Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
957 conjugacy classes of subgroups.
The subgroup lattice has 560 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10594718 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C2×#63809 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10594669 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3⋊D3×#108 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#4898 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10591010 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10590982 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10590981 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10590925 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #80929 | — | 3 | 2 | no | maximal |
| 11 | #64306 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#3796 | C22 | 1 | 2 | yes | — |
| 13 | M16×C3⋊D3 | C22 | 1 | 2 | yes | — |
| 14 | C2×C8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 15 | C3×#909 | C22 | 1 | 2 | yes | — |
| 16 | C3×#908 | C22 | 1 | 2 | yes | — |
| 17 | C2×C3×#204 | C22 | 1 | 2 | yes | complemented |
| 18 | C3×#901 | C22 | 1 | 2 | yes | — |
| 19 | C2×#3718 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #63827 | C22 | 1 | 2 | yes | — |
| 21 | #63823 | C22 | 1 | 2 | yes | — |
| 22 | C2×#3713 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #63818 | C22 | 1 | 1 | yes | characteristic |
| 24 | #63815 | C22 | 1 | 2 | yes | — |
| 25 | #63811 | — | 2 | 2 | no | — |
| 26 | #63810 | — | 2 | 2 | no | — |
| 27 | #63809 | — | 2 | 2 | no | — |
| 28 | #63809 | — | 2 | 1 | no | — |
| 29 | #63809 | — | 2 | 1 | no | — |
| 30 | #63809 | — | 2 | 1 | no | — |
| 31 | #63809 | — | 2 | 1 | no | — |
| 32 | #63805 | — | 2 | 1 | no | — |
| 33 | #63803 | — | 2 | 1 | no | — |
| 34 | #63798 | — | 2 | 2 | no | — |
| 35 | #63791 | — | 2 | 1 | no | — |
| 36 | D32×C8 | — | 2 | 1 | no | — |
| 37 | C32×#108 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | #63649 | C22 | 1 | 2 | yes | complemented |
| 39 | #63646 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | C3×#824 | C22 | 1 | 2 | yes | complemented |
| 41 | C3×#823 | C22 | 1 | 2 | yes | complemented |
| 42 | #63560 | C22 | 1 | 2 | yes | complemented |
| 43 | #63558 | C22 | 1 | 2 | yes | complemented |
| 44 | #5777 | — | 3 | 2 | no | — |
| 45 | #5773 | — | 3 | 2 | no | — |
| 46 | C2×#916 | — | 3 | 2 | no | — |
| 47 | D3×#131 | — | 3 | 2 | no | — |
| 48 | C3×#471 | — | 3 | 2 | no | — |
| 49 | #5204 | — | 3 | 2 | no | — |
| 50 | #5199 | — | 3 | 2 | no | — |
| 51 | #5177 | — | 3 | 2 | no | — |
| 52 | #5141 | — | 3 | 2 | no | — |
| 53 | #4898 | D3 | 1 | 2 | yes | complemented |
| 54 | D3×#108 | — | 3 | 2 | no | — |
| 55 | D3×#108 | — | 6 | 1 | no | — |
| 56 | #4755 | — | 3 | 2 | no | — |
| 57 | #4751 | — | 3 | 2 | no | — |
| 58 | #4749 | — | 3 | 2 | no | — |
| 59 | #4745 | — | 3 | 2 | no | — |
| 60 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 61 | C3×#235 | C23 | 1 | 2 | yes | — |
