Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
4790 conjugacy classes of subgroups.
The subgroup lattice has 670 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#5964 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#5825 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#5526 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C2×C3×#410 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#5006 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #78692 | C2 | 1 | 16 | yes | maximal, direct product factor |
| 7 | C2×#4742 | C2 | 1 | 8 | yes | maximal, complemented |
| 8 | C2×#3028 | — | 3 | 1 | no | maximal, Sylow |
| 9 | C22×C3×#41 | C22 | 1 | 1 | yes | characteristic |
| 10 | #5964 | — | 2 | 4 | no | — |
| 11 | #5964 | — | 2 | 8 | no | — |
| 12 | #5964 | C22 | 1 | 8 | yes | — |
| 13 | C2×#1010 | — | 2 | 2 | no | — |
| 14 | C2×#1009 | — | 2 | 2 | no | — |
| 15 | C2×D3×#41 | — | 2 | 4 | no | — |
| 16 | C2×#1007 | — | 2 | 1 | no | — |
| 17 | C2×#1004 | — | 2 | 1 | no | — |
| 18 | C2×#1004 | C22 | 1 | 4 | yes | — |
| 19 | C22×#235 | — | 2 | 2 | no | — |
| 20 | C22×#235 | C22 | 1 | 2 | yes | — |
| 21 | C23×Dic6 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C2×C3×#117 | C22 | 1 | 2 | yes | complemented |
| 23 | #5825 | — | 2 | 4 | no | — |
| 24 | #5825 | C22 | 1 | 8 | yes | complemented |
| 25 | C2×#944 | — | 2 | 1 | no | — |
| 26 | C2×#936 | — | 2 | 1 | no | — |
| 27 | C2×#935 | C22 | 1 | 4 | yes | complemented |
| 28 | C2×#926 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | C2×#924 | — | 2 | 2 | no | — |
| 30 | #5526 | — | 2 | 8 | no | — |
| 31 | #5526 | C22 | 1 | 16 | yes | complemented |
| 32 | C2×#897 | — | 2 | 4 | no | — |
| 33 | C2×#886 | C22 | 1 | 8 | yes | complemented |
| 34 | C2×#875 | — | 2 | 2 | no | — |
| 35 | C2×#869 | — | 2 | 2 | no | — |
| 36 | C3×#410 | C22 | 1 | 8 | yes | complemented |
| 37 | C2×C3×#99 | C22 | 1 | 4 | yes | complemented |
| 38 | #5006 | C22 | 1 | 16 | yes | complemented |
| 39 | C2×#806 | C22 | 1 | 8 | yes | complemented |
| 40 | #4742 | C22 | 1 | 64 | yes | complemented |
| 41 | C2×#585 | — | 3 | 1 | no | — |
| 42 | C2×#536 | — | 3 | 1 | no | — |
| 43 | C2×#536 | — | 3 | 2 | no | — |
| 44 | #3028 | — | 3 | 16 | no | — |
| 45 | C2×#458 | — | 3 | 8 | no | — |
| 46 | C2×#410 | — | 3 | 2 | no | — |
| 47 | C2×#410 | D3 | 1 | 1 | yes | characteristic, complemented |
| 48 | C2×C3×#41 | — | 2 | 2 | no | — |
| 49 | C2×C3×#41 | — | 2 | 2 | no | — |
| 50 | C2×C3×#41 | — | 2 | 4 | no | — |
| 51 | C2×C3×#41 | D4 | 1 | 4 | yes | — |
| 52 | C2×C3×#41 | C23 | 1 | 4 | yes | — |
| 53 | C22×C3×Q8 | D4 | 1 | 1 | yes | characteristic |
| 54 | C22×C3×D4 | D4 | 1 | 1 | yes | characteristic |
| 55 | C22×C3×D4 | C23 | 1 | 2 | yes | — |
| 56 | C23×C3×C4 | D4 | 1 | 2 | yes | — |
| 57 | C23×C3×C4 | C23 | 1 | 1 | yes | characteristic |
| 58 | C22×#67 | — | 2 | 4 | no | — |
| 59 | C22×#67 | C23 | 1 | 4 | yes | — |
| 60 | C23×Dic3 | C23 | 1 | 2 | yes | — |
| 61 | #1010 | — | 2 | 16 | no | — |
| 62 | #1010 | — | 2 | 16 | no | — |
| 63 | #1009 | — | 2 | 16 | no | — |
| 64 | #1009 | — | 2 | 16 | no | — |
| 65 | D3×#41 | — | 2 | 32 | no | — |
| 66 | D3×#41 | — | 2 | 32 | no | — |
| 67 | #1007 | — | 2 | 8 | no | — |
| 68 | #1007 | — | 2 | 8 | no | — |
| 69 | C2×#239 | — | 2 | 4 | no | — |
| 70 | C2×D3×Q8 | — | 2 | 4 | no | — |
| 71 | #1004 | — | 2 | 8 | no | — |
| 72 | #1004 | — | 2 | 8 | no | — |
| 73 | #1004 | — | 2 | 8 | no | — |
| 74 | #1004 | — | 2 | 16 | no | — |
| 75 | #1004 | C23 | 1 | 16 | yes | — |
| 76 | C2×#237 | — | 2 | 4 | no | — |
| 77 | C2×#237 | — | 2 | 8 | no | — |
