Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
579 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 579 conjugacy classes of subgroups — too many to draw. Only its 73 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 | #11722639 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11721870 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11721114 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11721068 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #63664⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11720322 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11720321 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10591686 | — | 3 | 1 | no | maximal |
| 9 | #10591684 | — | 3 | 1 | no | maximal |
| 10 | #41×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C4⋊#272 | C22 | 1 | 1 | yes | characteristic |
| 12 | Q8×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 13 | #3830⋊C3 | — | 2 | 1 | no | — |
| 14 | #3830⋊C3 | — | 2 | 2 | no | — |
| 15 | #3828⋊C3 | — | 2 | 1 | no | — |
| 16 | #3828⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#634⋊C3 | — | 2 | 1 | no | — |
| 18 | C2×#634⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 19 | #88549 | — | 2 | 1 | no | — |
| 20 | #88545 | — | 2 | 1 | no | — |
| 21 | #88538 | C22 | 1 | 1 | yes | characteristic |
| 22 | C4×(C3⋊Dic3)⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 23 | #3748⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 24 | #88451 | — | 2 | 2 | no | — |
| 25 | #88437 | — | 2 | 1 | no | — |
| 26 | #88436 | — | 2 | 1 | no | — |
| 27 | #64367 | D3 | 1 | 1 | yes | characteristic, complemented |
| 28 | C3×#1010 | — | 3 | 1 | no | — |
| 29 | C3×#949 | — | 3 | 1 | no | — |
| 30 | C3×#949 | — | 3 | 1 | no | — |
| 31 | C3×#949 | — | 6 | 1 | no | — |
| 32 | #63863 | — | 3 | 1 | no | — |
| 33 | #63860 | — | 3 | 1 | no | — |
| 34 | #63830 | — | 3 | 1 | no | — |
| 35 | #63823 | — | 3 | 1 | no | — |
| 36 | #63664 | D3 | 1 | 1 | yes | characteristic, complemented |
| 37 | C3×#837 | — | 3 | 1 | no | — |
| 38 | #63570 | — | 3 | 1 | no | — |
| 39 | #63568 | — | 3 | 1 | no | — |
| 40 | #63561 | — | 3 | 1 | no | — |
| 41 | #63560 | — | 3 | 1 | no | — |
| 42 | C22×#272 | — | 2 | 1 | no | — |
| 43 | Q8×H(3,𝔽3) | D4 | 1 | 1 | yes | characteristic |
| 44 | D4×H(3,𝔽3) | — | 2 | 1 | no | — |
| 45 | D4×H(3,𝔽3) | D4 | 1 | 1 | yes | characteristic |
| 46 | C2×C4×H(3,𝔽3) | — | 2 | 1 | no | — |
| 47 | C2×C4×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 48 | C4⋊#272 | — | 2 | 1 | no | — |
| 49 | C4⋊#272 | — | 2 | 1 | no | — |
| 50 | #638⋊C3 | — | 2 | 2 | no | — |
| 51 | #638⋊C3 | — | 2 | 1 | no | — |
| 52 | C2×(C3⋊Dic3)⋊C3 | — | 2 | 2 | no | — |