| 62 | C2×C3×D12 | C23 | 1 | 2 | yes | — |
| 63 | C2×C3×Dic6 | C23 | 1 | 2 | yes | — |
| 64 | #3811 | — | 2 | 1 | no | — |
| 65 | C2×#626 | — | 2 | 2 | no | — |
| 66 | #3805 | — | 2 | 1 | no | — |
| 67 | C2×D3×Dic3 | — | 2 | 2 | no | — |
| 68 | #3802 | D4 | 1 | 1 | yes | characteristic |
| 69 | C4×D32 | — | 2 | 1 | no | — |
| 70 | #3798 | — | 2 | 1 | no | — |
| 71 | #3797 | D4 | 1 | 1 | yes | characteristic |
| 72 | #3796 | — | 2 | 2 | no | — |
| 73 | #3796 | — | 2 | 2 | no | — |
| 74 | #3796 | — | 2 | 2 | no | — |
| 75 | #3796 | — | 2 | 2 | no | — |
| 76 | #3796 | D4 | 1 | 2 | yes | — |
| 77 | C32×M16 | C23 | 1 | 2 | yes | — |
| 78 | C2×C32×C8 | C23 | 1 | 1 | yes | characteristic |
| 79 | #3748 | C23 | 1 | 2 | yes | — |
| 80 | C2×C3⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 81 | #3743 | — | 2 | 2 | no | — |
| 82 | C8×C3⋊D3 | — | 2 | 2 | no | — |
| 83 | C8×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 84 | C8×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 85 | C8×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 86 | C8×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 87 | C3×#208 | C23 | 1 | 2 | yes | — |
| 88 | C3×Dic12 | — | 2 | 2 | no | — |
| 89 | C3×D24 | — | 2 | 2 | no | — |
| 90 | C3×#204 | — | 2 | 2 | no | — |
| 91 | C3×#204 | — | 2 | 2 | no | — |
| 92 | C3×#204 | — | 2 | 2 | no | — |
| 93 | C3×#204 | — | 2 | 2 | no | — |
| 94 | C3×ΓL(1,𝔽25) | — | 2 | 2 | no | — |
| 95 | C3×D3×C8 | — | 2 | 2 | no | — |
| 96 | #3718 | — | 2 | 2 | no | — |
| 97 | #3718 | — | 2 | 1 | no | — |
| 98 | #3718 | — | 2 | 1 | no | — |
| 99 | #3715 | — | 2 | 2 | no | — |
| 100 | #3715 | — | 2 | 2 | no | — |
| 101 | #3713 | — | 2 | 2 | no | — |
| 102 | #3713 | — | 2 | 1 | no | — |
| 103 | #3713 | — | 2 | 1 | no | — |
| 104 | #3712 | — | 2 | 1 | no | — |
| 105 | #3711 | — | 2 | 2 | no | — |
| 106 | #3710 | — | 2 | 1 | no | — |
| 107 | D3×C3⋊C8 | — | 2 | 2 | no | — |
| 108 | #3067 | — | 9 | 1 | no | Sylow |
| 109 | D3×#41 | — | 3 | 2 | no | — |
| 110 | C2×#239 | — | 3 | 2 | no | — |
| 111 | C2×#237 | — | 3 | 2 | no | — |
| 112 | C3×#137 | — | 3 | 2 | no | — |
| 113 | C3×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 114 | C2×C3×SD16 | — | 3 | 2 | no | — |
| 115 | C3×#131 | — | 3 | 2 | no | — |
| 116 | #951 | — | 3 | 2 | no | — |
| 117 | #949 | — | 3 | 2 | no | — |
| 118 | #948 | — | 3 | 2 | no | — |
| 119 | C2×#216 | — | 3 | 2 | no | — |
| 120 | #942 | — | 3 | 2 | no | — |
| 121 | #932 | — | 3 | 2 | no | — |
| 122 | C2×#213 | — | 3 | 2 | no | — |
| 123 | #919 | — | 6 | 2 | no | — |
| 124 | #918 | — | 6 | 2 | no | — |
| 125 | #916 | — | 6 | 2 | no | — |
| 126 | #916 | — | 6 | 2 | no | — |
| 127 | #916 | — | 6 | 2 | no | — |
| 128 | #916 | — | 6 | 2 | no | — |
| 129 | #916 | — | 6 | 2 | no | — |
| 130 | #916 | — | 6 | 2 | no | — |
| 131 | #915 | — | 6 | 2 | no | — |
| 132 | #914 | — | 6 | 2 | no | — |
| 133 | #912 | — | 6 | 2 | no | — |
| 134 | #911 | — | 6 | 2 | no | — |
| 135 | #909 | C2×D3 | 1 | 2 | yes | — |
