Finite Group DatabasebetaFinite Group Databasebeta← C2×A4×((C3⋊D3)⋊C3)⋊C2 #72242881
Order 2592.
1446 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 1446 conjugacy classes of subgroups — too many to draw. Only its 90 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×A4×#272 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×A4×(C3⋊D3)⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | A4×((C3⋊D3)⋊C3)⋊C2 | C2 | 1 | 4 | yes | maximal, direct product factor |
| 4 | C2×D32×A4 | — | 3 | 2 | no | maximal |
| 5 | C23×((C3⋊D3)⋊C3)⋊C2 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×A4×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 7 | C2×C3×((C3⋊D3)⋊C3)⋊C2 | — | 4 | 1 | no | maximal |
| 8 | A4×#272 | C22 | 1 | 2 | yes | complemented |
| 9 | A4×(C3⋊D3)⋊C3 | C22 | 1 | 4 | yes | complemented |
| 10 | C2×A4×C3⋊D3 | D3 | 1 | 2 | yes | complemented |
| 11 | C2×C3×D3×A4 | — | 3 | 2 | no | — |
| 12 | C2×C3×D3×A4 | — | 3 | 2 | no | — |
| 13 | C2×C3×D3×A4 | — | 6 | 1 | no | — |
| 14 | D32×A4 | — | 3 | 8 | no | — |
| 15 | C23×#272 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 16 | C23×(C3⋊D3)⋊C3 | C2×C3 | 1 | 2 | yes | complemented |
| 17 | C22×((C3⋊D3)⋊C3)⋊C2 | — | 3 | 1 | no | — |
| 18 | C22×((C3⋊D3)⋊C3)⋊C2 | — | 3 | 1 | no | — |
| 19 | C22×((C3⋊D3)⋊C3)⋊C2 | — | 3 | 2 | no | — |
| 20 | C22×((C3⋊D3)⋊C3)⋊C2 | — | 3 | 4 | no | — |
| 21 | C22×((C3⋊D3)⋊C3)⋊C2 | C2×C3 | 1 | 4 | yes | complemented |
| 22 | C2×(C3⋊D3)⋊A4 | — | 2 | 2 | no | — |
| 23 | C2×C3×#272 | — | 4 | 1 | no | — |
| 24 | C2×C3×(C3⋊D3)⋊C3 | — | 4 | 2 | no | — |
| 25 | A4×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic, complemented |
| 26 | C3×((C3⋊D3)⋊C3)⋊C2 | — | 4 | 4 | no | — |
| 27 | C23×D32 | — | 3 | 2 | no | — |
| 28 | C22×D3×A4 | — | 9 | 1 | no | — |
| 29 | C22×D3×A4 | — | 9 | 2 | no | — |
| 30 | C2×C32×A4 | — | 2 | 1 | no | — |
| 31 | C2×C32×A4 | C2×D3 | 1 | 2 | yes | complemented |
| 32 | C2×C3×D32 | — | 12 | 2 | no | — |
| 33 | A4×C3⋊D3 | C2×D3 | 1 | 4 | yes | complemented |
| 34 | C3×D3×A4 | — | 3 | 4 | no | — |
| 35 | C3×D3×A4 | — | 3 | 4 | no | — |
| 36 | C3×D3×A4 | — | 6 | 2 | no | — |
| 37 | C23×H(3,𝔽3) | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 38 | C22×#272 | — | 3 | 1 | no | — |
| 39 | C22×#272 | — | 3 | 1 | no | — |
| 40 | C22×#272 | — | 3 | 2 | no | — |
| 41 | C22×#272 | C22×C3 | 1 | 2 | yes | complemented |
| 42 | C22×(C3⋊D3)⋊C3 | — | 3 | 2 | no | — |
| 43 | C22×(C3⋊D3)⋊C3 | — | 3 | 2 | no | — |
| 44 | C22×(C3⋊D3)⋊C3 | — | 3 | 4 | no | — |
| 45 | C22×(C3⋊D3)⋊C3 | C22×C3 | 1 | 4 | yes | complemented |
| 46 | C2×C22⋊H(3,𝔽3) | — | 2 | 2 | no | — |
| 47 | C2×C22⋊H(3,𝔽3) | — | 4 | 1 | no | — |
| 48 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 3 | 2 | no | — |
