Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1460 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 1460 conjugacy classes of subgroups — too many to draw. Only its 144 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 | #11724685 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C32×#949 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11723429 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11723378 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#63664 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11722047 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11722030 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10592900 | — | 3 | 1 | no | maximal |
| 9 | #10591686 | — | 3 | 4 | no | maximal |
| 10 | C33×#41 | C22 | 1 | 1 | yes | characteristic |
| 11 | Q8×C3⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 12 | #89078 | — | 2 | 1 | no | — |
| 13 | #89078 | — | 2 | 2 | no | — |
| 14 | #89076 | — | 2 | 1 | no | — |
| 15 | #89076 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#6308 | — | 2 | 1 | no | — |
| 17 | C2×#6308 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C32×D12 | C22 | 1 | 1 | yes | characteristic |
| 19 | C3×C4×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 20 | C3×#3748 | C22 | 1 | 1 | yes | characteristic |
| 21 | C32×#215 | — | 2 | 1 | no | — |
| 22 | C32×#213 | — | 2 | 1 | no | — |
| 23 | C32×#208 | C22 | 1 | 1 | yes | characteristic |
| 24 | (C2×D3)⋊(C3⋊Dic3) | — | 2 | 2 | no | — |
| 25 | #88794 | — | 2 | 1 | no | — |
| 26 | #88790 | — | 2 | 1 | no | — |
| 27 | #64367 | — | 3 | 1 | no | — |
| 28 | #64367 | — | 3 | 4 | no | — |
| 29 | #64367 | — | 6 | 4 | no | — |
| 30 | C32×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 31 | #64145 | — | 3 | 1 | no | — |
| 32 | #64141 | — | 3 | 1 | no | — |
| 33 | C3×#949 | D3 | 1 | 4 | yes | complemented |
| 34 | #63860 | — | 3 | 4 | no | — |
| 35 | #63830 | — | 3 | 4 | no | — |
| 36 | #63664 | D3 | 1 | 1 | yes | characteristic, complemented |
| 37 | #63652 | — | 3 | 1 | no | — |
| 38 | #63651 | — | 3 | 1 | no | — |
| 39 | C3×#837 | — | 3 | 4 | no | — |
| 40 | #63570 | — | 3 | 4 | no | — |
| 41 | #63561 | — | 3 | 4 | no | — |
| 42 | C22×C32×D3 | — | 2 | 1 | no | — |
| 43 | C33×Q8 | D4 | 1 | 1 | yes | characteristic |
| 44 | C33×D4 | — | 2 | 1 | no | — |
| 45 | C33×D4 | D4 | 1 | 1 | yes | characteristic |
| 46 | C2×C33×C4 | — | 2 | 1 | no | — |
| 47 | C2×C33×C4 | C23 | 1 | 1 | yes | characteristic |
| 48 | #6312 | — | 2 | 2 | no | — |
| 49 | #6312 | — | 2 | 1 | no | — |
| 50 | C2×C3⋊(C3⋊Dic3) | — | 2 | 2 | no | — |
| 51 | C2×C3⋊(C3⋊Dic3) | D4 | 1 | 2 | yes | — |
| 52 | C4⋊(C3⋊(C3⋊D3)) | D4 | 1 | 1 | yes | characteristic |
| 53 | C4×C3⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 54 | C4×C3⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 55 | #6308 | — | 2 | 2 | no | — |
