Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1644 conjugacy classes of subgroups.
The subgroup lattice has 501 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10596756 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C32×#416 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10592935 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10592812 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10592809 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10592705 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10592704 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #70295 | — | 3 | 4 | no | maximal |
| 9 | C2×C32×#41 | C22 | 1 | 1 | yes | characteristic |
| 10 | #64367 | — | 2 | 1 | no | — |
| 11 | #64367 | C4 | 1 | 2 | yes | complemented |
| 12 | #64366 | — | 2 | 1 | no | — |
| 13 | #64366 | C4 | 1 | 2 | yes | complemented |
| 14 | #41×C3⋊D3 | — | 2 | 2 | no | — |
| 15 | #41×C3⋊D3 | — | 2 | 2 | no | — |
| 16 | #64364 | — | 2 | 1 | no | — |
| 17 | #64361 | — | 2 | 1 | no | — |
| 18 | #64361 | — | 2 | 2 | no | — |
| 19 | C2×#3828 | — | 2 | 2 | no | — |
| 20 | C2×#3828 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#3828 | C22 | 1 | 1 | yes | characteristic |
| 22 | C22×C32×C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C32×#117 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #64135 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C2×#3748 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C32×#103 | — | 2 | 1 | no | — |
| 27 | C32×#102 | — | 2 | 1 | no | — |
| 28 | #63664 | — | 2 | 2 | no | — |
| 29 | #63648 | — | 2 | 1 | no | — |
| 30 | #63647 | — | 2 | 2 | no | — |
| 31 | #63643 | — | 2 | 1 | no | — |
| 32 | #63633 | — | 2 | 2 | no | — |
| 33 | #63632 | — | 2 | 2 | no | — |
| 34 | #5964 | — | 3 | 4 | no | — |
| 35 | C3×#416 | D3 | 1 | 4 | yes | complemented |
| 36 | #5236 | — | 3 | 4 | no | — |
| 37 | #5113 | — | 3 | 4 | no | — |
| 38 | #5110 | — | 3 | 4 | no | — |
| 39 | #5006 | — | 3 | 4 | no | — |
| 40 | #5005 | — | 3 | 4 | no | — |
| 41 | C32×#41 | — | 2 | 1 | no | — |
| 42 | C32×#41 | — | 2 | 1 | no | — |
| 43 | C32×#41 | C2×C4 | 1 | 2 | yes | — |
| 44 | C32×#41 | D4 | 1 | 2 | yes | — |
| 45 | C2×C32×Q8 | D4 | 1 | 1 | yes | characteristic |
| 46 | C2×C32×D4 | — | 2 | 1 | no | — |
| 47 | C2×C32×D4 | D4 | 1 | 1 | yes | characteristic |
| 48 | C22×C32×C4 | — | 2 | 1 | no | — |
| 49 | C22×C32×C4 | C23 | 1 | 1 | yes | characteristic |
| 50 | C2×#638 | — | 2 | 4 | no | — |
| 51 | C2×#638 | — | 2 | 1 | no | — |
| 52 | C2×#638 | D4 | 1 | 2 | yes | — |
| 53 | #3832 | — | 2 | 2 | no | — |
| 54 | #3832 | — | 2 | 2 | no | — |
| 55 | Q8×C3⋊D3 | — | 2 | 2 | no | — |
| 56 | Q8×C3⋊D3 | — | 2 | 2 | no | — |
| 57 | #3830 | — | 2 | 4 | no | — |
