Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2598 conjugacy classes of subgroups.
The subgroup lattice has 644 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#5838 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C2×#5779 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×C3×#456 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#5204 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C2×#5095 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#5092 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #80303 | C2 | 1 | 16 | yes | maximal, direct product factor |
| 8 | C2×#4826 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C2×#4824 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C2×#4755 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C2×#3293 | — | 3 | 1 | no | maximal, Sylow |
| 12 | C2×C3×2−1+4 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#1010 | C22 | 1 | 2 | yes | — |
| 14 | C2×#1007 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C3×#137 | C22 | 1 | 2 | yes | — |
| 16 | C2×C3×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 17 | #5838 | — | 2 | 8 | no | — |
| 18 | #5838 | C22 | 1 | 16 | yes | complemented |
| 19 | C2×#951 | — | 2 | 2 | no | — |
| 20 | C2×#951 | C22 | 1 | 2 | yes | — |
| 21 | C2×#950 | — | 2 | 2 | no | — |
| 22 | C2×#950 | C22 | 1 | 2 | yes | — |
| 23 | C2×#948 | C22 | 1 | 2 | yes | — |
| 24 | C22×#216 | — | 2 | 2 | no | — |
| 25 | C22×#216 | C22 | 1 | 2 | yes | — |
| 26 | C22×#216 | C22 | 1 | 2 | yes | — |
| 27 | C2×#942 | — | 2 | 2 | no | — |
| 28 | C2×#942 | C22 | 1 | 2 | yes | — |
| 29 | #5779 | — | 2 | 8 | no | — |
| 30 | #5779 | C22 | 1 | 16 | yes | complemented |
| 31 | C2×#918 | — | 2 | 2 | no | — |
| 32 | C2×D3×Q16 | — | 2 | 2 | no | — |
| 33 | C2×#916 | — | 2 | 2 | no | — |
| 34 | C2×#915 | — | 2 | 2 | no | — |
| 35 | C2×#909 | C22 | 1 | 2 | yes | — |
| 36 | C2×#907 | C22 | 1 | 2 | yes | — |
| 37 | C2×#869 | C22 | 1 | 1 | yes | characteristic |
| 38 | C3×#456 | C22 | 1 | 8 | yes | complemented |
| 39 | C2×C3×#104 | C22 | 1 | 2 | yes | — |
| 40 | C2×C3×#101 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×#836 | C22 | 1 | 1 | yes | characteristic |
| 42 | #5204 | C22 | 1 | 16 | yes | complemented |
| 43 | C2×#824 | C22 | 1 | 2 | yes | — |
| 44 | C2×#822 | C22 | 1 | 2 | yes | — |
| 45 | #5095 | C22 | 1 | 8 | yes | complemented |
| 46 | #5092 | C22 | 1 | 8 | yes | complemented |
| 47 | C2×#805 | C22 | 1 | 2 | yes | — |
| 48 | C2×C4×C3⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 49 | #4826 | C22 | 1 | 16 | yes | complemented |
| 50 | #4824 | C22 | 1 | 16 | yes | complemented |
| 51 | #4755 | C22 | 1 | 16 | yes | complemented |
| 52 | C2×#578 | — | 3 | 2 | no | — |
| 53 | C2×#578 | — | 3 | 2 | no | — |
| 54 | #3293 | — | 3 | 16 | no | — |
| 55 | C2×#494 | — | 3 | 1 | no | — |
| 56 | C2×#473 | — | 3 | 2 | no | — |
| 57 | C2×#473 | — | 3 | 2 | no | — |
| 58 | C2×#456 | — | 3 | 2 | no | — |
| 59 | C2×#456 | — | 3 | 1 | no | — |
| 60 | C2×#456 | D3 | 1 | 1 | yes | characteristic, complemented |
| 61 | C2×#443 | — | 3 | 2 | no | — |
| 62 | C3×2−1+4 | — | 2 | 4 | no | — |
| 63 | C3×2−1+4 | — | 4 | 1 | no | — |
| 64 | C3×2−1+4 | C23 | 1 | 4 | yes | — |
| 65 | C2×C3×#41 | — | 2 | 2 | no | — |
| 66 | C2×C3×#41 | — | 4 | 1 | no | — |
| 67 | C2×C3×#41 | C23 | 1 | 2 | yes | — |
| 68 | C22×C3×Q8 | — | 2 | 2 | no | — |