| 56 | #6308 | — | 2 | 1 | no | — |
| 57 | #6308 | — | 2 | 1 | no | — |
| 58 | #6308 | D4 | 1 | 1 | yes | characteristic |
| 59 | C2×C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 60 | C32×D12 | — | 2 | 1 | no | — |
| 61 | C32×D12 | — | 2 | 1 | no | — |
| 62 | C3×C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 63 | C32×C3⋊C8 | — | 2 | 1 | no | — |
| 64 | #5201 | — | 9 | 4 | no | — |
| 65 | #4827 | — | 9 | 1 | no | — |
| 66 | C32×#41 | — | 2 | 4 | no | — |
| 67 | C32×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 68 | C32×#41 | C2×D3 | 1 | 4 | yes | — |
| 69 | C2×C32×D4 | — | 3 | 1 | no | — |
| 70 | Q8×C3⋊D3 | — | 6 | 8 | no | — |
| 71 | Q8×C3⋊D3 | — | 6 | 1 | no | — |
| 72 | Q8×C3⋊D3 | — | 6 | 4 | no | — |
| 73 | #3830 | — | 6 | 2 | no | — |
| 74 | #3830 | — | 6 | 8 | no | — |
| 75 | #3830 | — | 6 | 16 | no | — |
| 76 | #3830 | — | 6 | 8 | no | — |
| 77 | #3830 | — | 6 | 1 | no | — |
| 78 | #3830 | — | 6 | 4 | no | — |
| 79 | #3828 | — | 3 | 1 | no | — |
| 80 | #3828 | — | 3 | 4 | no | — |
| 81 | #3828 | — | 6 | 1 | no | — |
| 82 | #3828 | — | 6 | 4 | no | — |
| 83 | #3828 | — | 6 | 4 | no | — |
| 84 | #3828 | — | 6 | 8 | no | — |
| 85 | C2×#634 | — | 3 | 1 | no | — |
| 86 | C2×#634 | — | 3 | 4 | no | — |
| 87 | C2×#634 | — | 6 | 1 | no | — |
| 88 | C2×#634 | — | 6 | 4 | no | — |
| 89 | C2×#634 | — | 6 | 4 | no | — |
| 90 | C2×#634 | — | 6 | 8 | no | — |
| 91 | C2×C3×D12 | C2×D3 | 1 | 4 | yes | — |
| 92 | C32×SD16 | — | 6 | 1 | no | — |
| 93 | C32×D8 | — | 6 | 1 | no | — |
| 94 | C32×M16 | — | 3 | 1 | no | — |
| 95 | #3757 | — | 6 | 2 | no | — |
| 96 | #3754 | — | 6 | 1 | no | — |
| 97 | #3753 | — | 6 | 1 | no | — |
| 98 | C4×C3⋊Dic3 | C2×D3 | 1 | 1 | yes | characteristic |
| 99 | #3748 | C2×D3 | 1 | 1 | yes | characteristic |
| 100 | C3×#215 | — | 2 | 4 | no | — |
| 101 | C3×#213 | — | 2 | 4 | no | — |
| 102 | C3×C4×Dic3 | — | 3 | 4 | no | — |
| 103 | C3×#208 | — | 3 | 4 | no | — |
| 104 | C3×#208 | C2×D3 | 1 | 4 | yes | — |
| 105 | (C2×D3)⋊Dic3 | — | 6 | 8 | no | — |
| 106 | #3716 | — | 6 | 4 | no | — |
| 107 | #3714 | — | 6 | 4 | no | — |
| 108 | C22×C33 | — | 2 | 1 | no | — |
| 109 | C22×C33 | C2×D4 | 1 | 1 | yes | characteristic |
| 110 | C2×C3⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 111 | C2×C32×D3 | — | 4 | 2 | no | — |
| 112 | C2×C32×D3 | — | 4 | 1 | no | — |
| 113 | C33×C4 | — | 2 | 1 | no | — |
| 114 | C33×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | C33×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C3⋊(C3⋊Dic3) | — | 2 | 2 | no | — |
| 117 | C3⋊(C3⋊Dic3) | — | 2 | 1 | no | — |
| 118 | C3×C3⋊Dic3 | — | 4 | 1 | no | — |
| 119 | #1010 | — | 9 | 4 | no | — |
| 120 | #1010 | — | 9 | 1 | no | — |
| 121 | #1010 | — | 18 | 4 | no | — |
| 122 | C3×AGL(1,ℤ/8) | — | 3 | 4 | no | — |
| 123 | #949 | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 124 | #936 | — | 9 | 4 | no | — |