| 58 | #3830 | — | 2 | 2 | no | — |
| 59 | #3830 | — | 2 | 2 | no | — |
| 60 | #3830 | — | 2 | 4 | no | — |
| 61 | D4×C3⋊D3 | — | 2 | 4 | no | — |
| 62 | D4×C3⋊D3 | — | 2 | 2 | no | — |
| 63 | D4×C3⋊D3 | — | 2 | 4 | no | — |
| 64 | D4×C3⋊D3 | — | 2 | 2 | no | — |
| 65 | #3828 | — | 2 | 4 | no | — |
| 66 | #3828 | — | 2 | 4 | no | — |
| 67 | #3828 | — | 2 | 1 | no | — |
| 68 | #3828 | — | 2 | 1 | no | — |
| 69 | #3828 | — | 2 | 1 | no | — |
| 70 | #3828 | — | 2 | 1 | no | — |
| 71 | #3828 | — | 2 | 1 | no | — |
| 72 | #3828 | — | 2 | 1 | no | — |
| 73 | #3828 | — | 2 | 2 | no | — |
| 74 | #3828 | — | 2 | 2 | no | — |
| 75 | #3828 | C2×C4 | 1 | 2 | yes | — |
| 76 | #3828 | D4 | 1 | 2 | yes | — |
| 77 | C2×C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 78 | C2×C4⋊(C3⋊D3) | C2×C4 | 1 | 1 | yes | characteristic |
| 79 | C2×C4⋊(C3⋊D3) | D4 | 1 | 1 | yes | characteristic |
| 80 | C2×C4×C3⋊D3 | — | 2 | 4 | no | — |
| 81 | C2×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 82 | C2×C4×C3⋊D3 | D4 | 1 | 2 | yes | — |
| 83 | C2×#634 | — | 2 | 2 | no | — |
| 84 | C2×#634 | C2×C4 | 1 | 1 | yes | characteristic |
| 85 | C2×#634 | D4 | 1 | 1 | yes | characteristic |
| 86 | C2×C32×C8 | — | 2 | 1 | no | — |
| 87 | C2×C32×C8 | — | 2 | 1 | no | — |
| 88 | C2×C32×C8 | — | 2 | 1 | no | — |
| 89 | C32×C4⋊C4 | — | 2 | 1 | no | — |
| 90 | C32×C22⋊C4 | — | 2 | 1 | no | — |
| 91 | C32×C42 | — | 2 | 1 | no | — |
| 92 | #3757 | — | 2 | 1 | no | — |
| 93 | C4⋊(C3⋊Dic3) | — | 2 | 1 | no | — |
| 94 | C4×C3⋊Dic3 | — | 2 | 1 | no | — |
| 95 | #3748 | — | 2 | 1 | no | — |
| 96 | #3748 | — | 2 | 1 | no | — |
| 97 | C2×C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 98 | #1794 | — | 9 | 1 | no | Sylow |
| 99 | C2×C3×#41 | C2×D3 | 1 | 4 | yes | — |
| 100 | #1010 | — | 3 | 8 | no | — |
| 101 | #1010 | — | 6 | 4 | no | — |
| 102 | #1009 | — | 3 | 8 | no | — |
| 103 | #1009 | — | 6 | 4 | no | — |
| 104 | D3×#41 | — | 6 | 8 | no | — |
| 105 | D3×#41 | — | 6 | 8 | no | — |
| 106 | #1007 | — | 6 | 4 | no | — |
| 107 | #1004 | — | 6 | 8 | no | — |
| 108 | #1004 | — | 6 | 4 | no | — |
| 109 | C2×#235 | — | 3 | 4 | no | — |
| 110 | C2×#235 | — | 3 | 4 | no | — |
| 111 | C2×#235 | — | 6 | 8 | no | — |
| 112 | C22×C3×C8 | C2×D3 | 1 | 4 | yes | complemented |
| 113 | C3×#117 | C2×D3 | 1 | 4 | yes | complemented |
| 114 | #926 | — | 3 | 4 | no | — |
| 115 | C2×#208 | — | 3 | 4 | no | — |
| 116 | C3×#103 | — | 2 | 4 | no | — |
| 117 | C3×#102 | — | 2 | 4 | no | — |
| 118 | #837 | — | 6 | 8 | no | — |
| 119 | #821 | — | 6 | 4 | no | — |
| 120 | (C2×D3)⋊C8 | — | 6 | 8 | no | — |
| 121 | #816 | — | 6 | 4 | no | — |
| 122 | #806 | — | 6 | 8 | no | — |
| 123 | #805 | — | 6 | 8 | no | — |
