Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
968 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 968 conjugacy classes of subgroups — too many to draw. Only its 116 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×#88964 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#88963 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#88942 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#88938 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#88935 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×C3×#3775 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×D3×#622 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11724133 | C2 | 1 | 8 | yes | maximal, direct product factor |
| 9 | C2×#64237 | — | 3 | 1 | no | maximal |
| 10 | C2×#6296 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#6295 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×Dic3×C3⋊D3 | — | 2 | 1 | no | — |
| 13 | C2×D3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 14 | C2×D3×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C3×#627 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×C3×#626 | — | 2 | 1 | no | — |
| 17 | C2×C3×#625 | — | 2 | 1 | no | — |
| 18 | C2×C3×#625 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×C3⋊#622 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×C3×#622 | C22 | 1 | 1 | yes | characteristic |
| 21 | #88964 | — | 2 | 2 | no | — |
| 22 | #88964 | C22 | 1 | 4 | yes | complemented |
| 23 | #88963 | — | 2 | 2 | no | — |
| 24 | #88963 | C22 | 1 | 4 | yes | complemented |
| 25 | #88942 | C22 | 1 | 4 | yes | complemented |
| 26 | #88938 | C22 | 1 | 4 | yes | complemented |
| 27 | #88935 | C22 | 1 | 4 | yes | complemented |
| 28 | C3×#3775 | C22 | 1 | 4 | yes | complemented |
| 29 | D3×#622 | C22 | 1 | 4 | yes | complemented |
| 30 | C2×#3805 | — | 3 | 1 | no | — |
| 31 | C2×#3805 | — | 3 | 1 | no | — |
| 32 | C2×#3805 | — | 6 | 1 | no | — |
| 33 | C2×#3796 | — | 6 | 1 | no | — |
| 34 | C22×#622 | — | 3 | 1 | no | — |
| 35 | C2×#3776 | — | 3 | 1 | no | — |
| 36 | C2×#3775 | — | 3 | 1 | no | — |
| 37 | C2×#3775 | D3 | 1 | 1 | yes | characteristic, complemented |
| 38 | #64237 | — | 3 | 8 | no | — |
| 39 | C2×#3774 | — | 3 | 1 | no | — |
| 40 | C22×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 41 | C22×C32×D3 | — | 2 | 1 | no | — |
| 42 | C22×C32×D3 | D4 | 1 | 1 | yes | characteristic |
| 43 | C2×C3⋊(C3⋊Dic3) | D4 | 1 | 1 | yes | characteristic |
| 44 | C2×C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 45 | C2×C3×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 46 | C2×C32×Dic3 | — | 2 | 1 | no | — |
| 47 | #6296 | — | 2 | 1 | no | — |
| 48 | #6296 | C23 | 1 | 2 | yes | — |
| 49 | #6295 | — | 2 | 1 | no | — |
| 50 | #6295 | C23 | 1 | 2 | yes | — |
| 51 | Dic3×C3⋊D3 | — | 2 | 4 | no | — |
| 52 | D3×C3⋊Dic3 | — | 2 | 4 | no | — |
