Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
7941 conjugacy classes of subgroups; only the 760 normal subgroups are shown.
This group has 7941 conjugacy classes of subgroups — too many to draw. Only its 760 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×#10620215 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×D3×#1113 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | C2×D32×C3⋊D3 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | C2×C3×D33 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | D34 | C2 | 1 | 16 | yes | maximal, direct product factor |
| 6 | C22×D33 | — | 3 | 4 | no | maximal |
| 7 | C2×C3⋊#1113 | C22 | 1 | 6 | yes | complemented |
| 8 | C2×C3⋊D32 | C22 | 1 | 3 | yes | complemented |
| 9 | C2×D3×C3⋊(C3⋊D3) | C22 | 1 | 4 | yes | complemented |
| 10 | C2×C3×#1113 | C22 | 1 | 4 | yes | complemented |
| 11 | C2×C3×D3×C3⋊D3 | C22 | 1 | 12 | yes | complemented |
| 12 | C2×C32×D32 | C22 | 1 | 6 | yes | complemented |
| 13 | #10620215 | C22 | 1 | 8 | yes | complemented |
| 14 | D3×#1113 | C22 | 1 | 32 | yes | complemented |
| 15 | D32×C3⋊D3 | C22 | 1 | 48 | yes | complemented |
| 16 | C3×D33 | C22 | 1 | 32 | yes | complemented |
| 17 | C22×#1113 | — | 3 | 4 | no | — |
| 18 | C22×D3×C3⋊D3 | — | 3 | 12 | no | — |
| 19 | C22×C3×D32 | — | 3 | 12 | no | — |
| 20 | C2×D33 | — | 3 | 4 | no | — |
| 21 | C2×D33 | — | 3 | 12 | no | — |
| 22 | C2×D33 | — | 3 | 12 | no | — |
| 23 | C2×D33 | — | 3 | 64 | no | — |
| 24 | C2×D33 | — | 6 | 6 | no | — |
| 25 | C2×D33 | D3 | 1 | 4 | yes | direct product factor |
| 26 | C2×C3⋊(C3⋊(C3⋊D3)) | C23 | 1 | 1 | yes | characteristic, complemented |
| 27 | C2×C3×C3⋊(C3⋊D3) | C23 | 1 | 4 | yes | complemented |
| 28 | C2×C32×C3⋊D3 | C23 | 1 | 6 | yes | complemented |
| 29 | C2×C33×D3 | C23 | 1 | 4 | yes | complemented |
| 30 | C3⋊#1113 | C23 | 1 | 24 | yes | complemented |
| 31 | C3⋊D32 | C23 | 1 | 12 | yes | complemented |
| 32 | D3×C3⋊(C3⋊D3) | C23 | 1 | 16 | yes | complemented |
| 33 | C3×#1113 | C23 | 1 | 16 | yes | complemented |
| 34 | C3×D3×C3⋊D3 | C23 | 1 | 48 | yes | complemented |
| 35 | C32×D32 | C23 | 1 | 24 | yes | complemented |
| 36 | C23×D32 | — | 9 | 6 | no | — |
| 37 | C22×C3⋊(C3⋊D3) | — | 3 | 4 | no | — |
| 38 | C22×C3×C3⋊D3 | — | 3 | 12 | no | — |
| 39 | C22×C32×D3 | — | 3 | 12 | no | — |
| 40 | C2×#1113 | — | 3 | 12 | no | — |
| 41 | C2×#1113 | — | 3 | 32 | no | — |