| 124 | C23×C32 | — | 2 | 1 | no | — |
| 125 | C23×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 126 | C22×C3⋊D3 | — | 2 | 4 | no | — |
| 127 | C22×C3⋊D3 | — | 2 | 1 | no | — |
| 128 | C22×C3⋊D3 | C22⋊C4 | 1 | 2 | yes | — |
| 129 | C32×Q8 | — | 2 | 1 | no | — |
| 130 | C32×Q8 | C22⋊C4 | 1 | 2 | yes | — |
| 131 | C32×D4 | — | 2 | 2 | no | — |
| 132 | C32×D4 | — | 2 | 2 | no | — |
| 133 | C32×D4 | — | 2 | 1 | no | — |
| 134 | C32×D4 | C22⋊C4 | 1 | 2 | yes | — |
| 135 | C2×C32×C4 | — | 2 | 1 | no | — |
| 136 | C2×C32×C4 | — | 2 | 2 | no | — |
| 137 | C2×C32×C4 | — | 2 | 2 | no | — |
| 138 | C2×C32×C4 | — | 4 | 1 | no | — |
| 139 | C2×C32×C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 140 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 142 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 143 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 144 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | #638 | — | 2 | 4 | no | — |
| 146 | #638 | — | 2 | 4 | no | — |
| 147 | #638 | — | 2 | 2 | no | — |
| 148 | #638 | — | 2 | 2 | no | — |
| 149 | #638 | — | 2 | 2 | no | — |
| 150 | #638 | — | 2 | 2 | no | — |
| 151 | C2×C3⋊Dic3 | — | 2 | 4 | no | — |
| 152 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 153 | C2×C3⋊Dic3 | — | 4 | 1 | no | — |
| 154 | C2×C3⋊Dic3 | C22⋊C4 | 1 | 2 | yes | — |
| 155 | C4⋊(C3⋊D3) | — | 2 | 4 | no | — |
| 156 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 157 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 158 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 159 | C4⋊(C3⋊D3) | C22⋊C4 | 1 | 2 | yes | — |
| 160 | C4×C3⋊D3 | — | 2 | 4 | no | — |
| 161 | C4×C3⋊D3 | — | 2 | 4 | no | — |
| 162 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 163 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 164 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 165 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 166 | #634 | — | 2 | 4 | no | — |
| 167 | #634 | — | 2 | 1 | no | — |
| 168 | #634 | — | 2 | 1 | no | — |
| 169 | #634 | — | 2 | 1 | no | — |
| 170 | #634 | C22⋊C4 | 1 | 2 | yes | — |
| 171 | C32×C8 | — | 4 | 1 | no | — |
| 172 | C3⋊(C3⋊C8) | — | 4 | 1 | no | — |
| 173 | #585 | — | 9 | 1 | no | — |
| 174 | #421 | — | 9 | 1 | no | — |
| 175 | #421 | — | 9 | 1 | no | — |
| 176 | #416 | — | 9 | 1 | no | — |
| 177 | #416 | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 178 | #410 | — | 9 | 1 | no | — |
| 179 | #408 | — | 9 | 1 | no | — |
| 180 | C3×#41 | — | 2 | 4 | no | — |
| 181 | C3×#41 | — | 2 | 4 | no | — |
| 182 | C3×#41 | C4×D3 | 1 | 8 | yes | — |
| 183 | C3×#41 | D12 | 1 | 8 | yes | — |
| 184 | C2×C3×Q8 | #67 | 1 | 4 | yes | — |
| 185 | C2×C3×D4 | — | 2 | 4 | no | — |
