Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
646 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 646 conjugacy classes of subgroups — too many to draw. Only its 51 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 | C3×#64313 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11724315 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11724305 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11723703 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11723108 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11722762 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11722754 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10593463 | — | 3 | 1 | no | maximal |
| 9 | C2×D32⋊D3 | — | 2 | 2 | no | — |
| 10 | C3×#3830 | C22 | 1 | 1 | yes | characteristic |
| 11 | C32×D3×D4 | — | 2 | 1 | no | — |
| 12 | C4⋊#1113 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C3×D3×#67 | — | 2 | 2 | no | — |
| 14 | C2×C3×#625 | — | 2 | 1 | no | — |
| 15 | C3×#3805 | — | 2 | 1 | no | — |
| 16 | C3×#3802 | C22 | 1 | 1 | yes | characteristic |
| 17 | C3×#3798 | C22 | 1 | 1 | yes | characteristic |
| 18 | C3×#3795 | — | 2 | 1 | no | — |
| 19 | C4×C3⋊#157 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #88989 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #88936 | — | 2 | 1 | no | — |
| 22 | #88935 | — | 2 | 1 | no | — |
| 23 | C3×#3753 | — | 2 | 1 | no | — |
| 24 | #88811 | — | 2 | 1 | no | — |
| 25 | #88809 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C3×#1004 | — | 6 | 1 | no | — |
| 27 | #64313 | D3 | 1 | 1 | yes | characteristic, complemented |
| 28 | #64231 | — | 3 | 1 | no | — |
| 29 | #64224 | — | 3 | 1 | no | — |
| 30 | #63927 | — | 3 | 1 | no | — |
| 31 | #63925 | — | 6 | 1 | no | — |
| 32 | #63783 | — | 3 | 1 | no | — |
| 33 | #63731 | — | 3 | 1 | no | — |
| 34 | #63727 | — | 3 | 1 | no | — |
| 35 | C22×C32×D3 | — | 2 | 2 | no | — |
| 36 | C2×#1113 | — | 2 | 1 | no | — |
| 37 | C2×C3×D32 | D4 | 1 | 2 | yes | — |
| 38 | C2×C3⋊#157 | — | 2 | 1 | no | — |
| 39 | D32⋊D3 | — | 4 | 4 | no | — |
| 40 | C33×D4 | D4 | 1 | 1 | yes | characteristic, complemented |
| 41 | C3×#638 | — | 2 | 1 | no | — |
| 42 | C2×C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 43 | C3×C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 44 | C3×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 45 | C3×#634 | D4 | 1 | 1 | yes | characteristic, complemented |
| 46 | C32×#67 | — | 2 | 2 | no | — |
| 47 | C32×D12 | — | 2 | 1 | no | — |
| 48 | C32×C4×D3 | — | 2 | 1 | no | — |
| 49 | #6295 | — | 2 | 1 | no | — |
| 50 | C3×#627 | D4 | 1 | 1 | yes | characteristic, complemented |
| 51 | C3×#626 | — | 2 | 1 | no | — |
| 52 | C3×#625 | — | 2 | 2 | no | — |
| 53 | C3×#625 | — | 2 | 1 | no | — |