| 42 | C2×#1113 | — | 6 | 6 | no | — |
| 43 | C2×#1113 | C2×D3 | 1 | 4 | yes | complemented |
| 44 | C2×D3×C3⋊D3 | — | 3 | 12 | no | — |
| 45 | C2×D3×C3⋊D3 | — | 3 | 12 | no | — |
| 46 | C2×D3×C3⋊D3 | — | 3 | 12 | no | — |
| 47 | C2×D3×C3⋊D3 | — | 3 | 96 | no | — |
| 48 | C2×D3×C3⋊D3 | — | 6 | 12 | no | — |
| 49 | C2×D3×C3⋊D3 | — | 6 | 6 | no | — |
| 50 | C2×D3×C3⋊D3 | — | 12 | 4 | no | — |
| 51 | C2×D3×C3⋊D3 | C2×D3 | 1 | 12 | yes | complemented |
| 52 | C2×C3×D32 | — | 2 | 6 | no | — |
| 53 | C2×C3×D32 | — | 3 | 12 | no | — |
| 54 | C2×C3×D32 | — | 3 | 24 | no | — |
| 55 | C2×C3×D32 | — | 3 | 96 | no | — |
| 56 | C2×C3×D32 | — | 6 | 12 | no | — |
| 57 | C2×C3×D32 | C2×D3 | 1 | 12 | yes | complemented |
| 58 | D33 | — | 3 | 32 | no | — |
| 59 | D33 | — | 3 | 96 | no | — |
| 60 | D33 | — | 3 | 96 | no | — |
| 61 | D33 | — | 6 | 48 | no | — |
| 62 | D33 | C2×D3 | 1 | 32 | yes | direct product factor |
| 63 | C2×C34 | C24 | 1 | 1 | yes | characteristic, complemented |
| 64 | C3⋊(C3⋊(C3⋊D3)) | C24 | 1 | 2 | yes | complemented |
| 65 | C3×C3⋊(C3⋊D3) | C24 | 1 | 8 | yes | complemented |
| 66 | C32×C3⋊D3 | C24 | 1 | 12 | yes | complemented |
| 67 | C33×D3 | C24 | 1 | 8 | yes | complemented |
| 68 | C23×C3⋊D3 | — | 9 | 6 | no | — |
| 69 | C23×C3×D3 | — | 9 | 12 | no | — |
| 70 | C22×D32 | — | 3 | 12 | no | — |
| 71 | C22×D32 | — | 9 | 6 | no | — |
| 72 | C22×D32 | — | 9 | 12 | no | — |
| 73 | C22×D32 | — | 9 | 96 | no | — |
| 74 | C22×D32 | — | 9 | 24 | no | — |
| 75 | C22×D32 | — | 9 | 12 | no | — |
| 76 | C22×D32 | — | 9 | 6 | no | — |
| 77 | C22×D32 | — | 18 | 12 | no | — |
| 78 | C22×C33 | — | 3 | 4 | no | — |
| 79 | C2×C3⋊(C3⋊D3) | — | 3 | 4 | no | — |
| 80 | C2×C3⋊(C3⋊D3) | — | 3 | 16 | no | — |
| 81 | C2×C3⋊(C3⋊D3) | — | 6 | 6 | no | — |
| 82 | C2×C3⋊(C3⋊D3) | — | 12 | 4 | no | — |
| 83 | C2×C3⋊(C3⋊D3) | — | 24 | 1 | no | — |
| 84 | C2×C3⋊(C3⋊D3) | C22×D3 | 1 | 4 | yes | complemented |
| 85 | C2×C3×C3⋊D3 | — | 2 | 6 | no | — |
| 86 | C2×C3×C3⋊D3 | — | 3 | 12 | no | — |
| 87 | C2×C3×C3⋊D3 | — | 3 | 48 | no | — |
| 88 | C2×C3×C3⋊D3 | — | 6 | 12 | no | — |
| 89 | C2×C3×C3⋊D3 | — | 12 | 4 | no | — |
| 90 | C2×C3×C3⋊D3 | C22×D3 | 1 | 12 | yes | complemented |
| 91 | C2×C32×D3 | — | 2 | 12 | no | — |
| 92 | C2×C32×D3 | — | 3 | 12 | no | — |
| 93 | C2×C32×D3 | — | 3 | 48 | no | — |
| 94 | C2×C32×D3 | — | 4 | 4 | no | — |
| 95 | C2×C32×D3 | — | 6 | 6 | no | — |