| 186 | C2×C3×D4 | #67 | 1 | 4 | yes | — |
| 187 | C22×C3×C4 | — | 2 | 4 | no | — |
| 188 | C22×C3×C4 | C22×D3 | 1 | 4 | yes | — |
| 189 | C2×#67 | — | 3 | 8 | no | — |
| 190 | C2×#67 | — | 6 | 16 | no | — |
| 191 | C2×#67 | — | 6 | 4 | no | — |
| 192 | #239 | — | 6 | 8 | no | — |
| 193 | #239 | — | 6 | 8 | no | — |
| 194 | D3×Q8 | — | 6 | 8 | no | — |
| 195 | D3×Q8 | — | 6 | 8 | no | — |
| 196 | #237 | — | 6 | 16 | no | — |
| 197 | #237 | — | 6 | 16 | no | — |
| 198 | #237 | — | 6 | 8 | no | — |
| 199 | #237 | — | 6 | 8 | no | — |
| 200 | D3×D4 | — | 6 | 16 | no | — |
| 201 | D3×D4 | — | 6 | 16 | no | — |
| 202 | D3×D4 | — | 6 | 8 | no | — |
| 203 | D3×D4 | — | 6 | 8 | no | — |
| 204 | #235 | — | 3 | 8 | no | — |
| 205 | #235 | — | 3 | 8 | no | — |
| 206 | #235 | — | 6 | 8 | no | — |
| 207 | #235 | — | 6 | 8 | no | — |
| 208 | #235 | — | 6 | 16 | no | — |
| 209 | #235 | — | 6 | 16 | no | — |
| 210 | #235 | — | 6 | 4 | no | — |
| 211 | #235 | — | 6 | 4 | no | — |
| 212 | #235 | — | 6 | 4 | no | — |
| 213 | #235 | — | 6 | 4 | no | — |
| 214 | #235 | — | 6 | 4 | no | — |
| 215 | #235 | — | 6 | 4 | no | — |
| 216 | C2×D12 | — | 3 | 4 | no | — |
| 217 | C2×D12 | — | 3 | 4 | no | — |
| 218 | C2×D12 | — | 6 | 8 | no | — |
| 219 | C2×C4×D3 | — | 3 | 8 | no | — |
| 220 | C2×C4×D3 | — | 6 | 16 | no | — |
| 221 | C2×C4×D3 | — | 6 | 4 | no | — |
| 222 | C2×Dic6 | — | 3 | 4 | no | — |
| 223 | C2×Dic6 | — | 3 | 4 | no | — |
| 224 | C2×Dic6 | — | 6 | 8 | no | — |
| 225 | C2×C3×C8 | — | 2 | 4 | no | — |
| 226 | C2×C3×C8 | — | 2 | 4 | no | — |
| 227 | C2×C3×C8 | — | 2 | 4 | no | — |
| 228 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 229 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 230 | C3×C42 | — | 2 | 4 | no | — |
| 231 | #217 | — | 6 | 4 | no | — |
| 232 | C4⋊Dic3 | — | 6 | 4 | no | — |
| 233 | C4×Dic3 | — | 6 | 4 | no | — |
| 234 | #208 | — | 6 | 4 | no | — |
| 235 | #208 | — | 6 | 4 | no | — |
| 236 | C2×C3⋊C8 | — | 6 | 4 | no | — |
| 237 | C22×C32 | — | 2 | 2 | no | — |
| 238 | C22×C32 | — | 4 | 1 | no | — |
| 239 | C22×C32 | — | 8 | 1 | no | — |
| 240 | C22×C32 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 241 | C22×C32 | #120 | 1 | 1 | yes | characteristic |
| 242 | C22×C32 | #120 | 1 | 1 | yes | characteristic |
| 243 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 244 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 245 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 246 | C2×C3⋊D3 | — | 8 | 1 | no | — |
| 247 | C2×C3⋊D3 | — | 8 | 4 | no | — |
| 248 | C32×C4 | — | 2 | 2 | no | — |
| 249 | C32×C4 | — | 8 | 1 | no | — |
| 250 | C32×C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 251 | C32×C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 252 | C32×C4 | #120 | 1 | 1 | yes | characteristic |