| 49 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 3 | 4 | no | — |
| 50 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 3 | 8 | no | — |
| 51 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 3 | 1 | no | — |
| 52 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 3 | 2 | no | — |
| 53 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 3 | 4 | no | — |
| 54 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 3 | 4 | no | — |
| 55 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 3 | 4 | no | — |
| 56 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 3 | 8 | no | — |
| 57 | C2×((C3⋊D3)⋊C3)⋊C2 | A4 | 1 | 1 | yes | characteristic, direct product factor |
| 58 | (C3⋊D3)⋊A4 | — | 2 | 4 | no | — |
| 59 | C2×C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 60 | C3×#272 | — | 4 | 2 | no | — |
| 61 | C3×(C3⋊D3)⋊C3 | — | 4 | 4 | no | — |
| 62 | C23×C3⋊D3 | C3×D3 | 1 | 2 | yes | complemented |
| 63 | C23×C3×D3 | — | 3 | 2 | no | — |
| 64 | C23×C3×D3 | — | 3 | 2 | no | — |
| 65 | C23×C3×D3 | — | 6 | 1 | no | — |
| 66 | C22×C3×A4 | — | 9 | 2 | no | — |
| 67 | C22×C3×A4 | — | 9 | 1 | no | — |
| 68 | C22×D32 | — | 3 | 8 | no | — |
| 69 | C22×D32 | — | 9 | 2 | no | — |
| 70 | C22×D32 | — | 9 | 8 | no | — |
| 71 | C22×D32 | — | 9 | 2 | no | — |
| 72 | C22×D32 | — | 9 | 2 | no | — |
| 73 | C22×D32 | — | 9 | 2 | no | — |
| 74 | C2×D3×A4 | — | 3 | 2 | no | — |
| 75 | C2×D3×A4 | — | 3 | 2 | no | — |
| 76 | C2×D3×A4 | — | 6 | 2 | no | — |
| 77 | C2×D3×A4 | — | 6 | 1 | no | — |
| 78 | C2×D3×A4 | — | 6 | 2 | no | — |
| 79 | C2×D3×A4 | — | 6 | 2 | no | — |
| 80 | C2×D3×A4 | — | 9 | 4 | no | — |
| 81 | C2×D3×A4 | — | 9 | 8 | no | — |
| 82 | C2×D3×A4 | — | 9 | 2 | no | — |
| 83 | C2×C3×C3⋊D3 | — | 4 | 2 | no | — |
| 84 | C2×C32×D3 | — | 12 | 2 | no | — |
| 85 | C2×C32×D3 | — | 12 | 2 | no | — |
| 86 | C2×C32×D3 | — | 24 | 1 | no | — |
| 87 | C32×A4 | — | 2 | 1 | no | — |
| 88 | C32×A4 | C22×D3 | 1 | 2 | yes | complemented |
| 89 | C3×D32 | — | 12 | 8 | no | — |
| 90 | C22×H(3,𝔽3) | — | 3 | 1 | no | — |
| 91 | C22×H(3,𝔽3) | — | 3 | 1 | no | — |
| 92 | C22×H(3,𝔽3) | C23×C3 | 1 | 1 | yes | characteristic, complemented |
| 93 | C2×#272 | — | 3 | 2 | no | — |
| 94 | C2×#272 | — | 3 | 1 | no | — |
| 95 | C2×#272 | — | 3 | 2 | no | — |
| 96 | C2×#272 | — | 3 | 2 | no | — |
| 97 | C2×#272 | — | 3 | 2 | no | — |
| 98 | C2×#272 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 99 | C2×(C3⋊D3)⋊C3 | — | 3 | 4 | no | — |
| 100 | C2×(C3⋊D3)⋊C3 | — | 3 | 2 | no | — |
| 101 | C2×(C3⋊D3)⋊C3 | — | 3 | 4 | no | — |
| 102 | C2×(C3⋊D3)⋊C3 | — | 3 | 4 | no | — |
| 103 | C2×(C3⋊D3)⋊C3 | — | 3 | 4 | no | — |
| 104 | C2×(C3⋊D3)⋊C3 | — | 8 | 2 | no | — |
| 105 | C2×(C3⋊D3)⋊C3 | C2×A4 | 1 | 2 | yes | complemented |