| 53 | C2×(C3⋊Dic3)⋊C3 | — | 2 | 1 | no | — |
| 54 | C2×(C3⋊Dic3)⋊C3 | D4 | 1 | 2 | yes | — |
| 55 | C4⋊((C3⋊D3)⋊C3) | D4 | 1 | 1 | yes | characteristic |
| 56 | C4×(C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 57 | C4×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 58 | #634⋊C3 | — | 2 | 2 | no | — |
| 59 | #634⋊C3 | — | 2 | 1 | no | — |
| 60 | #634⋊C3 | — | 2 | 1 | no | — |
| 61 | #634⋊C3 | D4 | 1 | 1 | yes | characteristic |
| 62 | #6180 | — | 2 | 1 | no | — |
| 63 | (C3⋊(C3⋊C8))⋊C3 | — | 2 | 1 | no | — |
| 64 | #5245 | — | 9 | 1 | no | — |
| 65 | #5201 | — | 9 | 1 | no | — |
| 66 | #4827 | — | 9 | 1 | no | — |
| 67 | C32×#41 | — | 2 | 1 | no | — |
| 68 | C32×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 69 | C32×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 70 | Q8×C3⋊D3 | — | 2 | 1 | no | — |
| 71 | #3830 | — | 2 | 1 | no | — |
| 72 | #3830 | — | 2 | 2 | no | — |
| 73 | #3828 | — | 2 | 1 | no | — |
| 74 | #3828 | C2×D3 | 1 | 1 | yes | characteristic |
| 75 | C2×#634 | — | 2 | 1 | no | — |
| 76 | C2×#634 | C2×D3 | 1 | 1 | yes | characteristic |
| 77 | C3×D3×Q8 | — | 6 | 1 | no | — |
| 78 | C3×#237 | — | 6 | 2 | no | — |
| 79 | C3×#237 | — | 6 | 1 | no | — |
| 80 | C3×#235 | — | 3 | 1 | no | — |
| 81 | C3×#235 | — | 6 | 1 | no | — |
| 82 | C2×C3×D12 | — | 3 | 1 | no | — |
| 83 | C2×C3×D12 | — | 3 | 1 | no | — |
| 84 | C2×C3×D12 | — | 6 | 1 | no | — |
| 85 | C2×C3×Dic6 | — | 3 | 1 | no | — |
| 86 | C2×C3×Dic6 | — | 6 | 1 | no | — |
| 87 | C4×C3⋊Dic3 | C2×D3 | 1 | 1 | yes | characteristic |
| 88 | #3748 | C2×D3 | 1 | 1 | yes | characteristic |
| 89 | C3×#215 | — | 6 | 2 | no | — |
| 90 | C3×#215 | — | 6 | 1 | no | — |
| 91 | C3×#215 | — | 6 | 1 | no | — |
| 92 | C3×#213 | — | 6 | 2 | no | — |
| 93 | C3×#213 | — | 6 | 1 | no | — |
| 94 | C3×#213 | — | 6 | 1 | no | — |
| 95 | C3×C4×Dic3 | — | 3 | 1 | no | — |
| 96 | C3×#208 | — | 3 | 1 | no | — |
| 97 | C3×#208 | — | 3 | 1 | no | — |
| 98 | C3×#208 | — | 3 | 1 | no | — |
| 99 | C3×#208 | — | 6 | 1 | no | — |
| 100 | (C2×D3)⋊Dic3 | — | 6 | 2 | no | — |
| 101 | (C2×D3)⋊Dic3 | — | 6 | 2 | no | — |
| 102 | #3716 | — | 6 | 1 | no | — |
| 103 | #3715 | — | 6 | 1 | no | — |
| 104 | #3714 | — | 6 | 1 | no | — |
| 105 | #3713 | — | 6 | 1 | no | — |
| 106 | C22×H(3,𝔽3) | — | 2 | 1 | no | — |
| 107 | C22×H(3,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 108 | C2×#272 | — | 4 | 2 | no | — |
| 109 | C2×#272 | — | 4 | 1 | no | — |
| 110 | C2×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 111 | C4×H(3,𝔽3) | — | 2 | 1 | no | — |
| 112 | C4×H(3,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 113 | C4×H(3,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | (C3⋊Dic3)⋊C3 | — | 2 | 2 | no | — |