| 136 | #908 | C2×D3 | 1 | 2 | yes | — |
| 137 | #907 | — | 3 | 2 | no | — |
| 138 | #907 | — | 6 | 2 | no | — |
| 139 | D3×M16 | — | 3 | 2 | no | — |
| 140 | D3×M16 | — | 3 | 2 | no | — |
| 141 | D3×M16 | — | 3 | 2 | no | — |
| 142 | D3×M16 | — | 6 | 2 | no | — |
| 143 | D3×M16 | — | 6 | 2 | no | — |
| 144 | C2×#204 | C2×D3 | 1 | 2 | yes | complemented |
| 145 | #901 | — | 6 | 2 | no | — |
| 146 | #901 | C2×D3 | 1 | 2 | yes | — |
| 147 | C2×D3×C8 | — | 3 | 2 | no | — |
| 148 | C2×D3×C8 | — | 6 | 1 | no | — |
| 149 | C2×D3×C8 | — | 6 | 2 | no | — |
| 150 | C3×#108 | — | 2 | 1 | no | — |
| 151 | C3×#108 | C2×D3 | 1 | 2 | yes | complemented |
| 152 | C3×#101 | — | 3 | 2 | no | — |
| 153 | C3×#100 | — | 3 | 2 | no | — |
| 154 | #836 | — | 3 | 2 | no | — |
| 155 | #833 | — | 3 | 2 | no | — |
| 156 | #824 | — | 3 | 2 | no | — |
| 157 | #824 | C2×D3 | 1 | 2 | yes | complemented |
| 158 | #823 | — | 3 | 2 | no | — |
| 159 | #823 | C2×D3 | 1 | 2 | yes | complemented |
| 160 | #822 | — | 3 | 2 | no | — |
| 161 | #822 | — | 3 | 2 | no | — |
| 162 | #822 | — | 6 | 2 | no | — |
| 163 | #819 | — | 3 | 2 | no | — |
| 164 | #819 | — | 6 | 1 | no | — |
| 165 | C22×C3⋊D3 | #41 | 1 | 1 | yes | characteristic |
| 166 | C22×C3×D3 | — | 2 | 2 | no | — |
| 167 | C2×D32 | — | 2 | 1 | no | — |
| 168 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 169 | C2×C3⋊Dic3 | #41 | 1 | 1 | yes | characteristic |
| 170 | C4×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 171 | C4×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 172 | C4×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | C4×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C3×#67 | — | 2 | 2 | no | — |
| 175 | C2×C3×Dic3 | — | 2 | 2 | no | — |
| 176 | C3×D12 | — | 2 | 2 | no | — |
| 177 | C3×D12 | — | 2 | 2 | no | — |
| 178 | C3×D12 | C2×D4 | 1 | 2 | yes | — |
| 179 | C3×C4×D3 | — | 2 | 2 | no | — |
| 180 | C3×Dic6 | — | 2 | 2 | no | — |
| 181 | C3×Dic6 | — | 2 | 2 | no | — |
| 182 | C3×Dic6 | C2×D4 | 1 | 2 | yes | — |
| 183 | #627 | — | 2 | 1 | no | — |
| 184 | #626 | — | 2 | 2 | no | — |
| 185 | #626 | — | 4 | 2 | no | — |
| 186 | #626 | — | 4 | 2 | no | — |
| 187 | #625 | — | 2 | 1 | no | — |
| 188 | #624 | — | 2 | 1 | no | — |
| 189 | D3×Dic3 | — | 2 | 2 | no | — |
| 190 | D3×Dic3 | — | 4 | 2 | no | — |
| 191 | D3×Dic3 | — | 4 | 2 | no | — |
| 192 | C32×C8 | — | 2 | 2 | no | — |
| 193 | C32×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 194 | C32×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 195 | C3⋊(C3⋊C8) | — | 2 | 2 | no | — |
| 196 | C3⋊(C3⋊C8) | C2×D4 | 1 | 1 | yes | characteristic |
| 197 | C3⋊(C3⋊C8) | C2×D4 | 1 | 1 | yes | characteristic |
| 198 | C3×C3⋊C8 | — | 2 | 2 | no | — |
| 199 | #575 | — | 9 | 2 | no | — |
| 200 | C2×#135 | — | 9 | 1 | no | — |
| 201 | C2×#131 | — | 9 | 1 | no | — |
| 202 | #473 | — | 9 | 2 | no | — |
| 203 | #472 | — | 9 | 2 | no | — |
| 204 | #471 | — | 3 | 2 | no | — |
| 205 | #471 | — | 9 | 2 | no | — |
| 206 | C2×#108 | — | 9 | 1 | no | — |