| 106 | C22⋊H(3,𝔽3) | — | 2 | 2 | no | — |
| 107 | C22⋊H(3,𝔽3) | — | 4 | 1 | no | — |
| 108 | ((C3⋊D3)⋊C3)⋊C2 | — | 3 | 8 | no | — |
| 109 | ((C3⋊D3)⋊C3)⋊C2 | — | 3 | 4 | no | — |
| 110 | ((C3⋊D3)⋊C3)⋊C2 | — | 3 | 8 | no | — |
| 111 | ((C3⋊D3)⋊C3)⋊C2 | C2×A4 | 1 | 4 | yes | direct product factor |
| 112 | C24×D3 | — | 9 | 1 | no | — |
| 113 | C24×D3 | — | 9 | 2 | no | — |
| 114 | C23×A4 | — | 27 | 1 | no | — |
| 115 | C3×H(3,𝔽3) | — | 4 | 1 | no | Sylow |
| 116 | C23×C32 | — | 2 | 1 | no | — |
| 117 | C23×C32 | C2×C3×D3 | 1 | 2 | yes | complemented |
| 118 | C22×C3⋊D3 | — | 3 | 2 | no | — |
| 119 | C22×C3⋊D3 | — | 3 | 2 | no | — |
| 120 | C22×C3⋊D3 | — | 3 | 4 | no | — |
| 121 | C22×C3⋊D3 | C2×C3×D3 | 1 | 4 | yes | complemented |
| 122 | C22×C3×D3 | — | 3 | 4 | no | — |
| 123 | C22×C3×D3 | — | 3 | 4 | no | — |
| 124 | C22×C3×D3 | — | 6 | 2 | no | — |
| 125 | C22×C3×D3 | — | 9 | 2 | no | — |
| 126 | C22×C3×D3 | — | 9 | 2 | no | — |
| 127 | C22×C3×D3 | — | 9 | 4 | no | — |
| 128 | C22×C3×D3 | — | 9 | 2 | no | — |
| 129 | C22×C3×D3 | — | 9 | 4 | no | — |
| 130 | C22×C3×D3 | — | 9 | 2 | no | — |
| 131 | C22×C3×D3 | — | 18 | 1 | no | — |
| 132 | C22×C3×D3 | — | 18 | 2 | no | — |
| 133 | C22×C3×D3 | — | 18 | 1 | no | — |
| 134 | C22×C3×D3 | — | 36 | 1 | no | — |
| 135 | C22×C3×D3 | — | 36 | 2 | no | — |
| 136 | C2×C3×A4 | — | 2 | 2 | no | — |
| 137 | C2×C3×A4 | — | 3 | 2 | no | — |
| 138 | C2×C3×A4 | — | 4 | 1 | no | — |
| 139 | C2×C3×A4 | — | 6 | 2 | no | — |
| 140 | C2×C3×A4 | — | 6 | 2 | no | — |
| 141 | C2×C3×A4 | — | 6 | 1 | no | — |
| 142 | C2×C3×A4 | — | 9 | 4 | no | — |
| 143 | C2×C3×A4 | — | 9 | 2 | no | — |
| 144 | C2×C3×A4 | D32 | 1 | 1 | yes | characteristic |
| 145 | C2×D32 | — | 3 | 2 | no | — |
| 146 | C2×D32 | — | 9 | 8 | no | — |
| 147 | C2×D32 | — | 9 | 8 | no | — |
| 148 | C2×D32 | — | 9 | 2 | no | — |
| 149 | C2×D32 | — | 9 | 2 | no | — |
| 150 | C2×D32 | — | 9 | 8 | no | — |
| 151 | C2×D32 | — | 9 | 8 | no | — |
| 152 | C2×D32 | — | 9 | 4 | no | — |
| 153 | C2×D32 | — | 9 | 8 | no | — |
| 154 | C2×D32 | — | 9 | 2 | no | — |
| 155 | C2×D32 | — | 9 | 8 | no | — |
| 156 | C2×D32 | — | 9 | 8 | no | — |
| 157 | C2×D32 | — | 9 | 8 | no | — |
| 158 | D3×A4 | — | 3 | 4 | no | — |
| 159 | D3×A4 | — | 3 | 4 | no | — |
| 160 | D3×A4 | — | 6 | 2 | no | — |
| 161 | D3×A4 | — | 6 | 4 | no | — |
| 162 | D3×A4 | — | 6 | 4 | no | — |
| 163 | D3×A4 | — | 6 | 4 | no | — |
| 164 | D3×A4 | — | 9 | 4 | no | — |
| 165 | C2×C33 | — | 4 | 2 | no | — |
| 166 | C2×C33 | — | 8 | 1 | no | — |
| 167 | C3×C3⋊D3 | — | 4 | 4 | no | — |
| 168 | C32×D3 | — | 12 | 4 | no | — |
| 169 | C32×D3 | — | 12 | 4 | no | — |
| 170 | C32×D3 | — | 24 | 2 | no | — |
| 171 | C2×H(3,𝔽3) | — | 3 | 1 | no | — |
| 172 | C2×H(3,𝔽3) | — | 3 | 1 | no | — |