| 115 | (C3⋊Dic3)⋊C3 | — | 2 | 1 | no | — |
| 116 | (C3⋊Dic3)⋊C3 | — | 4 | 1 | no | — |
| 117 | C3×2−1+4 | — | 9 | 1 | no | — |
| 118 | #1010 | — | 3 | 1 | no | — |
| 119 | #1010 | — | 9 | 1 | no | — |
| 120 | C3×AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 121 | #949 | — | 3 | 1 | no | — |
| 122 | #949 | — | 3 | 1 | no | — |
| 123 | #949 | — | 6 | 1 | no | — |
| 124 | #949 | — | 9 | 1 | no | — |
| 125 | #947 | — | 9 | 1 | no | — |
| 126 | #936 | — | 9 | 1 | no | — |
| 127 | #932 | — | 9 | 1 | no | — |
| 128 | #908 | — | 9 | 1 | no | — |
| 129 | #875 | — | 9 | 1 | no | — |
| 130 | C3×#104 | — | 9 | 1 | no | — |
| 131 | #837 | — | 3 | 1 | no | — |
| 132 | #837 | — | 9 | 1 | no | — |
| 133 | #837 | — | 9 | 1 | no | — |
| 134 | #836 | — | 9 | 1 | no | — |
| 135 | #825 | — | 9 | 1 | no | — |
| 136 | #824 | — | 9 | 1 | no | — |
| 137 | #824 | — | 9 | 1 | no | — |
| 138 | #805 | — | 9 | 1 | no | — |
| 139 | C22×C3×D3 | — | 6 | 1 | no | — |
| 140 | C22×C3×D3 | — | 6 | 1 | no | — |
| 141 | C22×C3×D3 | — | 12 | 1 | no | — |
| 142 | C32×Q8 | — | 2 | 1 | no | — |
| 143 | C32×Q8 | D12 | 1 | 1 | yes | characteristic |
| 144 | C32×Q8 | #67 | 1 | 1 | yes | characteristic |
| 145 | C32×D4 | — | 2 | 1 | no | — |
| 146 | C32×D4 | — | 2 | 1 | no | — |
| 147 | C32×D4 | — | 2 | 1 | no | — |
| 148 | C32×D4 | — | 4 | 1 | no | — |
| 149 | C32×D4 | D12 | 1 | 1 | yes | characteristic |
| 150 | C32×D4 | #67 | 1 | 1 | yes | characteristic |
| 151 | C2×C32×C4 | — | 2 | 1 | no | — |
| 152 | C2×C32×C4 | — | 2 | 1 | no | — |
| 153 | C2×C32×C4 | — | 2 | 1 | no | — |
| 154 | C2×C32×C4 | — | 4 | 1 | no | — |
| 155 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 156 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 157 | #638 | — | 2 | 2 | no | — |
| 158 | #638 | — | 2 | 1 | no | — |
| 159 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 160 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 161 | C2×C3⋊Dic3 | #67 | 1 | 2 | yes | — |
| 162 | C4⋊(C3⋊D3) | #67 | 1 | 1 | yes | characteristic |
| 163 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 164 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 165 | #634 | — | 2 | 2 | no | — |
| 166 | #634 | — | 2 | 1 | no | — |
| 167 | #634 | — | 2 | 1 | no | — |
| 168 | #634 | #67 | 1 | 1 | yes | characteristic |
| 169 | C3×#67 | — | 6 | 2 | no | — |
| 170 | C3×#67 | — | 6 | 1 | no | — |
| 171 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 172 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 173 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 174 | C3×D12 | — | 3 | 1 | no | — |
| 175 | C3×D12 | — | 6 | 2 | no | — |
| 176 | C3×D12 | — | 6 | 1 | no | — |
| 177 | C3×D12 | — | 6 | 1 | no | — |
| 178 | C3×D12 | — | 6 | 1 | no | — |