| 53 | D3×C3⋊Dic3 | D4 | 1 | 2 | yes | — |
| 54 | D3×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 55 | C3×#627 | — | 2 | 1 | no | — |
| 56 | C3×#627 | C23 | 1 | 2 | yes | — |
| 57 | C3×#626 | — | 2 | 4 | no | — |
| 58 | C3×#625 | — | 2 | 4 | no | — |
| 59 | C3×#625 | — | 2 | 1 | no | — |
| 60 | C3×#625 | C23 | 1 | 2 | yes | — |
| 61 | C3⋊#622 | C23 | 1 | 2 | yes | — |
| 62 | C3×#622 | C23 | 1 | 2 | yes | — |
| 63 | C2×#916 | — | 9 | 1 | no | maximal |
| 64 | C22×C3⋊Dic3 | — | 3 | 1 | no | — |
| 65 | C22×C3⋊Dic3 | — | 6 | 1 | no | — |
| 66 | C2×C4×C3⋊D3 | — | 6 | 1 | no | — |
| 67 | C2×C3×#67 | — | 6 | 1 | no | — |
| 68 | C2×C3×#67 | — | 6 | 1 | no | — |
| 69 | C2×C3×#67 | — | 6 | 1 | no | — |
| 70 | C2×C3×#67 | — | 6 | 1 | no | — |
| 71 | C2×C3×D12 | — | 6 | 1 | no | — |
| 72 | C2×C3×Dic6 | — | 6 | 1 | no | — |
| 73 | C2×#627 | — | 3 | 1 | no | — |
| 74 | C2×#627 | — | 6 | 1 | no | — |
| 75 | C2×#627 | C2×D3 | 1 | 1 | yes | characteristic |
| 76 | C2×#626 | — | 2 | 1 | no | — |
| 77 | C2×#626 | — | 6 | 1 | no | — |
| 78 | C2×#625 | — | 2 | 1 | no | — |
| 79 | C2×#625 | — | 3 | 1 | no | — |
| 80 | C2×#625 | C2×D3 | 1 | 1 | yes | characteristic |
| 81 | #3805 | — | 3 | 4 | no | — |
| 82 | #3805 | — | 3 | 4 | no | — |
| 83 | #3805 | — | 6 | 2 | no | — |
| 84 | #3805 | — | 6 | 4 | no | — |
| 85 | #3805 | — | 6 | 4 | no | — |
| 86 | #3805 | — | 6 | 2 | no | — |
| 87 | C2×D3×Dic3 | — | 6 | 1 | no | — |
| 88 | C2×D3×Dic3 | — | 6 | 1 | no | — |
| 89 | C2×D3×Dic3 | — | 6 | 1 | no | — |
| 90 | C2×D3×Dic3 | — | 6 | 1 | no | — |
| 91 | C2×D3×Dic3 | — | 6 | 1 | no | — |
| 92 | C2×D3×Dic3 | — | 6 | 1 | no | — |
| 93 | C2×D3×Dic3 | — | 12 | 1 | no | — |
| 94 | C2×D3×Dic3 | — | 12 | 1 | no | — |
| 95 | #3796 | — | 6 | 4 | no | — |
| 96 | #3796 | — | 6 | 4 | no | — |
| 97 | C2×#622 | — | 3 | 1 | no | — |
| 98 | C2×#622 | — | 3 | 4 | no | — |
| 99 | C2×#622 | C2×D3 | 1 | 1 | yes | characteristic |
| 100 | #3776 | — | 3 | 4 | no | — |
| 101 | #3775 | — | 3 | 4 | no | — |
| 102 | #3775 | C2×D3 | 1 | 4 | yes | complemented |
| 103 | #3774 | — | 3 | 4 | no | — |
| 104 | C22×C33 | C2×D4 | 1 | 1 | yes | characteristic |
| 105 | C2×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 106 | C2×C3×C3⋊D3 | — | 4 | 2 | no | — |
| 107 | C2×C32×D3 | — | 2 | 2 | no | — |
| 108 | C2×C32×D3 | — | 2 | 2 | no | — |
| 109 | C2×C32×D3 | — | 4 | 2 | no | — |
| 110 | C2×C32×D3 | C2×D4 | 1 | 2 | yes | — |
| 111 | C3⋊(C3⋊Dic3) | C2×D4 | 1 | 2 | yes | — |
| 112 | C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 113 | C3×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | C3×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 115 | C32×Dic3 | — | 2 | 2 | no | — |
| 116 | C2×#239 | — | 9 | 1 | no | — |
| 117 | C2×#237 | — | 9 | 1 | no | — |
| 118 | C2×#237 | — | 18 | 1 | no | — |
| 119 | C2×#237 | — | 18 | 1 | no | — |
