Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
604 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
| 2 | C3×#64226 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#64221 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#63931 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#63783 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#63731 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C3×#63727 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10593461 | C3 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 9 | C3×#3830 | C22 | 1 | 1 | yes | characteristic |
| 10 | C32×D3×D4 | — | 2 | 1 | no | — |
| 11 | C3×D3×#67 | — | 2 | 2 | no | — |
| 12 | C2×C3×#625 | — | 2 | 1 | no | — |
| 13 | C3×#3805 | — | 2 | 1 | no | — |
| 14 | C3×#3802 | C22 | 1 | 1 | yes | characteristic |
| 15 | C3×#3798 | C22 | 1 | 1 | yes | characteristic |
| 16 | C3×#3797 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C3×#3795 | — | 2 | 1 | no | — |
| 18 | C3×C4×#157 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C3×#3788 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C3×#3776 | — | 2 | 1 | no | — |
| 21 | C3×#3775 | — | 2 | 1 | no | — |
| 22 | C3×D32⋊C4 | — | 2 | 2 | no | — |
| 23 | C32×#214 | — | 2 | 1 | no | — |
| 24 | C3×#3719 | — | 2 | 1 | no | — |
| 25 | C3×#3712 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C3×#1004 | — | 6 | 1 | no | — |
| 27 | #64313 | C2×C3 | 1 | 1 | yes | characteristic |
| 28 | #64226 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 29 | #64221 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 30 | C3×#915 | — | 6 | 1 | no | — |
| 31 | #63931 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 32 | #63783 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 33 | #63731 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 34 | #63727 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 35 | C22×C32×D3 | — | 2 | 2 | no | — |
| 36 | C2×C3×D32 | D4 | 1 | 2 | yes | — |
| 37 | C2×C3×#157 | — | 2 | 1 | no | — |
| 38 | C33×D4 | D4 | 1 | 1 | yes | characteristic |
| 39 | C3×#638 | — | 2 | 1 | no | — |
| 40 | C2×C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 41 | C3×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 42 | C3×#634 | D4 | 1 | 1 | yes | characteristic |
| 43 | C32×#67 | — | 2 | 2 | no | — |
| 44 | C32×D12 | — | 2 | 1 | no | — |
| 45 | C32×C4×D3 | — | 2 | 1 | no | — |
| 46 | C32×Dic6 | — | 2 | 1 | no | — |
| 47 | C3×#627 | — | 2 | 1 | no | — |
| 48 | C3×#627 | D4 | 1 | 1 | yes | characteristic |
| 49 | C3×#626 | — | 2 | 1 | no | — |
| 50 | C3×#625 | — | 2 | 2 | no | — |
| 51 | C3×#625 | — | 2 | 1 | no | — |