| 69 | C22×C3×Q8 | C23 | 1 | 1 | yes | characteristic |
| 70 | C22×C3×Q8 | C23 | 1 | 1 | yes | characteristic |
| 71 | #1010 | — | 2 | 4 | no | — |
| 72 | #1010 | — | 2 | 4 | no | — |
| 73 | #1010 | — | 4 | 2 | no | — |
| 74 | #1010 | C23 | 1 | 8 | yes | — |
| 75 | #1007 | — | 2 | 4 | no | — |
| 76 | #1007 | — | 4 | 1 | no | — |
| 77 | #1007 | C23 | 1 | 4 | yes | — |
| 78 | C2×#239 | — | 2 | 2 | no | — |
| 79 | C2×D3×Q8 | — | 2 | 2 | no | — |
| 80 | C2×D3×Q8 | — | 2 | 2 | no | — |
| 81 | C2×#237 | — | 2 | 2 | no | — |
| 82 | C2×#237 | — | 4 | 2 | no | — |
| 83 | C2×#235 | — | 2 | 2 | no | — |
| 84 | C2×#235 | — | 4 | 1 | no | — |
| 85 | C2×#235 | C23 | 1 | 2 | yes | — |
| 86 | C22×Dic6 | — | 2 | 2 | no | — |
| 87 | C22×Dic6 | C23 | 1 | 2 | yes | — |
| 88 | C3×#137 | — | 2 | 4 | no | — |
| 89 | C3×#137 | C23 | 1 | 8 | yes | — |
| 90 | C2×C3×Q16 | — | 2 | 2 | no | — |
| 91 | C2×C3×SD16 | — | 2 | 2 | no | — |
| 92 | C2×C3×M16 | C23 | 1 | 2 | yes | — |
| 93 | C3×C4⋊Q8 | — | 4 | 1 | no | — |
| 94 | C3×C4⋊Q8 | C23 | 1 | 4 | yes | — |
| 95 | C2×C3×C4⋊C4 | — | 4 | 1 | no | — |
| 96 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 97 | #951 | — | 2 | 4 | no | — |
| 98 | #951 | — | 2 | 16 | no | — |
| 99 | #951 | C23 | 1 | 8 | yes | — |
| 100 | #950 | — | 2 | 16 | no | — |
| 101 | #950 | D4 | 1 | 8 | yes | — |
| 102 | #950 | C23 | 1 | 8 | yes | — |
| 103 | #948 | — | 2 | 4 | no | — |
| 104 | #948 | C23 | 1 | 8 | yes | — |
| 105 | C2×#216 | — | 2 | 2 | no | — |
| 106 | C2×#216 | — | 2 | 2 | no | — |
| 107 | C2×#216 | — | 2 | 16 | no | — |
| 108 | C2×#216 | — | 2 | 2 | no | — |
| 109 | C2×#216 | — | 2 | 2 | no | — |
| 110 | C2×#216 | — | 2 | 4 | no | — |
| 111 | C2×#216 | — | 2 | 2 | no | — |
| 112 | C2×#216 | — | 2 | 2 | no | — |
| 113 | C2×#216 | — | 2 | 4 | no | — |
| 114 | C2×#216 | D4 | 1 | 2 | yes | — |
| 115 | C2×#216 | C23 | 1 | 8 | yes | — |
| 116 | C2×#216 | C23 | 1 | 8 | yes | — |
| 117 | #942 | — | 2 | 4 | no | — |
| 118 | #942 | — | 2 | 16 | no | — |
| 119 | #942 | C23 | 1 | 8 | yes | — |
| 120 | C2×#215 | — | 2 | 2 | no | — |
| 121 | C2×#215 | D4 | 1 | 2 | yes | — |
| 122 | C2×#214 | — | 2 | 2 | no | — |
| 123 | C2×#214 | D4 | 1 | 2 | yes | — |
| 124 | C2×#213 | D4 | 1 | 2 | yes | — |
| 125 | C2×C4⋊Dic3 | — | 4 | 1 | no | — |
| 126 | C2×#208 | — | 2 | 2 | no | — |
| 127 | C2×#208 | C23 | 1 | 2 | yes | — |
| 128 | C22×C3⋊C8 | — | 2 | 2 | no | — |
| 129 | C22×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 130 | #918 | — | 2 | 16 | no | — |
| 131 | D3×Q16 | — | 2 | 16 | no | — |
| 132 | #916 | — | 2 | 16 | no | — |
| 133 | #915 | — | 2 | 16 | no | — |
| 134 | #909 | — | 2 | 4 | no | — |
| 135 | #909 | C23 | 1 | 8 | yes | — |
| 136 | #907 | — | 2 | 4 | no | — |
| 137 | #907 | C23 | 1 | 8 | yes | — |
| 138 | C2×Dic12 | — | 2 | 2 | no | — |
| 139 | C2×#204 | — | 2 | 2 | no | — |
| 140 | C2×ΓL(1,𝔽25) | — | 2 | 2 | no | — |
| 141 | C2×D3×C8 | — | 2 | 2 | no | — |
| 142 | #869 | — | 4 | 1 | no | — |
| 143 | #869 | C23 | 1 | 4 | yes | — |
| 144 | C3×#104 | C23 | 1 | 8 | yes | — |
| 145 | C3×#101 | C23 | 1 | 4 | yes | — |
| 146 | #836 | C23 | 1 | 4 | yes | — |
| 147 | #824 | C23 | 1 | 8 | yes | — |
| 148 | #822 | C23 | 1 | 8 | yes | — |
| 149 | #805 | C23 | 1 | 8 | yes | — |
| 150 | C4×C3⋊C8 | C23 | 1 | 4 | yes | — |
| 151 | C2×2−1+4 | — | 3 | 2 | no | — |
| 152 | C2×2−1+4 | — | 3 | 1 | no | — |
| 153 | C2×2−1+4 | C2×D3 | 1 | 1 | yes | characteristic |