| 120 | C2×C3×SD16 | — | 9 | 1 | no | — |
| 121 | C2×#216 | — | 9 | 1 | no | — |
| 122 | C2×#213 | — | 9 | 1 | no | — |
| 123 | #916 | — | 9 | 8 | no | — |
| 124 | C2×#204 | — | 9 | 1 | no | — |
| 125 | C2×D3×C8 | — | 9 | 1 | no | — |
| 126 | C23×C32 | — | 3 | 1 | no | — |
| 127 | C23×C32 | — | 6 | 1 | no | — |
| 128 | C22×C3⋊D3 | — | 2 | 1 | no | — |
| 129 | C22×C3×D3 | — | 2 | 1 | no | — |
| 130 | C22×C3×D3 | — | 2 | 1 | no | — |
| 131 | C22×C3×D3 | — | 2 | 1 | no | — |
| 132 | C22×C3×D3 | — | 2 | 1 | no | — |
| 133 | C22×C3×D3 | — | 4 | 1 | no | — |
| 134 | C22×C3×D3 | — | 6 | 1 | no | — |
| 135 | C22×C3×D3 | — | 6 | 1 | no | — |
| 136 | C22×C3×D3 | — | 12 | 1 | no | — |
| 137 | C2×C32×C4 | — | 6 | 1 | no | — |
| 138 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 139 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 140 | C2×C3⋊Dic3 | — | 3 | 2 | no | — |
| 141 | C2×C3⋊Dic3 | — | 3 | 2 | no | — |
| 142 | C2×C3⋊Dic3 | — | 6 | 1 | no | — |
| 143 | C2×C3⋊Dic3 | — | 6 | 1 | no | — |
| 144 | C2×C3⋊Dic3 | — | 6 | 4 | no | — |
| 145 | C2×C3⋊Dic3 | — | 12 | 1 | no | — |
| 146 | C2×C3⋊Dic3 | — | 12 | 1 | no | — |
| 147 | C2×C3⋊Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 148 | C4×C3⋊D3 | — | 6 | 4 | no | — |
| 149 | C3×#67 | — | 6 | 2 | no | — |
| 150 | C3×#67 | — | 6 | 4 | no | — |
| 151 | C3×#67 | — | 6 | 4 | no | — |
| 152 | C3×#67 | — | 6 | 2 | no | — |
| 153 | C3×#67 | — | 6 | 4 | no | — |
| 154 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 155 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 156 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 157 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 158 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 159 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 160 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 161 | C2×C3×Dic3 | — | 12 | 1 | no | — |
| 162 | C3×D12 | — | 6 | 4 | no | — |
| 163 | C3×Dic6 | — | 6 | 2 | no | — |
| 164 | C3×Dic6 | — | 6 | 2 | no | — |
| 165 | #627 | — | 2 | 1 | no | — |
| 166 | #627 | — | 3 | 2 | no | — |
| 167 | #627 | — | 6 | 2 | no | — |
| 168 | #627 | — | 6 | 2 | no | — |
| 169 | #627 | — | 6 | 1 | no | — |
| 170 | #627 | C22×D3 | 1 | 2 | yes | — |
| 171 | #626 | — | 2 | 4 | no | — |
| 172 | #626 | — | 6 | 2 | no | — |
| 173 | #626 | — | 6 | 2 | no | — |
| 174 | #625 | — | 2 | 4 | no | — |
| 175 | #625 | — | 2 | 1 | no | — |
| 176 | #625 | — | 3 | 2 | no | — |
| 177 | #625 | — | 6 | 1 | no | — |
| 178 | #625 | C22×D3 | 1 | 2 | yes | — |
| 179 | D3×Dic3 | — | 6 | 2 | no | — |
| 180 | D3×Dic3 | — | 6 | 2 | no | — |
| 181 | D3×Dic3 | — | 6 | 2 | no | — |
| 182 | D3×Dic3 | — | 6 | 2 | no | — |
| 183 | D3×Dic3 | — | 6 | 4 | no | — |
| 184 | D3×Dic3 | — | 6 | 4 | no | — |
| 185 | D3×Dic3 | — | 6 | 4 | no | — |
| 186 | D3×Dic3 | — | 6 | 4 | no | — |
| 187 | D3×Dic3 | — | 12 | 4 | no | — |