| 52 | C3×#625 | D4 | 1 | 1 | yes | characteristic |
| 53 | C3×#624 | — | 2 | 1 | no | — |
| 54 | C3×D3×Dic3 | — | 2 | 2 | no | — |
| 55 | C3×#622 | — | 2 | 1 | no | — |
| 56 | C32×C3⋊C8 | — | 2 | 1 | no | — |
| 57 | C3×#455 | — | 9 | 1 | no | maximal |
| 58 | C2×C32×D4 | — | 6 | 1 | no | — |
| 59 | #3830 | C22×C3 | 1 | 1 | yes | characteristic |
| 60 | C2×C3×#67 | — | 6 | 2 | no | — |
| 61 | C2×C3×#67 | — | 6 | 2 | no | — |
| 62 | C3×D3×Q8 | — | 6 | 1 | no | — |
| 63 | C3×#237 | — | 6 | 1 | no | — |
| 64 | C3×#237 | — | 6 | 2 | no | — |
| 65 | C3×#237 | — | 6 | 1 | no | — |
| 66 | C3×#237 | — | 6 | 1 | no | — |
| 67 | C3×D3×D4 | — | 2 | 1 | no | — |
| 68 | C3×D3×D4 | — | 2 | 1 | no | — |
| 69 | C3×D3×D4 | — | 4 | 1 | no | — |
| 70 | C3×D3×D4 | — | 6 | 1 | no | — |
| 71 | C3×D3×D4 | — | 6 | 2 | no | — |
| 72 | C3×#235 | — | 6 | 1 | no | — |
| 73 | C3×#235 | — | 6 | 1 | no | — |
| 74 | D3×#67 | — | 2 | 2 | no | — |
| 75 | C2×#625 | — | 2 | 1 | no | — |
| 76 | #3805 | — | 2 | 1 | no | — |
| 77 | #3802 | C22×C3 | 1 | 1 | yes | characteristic |
| 78 | #3798 | C22×C3 | 1 | 1 | yes | characteristic |
| 79 | #3797 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 80 | #3795 | — | 2 | 1 | no | — |
| 81 | C4×#157 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 82 | #3788 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 83 | #3776 | — | 2 | 1 | no | — |
| 84 | #3775 | — | 2 | 1 | no | — |
| 85 | D32⋊C4 | — | 2 | 2 | no | — |
| 86 | C32×SD16 | — | 6 | 1 | no | — |
| 87 | C3×#216 | — | 6 | 1 | no | — |
| 88 | C3×#214 | — | 2 | 1 | no | — |
| 89 | C3×#214 | — | 2 | 1 | no | — |
| 90 | C3×#214 | — | 4 | 1 | no | — |
| 91 | C3×Dic12 | — | 6 | 1 | no | — |
| 92 | C3×ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 93 | #3719 | — | 2 | 1 | no | — |
| 94 | #3712 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 95 | C22×C33 | — | 2 | 1 | no | — |
| 96 | C2×C3×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | C2×C32×D3 | — | 2 | 2 | no | — |
| 98 | C2×C32×D3 | — | 2 | 1 | no | — |
| 99 | C2×C32×D3 | — | 8 | 2 | no | — |
| 100 | C3×D32 | — | 4 | 2 | no | — |
| 101 | C3×#157 | — | 4 | 1 | no | — |
| 102 | C33×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 103 | C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 104 | C3×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 105 | C32×Dic3 | — | 2 | 1 | no | — |
| 106 | C32×Dic3 | — | 4 | 1 | no | — |
| 107 | C3×H(5,𝔽2) | — | 9 | 1 | no | — |
| 108 | #1004 | — | 6 | 1 | no | — |
| 109 | C3×#137 | — | 9 | 1 | no | — |
| 110 | C3×#137 | — | 9 | 1 | no | — |
| 111 | C3×#124 | — | 9 | 1 | no | — |