| 78 | C2×D3×D4 | — | 2 | 4 | no | — |
| 79 | C2×D3×D4 | — | 2 | 8 | no | — |
| 80 | C2×#235 | — | 2 | 4 | no | — |
| 81 | C2×#235 | — | 2 | 4 | no | — |
| 82 | C2×#235 | — | 2 | 16 | no | — |
| 83 | C2×#235 | — | 2 | 2 | no | — |
| 84 | C2×#235 | — | 2 | 4 | no | — |
| 85 | C2×#235 | — | 2 | 16 | no | — |
| 86 | C2×#235 | — | 2 | 2 | no | — |
| 87 | C2×#235 | — | 2 | 2 | no | — |
| 88 | C2×#235 | — | 2 | 2 | no | — |
| 89 | C2×#235 | — | 2 | 4 | no | — |
| 90 | C2×#235 | — | 2 | 4 | no | — |
| 91 | C2×#235 | D4 | 1 | 8 | yes | — |
| 92 | C2×#235 | C23 | 1 | 8 | yes | — |
| 93 | C22×D12 | — | 2 | 2 | no | — |
| 94 | C22×D12 | D4 | 1 | 2 | yes | — |
| 95 | C22×C4×D3 | — | 2 | 4 | no | — |
| 96 | C22×C4×D3 | D4 | 1 | 4 | yes | — |
| 97 | C22×Dic6 | — | 2 | 2 | no | — |
| 98 | C22×Dic6 | — | 2 | 2 | no | — |
| 99 | C22×Dic6 | — | 2 | 2 | no | — |
| 100 | C22×Dic6 | — | 2 | 4 | no | — |
| 101 | C22×Dic6 | — | 2 | 1 | no | — |
| 102 | C22×Dic6 | — | 2 | 1 | no | — |
| 103 | C22×Dic6 | — | 2 | 2 | no | — |
| 104 | C22×Dic6 | D4 | 1 | 2 | yes | — |
| 105 | C22×Dic6 | C23 | 1 | 4 | yes | complemented |
| 106 | C3×#117 | — | 2 | 4 | no | — |
| 107 | C3×#117 | C23 | 1 | 8 | yes | complemented |
| 108 | C2×C3×C4⋊C4 | — | 2 | 2 | no | — |
| 109 | C2×C3×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 110 | C2×C3×C42 | — | 2 | 2 | no | — |
| 111 | C2×#217 | — | 2 | 4 | no | — |
| 112 | C2×#217 | C23 | 1 | 2 | yes | — |
| 113 | #944 | — | 2 | 8 | no | — |
| 114 | #936 | — | 2 | 8 | no | — |
| 115 | #935 | — | 2 | 8 | no | — |
| 116 | #935 | C23 | 1 | 16 | yes | complemented |
| 117 | C2×(C2×D3)⋊C4 | — | 2 | 8 | no | — |
| 118 | #926 | — | 2 | 2 | no | — |
| 119 | #926 | C23 | 1 | 4 | yes | complemented |
| 120 | C2×C4⋊Dic3 | — | 2 | 1 | no | — |
| 121 | C2×C4⋊Dic3 | — | 2 | 8 | no | — |
| 122 | #924 | — | 2 | 16 | no | — |
| 123 | C2×Dic3⋊C4 | — | 2 | 4 | no | — |
| 124 | C2×C4×Dic3 | — | 2 | 1 | no | — |
| 125 | #897 | — | 2 | 32 | no | — |
| 126 | #886 | — | 2 | 16 | no | — |
| 127 | #886 | C23 | 1 | 32 | yes | complemented |
| 128 | #875 | — | 2 | 16 | no | — |
| 129 | #869 | — | 2 | 16 | no | — |
| 130 | C3×#99 | C23 | 1 | 16 | yes | complemented |
| 131 | #806 | C23 | 1 | 32 | yes | complemented |
| 132 | #585 | — | 3 | 8 | no | — |
| 133 | #585 | — | 6 | 8 | no | — |
| 134 | #585 | — | 6 | 4 | no | — |
| 135 | C2×2−1+4 | — | 6 | 2 | no | — |
| 136 | C2×2−1+4 | — | 6 | 1 | no | — |
| 137 | C2×H(5,𝔽2) | — | 3 | 4 | no | — |
| 138 | C2×H(5,𝔽2) | — | 6 | 2 | no | — |
| 139 | C2×H(5,𝔽2) | — | 6 | 1 | no | — |
| 140 | C22×#41 | — | 3 | 2 | no | — |
| 141 | C22×#41 | — | 6 | 4 | no | — |
| 142 | C22×#41 | — | 6 | 2 | no | — |
| 143 | C22×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 144 | C23×Q8 | — | 3 | 1 | no | — |
| 145 | #536 | — | 3 | 8 | no | — |
| 146 | #536 | — | 3 | 16 | no | — |
| 147 | #536 | — | 6 | 8 | no | — |
| 148 | #536 | — | 6 | 4 | no | — |
| 149 | C2×C4⋊Q8 | — | 6 | 2 | no | — |
| 150 | C2×C4⋊Q8 | — | 6 | 1 | no | — |
| 151 | C2×#124 | — | 6 | 2 | no | — |
| 152 | C2×#124 | — | 6 | 1 | no | — |
| 153 | C2×#123 | — | 3 | 4 | no | — |
| 154 | C2×#123 | — | 3 | 8 | no | — |
| 155 | C2×C22⋊Q8 | — | 6 | 4 | no | — |
| 156 | C2×C22⋊Q8 | — | 6 | 2 | no | — |
| 157 | C2×#117 | — | 3 | 1 | no | — |
| 158 | C2×#117 | C2×D3 | 1 | 2 | yes | complemented |
| 159 | #458 | — | 3 | 64 | no | — |
| 160 | #410 | — | 3 | 16 | no | — |
| 161 | #410 | C2×D3 | 1 | 8 | yes | complemented |
| 162 | C2×#99 | — | 3 | 8 | no | — |
| 163 | C2×#99 | C2×D3 | 1 | 4 | yes | complemented |
| 164 | C24×C3 | C2×D4 | 1 | 2 | yes | — |