| 207 | #413 | — | 9 | 2 | no | — |
| 208 | C3×#41 | — | 3 | 2 | no | — |
| 209 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 210 | C2×C3×D4 | — | 3 | 2 | no | — |
| 211 | C2×#67 | — | 6 | 2 | no | — |
| 212 | C22×Dic3 | — | 6 | 2 | no | — |
| 213 | #239 | — | 3 | 2 | no | — |
| 214 | #239 | — | 6 | 2 | no | — |
| 215 | #239 | — | 6 | 2 | no | — |
| 216 | #239 | — | 6 | 2 | no | — |
| 217 | #239 | — | 6 | 2 | no | — |
| 218 | D3×Q8 | — | 3 | 2 | no | — |
| 219 | #237 | — | 3 | 2 | no | — |
| 220 | #237 | — | 6 | 2 | no | — |
| 221 | #237 | — | 6 | 2 | no | — |
| 222 | #237 | — | 6 | 2 | no | — |
| 223 | #237 | — | 6 | 2 | no | — |
| 224 | #237 | — | 6 | 2 | no | — |
| 225 | D3×D4 | — | 3 | 2 | no | — |
| 226 | D3×D4 | — | 6 | 2 | no | — |
| 227 | #235 | — | 6 | 2 | no | — |
| 228 | #235 | C22×D3 | 1 | 2 | yes | — |
| 229 | C2×D12 | — | 6 | 2 | no | — |
| 230 | C2×D12 | C22×D3 | 1 | 2 | yes | — |
| 231 | C2×C4×D3 | — | 3 | 2 | no | — |
| 232 | C2×C4×D3 | — | 6 | 1 | no | — |
| 233 | C2×C4×D3 | — | 6 | 2 | no | — |
| 234 | C2×C4×D3 | — | 6 | 2 | no | — |
| 235 | C2×Dic6 | C22×D3 | 1 | 2 | yes | — |
| 236 | C3×Q16 | — | 6 | 2 | no | — |
| 237 | C3×SD16 | — | 6 | 2 | no | — |
| 238 | C3×SD16 | — | 6 | 2 | no | — |
| 239 | C3×SD16 | — | 6 | 2 | no | — |
| 240 | C3×SD16 | — | 6 | 2 | no | — |
| 241 | C3×D8 | — | 6 | 2 | no | — |
| 242 | C3×M16 | — | 2 | 2 | no | — |
| 243 | C3×M16 | — | 3 | 2 | no | — |
| 244 | C3×M16 | — | 6 | 2 | no | — |
| 245 | C3×M16 | C22×D3 | 1 | 2 | yes | — |
| 246 | C3×M16 | C22×D3 | 1 | 2 | yes | — |
| 247 | C2×C3×C8 | — | 2 | 1 | no | — |
| 248 | C2×C3×C8 | — | 6 | 2 | no | — |
| 249 | C2×C3×C8 | C22×D3 | 1 | 2 | yes | — |
| 250 | #216 | — | 6 | 2 | no | — |
| 251 | #216 | — | 6 | 2 | no | — |
| 252 | #216 | — | 6 | 2 | no | — |
| 253 | #216 | — | 6 | 2 | no | — |
| 254 | #215 | — | 6 | 2 | no | — |
| 255 | #215 | — | 6 | 2 | no | — |
| 256 | #214 | — | 6 | 2 | no | — |
| 257 | #214 | — | 6 | 2 | no | — |
| 258 | #213 | — | 6 | 2 | no | — |
| 259 | #213 | — | 6 | 2 | no | — |
| 260 | #213 | — | 6 | 2 | no | — |
| 261 | #213 | — | 6 | 2 | no | — |
| 262 | #208 | — | 3 | 2 | no | — |
| 263 | #208 | — | 3 | 2 | no | — |
| 264 | #208 | — | 6 | 2 | no | — |
| 265 | #208 | — | 6 | 2 | no | — |
| 266 | #208 | C22×D3 | 1 | 2 | yes | — |
| 267 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 268 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 269 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 270 | Dic12 | — | 2 | 2 | no | — |
| 271 | D24 | — | 2 | 2 | no | — |
| 272 | #204 | — | 2 | 2 | no | — |
| 273 | #204 | — | 2 | 2 | no | — |
| 274 | #204 | — | 2 | 2 | no | — |
| 275 | #204 | — | 2 | 2 | no | — |
| 276 | ΓL(1,𝔽25) | — | 2 | 2 | no | — |
| 277 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 278 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 279 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 280 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 281 | ΓL(1,𝔽25) | — | 12 | 2 | no | — |