| 125 | #932 | — | 9 | 4 | no | — |
| 126 | #908 | — | 9 | 1 | no | — |
| 127 | #875 | — | 9 | 1 | no | — |
| 128 | C3×#104 | — | 9 | 1 | no | — |
| 129 | #837 | — | 3 | 4 | no | — |
| 130 | #825 | — | 9 | 4 | no | — |
| 131 | #824 | — | 9 | 4 | no | — |
| 132 | #824 | — | 9 | 1 | no | — |
| 133 | #805 | — | 9 | 1 | no | — |
| 134 | C23×C32 | — | 6 | 1 | no | — |
| 135 | C22×C3×D3 | — | 2 | 4 | no | — |
| 136 | C32×Q8 | — | 2 | 4 | no | — |
| 137 | C32×Q8 | D12 | 1 | 1 | yes | characteristic |
| 138 | C32×Q8 | #67 | 1 | 4 | yes | — |
| 139 | C32×D4 | — | 2 | 8 | no | — |
| 140 | C32×D4 | — | 2 | 4 | no | — |
| 141 | C32×D4 | — | 2 | 1 | no | — |
| 142 | C32×D4 | — | 2 | 4 | no | — |
| 143 | C32×D4 | — | 6 | 1 | no | — |
| 144 | C32×D4 | — | 6 | 1 | no | — |
| 145 | C32×D4 | D12 | 1 | 1 | yes | characteristic |
| 146 | C32×D4 | #67 | 1 | 4 | yes | — |
| 147 | C2×C32×C4 | — | 2 | 8 | no | — |
| 148 | C2×C32×C4 | — | 2 | 4 | no | — |
| 149 | C2×C32×C4 | — | 2 | 1 | no | — |
| 150 | C2×C32×C4 | — | 2 | 4 | no | — |
| 151 | C2×C32×C4 | C22×D3 | 1 | 4 | yes | — |
| 152 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 153 | #638 | — | 6 | 16 | no | — |
| 154 | #638 | — | 6 | 2 | no | — |
| 155 | #638 | — | 6 | 8 | no | — |
| 156 | #638 | — | 6 | 8 | no | — |
| 157 | #638 | — | 6 | 4 | no | — |
| 158 | #638 | — | 6 | 1 | no | — |
| 159 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 160 | C2×C3⋊Dic3 | — | 3 | 2 | no | — |
| 161 | C2×C3⋊Dic3 | — | 3 | 8 | no | — |
| 162 | C2×C3⋊Dic3 | — | 6 | 8 | no | — |
| 163 | C2×C3⋊Dic3 | — | 6 | 16 | no | — |
| 164 | C2×C3⋊Dic3 | — | 6 | 2 | no | — |
| 165 | C2×C3⋊Dic3 | — | 6 | 8 | no | — |
| 166 | C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 167 | C4⋊(C3⋊D3) | — | 3 | 4 | no | — |
| 168 | C4⋊(C3⋊D3) | — | 6 | 4 | no | — |
| 169 | C4×C3⋊D3 | — | 6 | 16 | no | — |
| 170 | C4×C3⋊D3 | — | 6 | 2 | no | — |
| 171 | C4×C3⋊D3 | — | 6 | 8 | no | — |
| 172 | C4×C3⋊D3 | — | 6 | 8 | no | — |
| 173 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 174 | C4×C3⋊D3 | — | 6 | 4 | no | — |
| 175 | #634 | — | 3 | 1 | no | — |
| 176 | #634 | — | 3 | 4 | no | — |
| 177 | #634 | — | 6 | 4 | no | — |
| 178 | #634 | — | 6 | 8 | no | — |
| 179 | #634 | — | 6 | 16 | no | — |
| 180 | #634 | — | 6 | 2 | no | — |
| 181 | #634 | — | 6 | 8 | no | — |
| 182 | #634 | — | 6 | 8 | no | — |
| 183 | #634 | — | 6 | 1 | no | — |
| 184 | #634 | — | 6 | 4 | no | — |
| 185 | #634 | — | 6 | 1 | no | — |
| 186 | #634 | — | 6 | 4 | no | — |
| 187 | C2×C3×Dic3 | — | 6 | 4 | no | — |
| 188 | C3×D12 | — | 2 | 4 | no | — |
| 189 | C3×D12 | — | 2 | 4 | no | — |
| 190 | C32×C8 | — | 6 | 1 | no | — |
| 191 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 192 | C3×C3⋊C8 | — | 2 | 4 | no | — |
| 193 | C3×C3⋊C8 | — | 6 | 4 | no | — |
| 194 | #454 | — | 27 | 1 | no | Sylow |