| 165 | C24×C3 | C24 | 1 | 1 | yes | characteristic |
| 166 | C23×D3 | — | 2 | 4 | no | — |
| 167 | C23×D3 | C2×D4 | 1 | 4 | yes | — |
| 168 | C3×#41 | — | 2 | 8 | no | — |
| 169 | C3×#41 | — | 2 | 8 | no | — |
| 170 | C3×#41 | — | 2 | 8 | no | — |
| 171 | C3×#41 | — | 2 | 8 | no | — |
| 172 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 173 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 174 | C2×C3×Q8 | C2×D4 | 1 | 4 | yes | — |
| 175 | C2×C3×D4 | — | 2 | 4 | no | — |
| 176 | C2×C3×D4 | — | 2 | 4 | no | — |
| 177 | C2×C3×D4 | — | 2 | 2 | no | — |
| 178 | C2×C3×D4 | — | 2 | 2 | no | — |
| 179 | C2×C3×D4 | C2×D4 | 1 | 4 | yes | — |
| 180 | C2×C3×D4 | C2×D4 | 1 | 4 | yes | — |
| 181 | C2×C3×D4 | C24 | 1 | 4 | yes | — |
| 182 | C22×C3×C4 | — | 2 | 2 | no | — |
| 183 | C22×C3×C4 | — | 2 | 2 | no | — |
| 184 | C22×C3×C4 | — | 2 | 4 | no | — |
| 185 | C22×C3×C4 | — | 2 | 4 | no | — |
| 186 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 187 | C22×C3×C4 | C2×D4 | 1 | 8 | yes | — |
| 188 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 189 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 190 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 191 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 192 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 193 | C22×C3×C4 | C2×D4 | 1 | 4 | yes | — |
| 194 | C22×C3×C4 | C24 | 1 | 2 | yes | — |
| 195 | C2×#67 | — | 2 | 8 | no | — |
| 196 | C2×#67 | — | 2 | 16 | no | — |
| 197 | C2×#67 | — | 2 | 4 | no | — |
| 198 | C2×#67 | — | 2 | 4 | no | — |
| 199 | C2×#67 | — | 2 | 4 | no | — |
| 200 | C2×#67 | — | 2 | 4 | no | — |
| 201 | C2×#67 | — | 2 | 16 | no | — |
| 202 | C2×#67 | C2×D4 | 1 | 8 | yes | — |
| 203 | C2×#67 | C24 | 1 | 8 | yes | — |
| 204 | C22×Dic3 | — | 2 | 4 | no | — |
| 205 | C22×Dic3 | — | 2 | 4 | no | — |
| 206 | C22×Dic3 | — | 2 | 2 | no | — |
| 207 | C22×Dic3 | — | 2 | 2 | no | — |
| 208 | C22×Dic3 | — | 2 | 4 | no | — |
| 209 | C22×Dic3 | — | 2 | 2 | no | — |
| 210 | C22×Dic3 | C2×D4 | 1 | 4 | yes | — |
| 211 | C22×Dic3 | C24 | 1 | 4 | yes | — |
| 212 | #239 | — | 2 | 32 | no | — |
| 213 | D3×Q8 | — | 2 | 32 | no | — |
| 214 | #237 | — | 2 | 32 | no | — |
| 215 | #237 | — | 2 | 32 | no | — |
| 216 | #237 | — | 2 | 32 | no | — |
| 217 | D3×D4 | — | 2 | 32 | no | — |
| 218 | D3×D4 | — | 2 | 32 | no | — |
| 219 | D3×D4 | — | 2 | 32 | no | — |
| 220 | #235 | — | 2 | 16 | no | — |
| 221 | #235 | — | 2 | 32 | no | — |
| 222 | #235 | — | 2 | 32 | no | — |
| 223 | #235 | — | 2 | 8 | no | — |
| 224 | #235 | — | 2 | 8 | no | — |
| 225 | #235 | — | 2 | 8 | no | — |
| 226 | #235 | — | 2 | 8 | no | — |
| 227 | #235 | — | 2 | 8 | no | — |
| 228 | #235 | — | 2 | 16 | no | — |
| 229 | #235 | — | 2 | 8 | no | — |
| 230 | #235 | — | 2 | 8 | no | — |
| 231 | #235 | — | 2 | 8 | no | — |
| 232 | C2×D12 | — | 2 | 4 | no | — |
| 233 | C2×D12 | — | 2 | 16 | no | — |
| 234 | C2×D12 | — | 2 | 2 | no | — |
| 235 | C2×D12 | — | 2 | 2 | no | — |
| 236 | C2×D12 | — | 2 | 4 | no | — |
| 237 | C2×D12 | C2×D4 | 1 | 8 | yes | — |
| 238 | C2×C4×D3 | — | 2 | 8 | no | — |
| 239 | C2×C4×D3 | — | 2 | 32 | no | — |
| 240 | C2×C4×D3 | — | 2 | 4 | no | — |
| 241 | C2×C4×D3 | — | 2 | 4 | no | — |
| 242 | C2×C4×D3 | — | 2 | 8 | no | — |
| 243 | C2×C4×D3 | C2×D4 | 1 | 16 | yes | — |
| 244 | C2×Dic6 | — | 2 | 4 | no | — |
| 245 | C2×Dic6 | — | 2 | 16 | no | — |
| 246 | C2×Dic6 | — | 2 | 2 | no | — |
| 247 | C2×Dic6 | — | 2 | 2 | no | — |
| 248 | C2×Dic6 | — | 2 | 4 | no | — |
| 249 | C2×Dic6 | — | 2 | 8 | no | — |
| 250 | C2×Dic6 | — | 2 | 8 | no | — |
| 251 | C2×Dic6 | — | 2 | 4 | no | — |