| 253 | C32×C4 | #120 | 1 | 1 | yes | characteristic |
| 254 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 255 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 256 | C3⋊Dic3 | — | 8 | 1 | no | — |
| 257 | 2−1+4 | — | 9 | 2 | no | — |
| 258 | 2−1+4 | — | 18 | 1 | no | — |
| 259 | 2−1+4 | — | 18 | 1 | no | — |
| 260 | H(5,𝔽2) | — | 9 | 2 | no | — |
| 261 | H(5,𝔽2) | — | 18 | 2 | no | — |
| 262 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 263 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 264 | C2×#41 | — | 9 | 1 | no | — |
| 265 | C2×#41 | — | 9 | 1 | no | — |
| 266 | C2×#41 | — | 18 | 2 | no | — |
| 267 | C2×#41 | — | 18 | 2 | no | — |
| 268 | C2×#41 | — | 18 | 2 | no | — |
| 269 | C2×#41 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 270 | C2×M16 | — | 9 | 1 | no | — |
| 271 | C22×C8 | C2×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 272 | #117 | — | 9 | 1 | no | — |
| 273 | #117 | C2×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 274 | #104 | — | 18 | 2 | no | — |
| 275 | #104 | — | 18 | 2 | no | — |
| 276 | #103 | — | 2 | 1 | no | — |
| 277 | #103 | — | 18 | 1 | no | — |
| 278 | #102 | — | 2 | 1 | no | — |
| 279 | #102 | — | 18 | 1 | no | — |
| 280 | #99 | — | 18 | 2 | no | — |
| 281 | C22⋊C8 | — | 18 | 2 | no | — |
| 282 | C23×C3 | — | 2 | 4 | no | — |
| 283 | C23×C3 | D3×D4 | 1 | 4 | yes | — |
| 284 | C22×D3 | — | 3 | 8 | no | — |
| 285 | C22×D3 | — | 6 | 16 | no | — |
| 286 | C22×D3 | — | 6 | 4 | no | — |
| 287 | C3×Q8 | — | 2 | 4 | no | — |
| 288 | C3×Q8 | (C2×D3)⋊C4 | 1 | 8 | yes | — |
| 289 | C3×D4 | — | 2 | 8 | no | — |
| 290 | C3×D4 | — | 2 | 8 | no | — |
| 291 | C3×D4 | — | 2 | 4 | no | — |
| 292 | C3×D4 | (C2×D3)⋊C4 | 1 | 8 | yes | — |
| 293 | C2×C3×C4 | — | 2 | 4 | no | — |
| 294 | C2×C3×C4 | — | 2 | 8 | no | — |
| 295 | C2×C3×C4 | — | 2 | 8 | no | — |
| 296 | C2×C3×C4 | — | 4 | 4 | no | — |
| 297 | C2×C3×C4 | C2×C4×D3 | 1 | 4 | yes | — |
| 298 | C2×C3×C4 | C2×D12 | 1 | 4 | yes | — |
| 299 | C2×C3×C4 | D3×D4 | 1 | 4 | yes | — |
| 300 | C2×C3×C4 | D3×D4 | 1 | 4 | yes | — |
| 301 | C2×C3×C4 | D3×D4 | 1 | 4 | yes | — |
| 302 | C2×C3×C4 | C2×#67 | 1 | 4 | yes | — |
| 303 | #67 | — | 6 | 16 | no | — |
| 304 | #67 | — | 6 | 16 | no | — |
| 305 | #67 | — | 6 | 8 | no | — |
| 306 | #67 | — | 6 | 8 | no | — |
| 307 | #67 | — | 6 | 8 | no | — |
| 308 | #67 | — | 6 | 8 | no | — |
| 309 | C2×Dic3 | — | 3 | 8 | no | — |
| 310 | C2×Dic3 | — | 6 | 16 | no | — |
| 311 | C2×Dic3 | — | 6 | 4 | no | — |
| 312 | C2×Dic3 | — | 12 | 4 | no | — |
| 313 | D12 | — | 3 | 8 | no | — |
| 314 | D12 | — | 6 | 16 | no | — |
| 315 | D12 | — | 6 | 4 | no | — |
| 316 | D12 | — | 6 | 4 | no | — |