| 154 | #578 | — | 3 | 16 | no | — |
| 155 | #578 | — | 3 | 16 | no | — |
| 156 | #578 | — | 6 | 8 | no | — |
| 157 | #578 | — | 6 | 8 | no | — |
| 158 | C2×#137 | — | 3 | 2 | no | — |
| 159 | C2×#137 | — | 3 | 2 | no | — |
| 160 | C2×#137 | — | 3 | 2 | no | — |
| 161 | C2×#137 | — | 6 | 2 | no | — |
| 162 | C2×#137 | — | 6 | 2 | no | — |
| 163 | C2×#137 | — | 6 | 2 | no | — |
| 164 | C2×#137 | — | 6 | 2 | no | — |
| 165 | C2×#137 | C2×D3 | 1 | 2 | yes | — |
| 166 | C2×#135 | — | 3 | 2 | no | — |
| 167 | C2×#135 | — | 6 | 2 | no | — |
| 168 | C2×#135 | — | 6 | 2 | no | — |
| 169 | C22×Q16 | — | 3 | 2 | no | — |
| 170 | C22×Q16 | — | 3 | 2 | no | — |
| 171 | C22×Q16 | — | 6 | 2 | no | — |
| 172 | C22×Q16 | — | 6 | 2 | no | — |
| 173 | C2×#131 | — | 3 | 2 | no | — |
| 174 | C2×#131 | — | 3 | 2 | no | — |
| 175 | C2×C4⋊Q8 | — | 3 | 1 | no | — |
| 176 | C2×C4⋊Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 177 | #494 | — | 3 | 8 | no | — |
| 178 | #473 | — | 3 | 16 | no | — |
| 179 | #473 | — | 3 | 16 | no | — |
| 180 | #456 | — | 3 | 8 | no | — |
| 181 | #456 | — | 3 | 16 | no | — |
| 182 | #456 | C2×D3 | 1 | 8 | yes | complemented |
| 183 | #443 | — | 3 | 16 | no | — |
| 184 | C2×#108 | — | 3 | 2 | no | — |
| 185 | C2×#104 | — | 3 | 2 | no | — |
| 186 | C2×#104 | C2×D3 | 1 | 2 | yes | — |
| 187 | C2×#101 | — | 3 | 1 | no | — |
| 188 | C2×#101 | — | 3 | 2 | no | — |
| 189 | C2×#101 | C2×D3 | 1 | 1 | yes | characteristic |
| 190 | C2×C4×C8 | — | 3 | 1 | no | — |
| 191 | C3×#41 | — | 2 | 2 | no | — |
| 192 | C3×#41 | — | 2 | 2 | no | — |
| 193 | C3×#41 | — | 2 | 8 | no | — |
| 194 | C3×#41 | — | 4 | 4 | no | — |
| 195 | C3×#41 | — | 4 | 4 | no | — |
| 196 | C3×#41 | — | 4 | 4 | no | — |
| 197 | C3×#41 | C2×D4 | 1 | 4 | yes | — |
| 198 | C3×#41 | C24 | 1 | 4 | yes | — |
| 199 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 200 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 201 | C2×C3×Q8 | — | 2 | 8 | no | — |
| 202 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 203 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 204 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 205 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 206 | C2×C3×Q8 | — | 4 | 1 | no | — |
| 207 | C2×C3×Q8 | — | 4 | 4 | no | — |
| 208 | C2×C3×Q8 | C2×D4 | 1 | 2 | yes | — |
| 209 | C2×C3×Q8 | C24 | 1 | 2 | yes | — |
| 210 | C2×C3×Q8 | C24 | 1 | 2 | yes | — |
| 211 | C2×C3×D4 | — | 2 | 2 | no | — |
| 212 | C2×C3×D4 | — | 4 | 1 | no | — |
| 213 | C2×C3×D4 | C2×D4 | 1 | 2 | yes | — |
| 214 | C22×C3×C4 | — | 2 | 1 | no | — |
| 215 | C22×C3×C4 | — | 2 | 2 | no | — |
| 216 | C22×C3×C4 | — | 2 | 1 | no | — |
| 217 | C22×C3×C4 | — | 2 | 1 | no | — |
| 218 | C22×C3×C4 | — | 4 | 2 | no | — |
| 219 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 220 | C2×#67 | — | 2 | 2 | no | — |
| 221 | C2×#67 | — | 4 | 2 | no | — |
| 222 | C22×Dic3 | — | 2 | 2 | no | — |
| 223 | C22×Dic3 | — | 4 | 2 | no | — |
| 224 | #239 | — | 2 | 8 | no | — |
| 225 | #239 | — | 4 | 4 | no | — |
| 226 | D3×Q8 | — | 2 | 8 | no | — |
| 227 | D3×Q8 | — | 2 | 8 | no | — |
| 228 | D3×Q8 | — | 4 | 4 | no | — |
| 229 | D3×Q8 | — | 4 | 4 | no | — |
| 230 | #237 | — | 2 | 8 | no | — |
| 231 | #237 | — | 4 | 4 | no | — |
| 232 | #237 | — | 4 | 8 | no | — |
| 233 | #237 | — | 4 | 8 | no | — |
| 234 | #235 | — | 2 | 2 | no | — |