| 195 | C2×C33 | — | 2 | 1 | no | — |
| 196 | C2×C33 | — | 4 | 1 | no | — |
| 197 | C2×C33 | #120 | 1 | 1 | yes | characteristic |
| 198 | C3⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 199 | C32×D3 | — | 8 | 1 | no | — |
| 200 | C3×#41 | — | 2 | 4 | no | — |
| 201 | C3×#41 | D32 | 1 | 4 | yes | — |
| 202 | C3×#41 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 203 | C2×C3×D4 | — | 3 | 4 | no | — |
| 204 | D3×Q8 | — | 18 | 8 | no | — |
| 205 | D3×Q8 | — | 18 | 4 | no | — |
| 206 | D3×Q8 | — | 18 | 1 | no | — |
| 207 | #237 | — | 18 | 8 | no | — |
| 208 | #237 | — | 18 | 2 | no | — |
| 209 | #237 | — | 18 | 16 | no | — |
| 210 | #237 | — | 18 | 8 | no | — |
| 211 | #237 | — | 18 | 4 | no | — |
| 212 | #237 | — | 18 | 1 | no | — |
| 213 | #235 | — | 9 | 4 | no | — |
| 214 | #235 | — | 9 | 1 | no | — |
| 215 | #235 | — | 18 | 4 | no | — |
| 216 | #235 | — | 18 | 4 | no | — |
| 217 | #235 | — | 18 | 1 | no | — |
| 218 | #235 | — | 18 | 8 | no | — |
| 219 | C2×D12 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 220 | C2×Dic6 | — | 9 | 4 | no | — |
| 221 | C2×Dic6 | — | 9 | 1 | no | — |
| 222 | C2×Dic6 | — | 18 | 4 | no | — |
| 223 | C2×Dic6 | — | 18 | 4 | no | — |
| 224 | C2×Dic6 | — | 18 | 1 | no | — |
| 225 | C2×Dic6 | — | 18 | 8 | no | — |
| 226 | C3×SD16 | — | 6 | 4 | no | — |
| 227 | C3×D8 | — | 6 | 4 | no | — |
| 228 | C3×M16 | — | 3 | 4 | no | — |
| 229 | C3×M16 | — | 9 | 1 | no | — |
| 230 | C3×C42 | — | 9 | 1 | no | — |
| 231 | #217 | — | 18 | 8 | no | — |
| 232 | #215 | — | 2 | 1 | no | — |
| 233 | #214 | — | 18 | 4 | no | — |
| 234 | #213 | — | 2 | 1 | no | — |
| 235 | #213 | — | 18 | 4 | no | — |
| 236 | (C2×D3)⋊C4 | — | 18 | 2 | no | — |
| 237 | C4×Dic3 | — | 3 | 4 | no | — |
| 238 | #208 | — | 3 | 4 | no | — |
| 239 | #208 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 240 | D24 | — | 18 | 1 | no | — |
| 241 | #204 | — | 18 | 1 | no | — |
| 242 | C22×C32 | — | 2 | 8 | no | — |
| 243 | C22×C32 | — | 2 | 1 | no | — |
| 244 | C22×C32 | — | 2 | 4 | no | — |
| 245 | C22×C32 | — | 2 | 4 | no | — |
| 246 | C22×C32 | — | 12 | 2 | no | — |
| 247 | C22×C32 | — | 12 | 1 | no | — |
| 248 | C22×C32 | D3×D4 | 1 | 4 | yes | — |
| 249 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic |
| 250 | C2×C3⋊D3 | — | 6 | 8 | no | — |
| 251 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 252 | C2×C3⋊D3 | — | 6 | 4 | no | — |
| 253 | C2×C3×D3 | — | 4 | 8 | no | — |
| 254 | C2×C3×D3 | — | 4 | 4 | no | — |
| 255 | C32×C4 | — | 2 | 8 | no | — |
| 256 | C32×C4 | — | 2 | 1 | no | — |
| 257 | C32×C4 | — | 2 | 4 | no | — |
| 258 | C32×C4 | — | 2 | 4 | no | — |
| 259 | C32×C4 | — | 2 | 4 | no | — |
| 260 | C32×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 261 | C32×C4 | D3×D4 | 1 | 4 | yes | — |
| 262 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 263 | C32×C4 | C2×#67 | 1 | 4 | yes | — |