| 173 | C2×H(3,𝔽3) | — | 8 | 2 | no | — |
| 174 | C2×H(3,𝔽3) | — | 16 | 1 | no | — |
| 175 | C2×H(3,𝔽3) | C22×A4 | 1 | 1 | yes | characteristic, complemented |
| 176 | #272 | — | 3 | 2 | no | — |
| 177 | #272 | C22×A4 | 1 | 2 | yes | complemented |
| 178 | (C3⋊D3)⋊C3 | — | 3 | 4 | no | — |
| 179 | (C3⋊D3)⋊C3 | — | 8 | 4 | no | — |
| 180 | (C3⋊D3)⋊C3 | C22×A4 | 1 | 4 | yes | complemented |
| 181 | C24×C3 | — | 9 | 2 | no | — |
| 182 | C24×C3 | — | 9 | 1 | no | — |
| 183 | C23×D3 | — | 3 | 2 | no | — |
| 184 | C23×D3 | — | 3 | 2 | no | — |
| 185 | C23×D3 | — | 6 | 1 | no | — |
| 186 | C23×D3 | — | 9 | 2 | no | — |
| 187 | C23×D3 | — | 9 | 4 | no | — |
| 188 | C23×D3 | — | 9 | 8 | no | — |
| 189 | C23×D3 | — | 27 | 1 | no | — |
| 190 | C23×D3 | — | 27 | 2 | no | — |
| 191 | C23×D3 | — | 27 | 2 | no | — |
| 192 | C23×D3 | — | 27 | 4 | no | — |
| 193 | C23×D3 | — | 27 | 1 | no | — |
| 194 | C23×D3 | — | 27 | 2 | no | — |
| 195 | C23×D3 | — | 27 | 2 | no | — |
| 196 | C23×D3 | — | 27 | 8 | no | — |
| 197 | C23×D3 | — | 27 | 2 | no | — |
| 198 | C22×A4 | — | 9 | 1 | no | — |
| 199 | C22×A4 | — | 9 | 2 | no | — |
| 200 | C22×A4 | — | 18 | 1 | no | — |
| 201 | C22×A4 | — | 18 | 2 | no | — |
| 202 | C22×A4 | — | 27 | 4 | no | — |
| 203 | C22×C32 | — | 2 | 1 | no | — |
| 204 | C22×C32 | — | 3 | 2 | no | — |
| 205 | C22×C32 | — | 3 | 2 | no | — |
| 206 | C22×C32 | — | 6 | 1 | no | — |
| 207 | C22×C32 | — | 6 | 1 | no | — |
| 208 | C22×C32 | — | 36 | 1 | no | — |
| 209 | C22×C32 | — | 36 | 2 | no | — |
| 210 | C22×C32 | C22×C3×D3 | 1 | 2 | yes | complemented |
| 211 | C2×C3⋊D3 | — | 3 | 4 | no | — |
| 212 | C2×C3⋊D3 | — | 3 | 2 | no | — |
| 213 | C2×C3⋊D3 | — | 3 | 4 | no | — |
| 214 | C2×C3⋊D3 | — | 3 | 4 | no | — |
| 215 | C2×C3⋊D3 | — | 3 | 4 | no | — |
| 216 | C2×C3⋊D3 | D3×A4 | 1 | 2 | yes | complemented |
| 217 | C2×C3×D3 | — | 3 | 2 | no | — |
| 218 | C2×C3×D3 | — | 3 | 2 | no | — |
| 219 | C2×C3×D3 | — | 6 | 1 | no | — |
| 220 | C2×C3×D3 | — | 9 | 4 | no | — |
| 221 | C2×C3×D3 | — | 9 | 4 | no | — |
| 222 | C2×C3×D3 | — | 9 | 4 | no | — |
| 223 | C2×C3×D3 | — | 9 | 4 | no | — |
| 224 | C2×C3×D3 | — | 9 | 4 | no | — |
| 225 | C2×C3×D3 | — | 9 | 4 | no | — |
| 226 | C2×C3×D3 | — | 9 | 2 | no | — |
| 227 | C2×C3×D3 | — | 9 | 2 | no | — |
| 228 | C2×C3×D3 | — | 9 | 4 | no | — |
| 229 | C2×C3×D3 | — | 9 | 4 | no | — |
| 230 | C2×C3×D3 | — | 12 | 2 | no | — |
| 231 | C2×C3×D3 | — | 12 | 2 | no | — |
| 232 | C2×C3×D3 | — | 18 | 2 | no | — |
| 233 | C2×C3×D3 | — | 18 | 2 | no | — |
| 234 | C2×C3×D3 | — | 18 | 1 | no | — |
| 235 | C2×C3×D3 | — | 18 | 2 | no | — |
| 236 | C2×C3×D3 | — | 18 | 2 | no | — |
| 237 | C2×C3×D3 | — | 24 | 2 | no | — |
| 238 | C2×C3×D3 | — | 24 | 2 | no | — |