| 112 | #915 | — | 6 | 1 | no | — |
| 113 | C3×#104 | — | 9 | 1 | no | — |
| 114 | C3×#104 | — | 9 | 1 | no | — |
| 115 | C3×#100 | — | 9 | 1 | no | — |
| 116 | C23×C32 | — | 6 | 2 | no | — |
| 117 | C22×C3×D3 | — | 2 | 2 | no | — |
| 118 | C22×C3×D3 | — | 2 | 2 | no | — |
| 119 | C22×C3×D3 | — | 4 | 2 | no | — |
| 120 | C22×C3×D3 | — | 6 | 2 | no | — |
| 121 | C2×D32 | C3×D4 | 1 | 2 | yes | — |
| 122 | C2×#157 | — | 2 | 1 | no | — |
| 123 | C32×Q8 | — | 6 | 1 | no | — |
| 124 | C32×D4 | — | 2 | 1 | no | — |
| 125 | C32×D4 | — | 2 | 1 | no | — |
| 126 | C32×D4 | — | 4 | 1 | no | — |
| 127 | C32×D4 | — | 4 | 1 | no | — |
| 128 | C32×D4 | — | 6 | 1 | no | — |
| 129 | C32×D4 | — | 6 | 2 | no | — |
| 130 | C32×D4 | C3×D4 | 1 | 1 | yes | characteristic |
| 131 | C2×C32×C4 | — | 6 | 1 | no | — |
| 132 | #638 | — | 2 | 1 | no | — |
| 133 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 134 | C4×C3⋊D3 | C23×C3 | 1 | 1 | yes | characteristic |
| 135 | #634 | C3×D4 | 1 | 1 | yes | characteristic |
| 136 | C3×#67 | — | 2 | 2 | no | — |
| 137 | C3×#67 | — | 2 | 2 | no | — |
| 138 | C3×#67 | — | 4 | 2 | no | — |
| 139 | C3×#67 | — | 6 | 1 | no | — |
| 140 | C3×#67 | — | 6 | 1 | no | — |
| 141 | C3×#67 | — | 6 | 2 | no | — |
| 142 | C3×#67 | — | 6 | 2 | no | — |
| 143 | C3×#67 | — | 6 | 2 | no | — |
| 144 | C3×#67 | — | 6 | 2 | no | — |
| 145 | C3×#67 | — | 12 | 1 | no | — |
| 146 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 147 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 148 | C2×C3×Dic3 | — | 12 | 1 | no | — |
| 149 | C3×D12 | — | 2 | 1 | no | — |
| 150 | C3×D12 | — | 2 | 1 | no | — |
| 151 | C3×D12 | — | 4 | 1 | no | — |
| 152 | C3×D12 | — | 6 | 1 | no | — |
| 153 | C3×C4×D3 | — | 2 | 1 | no | — |
| 154 | C3×C4×D3 | — | 2 | 1 | no | — |
| 155 | C3×C4×D3 | — | 4 | 1 | no | — |
| 156 | C3×C4×D3 | — | 6 | 1 | no | — |
| 157 | C3×C4×D3 | — | 6 | 1 | no | — |
| 158 | C3×C4×D3 | — | 6 | 2 | no | — |
| 159 | C3×C4×D3 | — | 12 | 1 | no | — |
| 160 | C3×Dic6 | — | 2 | 1 | no | — |
| 161 | C3×Dic6 | — | 2 | 1 | no | — |
| 162 | C3×Dic6 | — | 4 | 1 | no | — |
| 163 | C3×Dic6 | — | 6 | 1 | no | — |
| 164 | C3×Dic6 | — | 6 | 1 | no | — |
| 165 | C3×Dic6 | — | 6 | 1 | no | — |
| 166 | C3×Dic6 | — | 12 | 1 | no | — |
| 167 | #627 | — | 2 | 1 | no | — |
| 168 | #627 | C3×D4 | 1 | 1 | yes | characteristic |
| 169 | #626 | — | 2 | 1 | no | — |
| 170 | #625 | — | 2 | 2 | no | — |
| 171 | #625 | — | 2 | 1 | no | — |
| 172 | #625 | C3×D4 | 1 | 1 | yes | characteristic |
| 173 | #624 | — | 2 | 1 | no | — |
| 174 | D3×Dic3 | — | 2 | 2 | no | — |
| 175 | #622 | — | 2 | 1 | no | — |
| 176 | C32×C8 | — | 6 | 1 | no | — |