| 317 | D12 | — | 6 | 4 | no | — |
| 318 | C4×D3 | — | 6 | 16 | no | — |
| 319 | C4×D3 | — | 6 | 16 | no | — |
| 320 | C4×D3 | — | 6 | 8 | no | — |
| 321 | C4×D3 | — | 6 | 8 | no | — |
| 322 | C4×D3 | — | 6 | 8 | no | — |
| 323 | C4×D3 | — | 6 | 8 | no | — |
| 324 | Dic6 | — | 3 | 8 | no | — |
| 325 | Dic6 | — | 6 | 16 | no | — |
| 326 | Dic6 | — | 6 | 4 | no | — |
| 327 | Dic6 | — | 6 | 4 | no | — |
| 328 | Dic6 | — | 6 | 4 | no | — |
| 329 | C3×C8 | — | 4 | 4 | no | — |
| 330 | C3⋊C8 | — | 12 | 4 | no | — |
| 331 | C2×C32 | — | 2 | 1 | no | — |
| 332 | C2×C32 | — | 2 | 1 | no | — |
| 333 | C2×C32 | — | 2 | 1 | no | — |
| 334 | C2×C32 | — | 4 | 2 | no | — |
| 335 | C2×C32 | #379 | 1 | 1 | yes | characteristic |
| 336 | C3⋊D3 | — | 4 | 2 | no | — |
| 337 | C3⋊D3 | — | 4 | 2 | no | — |
| 338 | #41 | — | 2 | 1 | no | — |
| 339 | #41 | — | 2 | 1 | no | — |
| 340 | #41 | — | 9 | 2 | no | — |
| 341 | #41 | — | 9 | 2 | no | — |
| 342 | #41 | — | 18 | 2 | no | — |
| 343 | #41 | — | 18 | 2 | no | — |
| 344 | #41 | — | 18 | 4 | no | — |
| 345 | #41 | — | 18 | 4 | no | — |
| 346 | #41 | — | 18 | 4 | no | — |
| 347 | #41 | — | 18 | 4 | no | — |
| 348 | #41 | — | 18 | 2 | no | — |
| 349 | #41 | — | 18 | 2 | no | — |
| 350 | #41 | — | 18 | 2 | no | — |
| 351 | #41 | — | 18 | 2 | no | — |
| 352 | #41 | — | 18 | 1 | no | — |
| 353 | #41 | — | 18 | 1 | no | — |
| 354 | #41 | — | 18 | 1 | no | — |
| 355 | #41 | — | 18 | 1 | no | — |
| 356 | #41 | — | 18 | 1 | no | — |
| 357 | #41 | — | 18 | 1 | no | — |
| 358 | #41 | C4×C3⋊D3 | 1 | 2 | yes | — |
| 359 | #41 | C4⋊(C3⋊D3) | 1 | 2 | yes | — |
| 360 | C2×Q8 | — | 9 | 1 | no | — |
| 361 | C2×Q8 | — | 9 | 1 | no | — |
| 362 | C2×Q8 | — | 18 | 2 | no | — |
| 363 | C2×Q8 | — | 18 | 2 | no | — |
| 364 | C2×Q8 | — | 18 | 2 | no | — |
| 365 | C2×Q8 | #638 | 1 | 1 | yes | characteristic |
| 366 | C2×D4 | — | 2 | 1 | no | — |
| 367 | C2×D4 | — | 9 | 2 | no | — |
| 368 | C2×D4 | — | 9 | 1 | no | — |
| 369 | C2×D4 | — | 9 | 1 | no | — |
| 370 | C2×D4 | — | 18 | 2 | no | — |
| 371 | C2×D4 | — | 18 | 4 | no | — |
| 372 | C2×D4 | — | 18 | 4 | no | — |
| 373 | C2×D4 | — | 18 | 2 | no | — |
| 374 | C2×D4 | — | 18 | 4 | no | — |
| 375 | C2×D4 | — | 18 | 1 | no | — |
| 376 | C2×D4 | — | 18 | 2 | no | — |
| 377 | C2×D4 | #638 | 1 | 1 | yes | characteristic |
| 378 | C22×C4 | — | 2 | 1 | no | — |
| 379 | C22×C4 | — | 9 | 2 | no | — |
| 380 | C22×C4 | — | 18 | 4 | no | — |
| 381 | C22×C4 | — | 18 | 1 | no | — |
| 382 | C22×C4 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 383 | M16 | — | 18 | 1 | no | — |
| 384 | M16 | — | 18 | 1 | no | — |
| 385 | C2×C8 | — | 2 | 1 | no | — |
| 386 | C2×C8 | — | 2 | 1 | no | — |
| 387 | C2×C8 | — | 2 | 1 | no | — |