| 179 | C3×D12 | — | 6 | 1 | no | — |
| 180 | C3×D12 | — | 12 | 1 | no | — |
| 181 | C3×C4×D3 | — | 6 | 2 | no | — |
| 182 | C3×C4×D3 | — | 6 | 1 | no | — |
| 183 | C3×Dic6 | — | 3 | 1 | no | — |
| 184 | C3×Dic6 | — | 6 | 2 | no | — |
| 185 | C3×Dic6 | — | 6 | 1 | no | — |
| 186 | C3×Dic6 | — | 6 | 1 | no | — |
| 187 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 188 | C3×C3⋊C8 | — | 6 | 2 | no | — |
| 189 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 190 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 191 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 192 | #454 | — | 27 | 1 | no | Sylow |
| 193 | C2×H(3,𝔽3) | — | 2 | 1 | no | — |
| 194 | C2×H(3,𝔽3) | — | 4 | 1 | no | — |
| 195 | C2×H(3,𝔽3) | #120 | 1 | 1 | yes | characteristic |
| 196 | #272 | — | 8 | 1 | no | — |
| 197 | (C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 198 | C3×#41 | — | 3 | 1 | no | — |
| 199 | C3×#41 | — | 3 | 1 | no | — |
| 200 | C3×#41 | — | 6 | 1 | no | — |
| 201 | C3×#41 | — | 9 | 1 | no | — |
| 202 | C3×#41 | — | 18 | 1 | no | — |
| 203 | C3×#41 | — | 18 | 2 | no | — |
| 204 | C3×#41 | — | 18 | 1 | no | — |
| 205 | C3×#41 | D32 | 1 | 1 | yes | characteristic |
| 206 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 207 | C2×C3×Q8 | — | 18 | 1 | no | — |
| 208 | C2×C3×Q8 | — | 18 | 1 | no | — |
| 209 | C2×C3×D4 | — | 9 | 1 | no | — |
| 210 | D3×Q8 | — | 6 | 1 | no | — |
| 211 | D3×Q8 | — | 18 | 1 | no | — |
| 212 | #237 | — | 6 | 2 | no | — |
| 213 | #237 | — | 6 | 1 | no | — |
| 214 | #237 | — | 18 | 2 | no | — |
| 215 | #237 | — | 18 | 1 | no | — |
| 216 | #235 | — | 3 | 1 | no | — |
| 217 | #235 | — | 6 | 1 | no | — |
| 218 | #235 | — | 9 | 1 | no | — |
| 219 | #235 | — | 18 | 1 | no | — |
| 220 | C2×D12 | — | 3 | 1 | no | — |
| 221 | C2×D12 | — | 3 | 1 | no | — |
| 222 | C2×D12 | — | 6 | 1 | no | — |
| 223 | C2×Dic6 | — | 3 | 1 | no | — |
| 224 | C2×Dic6 | — | 6 | 1 | no | — |
| 225 | C2×Dic6 | — | 9 | 1 | no | — |
| 226 | C2×Dic6 | — | 18 | 1 | no | — |
| 227 | C3×SD16 | — | 18 | 1 | no | — |
| 228 | C3×D8 | — | 18 | 1 | no | — |
| 229 | C3×M16 | — | 9 | 1 | no | — |
| 230 | C3×M16 | — | 9 | 1 | no | — |
| 231 | C3×C42 | — | 9 | 1 | no | — |
| 232 | #217 | — | 18 | 2 | no | — |
| 233 | #215 | — | 6 | 1 | no | — |
| 234 | #215 | — | 6 | 1 | no | — |
| 235 | #215 | — | 6 | 2 | no | — |
| 236 | #215 | — | 18 | 1 | no | — |
| 237 | #214 | — | 18 | 1 | no | — |
| 238 | #213 | — | 6 | 1 | no | — |
| 239 | #213 | — | 6 | 1 | no | — |
| 240 | #213 | — | 6 | 2 | no | — |
| 241 | #213 | — | 18 | 1 | no | — |
| 242 | #213 | — | 18 | 1 | no | — |
| 243 | (C2×D3)⋊C4 | — | 18 | 2 | no | — |
| 244 | (C2×D3)⋊C4 | — | 18 | 2 | no | — |