| 177 | C3×C3⋊C8 | — | 2 | 1 | no | — |
| 178 | C3×C3⋊C8 | — | 2 | 1 | no | — |
| 179 | C3×C3⋊C8 | — | 4 | 1 | no | — |
| 180 | #455 | — | 9 | 1 | no | Sylow |
| 181 | C2×C33 | — | 4 | 1 | no | — |
| 182 | C2×C33 | #120 | 1 | 1 | yes | characteristic |
| 183 | C3×C3⋊D3 | — | 2 | 1 | no | — |
| 184 | C32×D3 | — | 4 | 1 | no | — |
| 185 | C32×D3 | — | 4 | 2 | no | — |
| 186 | C3×#41 | — | 9 | 1 | no | — |
| 187 | C3×#41 | — | 9 | 1 | no | — |
| 188 | C3×#41 | — | 18 | 1 | no | — |
| 189 | C3×#41 | — | 18 | 1 | no | — |
| 190 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 191 | C2×C3×D4 | — | 6 | 1 | no | — |
| 192 | C2×C3×D4 | — | 6 | 1 | no | — |
| 193 | C2×C3×D4 | — | 9 | 1 | no | — |
| 194 | C2×C3×D4 | — | 12 | 1 | no | — |
| 195 | C2×C3×D4 | — | 18 | 2 | no | — |
| 196 | C2×C3×D4 | — | 18 | 1 | no | — |
| 197 | C2×#67 | — | 6 | 2 | no | — |
| 198 | C2×#67 | — | 6 | 2 | no | — |
| 199 | D3×Q8 | — | 6 | 1 | no | — |
| 200 | #237 | — | 6 | 1 | no | — |
| 201 | #237 | — | 6 | 1 | no | — |
| 202 | #237 | — | 6 | 1 | no | — |
| 203 | #237 | — | 6 | 2 | no | — |
| 204 | D3×D4 | — | 2 | 1 | no | — |
| 205 | D3×D4 | — | 6 | 1 | no | — |
| 206 | D3×D4 | — | 6 | 2 | no | — |
| 207 | #235 | — | 6 | 1 | no | — |
| 208 | #235 | — | 6 | 1 | no | — |
| 209 | C3×Q16 | — | 18 | 1 | no | — |
| 210 | C3×Q16 | — | 18 | 1 | no | — |
| 211 | C3×SD16 | — | 6 | 1 | no | — |
| 212 | C3×SD16 | — | 6 | 1 | no | — |
| 213 | C3×SD16 | — | 12 | 1 | no | — |
| 214 | C3×SD16 | — | 18 | 1 | no | — |
| 215 | C3×M16 | — | 9 | 1 | no | — |
| 216 | C3×M16 | — | 9 | 1 | no | — |
| 217 | C3×C22⋊C4 | — | 18 | 2 | no | — |
| 218 | C3×C42 | — | 9 | 1 | no | — |
| 219 | #216 | — | 6 | 1 | no | — |
| 220 | #214 | — | 2 | 1 | no | — |
| 221 | Dic12 | — | 6 | 1 | no | — |
| 222 | ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 223 | C22×C32 | — | 2 | 2 | no | — |
| 224 | C22×C32 | — | 2 | 1 | no | — |
| 225 | C22×C32 | — | 4 | 1 | no | — |
| 226 | C22×C32 | — | 4 | 2 | no | — |
| 227 | C22×C32 | — | 6 | 2 | no | — |
| 228 | C22×C32 | — | 6 | 1 | no | — |
| 229 | C22×C32 | — | 8 | 1 | no | — |
| 230 | C22×C32 | — | 24 | 2 | no | — |
| 231 | C2×C3⋊D3 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 232 | C2×C3×D3 | — | 2 | 1 | no | — |
| 233 | C2×C3×D3 | — | 2 | 2 | no | — |
| 234 | C2×C3×D3 | — | 2 | 2 | no | — |
| 235 | C2×C3×D3 | — | 2 | 1 | no | — |
| 236 | C2×C3×D3 | — | 4 | 1 | no | — |
| 237 | C2×C3×D3 | — | 4 | 2 | no | — |
| 238 | C2×C3×D3 | — | 6 | 1 | no | — |
| 239 | C2×C3×D3 | — | 6 | 1 | no | — |
| 240 | C2×C3×D3 | — | 8 | 2 | no | — |
| 241 | C2×C3×D3 | — | 8 | 2 | no | — |