| 54 | C3×#625 | D4 | 1 | 1 | yes | characteristic, complemented |
| 55 | C3×D3×Dic3 | — | 2 | 2 | no | — |
| 56 | C3⋊#622 | — | 2 | 1 | no | — |
| 57 | C3×C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 58 | #5241 | — | 9 | 1 | no | maximal |
| 59 | C2×GO+(4,𝔽2) | — | 6 | 2 | no | — |
| 60 | C2×C32×D4 | — | 6 | 1 | no | — |
| 61 | #3830 | C2×D3 | 1 | 1 | yes | characteristic |
| 62 | C2×C3×#67 | — | 6 | 2 | no | — |
| 63 | C2×C3×#67 | — | 6 | 2 | no | — |
| 64 | C3×#237 | — | 6 | 1 | no | — |
| 65 | C3×#237 | — | 6 | 2 | no | — |
| 66 | C3×#237 | — | 6 | 1 | no | — |
| 67 | C3×#237 | — | 6 | 1 | no | — |
| 68 | C3×D3×D4 | — | 2 | 1 | no | — |
| 69 | C3×D3×D4 | — | 2 | 1 | no | — |
| 70 | C3×D3×D4 | — | 4 | 1 | no | — |
| 71 | C3×D3×D4 | — | 6 | 1 | no | — |
| 72 | C3×D3×D4 | — | 6 | 2 | no | — |
| 73 | C3×#235 | — | 6 | 1 | no | — |
| 74 | C3×#235 | — | 6 | 1 | no | — |
| 75 | D3×#67 | — | 2 | 2 | no | — |
| 76 | C2×#625 | — | 2 | 1 | no | — |
| 77 | #3805 | — | 2 | 1 | no | — |
| 78 | #3802 | — | 3 | 1 | no | — |
| 79 | #3802 | C2×D3 | 1 | 1 | yes | characteristic |
| 80 | D3×D12 | — | 6 | 1 | no | — |
| 81 | #3798 | C2×D3 | 1 | 1 | yes | characteristic |
| 82 | #3795 | — | 2 | 1 | no | — |
| 83 | C4×#157 | — | 3 | 1 | no | — |
| 84 | #3788 | — | 3 | 1 | no | — |
| 85 | #3775 | — | 6 | 1 | no | — |
| 86 | #3774 | — | 6 | 1 | no | — |
| 87 | #3753 | — | 2 | 1 | no | — |
| 88 | C3×#213 | — | 6 | 1 | no | — |
| 89 | C3×#213 | — | 6 | 1 | no | — |
| 90 | C3×#213 | — | 12 | 1 | no | — |
| 91 | #3717 | — | 6 | 1 | no | — |
| 92 | #3716 | — | 6 | 1 | no | — |
| 93 | #3715 | — | 6 | 1 | no | — |
| 94 | #3712 | — | 3 | 1 | no | — |
| 95 | #3711 | — | 6 | 1 | no | — |
| 96 | C22×C33 | — | 2 | 1 | no | — |
| 97 | C2×C3×C3⋊D3 | — | 4 | 1 | no | — |
| 98 | C2×C3×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 99 | C2×C32×D3 | — | 2 | 2 | no | — |
| 100 | C2×C32×D3 | — | 2 | 1 | no | — |
| 101 | C2×C32×D3 | — | 8 | 2 | no | — |
| 102 | #1113 | — | 4 | 2 | no | — |
| 103 | C3×D32 | — | 4 | 2 | no | — |
| 104 | C3⋊#157 | — | 2 | 2 | no | — |
| 105 | C33×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 106 | C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 107 | C3×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 108 | C32×Dic3 | — | 2 | 1 | no | — |
| 109 | C3×H(5,𝔽2) | — | 9 | 1 | no | — |
| 110 | #1004 | — | 6 | 1 | no | — |
| 111 | #949 | — | 9 | 1 | no | — |
| 112 | #949 | — | 9 | 1 | no | — |
| 113 | #940 | — | 9 | 1 | no | — |
| 114 | #911 | — | 18 | 1 | no | — |
| 115 | #837 | — | 9 | 1 | no | — |
| 116 | #837 | — | 9 | 1 | no | — |
| 117 | #833 | — | 9 | 1 | no | — |
| 118 | C23×C32 | — | 6 | 2 | no | — |
| 119 | C22×C3×D3 | — | 2 | 2 | no | — |
| 120 | C22×C3×D3 | — | 2 | 2 | no | — |