| 252 | C2×Dic6 | — | 2 | 4 | no | — |
| 253 | C2×Dic6 | — | 4 | 1 | no | — |
| 254 | C2×Dic6 | — | 4 | 2 | no | — |
| 255 | C2×Dic6 | — | 4 | 4 | no | — |
| 256 | C2×Dic6 | — | 4 | 1 | no | — |
| 257 | C2×Dic6 | — | 4 | 4 | no | — |
| 258 | C2×Dic6 | — | 4 | 2 | no | — |
| 259 | C2×Dic6 | — | 4 | 2 | no | — |
| 260 | C2×Dic6 | C2×D4 | 1 | 8 | yes | — |
| 261 | C3×C4⋊C4 | — | 2 | 8 | no | — |
| 262 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 263 | C3×C22⋊C4 | C24 | 1 | 8 | yes | — |
| 264 | C3×C42 | — | 2 | 8 | no | — |
| 265 | #217 | — | 2 | 16 | no | — |
| 266 | #217 | — | 2 | 2 | no | — |
| 267 | #217 | C24 | 1 | 4 | yes | — |
| 268 | (C2×D3)⋊C4 | — | 2 | 32 | no | — |
| 269 | C4⋊Dic3 | — | 2 | 4 | no | — |
| 270 | C4⋊Dic3 | — | 2 | 32 | no | — |
| 271 | Dic3⋊C4 | — | 2 | 16 | no | — |
| 272 | C4×Dic3 | — | 2 | 4 | no | — |
| 273 | 2−1+4 | — | 6 | 8 | no | — |
| 274 | 2−1+4 | — | 6 | 16 | no | — |
| 275 | 2−1+4 | — | 6 | 16 | no | — |
| 276 | 2−1+4 | — | 6 | 8 | no | — |
| 277 | H(5,𝔽2) | — | 3 | 16 | no | — |
| 278 | H(5,𝔽2) | — | 6 | 16 | no | — |
| 279 | H(5,𝔽2) | — | 6 | 8 | no | — |
| 280 | H(5,𝔽2) | — | 6 | 16 | no | — |
| 281 | H(5,𝔽2) | — | 6 | 16 | no | — |
| 282 | H(5,𝔽2) | — | 6 | 8 | no | — |
| 283 | H(5,𝔽2) | — | 6 | 8 | no | — |
| 284 | C2×#41 | — | 2 | 2 | no | — |
| 285 | C2×#41 | — | 2 | 2 | no | — |
| 286 | C2×#41 | — | 2 | 4 | no | — |
| 287 | C2×#41 | — | 3 | 8 | no | — |
| 288 | C2×#41 | — | 3 | 8 | no | — |
| 289 | C2×#41 | — | 6 | 4 | no | — |
| 290 | C2×#41 | — | 6 | 4 | no | — |
| 291 | C2×#41 | — | 6 | 16 | no | — |
| 292 | C2×#41 | — | 6 | 8 | no | — |
| 293 | C2×#41 | — | 6 | 32 | no | — |
| 294 | C2×#41 | — | 6 | 4 | no | — |
| 295 | C2×#41 | — | 6 | 4 | no | — |
| 296 | C2×#41 | — | 6 | 32 | no | — |
| 297 | C2×#41 | — | 6 | 2 | no | — |
| 298 | C2×#41 | — | 6 | 2 | no | — |
| 299 | C2×#41 | — | 6 | 4 | no | — |
| 300 | C2×#41 | — | 6 | 4 | no | — |
| 301 | C2×#41 | — | 6 | 16 | no | — |
| 302 | C2×#41 | — | 6 | 2 | no | — |
| 303 | C2×#41 | — | 6 | 2 | no | — |
| 304 | C2×#41 | — | 6 | 4 | no | — |
| 305 | C2×#41 | D12 | 1 | 4 | yes | — |
| 306 | C2×#41 | C22×D3 | 1 | 4 | yes | — |
| 307 | C22×Q8 | — | 3 | 2 | no | — |
| 308 | C22×Q8 | — | 3 | 4 | no | — |
| 309 | C22×Q8 | — | 6 | 2 | no | — |
| 310 | C22×Q8 | — | 6 | 4 | no | — |
| 311 | C22×Q8 | — | 6 | 1 | no | — |
| 312 | C22×Q8 | — | 6 | 1 | no | — |
| 313 | C22×Q8 | — | 6 | 2 | no | — |
| 314 | C22×Q8 | — | 6 | 2 | no | — |
| 315 | C22×Q8 | — | 6 | 2 | no | — |
| 316 | C22×Q8 | — | 6 | 4 | no | — |
| 317 | C22×Q8 | D12 | 1 | 1 | yes | characteristic |
| 318 | C22×D4 | — | 3 | 4 | no | — |
| 319 | C22×D4 | — | 3 | 2 | no | — |
| 320 | C22×D4 | — | 6 | 2 | no | — |
| 321 | C22×D4 | — | 6 | 8 | no | — |
| 322 | C22×D4 | — | 6 | 4 | no | — |
| 323 | C22×D4 | — | 6 | 4 | no | — |
| 324 | C22×D4 | D12 | 1 | 1 | yes | characteristic |
| 325 | C22×D4 | C22×D3 | 1 | 2 | yes | — |
| 326 | C23×C4 | — | 3 | 4 | no | — |
| 327 | C23×C4 | — | 3 | 2 | no | — |
| 328 | C23×C4 | — | 6 | 4 | no | — |
| 329 | C23×C4 | D12 | 1 | 2 | yes | — |
| 330 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 331 | C4⋊Q8 | — | 6 | 16 | no | — |
| 332 | C4⋊Q8 | — | 6 | 8 | no | — |
| 333 | #124 | — | 6 | 16 | no | — |
| 334 | #124 | — | 6 | 8 | no | — |
| 335 | #123 | — | 3 | 16 | no | — |
| 336 | #123 | — | 3 | 32 | no | — |
| 337 | #123 | — | 6 | 16 | no | — |
| 338 | #123 | — | 6 | 8 | no | — |
| 339 | C22⋊Q8 | — | 6 | 32 | no | — |
| 340 | C22⋊Q8 | — | 6 | 16 | no | — |
| 341 | #117 | — | 2 | 4 | no | — |
| 342 | #117 | — | 3 | 4 | no | — |