| 264 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 265 | C3⋊Dic3 | — | 6 | 8 | no | — |
| 266 | C3⋊Dic3 | — | 6 | 16 | no | — |
| 267 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 268 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 269 | C3⋊Dic3 | — | 6 | 4 | no | — |
| 270 | C3⋊Dic3 | — | 6 | 8 | no | — |
| 271 | C3×Dic3 | — | 12 | 4 | no | — |
| 272 | 2−1+4 | — | 27 | 1 | no | — |
| 273 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 274 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 275 | #124 | — | 27 | 1 | no | — |
| 276 | #104 | — | 9 | 1 | no | — |
| 277 | #104 | — | 27 | 1 | no | — |
| 278 | #101 | — | 27 | 1 | no | — |
| 279 | C33 | #454 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 280 | C23×C3 | — | 6 | 4 | no | — |
| 281 | C22×D3 | — | 2 | 1 | no | — |
| 282 | C3×Q8 | — | 2 | 4 | no | — |
| 283 | C3×Q8 | #626 | 1 | 4 | yes | — |
| 284 | C3×Q8 | #638 | 1 | 1 | yes | characteristic |
| 285 | C3×D4 | — | 2 | 8 | no | — |
| 286 | C3×D4 | — | 2 | 4 | no | — |
| 287 | C3×D4 | — | 2 | 1 | no | — |
| 288 | C3×D4 | — | 2 | 4 | no | — |
| 289 | C3×D4 | — | 6 | 4 | no | — |
| 290 | C3×D4 | — | 6 | 4 | no | — |
| 291 | C3×D4 | #626 | 1 | 4 | yes | — |
| 292 | C3×D4 | #638 | 1 | 1 | yes | characteristic |
| 293 | C2×C3×C4 | — | 2 | 8 | no | — |
| 294 | C2×C3×C4 | — | 2 | 4 | no | — |
| 295 | C2×C3×C4 | — | 2 | 1 | no | — |
| 296 | C2×C3×C4 | — | 2 | 4 | no | — |
| 297 | C2×C3×C4 | — | 18 | 1 | no | — |
| 298 | C2×C3×C4 | C2×D32 | 1 | 4 | yes | — |
| 299 | C2×C3×C4 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 300 | #67 | — | 18 | 16 | no | — |
| 301 | #67 | — | 18 | 2 | no | — |
| 302 | #67 | — | 18 | 8 | no | — |
| 303 | #67 | — | 18 | 8 | no | — |
| 304 | #67 | — | 18 | 4 | no | — |
| 305 | #67 | — | 18 | 1 | no | — |
| 306 | C2×Dic3 | — | 6 | 4 | no | — |
| 307 | C2×Dic3 | — | 9 | 8 | no | — |
| 308 | C2×Dic3 | — | 9 | 2 | no | — |
| 309 | C2×Dic3 | — | 18 | 8 | no | — |
| 310 | C2×Dic3 | — | 18 | 16 | no | — |
| 311 | C2×Dic3 | — | 18 | 2 | no | — |
| 312 | C2×Dic3 | — | 18 | 8 | no | — |
| 313 | D12 | — | 2 | 1 | no | — |
| 314 | D12 | — | 2 | 1 | no | — |
| 315 | D12 | — | 9 | 4 | no | — |
| 316 | D12 | — | 9 | 1 | no | — |
| 317 | D12 | — | 18 | 4 | no | — |
| 318 | C4×D3 | — | 18 | 16 | no | — |
| 319 | C4×D3 | — | 18 | 2 | no | — |
| 320 | C4×D3 | — | 18 | 8 | no | — |
| 321 | C4×D3 | — | 18 | 8 | no | — |
| 322 | C4×D3 | — | 18 | 4 | no | — |
| 323 | C4×D3 | — | 18 | 1 | no | — |
| 324 | Dic6 | — | 9 | 4 | no | — |
| 325 | Dic6 | — | 9 | 1 | no | — |
| 326 | Dic6 | — | 18 | 4 | no | — |
| 327 | Dic6 | — | 18 | 8 | no | — |
| 328 | Dic6 | — | 18 | 16 | no | — |
| 329 | Dic6 | — | 18 | 2 | no | — |
| 330 | Dic6 | — | 18 | 8 | no | — |
| 331 | Dic6 | — | 18 | 8 | no | — |
| 332 | Dic6 | — | 18 | 4 | no | — |
| 333 | Dic6 | — | 18 | 4 | no | — |