| 235 | #235 | — | 2 | 2 | no | — |
| 236 | #235 | — | 2 | 8 | no | — |
| 237 | #235 | — | 4 | 4 | no | — |
| 238 | #235 | — | 4 | 4 | no | — |
| 239 | #235 | — | 4 | 4 | no | — |
| 240 | #235 | C2×D4 | 1 | 4 | yes | — |
| 241 | #235 | C24 | 1 | 4 | yes | — |
| 242 | C2×D12 | — | 4 | 1 | no | — |
| 243 | C2×D12 | C2×D4 | 1 | 2 | yes | — |
| 244 | C2×C4×D3 | — | 2 | 2 | no | — |
| 245 | C2×C4×D3 | — | 4 | 2 | no | — |
| 246 | C2×C4×D3 | — | 4 | 2 | no | — |
| 247 | C2×Dic6 | — | 2 | 2 | no | — |
| 248 | C2×Dic6 | — | 2 | 2 | no | — |
| 249 | C2×Dic6 | — | 2 | 2 | no | — |
| 250 | C2×Dic6 | — | 2 | 2 | no | — |
| 251 | C2×Dic6 | — | 2 | 8 | no | — |
| 252 | C2×Dic6 | — | 2 | 2 | no | — |
| 253 | C2×Dic6 | — | 4 | 4 | no | — |
| 254 | C2×Dic6 | — | 4 | 1 | no | — |
| 255 | C2×Dic6 | — | 4 | 2 | no | — |
| 256 | C2×Dic6 | C2×D4 | 1 | 2 | yes | — |
| 257 | C2×Dic6 | C24 | 1 | 4 | yes | — |
| 258 | C3×Q16 | — | 2 | 8 | no | — |
| 259 | C3×SD16 | — | 2 | 8 | no | — |
| 260 | C3×M16 | — | 2 | 2 | no | — |
| 261 | C3×M16 | C24 | 1 | 4 | yes | — |
| 262 | C2×C3×C8 | — | 2 | 2 | no | — |
| 263 | C3×C4⋊C4 | — | 4 | 4 | no | — |
| 264 | C3×C42 | — | 2 | 1 | no | — |
| 265 | C3×C42 | C24 | 1 | 2 | yes | — |
| 266 | #216 | — | 2 | 8 | no | — |
| 267 | #216 | — | 2 | 8 | no | — |
| 268 | #216 | — | 2 | 8 | no | — |
| 269 | #216 | — | 2 | 8 | no | — |
| 270 | #216 | — | 2 | 8 | no | — |
| 271 | #216 | — | 2 | 8 | no | — |
| 272 | #216 | C2×D4 | 1 | 8 | yes | — |
| 273 | #215 | — | 2 | 8 | no | — |
| 274 | #215 | C2×D4 | 1 | 8 | yes | — |
| 275 | #214 | — | 2 | 8 | no | — |
| 276 | #214 | C2×D4 | 1 | 8 | yes | — |
| 277 | #213 | C2×D4 | 1 | 8 | yes | — |
| 278 | C4⋊Dic3 | — | 4 | 4 | no | — |
| 279 | #208 | — | 2 | 2 | no | — |
| 280 | #208 | — | 2 | 8 | no | — |
| 281 | #208 | C24 | 1 | 4 | yes | — |
| 282 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 283 | C2×C3⋊C8 | — | 2 | 8 | no | — |
| 284 | C2×C3⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 285 | C2×C3⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 286 | C2×C3⋊C8 | C2×D4 | 1 | 4 | yes | — |
| 287 | C2×C3⋊C8 | C24 | 1 | 4 | yes | — |
| 288 | Dic12 | — | 2 | 8 | no | — |
| 289 | #204 | — | 2 | 8 | no | — |
| 290 | ΓL(1,𝔽25) | — | 2 | 8 | no | — |
| 291 | D3×C8 | — | 2 | 8 | no | — |
| 292 | 2−1+4 | — | 2 | 4 | no | — |
| 293 | 2−1+4 | — | 3 | 8 | no | — |
| 294 | 2−1+4 | — | 3 | 4 | no | — |
| 295 | 2−1+4 | — | 4 | 1 | no | — |
| 296 | 2−1+4 | — | 6 | 4 | no | — |
| 297 | 2−1+4 | — | 6 | 4 | no | — |
| 298 | 2−1+4 | — | 6 | 4 | no | — |
| 299 | 2−1+4 | — | 12 | 1 | no | — |
| 300 | 2−1+4 | — | 12 | 2 | no | — |
| 301 | 2−1+4 | C22×D3 | 1 | 4 | yes | — |
| 302 | C2×#41 | — | 2 | 2 | no | — |
| 303 | C2×#41 | — | 3 | 2 | no | — |
| 304 | C2×#41 | — | 4 | 1 | no | — |
| 305 | C2×#41 | — | 6 | 2 | no | — |
| 306 | C2×#41 | — | 6 | 2 | no | — |
| 307 | C2×#41 | — | 6 | 2 | no | — |
| 308 | C2×#41 | — | 12 | 1 | no | — |
| 309 | C2×#41 | — | 12 | 2 | no | — |
| 310 | C2×#41 | C22×D3 | 1 | 2 | yes | — |
| 311 | C22×Q8 | — | 2 | 2 | no | — |
| 312 | C22×Q8 | — | 3 | 2 | no | — |
| 313 | C22×Q8 | — | 6 | 2 | no | — |
| 314 | C22×Q8 | — | 6 | 2 | no | — |
| 315 | C22×Q8 | — | 6 | 2 | no | — |
| 316 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 317 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 318 | #137 | — | 2 | 4 | no | — |
| 319 | #137 | — | 3 | 8 | no | — |