| 343 | #117 | — | 6 | 2 | no | — |
| 344 | #117 | C22×D3 | 1 | 8 | yes | complemented |
| 345 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 346 | C2×C4⋊C4 | — | 6 | 8 | no | — |
| 347 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 348 | C2×C4⋊C4 | — | 6 | 4 | no | — |
| 349 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 350 | C2×C22⋊C4 | — | 6 | 8 | no | — |
| 351 | C2×C22⋊C4 | — | 6 | 4 | no | — |
| 352 | C2×C22⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 353 | C2×C42 | — | 2 | 2 | no | — |
| 354 | C2×C42 | — | 6 | 1 | no | — |
| 355 | #99 | — | 3 | 32 | no | — |
| 356 | #99 | C22×D3 | 1 | 16 | yes | complemented |
| 357 | C23×C3 | — | 2 | 2 | no | — |
| 358 | C23×C3 | — | 2 | 2 | no | — |
| 359 | C23×C3 | — | 4 | 2 | no | — |
| 360 | C23×C3 | — | 4 | 4 | no | — |
| 361 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 362 | C23×C3 | C22×D4 | 1 | 4 | yes | — |
| 363 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 364 | C23×C3 | C22×D4 | 1 | 2 | yes | — |
| 365 | C23×C3 | C22×D4 | 1 | 2 | yes | — |
| 366 | C23×C3 | C25 | 1 | 1 | yes | characteristic |
| 367 | C22×D3 | — | 2 | 4 | no | — |
| 368 | C22×D3 | — | 2 | 16 | no | — |
| 369 | C22×D3 | — | 2 | 4 | no | — |
| 370 | C22×D3 | — | 4 | 8 | no | — |
| 371 | C22×D3 | — | 8 | 8 | no | — |
| 372 | C22×D3 | C22×D4 | 1 | 8 | yes | — |
| 373 | C3×Q8 | — | 2 | 8 | no | — |
| 374 | C3×D4 | — | 2 | 8 | no | — |
| 375 | C3×D4 | — | 2 | 8 | no | — |
| 376 | C3×D4 | — | 2 | 8 | no | — |
| 377 | C2×C3×C4 | — | 2 | 2 | no | — |
| 378 | C2×C3×C4 | — | 2 | 2 | no | — |
| 379 | C2×C3×C4 | — | 2 | 8 | no | — |
| 380 | C2×C3×C4 | — | 2 | 8 | no | — |
| 381 | C2×C3×C4 | — | 2 | 8 | no | — |
| 382 | C2×C3×C4 | — | 4 | 8 | no | — |
| 383 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 384 | C2×C3×C4 | #120 | 1 | 2 | yes | — |
| 385 | C2×C3×C4 | #120 | 1 | 4 | yes | — |
| 386 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 387 | C2×C3×C4 | #120 | 1 | 4 | yes | — |
| 388 | C2×C3×C4 | #120 | 1 | 2 | yes | — |
| 389 | C2×C3×C4 | #120 | 1 | 2 | yes | — |
| 390 | C2×C3×C4 | C22×D4 | 1 | 4 | yes | — |
| 391 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 392 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 393 | C2×C3×C4 | C22×D4 | 1 | 4 | yes | — |
| 394 | C2×C3×C4 | C22×D4 | 1 | 4 | yes | — |
| 395 | #67 | — | 2 | 32 | no | — |
| 396 | #67 | — | 2 | 8 | no | — |
| 397 | #67 | — | 2 | 8 | no | — |
| 398 | #67 | — | 2 | 8 | no | — |
| 399 | #67 | — | 2 | 8 | no | — |
| 400 | C2×Dic3 | — | 2 | 16 | no | — |
| 401 | C2×Dic3 | — | 2 | 4 | no | — |
| 402 | C2×Dic3 | — | 2 | 4 | no | — |
| 403 | C2×Dic3 | — | 2 | 4 | no | — |
| 404 | C2×Dic3 | — | 2 | 4 | no | — |
| 405 | C2×Dic3 | — | 2 | 8 | no | — |
| 406 | C2×Dic3 | — | 4 | 4 | no | — |
| 407 | C2×Dic3 | — | 4 | 4 | no | — |
| 408 | C2×Dic3 | — | 4 | 2 | no | — |
| 409 | C2×Dic3 | — | 4 | 2 | no | — |
| 410 | C2×Dic3 | C22×D4 | 1 | 8 | yes | — |
| 411 | D12 | — | 2 | 16 | no | — |
| 412 | D12 | — | 2 | 8 | no | — |
| 413 | D12 | — | 2 | 8 | no | — |
| 414 | C4×D3 | — | 2 | 32 | no | — |
| 415 | C4×D3 | — | 2 | 16 | no | — |
| 416 | C4×D3 | — | 2 | 16 | no | — |
| 417 | Dic6 | — | 2 | 16 | no | — |
| 418 | Dic6 | — | 2 | 8 | no | — |
| 419 | Dic6 | — | 2 | 8 | no | — |
| 420 | Dic6 | — | 4 | 4 | no | — |
| 421 | Dic6 | — | 4 | 8 | no | — |
| 422 | Dic6 | — | 4 | 4 | no | — |
| 423 | C24 | — | 3 | 4 | no | — |
| 424 | C24 | — | 6 | 4 | no | — |
| 425 | C24 | C2×D12 | 1 | 2 | yes | — |
| 426 | C24 | C23×D3 | 1 | 1 | yes | characteristic |
| 427 | #41 | — | 2 | 8 | no | — |