| 245 | C4×Dic3 | — | 3 | 1 | no | — |
| 246 | C4×Dic3 | — | 9 | 1 | no | — |
| 247 | #208 | — | 3 | 1 | no | — |
| 248 | #208 | — | 3 | 1 | no | — |
| 249 | #208 | — | 3 | 1 | no | — |
| 250 | #208 | — | 6 | 1 | no | — |
| 251 | #208 | — | 9 | 1 | no | — |
| 252 | D24 | — | 18 | 1 | no | — |
| 253 | #204 | — | 18 | 1 | no | — |
| 254 | C22×C32 | — | 2 | 1 | no | — |
| 255 | C22×C32 | — | 2 | 1 | no | — |
| 256 | C22×C32 | — | 2 | 1 | no | — |
| 257 | C22×C32 | — | 4 | 1 | no | — |
| 258 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic |
| 259 | C22×C32 | C2×#67 | 1 | 1 | yes | characteristic |
| 260 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 261 | C2×C3×D3 | — | 6 | 1 | no | — |
| 262 | C2×C3×D3 | — | 12 | 2 | no | — |
| 263 | C2×C3×D3 | — | 12 | 2 | no | — |
| 264 | C2×C3×D3 | — | 12 | 2 | no | — |
| 265 | C2×C3×D3 | — | 12 | 1 | no | — |
| 266 | C2×C3×D3 | — | 12 | 1 | no | — |
| 267 | C2×C3×D3 | — | 24 | 2 | no | — |
| 268 | C32×C4 | — | 2 | 1 | no | — |
| 269 | C32×C4 | — | 2 | 1 | no | — |
| 270 | C32×C4 | — | 2 | 1 | no | — |
| 271 | C32×C4 | — | 2 | 1 | no | — |
| 272 | C32×C4 | — | 4 | 1 | no | — |
| 273 | C32×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 274 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 275 | C32×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 276 | C32×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 277 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 278 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 279 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 280 | C3×Dic3 | — | 6 | 1 | no | — |
| 281 | C3×Dic3 | — | 6 | 2 | no | — |
| 282 | C3×Dic3 | — | 12 | 1 | no | — |
| 283 | 2−1+4 | — | 9 | 1 | no | — |
| 284 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 285 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 286 | #124 | — | 27 | 1 | no | — |
| 287 | #104 | — | 9 | 1 | no | — |
| 288 | #104 | — | 27 | 1 | no | — |
| 289 | #101 | — | 27 | 1 | no | — |
| 290 | H(3,𝔽3) | #454 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 291 | C23×C3 | — | 18 | 1 | no | — |
| 292 | C22×D3 | — | 6 | 1 | no | — |
| 293 | C22×D3 | — | 6 | 1 | no | — |
| 294 | C22×D3 | — | 12 | 1 | no | — |
| 295 | C3×Q8 | — | 3 | 1 | no | — |
| 296 | C3×Q8 | — | 3 | 1 | no | — |
| 297 | C3×Q8 | — | 6 | 1 | no | — |
| 298 | C3×Q8 | — | 9 | 1 | no | — |
| 299 | C3×Q8 | — | 18 | 1 | no | — |
| 300 | C3×Q8 | — | 18 | 1 | no | — |
| 301 | C3×Q8 | — | 18 | 2 | no | — |
| 302 | C3×Q8 | #626 | 1 | 1 | yes | characteristic |
| 303 | C3×D4 | — | 2 | 1 | no | — |
| 304 | C3×D4 | — | 3 | 1 | no | — |
| 305 | C3×D4 | — | 3 | 1 | no | — |
| 306 | C3×D4 | — | 6 | 1 | no | — |
| 307 | C3×D4 | — | 6 | 1 | no | — |