| 320 | #137 | — | 3 | 8 | no | — |
| 321 | #137 | — | 3 | 8 | no | — |
| 322 | #137 | — | 6 | 4 | no | — |
| 323 | #137 | — | 6 | 16 | no | — |
| 324 | #137 | — | 6 | 16 | no | — |
| 325 | #137 | — | 6 | 16 | no | — |
| 326 | #137 | — | 6 | 16 | no | — |
| 327 | #137 | — | 6 | 4 | no | — |
| 328 | #137 | — | 6 | 4 | no | — |
| 329 | #137 | C22×D3 | 1 | 8 | yes | — |
| 330 | #135 | — | 3 | 8 | no | — |
| 331 | #135 | — | 3 | 8 | no | — |
| 332 | #135 | — | 6 | 16 | no | — |
| 333 | #135 | — | 6 | 16 | no | — |
| 334 | C2×Q16 | — | 2 | 2 | no | — |
| 335 | C2×Q16 | — | 3 | 2 | no | — |
| 336 | C2×Q16 | — | 3 | 8 | no | — |
| 337 | C2×Q16 | — | 3 | 8 | no | — |
| 338 | C2×Q16 | — | 6 | 2 | no | — |
| 339 | C2×Q16 | — | 6 | 2 | no | — |
| 340 | C2×Q16 | — | 6 | 2 | no | — |
| 341 | C2×Q16 | — | 6 | 2 | no | — |
| 342 | C2×Q16 | — | 6 | 2 | no | — |
| 343 | C2×Q16 | — | 6 | 4 | no | — |
| 344 | C2×Q16 | — | 6 | 4 | no | — |
| 345 | C2×Q16 | — | 6 | 16 | no | — |
| 346 | C2×Q16 | — | 6 | 16 | no | — |
| 347 | C2×Q16 | — | 6 | 2 | no | — |
| 348 | C2×Q16 | — | 6 | 2 | no | — |
| 349 | C2×SD16 | — | 2 | 2 | no | — |
| 350 | C2×SD16 | — | 3 | 2 | no | — |
| 351 | C2×SD16 | — | 3 | 2 | no | — |
| 352 | C2×SD16 | — | 6 | 2 | no | — |
| 353 | C2×SD16 | — | 6 | 2 | no | — |
| 354 | C2×SD16 | — | 6 | 2 | no | — |
| 355 | C2×D8 | — | 3 | 2 | no | — |
| 356 | #131 | — | 3 | 8 | no | — |
| 357 | #131 | — | 3 | 8 | no | — |
| 358 | #131 | — | 6 | 4 | no | — |
| 359 | #131 | — | 6 | 4 | no | — |
| 360 | C2×M16 | — | 3 | 2 | no | — |
| 361 | C2×M16 | — | 6 | 2 | no | — |
| 362 | C2×M16 | — | 6 | 2 | no | — |
| 363 | C2×M16 | C22×D3 | 1 | 2 | yes | — |
| 364 | C22×C8 | — | 3 | 2 | no | — |
| 365 | C22×C8 | — | 6 | 2 | no | — |
| 366 | C22×C8 | — | 6 | 2 | no | — |
| 367 | C4⋊Q8 | — | 3 | 4 | no | — |
| 368 | C4⋊Q8 | — | 4 | 1 | no | — |
| 369 | C4⋊Q8 | — | 12 | 1 | no | — |
| 370 | C4⋊Q8 | C22×D3 | 1 | 4 | yes | — |
| 371 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 372 | C2×C4⋊C4 | — | 12 | 1 | no | — |
| 373 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 374 | #108 | — | 3 | 8 | no | — |
| 375 | #104 | — | 3 | 8 | no | — |
| 376 | #104 | C22×D3 | 1 | 8 | yes | — |
| 377 | #101 | — | 3 | 4 | no | — |
| 378 | #101 | — | 3 | 8 | no | — |
| 379 | #101 | C22×D3 | 1 | 4 | yes | — |
| 380 | C4×C8 | — | 3 | 4 | no | — |
| 381 | C23×C3 | — | 2 | 2 | no | — |
| 382 | C23×C3 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 383 | C22×D3 | — | 2 | 2 | no | — |
| 384 | C3×Q8 | — | 2 | 2 | no | — |
| 385 | C3×Q8 | — | 2 | 4 | no | — |
| 386 | C3×Q8 | — | 2 | 4 | no | — |
| 387 | C3×Q8 | — | 4 | 4 | no | — |
| 388 | C3×Q8 | — | 4 | 2 | no | — |
| 389 | C3×Q8 | — | 4 | 2 | no | — |
| 390 | C3×Q8 | C22×D4 | 1 | 4 | yes | — |
| 391 | C3×D4 | — | 2 | 4 | no | — |
| 392 | C3×D4 | — | 2 | 4 | no | — |
| 393 | C3×D4 | — | 2 | 2 | no | — |
| 394 | C3×D4 | — | 4 | 4 | no | — |
| 395 | C3×D4 | C22×D4 | 1 | 4 | yes | — |
| 396 | C2×C3×C4 | — | 2 | 4 | no | — |
| 397 | C2×C3×C4 | — | 2 | 2 | no | — |
| 398 | C2×C3×C4 | — | 2 | 2 | no | — |
| 399 | C2×C3×C4 | — | 2 | 4 | no | — |
| 400 | C2×C3×C4 | — | 2 | 4 | no | — |
| 401 | C2×C3×C4 | — | 2 | 2 | no | — |
| 402 | C2×C3×C4 | — | 2 | 2 | no | — |
| 403 | C2×C3×C4 | — | 4 | 8 | no | — |
| 404 | C2×C3×C4 | — | 4 | 1 | no | — |
| 405 | C2×C3×C4 | — | 4 | 1 | no | — |
| 406 | C2×C3×C4 | — | 4 | 1 | no | — |