| 428 | #41 | — | 2 | 8 | no | — |
| 429 | #41 | — | 2 | 8 | no | — |
| 430 | #41 | — | 2 | 8 | no | — |
| 431 | #41 | — | 6 | 32 | no | — |
| 432 | #41 | — | 6 | 16 | no | — |
| 433 | #41 | — | 6 | 32 | no | — |
| 434 | #41 | — | 6 | 32 | no | — |
| 435 | #41 | — | 6 | 32 | no | — |
| 436 | #41 | — | 6 | 32 | no | — |
| 437 | #41 | — | 6 | 32 | no | — |
| 438 | #41 | — | 6 | 8 | no | — |
| 439 | #41 | — | 6 | 8 | no | — |
| 440 | #41 | — | 6 | 8 | no | — |
| 441 | #41 | — | 6 | 8 | no | — |
| 442 | #41 | — | 6 | 8 | no | — |
| 443 | #41 | — | 6 | 8 | no | — |
| 444 | #41 | — | 6 | 16 | no | — |
| 445 | #41 | — | 6 | 8 | no | — |
| 446 | #41 | — | 6 | 8 | no | — |
| 447 | C2×Q8 | — | 2 | 2 | no | — |
| 448 | C2×Q8 | — | 2 | 2 | no | — |
| 449 | C2×Q8 | — | 3 | 8 | no | — |
| 450 | C2×Q8 | — | 6 | 4 | no | — |
| 451 | C2×Q8 | — | 6 | 16 | no | — |
| 452 | C2×Q8 | — | 6 | 32 | no | — |
| 453 | C2×Q8 | — | 6 | 2 | no | — |
| 454 | C2×Q8 | — | 6 | 2 | no | — |
| 455 | C2×Q8 | — | 6 | 4 | no | — |
| 456 | C2×Q8 | — | 6 | 4 | no | — |
| 457 | C2×Q8 | — | 6 | 4 | no | — |
| 458 | C2×Q8 | — | 6 | 8 | no | — |
| 459 | C2×Q8 | — | 6 | 8 | no | — |
| 460 | C2×Q8 | — | 12 | 2 | no | — |
| 461 | C2×Q8 | — | 12 | 4 | no | — |
| 462 | C2×Q8 | — | 12 | 2 | no | — |
| 463 | C2×Q8 | — | 12 | 4 | no | — |
| 464 | C2×Q8 | — | 12 | 1 | no | — |
| 465 | C2×Q8 | — | 12 | 1 | no | — |
| 466 | C2×Q8 | — | 12 | 2 | no | — |
| 467 | C2×Q8 | C2×D12 | 1 | 4 | yes | — |
| 468 | C2×D4 | — | 2 | 4 | no | — |
| 469 | C2×D4 | — | 2 | 4 | no | — |
| 470 | C2×D4 | — | 2 | 2 | no | — |
| 471 | C2×D4 | — | 2 | 2 | no | — |
| 472 | C2×D4 | — | 3 | 8 | no | — |
| 473 | C2×D4 | — | 3 | 8 | no | — |
| 474 | C2×D4 | — | 3 | 8 | no | — |
| 475 | C2×D4 | — | 6 | 4 | no | — |
| 476 | C2×D4 | — | 6 | 16 | no | — |
| 477 | C2×D4 | — | 6 | 32 | no | — |
| 478 | C2×D4 | — | 6 | 32 | no | — |
| 479 | C2×D4 | — | 6 | 32 | no | — |
| 480 | C2×D4 | — | 6 | 8 | no | — |
| 481 | C2×D4 | — | 6 | 16 | no | — |
| 482 | C2×D4 | — | 6 | 4 | no | — |
| 483 | C2×D4 | — | 6 | 4 | no | — |
| 484 | C2×D4 | — | 6 | 16 | no | — |
| 485 | C2×D4 | — | 6 | 4 | no | — |
| 486 | C2×D4 | — | 6 | 4 | no | — |
| 487 | C2×D4 | — | 6 | 2 | no | — |
| 488 | C2×D4 | — | 6 | 2 | no | — |
| 489 | C2×D4 | — | 6 | 4 | no | — |
| 490 | C2×D4 | C2×D12 | 1 | 4 | yes | — |
| 491 | C2×D4 | C2×D12 | 1 | 4 | yes | — |
| 492 | C2×D4 | C23×D3 | 1 | 4 | yes | — |
| 493 | C22×C4 | — | 2 | 2 | no | — |
| 494 | C22×C4 | — | 2 | 2 | no | — |
| 495 | C22×C4 | — | 2 | 4 | no | — |
| 496 | C22×C4 | — | 2 | 4 | no | — |
| 497 | C22×C4 | — | 3 | 4 | no | — |
| 498 | C22×C4 | — | 3 | 16 | no | — |
| 499 | C22×C4 | — | 3 | 4 | no | — |
| 500 | C22×C4 | — | 6 | 8 | no | — |
| 501 | C22×C4 | — | 6 | 32 | no | — |
| 502 | C22×C4 | — | 6 | 4 | no | — |
| 503 | C22×C4 | — | 6 | 4 | no | — |
| 504 | C22×C4 | — | 6 | 4 | no | — |
| 505 | C22×C4 | — | 6 | 8 | no | — |
| 506 | C22×C4 | — | 6 | 2 | no | — |
| 507 | C22×C4 | — | 6 | 2 | no | — |
| 508 | C22×C4 | — | 6 | 2 | no | — |
| 509 | C22×C4 | — | 6 | 4 | no | — |
| 510 | C22×C4 | — | 6 | 4 | no | — |
| 511 | C22×C4 | C2×D12 | 1 | 2 | yes | — |
| 512 | C22×C4 | C2×D12 | 1 | 8 | yes | — |
| 513 | C22×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 514 | C22×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 515 | C22×C4 | C2×D12 | 1 | 2 | yes | — |
| 516 | C22×C4 | D3×D4 | 1 | 2 | yes | — |
| 517 | C22×C4 | D3×D4 | 1 | 2 | yes | — |
| 518 | C22×C4 | D3×D4 | 1 | 4 | yes | — |
| 519 | C22×C4 | C23×D3 | 1 | 2 | yes | — |
| 520 | C4⋊C4 | — | 2 | 8 | no | — |
| 521 | C4⋊C4 | — | 6 | 32 | no | — |