| 242 | C2×C3×D3 | — | 8 | 4 | no | — |
| 243 | C2×C3×D3 | — | 24 | 2 | no | — |
| 244 | D32 | — | 4 | 2 | no | — |
| 245 | #157 | — | 4 | 1 | no | — |
| 246 | C32×C4 | — | 2 | 1 | no | — |
| 247 | C32×C4 | — | 2 | 1 | no | — |
| 248 | C32×C4 | — | 4 | 1 | no | — |
| 249 | C32×C4 | — | 4 | 1 | no | — |
| 250 | C32×C4 | — | 6 | 1 | no | — |
| 251 | C32×C4 | — | 12 | 1 | no | — |
| 252 | C32×C4 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 253 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 254 | C3⋊Dic3 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 255 | C3×Dic3 | — | 2 | 1 | no | — |
| 256 | C3×Dic3 | — | 2 | 1 | no | — |
| 257 | C3×Dic3 | — | 4 | 1 | no | — |
| 258 | C3×Dic3 | — | 4 | 1 | no | — |
| 259 | C3×Dic3 | — | 4 | 1 | no | — |
| 260 | C3×Dic3 | — | 6 | 1 | no | — |
| 261 | C3×Dic3 | — | 6 | 1 | no | — |
| 262 | C3×Dic3 | — | 6 | 2 | no | — |
| 263 | C3×Dic3 | — | 8 | 1 | no | — |
| 264 | C3×Dic3 | — | 12 | 1 | no | — |
| 265 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 266 | #137 | — | 9 | 1 | no | — |
| 267 | #137 | — | 9 | 1 | no | — |
| 268 | #124 | — | 9 | 1 | no | — |
| 269 | #104 | — | 9 | 1 | no | — |
| 270 | #104 | — | 9 | 1 | no | — |
| 271 | #100 | — | 9 | 1 | no | — |
| 272 | C33 | #455 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 273 | C23×C3 | — | 6 | 2 | no | — |
| 274 | C23×C3 | — | 6 | 2 | no | — |
| 275 | C23×C3 | — | 9 | 2 | no | — |
| 276 | C23×C3 | — | 12 | 2 | no | — |
| 277 | C22×D3 | — | 2 | 2 | no | — |
| 278 | C22×D3 | — | 6 | 2 | no | — |
| 279 | C3×Q8 | — | 6 | 1 | no | — |
| 280 | C3×Q8 | — | 6 | 1 | no | — |
| 281 | C3×Q8 | — | 9 | 1 | no | — |
| 282 | C3×Q8 | — | 9 | 1 | no | — |
| 283 | C3×Q8 | — | 12 | 1 | no | — |
| 284 | C3×Q8 | — | 18 | 1 | no | — |
| 285 | C3×D4 | — | 2 | 1 | no | — |
| 286 | C3×D4 | — | 2 | 1 | no | — |
| 287 | C3×D4 | — | 4 | 1 | no | — |
| 288 | C3×D4 | — | 4 | 1 | no | — |
| 289 | C3×D4 | — | 6 | 1 | no | — |
| 290 | C3×D4 | — | 6 | 2 | no | — |
| 291 | C3×D4 | — | 6 | 2 | no | — |
| 292 | C3×D4 | — | 6 | 1 | no | — |
| 293 | C3×D4 | — | 9 | 1 | no | — |
| 294 | C3×D4 | — | 12 | 1 | no | — |
| 295 | C3×D4 | — | 12 | 2 | no | — |
| 296 | C3×D4 | — | 18 | 1 | no | — |
| 297 | C3×D4 | — | 18 | 1 | no | — |
| 298 | C3×D4 | — | 18 | 1 | no | — |
| 299 | C3×D4 | — | 18 | 2 | no | — |
| 300 | C3×D4 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 301 | C2×C3×C4 | — | 6 | 1 | no | — |
| 302 | C2×C3×C4 | — | 6 | 1 | no | — |
| 303 | C2×C3×C4 | — | 9 | 1 | no | — |
| 304 | C2×C3×C4 | — | 12 | 1 | no | — |
| 305 | C2×C3×C4 | — | 18 | 2 | no | — |
| 306 | C2×C3×C4 | — | 18 | 1 | no | — |