| 96 | C2×C32×D3 | C22×D3 | 1 | 12 | yes | complemented |
| 97 | #1113 | — | 3 | 48 | no | — |
| 98 | #1113 | — | 6 | 24 | no | — |
| 99 | #1113 | C22×D3 | 1 | 16 | yes | complemented |
| 100 | D3×C3⋊D3 | — | 3 | 48 | no | — |
| 101 | D3×C3⋊D3 | — | 3 | 48 | no | — |
| 102 | D3×C3⋊D3 | — | 3 | 48 | no | — |
| 103 | D3×C3⋊D3 | — | 6 | 48 | no | — |
| 104 | D3×C3⋊D3 | — | 6 | 24 | no | — |
| 105 | D3×C3⋊D3 | — | 12 | 16 | no | — |
| 106 | D3×C3⋊D3 | C22×D3 | 1 | 48 | yes | complemented |
| 107 | C3×D32 | — | 2 | 24 | no | — |
| 108 | C3×D32 | — | 3 | 48 | no | — |
| 109 | C3×D32 | — | 3 | 96 | no | — |
| 110 | C3×D32 | — | 6 | 48 | no | — |
| 111 | C3×D32 | C22×D3 | 1 | 48 | yes | complemented |
| 112 | C24×D3 | — | 27 | 4 | no | — |
| 113 | C34 | C25 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 114 | C23×C32 | — | 9 | 6 | no | — |
| 115 | C22×C3⋊D3 | — | 3 | 12 | no | — |
| 116 | C22×C3⋊D3 | — | 9 | 6 | no | — |
| 117 | C22×C3⋊D3 | — | 9 | 48 | no | — |
| 118 | C22×C3⋊D3 | — | 9 | 12 | no | — |
| 119 | C22×C3⋊D3 | — | 9 | 6 | no | — |
| 120 | C22×C3⋊D3 | — | 18 | 12 | no | — |
| 121 | C22×C3⋊D3 | — | 36 | 4 | no | — |
| 122 | C22×C3×D3 | — | 3 | 24 | no | — |
| 123 | C22×C3×D3 | — | 6 | 12 | no | — |
| 124 | C22×C3×D3 | — | 9 | 12 | no | — |
| 125 | C22×C3×D3 | — | 9 | 96 | no | — |
| 126 | C22×C3×D3 | — | 9 | 24 | no | — |
| 127 | C22×C3×D3 | — | 9 | 12 | no | — |
| 128 | C22×C3×D3 | — | 18 | 12 | no | — |
| 129 | C2×D32 | — | 3 | 12 | no | — |
| 130 | C2×D32 | — | 3 | 24 | no | — |
| 131 | C2×D32 | — | 3 | 96 | no | — |
| 132 | C2×D32 | — | 6 | 12 | no | — |
| 133 | C2×D32 | — | 9 | 48 | no | — |
| 134 | C2×D32 | — | 9 | 96 | no | — |
| 135 | C2×D32 | — | 9 | 192 | no | — |
| 136 | C2×D32 | — | 9 | 96 | no | — |
| 137 | C2×D32 | — | 9 | 12 | no | — |
| 138 | C2×D32 | — | 9 | 24 | no | — |
| 139 | C2×D32 | — | 9 | 6 | no | — |
| 140 | C2×D32 | — | 9 | 12 | no | — |
| 141 | C2×D32 | — | 9 | 48 | no | — |
| 142 | C2×D32 | — | 18 | 96 | no | — |
| 143 | C2×D32 | — | 18 | 12 | no | — |
| 144 | C2×D32 | — | 18 | 12 | no | — |
| 145 | C2×D32 | — | 18 | 12 | no | — |
| 146 | C2×D32 | — | 36 | 4 | no | — |
| 147 | C2×D32 | — | 36 | 3 | no | — |
| 148 | C2×D32 | D32 | 1 | 6 | yes | direct product factor |
| 149 | C2×C33 | — | 2 | 6 | no | — |
| 150 | C2×C33 | — | 3 | 8 | no | — |
| 151 | C2×C33 | — | 4 | 4 | no | — |
| 152 | C2×C33 | — | 8 | 1 | no | — |