| 522 | C4⋊C4 | — | 6 | 4 | no | — |
| 523 | C4⋊C4 | — | 6 | 16 | no | — |
| 524 | C22⋊C4 | — | 2 | 4 | no | — |
| 525 | C22⋊C4 | — | 3 | 4 | no | — |
| 526 | C22⋊C4 | — | 6 | 32 | no | — |
| 527 | C22⋊C4 | — | 6 | 2 | no | — |
| 528 | C22⋊C4 | — | 6 | 16 | no | — |
| 529 | C22⋊C4 | C23×D3 | 1 | 8 | yes | — |
| 530 | C42 | — | 2 | 8 | no | — |
| 531 | C42 | — | 6 | 4 | no | — |
| 532 | C22×C3 | — | 2 | 2 | no | — |
| 533 | C22×C3 | — | 2 | 4 | no | — |
| 534 | C22×C3 | — | 2 | 4 | no | — |
| 535 | C22×C3 | — | 4 | 1 | no | — |
| 536 | C22×C3 | — | 4 | 2 | no | — |
| 537 | C22×C3 | — | 4 | 1 | no | — |
| 538 | C22×C3 | — | 4 | 4 | no | — |
| 539 | C22×C3 | — | 4 | 4 | no | — |
| 540 | C22×C3 | — | 8 | 2 | no | — |
| 541 | C22×C3 | C2×#120 | 1 | 2 | yes | — |
| 542 | C22×C3 | C2×#120 | 1 | 1 | yes | characteristic |
| 543 | C22×C3 | C2×#120 | 1 | 1 | yes | characteristic |
| 544 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 545 | C22×C3 | C23×D4 | 1 | 2 | yes | — |
| 546 | C2×D3 | — | 2 | 8 | no | — |
| 547 | C2×D3 | — | 4 | 8 | no | — |
| 548 | C2×D3 | — | 4 | 8 | no | — |
| 549 | C2×D3 | — | 8 | 4 | no | — |
| 550 | C2×D3 | — | 8 | 16 | no | — |
| 551 | C3×C4 | — | 2 | 4 | no | — |
| 552 | C3×C4 | — | 4 | 8 | no | — |
| 553 | C3×C4 | C2×#120 | 1 | 2 | yes | — |
| 554 | C3×C4 | C2×#120 | 1 | 4 | yes | — |
| 555 | C3×C4 | C2×#120 | 1 | 2 | yes | — |
| 556 | Dic3 | — | 2 | 8 | no | — |
| 557 | Dic3 | — | 4 | 4 | no | — |
| 558 | Dic3 | — | 4 | 4 | no | — |
| 559 | C23 | — | 2 | 2 | no | — |
| 560 | C23 | — | 2 | 2 | no | — |
| 561 | C23 | — | 3 | 8 | no | — |
| 562 | C23 | — | 4 | 2 | no | — |
| 563 | C23 | — | 4 | 4 | no | — |
| 564 | C23 | — | 6 | 16 | no | — |
| 565 | C23 | — | 6 | 4 | no | — |
| 566 | C23 | — | 6 | 4 | no | — |
| 567 | C23 | — | 12 | 8 | no | — |
| 568 | C23 | — | 24 | 8 | no | — |
| 569 | C23 | C22×D12 | 1 | 1 | yes | characteristic |
| 570 | C23 | C22×D12 | 1 | 4 | yes | — |
| 571 | C23 | C22×D12 | 1 | 1 | yes | characteristic |
| 572 | C23 | C2×D3×D4 | 1 | 2 | yes | — |
| 573 | C23 | C2×D3×D4 | 1 | 2 | yes | — |
| 574 | C23 | C24×D3 | 1 | 1 | yes | characteristic |
| 575 | Q8 | — | 2 | 8 | no | — |
| 576 | Q8 | — | 6 | 16 | no | — |
| 577 | Q8 | — | 6 | 8 | no | — |
| 578 | Q8 | — | 6 | 8 | no | — |
| 579 | Q8 | — | 12 | 4 | no | — |
| 580 | Q8 | — | 12 | 4 | no | — |
| 581 | Q8 | — | 12 | 8 | no | — |
| 582 | D4 | — | 2 | 8 | no | — |
| 583 | D4 | — | 2 | 8 | no | — |
| 584 | D4 | — | 2 | 8 | no | — |
| 585 | D4 | — | 6 | 16 | no | — |
| 586 | D4 | — | 6 | 32 | no | — |
| 587 | D4 | — | 6 | 8 | no | — |
| 588 | D4 | — | 6 | 8 | no | — |
| 589 | D4 | — | 6 | 8 | no | — |
| 590 | D4 | — | 6 | 8 | no | — |
| 591 | D4 | — | 6 | 8 | no | — |
| 592 | D4 | — | 6 | 8 | no | — |
| 593 | C2×C4 | — | 2 | 2 | no | — |
| 594 | C2×C4 | — | 2 | 2 | no | — |
| 595 | C2×C4 | — | 2 | 8 | no | — |
| 596 | C2×C4 | — | 2 | 8 | no | — |
| 597 | C2×C4 | — | 2 | 8 | no | — |
| 598 | C2×C4 | — | 3 | 8 | no | — |
| 599 | C2×C4 | — | 4 | 8 | no | — |
| 600 | C2×C4 | — | 6 | 32 | no | — |
| 601 | C2×C4 | — | 6 | 16 | no | — |
| 602 | C2×C4 | — | 6 | 4 | no | — |
| 603 | C2×C4 | — | 6 | 4 | no | — |
| 604 | C2×C4 | — | 6 | 16 | no | — |
| 605 | C2×C4 | — | 6 | 16 | no | — |
| 606 | C2×C4 | — | 6 | 4 | no | — |
| 607 | C2×C4 | — | 6 | 4 | no | — |
| 608 | C2×C4 | — | 6 | 8 | no | — |
| 609 | C2×C4 | — | 12 | 4 | no | — |
| 610 | C2×C4 | — | 12 | 2 | no | — |
| 611 | C2×C4 | — | 12 | 4 | no | — |
| 612 | C2×C4 | — | 12 | 2 | no | — |
| 613 | C2×C4 | #882 | 1 | 2 | yes | — |
| 614 | C2×C4 | #882 | 1 | 4 | yes | — |