| 121 | C22×C3×D3 | — | 4 | 2 | no | — |
| 122 | C22×C3×D3 | — | 6 | 2 | no | — |
| 123 | C2×D32 | — | 6 | 1 | no | — |
| 124 | C2×D32 | — | 12 | 1 | no | — |
| 125 | C2×D32 | #67 | 1 | 2 | yes | — |
| 126 | C2×#157 | — | 6 | 1 | no | — |
| 127 | GO+(4,𝔽2) | — | 12 | 4 | no | — |
| 128 | C32×D4 | — | 2 | 1 | no | — |
| 129 | C32×D4 | — | 2 | 1 | no | — |
| 130 | C32×D4 | — | 4 | 1 | no | — |
| 131 | C32×D4 | — | 4 | 1 | no | — |
| 132 | C32×D4 | — | 6 | 1 | no | — |
| 133 | C32×D4 | — | 6 | 2 | no | — |
| 134 | C32×D4 | #67 | 1 | 1 | yes | characteristic, complemented |
| 135 | C2×C32×C4 | — | 6 | 1 | no | — |
| 136 | #638 | — | 2 | 1 | no | — |
| 137 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 138 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 139 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 140 | #634 | #67 | 1 | 1 | yes | characteristic, complemented |
| 141 | C3×#67 | — | 2 | 2 | no | — |
| 142 | C3×#67 | — | 2 | 2 | no | — |
| 143 | C3×#67 | — | 4 | 2 | no | — |
| 144 | C3×#67 | — | 6 | 1 | no | — |
| 145 | C3×#67 | — | 6 | 1 | no | — |
| 146 | C3×#67 | — | 6 | 2 | no | — |
| 147 | C3×#67 | — | 6 | 2 | no | — |
| 148 | C3×#67 | — | 6 | 2 | no | — |
| 149 | C3×#67 | — | 6 | 2 | no | — |
| 150 | C3×#67 | — | 12 | 1 | no | — |
| 151 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 152 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 153 | C2×C3×Dic3 | — | 12 | 1 | no | — |
| 154 | C3×D12 | — | 2 | 1 | no | — |
| 155 | C3×D12 | — | 2 | 1 | no | — |
| 156 | C3×D12 | — | 4 | 1 | no | — |
| 157 | C3×D12 | — | 6 | 1 | no | — |
| 158 | C3×D12 | — | 6 | 1 | no | — |
| 159 | C3×D12 | — | 6 | 1 | no | — |
| 160 | C3×D12 | — | 12 | 1 | no | — |
| 161 | C3×C4×D3 | — | 2 | 1 | no | — |
| 162 | C3×C4×D3 | — | 2 | 1 | no | — |
| 163 | C3×C4×D3 | — | 4 | 1 | no | — |
| 164 | C3×C4×D3 | — | 6 | 1 | no | — |
| 165 | C3×C4×D3 | — | 6 | 1 | no | — |
| 166 | C3×C4×D3 | — | 6 | 2 | no | — |
| 167 | C3×Dic6 | — | 6 | 1 | no | — |
| 168 | C3×Dic6 | — | 6 | 1 | no | — |
| 169 | C3×Dic6 | — | 6 | 1 | no | — |
| 170 | #627 | #67 | 1 | 1 | yes | characteristic, complemented |
| 171 | #626 | — | 2 | 1 | no | — |
| 172 | #626 | — | 12 | 1 | no | — |
| 173 | #625 | — | 2 | 2 | no | — |
| 174 | #625 | — | 2 | 1 | no | — |
| 175 | #625 | — | 6 | 1 | no | — |
| 176 | #625 | #67 | 1 | 1 | yes | characteristic, complemented |
| 177 | D3×Dic3 | — | 2 | 2 | no | — |
| 178 | #622 | — | 6 | 1 | no | — |
| 179 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 180 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 181 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 182 | C3×C3⋊C8 | — | 12 | 1 | no | — |
| 183 | #453 | — | 27 | 1 | no | Sylow |
| 184 | C2×C33 | — | 4 | 1 | no | — |