| 153 | C2×C33 | C23×D3 | 1 | 4 | yes | complemented |
| 154 | C3⋊(C3⋊D3) | — | 3 | 8 | no | — |
| 155 | C3⋊(C3⋊D3) | — | 6 | 12 | no | — |
| 156 | C3⋊(C3⋊D3) | — | 12 | 8 | no | — |
| 157 | C3⋊(C3⋊D3) | — | 24 | 2 | no | — |
| 158 | C3⋊(C3⋊D3) | C23×D3 | 1 | 8 | yes | complemented |
| 159 | C3×C3⋊D3 | — | 2 | 12 | no | — |
| 160 | C3×C3⋊D3 | — | 3 | 24 | no | — |
| 161 | C3×C3⋊D3 | — | 6 | 24 | no | — |
| 162 | C3×C3⋊D3 | — | 12 | 8 | no | — |
| 163 | C3×C3⋊D3 | C23×D3 | 1 | 24 | yes | complemented |
| 164 | C32×D3 | — | 2 | 24 | no | — |
| 165 | C32×D3 | — | 3 | 24 | no | — |
| 166 | C32×D3 | — | 4 | 8 | no | — |
| 167 | C32×D3 | — | 6 | 12 | no | — |
| 168 | C32×D3 | C23×D3 | 1 | 24 | yes | complemented |
| 169 | C24×C3 | — | 27 | 4 | no | — |
| 170 | C23×D3 | — | 9 | 12 | no | — |
| 171 | C23×D3 | — | 27 | 12 | no | — |
| 172 | C23×D3 | — | 27 | 64 | no | — |
| 173 | C23×D3 | — | 27 | 4 | no | — |
| 174 | C23×D3 | — | 27 | 12 | no | — |
| 175 | C23×D3 | — | 27 | 4 | no | — |
| 176 | C23×D3 | — | 27 | 12 | no | — |
| 177 | C23×D3 | — | 54 | 6 | no | — |
| 178 | C22×C32 | — | 3 | 12 | no | — |
| 179 | C22×C32 | — | 6 | 12 | no | — |
| 180 | C22×C32 | — | 9 | 24 | no | — |
| 181 | C22×C32 | — | 9 | 6 | no | — |
| 182 | C22×C32 | — | 12 | 4 | no | — |
| 183 | C2×C3⋊D3 | — | 3 | 12 | no | — |
| 184 | C2×C3⋊D3 | — | 3 | 48 | no | — |
| 185 | C2×C3⋊D3 | — | 6 | 12 | no | — |
| 186 | C2×C3⋊D3 | — | 9 | 24 | no | — |
| 187 | C2×C3⋊D3 | — | 9 | 48 | no | — |
| 188 | C2×C3⋊D3 | — | 9 | 6 | no | — |
| 189 | C2×C3⋊D3 | — | 9 | 24 | no | — |
| 190 | C2×C3⋊D3 | — | 12 | 4 | no | — |
| 191 | C2×C3⋊D3 | — | 18 | 48 | no | — |
| 192 | C2×C3⋊D3 | — | 18 | 12 | no | — |
| 193 | C2×C3⋊D3 | — | 36 | 4 | no | — |
| 194 | C2×C3⋊D3 | — | 36 | 16 | no | — |
| 195 | C2×C3⋊D3 | — | 36 | 4 | no | — |
| 196 | C2×C3⋊D3 | — | 36 | 3 | no | — |
| 197 | C2×C3⋊D3 | — | 72 | 6 | no | — |
| 198 | C2×C3⋊D3 | — | 72 | 1 | no | — |
| 199 | C2×C3⋊D3 | C2×D32 | 1 | 6 | yes | complemented |
| 200 | C2×C3×D3 | — | 2 | 12 | no | — |
| 201 | C2×C3×D3 | — | 3 | 24 | no | — |
| 202 | C2×C3×D3 | — | 3 | 96 | no | — |
| 203 | C2×C3×D3 | — | 4 | 4 | no | — |
| 204 | C2×C3×D3 | — | 6 | 48 | no | — |
| 205 | C2×C3×D3 | — | 6 | 12 | no | — |
| 206 | C2×C3×D3 | — | 6 | 12 | no | — |
| 207 | C2×C3×D3 | — | 9 | 48 | no | — |
| 208 | C2×C3×D3 | — | 9 | 96 | no | — |
| 209 | C2×C3×D3 | — | 9 | 12 | no | — |