| 282 | D3×C8 | — | 2 | 2 | no | — |
| 283 | D3×C8 | — | 3 | 2 | no | — |
| 284 | D3×C8 | — | 3 | 2 | no | — |
| 285 | D3×C8 | — | 3 | 2 | no | — |
| 286 | D3×C8 | — | 3 | 2 | no | — |
| 287 | D3×C8 | — | 6 | 1 | no | — |
| 288 | D3×C8 | — | 6 | 1 | no | — |
| 289 | D3×C8 | — | 6 | 1 | no | — |
| 290 | D3×C8 | — | 6 | 1 | no | — |
| 291 | D3×C8 | — | 6 | 2 | no | — |
| 292 | D3×C8 | — | 6 | 2 | no | — |
| 293 | D3×C8 | — | 6 | 2 | no | — |
| 294 | D3×C8 | — | 6 | 2 | no | — |
| 295 | D3×C8 | — | 12 | 2 | no | — |
| 296 | C22×C32 | C2×#41 | 1 | 1 | yes | characteristic |
| 297 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 298 | C2×C3⋊D3 | #121 | 1 | 1 | yes | characteristic |
| 299 | C2×C3⋊D3 | #121 | 1 | 1 | yes | characteristic |
| 300 | C2×C3×D3 | — | 2 | 2 | no | — |
| 301 | C2×C3×D3 | — | 4 | 2 | no | — |
| 302 | C2×C3×D3 | — | 8 | 2 | no | — |
| 303 | D32 | — | 4 | 2 | no | — |
| 304 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 305 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 306 | C3⋊Dic3 | #121 | 1 | 1 | yes | characteristic |
| 307 | C3⋊Dic3 | #121 | 1 | 1 | yes | characteristic |
| 308 | C3×Dic3 | — | 2 | 2 | no | — |
| 309 | C3×Dic3 | — | 4 | 2 | no | — |
| 310 | C2×#41 | — | 9 | 2 | no | — |
| 311 | C2×#41 | — | 9 | 1 | no | — |
| 312 | #137 | — | 3 | 2 | no | — |
| 313 | #137 | — | 9 | 2 | no | — |
| 314 | #137 | — | 18 | 2 | no | — |
| 315 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 316 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 317 | AGL(1,ℤ/8) | — | 18 | 2 | no | — |
| 318 | #135 | — | 18 | 1 | no | — |
| 319 | #135 | — | 18 | 1 | no | — |
| 320 | #135 | — | 18 | 1 | no | — |
| 321 | #135 | — | 18 | 1 | no | — |
| 322 | #135 | — | 18 | 2 | no | — |
| 323 | #135 | — | 18 | 2 | no | — |
| 324 | C2×Q16 | — | 9 | 1 | no | — |
| 325 | C2×SD16 | — | 3 | 2 | no | — |
| 326 | C2×D8 | — | 9 | 1 | no | — |
| 327 | #131 | — | 3 | 2 | no | — |
| 328 | #131 | — | 9 | 2 | no | — |
| 329 | #131 | — | 18 | 1 | no | — |
| 330 | #131 | — | 18 | 1 | no | — |
| 331 | C2×M16 | — | 9 | 1 | no | — |
| 332 | C2×M16 | — | 9 | 2 | no | — |
| 333 | C2×M16 | — | 18 | 1 | no | — |
| 334 | C22×C8 | — | 9 | 1 | no | — |
| 335 | C22×C8 | — | 18 | 1 | no | — |
| 336 | #108 | — | 9 | 2 | no | — |
| 337 | #108 | — | 9 | 1 | no | — |
| 338 | #108 | D32 | 1 | 1 | yes | characteristic, complemented |
| 339 | #101 | — | 3 | 2 | no | — |
| 340 | #101 | — | 9 | 2 | no | — |
| 341 | #100 | — | 3 | 2 | no | — |
| 342 | #100 | — | 9 | 2 | no | — |
| 343 | C23×C3 | — | 6 | 2 | no | — |
| 344 | C22×D3 | — | 2 | 2 | no | — |
| 345 | C22×D3 | — | 3 | 2 | no | — |
| 346 | C22×D3 | — | 6 | 1 | no | — |
| 347 | C22×D3 | — | 6 | 2 | no | — |
| 348 | C3×Q8 | — | 3 | 2 | no | — |
| 349 | C3×Q8 | — | 6 | 2 | no | — |
| 350 | C3×Q8 | — | 6 | 2 | no | — |
| 351 | C3×D4 | — | 3 | 2 | no | — |
| 352 | C3×D4 | — | 6 | 2 | no | — |
| 353 | C3×D4 | — | 6 | 2 | no | — |
| 354 | C3×D4 | — | 6 | 2 | no | — |