| 308 | C3×D4 | — | 6 | 1 | no | — |
| 309 | C3×D4 | — | 9 | 1 | no | — |
| 310 | C3×D4 | — | 12 | 1 | no | — |
| 311 | C3×D4 | — | 18 | 1 | no | — |
| 312 | C3×D4 | — | 18 | 2 | no | — |
| 313 | C3×D4 | — | 18 | 1 | no | — |
| 314 | C3×D4 | — | 18 | 1 | no | — |
| 315 | C3×D4 | #626 | 1 | 1 | yes | characteristic |
| 316 | C2×C3×C4 | — | 2 | 1 | no | — |
| 317 | C2×C3×C4 | — | 3 | 1 | no | — |
| 318 | C2×C3×C4 | — | 3 | 1 | no | — |
| 319 | C2×C3×C4 | — | 6 | 1 | no | — |
| 320 | C2×C3×C4 | — | 6 | 1 | no | — |
| 321 | C2×C3×C4 | — | 6 | 1 | no | — |
| 322 | C2×C3×C4 | — | 9 | 2 | no | — |
| 323 | C2×C3×C4 | — | 12 | 1 | no | — |
| 324 | C2×C3×C4 | — | 18 | 1 | no | — |
| 325 | C2×C3×C4 | — | 18 | 2 | no | — |
| 326 | C2×C3×C4 | — | 18 | 2 | no | — |
| 327 | C2×C3×C4 | — | 18 | 1 | no | — |
| 328 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 329 | #67 | — | 6 | 2 | no | — |
| 330 | #67 | — | 6 | 1 | no | — |
| 331 | #67 | — | 18 | 1 | no | — |
| 332 | #67 | — | 18 | 2 | no | — |
| 333 | C2×Dic3 | — | 3 | 2 | no | — |
| 334 | C2×Dic3 | — | 6 | 2 | no | — |
| 335 | C2×Dic3 | — | 6 | 1 | no | — |
| 336 | C2×Dic3 | — | 9 | 2 | no | — |
| 337 | C2×Dic3 | — | 18 | 2 | no | — |
| 338 | C2×Dic3 | — | 18 | 1 | no | — |
| 339 | D12 | — | 3 | 1 | no | — |
| 340 | D12 | — | 6 | 1 | no | — |
| 341 | D12 | — | 6 | 1 | no | — |
| 342 | D12 | — | 6 | 1 | no | — |
| 343 | D12 | — | 6 | 1 | no | — |
| 344 | D12 | — | 6 | 2 | no | — |
| 345 | D12 | — | 9 | 1 | no | — |
| 346 | D12 | — | 12 | 1 | no | — |
| 347 | C4×D3 | — | 6 | 2 | no | — |
| 348 | C4×D3 | — | 6 | 1 | no | — |
| 349 | C4×D3 | — | 18 | 1 | no | — |
| 350 | C4×D3 | — | 18 | 2 | no | — |
| 351 | Dic6 | — | 3 | 1 | no | — |
| 352 | Dic6 | — | 6 | 2 | no | — |
| 353 | Dic6 | — | 6 | 1 | no | — |
| 354 | Dic6 | — | 6 | 1 | no | — |
| 355 | Dic6 | — | 9 | 1 | no | — |
| 356 | Dic6 | — | 18 | 1 | no | — |
| 357 | Dic6 | — | 18 | 1 | no | — |
| 358 | Dic6 | — | 18 | 2 | no | — |
| 359 | C3×C8 | — | 18 | 1 | no | — |
| 360 | C3×C8 | — | 18 | 1 | no | — |
| 361 | C3⋊C8 | — | 6 | 1 | no | — |
| 362 | C3⋊C8 | — | 6 | 1 | no | — |
| 363 | C3⋊C8 | — | 6 | 2 | no | — |
| 364 | C3⋊C8 | — | 6 | 1 | no | — |
| 365 | C3⋊C8 | — | 18 | 1 | no | — |
| 366 | C2×C32 | — | 2 | 1 | no | — |
| 367 | C2×C32 | — | 2 | 1 | no | — |
| 368 | C2×C32 | — | 2 | 1 | no | — |
| 369 | C2×C32 | — | 4 | 1 | no | — |
| 370 | C2×C32 | — | 4 | 1 | no | — |
| 371 | C2×C32 | — | 4 | 1 | no | — |
| 372 | C2×C32 | — | 8 | 1 | no | — |
| 373 | C2×C32 | #882 | 1 | 1 | yes | characteristic |
| 374 | C2×C32 | #953 | 1 | 1 | yes | characteristic |
| 375 | C3⋊D3 | — | 4 | 1 | no | — |
| 376 | C3×D3 | — | 12 | 1 | no | — |
| 377 | C3×D3 | — | 24 | 2 | no | — |