| 185 | C2×C33 | #120 | 1 | 1 | yes | characteristic |
| 186 | C3×C3⋊D3 | — | 2 | 1 | no | — |
| 187 | C3×C3⋊D3 | — | 8 | 1 | no | — |
| 188 | C32×D3 | — | 4 | 1 | no | — |
| 189 | C32×D3 | — | 4 | 2 | no | — |
| 190 | C3×#41 | — | 9 | 1 | no | — |
| 191 | C3×#41 | — | 9 | 1 | no | — |
| 192 | C3×#41 | — | 18 | 1 | no | — |
| 193 | C3×#41 | — | 18 | 1 | no | — |
| 194 | C2×C3×D4 | — | 6 | 1 | no | — |
| 195 | C2×C3×D4 | — | 6 | 1 | no | — |
| 196 | C2×C3×D4 | — | 9 | 1 | no | — |
| 197 | C2×C3×D4 | — | 12 | 1 | no | — |
| 198 | C2×C3×D4 | — | 18 | 2 | no | — |
| 199 | C2×C3×D4 | — | 18 | 1 | no | — |
| 200 | C2×#67 | — | 6 | 2 | no | — |
| 201 | C2×#67 | — | 6 | 2 | no | — |
| 202 | C2×#67 | — | 18 | 2 | no | — |
| 203 | #237 | — | 6 | 1 | no | — |
| 204 | #237 | — | 6 | 1 | no | — |
| 205 | #237 | — | 6 | 1 | no | — |
| 206 | #237 | — | 6 | 2 | no | — |
| 207 | D3×D4 | — | 2 | 1 | no | — |
| 208 | D3×D4 | — | 6 | 1 | no | — |
| 209 | D3×D4 | — | 6 | 2 | no | — |
| 210 | D3×D4 | — | 18 | 1 | no | — |
| 211 | #235 | — | 6 | 1 | no | — |
| 212 | #235 | — | 6 | 1 | no | — |
| 213 | C2×D12 | — | 9 | 1 | no | — |
| 214 | C3×D8 | — | 18 | 1 | no | — |
| 215 | #215 | — | 18 | 1 | no | — |
| 216 | #215 | — | 18 | 1 | no | — |
| 217 | #214 | — | 18 | 1 | no | — |
| 218 | #213 | — | 6 | 1 | no | — |
| 219 | #213 | — | 6 | 1 | no | — |
| 220 | #213 | — | 12 | 1 | no | — |
| 221 | #213 | — | 18 | 1 | no | — |
| 222 | C4×Dic3 | — | 9 | 1 | no | — |
| 223 | #208 | — | 9 | 1 | no | — |
| 224 | #208 | — | 9 | 1 | no | — |
| 225 | #204 | — | 18 | 1 | no | — |
| 226 | ΓL(1,𝔽25) | — | 18 | 1 | no | — |
| 227 | C22×C32 | — | 2 | 2 | no | — |
| 228 | C22×C32 | — | 2 | 1 | no | — |
| 229 | C22×C32 | — | 4 | 1 | no | — |
| 230 | C22×C32 | — | 4 | 2 | no | — |
| 231 | C22×C32 | — | 6 | 2 | no | — |
| 232 | C22×C32 | — | 6 | 1 | no | — |
| 233 | C22×C32 | — | 8 | 1 | no | — |
| 234 | C22×C32 | — | 24 | 2 | no | — |
| 235 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 236 | C2×C3⋊D3 | C2×#67 | 1 | 1 | yes | characteristic |
| 237 | C2×C3×D3 | — | 2 | 1 | no | — |
| 238 | C2×C3×D3 | — | 2 | 2 | no | — |
| 239 | C2×C3×D3 | — | 2 | 2 | no | — |
| 240 | C2×C3×D3 | — | 2 | 1 | no | — |
| 241 | C2×C3×D3 | — | 4 | 1 | no | — |
| 242 | C2×C3×D3 | — | 4 | 2 | no | — |
| 243 | C2×C3×D3 | — | 6 | 1 | no | — |
| 244 | C2×C3×D3 | — | 6 | 1 | no | — |
| 245 | C2×C3×D3 | — | 8 | 2 | no | — |
| 246 | C2×C3×D3 | — | 8 | 2 | no | — |
| 247 | C2×C3×D3 | — | 8 | 4 | no | — |
| 248 | C2×C3×D3 | — | 12 | 1 | no | — |
| 249 | C2×C3×D3 | — | 12 | 1 | no | — |
| 250 | C2×C3×D3 | — | 24 | 2 | no | — |
| 251 | C2×C3×D3 | — | 24 | 1 | no | — |
| 252 | D32 | — | 4 | 2 | no | — |
| 253 | D32 | — | 12 | 2 | no | — |
| 254 | D32 | — | 24 | 2 | no | — |