| 407 | C2×C3×C4 | — | 4 | 1 | no | — |
| 408 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 409 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 410 | C2×C3×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 411 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 412 | #67 | — | 2 | 4 | no | — |
| 413 | #67 | — | 2 | 4 | no | — |
| 414 | #67 | — | 4 | 8 | no | — |
| 415 | C2×Dic3 | — | 2 | 2 | no | — |
| 416 | C2×Dic3 | — | 2 | 4 | no | — |
| 417 | C2×Dic3 | — | 4 | 8 | no | — |
| 418 | C2×Dic3 | — | 4 | 2 | no | — |
| 419 | C2×Dic3 | — | 4 | 2 | no | — |
| 420 | D12 | — | 2 | 2 | no | — |
| 421 | D12 | — | 4 | 4 | no | — |
| 422 | D12 | C22×D4 | 1 | 4 | yes | — |
| 423 | C4×D3 | — | 2 | 4 | no | — |
| 424 | C4×D3 | — | 2 | 4 | no | — |
| 425 | C4×D3 | — | 4 | 8 | no | — |
| 426 | C4×D3 | — | 4 | 8 | no | — |
| 427 | Dic6 | — | 2 | 2 | no | — |
| 428 | Dic6 | — | 2 | 4 | no | — |
| 429 | Dic6 | — | 2 | 4 | no | — |
| 430 | Dic6 | — | 4 | 4 | no | — |
| 431 | Dic6 | — | 4 | 8 | no | — |
| 432 | Dic6 | — | 4 | 2 | no | — |
| 433 | Dic6 | — | 4 | 2 | no | — |
| 434 | Dic6 | C22×D4 | 1 | 4 | yes | — |
| 435 | C3×C8 | — | 2 | 4 | no | — |
| 436 | C3⋊C8 | — | 2 | 4 | no | — |
| 437 | C3⋊C8 | C22×D4 | 1 | 4 | yes | — |
| 438 | C3⋊C8 | C22×D4 | 1 | 4 | yes | — |
| 439 | #41 | — | 2 | 2 | no | — |
| 440 | #41 | — | 2 | 2 | no | — |
| 441 | #41 | — | 2 | 8 | no | — |
| 442 | #41 | — | 3 | 4 | no | — |
| 443 | #41 | — | 3 | 4 | no | — |
| 444 | #41 | — | 4 | 4 | no | — |
| 445 | #41 | — | 4 | 4 | no | — |
| 446 | #41 | — | 4 | 4 | no | — |
| 447 | #41 | — | 6 | 8 | no | — |
| 448 | #41 | — | 6 | 2 | no | — |
| 449 | #41 | — | 6 | 2 | no | — |
| 450 | #41 | — | 6 | 8 | no | — |
| 451 | #41 | — | 6 | 8 | no | — |
| 452 | #41 | — | 12 | 4 | no | — |
| 453 | #41 | — | 12 | 4 | no | — |
| 454 | #41 | — | 12 | 4 | no | — |
| 455 | #41 | — | 12 | 8 | no | — |
| 456 | #41 | — | 12 | 4 | no | — |
| 457 | #41 | — | 12 | 4 | no | — |
| 458 | #41 | — | 12 | 8 | no | — |
| 459 | #41 | D3×D4 | 1 | 4 | yes | — |
| 460 | #41 | C23×D3 | 1 | 4 | yes | — |
| 461 | C2×Q8 | — | 2 | 1 | no | — |
| 462 | C2×Q8 | — | 2 | 1 | no | — |
| 463 | C2×Q8 | — | 2 | 8 | no | — |
| 464 | C2×Q8 | — | 2 | 2 | no | — |
| 465 | C2×Q8 | — | 2 | 2 | no | — |
| 466 | C2×Q8 | — | 2 | 2 | no | — |
| 467 | C2×Q8 | — | 2 | 2 | no | — |
| 468 | C2×Q8 | — | 3 | 2 | no | — |
| 469 | C2×Q8 | — | 3 | 4 | no | — |
| 470 | C2×Q8 | — | 4 | 1 | no | — |
| 471 | C2×Q8 | — | 4 | 4 | no | — |
| 472 | C2×Q8 | — | 6 | 8 | no | — |
| 473 | C2×Q8 | — | 6 | 2 | no | — |
| 474 | C2×Q8 | — | 6 | 8 | no | — |
| 475 | C2×Q8 | — | 6 | 8 | no | — |
| 476 | C2×Q8 | — | 6 | 2 | no | — |
| 477 | C2×Q8 | — | 6 | 2 | no | — |
| 478 | C2×Q8 | — | 6 | 2 | no | — |
| 479 | C2×Q8 | — | 6 | 2 | no | — |
| 480 | C2×Q8 | — | 12 | 2 | no | — |
| 481 | C2×Q8 | — | 12 | 4 | no | — |
| 482 | C2×Q8 | — | 12 | 1 | no | — |
| 483 | C2×Q8 | — | 12 | 4 | no | — |
| 484 | C2×Q8 | — | 12 | 4 | no | — |
| 485 | C2×Q8 | D3×D4 | 1 | 2 | yes | — |
| 486 | C2×Q8 | C23×D3 | 1 | 2 | yes | — |
| 487 | C2×Q8 | C23×D3 | 1 | 2 | yes | — |
| 488 | C2×D4 | — | 2 | 2 | no | — |
| 489 | C2×D4 | — | 3 | 2 | no | — |
| 490 | C2×D4 | — | 4 | 1 | no | — |
| 491 | C2×D4 | — | 6 | 2 | no | — |
| 492 | C2×D4 | — | 12 | 1 | no | — |
| 493 | C2×D4 | — | 12 | 2 | no | — |
| 494 | C2×D4 | D3×D4 | 1 | 2 | yes | — |