| 188 | D3×Dic3 | — | 12 | 4 | no | — |
| 189 | #622 | — | 3 | 2 | no | — |
| 190 | #622 | C22×D3 | 1 | 2 | yes | — |
| 191 | C2×#135 | — | 27 | 1 | no | Sylow |
| 192 | C2×C33 | #135 | 1 | 2 | yes | complemented |
| 193 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 194 | C3×C3⋊D3 | — | 4 | 2 | no | — |
| 195 | C32×D3 | — | 2 | 2 | no | — |
| 196 | C32×D3 | — | 4 | 2 | no | — |
| 197 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 198 | C2×C3×D4 | — | 9 | 1 | no | — |
| 199 | C2×C3×D4 | — | 18 | 1 | no | — |
| 200 | C2×C3×D4 | — | 18 | 1 | no | — |
| 201 | C2×#67 | — | 6 | 1 | no | — |
| 202 | C2×#67 | — | 6 | 1 | no | — |
| 203 | C2×#67 | — | 6 | 1 | no | — |
| 204 | C2×#67 | — | 6 | 1 | no | — |
| 205 | C2×#67 | — | 18 | 1 | no | — |
| 206 | C22×Dic3 | — | 18 | 1 | no | — |
| 207 | C22×Dic3 | — | 18 | 1 | no | — |
| 208 | C22×Dic3 | — | 18 | 1 | no | — |
| 209 | C22×Dic3 | — | 18 | 1 | no | — |
| 210 | C22×Dic3 | — | 18 | 1 | no | — |
| 211 | C22×Dic3 | — | 36 | 1 | no | — |
| 212 | #239 | — | 9 | 4 | no | — |
| 213 | #239 | — | 18 | 2 | no | — |
| 214 | #237 | — | 9 | 4 | no | — |
| 215 | #237 | — | 18 | 4 | no | — |
| 216 | #237 | — | 18 | 4 | no | — |
| 217 | #237 | — | 18 | 4 | no | — |
| 218 | #237 | — | 18 | 2 | no | — |
| 219 | #237 | — | 18 | 4 | no | — |
| 220 | C2×D12 | — | 6 | 1 | no | — |
| 221 | C2×D12 | — | 9 | 1 | no | — |
| 222 | C2×C4×D3 | — | 9 | 1 | no | — |
| 223 | C2×C4×D3 | — | 18 | 1 | no | — |
| 224 | C2×C4×D3 | — | 18 | 1 | no | — |
| 225 | C2×C4×D3 | — | 18 | 1 | no | — |
| 226 | C2×C4×D3 | — | 36 | 1 | no | — |
| 227 | C2×Dic6 | — | 6 | 1 | no | — |
| 228 | C2×Dic6 | — | 9 | 1 | no | — |
| 229 | C2×Dic6 | — | 18 | 1 | no | — |
| 230 | C3×SD16 | — | 9 | 4 | no | — |
| 231 | C2×C3×C8 | — | 9 | 1 | no | — |
| 232 | #216 | — | 9 | 4 | no | — |
| 233 | #213 | — | 9 | 4 | no | — |
| 234 | C2×C3⋊C8 | — | 9 | 1 | no | — |
| 235 | #204 | — | 9 | 4 | no | — |
| 236 | D3×C8 | — | 9 | 4 | no | — |
| 237 | C22×C32 | — | 2 | 1 | no | — |
| 238 | C22×C32 | — | 2 | 1 | no | — |
| 239 | C22×C32 | — | 3 | 2 | no | — |
| 240 | C22×C32 | — | 4 | 1 | no | — |
| 241 | C22×C32 | — | 4 | 1 | no | — |
| 242 | C22×C32 | — | 6 | 2 | no | — |
| 243 | C22×C32 | — | 6 | 2 | no | — |
| 244 | C22×C32 | — | 12 | 2 | no | — |
| 245 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic |
| 246 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 247 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 248 | C2×C3×D3 | — | 2 | 2 | no | — |
| 249 | C2×C3×D3 | — | 2 | 2 | no | — |
| 250 | C2×C3×D3 | — | 2 | 2 | no | — |
| 251 | C2×C3×D3 | — | 2 | 2 | no | — |
| 252 | C2×C3×D3 | — | 4 | 2 | no | — |
| 253 | C2×C3×D3 | — | 4 | 2 | no | — |
| 254 | C2×C3×D3 | — | 4 | 2 | no | — |
| 255 | C2×C3×D3 | — | 4 | 2 | no | — |
| 256 | C2×C3×D3 | — | 4 | 4 | no | — |