| 255 | #157 | — | 6 | 2 | no | — |
| 256 | C32×C4 | — | 2 | 1 | no | — |
| 257 | C32×C4 | — | 2 | 1 | no | — |
| 258 | C32×C4 | — | 4 | 1 | no | — |
| 259 | C32×C4 | — | 4 | 1 | no | — |
| 260 | C32×C4 | — | 6 | 1 | no | — |
| 261 | C32×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 262 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 263 | C3⋊Dic3 | C2×#67 | 1 | 1 | yes | characteristic |
| 264 | C3×Dic3 | — | 2 | 1 | no | — |
| 265 | C3×Dic3 | — | 2 | 1 | no | — |
| 266 | C3×Dic3 | — | 4 | 1 | no | — |
| 267 | C3×Dic3 | — | 6 | 1 | no | — |
| 268 | C3×Dic3 | — | 6 | 1 | no | — |
| 269 | C3×Dic3 | — | 6 | 2 | no | — |
| 270 | C3×Dic3 | — | 12 | 1 | no | — |
| 271 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 272 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 273 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 274 | #127 | — | 27 | 1 | no | — |
| 275 | #104 | — | 27 | 1 | no | — |
| 276 | #104 | — | 27 | 1 | no | — |
| 277 | #100 | — | 27 | 1 | no | — |
| 278 | C33 | #453 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 279 | C23×C3 | — | 6 | 2 | no | — |
| 280 | C23×C3 | — | 6 | 2 | no | — |
| 281 | C23×C3 | — | 9 | 2 | no | — |
| 282 | C23×C3 | — | 12 | 2 | no | — |
| 283 | C22×D3 | — | 2 | 2 | no | — |
| 284 | C22×D3 | — | 6 | 2 | no | — |
| 285 | C22×D3 | — | 18 | 1 | no | — |
| 286 | C22×D3 | — | 36 | 1 | no | — |
| 287 | C3×Q8 | — | 9 | 1 | no | — |
| 288 | C3×Q8 | — | 9 | 1 | no | — |
| 289 | C3×D4 | — | 2 | 1 | no | — |
| 290 | C3×D4 | — | 2 | 1 | no | — |
| 291 | C3×D4 | — | 4 | 1 | no | — |
| 292 | C3×D4 | — | 4 | 1 | no | — |
| 293 | C3×D4 | — | 6 | 1 | no | — |
| 294 | C3×D4 | — | 6 | 2 | no | — |
| 295 | C3×D4 | — | 6 | 2 | no | — |
| 296 | C3×D4 | — | 6 | 1 | no | — |
| 297 | C3×D4 | — | 9 | 1 | no | — |
| 298 | C3×D4 | — | 12 | 1 | no | — |
| 299 | C3×D4 | — | 12 | 2 | no | — |
| 300 | C3×D4 | — | 18 | 1 | no | — |
| 301 | C3×D4 | — | 18 | 1 | no | — |
| 302 | C3×D4 | — | 18 | 1 | no | — |
| 303 | C3×D4 | — | 18 | 1 | no | — |
| 304 | C3×D4 | — | 18 | 2 | no | — |
| 305 | C3×D4 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 306 | C2×C3×C4 | — | 6 | 1 | no | — |
| 307 | C2×C3×C4 | — | 6 | 1 | no | — |
| 308 | C2×C3×C4 | — | 9 | 1 | no | — |
| 309 | C2×C3×C4 | — | 12 | 1 | no | — |
| 310 | C2×C3×C4 | — | 18 | 2 | no | — |
| 311 | C2×C3×C4 | — | 18 | 1 | no | — |
| 312 | #67 | — | 2 | 2 | no | — |
| 313 | #67 | — | 6 | 1 | no | — |
| 314 | #67 | — | 6 | 1 | no | — |
| 315 | #67 | — | 6 | 2 | no | — |
| 316 | #67 | — | 6 | 2 | no | — |
| 317 | #67 | — | 6 | 2 | no | — |
| 318 | #67 | — | 6 | 2 | no | — |
| 319 | #67 | — | 12 | 1 | no | — |
| 320 | #67 | — | 36 | 1 | no | — |
| 321 | #67 | — | 36 | 4 | no | — |
| 322 | C2×Dic3 | — | 6 | 2 | no | — |