| 355 | C2×C3×C4 | — | 2 | 1 | no | — |
| 356 | C2×C3×C4 | — | 6 | 2 | no | — |
| 357 | C2×C3×C4 | — | 6 | 2 | no | — |
| 358 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 359 | #67 | — | 2 | 2 | no | — |
| 360 | #67 | — | 6 | 2 | no | — |
| 361 | #67 | — | 6 | 2 | no | — |
| 362 | #67 | — | 12 | 2 | no | — |
| 363 | #67 | — | 12 | 2 | no | — |
| 364 | C2×Dic3 | — | 2 | 2 | no | — |
| 365 | C2×Dic3 | — | 3 | 2 | no | — |
| 366 | C2×Dic3 | — | 6 | 1 | no | — |
| 367 | C2×Dic3 | — | 6 | 2 | no | — |
| 368 | C2×Dic3 | — | 12 | 2 | no | — |
| 369 | C2×Dic3 | — | 12 | 2 | no | — |
| 370 | D12 | — | 2 | 2 | no | — |
| 371 | D12 | — | 2 | 2 | no | — |
| 372 | D12 | — | 6 | 2 | no | — |
| 373 | D12 | — | 12 | 2 | no | — |
| 374 | D12 | — | 12 | 2 | no | — |
| 375 | D12 | D3×D4 | 1 | 2 | yes | — |
| 376 | C4×D3 | — | 2 | 2 | no | — |
| 377 | C4×D3 | — | 3 | 2 | no | — |
| 378 | C4×D3 | — | 3 | 2 | no | — |
| 379 | C4×D3 | — | 3 | 2 | no | — |
| 380 | C4×D3 | — | 3 | 2 | no | — |
| 381 | C4×D3 | — | 6 | 1 | no | — |
| 382 | C4×D3 | — | 6 | 1 | no | — |
| 383 | C4×D3 | — | 6 | 1 | no | — |
| 384 | C4×D3 | — | 6 | 1 | no | — |
| 385 | C4×D3 | — | 6 | 2 | no | — |
| 386 | C4×D3 | — | 6 | 2 | no | — |
| 387 | C4×D3 | — | 12 | 2 | no | — |
| 388 | C4×D3 | — | 12 | 2 | no | — |
| 389 | Dic6 | — | 2 | 2 | no | — |
| 390 | Dic6 | — | 2 | 2 | no | — |
| 391 | Dic6 | — | 6 | 2 | no | — |
| 392 | Dic6 | D3×D4 | 1 | 2 | yes | — |
| 393 | C3×C8 | — | 2 | 2 | no | — |
| 394 | C3×C8 | — | 2 | 2 | no | — |
| 395 | C3×C8 | — | 2 | 1 | no | — |
| 396 | C3×C8 | — | 2 | 1 | no | — |
| 397 | C3×C8 | — | 4 | 2 | no | — |
| 398 | C3×C8 | — | 6 | 2 | no | — |
| 399 | C3×C8 | D3×D4 | 1 | 2 | yes | — |
| 400 | C3×C8 | D3×D4 | 1 | 2 | yes | — |
| 401 | C3⋊C8 | — | 2 | 2 | no | — |
| 402 | C3⋊C8 | — | 3 | 2 | no | — |
| 403 | C3⋊C8 | — | 3 | 2 | no | — |
| 404 | C3⋊C8 | — | 6 | 1 | no | — |
| 405 | C3⋊C8 | — | 6 | 1 | no | — |
| 406 | C3⋊C8 | — | 6 | 2 | no | — |
| 407 | C3⋊C8 | — | 6 | 2 | no | — |
| 408 | C3⋊C8 | — | 12 | 2 | no | — |
| 409 | C2×C32 | — | 2 | 1 | no | — |
| 410 | C2×C32 | C2×#121 | 1 | 1 | yes | characteristic |
| 411 | C3⋊D3 | — | 2 | 1 | no | — |
| 412 | C3⋊D3 | — | 2 | 1 | no | — |
| 413 | C3×D3 | — | 4 | 2 | no | — |
| 414 | C3×D3 | — | 8 | 2 | no | — |
| 415 | #41 | — | 3 | 2 | no | — |
| 416 | #41 | — | 9 | 2 | no | — |
| 417 | #41 | — | 18 | 1 | no | — |
| 418 | #41 | — | 18 | 1 | no | — |
| 419 | #41 | — | 18 | 2 | no | — |
| 420 | #41 | — | 18 | 2 | no | — |
| 421 | #41 | — | 18 | 2 | no | — |
| 422 | #41 | — | 18 | 2 | no | — |
| 423 | C2×Q8 | — | 3 | 2 | no | — |
| 424 | C2×Q8 | — | 9 | 1 | no | — |
| 425 | C2×D4 | — | 3 | 2 | no | — |
| 426 | C2×D4 | — | 9 | 1 | no | — |
| 427 | C2×D4 | — | 18 | 2 | no | — |
| 428 | C2×D4 | — | 18 | 1 | no | — |
| 429 | C22×C4 | — | 9 | 1 | no | — |
| 430 | C22×C4 | — | 18 | 1 | no | — |
| 431 | C22×C4 | — | 18 | 2 | no | — |
| 432 | Q16 | — | 6 | 2 | no | — |
| 433 | Q16 | — | 18 | 1 | no | — |