| 257 | C2×C3×D3 | — | 4 | 2 | no | — |
| 258 | C2×C3×D3 | — | 6 | 2 | no | — |
| 259 | C2×C3×D3 | — | 6 | 2 | no | — |
| 260 | C2×C3×D3 | — | 12 | 2 | no | — |
| 261 | C2×C3×D3 | — | 12 | 2 | no | — |
| 262 | C2×C3×D3 | — | 12 | 4 | no | — |
| 263 | C2×C3×D3 | — | 12 | 2 | no | — |
| 264 | C32×C4 | — | 6 | 2 | no | — |
| 265 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 266 | C3⋊Dic3 | — | 3 | 2 | no | — |
| 267 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 268 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 269 | C3⋊Dic3 | — | 12 | 2 | no | — |
| 270 | C3⋊Dic3 | — | 12 | 2 | no | — |
| 271 | C3⋊Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 272 | C3⋊Dic3 | C23×D3 | 1 | 1 | yes | characteristic |
| 273 | C3×Dic3 | — | 2 | 2 | no | — |
| 274 | C3×Dic3 | — | 2 | 2 | no | — |
| 275 | C3×Dic3 | — | 4 | 2 | no | — |
| 276 | C3×Dic3 | — | 6 | 1 | no | — |
| 277 | C3×Dic3 | — | 6 | 1 | no | — |
| 278 | C3×Dic3 | — | 6 | 1 | no | — |
| 279 | C3×Dic3 | — | 6 | 1 | no | — |
| 280 | C3×Dic3 | — | 6 | 2 | no | — |
| 281 | C3×Dic3 | — | 6 | 2 | no | — |
| 282 | C3×Dic3 | — | 12 | 2 | no | — |
| 283 | C2×#41 | — | 27 | 1 | no | — |
| 284 | C2×#41 | — | 27 | 1 | no | — |
| 285 | #135 | — | 27 | 8 | no | — |
| 286 | C2×Q16 | — | 27 | 1 | no | — |
| 287 | C2×SD16 | — | 9 | 1 | no | — |
| 288 | C2×SD16 | — | 27 | 1 | no | — |
| 289 | C2×D8 | — | 27 | 1 | no | — |
| 290 | C22×C8 | — | 27 | 1 | no | — |
| 291 | C33 | C2×#135 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 292 | C23×C3 | — | 6 | 1 | no | — |
| 293 | C23×C3 | — | 6 | 1 | no | — |
| 294 | C23×C3 | — | 6 | 1 | no | — |
| 295 | C23×C3 | — | 6 | 1 | no | — |
| 296 | C23×C3 | — | 12 | 1 | no | — |
| 297 | C23×C3 | — | 18 | 1 | no | — |
| 298 | C22×D3 | — | 2 | 1 | no | — |
| 299 | C22×D3 | — | 6 | 1 | no | — |
| 300 | C22×D3 | — | 6 | 1 | no | — |
| 301 | C22×D3 | — | 12 | 1 | no | — |
| 302 | C22×D3 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 303 | C3×Q8 | — | 9 | 2 | no | — |
| 304 | C3×Q8 | — | 18 | 1 | no | — |
| 305 | C3×D4 | — | 9 | 2 | no | — |
| 306 | C3×D4 | — | 18 | 4 | no | — |
| 307 | C3×D4 | — | 18 | 1 | no | — |
| 308 | C3×D4 | — | 18 | 4 | no | — |
| 309 | C2×C3×C4 | — | 6 | 1 | no | — |
| 310 | C2×C3×C4 | — | 6 | 1 | no | — |
| 311 | C2×C3×C4 | — | 9 | 1 | no | — |
| 312 | C2×C3×C4 | — | 12 | 1 | no | — |
| 313 | C2×C3×C4 | — | 18 | 1 | no | — |
| 314 | #67 | — | 6 | 2 | no | — |
| 315 | #67 | — | 6 | 4 | no | — |
| 316 | #67 | — | 6 | 2 | no | — |
| 317 | #67 | — | 6 | 4 | no | — |
| 318 | #67 | — | 6 | 4 | no | — |
| 319 | #67 | — | 18 | 2 | no | — |
| 320 | #67 | — | 18 | 2 | no | — |
| 321 | C2×Dic3 | — | 2 | 1 | no | — |
| 322 | C2×Dic3 | — | 6 | 1 | no | — |
| 323 | C2×Dic3 | — | 6 | 1 | no | — |
| 324 | C2×Dic3 | — | 6 | 1 | no | — |
| 325 | C2×Dic3 | — | 6 | 1 | no | — |
| 326 | C2×Dic3 | — | 9 | 1 | no | — |