| 323 | C2×Dic3 | — | 6 | 2 | no | — |
| 324 | C2×Dic3 | — | 12 | 1 | no | — |
| 325 | C2×Dic3 | — | 18 | 1 | no | — |
| 326 | D12 | — | 2 | 1 | no | — |
| 327 | D12 | — | 6 | 1 | no | — |
| 328 | D12 | — | 6 | 1 | no | — |
| 329 | D12 | — | 6 | 1 | no | — |
| 330 | D12 | — | 12 | 1 | no | — |
| 331 | D12 | — | 18 | 1 | no | — |
| 332 | C4×D3 | — | 2 | 1 | no | — |
| 333 | C4×D3 | — | 6 | 1 | no | — |
| 334 | C4×D3 | — | 6 | 1 | no | — |
| 335 | C4×D3 | — | 6 | 2 | no | — |
| 336 | Dic6 | — | 6 | 1 | no | — |
| 337 | Dic6 | — | 6 | 1 | no | — |
| 338 | Dic6 | — | 6 | 1 | no | — |
| 339 | C3×C8 | — | 18 | 1 | no | — |
| 340 | C3⋊C8 | — | 6 | 1 | no | — |
| 341 | C3⋊C8 | — | 6 | 1 | no | — |
| 342 | C3⋊C8 | — | 12 | 1 | no | — |
| 343 | C3⋊C8 | — | 18 | 1 | no | — |
| 344 | C2×C32 | — | 2 | 1 | no | — |
| 345 | C2×C32 | — | 2 | 1 | no | — |
| 346 | C2×C32 | — | 4 | 1 | no | — |
| 347 | C2×C32 | — | 4 | 1 | no | — |
| 348 | C2×C32 | — | 4 | 2 | no | — |
| 349 | C2×C32 | — | 4 | 1 | no | — |
| 350 | C2×C32 | — | 8 | 1 | no | — |
| 351 | C2×C32 | — | 8 | 2 | no | — |
| 352 | C2×C32 | — | 12 | 1 | no | — |
| 353 | C2×C32 | — | 12 | 2 | no | — |
| 354 | C2×C32 | — | 16 | 1 | no | — |
| 355 | C2×C32 | #953 | 1 | 1 | yes | characteristic |
| 356 | C3⋊D3 | — | 2 | 1 | no | — |
| 357 | C3⋊D3 | — | 8 | 1 | no | — |
| 358 | C3×D3 | — | 4 | 1 | no | — |
| 359 | C3×D3 | — | 4 | 2 | no | — |
| 360 | C3×D3 | — | 4 | 2 | no | — |
| 361 | C3×D3 | — | 4 | 2 | no | — |
| 362 | C3×D3 | — | 4 | 1 | no | — |
| 363 | C3×D3 | — | 8 | 2 | no | — |
| 364 | C3×D3 | — | 12 | 1 | no | — |
| 365 | C3×D3 | — | 12 | 1 | no | — |
| 366 | C3×D3 | — | 24 | 1 | no | — |
| 367 | C3×D3 | — | 24 | 1 | no | — |
| 368 | C3×D3 | — | 48 | 1 | no | — |
| 369 | #41 | — | 9 | 1 | no | — |
| 370 | #41 | — | 9 | 1 | no | — |
| 371 | #41 | — | 18 | 1 | no | — |
| 372 | #41 | — | 18 | 1 | no | — |
| 373 | C2×D4 | — | 6 | 1 | no | — |
| 374 | C2×D4 | — | 9 | 1 | no | — |
| 375 | C2×D4 | — | 18 | 2 | no | — |
| 376 | C2×D4 | — | 18 | 1 | no | — |
| 377 | C2×D4 | — | 27 | 1 | no | — |
| 378 | C2×D4 | — | 54 | 2 | no | — |
| 379 | SD16 | — | 54 | 1 | no | — |
| 380 | SD16 | — | 54 | 1 | no | — |
| 381 | D8 | — | 18 | 1 | no | — |
| 382 | D8 | — | 54 | 1 | no | — |
| 383 | M16 | — | 27 | 1 | no | — |
| 384 | M16 | — | 27 | 1 | no | — |
| 385 | C42 | — | 27 | 1 | no | — |
| 386 | C22×C3 | — | 2 | 2 | no | — |
| 387 | C22×C3 | — | 2 | 1 | no | — |
| 388 | C22×C3 | — | 4 | 1 | no | — |
| 389 | C22×C3 | — | 4 | 2 | no | — |
| 390 | C22×C3 | — | 6 | 2 | no | — |
| 391 | C22×C3 | — | 6 | 1 | no | — |
| 392 | C22×C3 | — | 6 | 1 | no | — |
| 393 | C22×C3 | — | 6 | 2 | no | — |
| 394 | C22×C3 | — | 8 | 1 | no | — |
| 395 | C22×C3 | — | 9 | 1 | no | — |
| 396 | C22×C3 | — | 12 | 1 | no | — |