| 388 | C2×C8 | — | 18 | 1 | no | — |
| 389 | C4⋊C4 | — | 2 | 1 | no | — |
| 390 | C4⋊C4 | — | 18 | 1 | no | — |
| 391 | C22⋊C4 | — | 2 | 1 | no | — |
| 392 | C22⋊C4 | — | 18 | 1 | no | — |
| 393 | C42 | — | 2 | 1 | no | — |
| 394 | C42 | — | 18 | 1 | no | — |
| 395 | C22×C3 | — | 2 | 8 | no | — |
| 396 | C22×C3 | — | 4 | 4 | no | — |
| 397 | C22×C3 | — | 8 | 4 | no | — |
| 398 | C22×C3 | D3×C22⋊C4 | 1 | 4 | yes | — |
| 399 | C22×C3 | #882 | 1 | 4 | yes | — |
| 400 | C22×C3 | #937 | 1 | 4 | yes | — |
| 401 | C2×D3 | — | 6 | 8 | no | — |
| 402 | C2×D3 | — | 6 | 8 | no | — |
| 403 | C2×D3 | — | 12 | 8 | no | — |
| 404 | C2×D3 | — | 24 | 4 | no | — |
| 405 | C2×D3 | — | 24 | 16 | no | — |
| 406 | C3×C4 | — | 2 | 8 | no | — |
| 407 | C3×C4 | — | 8 | 4 | no | — |
| 408 | C3×C4 | D3×C22⋊C4 | 1 | 4 | yes | — |
| 409 | C3×C4 | #882 | 1 | 4 | yes | — |
| 410 | C3×C4 | C2×(C2×D3)⋊C4 | 1 | 4 | yes | — |
| 411 | C3×C4 | #937 | 1 | 4 | yes | — |
| 412 | Dic3 | — | 6 | 8 | no | — |
| 413 | Dic3 | — | 6 | 8 | no | — |
| 414 | Dic3 | — | 24 | 4 | no | — |
| 415 | C32 | #1794 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 416 | C23 | — | 2 | 1 | no | — |
| 417 | C23 | — | 9 | 2 | no | — |
| 418 | C23 | — | 18 | 4 | no | — |
| 419 | C23 | — | 18 | 1 | no | — |
| 420 | C23 | D4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 421 | Q8 | — | 2 | 1 | no | — |
| 422 | Q8 | — | 9 | 2 | no | — |
| 423 | Q8 | — | 18 | 4 | no | — |
| 424 | Q8 | — | 18 | 1 | no | — |
| 425 | Q8 | — | 18 | 1 | no | — |
| 426 | Q8 | — | 18 | 1 | no | — |
| 427 | Q8 | #3752 | 1 | 2 | yes | — |
| 428 | D4 | — | 2 | 2 | no | — |
| 429 | D4 | — | 2 | 2 | no | — |
| 430 | D4 | — | 2 | 1 | no | — |
| 431 | D4 | — | 9 | 2 | no | — |
| 432 | D4 | — | 18 | 4 | no | — |
| 433 | D4 | — | 18 | 4 | no | — |
| 434 | D4 | — | 18 | 4 | no | — |
| 435 | D4 | — | 18 | 2 | no | — |
| 436 | D4 | — | 18 | 2 | no | — |
| 437 | D4 | — | 18 | 2 | no | — |
| 438 | D4 | — | 18 | 2 | no | — |
| 439 | D4 | — | 18 | 1 | no | — |
| 440 | D4 | — | 18 | 1 | no | — |
| 441 | D4 | — | 18 | 1 | no | — |
| 442 | D4 | #3752 | 1 | 2 | yes | — |
| 443 | C2×C4 | — | 2 | 1 | no | — |
| 444 | C2×C4 | — | 2 | 2 | no | — |
| 445 | C2×C4 | — | 2 | 2 | no | — |
| 446 | C2×C4 | — | 4 | 1 | no | — |
| 447 | C2×C4 | — | 9 | 2 | no | — |
| 448 | C2×C4 | — | 18 | 4 | no | — |
| 449 | C2×C4 | — | 18 | 4 | no | — |
| 450 | C2×C4 | — | 18 | 4 | no | — |
| 451 | C2×C4 | — | 18 | 1 | no | — |
| 452 | C2×C4 | — | 18 | 2 | no | — |
| 453 | C2×C4 | — | 18 | 2 | no | — |
| 454 | C2×C4 | — | 18 | 2 | no | — |
| 455 | C2×C4 | — | 18 | 2 | no | — |
| 456 | C2×C4 | — | 36 | 1 | no | — |
| 457 | C2×C4 | C2×C4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 458 | C2×C4 | C2×C4⋊(C3⋊D3) | 1 | 1 | yes | characteristic |