| 210 | C2×C3×D3 | — | 9 | 48 | no | — |
| 211 | C2×C3×D3 | — | 12 | 6 | no | — |
| 212 | C2×C3×D3 | — | 18 | 48 | no | — |
| 213 | C2×C3×D3 | — | 18 | 12 | no | — |
| 214 | C2×C3×D3 | — | 36 | 4 | no | — |
| 215 | C2×C3×D3 | C2×D32 | 1 | 12 | yes | complemented |
| 216 | D32 | — | 3 | 48 | no | — |
| 217 | D32 | — | 3 | 96 | no | — |
| 218 | D32 | — | 6 | 48 | no | — |
| 219 | D32 | — | 9 | 48 | no | — |
| 220 | D32 | — | 9 | 96 | no | — |
| 221 | D32 | — | 9 | 24 | no | — |
| 222 | D32 | — | 9 | 48 | no | — |
| 223 | D32 | — | 18 | 48 | no | — |
| 224 | D32 | — | 18 | 48 | no | — |
| 225 | D32 | — | 18 | 48 | no | — |
| 226 | D32 | — | 36 | 16 | no | — |
| 227 | D32 | — | 36 | 12 | no | — |
| 228 | D32 | C2×D32 | 1 | 24 | yes | direct product factor |
| 229 | C25 | — | 81 | 1 | no | Sylow |
| 230 | C33 | — | 2 | 6 | no | — |
| 231 | C33 | — | 4 | 4 | no | — |
| 232 | C33 | — | 8 | 1 | no | — |
| 233 | C33 | C24×D3 | 1 | 4 | yes | complemented |
| 234 | C23×C3 | — | 9 | 12 | no | — |
| 235 | C23×C3 | — | 18 | 6 | no | — |
| 236 | C23×C3 | — | 27 | 12 | no | — |
| 237 | C23×C3 | — | 27 | 32 | no | — |
| 238 | C23×C3 | — | 27 | 4 | no | — |
| 239 | C22×D3 | — | 3 | 12 | no | — |
| 240 | C22×D3 | — | 9 | 12 | no | — |
| 241 | C22×D3 | — | 9 | 96 | no | — |
| 242 | C22×D3 | — | 9 | 24 | no | — |
| 243 | C22×D3 | — | 9 | 12 | no | — |
| 244 | C22×D3 | — | 18 | 12 | no | — |
| 245 | C22×D3 | — | 27 | 12 | no | — |
| 246 | C22×D3 | — | 27 | 96 | no | — |
| 247 | C22×D3 | — | 27 | 12 | no | — |
| 248 | C22×D3 | — | 27 | 32 | no | — |
| 249 | C22×D3 | — | 27 | 96 | no | — |
| 250 | C22×D3 | — | 27 | 32 | no | — |
| 251 | C22×D3 | — | 27 | 96 | no | — |
| 252 | C22×D3 | — | 27 | 12 | no | — |
| 253 | C22×D3 | — | 27 | 12 | no | — |
| 254 | C22×D3 | — | 27 | 4 | no | — |
| 255 | C22×D3 | — | 54 | 6 | no | — |
| 256 | C22×D3 | — | 54 | 48 | no | — |
| 257 | C22×D3 | — | 54 | 6 | no | — |
| 258 | C22×D3 | — | 54 | 12 | no | — |
| 259 | C22×D3 | — | 108 | 4 | no | — |
| 260 | C2×C32 | — | 2 | 12 | no | — |
| 261 | C2×C32 | — | 3 | 24 | no | — |
| 262 | C2×C32 | — | 4 | 4 | no | — |
| 263 | C2×C32 | — | 4 | 3 | no | — |
| 264 | C2×C32 | — | 4 | 4 | no | — |
| 265 | C2×C32 | — | 6 | 24 | no | — |
| 266 | C2×C32 | — | 8 | 6 | no | — |
| 267 | C2×C32 | — | 8 | 1 | no | — |
| 268 | C2×C32 | — | 9 | 12 | no | — |
| 269 | C2×C32 | — | 12 | 8 | no | — |