| 239 | C2×C3×D3 | — | 24 | 1 | no | — |
| 240 | C2×C3×D3 | — | 24 | 2 | no | — |
| 241 | C2×C3×D3 | — | 36 | 2 | no | — |
| 242 | C2×C3×D3 | — | 36 | 4 | no | — |
| 243 | C2×C3×D3 | — | 36 | 8 | no | — |
| 244 | C3×A4 | — | 2 | 2 | no | — |
| 245 | C3×A4 | — | 3 | 2 | no | — |
| 246 | C3×A4 | — | 4 | 1 | no | — |
| 247 | C3×A4 | — | 6 | 2 | no | — |
| 248 | C3×A4 | — | 6 | 2 | no | — |
| 249 | C3×A4 | — | 6 | 1 | no | — |
| 250 | C3×A4 | C2×D32 | 1 | 1 | yes | characteristic |
| 251 | D32 | — | 3 | 8 | no | — |
| 252 | D32 | — | 9 | 8 | no | — |
| 253 | D32 | — | 9 | 8 | no | — |
| 254 | D32 | — | 9 | 16 | no | — |
| 255 | D32 | — | 9 | 8 | no | — |
| 256 | C25 | — | 27 | 1 | no | Sylow |
| 257 | C33 | — | 4 | 2 | no | — |
| 258 | C33 | — | 8 | 1 | no | — |
| 259 | H(3,𝔽3) | — | 8 | 2 | no | — |
| 260 | H(3,𝔽3) | — | 16 | 1 | no | — |
| 261 | H(3,𝔽3) | C23×A4 | 1 | 1 | yes | characteristic, complemented |
| 262 | C23×C3 | — | 3 | 2 | no | — |
| 263 | C23×C3 | — | 6 | 1 | no | — |
| 264 | C23×C3 | — | 9 | 4 | no | — |
| 265 | C23×C3 | — | 9 | 2 | no | — |
| 266 | C23×C3 | — | 27 | 1 | no | — |
| 267 | C23×C3 | — | 27 | 2 | no | — |
| 268 | C23×C3 | — | 27 | 1 | no | — |
| 269 | C23×C3 | — | 27 | 2 | no | — |
| 270 | C23×C3 | — | 27 | 2 | no | — |
| 271 | C23×C3 | — | 27 | 4 | no | — |
| 272 | C23×C3 | — | 108 | 1 | no | — |
| 273 | C23×C3 | C3×D32 | 1 | 1 | yes | characteristic |
| 274 | C22×D3 | — | 3 | 4 | no | — |
| 275 | C22×D3 | — | 3 | 4 | no | — |
| 276 | C22×D3 | — | 6 | 2 | no | — |
| 277 | C22×D3 | — | 9 | 4 | no | — |
| 278 | C22×D3 | — | 9 | 1 | no | — |
| 279 | C22×D3 | — | 9 | 2 | no | — |
| 280 | C22×D3 | — | 9 | 2 | no | — |
| 281 | C22×D3 | — | 9 | 2 | no | — |
| 282 | C22×D3 | — | 9 | 4 | no | — |
| 283 | C22×D3 | — | 9 | 2 | no | — |
| 284 | C22×D3 | — | 9 | 4 | no | — |
| 285 | C22×D3 | — | 9 | 2 | no | — |
| 286 | C22×D3 | — | 18 | 1 | no | — |
| 287 | C22×D3 | — | 18 | 2 | no | — |
| 288 | C22×D3 | — | 18 | 1 | no | — |
| 289 | C22×D3 | — | 27 | 2 | no | — |
| 290 | C22×D3 | — | 27 | 4 | no | — |
| 291 | C22×D3 | — | 27 | 2 | no | — |
| 292 | C22×D3 | — | 27 | 2 | no | — |
| 293 | C22×D3 | — | 27 | 2 | no | — |
| 294 | C22×D3 | — | 27 | 4 | no | — |
| 295 | C22×D3 | — | 27 | 4 | no | — |
| 296 | C22×D3 | — | 27 | 1 | no | — |
| 297 | C22×D3 | — | 27 | 8 | no | — |
| 298 | C22×D3 | — | 27 | 4 | no | — |
| 299 | C22×D3 | — | 27 | 2 | no | — |
| 300 | C22×D3 | — | 27 | 8 | no | — |
| 301 | C22×D3 | — | 27 | 2 | no | — |
| 302 | C22×D3 | — | 27 | 8 | no | — |
| 303 | C22×D3 | — | 27 | 8 | no | — |
| 304 | C22×D3 | — | 27 | 4 | no | — |
| 305 | C22×D3 | — | 27 | 2 | no | — |
| 306 | C22×D3 | — | 27 | 8 | no | — |
| 307 | C22×D3 | — | 27 | 4 | no | — |
| 308 | C22×D3 | — | 27 | 8 | no | — |