| 327 | C2×Dic3 | — | 12 | 1 | no | — |
| 328 | C2×Dic3 | — | 18 | 2 | no | — |
| 329 | C2×Dic3 | — | 18 | 2 | no | — |
| 330 | C2×Dic3 | — | 18 | 2 | no | — |
| 331 | C2×Dic3 | — | 18 | 2 | no | — |
| 332 | C2×Dic3 | — | 18 | 1 | no | — |
| 333 | C2×Dic3 | — | 18 | 1 | no | — |
| 334 | C2×Dic3 | — | 18 | 4 | no | — |
| 335 | C2×Dic3 | — | 18 | 4 | no | — |
| 336 | C2×Dic3 | — | 18 | 4 | no | — |
| 337 | C2×Dic3 | — | 36 | 1 | no | — |
| 338 | C2×Dic3 | — | 36 | 1 | no | — |
| 339 | C2×Dic3 | — | 36 | 4 | no | — |
| 340 | D12 | — | 6 | 4 | no | — |
| 341 | D12 | — | 9 | 2 | no | — |
| 342 | D12 | — | 18 | 1 | no | — |
| 343 | C4×D3 | — | 9 | 2 | no | — |
| 344 | C4×D3 | — | 9 | 2 | no | — |
| 345 | C4×D3 | — | 18 | 4 | no | — |
| 346 | C4×D3 | — | 18 | 4 | no | — |
| 347 | C4×D3 | — | 18 | 4 | no | — |
| 348 | C4×D3 | — | 36 | 4 | no | — |
| 349 | Dic6 | — | 6 | 2 | no | — |
| 350 | Dic6 | — | 6 | 2 | no | — |
| 351 | Dic6 | — | 9 | 2 | no | — |
| 352 | Dic6 | — | 18 | 2 | no | — |
| 353 | Dic6 | — | 18 | 1 | no | — |
| 354 | Dic6 | — | 18 | 2 | no | — |
| 355 | C3×C8 | — | 9 | 2 | no | — |
| 356 | C3⋊C8 | — | 9 | 2 | no | — |
| 357 | C2×C32 | — | 2 | 1 | no | — |
| 358 | C2×C32 | — | 2 | 1 | no | — |
| 359 | C2×C32 | — | 2 | 2 | no | — |
| 360 | C2×C32 | — | 2 | 2 | no | — |
| 361 | C2×C32 | — | 4 | 2 | no | — |
| 362 | C2×C32 | — | 4 | 2 | no | — |
| 363 | C2×C32 | — | 4 | 1 | no | — |
| 364 | C2×C32 | — | 4 | 1 | no | — |
| 365 | C2×C32 | — | 6 | 2 | no | — |
| 366 | C2×C32 | — | 12 | 2 | no | — |
| 367 | C2×C32 | #916 | 1 | 2 | yes | complemented |
| 368 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 369 | C3⋊D3 | — | 4 | 2 | no | — |
| 370 | C3×D3 | — | 4 | 2 | no | — |
| 371 | C3×D3 | — | 4 | 2 | no | — |
| 372 | C3×D3 | — | 4 | 2 | no | — |
| 373 | C3×D3 | — | 4 | 4 | no | — |
| 374 | C3×D3 | — | 4 | 2 | no | — |
| 375 | C3×D3 | — | 12 | 2 | no | — |
| 376 | C3×D3 | — | 12 | 4 | no | — |
| 377 | C3×D3 | — | 12 | 2 | no | — |
| 378 | #41 | — | 27 | 4 | no | — |
| 379 | #41 | — | 27 | 4 | no | — |
| 380 | #41 | — | 54 | 2 | no | — |
| 381 | #41 | — | 54 | 2 | no | — |
| 382 | C2×Q8 | — | 9 | 1 | no | — |
| 383 | C2×Q8 | — | 27 | 1 | no | — |
| 384 | C2×D4 | — | 9 | 1 | no | — |
| 385 | C2×D4 | — | 18 | 1 | no | — |
| 386 | C2×D4 | — | 18 | 1 | no | — |
| 387 | C2×D4 | — | 27 | 1 | no | — |
| 388 | C22×C4 | — | 27 | 1 | no | — |
| 389 | C22×C4 | — | 54 | 1 | no | — |
| 390 | C22×C4 | — | 54 | 1 | no | — |
| 391 | Q16 | — | 27 | 4 | no | — |
| 392 | SD16 | — | 9 | 4 | no | — |
| 393 | SD16 | — | 27 | 4 | no | — |
| 394 | D8 | — | 27 | 4 | no | — |
| 395 | C2×C8 | — | 9 | 1 | no | — |
| 396 | C2×C8 | — | 27 | 4 | no | — |
| 397 | C2×C8 | — | 27 | 1 | no | — |
| 398 | C22×C3 | — | 2 | 1 | no | — |
| 399 | C22×C3 | — | 2 | 1 | no | — |
| 400 | C22×C3 | — | 4 | 1 | no | — |