| 307 | C2×C3×C4 | — | 18 | 1 | no | — |
| 308 | C2×C3×C4 | — | 18 | 1 | no | — |
| 309 | #67 | — | 2 | 2 | no | — |
| 310 | #67 | — | 6 | 1 | no | — |
| 311 | #67 | — | 6 | 1 | no | — |
| 312 | #67 | — | 6 | 2 | no | — |
| 313 | #67 | — | 6 | 2 | no | — |
| 314 | #67 | — | 6 | 2 | no | — |
| 315 | #67 | — | 6 | 2 | no | — |
| 316 | #67 | — | 12 | 1 | no | — |
| 317 | C2×Dic3 | — | 6 | 2 | no | — |
| 318 | C2×Dic3 | — | 6 | 2 | no | — |
| 319 | C2×Dic3 | — | 12 | 1 | no | — |
| 320 | D12 | — | 2 | 1 | no | — |
| 321 | D12 | — | 6 | 1 | no | — |
| 322 | C4×D3 | — | 2 | 1 | no | — |
| 323 | C4×D3 | — | 6 | 1 | no | — |
| 324 | C4×D3 | — | 6 | 1 | no | — |
| 325 | C4×D3 | — | 6 | 2 | no | — |
| 326 | C4×D3 | — | 12 | 1 | no | — |
| 327 | Dic6 | — | 2 | 1 | no | — |
| 328 | Dic6 | — | 6 | 1 | no | — |
| 329 | Dic6 | — | 6 | 1 | no | — |
| 330 | Dic6 | — | 6 | 1 | no | — |
| 331 | Dic6 | — | 12 | 1 | no | — |
| 332 | C3×C8 | — | 6 | 1 | no | — |
| 333 | C3×C8 | — | 6 | 1 | no | — |
| 334 | C3×C8 | — | 12 | 1 | no | — |
| 335 | C3×C8 | — | 18 | 1 | no | — |
| 336 | C3⋊C8 | — | 2 | 1 | no | — |
| 337 | C2×C32 | — | 2 | 1 | no | — |
| 338 | C2×C32 | — | 2 | 1 | no | — |
| 339 | C2×C32 | — | 4 | 1 | no | — |
| 340 | C2×C32 | — | 4 | 1 | no | — |
| 341 | C2×C32 | — | 4 | 2 | no | — |
| 342 | C2×C32 | — | 4 | 1 | no | — |
| 343 | C2×C32 | — | 8 | 1 | no | — |
| 344 | C2×C32 | — | 8 | 2 | no | — |
| 345 | C2×C32 | — | 12 | 1 | no | — |
| 346 | C2×C32 | — | 12 | 2 | no | — |
| 347 | C2×C32 | — | 16 | 1 | no | — |
| 348 | C2×C32 | C3×#120 | 1 | 1 | yes | characteristic |
| 349 | C3⋊D3 | — | 2 | 1 | no | — |
| 350 | C3×D3 | — | 4 | 1 | no | — |
| 351 | C3×D3 | — | 4 | 2 | no | — |
| 352 | C3×D3 | — | 4 | 2 | no | — |
| 353 | C3×D3 | — | 4 | 2 | no | — |
| 354 | C3×D3 | — | 4 | 1 | no | — |
| 355 | C3×D3 | — | 8 | 2 | no | — |
| 356 | C3×D3 | — | 12 | 1 | no | — |
| 357 | C3×D3 | — | 12 | 1 | no | — |
| 358 | #41 | — | 9 | 1 | no | — |
| 359 | #41 | — | 9 | 1 | no | — |
| 360 | #41 | — | 18 | 1 | no | — |
| 361 | #41 | — | 18 | 1 | no | — |
| 362 | C2×Q8 | — | 9 | 1 | no | — |
| 363 | C2×D4 | — | 6 | 1 | no | — |
| 364 | C2×D4 | — | 9 | 1 | no | — |
| 365 | C2×D4 | — | 18 | 2 | no | — |
| 366 | C2×D4 | — | 18 | 1 | no | — |
| 367 | Q16 | — | 18 | 1 | no | — |
| 368 | Q16 | — | 18 | 1 | no | — |
| 369 | SD16 | — | 6 | 1 | no | — |
| 370 | SD16 | — | 18 | 1 | no | — |
| 371 | M16 | — | 9 | 1 | no | — |
| 372 | M16 | — | 9 | 1 | no | — |
| 373 | C22⋊C4 | — | 18 | 2 | no | — |
| 374 | C42 | — | 9 | 1 | no | — |
| 375 | C22×C3 | — | 2 | 2 | no | — |
| 376 | C22×C3 | — | 2 | 1 | no | — |
| 377 | C22×C3 | — | 4 | 1 | no | — |