| 378 | C3×D3 | — | 24 | 1 | no | — |
| 379 | C3×D3 | — | 24 | 1 | no | — |
| 380 | #41 | — | 9 | 1 | no | — |
| 381 | #41 | — | 18 | 1 | no | — |
| 382 | #41 | — | 18 | 2 | no | — |
| 383 | #41 | — | 18 | 1 | no | — |
| 384 | #41 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 385 | C2×Q8 | — | 9 | 1 | no | — |
| 386 | C2×Q8 | — | 18 | 1 | no | — |
| 387 | C2×Q8 | — | 18 | 1 | no | — |
| 388 | C2×D4 | — | 9 | 1 | no | — |
| 389 | SD16 | — | 18 | 1 | no | — |
| 390 | SD16 | — | 54 | 1 | no | — |
| 391 | D8 | — | 18 | 1 | no | — |
| 392 | D8 | — | 54 | 1 | no | — |
| 393 | M16 | — | 9 | 1 | no | — |
| 394 | M16 | — | 9 | 1 | no | — |
| 395 | C22⋊C4 | — | 54 | 2 | no | — |
| 396 | C42 | — | 9 | 1 | no | — |
| 397 | C22×C3 | — | 2 | 1 | no | — |
| 398 | C22×C3 | — | 3 | 1 | no | — |
| 399 | C22×C3 | — | 3 | 1 | no | — |
| 400 | C22×C3 | — | 6 | 1 | no | — |
| 401 | C22×C3 | — | 6 | 1 | no | — |
| 402 | C22×C3 | — | 6 | 1 | no | — |
| 403 | C22×C3 | — | 12 | 1 | no | — |
| 404 | C22×C3 | — | 18 | 1 | no | — |
| 405 | C22×C3 | — | 36 | 2 | no | — |
| 406 | C22×C3 | — | 36 | 1 | no | — |
| 407 | C22×C3 | D3×#67 | 1 | 1 | yes | characteristic |
| 408 | C2×D3 | — | 6 | 1 | no | — |
| 409 | C2×D3 | — | 12 | 1 | no | — |
| 410 | C2×D3 | — | 12 | 1 | no | — |
| 411 | C2×D3 | — | 12 | 2 | no | — |
| 412 | C2×D3 | — | 12 | 2 | no | — |
| 413 | C2×D3 | — | 12 | 2 | no | — |
| 414 | C2×D3 | — | 18 | 1 | no | — |
| 415 | C2×D3 | — | 24 | 2 | no | — |
| 416 | C3×C4 | — | 2 | 1 | no | — |
| 417 | C3×C4 | — | 3 | 1 | no | — |
| 418 | C3×C4 | — | 3 | 1 | no | — |
| 419 | C3×C4 | — | 3 | 1 | no | — |
| 420 | C3×C4 | — | 3 | 1 | no | — |
| 421 | C3×C4 | — | 6 | 1 | no | — |
| 422 | C3×C4 | — | 6 | 1 | no | — |
| 423 | C3×C4 | — | 6 | 1 | no | — |
| 424 | C3×C4 | — | 6 | 1 | no | — |
| 425 | C3×C4 | — | 12 | 1 | no | — |
| 426 | C3×C4 | — | 18 | 2 | no | — |
| 427 | C3×C4 | — | 18 | 1 | no | — |
| 428 | C3×C4 | — | 36 | 1 | no | — |
| 429 | C3×C4 | C2×#626 | 1 | 1 | yes | characteristic |
| 430 | C3×C4 | D3×#67 | 1 | 1 | yes | characteristic |
| 431 | Dic3 | — | 6 | 1 | no | — |
| 432 | Dic3 | — | 6 | 2 | no | — |
| 433 | Dic3 | — | 12 | 1 | no | — |
| 434 | Dic3 | — | 18 | 1 | no | — |
| 435 | Dic3 | — | 18 | 2 | no | — |
| 436 | Dic3 | — | 36 | 1 | no | — |
| 437 | C32 | — | 2 | 1 | no | — |
| 438 | C32 | #4827 | 1 | 1 | yes | characteristic, complemented |
| 439 | C32 | #5245 | 1 | 1 | yes | characteristic, complemented |
| 440 | C23 | — | 18 | 1 | no | — |
| 441 | Q8 | — | 9 | 1 | no | — |
| 442 | Q8 | — | 18 | 2 | no | — |
| 443 | Q8 | — | 18 | 1 | no | — |
| 444 | Q8 | — | 18 | 1 | no | — |
| 445 | Q8 | #6200 | 1 | 1 | yes | characteristic |
| 446 | D4 | — | 2 | 1 | no | — |