| 397 | C22×C3 | — | 12 | 2 | no | — |
| 398 | C22×C3 | — | 24 | 2 | no | — |
| 399 | C22×C3 | — | 24 | 2 | no | — |
| 400 | C22×C3 | — | 24 | 4 | no | — |
| 401 | C22×C3 | — | 36 | 1 | no | — |
| 402 | C22×C3 | — | 36 | 2 | no | — |
| 403 | C2×D3 | — | 2 | 1 | no | — |
| 404 | C2×D3 | — | 2 | 2 | no | — |
| 405 | C2×D3 | — | 6 | 1 | no | — |
| 406 | C2×D3 | — | 6 | 1 | no | — |
| 407 | C2×D3 | — | 8 | 2 | no | — |
| 408 | C2×D3 | — | 12 | 1 | no | — |
| 409 | C2×D3 | — | 12 | 1 | no | — |
| 410 | C2×D3 | — | 24 | 2 | no | — |
| 411 | C2×D3 | — | 24 | 1 | no | — |
| 412 | C2×D3 | — | 36 | 2 | no | — |
| 413 | C2×D3 | — | 72 | 2 | no | — |
| 414 | C3×C4 | — | 2 | 1 | no | — |
| 415 | C3×C4 | — | 2 | 1 | no | — |
| 416 | C3×C4 | — | 4 | 1 | no | — |
| 417 | C3×C4 | — | 4 | 1 | no | — |
| 418 | C3×C4 | — | 6 | 1 | no | — |
| 419 | C3×C4 | — | 6 | 1 | no | — |
| 420 | C3×C4 | — | 9 | 1 | no | — |
| 421 | C3×C4 | — | 12 | 1 | no | — |
| 422 | C3×C4 | — | 18 | 1 | no | — |
| 423 | C3×C4 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 424 | Dic3 | — | 2 | 1 | no | — |
| 425 | Dic3 | — | 6 | 1 | no | — |
| 426 | Dic3 | — | 6 | 1 | no | — |
| 427 | Dic3 | — | 6 | 2 | no | — |
| 428 | Dic3 | — | 12 | 1 | no | — |
| 429 | Dic3 | — | 18 | 2 | no | — |
| 430 | C32 | — | 2 | 1 | no | — |
| 431 | C32 | — | 2 | 1 | no | — |
| 432 | C32 | — | 4 | 1 | no | — |
| 433 | C32 | — | 4 | 1 | no | — |
| 434 | C32 | #5241 | 1 | 1 | yes | characteristic, complemented |
| 435 | C23 | — | 6 | 2 | no | — |
| 436 | C23 | — | 9 | 2 | no | — |
| 437 | C23 | — | 54 | 1 | no | — |
| 438 | Q8 | — | 9 | 1 | no | — |
| 439 | Q8 | — | 9 | 1 | no | — |
| 440 | D4 | — | 6 | 2 | no | — |
| 441 | D4 | — | 6 | 1 | no | — |
| 442 | D4 | — | 9 | 1 | no | — |
| 443 | D4 | — | 18 | 1 | no | — |
| 444 | D4 | — | 18 | 1 | no | — |
| 445 | D4 | — | 18 | 1 | no | — |
| 446 | D4 | — | 18 | 2 | no | — |
| 447 | D4 | — | 18 | 1 | no | — |
| 448 | D4 | — | 54 | 1 | no | — |
| 449 | D4 | — | 108 | 4 | no | — |
| 450 | D4 | D32⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 451 | C2×C4 | — | 6 | 1 | no | — |
| 452 | C2×C4 | — | 9 | 1 | no | — |
| 453 | C2×C4 | — | 18 | 2 | no | — |
| 454 | C2×C4 | — | 18 | 1 | no | — |
| 455 | C2×C4 | — | 54 | 1 | no | — |
| 456 | C8 | — | 18 | 1 | no | — |
| 457 | C8 | — | 54 | 1 | no | — |
| 458 | C2×C3 | — | 2 | 1 | no | — |
| 459 | C2×C3 | — | 2 | 1 | no | — |
| 460 | C2×C3 | — | 4 | 2 | no | — |
| 461 | C2×C3 | — | 4 | 1 | no | — |
| 462 | C2×C3 | — | 4 | 1 | no | — |
| 463 | C2×C3 | — | 4 | 1 | no | — |
| 464 | C2×C3 | — | 8 | 1 | no | — |
| 465 | C2×C3 | — | 8 | 2 | no | — |
| 466 | C2×C3 | — | 12 | 2 | no | — |
| 467 | C2×C3 | — | 12 | 1 | no | — |
| 468 | C2×C3 | — | 12 | 2 | no | — |
| 469 | C2×C3 | — | 12 | 1 | no | — |