| 334 | Dic6 | — | 18 | 1 | no | — |
| 335 | Dic6 | — | 18 | 1 | no | — |
| 336 | C3×C8 | — | 6 | 4 | no | — |
| 337 | C3×C8 | — | 18 | 1 | no | — |
| 338 | C3⋊C8 | — | 2 | 1 | no | — |
| 339 | C3⋊C8 | — | 6 | 4 | no | — |
| 340 | C2×C32 | — | 2 | 1 | no | — |
| 341 | C2×C32 | — | 2 | 4 | no | — |
| 342 | C2×C32 | — | 2 | 4 | no | — |
| 343 | C2×C32 | — | 4 | 4 | no | — |
| 344 | C2×C32 | — | 4 | 8 | no | — |
| 345 | C2×C32 | — | 4 | 4 | no | — |
| 346 | C2×C32 | — | 4 | 1 | no | — |
| 347 | C2×C32 | — | 24 | 1 | no | — |
| 348 | C2×C32 | #882 | 1 | 1 | yes | characteristic |
| 349 | C2×C32 | #937 | 1 | 4 | yes | — |
| 350 | C3⋊D3 | — | 12 | 8 | no | — |
| 351 | C3⋊D3 | — | 12 | 4 | no | — |
| 352 | C3⋊D3 | — | 12 | 1 | no | — |
| 353 | C3×D3 | — | 8 | 4 | no | — |
| 354 | #41 | — | 27 | 1 | no | — |
| 355 | #41 | — | 54 | 1 | no | — |
| 356 | #41 | — | 54 | 2 | no | — |
| 357 | #41 | — | 54 | 1 | no | — |
| 358 | #41 | D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 359 | C2×Q8 | — | 27 | 1 | no | — |
| 360 | C2×Q8 | — | 54 | 1 | no | — |
| 361 | C2×Q8 | — | 54 | 1 | no | — |
| 362 | C2×D4 | — | 3 | 1 | no | — |
| 363 | SD16 | — | 6 | 1 | no | — |
| 364 | SD16 | — | 54 | 1 | no | — |
| 365 | D8 | — | 6 | 1 | no | — |
| 366 | D8 | — | 54 | 1 | no | — |
| 367 | M16 | — | 3 | 1 | no | — |
| 368 | M16 | — | 9 | 1 | no | — |
| 369 | C22⋊C4 | — | 54 | 2 | no | — |
| 370 | C42 | — | 9 | 1 | no | — |
| 371 | C22×C3 | — | 2 | 8 | no | — |
| 372 | C22×C3 | — | 2 | 1 | no | — |
| 373 | C22×C3 | — | 2 | 4 | no | — |
| 374 | C22×C3 | — | 2 | 4 | no | — |
| 375 | C22×C3 | — | 12 | 8 | no | — |
| 376 | C22×C3 | — | 12 | 4 | no | — |
| 377 | C22×C3 | #3811 | 1 | 4 | yes | — |
| 378 | C22×C3 | D4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 379 | C2×D3 | — | 4 | 2 | no | — |
| 380 | C2×D3 | — | 4 | 1 | no | — |
| 381 | C2×D3 | — | 18 | 8 | no | — |
| 382 | C2×D3 | — | 18 | 1 | no | — |
| 383 | C2×D3 | — | 18 | 4 | no | — |
| 384 | C3×C4 | — | 2 | 8 | no | — |
| 385 | C3×C4 | — | 2 | 1 | no | — |
| 386 | C3×C4 | — | 2 | 4 | no | — |
| 387 | C3×C4 | — | 2 | 4 | no | — |
| 388 | C3×C4 | — | 2 | 4 | no | — |
| 389 | C3×C4 | — | 36 | 1 | no | — |
| 390 | C3×C4 | C2×#626 | 1 | 4 | yes | — |
| 391 | C3×C4 | #3811 | 1 | 4 | yes | — |
| 392 | C3×C4 | D4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 393 | C3×C4 | C2×#638 | 1 | 1 | yes | characteristic |
| 394 | Dic3 | — | 12 | 4 | no | — |
| 395 | Dic3 | — | 18 | 16 | no | — |
| 396 | Dic3 | — | 18 | 8 | no | — |
| 397 | Dic3 | — | 18 | 1 | no | — |
| 398 | Dic3 | — | 18 | 2 | no | — |
| 399 | Dic3 | — | 18 | 4 | no | — |
| 400 | Dic3 | — | 18 | 8 | no | — |
| 401 | C32 | — | 2 | 4 | no | — |
| 402 | C32 | #4827 | 1 | 1 | yes | characteristic, complemented |
| 403 | C32 | #5201 | 1 | 4 | yes | complemented |
| 404 | C23 | — | 6 | 1 | no | — |
| 405 | Q8 | — | 27 | 1 | no | — |
