
| 702 | C2 | — | 12 | 2 | no | — |
| 703 | C2 | — | 12 | 2 | no | — |
| 704 | C2 | — | 36 | 1 | no | — |
| 705 | C2 | #11724414 | 1 | 2 | yes | — |
| 706 | C2 | #11724415 | 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 | H(3,𝔽4) |
| 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. #11723718 | C2 | semidirect |
| 2. #11723629 | C2 | semidirect |
| 3. #11723600 | C2 | semidirect |
| 4. C3×#63983 | C2 | semidirect |
| 5. C3×#63976 | C2 | semidirect |
| 6. #11723009 | C2 | semidirect |
| 7. #11723006 | C2 | semidirect |
| 8. #11723004 | C2 | semidirect |
| 9. #11722946 | C2 | semidirect |
| 12. C23×C32×D3 | C22 | semidirect |
| 13. C22×C3×D32 | C22 | semidirect |
| 16. C2×#6296 | C22 | semidirect |
| 17. C2×#6293 | C22 | semidirect |
| 21. #88864 | C22 | semidirect |
| 22. C3×#3757 | C22 | semidirect |
| 23. #88814 | C22 | semidirect |
| 24. #88813 | C22 | semidirect |
| 25. (C2×D3)⋊(C3⋊Dic3) | C22 | semidirect |
| 26. (C2×D3)⋊(C3⋊Dic3) | C22 | semidirect |
| 27. (C2×D3)⋊(C3⋊Dic3) | C22 | semidirect |
| 28. Dic3×C3⋊Dic3 | C22 | semidirect |
| 29. C3×#3722 | C22 | semidirect |
| 30. C3×(C2×D3)⋊Dic3 | C22 | semidirect |
| 31. C3×(C2×D3)⋊Dic3 | C22 | semidirect |
| 32. C3×(C2×D3)⋊Dic3 | C22 | semidirect |
| 39. #63983 | D3 | semidirect |
| 44. #63976 | D3 | semidirect |
| 84. C23×C3×D3 | C2×D3 | semidirect |
| 85. C22×D32 | C2×D3 | semidirect |
| 117. #3757 | C2×D3 | semidirect |
| 130. #3722 | C2×D3 | semidirect |
| 142. (C2×D3)⋊Dic3 | C2×D3 | semidirect |
| 143. (C2×D3)⋊Dic3 | C2×D3 | semidirect |
| 144. (C2×D3)⋊Dic3 | C2×D3 | semidirect |
| 278. C23×D3 | D32 | semidirect |
| 427. C33 | H(3,𝔽4) | semidirect |
| 628. C32 | #5594 | semidirect |
| 629. C32 | #5594 | semidirect |
| 699. C3 | #10595256 | semidirect |
| 700. C3 | #10595529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723718 | 2 |
| #11723629 | 2 |
| #11723600 | 2 |
| C3×#63983 | 2 |
| C3×#63976 | 2 |
| #11723009 | 2 |
| #11723006 | 2 |
| #11723004 | 2 |
| #11722946 | 2 |
| #10595529 | 3 |
| #10595256 | 3 |