| 309 | C22×D3 | — | 27 | 8 | no | — |
| 310 | C22×D3 | — | 27 | 8 | no | — |
| 311 | C22×D3 | — | 27 | 8 | no | — |
| 312 | C22×D3 | — | 27 | 8 | no | — |
| 313 | C2×A4 | — | 2 | 1 | no | — |
| 314 | C2×A4 | — | 6 | 2 | no | — |
| 315 | C2×A4 | — | 9 | 2 | no | — |
| 316 | C2×A4 | — | 9 | 4 | no | — |
| 317 | C2×A4 | — | 12 | 1 | no | — |
| 318 | C2×A4 | — | 18 | 2 | no | — |
| 319 | C2×A4 | — | 18 | 4 | no | — |
| 320 | C2×A4 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, direct product factor |
| 321 | C2×C32 | — | 2 | 1 | no | — |
| 322 | C2×C32 | — | 3 | 2 | no | — |
| 323 | C2×C32 | — | 3 | 2 | no | — |
| 324 | C2×C32 | — | 4 | 1 | no | — |
| 325 | C2×C32 | — | 6 | 1 | no | — |
| 326 | C2×C32 | — | 6 | 1 | no | — |
| 327 | C2×C32 | — | 8 | 2 | no | — |
| 328 | C2×C32 | — | 12 | 2 | no | — |
| 329 | C2×C32 | — | 16 | 1 | no | — |
| 330 | C2×C32 | — | 24 | 2 | no | — |
| 331 | C2×C32 | — | 24 | 1 | no | — |
| 332 | C2×C32 | — | 24 | 2 | no | — |
| 333 | C2×C32 | — | 36 | 2 | no | — |
| 334 | C2×C32 | — | 36 | 4 | no | — |
| 335 | C2×C32 | C2×D3×A4 | 1 | 2 | yes | complemented |
| 336 | C3⋊D3 | — | 3 | 4 | no | — |
| 337 | C3⋊D3 | C2×D3×A4 | 1 | 4 | yes | complemented |
| 338 | C3×D3 | — | 3 | 4 | no | — |
| 339 | C3×D3 | — | 3 | 4 | no | — |
| 340 | C3×D3 | — | 6 | 2 | no | — |
| 341 | C3×D3 | — | 9 | 4 | no | — |
| 342 | C3×D3 | — | 9 | 4 | no | — |
| 343 | C3×D3 | — | 12 | 4 | no | — |
| 344 | C3×D3 | — | 12 | 4 | no | — |
| 345 | C3×D3 | — | 18 | 2 | no | — |
| 346 | C3×D3 | — | 24 | 4 | no | — |
| 347 | C3×D3 | — | 24 | 4 | no | — |
| 348 | C3×D3 | — | 24 | 2 | no | — |
| 349 | C3×D3 | — | 24 | 4 | no | — |
| 350 | C3×D3 | — | 36 | 4 | no | — |
| 351 | C24 | — | 9 | 1 | no | — |
| 352 | C24 | — | 9 | 2 | no | — |
| 353 | C24 | — | 27 | 4 | no | — |
| 354 | C24 | — | 81 | 1 | no | — |
| 355 | C24 | — | 81 | 1 | no | — |
| 356 | C24 | — | 81 | 2 | no | — |
| 357 | C24 | — | 81 | 4 | no | — |
| 358 | C22×C3 | — | 3 | 1 | no | — |
| 359 | C22×C3 | — | 3 | 1 | no | — |
| 360 | C22×C3 | — | 3 | 2 | no | — |
| 361 | C22×C3 | — | 6 | 1 | no | — |
| 362 | C22×C3 | — | 9 | 2 | no | — |
| 363 | C22×C3 | — | 9 | 2 | no | — |
| 364 | C22×C3 | — | 9 | 2 | no | — |
| 365 | C22×C3 | — | 9 | 1 | no | — |
| 366 | C22×C3 | — | 18 | 1 | no | — |
| 367 | C22×C3 | — | 18 | 1 | no | — |
| 368 | C22×C3 | — | 27 | 2 | no | — |
| 369 | C22×C3 | — | 27 | 2 | no | — |
| 370 | C22×C3 | — | 27 | 2 | no | — |
| 371 | C22×C3 | — | 27 | 2 | no | — |
| 372 | C22×C3 | — | 27 | 2 | no | — |
| 373 | C22×C3 | — | 27 | 4 | no | — |
| 374 | C22×C3 | — | 27 | 4 | no | — |
| 375 | C22×C3 | — | 27 | 4 | no | — |
| 376 | C22×C3 | — | 27 | 4 | no | — |
| 377 | C22×C3 | — | 27 | 1 | no | — |
| 378 | C22×C3 | — | 36 | 1 | no | — |