| 434 | Q16 | — | 18 | 1 | no | — |
| 435 | Q16 | — | 18 | 2 | no | — |
| 436 | SD16 | — | 6 | 2 | no | — |
| 437 | SD16 | — | 6 | 2 | no | — |
| 438 | SD16 | — | 6 | 2 | no | — |
| 439 | SD16 | — | 6 | 2 | no | — |
| 440 | SD16 | — | 18 | 2 | no | — |
| 441 | SD16 | — | 18 | 2 | no | — |
| 442 | D8 | — | 6 | 2 | no | — |
| 443 | D8 | — | 18 | 1 | no | — |
| 444 | D8 | — | 18 | 1 | no | — |
| 445 | D8 | — | 18 | 2 | no | — |
| 446 | M16 | — | 3 | 2 | no | — |
| 447 | M16 | — | 6 | 2 | no | — |
| 448 | M16 | — | 9 | 2 | no | — |
| 449 | M16 | — | 18 | 2 | no | — |
| 450 | M16 | — | 18 | 1 | no | — |
| 451 | M16 | — | 18 | 2 | no | — |
| 452 | M16 | C2×D32 | 1 | 2 | yes | — |
| 453 | C2×C8 | — | 6 | 2 | no | — |
| 454 | C2×C8 | — | 9 | 1 | no | — |
| 455 | C2×C8 | — | 9 | 1 | no | — |
| 456 | C2×C8 | — | 9 | 1 | no | — |
| 457 | C2×C8 | — | 9 | 1 | no | — |
| 458 | C2×C8 | — | 9 | 1 | no | — |
| 459 | C2×C8 | — | 18 | 2 | no | — |
| 460 | C2×C8 | — | 18 | 1 | no | — |
| 461 | C2×C8 | — | 18 | 2 | no | — |
| 462 | C2×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 463 | C22×C3 | — | 2 | 1 | no | — |
| 464 | C22×C3 | — | 6 | 2 | no | — |
| 465 | C22×C3 | — | 12 | 2 | no | — |
| 466 | C22×C3 | — | 24 | 2 | no | — |
| 467 | C22×C3 | D3×#41 | 1 | 2 | yes | — |
| 468 | C2×D3 | — | 2 | 2 | no | — |
| 469 | C2×D3 | — | 3 | 2 | no | — |
| 470 | C2×D3 | — | 3 | 2 | no | — |
| 471 | C2×D3 | — | 4 | 2 | no | — |
| 472 | C2×D3 | — | 6 | 1 | no | — |
| 473 | C2×D3 | — | 6 | 1 | no | — |
| 474 | C2×D3 | — | 8 | 2 | no | — |
| 475 | C2×D3 | — | 12 | 4 | no | — |
| 476 | C2×D3 | — | 12 | 2 | no | — |
| 477 | C2×D3 | — | 12 | 2 | no | — |
| 478 | C3×C4 | — | 2 | 1 | no | — |
| 479 | C3×C4 | — | 2 | 1 | no | — |
| 480 | C3×C4 | — | 6 | 2 | no | — |
| 481 | C3×C4 | — | 12 | 2 | no | — |
| 482 | C3×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 483 | C3×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 484 | Dic3 | — | 2 | 2 | no | — |
| 485 | Dic3 | — | 3 | 2 | no | — |
| 486 | Dic3 | — | 3 | 2 | no | — |
| 487 | Dic3 | — | 4 | 2 | no | — |
| 488 | Dic3 | — | 6 | 1 | no | — |
| 489 | Dic3 | — | 6 | 1 | no | — |
| 490 | C32 | #3067 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 491 | C23 | — | 6 | 2 | no | — |
| 492 | C23 | — | 9 | 1 | no | — |
| 493 | C23 | — | 18 | 1 | no | — |
| 494 | Q8 | — | 3 | 2 | no | — |
| 495 | Q8 | — | 6 | 2 | no | — |
| 496 | Q8 | — | 6 | 2 | no | — |
| 497 | Q8 | — | 18 | 1 | no | — |
| 498 | D4 | — | 3 | 2 | no | — |
| 499 | D4 | — | 6 | 2 | no | — |
| 500 | D4 | — | 6 | 2 | no | — |
| 501 | D4 | — | 6 | 2 | no | — |
| 502 | D4 | — | 18 | 2 | no | — |
| 503 | D4 | — | 18 | 1 | no | — |
| 504 | D4 | — | 36 | 2 | no | — |
| 505 | D4 | — | 36 | 2 | no | — |
| 506 | C2×C4 | — | 6 | 2 | no | — |
| 507 | C2×C4 | — | 6 | 2 | no | — |
| 508 | C2×C4 | — | 9 | 1 | no | — |
| 509 | C2×C4 | — | 9 | 1 | no | — |
| 510 | C2×C4 | — | 9 | 1 | no | — |
| 511 | C2×C4 | — | 9 | 1 | no | — |