| 378 | C22×C3 | — | 4 | 2 | no | — |
| 379 | C22×C3 | — | 6 | 2 | no | — |
| 380 | C22×C3 | — | 6 | 1 | no | — |
| 381 | C22×C3 | — | 6 | 1 | no | — |
| 382 | C22×C3 | — | 6 | 2 | no | — |
| 383 | C22×C3 | — | 8 | 1 | no | — |
| 384 | C22×C3 | — | 9 | 1 | no | — |
| 385 | C22×C3 | — | 12 | 1 | no | — |
| 386 | C22×C3 | — | 12 | 2 | no | — |
| 387 | C22×C3 | — | 24 | 2 | no | — |
| 388 | C22×C3 | — | 24 | 2 | no | — |
| 389 | C22×C3 | — | 24 | 4 | no | — |
| 390 | C22×C3 | — | 36 | 2 | no | — |
| 391 | C2×D3 | — | 2 | 1 | no | — |
| 392 | C2×D3 | — | 2 | 2 | no | — |
| 393 | C2×D3 | — | 6 | 1 | no | — |
| 394 | C2×D3 | — | 6 | 1 | no | — |
| 395 | C2×D3 | — | 8 | 2 | no | — |
| 396 | C2×D3 | — | 24 | 2 | no | — |
| 397 | C3×C4 | — | 2 | 1 | no | — |
| 398 | C3×C4 | — | 2 | 1 | no | — |
| 399 | C3×C4 | — | 4 | 1 | no | — |
| 400 | C3×C4 | — | 4 | 1 | no | — |
| 401 | C3×C4 | — | 6 | 1 | no | — |
| 402 | C3×C4 | — | 6 | 1 | no | — |
| 403 | C3×C4 | — | 9 | 1 | no | — |
| 404 | C3×C4 | — | 12 | 1 | no | — |
| 405 | C3×C4 | — | 12 | 1 | no | — |
| 406 | C3×C4 | — | 12 | 1 | no | — |
| 407 | C3×C4 | — | 18 | 1 | no | — |
| 408 | C3×C4 | — | 24 | 1 | no | — |
| 409 | C3×C4 | — | 36 | 1 | no | — |
| 410 | C3×C4 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 411 | Dic3 | — | 2 | 1 | no | — |
| 412 | Dic3 | — | 4 | 1 | no | — |
| 413 | Dic3 | — | 6 | 1 | no | — |
| 414 | Dic3 | — | 6 | 1 | no | — |
| 415 | Dic3 | — | 6 | 2 | no | — |
| 416 | Dic3 | — | 12 | 1 | no | — |
| 417 | C32 | — | 2 | 1 | no | — |
| 418 | C32 | — | 2 | 1 | no | — |
| 419 | C32 | — | 4 | 1 | no | — |
| 420 | C32 | — | 4 | 1 | no | — |
| 421 | C32 | C3×#455 | 1 | 1 | yes | characteristic, complemented |
| 422 | C23 | — | 6 | 2 | no | — |
| 423 | C23 | — | 9 | 2 | no | — |
| 424 | Q8 | — | 6 | 1 | no | — |
| 425 | Q8 | — | 9 | 1 | no | — |
| 426 | Q8 | — | 9 | 1 | no | — |
| 427 | Q8 | — | 18 | 1 | no | — |
| 428 | D4 | — | 6 | 2 | no | — |
| 429 | D4 | — | 6 | 1 | no | — |
| 430 | D4 | — | 9 | 1 | no | — |
| 431 | D4 | — | 18 | 1 | no | — |
| 432 | D4 | — | 18 | 1 | no | — |
| 433 | D4 | — | 18 | 1 | no | — |
| 434 | D4 | — | 18 | 2 | no | — |
| 435 | D4 | C3×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 436 | C2×C4 | — | 6 | 1 | no | — |
| 437 | C2×C4 | — | 9 | 1 | no | — |
| 438 | C2×C4 | — | 18 | 2 | no | — |
| 439 | C2×C4 | — | 18 | 1 | no | — |
| 440 | C2×C4 | — | 18 | 1 | no | — |
| 441 | C2×C4 | — | 18 | 1 | no | — |
| 442 | C8 | — | 6 | 1 | no | — |
| 443 | C8 | — | 18 | 1 | no | — |
| 444 | C2×C3 | — | 2 | 1 | no | — |
| 445 | C2×C3 | — | 2 | 1 | no | — |
| 446 | C2×C3 | — | 4 | 2 | no | — |