| 379 | C22×C3 | — | 36 | 2 | no | — |
| 380 | C22×C3 | — | 72 | 1 | no | — |
| 381 | C22×C3 | — | 72 | 2 | no | — |
| 382 | C22×C3 | — | 108 | 4 | no | — |
| 383 | C22×C3 | C2×C3×D32 | 1 | 1 | yes | characteristic |
| 384 | C2×D3 | — | 3 | 2 | no | — |
| 385 | C2×D3 | — | 3 | 2 | no | — |
| 386 | C2×D3 | — | 6 | 1 | no | — |
| 387 | C2×D3 | — | 9 | 2 | no | — |
| 388 | C2×D3 | — | 9 | 4 | no | — |
| 389 | C2×D3 | — | 9 | 4 | no | — |
| 390 | C2×D3 | — | 9 | 4 | no | — |
| 391 | C2×D3 | — | 9 | 4 | no | — |
| 392 | C2×D3 | — | 9 | 4 | no | — |
| 393 | C2×D3 | — | 9 | 8 | no | — |
| 394 | C2×D3 | — | 9 | 4 | no | — |
| 395 | C2×D3 | — | 9 | 2 | no | — |
| 396 | C2×D3 | — | 9 | 4 | no | — |
| 397 | C2×D3 | — | 9 | 2 | no | — |
| 398 | C2×D3 | — | 9 | 4 | no | — |
| 399 | C2×D3 | — | 9 | 4 | no | — |
| 400 | C2×D3 | — | 18 | 2 | no | — |
| 401 | C2×D3 | — | 18 | 2 | no | — |
| 402 | C2×D3 | — | 18 | 1 | no | — |
| 403 | C2×D3 | — | 18 | 2 | no | — |
| 404 | C2×D3 | — | 18 | 2 | no | — |
| 405 | C2×D3 | — | 27 | 4 | no | — |
| 406 | C2×D3 | — | 27 | 4 | no | — |
| 407 | C2×D3 | — | 27 | 2 | no | — |
| 408 | C2×D3 | — | 27 | 4 | no | — |
| 409 | C2×D3 | — | 27 | 4 | no | — |
| 410 | C2×D3 | — | 27 | 8 | no | — |
| 411 | C2×D3 | — | 27 | 8 | no | — |
| 412 | C2×D3 | — | 27 | 4 | no | — |
| 413 | C2×D3 | — | 27 | 8 | no | — |
| 414 | C2×D3 | — | 27 | 8 | no | — |
| 415 | C2×D3 | — | 27 | 8 | no | — |
| 416 | C2×D3 | — | 27 | 16 | no | — |
| 417 | A4 | — | 2 | 1 | no | — |
| 418 | A4 | — | 6 | 2 | no | — |
| 419 | A4 | — | 12 | 1 | no | — |
| 420 | A4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, direct product factor |
| 421 | C32 | — | 2 | 1 | no | — |
| 422 | C32 | — | 4 | 1 | no | — |
| 423 | C32 | — | 8 | 2 | no | — |
| 424 | C32 | — | 12 | 2 | no | — |
| 425 | C32 | — | 16 | 1 | no | — |
| 426 | C32 | — | 24 | 2 | no | — |
| 427 | C32 | — | 24 | 1 | no | — |
| 428 | C32 | — | 24 | 2 | no | — |
| 429 | C32 | C22×D3×A4 | 1 | 2 | yes | complemented |
| 430 | C23 | — | 9 | 2 | no | — |
| 431 | C23 | — | 9 | 4 | no | — |
| 432 | C23 | — | 27 | 1 | no | — |
| 433 | C23 | — | 27 | 2 | no | — |
| 434 | C23 | — | 27 | 2 | no | — |
| 435 | C23 | — | 27 | 1 | no | — |
| 436 | C23 | — | 27 | 4 | no | — |
| 437 | C23 | — | 27 | 2 | no | — |
| 438 | C23 | — | 27 | 1 | no | — |
| 439 | C23 | — | 81 | 1 | no | — |
| 440 | C23 | — | 81 | 2 | no | — |
| 441 | C23 | — | 81 | 4 | no | — |
| 442 | C23 | — | 81 | 4 | no | — |
| 443 | C23 | — | 81 | 4 | no | — |
| 444 | C23 | — | 81 | 8 | no | — |
| 445 | C23 | — | 81 | 4 | no | — |
| 446 | C23 | — | 81 | 8 | no | — |
| 447 | C23 | — | 81 | 2 | no | — |
| 448 | C23 | C3×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 449 | C2×C3 | — | 3 | 1 | no | — |
| 450 | C2×C3 | — | 3 | 1 | no | — |