| 270 | C2×C32 | C22×D32 | 1 | 6 | yes | complemented |
| 271 | C3⋊D3 | — | 3 | 24 | no | — |
| 272 | C3⋊D3 | — | 6 | 24 | no | — |
| 273 | C3⋊D3 | — | 9 | 12 | no | — |
| 274 | C3⋊D3 | — | 12 | 8 | no | — |
| 275 | C3⋊D3 | — | 18 | 24 | no | — |
| 276 | C3⋊D3 | — | 36 | 8 | no | — |
| 277 | C3⋊D3 | — | 36 | 8 | no | — |
| 278 | C3⋊D3 | — | 36 | 6 | no | — |
| 279 | C3⋊D3 | — | 72 | 12 | no | — |
| 280 | C3⋊D3 | — | 72 | 2 | no | — |
| 281 | C3⋊D3 | C22×D32 | 1 | 12 | yes | complemented |
| 282 | C3×D3 | — | 2 | 24 | no | — |
| 283 | C3×D3 | — | 3 | 48 | no | — |
| 284 | C3×D3 | — | 4 | 8 | no | — |
| 285 | C3×D3 | — | 6 | 24 | no | — |
| 286 | C3×D3 | — | 6 | 24 | no | — |
| 287 | C3×D3 | — | 9 | 24 | no | — |
| 288 | C3×D3 | — | 12 | 12 | no | — |
| 289 | C3×D3 | — | 18 | 24 | no | — |
| 290 | C3×D3 | — | 36 | 8 | no | — |
| 291 | C3×D3 | C22×D32 | 1 | 24 | yes | complemented |
| 292 | C24 | — | 27 | 4 | no | — |
| 293 | C24 | — | 81 | 6 | no | — |
| 294 | C24 | — | 81 | 4 | no | — |
| 295 | C24 | — | 81 | 1 | no | — |
| 296 | C24 | — | 81 | 16 | no | — |
| 297 | C22×C3 | — | 3 | 12 | no | — |
| 298 | C22×C3 | — | 6 | 12 | no | — |
| 299 | C22×C3 | — | 9 | 48 | no | — |
| 300 | C22×C3 | — | 9 | 12 | no | — |
| 301 | C22×C3 | — | 12 | 4 | no | — |
| 302 | C22×C3 | — | 18 | 6 | no | — |
| 303 | C22×C3 | — | 18 | 24 | no | — |
| 304 | C22×C3 | — | 27 | 48 | no | — |
| 305 | C22×C3 | — | 27 | 16 | no | — |
| 306 | C22×C3 | — | 27 | 4 | no | — |
| 307 | C2×D3 | — | 3 | 12 | no | — |
| 308 | C2×D3 | — | 3 | 48 | no | — |
| 309 | C2×D3 | — | 6 | 6 | no | — |
| 310 | C2×D3 | — | 9 | 48 | no | — |
| 311 | C2×D3 | — | 9 | 96 | no | — |
| 312 | C2×D3 | — | 9 | 12 | no | — |
| 313 | C2×D3 | — | 9 | 48 | no | — |
| 314 | C2×D3 | — | 18 | 48 | no | — |
| 315 | C2×D3 | — | 18 | 12 | no | — |
| 316 | C2×D3 | — | 27 | 48 | no | — |
| 317 | C2×D3 | — | 27 | 48 | no | — |
| 318 | C2×D3 | — | 27 | 48 | no | — |
| 319 | C2×D3 | — | 27 | 48 | no | — |
| 320 | C2×D3 | — | 27 | 4 | no | — |
| 321 | C2×D3 | — | 27 | 16 | no | — |
| 322 | C2×D3 | — | 36 | 4 | no | — |
| 323 | C2×D3 | — | 54 | 24 | no | — |
| 324 | C2×D3 | — | 54 | 24 | no | — |
| 325 | C2×D3 | — | 54 | 48 | no | — |
| 326 | C2×D3 | — | 54 | 6 | no | — |
| 327 | C2×D3 | — | 108 | 16 | no | — |
| 328 | C2×D3 | — | 108 | 4 | no | — |
| 329 | C2×D3 | — | 216 | 1 | no | — |
| 330 | C2×D3 | D33 | 1 | 4 | yes | direct product factor |