| 447 | C2×C3 | — | 4 | 1 | no | — |
| 448 | C2×C3 | — | 4 | 1 | no | — |
| 449 | C2×C3 | — | 4 | 1 | no | — |
| 450 | C2×C3 | — | 8 | 1 | no | — |
| 451 | C2×C3 | — | 8 | 2 | no | — |
| 452 | C2×C3 | — | 12 | 2 | no | — |
| 453 | C2×C3 | — | 12 | 1 | no | — |
| 454 | C2×C3 | — | 12 | 2 | no | — |
| 455 | C2×C3 | — | 12 | 1 | no | — |
| 456 | C2×C3 | — | 12 | 2 | no | — |
| 457 | C2×C3 | — | 16 | 1 | no | — |
| 458 | C2×C3 | — | 18 | 1 | no | — |
| 459 | C2×C3 | — | 24 | 2 | no | — |
| 460 | C2×C3 | #64241 | 1 | 1 | yes | characteristic |
| 461 | D3 | — | 4 | 1 | no | — |
| 462 | D3 | — | 4 | 2 | no | — |
| 463 | D3 | — | 12 | 1 | no | — |
| 464 | D3 | — | 12 | 1 | no | — |
| 465 | C22 | — | 2 | 1 | no | — |
| 466 | C22 | — | 6 | 1 | no | — |
| 467 | C22 | — | 6 | 2 | no | — |
| 468 | C22 | — | 9 | 1 | no | — |
| 469 | C22 | — | 24 | 2 | no | — |
| 470 | C22 | — | 36 | 2 | no | — |
| 471 | C4 | — | 6 | 1 | no | — |
| 472 | C4 | — | 9 | 1 | no | — |
| 473 | C4 | — | 12 | 1 | no | — |
| 474 | C4 | — | 18 | 1 | no | — |
| 475 | C4 | — | 36 | 1 | no | — |
| 476 | C4 | C2×C3×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 477 | C3 | — | 2 | 1 | no | — |
| 478 | C3 | — | 2 | 1 | no | — |
| 479 | C3 | — | 4 | 1 | no | — |
| 480 | C3 | — | 4 | 1 | no | — |
| 481 | C3 | #10593461 | 1 | 1 | yes | characteristic, direct product factor |
| 482 | C2 | — | 4 | 1 | no | — |
| 483 | C2 | — | 12 | 1 | no | — |
| 484 | C2 | — | 12 | 2 | no | — |
| 485 | C2 | — | 18 | 1 | no | — |
| 486 | C2 | C3×#64241 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#64226 | C2 | semidirect |
| 3. C3×#64221 | C2 | semidirect |
| 4. C3×#63931 | C2 | semidirect |
| 5. C3×#63783 | C2 | semidirect |
| 6. C3×#63731 | C2 | semidirect |
| 7. C3×#63727 | C2 | semidirect |
| 8. #10593461 | C3 | direct (N × H) |
| 16. C3×#3797 | C22 | semidirect |
| 18. C3×C4×#157 | C22 | semidirect |
| 19. C3×#3788 | C22 | semidirect |
| 25. C3×#3712 | C22 | semidirect |
| 28. #64226 | C2×C3 | semidirect |
| 29. #64221 | C2×C3 | semidirect |
| 31. #63931 | C2×C3 | semidirect |
| 32. #63783 | C2×C3 | semidirect |
| 33. #63731 | C2×C3 | semidirect |
| 34. #63727 | C2×C3 | semidirect |
| 79. #3797 | C22×C3 | semidirect |
| 81. C4×#157 | C22×C3 | semidirect |
| 82. #3788 | C22×C3 | semidirect |
| 94. #3712 | C22×C3 | semidirect |
| 272. C33 | #455 | semidirect |
| 421. C32 | C3×#455 | semidirect |
| 481. C3 | #10593461 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64313 | 2 |
| C3×#64226 | 2 |
| C3×#64221 | 2 |
| C3×#63931 | 2 |
| C3×#63783 | 2 |
| C3×#63731 | 2 |
| C3×#63727 | 2 |
| #10593461 | 3 |
| C3×#455 | 9 |