| 495 | C22×C4 | — | 2 | 1 | no | — |
| 496 | C22×C4 | — | 2 | 2 | no | — |
| 497 | C22×C4 | — | 2 | 1 | no | — |
| 498 | C22×C4 | — | 2 | 1 | no | — |
| 499 | C22×C4 | — | 4 | 2 | no | — |
| 500 | C22×C4 | — | 6 | 2 | no | — |
| 501 | C22×C4 | — | 6 | 2 | no | — |
| 502 | C22×C4 | — | 12 | 2 | no | — |
| 503 | C22×C4 | — | 12 | 2 | no | — |
| 504 | C22×C4 | — | 12 | 2 | no | — |
| 505 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 506 | Q16 | — | 2 | 8 | no | — |
| 507 | Q16 | — | 3 | 8 | no | — |
| 508 | Q16 | — | 6 | 8 | no | — |
| 509 | Q16 | — | 6 | 8 | no | — |
| 510 | Q16 | — | 6 | 8 | no | — |
| 511 | Q16 | — | 6 | 8 | no | — |
| 512 | Q16 | — | 6 | 8 | no | — |
| 513 | Q16 | — | 6 | 8 | no | — |
| 514 | Q16 | — | 6 | 8 | no | — |
| 515 | SD16 | — | 2 | 8 | no | — |
| 516 | SD16 | — | 3 | 8 | no | — |
| 517 | SD16 | — | 3 | 8 | no | — |
| 518 | SD16 | — | 6 | 8 | no | — |
| 519 | SD16 | — | 6 | 8 | no | — |
| 520 | SD16 | — | 6 | 8 | no | — |
| 521 | D8 | — | 3 | 8 | no | — |
| 522 | M16 | — | 2 | 2 | no | — |
| 523 | M16 | — | 3 | 4 | no | — |
| 524 | M16 | — | 6 | 8 | no | — |
| 525 | M16 | — | 6 | 8 | no | — |
| 526 | M16 | — | 6 | 2 | no | — |
| 527 | M16 | C23×D3 | 1 | 4 | yes | — |
| 528 | C2×C8 | — | 2 | 2 | no | — |
| 529 | C2×C8 | — | 3 | 2 | no | — |
| 530 | C2×C8 | — | 3 | 2 | no | — |
| 531 | C2×C8 | — | 3 | 4 | no | — |
| 532 | C2×C8 | — | 3 | 4 | no | — |
| 533 | C2×C8 | — | 6 | 8 | no | — |
| 534 | C2×C8 | — | 6 | 8 | no | — |
| 535 | C2×C8 | — | 6 | 2 | no | — |
| 536 | C4⋊C4 | — | 4 | 4 | no | — |
| 537 | C4⋊C4 | — | 12 | 4 | no | — |
| 538 | C42 | — | 2 | 1 | no | — |
| 539 | C42 | C23×D3 | 1 | 2 | yes | — |
| 540 | C22×C3 | — | 2 | 2 | no | — |
| 541 | C22×C3 | — | 2 | 4 | no | — |
| 542 | C22×C3 | — | 4 | 4 | no | — |
| 543 | C22×C3 | D42 | 1 | 1 | yes | characteristic |
| 544 | C22×C3 | D42 | 1 | 1 | yes | characteristic |
| 545 | C22×C3 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 546 | C2×D3 | — | 2 | 4 | no | — |
| 547 | C2×D3 | — | 4 | 4 | no | — |
| 548 | C3×C4 | — | 2 | 4 | no | — |
| 549 | C3×C4 | — | 2 | 4 | no | — |
| 550 | C3×C4 | — | 4 | 2 | no | — |
| 551 | C3×C4 | — | 4 | 2 | no | — |
| 552 | C3×C4 | D42 | 1 | 2 | yes | — |
| 553 | C3×C4 | C23×D4 | 1 | 2 | yes | — |
| 554 | Dic3 | — | 2 | 4 | no | — |
| 555 | Dic3 | — | 4 | 4 | no | — |
| 556 | C23 | — | 2 | 2 | no | — |
| 557 | C23 | — | 6 | 2 | no | — |
| 558 | C23 | #1004 | 1 | 1 | yes | characteristic |
| 559 | Q8 | — | 2 | 2 | no | — |
| 560 | Q8 | — | 2 | 4 | no | — |
| 561 | Q8 | — | 2 | 4 | no | — |
| 562 | Q8 | — | 3 | 4 | no | — |
| 563 | Q8 | — | 4 | 4 | no | — |
| 564 | Q8 | — | 4 | 2 | no | — |
| 565 | Q8 | — | 4 | 2 | no | — |
| 566 | Q8 | — | 6 | 2 | no | — |
| 567 | Q8 | — | 6 | 4 | no | — |
| 568 | Q8 | — | 6 | 4 | no | — |
| 569 | Q8 | — | 12 | 8 | no | — |
| 570 | Q8 | — | 12 | 4 | no | — |
| 571 | Q8 | — | 12 | 2 | no | — |
| 572 | Q8 | — | 12 | 2 | no | — |
| 573 | Q8 | C2×D3×D4 | 1 | 4 | yes | — |
| 574 | D4 | — | 2 | 4 | no | — |
| 575 | D4 | — | 2 | 4 | no | — |
| 576 | D4 | — | 2 | 2 | no | — |
| 577 | D4 | — | 3 | 4 | no | — |
| 578 | D4 | — | 4 | 4 | no | — |
| 579 | D4 | — | 6 | 4 | no | — |
| 580 | D4 | — | 6 | 4 | no | — |
| 581 | D4 | — | 6 | 2 | no | — |
| 582 | D4 | — | 12 | 4 | no | — |
| 583 | D4 | — | 12 | 8 | no | — |
| 584 | D4 | C2×D3×D4 | 1 | 4 | yes | — |
| 585 | C2×C4 | — | 2 | 4 | no | — |