| 470 | C2×C3 | — | 12 | 2 | no | — |
| 471 | C2×C3 | — | 16 | 1 | no | — |
| 472 | C2×C3 | — | 18 | 1 | no | — |
| 473 | C2×C3 | — | 24 | 2 | no | — |
| 474 | C2×C3 | — | 72 | 1 | no | — |
| 475 | C2×C3 | #64241 | 1 | 1 | yes | characteristic |
| 476 | D3 | — | 4 | 1 | no | — |
| 477 | D3 | — | 4 | 2 | no | — |
| 478 | D3 | — | 12 | 1 | no | — |
| 479 | D3 | — | 12 | 1 | no | — |
| 480 | D3 | — | 24 | 1 | no | — |
| 481 | D3 | — | 24 | 1 | no | — |
| 482 | D3 | — | 48 | 1 | no | — |
| 483 | C22 | — | 2 | 1 | no | — |
| 484 | C22 | — | 6 | 1 | no | — |
| 485 | C22 | — | 6 | 2 | no | — |
| 486 | C22 | — | 9 | 1 | no | — |
| 487 | C22 | — | 24 | 2 | no | — |
| 488 | C22 | — | 36 | 2 | no | — |
| 489 | C22 | — | 36 | 1 | no | — |
| 490 | C22 | — | 108 | 2 | no | — |
| 491 | C4 | — | 6 | 1 | no | — |
| 492 | C4 | — | 9 | 1 | no | — |
| 493 | C4 | — | 18 | 1 | no | — |
| 494 | C4 | — | 54 | 2 | no | — |
| 495 | C4 | C2×D32⋊D3 | 1 | 1 | yes | characteristic |
| 496 | C3 | — | 2 | 1 | no | — |
| 497 | C3 | — | 2 | 1 | no | — |
| 498 | C3 | — | 4 | 1 | no | — |
| 499 | C3 | — | 4 | 1 | no | — |
| 500 | C3 | #10593463 | 1 | 1 | yes | characteristic, complemented |
| 501 | C2 | — | 4 | 1 | no | — |
| 502 | C2 | — | 12 | 1 | no | — |
| 503 | C2 | — | 12 | 2 | no | — |
| 504 | C2 | — | 18 | 1 | no | — |
| 505 | C2 | — | 72 | 1 | no | — |
| 506 | C2 | #11724331 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #11724331 |
| commutator, cosocle | C3×C4×C3⋊D3 | C23 |
| Frattini | C4 | C2×D32⋊D3 |
| Fitting | C33×D4 | D4 |
| socle | C2×C33 | #120 |
| hypercenter | D4 | D32⋊D3 |
| hypocenter | C33 | #453 |
| LCS | G ▷ C3×C4×C3⋊D3 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#64313 | C2 | semidirect |
| 2. #11724315 | C2 | semidirect |
| 3. #11724305 | C2 | semidirect |
| 4. #11723703 | C2 | semidirect |
| 5. #11723108 | C2 | semidirect |
| 6. #11722762 | C2 | semidirect |
| 7. #11722754 | C2 | semidirect |
| 12. C4⋊#1113 | C22 | semidirect |
| 19. C4×C3⋊#157 | C22 | semidirect |
| 20. #88989 | C22 | semidirect |
| 25. #88809 | C22 | semidirect |
| 27. #64313 | D3 | semidirect |
| 40. C33×D4 | D4 | semidirect |
| 45. C3×#634 | D4 | semidirect |
| 50. C3×#627 | D4 | semidirect |
| 54. C3×#625 | D4 | semidirect |
| 134. C32×D4 | #67 | semidirect |
| 140. #634 | #67 | semidirect |
| 170. #627 | #67 | semidirect |
| 176. #625 | #67 | semidirect |
| 278. C33 | #453 | semidirect |
| 305. C3×D4 | GO+(4,𝔽2) | semidirect |
| 434. C32 | #5241 | semidirect |
| 450. D4 | D32⋊D3 | semidirect |
| 500. C3 | #10593463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64313 | 2 |
| #11724315 | 2 |
| #11724305 | 2 |
| #11723703 | 2 |
| #11723108 | 2 |
| #11722762 | 2 |
| #11722754 | 2 |
| #10593463 | 3 |
| #5241 | 9 |