| 615 | C2×C4 | #882 | 1 | 2 | yes | — |
| 616 | C2×C4 | #882 | 1 | 4 | yes | — |
| 617 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 618 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 619 | C2×C4 | #882 | 1 | 2 | yes | — |
| 620 | C2×C4 | C22×D12 | 1 | 4 | yes | — |
| 621 | C2×C4 | C22×D12 | 1 | 2 | yes | — |
| 622 | C2×C4 | C22×D12 | 1 | 2 | yes | — |
| 623 | C2×C4 | C2×D3×D4 | 1 | 4 | yes | — |
| 624 | C2×C4 | C2×D3×D4 | 1 | 4 | yes | — |
| 625 | C2×C3 | — | 2 | 1 | no | — |
| 626 | C2×C3 | — | 2 | 2 | no | — |
| 627 | C2×C3 | — | 2 | 2 | no | — |
| 628 | C2×C3 | — | 2 | 1 | no | — |
| 629 | C2×C3 | — | 4 | 4 | no | — |
| 630 | C2×C3 | #3028 | 1 | 2 | yes | complemented |
| 631 | C2×C3 | C22×#120 | 1 | 1 | yes | characteristic |
| 632 | D3 | — | 4 | 8 | no | — |
| 633 | C22 | — | 2 | 4 | no | — |
| 634 | C22 | — | 2 | 2 | no | — |
| 635 | C22 | — | 2 | 4 | no | — |
| 636 | C22 | — | 4 | 1 | no | — |
| 637 | C22 | — | 4 | 2 | no | — |
| 638 | C22 | — | 4 | 1 | no | — |
| 639 | C22 | — | 4 | 4 | no | — |
| 640 | C22 | — | 4 | 4 | no | — |
| 641 | C22 | — | 6 | 8 | no | — |
| 642 | C22 | — | 8 | 2 | no | — |
| 643 | C22 | — | 12 | 8 | no | — |
| 644 | C22 | — | 12 | 8 | no | — |
| 645 | C22 | — | 24 | 4 | no | — |
| 646 | C22 | — | 24 | 16 | no | — |
| 647 | C22 | C2×#882 | 1 | 1 | yes | characteristic |
| 648 | C22 | C2×#882 | 1 | 2 | yes | — |
| 649 | C22 | C2×#882 | 1 | 1 | yes | characteristic |
| 650 | C22 | C23×D12 | 1 | 1 | yes | characteristic |
| 651 | C22 | C22×D3×D4 | 1 | 2 | yes | — |
| 652 | C4 | — | 2 | 4 | no | — |
| 653 | C4 | — | 4 | 8 | no | — |
| 654 | C4 | — | 6 | 8 | no | — |
| 655 | C4 | — | 12 | 4 | no | — |
| 656 | C4 | — | 12 | 4 | no | — |
| 657 | C4 | C2×#882 | 1 | 2 | yes | — |
| 658 | C4 | C2×#882 | 1 | 2 | yes | — |
| 659 | C4 | C2×#882 | 1 | 4 | yes | — |
| 660 | C3 | C2×#3028 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 661 | C2 | — | 2 | 2 | no | — |
| 662 | C2 | — | 2 | 1 | no | — |
| 663 | C2 | — | 2 | 1 | no | — |
| 664 | C2 | — | 2 | 2 | no | — |
| 665 | C2 | — | 4 | 4 | no | — |
| 666 | C2 | — | 12 | 8 | no | — |
| 667 | C2 | #78692 | 1 | 2 | yes | direct product factor |
| 668 | C2 | C22×#882 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#5825 | C2 | semidirect |
| 3. C2×#5526 | C2 | semidirect |
| 4. C2×C3×#410 | C2 | semidirect |
| 5. C2×#5006 | C2 | semidirect |
| 6. #78692 | C2 | direct (N × H) |
| 7. C2×#4742 | C2 | semidirect |
| 21. C23×Dic6 | C22 | semidirect |
| 22. C2×C3×#117 | C22 | semidirect |
| 24. #5825 | C22 | semidirect |
| 27. C2×#935 | C22 | semidirect |
| 28. C2×#926 | C22 | semidirect |
| 31. #5526 | C22 | semidirect |
| 33. C2×#886 | C22 | semidirect |
| 36. C3×#410 | C22 | semidirect |
| 37. C2×C3×#99 | C22 | semidirect |
| 38. #5006 | C22 | semidirect |
| 39. C2×#806 | C22 | semidirect |
| 40. #4742 | C22 | semidirect |
| 47. C2×#410 | D3 | semidirect |
| 105. C22×Dic6 | C23 | semidirect |
| 107. C3×#117 | C23 | semidirect |
| 116. #935 | C23 | semidirect |
| 119. #926 | C23 | semidirect |
| 127. #886 | C23 | semidirect |
| 130. C3×#99 | C23 | semidirect |
| 131. #806 | C23 | semidirect |
| 158. C2×#117 | C2×D3 | semidirect |
| 161. #410 | C2×D3 | semidirect |
| 163. C2×#99 | C2×D3 | semidirect |
| 344. #117 | C22×D3 | semidirect |
| 356. #99 | C22×D3 | semidirect |
| 630. C2×C3 | #3028 | semidirect |
| 660. C3 | C2×#3028 | semidirect |
| 667. C2 | #78692 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5964 | 2 |
| C2×#5825 | 2 |
| C2×#5526 | 2 |
| C2×C3×#410 | 2 |
| C2×#5006 | 2 |
| #78692 | 2 |
| C2×#4742 | 2 |
| C2×#3028 | 3 |