| 451 | C2×C3 | — | 3 | 2 | no | — |
| 452 | C2×C3 | — | 4 | 1 | no | — |
| 453 | C2×C3 | — | 6 | 1 | no | — |
| 454 | C2×C3 | — | 8 | 1 | no | — |
| 455 | C2×C3 | — | 9 | 2 | no | — |
| 456 | C2×C3 | — | 9 | 2 | no | — |
| 457 | C2×C3 | — | 9 | 4 | no | — |
| 458 | C2×C3 | — | 9 | 2 | no | — |
| 459 | C2×C3 | — | 18 | 1 | no | — |
| 460 | C2×C3 | — | 18 | 1 | no | — |
| 461 | C2×C3 | — | 24 | 2 | no | — |
| 462 | C2×C3 | — | 27 | 4 | no | — |
| 463 | C2×C3 | — | 27 | 2 | no | — |
| 464 | C2×C3 | — | 36 | 2 | no | — |
| 465 | C2×C3 | — | 36 | 4 | no | — |
| 466 | C2×C3 | — | 48 | 1 | no | — |
| 467 | C2×C3 | — | 72 | 2 | no | — |
| 468 | C2×C3 | — | 72 | 4 | no | — |
| 469 | C2×C3 | D32×A4 | 1 | 1 | yes | characteristic |
| 470 | D3 | — | 3 | 4 | no | — |
| 471 | D3 | — | 3 | 4 | no | — |
| 472 | D3 | — | 6 | 2 | no | — |
| 473 | D3 | — | 9 | 4 | no | — |
| 474 | D3 | — | 9 | 4 | no | — |
| 475 | D3 | — | 9 | 4 | no | — |
| 476 | D3 | — | 18 | 2 | no | — |
| 477 | D3 | — | 27 | 4 | no | — |
| 478 | C22 | — | 3 | 1 | no | — |
| 479 | C22 | — | 3 | 1 | no | — |
| 480 | C22 | — | 9 | 1 | no | — |
| 481 | C22 | — | 9 | 2 | no | — |
| 482 | C22 | — | 27 | 2 | no | — |
| 483 | C22 | — | 27 | 4 | no | — |
| 484 | C22 | — | 27 | 2 | no | — |
| 485 | C22 | — | 27 | 4 | no | — |
| 486 | C22 | — | 27 | 2 | no | — |
| 487 | C22 | — | 27 | 4 | no | — |
| 488 | C22 | — | 27 | 2 | no | — |
| 489 | C22 | — | 27 | 4 | no | — |
| 490 | C22 | — | 27 | 4 | no | — |
| 491 | C22 | — | 27 | 1 | no | — |
| 492 | C22 | — | 27 | 2 | no | — |
| 493 | C22 | — | 81 | 4 | no | — |
| 494 | C22 | — | 81 | 8 | no | — |
| 495 | C22 | — | 81 | 8 | no | — |
| 496 | C22 | C2×C3×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 497 | C3 | — | 3 | 2 | no | — |
| 498 | C3 | — | 4 | 1 | no | — |
| 499 | C3 | — | 6 | 1 | no | — |
| 500 | C3 | — | 8 | 1 | no | — |
| 501 | C3 | — | 24 | 2 | no | — |
| 502 | C3 | — | 48 | 1 | no | — |
| 503 | C3 | C2×D32×A4 | 1 | 1 | yes | characteristic |
| 504 | C2 | — | 3 | 1 | no | — |
| 505 | C2 | — | 3 | 1 | no | — |
| 506 | C2 | — | 9 | 2 | no | — |
| 507 | C2 | — | 9 | 4 | no | — |
| 508 | C2 | — | 27 | 2 | no | — |
| 509 | C2 | — | 27 | 4 | no | — |
| 510 | C2 | A4×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, direct product factor |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | A4×((C3⋊D3)⋊C3)⋊C2 |
| commutator, cosocle, hypocenter | C22×H(3,𝔽3) | C23×C3 |
| Frattini | C3 | C2×D32×A4 |
| Fitting | C23×H(3,𝔽3) | C22×C3 |
| socle | C23×C3 | C3×D32 |
| LCS | G ▷ C22×H(3,𝔽3) | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×A4×#272 | 2 |
| C2×A4×(C3⋊D3)⋊C3 | 2 |
| A4×((C3⋊D3)⋊C3)⋊C2 | 2 |
| C2×D32×A4 | 3 |
| C23×((C3⋊D3)⋊C3)⋊C2 | 3 |
| C2×C3×((C3⋊D3)⋊C3)⋊C2 | 4 |