| 447 | D4 | — | 9 | 1 | no | — |
| 448 | D4 | — | 18 | 2 | no | — |
| 449 | D4 | — | 18 | 1 | no | — |
| 450 | D4 | — | 18 | 1 | no | — |
| 451 | D4 | — | 18 | 1 | no | — |
| 452 | D4 | #6200 | 1 | 1 | yes | characteristic |
| 453 | C2×C4 | — | 2 | 1 | no | — |
| 454 | C2×C4 | — | 9 | 2 | no | — |
| 455 | C2×C4 | — | 18 | 2 | no | — |
| 456 | C2×C4 | — | 18 | 2 | no | — |
| 457 | C2×C4 | — | 18 | 1 | no | — |
| 458 | C2×C4 | — | 18 | 1 | no | — |
| 459 | C2×C4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 460 | C8 | — | 18 | 1 | no | — |
| 461 | C8 | — | 18 | 1 | no | — |
| 462 | C2×C3 | — | 2 | 1 | no | — |
| 463 | C2×C3 | — | 3 | 1 | no | — |
| 464 | C2×C3 | — | 3 | 1 | no | — |
| 465 | C2×C3 | — | 4 | 1 | no | — |
| 466 | C2×C3 | — | 6 | 1 | no | — |
| 467 | C2×C3 | — | 6 | 1 | no | — |
| 468 | C2×C3 | — | 6 | 1 | no | — |
| 469 | C2×C3 | — | 12 | 1 | no | — |
| 470 | C2×C3 | — | 12 | 1 | no | — |
| 471 | C2×C3 | — | 12 | 1 | no | — |
| 472 | C2×C3 | — | 24 | 1 | no | — |
| 473 | C2×C3 | — | 36 | 1 | no | — |
| 474 | C2×C3 | — | 72 | 1 | no | — |
| 475 | C2×C3 | #63977 | 1 | 1 | yes | characteristic |
| 476 | D3 | — | 12 | 1 | no | — |
| 477 | D3 | — | 24 | 1 | no | — |
| 478 | D3 | — | 24 | 1 | no | — |
| 479 | D3 | — | 24 | 2 | no | — |
| 480 | D3 | — | 36 | 1 | no | — |
| 481 | C22 | — | 2 | 1 | no | — |
| 482 | C22 | — | 18 | 1 | no | — |
| 483 | C22 | — | 36 | 2 | no | — |
| 484 | C22 | — | 36 | 1 | no | — |
| 485 | C22 | #88676 | 1 | 1 | yes | characteristic |
| 486 | C4 | — | 2 | 1 | no | — |
| 487 | C4 | — | 18 | 2 | no | — |
| 488 | C4 | — | 18 | 1 | no | — |
| 489 | C4 | — | 36 | 1 | no | — |
| 490 | C4 | C2×#6200 | 1 | 1 | yes | characteristic |
| 491 | C4 | #88676 | 1 | 1 | yes | characteristic |
| 492 | C3 | — | 3 | 1 | no | — |
| 493 | C3 | — | 3 | 1 | no | — |
| 494 | C3 | — | 6 | 1 | no | — |
| 495 | C3 | #10591685 | 1 | 1 | yes | characteristic |
| 496 | C2 | — | 2 | 1 | no | — |
| 497 | C2 | — | 4 | 1 | no | — |
| 498 | C2 | — | 36 | 1 | no | — |
| 499 | C2 | — | 72 | 1 | no | — |
| 500 | C2 | #11721321 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11722639 | C2 | semidirect |
| 2. #11721870 | C2 | semidirect |
| 3. #11721114 | C2 | semidirect |
| 4. #11721068 | C2 | semidirect |
| 5. #63664⋊C3 | C2 | semidirect |
| 6. #11720322 | C2 | semidirect |
| 7. #11720321 | C2 | semidirect |
| 27. #64367 | D3 | semidirect |
| 36. #63664 | D3 | semidirect |
| 290. H(3,𝔽3) | #454 | semidirect |
| 438. C32 | #4827 | semidirect |
| 439. C32 | #5245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722639 | 2 |
| #11721870 | 2 |
| #11721114 | 2 |
| #11721068 | 2 |
| #63664⋊C3 | 2 |
| #11720322 | 2 |
| #11720321 | 2 |
| #10591686 | 3 |
| #10591684 | 3 |