| 331 | C32 | — | 2 | 12 | no | — |
| 332 | C32 | — | 4 | 4 | no | — |
| 333 | C32 | — | 4 | 3 | no | — |
| 334 | C32 | — | 4 | 4 | no | — |
| 335 | C32 | — | 8 | 6 | no | — |
| 336 | C32 | — | 8 | 1 | no | — |
| 337 | C32 | C23×D32 | 1 | 6 | yes | complemented |
| 338 | C23 | — | 9 | 6 | no | — |
| 339 | C23 | — | 27 | 12 | no | — |
| 340 | C23 | — | 27 | 32 | no | — |
| 341 | C23 | — | 27 | 4 | no | — |
| 342 | C23 | — | 81 | 4 | no | — |
| 343 | C23 | — | 81 | 3 | no | — |
| 344 | C23 | — | 81 | 48 | no | — |
| 345 | C23 | — | 81 | 6 | no | — |
| 346 | C23 | — | 81 | 32 | no | — |
| 347 | C23 | — | 81 | 8 | no | — |
| 348 | C2×C3 | — | 2 | 6 | no | — |
| 349 | C2×C3 | — | 3 | 24 | no | — |
| 350 | C2×C3 | — | 4 | 4 | no | — |
| 351 | C2×C3 | — | 6 | 24 | no | — |
| 352 | C2×C3 | — | 8 | 1 | no | — |
| 353 | C2×C3 | — | 9 | 24 | no | — |
| 354 | C2×C3 | — | 12 | 8 | no | — |
| 355 | C2×C3 | — | 18 | 12 | no | — |
| 356 | C2×C3 | — | 27 | 8 | no | — |
| 357 | C2×C3 | C2×D33 | 1 | 4 | yes | complemented |
| 358 | D3 | — | 3 | 24 | no | — |
| 359 | D3 | — | 6 | 12 | no | — |
| 360 | D3 | — | 9 | 24 | no | — |
| 361 | D3 | — | 18 | 24 | no | — |
| 362 | D3 | — | 27 | 8 | no | — |
| 363 | D3 | — | 36 | 8 | no | — |
| 364 | D3 | — | 54 | 12 | no | — |
| 365 | D3 | — | 108 | 8 | no | — |
| 366 | D3 | — | 216 | 2 | no | — |
| 367 | D3 | C2×D33 | 1 | 8 | yes | direct product factor |
| 368 | C22 | — | 3 | 4 | no | — |
| 369 | C22 | — | 9 | 24 | no | — |
| 370 | C22 | — | 9 | 6 | no | — |
| 371 | C22 | — | 27 | 48 | no | — |
| 372 | C22 | — | 27 | 16 | no | — |
| 373 | C22 | — | 27 | 4 | no | — |
| 374 | C22 | — | 81 | 16 | no | — |
| 375 | C22 | — | 81 | 12 | no | — |
| 376 | C22 | — | 81 | 24 | no | — |
| 377 | C22 | — | 81 | 1 | no | — |
| 378 | C3 | — | 2 | 6 | no | — |
| 379 | C3 | — | 4 | 4 | no | — |
| 380 | C3 | — | 8 | 1 | no | — |
| 381 | C3 | C22×D33 | 1 | 4 | yes | complemented |
| 382 | C2 | — | 3 | 8 | no | — |
| 383 | C2 | — | 9 | 12 | no | — |
| 384 | C2 | — | 27 | 8 | no | — |
| 385 | C2 | — | 81 | 2 | no | — |
| 386 | C2 | D34 | 1 | 1 | yes | characteristic, direct product factor |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D34 |
| commutator, cosocle, hypocenter | C34 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C2×C34 | C24 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10620215 | C2 | semidirect |