| 512 | C2×C4 | — | 9 | 1 | no | — |
| 513 | C2×C4 | — | 18 | 1 | no | — |
| 514 | C2×C4 | — | 18 | 2 | no | — |
| 515 | C2×C4 | — | 36 | 2 | no | — |
| 516 | C2×C4 | — | 36 | 2 | no | — |
| 517 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 518 | C8 | — | 2 | 2 | no | — |
| 519 | C8 | — | 6 | 2 | no | — |
| 520 | C8 | — | 9 | 1 | no | — |
| 521 | C8 | — | 9 | 1 | no | — |
| 522 | C8 | — | 18 | 2 | no | — |
| 523 | C8 | #3802 | 1 | 1 | yes | characteristic |
| 524 | C8 | #3802 | 1 | 1 | yes | characteristic |
| 525 | C2×C3 | — | 2 | 2 | no | — |
| 526 | C2×C3 | — | 2 | 1 | no | — |
| 527 | C2×C3 | — | 4 | 1 | no | — |
| 528 | C2×C3 | — | 12 | 2 | no | — |
| 529 | C2×C3 | — | 24 | 2 | no | — |
| 530 | C2×C3 | D3×#121 | 1 | 2 | yes | — |
| 531 | D3 | — | 4 | 2 | no | — |
| 532 | D3 | — | 6 | 2 | no | — |
| 533 | D3 | — | 6 | 2 | no | — |
| 534 | D3 | — | 6 | 2 | no | — |
| 535 | D3 | — | 8 | 2 | no | — |
| 536 | D3 | — | 12 | 1 | no | — |
| 537 | C22 | — | 6 | 2 | no | — |
| 538 | C22 | — | 9 | 1 | no | — |
| 539 | C22 | — | 9 | 1 | no | — |
| 540 | C22 | — | 12 | 2 | no | — |
| 541 | C22 | — | 24 | 2 | no | — |
| 542 | C22 | — | 36 | 1 | no | — |
| 543 | C22 | — | 36 | 2 | no | — |
| 544 | C22 | #64319 | 1 | 1 | yes | characteristic |
| 545 | C4 | — | 6 | 2 | no | — |
| 546 | C4 | — | 9 | 1 | no | — |
| 547 | C4 | — | 9 | 1 | no | — |
| 548 | C4 | — | 12 | 2 | no | — |
| 549 | C4 | C2×#3802 | 1 | 1 | yes | characteristic |
| 550 | C4 | D32×D4 | 1 | 1 | yes | characteristic |
| 551 | C3 | — | 2 | 1 | no | — |
| 552 | C3 | #80929 | 1 | 2 | yes | complemented |
| 553 | C2 | — | 2 | 1 | no | — |
| 554 | C2 | — | 12 | 2 | no | — |
| 555 | C2 | — | 18 | 1 | no | — |
| 556 | C2 | — | 18 | 1 | no | — |
| 557 | C2 | — | 24 | 2 | no | — |
| 558 | C2 | #10594612 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10594718 | C2 | semidirect |
| 2. C2×#63809 | C2 | semidirect |
| 3. #10594669 | C2 | semidirect |
| 4. C3⋊D3×#108 | C2 | semidirect |
| 5. C3×#4898 | C2 | semidirect |
| 6. #10591010 | C2 | semidirect |
| 7. #10590982 | C2 | semidirect |
| 8. #10590981 | C2 | semidirect |
| 9. #10590925 | C2 | semidirect |
| 17. C2×C3×#204 | C22 | semidirect |
| 19. C2×#3718 | C22 | semidirect |
| 22. C2×#3713 | C22 | semidirect |
| 37. C32×#108 | C22 | semidirect |
| 38. #63649 | C22 | semidirect |
| 39. #63646 | C22 | semidirect |
| 40. C3×#824 | C22 | semidirect |
| 41. C3×#823 | C22 | semidirect |
| 42. #63560 | C22 | semidirect |
| 43. #63558 | C22 | semidirect |
| 53. #4898 | D3 | semidirect |
| 144. C2×#204 | C2×D3 | semidirect |
| 151. C3×#108 | C2×D3 | semidirect |
| 157. #824 | C2×D3 | semidirect |
| 159. #823 | C2×D3 | semidirect |
| 338. #108 | D32 | semidirect |
| 490. C32 | #3067 | semidirect |
| 552. C3 | #80929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10594718 | 2 |
| C2×#63809 | 2 |
| #10594669 | 2 |
| C3⋊D3×#108 | 2 |
| C3×#4898 | 2 |
| #10591010 | 2 |
| #10590982 | 2 |
| #10590981 | 2 |
| #10590925 | 2 |
| #80929 | 3 |