| 401 | C22×C3 | — | 4 | 1 | no | — |
| 402 | C22×C3 | — | 6 | 2 | no | — |
| 403 | C22×C3 | — | 6 | 2 | no | — |
| 404 | C22×C3 | — | 6 | 2 | no | — |
| 405 | C22×C3 | — | 6 | 2 | no | — |
| 406 | C22×C3 | — | 12 | 2 | no | — |
| 407 | C22×C3 | — | 12 | 2 | no | — |
| 408 | C22×C3 | — | 12 | 2 | no | — |
| 409 | C22×C3 | — | 12 | 2 | no | — |
| 410 | C22×C3 | — | 12 | 4 | no | — |
| 411 | C22×C3 | — | 12 | 2 | no | — |
| 412 | C22×C3 | — | 18 | 2 | no | — |
| 413 | C22×C3 | — | 36 | 2 | no | — |
| 414 | C22×C3 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 415 | C2×D3 | — | 2 | 2 | no | — |
| 416 | C2×D3 | — | 2 | 2 | no | — |
| 417 | C2×D3 | — | 4 | 2 | no | — |
| 418 | C2×D3 | — | 6 | 2 | no | — |
| 419 | C2×D3 | — | 6 | 2 | no | — |
| 420 | C2×D3 | — | 12 | 2 | no | — |
| 421 | C2×D3 | — | 12 | 2 | no | — |
| 422 | C2×D3 | — | 12 | 4 | no | — |
| 423 | C2×D3 | — | 12 | 2 | no | — |
| 424 | C2×D3 | C2×GO+(4,𝔽2) | 1 | 2 | yes | — |
| 425 | C3×C4 | — | 6 | 2 | no | — |
| 426 | C3×C4 | — | 6 | 2 | no | — |
| 427 | C3×C4 | — | 9 | 1 | no | — |
| 428 | C3×C4 | — | 9 | 1 | no | — |
| 429 | C3×C4 | — | 12 | 2 | no | — |
| 430 | C3×C4 | — | 18 | 2 | no | — |
| 431 | Dic3 | — | 2 | 2 | no | — |
| 432 | Dic3 | — | 6 | 1 | no | — |
| 433 | Dic3 | — | 6 | 1 | no | — |
| 434 | Dic3 | — | 6 | 1 | no | — |
| 435 | Dic3 | — | 6 | 1 | no | — |
| 436 | Dic3 | — | 6 | 2 | no | — |
| 437 | Dic3 | — | 6 | 2 | no | — |
| 438 | Dic3 | — | 9 | 2 | no | — |
| 439 | Dic3 | — | 12 | 2 | no | — |
| 440 | Dic3 | — | 18 | 2 | no | — |
| 441 | Dic3 | — | 18 | 2 | no | — |
| 442 | Dic3 | — | 36 | 2 | no | — |
| 443 | Dic3 | — | 36 | 2 | no | — |
| 444 | C32 | — | 2 | 1 | no | — |
| 445 | C32 | — | 2 | 1 | no | — |
| 446 | C32 | — | 4 | 1 | no | — |
| 447 | C32 | — | 4 | 1 | no | — |
| 448 | C32 | C2×#916 | 1 | 1 | yes | characteristic, complemented |
| 449 | C23 | — | 3 | 1 | no | — |
| 450 | C23 | — | 6 | 1 | no | — |
| 451 | C23 | — | 18 | 1 | no | — |
| 452 | Q8 | — | 9 | 2 | no | — |
| 453 | Q8 | — | 18 | 1 | no | — |
| 454 | Q8 | — | 27 | 2 | no | — |
| 455 | Q8 | — | 54 | 1 | no | — |
| 456 | D4 | — | 9 | 2 | no | — |
| 457 | D4 | — | 18 | 4 | no | — |
| 458 | D4 | — | 18 | 1 | no | — |
| 459 | D4 | — | 18 | 4 | no | — |
| 460 | D4 | — | 27 | 2 | no | — |
| 461 | D4 | — | 54 | 1 | no | — |
| 462 | C2×C4 | — | 6 | 1 | no | — |
| 463 | C2×C4 | — | 9 | 1 | no | — |
| 464 | C2×C4 | — | 18 | 1 | no | — |
| 465 | C2×C4 | — | 27 | 2 | no | — |
| 466 | C2×C4 | — | 27 | 2 | no | — |
| 467 | C2×C4 | — | 27 | 1 | no | — |
| 468 | C2×C4 | — | 54 | 4 | no | — |
| 469 | C2×C4 | — | 54 | 4 | no | — |
| 470 | C8 | — | 9 | 2 | no | — |
| 471 | C8 | — | 27 | 2 | no | — |
| 472 | C2×C3 | — | 2 | 2 | no | — |
| 473 | C2×C3 | — | 2 | 2 | no | — |
| 474 | C2×C3 | — | 2 | 1 | no | — |
| 475 | C2×C3 | — | 2 | 1 | no | — |
| 476 | C2×C3 | — | 4 | 2 | no | — |