| 459 | C2×C4 | D4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 460 | C2×C4 | D4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 461 | C2×C4 | D4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 462 | C2×C4 | C2×#638 | 1 | 1 | yes | characteristic |
| 463 | C8 | — | 4 | 1 | no | — |
| 464 | C8 | — | 36 | 1 | no | — |
| 465 | C2×C3 | — | 2 | 4 | no | — |
| 466 | C2×C3 | — | 2 | 4 | no | — |
| 467 | C2×C3 | — | 2 | 4 | no | — |
| 468 | C2×C3 | — | 4 | 8 | no | — |
| 469 | C2×C3 | #4955 | 1 | 4 | yes | — |
| 470 | D3 | — | 12 | 8 | no | — |
| 471 | D3 | — | 12 | 8 | no | — |
| 472 | C22 | — | 2 | 2 | no | — |
| 473 | C22 | — | 4 | 1 | no | — |
| 474 | C22 | — | 8 | 1 | no | — |
| 475 | C22 | — | 18 | 2 | no | — |
| 476 | C22 | — | 18 | 2 | no | — |
| 477 | C22 | — | 36 | 2 | no | — |
| 478 | C22 | — | 72 | 1 | no | — |
| 479 | C22 | — | 72 | 4 | no | — |
| 480 | C22 | C22⋊C4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 481 | C22 | #64091 | 1 | 1 | yes | characteristic |
| 482 | C22 | #64146 | 1 | 1 | yes | characteristic |
| 483 | C4 | — | 2 | 2 | no | — |
| 484 | C4 | — | 8 | 1 | no | — |
| 485 | C4 | — | 18 | 2 | no | — |
| 486 | C4 | — | 18 | 2 | no | — |
| 487 | C4 | — | 72 | 1 | no | — |
| 488 | C4 | C22⋊C4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 489 | C4 | #64091 | 1 | 1 | yes | characteristic |
| 490 | C4 | C2×#3752 | 1 | 1 | yes | characteristic |
| 491 | C4 | #64146 | 1 | 1 | yes | characteristic |
| 492 | C3 | #70295 | 1 | 4 | yes | complemented |
| 493 | C2 | — | 2 | 1 | no | — |
| 494 | C2 | — | 2 | 1 | no | — |
| 495 | C2 | — | 2 | 1 | no | — |
| 496 | C2 | — | 4 | 2 | no | — |
| 497 | C2 | — | 36 | 2 | no | — |
| 498 | C2 | — | 36 | 2 | no | — |
| 499 | C2 | #10592654 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C32×#416 | C2 | semidirect |
| 3. #10592935 | C2 | semidirect |
| 4. #10592812 | C2 | semidirect |
| 5. #10592809 | C2 | semidirect |
| 6. #10592705 | C2 | semidirect |
| 7. #10592704 | C2 | semidirect |
| 11. #64367 | C4 | semidirect |
| 13. #64366 | C4 | semidirect |
| 22. C22×C32×C8 | C22 | semidirect |
| 23. C32×#117 | C22 | semidirect |
| 24. #64135 | C22 | semidirect |
| 25. C2×#3748 | C22 | semidirect |
| 35. C3×#416 | D3 | semidirect |
| 112. C22×C3×C8 | C2×D3 | semidirect |
| 113. C3×#117 | C2×D3 | semidirect |
| 177. #416 | C3⋊D3 | semidirect |
| 271. C22×C8 | C2×C3⋊D3 | semidirect |
| 273. #117 | C2×C3⋊D3 | semidirect |
| 415. C32 | #1794 | semidirect |
| 492. C3 | #70295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596756 | 2 |
| C32×#416 | 2 |
| #10592935 | 2 |
| #10592812 | 2 |
| #10592809 | 2 |
| #10592705 | 2 |
| #10592704 | 2 |
| #70295 | 3 |