| 2. C2×D3×#1113 | C2 | semidirect |
| 3. C2×D32×C3⋊D3 | C2 | semidirect |
| 4. C2×C3×D33 | C2 | semidirect |
| 5. D34 | C2 | direct (N × H) |
| 7. C2×C3⋊#1113 | C22 | semidirect |
| 8. C2×C3⋊D32 | C22 | semidirect |
| 9. C2×D3×C3⋊(C3⋊D3) | C22 | semidirect |
| 10. C2×C3×#1113 | C22 | semidirect |
| 11. C2×C3×D3×C3⋊D3 | C22 | semidirect |
| 12. C2×C32×D32 | C22 | semidirect |
| 13. #10620215 | C22 | semidirect |
| 14. D3×#1113 | C22 | semidirect |
| 15. D32×C3⋊D3 | C22 | semidirect |
| 16. C3×D33 | C22 | semidirect |
| 25. C2×D33 | D3 | direct (N × H) |
| 26. C2×C3⋊(C3⋊(C3⋊D3)) | C23 | semidirect |
| 27. C2×C3×C3⋊(C3⋊D3) | C23 | semidirect |
| 28. C2×C32×C3⋊D3 | C23 | semidirect |
| 29. C2×C33×D3 | C23 | semidirect |
| 30. C3⋊#1113 | C23 | semidirect |
| 31. C3⋊D32 | C23 | semidirect |
| 32. D3×C3⋊(C3⋊D3) | C23 | semidirect |
| 33. C3×#1113 | C23 | semidirect |
| 34. C3×D3×C3⋊D3 | C23 | semidirect |
| 35. C32×D32 | C23 | semidirect |
| 43. C2×#1113 | C2×D3 | semidirect |
| 51. C2×D3×C3⋊D3 | C2×D3 | semidirect |
| 57. C2×C3×D32 | C2×D3 | semidirect |
| 62. D33 | C2×D3 | direct (N × H) |
| 63. C2×C34 | C24 | semidirect |
| 64. C3⋊(C3⋊(C3⋊D3)) | C24 | semidirect |
| 65. C3×C3⋊(C3⋊D3) | C24 | semidirect |
| 66. C32×C3⋊D3 | C24 | semidirect |
| 67. C33×D3 | C24 | semidirect |
| 84. C2×C3⋊(C3⋊D3) | C22×D3 | semidirect |
| 90. C2×C3×C3⋊D3 | C22×D3 | semidirect |
| 96. C2×C32×D3 | C22×D3 | semidirect |
| 99. #1113 | C22×D3 | semidirect |
| 106. D3×C3⋊D3 | C22×D3 | semidirect |
| 111. C3×D32 | C22×D3 | semidirect |
| 113. C34 | C25 | semidirect |
| 148. C2×D32 | D32 | direct (N × H) |
| 153. C2×C33 | C23×D3 | semidirect |
| 158. C3⋊(C3⋊D3) | C23×D3 | semidirect |
| 163. C3×C3⋊D3 | C23×D3 | semidirect |
| 168. C32×D3 | C23×D3 | semidirect |
| 199. C2×C3⋊D3 | C2×D32 | semidirect |
| 215. C2×C3×D3 | C2×D32 | semidirect |
| 228. D32 | C2×D32 | direct (N × H) |
| 233. C33 | C24×D3 | semidirect |
| 270. C2×C32 | C22×D32 | semidirect |
| 281. C3⋊D3 | C22×D32 | semidirect |
| 291. C3×D3 | C22×D32 | semidirect |
| 330. C2×D3 | D33 | direct (N × H) |
| 337. C32 | C23×D32 | semidirect |
| 357. C2×C3 | C2×D33 | semidirect |
| 367. D3 | C2×D33 | direct (N × H) |
| 381. C3 | C22×D33 | semidirect |
| 386. C2 | D34 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10620215 | 2 |
| C2×D3×#1113 | 2 |
| C2×D32×C3⋊D3 | 2 |
| C2×C3×D33 | 2 |
| D34 | 2 |
| C22×D33 | 3 |