| 406 | Q8 | — | 54 | 2 | no | — |
| 407 | Q8 | — | 54 | 1 | no | — |
| 408 | Q8 | — | 54 | 1 | no | — |
| 409 | Q8 | #6291 | 1 | 1 | yes | characteristic |
| 410 | D4 | — | 2 | 1 | no | — |
| 411 | D4 | — | 6 | 1 | no | — |
| 412 | D4 | — | 6 | 1 | no | — |
| 413 | D4 | — | 27 | 1 | no | — |
| 414 | D4 | — | 54 | 2 | no | — |
| 415 | D4 | — | 54 | 1 | no | — |
| 416 | D4 | #6291 | 1 | 1 | yes | characteristic |
| 417 | C2×C4 | — | 2 | 1 | no | — |
| 418 | C2×C4 | — | 18 | 1 | no | — |
| 419 | C2×C4 | — | 27 | 2 | no | — |
| 420 | C2×C4 | — | 54 | 2 | no | — |
| 421 | C2×C4 | — | 54 | 2 | no | — |
| 422 | C2×C4 | — | 54 | 1 | no | — |
| 423 | C2×C4 | C2×D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 424 | C8 | — | 6 | 1 | no | — |
| 425 | C8 | — | 18 | 1 | no | — |
| 426 | C2×C3 | — | 2 | 1 | no | — |
| 427 | C2×C3 | — | 2 | 4 | no | — |
| 428 | C2×C3 | — | 2 | 4 | no | — |
| 429 | C2×C3 | — | 4 | 4 | no | — |
| 430 | C2×C3 | — | 4 | 8 | no | — |
| 431 | C2×C3 | — | 4 | 1 | no | — |
| 432 | C2×C3 | — | 4 | 4 | no | — |
| 433 | C2×C3 | — | 24 | 4 | no | — |
| 434 | C2×C3 | #63981 | 1 | 4 | yes | — |
| 435 | C2×C3 | #64146 | 1 | 1 | yes | characteristic |
| 436 | D3 | — | 8 | 1 | no | — |
| 437 | D3 | — | 36 | 8 | no | — |
| 438 | D3 | — | 36 | 1 | no | — |
| 439 | D3 | — | 36 | 4 | no | — |
| 440 | C22 | — | 2 | 1 | no | — |
| 441 | C22 | — | 12 | 2 | no | — |
| 442 | C22 | — | 12 | 1 | no | — |
| 443 | C22 | — | 54 | 1 | no | — |
| 444 | C22 | #89039 | 1 | 1 | yes | characteristic |
| 445 | C4 | — | 2 | 1 | no | — |
| 446 | C4 | — | 36 | 1 | no | — |
| 447 | C4 | — | 54 | 2 | no | — |
| 448 | C4 | — | 54 | 1 | no | — |
| 449 | C4 | C2×#6291 | 1 | 1 | yes | characteristic |
| 450 | C4 | #89039 | 1 | 1 | yes | characteristic |
| 451 | C3 | — | 2 | 4 | no | — |
| 452 | C3 | #10591686 | 1 | 4 | yes | complemented |
| 453 | C3 | #10592900 | 1 | 1 | yes | characteristic, complemented |
| 454 | C2 | — | 2 | 1 | no | — |
| 455 | C2 | — | 4 | 1 | no | — |
| 456 | C2 | — | 24 | 1 | no | — |
| 457 | C2 | — | 108 | 1 | no | — |
| 458 | C2 | #11723638 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11724685 | C2 | semidirect |
| 2. C32×#949 | C2 | semidirect |
| 3. #11723429 | C2 | semidirect |
| 4. #11723378 | C2 | semidirect |
| 5. C3×#63664 | C2 | semidirect |
| 6. #11722047 | C2 | semidirect |
| 7. #11722030 | C2 | semidirect |
| 33. C3×#949 | D3 | semidirect |
| 36. #63664 | D3 | semidirect |
| 123. #949 | C3⋊D3 | semidirect |
| 279. C33 | #454 | semidirect |
| 402. C32 | #4827 | semidirect |
| 403. C32 | #5201 | semidirect |
| 452. C3 | #10591686 | semidirect |
| 453. C3 | #10592900 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724685 | 2 |
| C32×#949 | 2 |
| #11723429 | 2 |
| #11723378 | 2 |
| C3×#63664 | 2 |
| #11722047 | 2 |
| #11722030 | 2 |
| #10592900 | 3 |
| #10591686 | 3 |