| 477 | C2×C3 | — | 4 | 2 | no | — |
| 478 | C2×C3 | — | 4 | 1 | no | — |
| 479 | C2×C3 | — | 4 | 1 | no | — |
| 480 | C2×C3 | — | 12 | 2 | no | — |
| 481 | C2×C3 | — | 12 | 2 | no | — |
| 482 | C2×C3 | — | 12 | 2 | no | — |
| 483 | C2×C3 | — | 12 | 4 | no | — |
| 484 | C2×C3 | — | 12 | 2 | no | — |
| 485 | C2×C3 | — | 36 | 2 | no | — |
| 486 | C2×C3 | #64237 | 1 | 2 | yes | complemented |
| 487 | C2×C3 | C22×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 488 | D3 | — | 2 | 2 | no | — |
| 489 | D3 | — | 4 | 2 | no | — |
| 490 | D3 | — | 12 | 2 | no | — |
| 491 | D3 | — | 12 | 4 | no | — |
| 492 | D3 | — | 12 | 2 | no | — |
| 493 | C22 | — | 3 | 2 | no | — |
| 494 | C22 | — | 6 | 2 | no | — |
| 495 | C22 | — | 6 | 2 | no | — |
| 496 | C22 | — | 12 | 2 | no | — |
| 497 | C22 | — | 18 | 2 | no | — |
| 498 | C22 | — | 36 | 2 | no | — |
| 499 | C22 | D3×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 500 | C4 | — | 6 | 2 | no | — |
| 501 | C4 | — | 9 | 1 | no | — |
| 502 | C4 | — | 9 | 1 | no | — |
| 503 | C4 | — | 18 | 2 | no | — |
| 504 | C4 | — | 27 | 2 | no | — |
| 505 | C3 | — | 2 | 1 | no | — |
| 506 | C3 | — | 2 | 1 | no | — |
| 507 | C3 | — | 4 | 1 | no | — |
| 508 | C3 | — | 4 | 1 | no | — |
| 509 | C3 | C2×#64237 | 1 | 1 | yes | characteristic, complemented |
| 510 | C2 | — | 6 | 2 | no | — |
| 511 | C2 | — | 12 | 2 | no | — |
| 512 | C2 | — | 36 | 2 | no | — |
| 513 | C2 | #11724133 | 1 | 2 | yes | direct product factor |
| 514 | C2 | C2×D3×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×GO+(4,𝔽2) |
| commutator, cosocle | C3×C3⋊Dic3 | C24 |
| Frattini | C2 | C2×D3×GO+(4,𝔽2) |
| Fitting, socle | C22×C33 | C2×D4 |
| hypocenter | C33 | C2×#135 |
| LCS | G ▷ C3×C3⋊Dic3 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#88964 | C2 | semidirect |
| 2. C2×#88963 | C2 | semidirect |
| 3. C2×#88942 | C2 | semidirect |
| 4. C2×#88938 | C2 | semidirect |
| 5. C2×#88935 | C2 | semidirect |
| 6. C2×C3×#3775 | C2 | semidirect |
| 7. C2×D3×#622 | C2 | semidirect |
| 8. #11724133 | C2 | direct (N × H) |
| 22. #88964 | C22 | semidirect |
| 24. #88963 | C22 | semidirect |
| 25. #88942 | C22 | semidirect |
| 26. #88938 | C22 | semidirect |
| 27. #88935 | C22 | semidirect |
| 28. C3×#3775 | C22 | semidirect |
| 29. D3×#622 | C22 | semidirect |
| 37. C2×#3775 | D3 | semidirect |
| 102. #3775 | C2×D3 | semidirect |
| 192. C2×C33 | #135 | semidirect |
| 291. C33 | C2×#135 | semidirect |
| 367. C2×C32 | #916 | semidirect |
| 448. C32 | C2×#916 | semidirect |
| 486. C2×C3 | #64237 | semidirect |
| 509. C3 | C2×#64237 | semidirect |
| 513. C2 | #11724133 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88964 | 2 |
| C2×#88963 | 2 |
| C2×#88942 | 2 |
| C2×#88938 | 2 |
| C2×#88935 | 2 |
| C2×C3×#3775 | 2 |
| C2×D3×#622 | 2 |
| #11724133 | 2 |
| C2×#64237 | 3 |
| C2×#916 | 9 |