| 586 | C2×C4 | — | 2 | 2 | no | — |
| 587 | C2×C4 | — | 2 | 2 | no | — |
| 588 | C2×C4 | — | 2 | 4 | no | — |
| 589 | C2×C4 | — | 2 | 4 | no | — |
| 590 | C2×C4 | — | 2 | 2 | no | — |
| 591 | C2×C4 | — | 2 | 2 | no | — |
| 592 | C2×C4 | — | 4 | 8 | no | — |
| 593 | C2×C4 | — | 4 | 1 | no | — |
| 594 | C2×C4 | — | 4 | 1 | no | — |
| 595 | C2×C4 | — | 4 | 1 | no | — |
| 596 | C2×C4 | — | 4 | 1 | no | — |
| 597 | C2×C4 | — | 6 | 2 | no | — |
| 598 | C2×C4 | — | 6 | 4 | no | — |
| 599 | C2×C4 | — | 6 | 4 | no | — |
| 600 | C2×C4 | — | 6 | 4 | no | — |
| 601 | C2×C4 | — | 12 | 8 | no | — |
| 602 | C2×C4 | — | 12 | 8 | no | — |
| 603 | C2×C4 | — | 12 | 8 | no | — |
| 604 | C2×C4 | — | 12 | 2 | no | — |
| 605 | C2×C4 | — | 12 | 2 | no | — |
| 606 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 607 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 608 | C2×C4 | #1004 | 1 | 1 | yes | characteristic |
| 609 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 610 | C8 | — | 2 | 4 | no | — |
| 611 | C8 | — | 3 | 4 | no | — |
| 612 | C8 | — | 3 | 4 | no | — |
| 613 | C8 | — | 6 | 4 | no | — |
| 614 | C2×C3 | — | 2 | 1 | no | — |
| 615 | C2×C3 | — | 2 | 1 | no | — |
| 616 | C2×C3 | — | 4 | 4 | no | — |
| 617 | C2×C3 | #3293 | 1 | 2 | yes | complemented |
| 618 | C2×C3 | C2×D42 | 1 | 1 | yes | characteristic |
| 619 | D3 | — | 4 | 4 | no | — |
| 620 | C22 | — | 2 | 2 | no | — |
| 621 | C22 | — | 2 | 4 | no | — |
| 622 | C22 | — | 4 | 4 | no | — |
| 623 | C22 | — | 6 | 4 | no | — |
| 624 | C22 | — | 12 | 4 | no | — |
| 625 | C22 | #5590 | 1 | 1 | yes | characteristic |
| 626 | C22 | #5590 | 1 | 1 | yes | characteristic |
| 627 | C22 | C2×#1004 | 1 | 1 | yes | characteristic |
| 628 | C4 | — | 2 | 4 | no | — |
| 629 | C4 | — | 2 | 4 | no | — |
| 630 | C4 | — | 4 | 2 | no | — |
| 631 | C4 | — | 4 | 2 | no | — |
| 632 | C4 | — | 6 | 4 | no | — |
| 633 | C4 | — | 12 | 4 | no | — |
| 634 | C4 | #5590 | 1 | 2 | yes | — |
| 635 | C4 | C22×D3×D4 | 1 | 2 | yes | — |
| 636 | C3 | C2×#3293 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 637 | C2 | — | 2 | 1 | no | — |
| 638 | C2 | — | 2 | 1 | no | — |
| 639 | C2 | — | 4 | 4 | no | — |
| 640 | C2 | — | 12 | 4 | no | — |
| 641 | C2 | #80303 | 1 | 2 | yes | direct product factor |
| 642 | C2 | C2×#5590 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#5838 | C2 | semidirect |
| 2. C2×#5779 | C2 | semidirect |
| 3. C2×C3×#456 | C2 | semidirect |
| 4. C2×#5204 | C2 | semidirect |
| 5. C2×#5095 | C2 | semidirect |
| 6. C2×#5092 | C2 | semidirect |
| 7. #80303 | C2 | direct (N × H) |
| 8. C2×#4826 | C2 | semidirect |
| 9. C2×#4824 | C2 | semidirect |
| 10. C2×#4755 | C2 | semidirect |
| 18. #5838 | C22 | semidirect |
| 30. #5779 | C22 | semidirect |
| 38. C3×#456 | C22 | semidirect |
| 42. #5204 | C22 | semidirect |
| 45. #5095 | C22 | semidirect |
| 46. #5092 | C22 | semidirect |
| 49. #4826 | C22 | semidirect |
| 50. #4824 | C22 | semidirect |
| 51. #4755 | C22 | semidirect |
| 60. C2×#456 | D3 | semidirect |
| 182. #456 | C2×D3 | semidirect |
| 617. C2×C3 | #3293 | semidirect |
| 636. C3 | C2×#3293 | semidirect |
| 641. C2 | #80303 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5838 | 2 |
| C2×#5779 | 2 |
| C2×C3×#456 | 2 |
| C2×#5204 | 2 |
| C2×#5095 | 2 |
| C2×#5092 | 2 |
| #80303 | 2 |
| C2×#4826 | 2 |
| C2×#4824 | 2 |
| C2×#4755 | 2 |
| C2×#3293 | 3 |