Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1922 conjugacy classes of subgroups.
The subgroup lattice has 650 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#5777 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C22×#919 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#4751 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | D3×#408 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#2020 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72107 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #72074 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #70117 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #70006 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #68942 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | D3×#341 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #23438 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C2×D3×#41 | C22 | 1 | 1 | yes | characteristic |
| 14 | C22×#239 | C22 | 1 | 2 | yes | — |
| 15 | C2×C3×#137 | C22 | 1 | 2 | yes | — |
| 16 | C22×C3×Q16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C2×#949 | C22 | 1 | 2 | yes | — |
| 18 | C2×#942 | C22 | 1 | 2 | yes | — |
| 19 | C22×#215 | C22 | 1 | 2 | yes | complemented |
| 20 | #5777 | — | 2 | 8 | no | — |
| 21 | #5777 | — | 2 | 8 | no | — |
| 22 | C2×#919 | — | 2 | 8 | no | — |
| 23 | C2×#919 | — | 2 | 2 | no | — |
| 24 | C2×#919 | — | 2 | 2 | no | — |
| 25 | C2×#919 | — | 2 | 2 | no | — |
| 26 | C2×#918 | — | 2 | 2 | no | — |
| 27 | C2×#916 | — | 2 | 2 | no | — |
| 28 | C2×#914 | — | 2 | 2 | no | — |
| 29 | C2×#908 | C22 | 1 | 2 | yes | — |
| 30 | C2×D3×M16 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×D3×M16 | C22 | 1 | 2 | yes | — |
| 32 | C22×D24 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | C22×D3×C8 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×C3×#101 | C22 | 1 | 2 | yes | complemented |
| 35 | C3×#408 | C22 | 1 | 1 | yes | characteristic |
| 36 | #5234 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×#836 | C22 | 1 | 2 | yes | complemented |
| 38 | C2×#823 | C22 | 1 | 2 | yes | complemented |
| 39 | C2×#823 | C22 | 1 | 2 | yes | complemented |
| 40 | #5129 | C22 | 1 | 1 | yes | characteristic |
| 41 | #5110 | C22 | 1 | 1 | yes | characteristic |
| 42 | #4751 | — | 2 | 8 | no | — |
| 43 | #4727 | — | 2 | 2 | no | — |
| 44 | D3×C22⋊C8 | — | 2 | 2 | no | — |
| 45 | C3×#341 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #4558 | C22 | 1 | 2 | yes | complemented |
| 47 | #4552 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | C2×#575 | — | 3 | 2 | no | — |
| 49 | C22×#135 | — | 3 | 1 | no | — |
| 50 | C2×#413 | — | 3 | 2 | no | — |
| 51 | C2×#408 | — | 3 | 1 | no | — |
| 52 | #2020 | — | 3 | 1 | no | — |
| 53 | #2020 | D3 | 1 | 1 | yes | characteristic, complemented |
| 54 | #2019 | — | 3 | 2 | no | — |
| 55 | #2019 | — | 3 | 2 | no | — |
| 56 | #2018 | — | 3 | 1 | no | — |
| 57 | #2018 | — | 3 | 1 | no | — |
| 58 | C2×#341 | — | 3 | 1 | no | — |
| 59 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 60 | C22×C3×Q8 | C23 | 1 | 2 | yes | — |
| 61 | D3×#41 | — | 2 | 4 | no | — |
| 62 | D3×#41 | — | 2 | 4 | no | — |
| 63 | C2×#239 | — | 2 | 4 | no | — |
| 64 | C2×#239 | — | 2 | 2 | no | — |
| 65 | C2×#239 | — | 2 | 2 | no | — |
| 66 | C2×#239 | — | 2 | 4 | no | — |
| 67 | C2×#239 | — | 2 | 2 | no | — |
| 68 | C2×#239 | — | 2 | 2 | no | — |
| 69 | C2×#239 | — | 2 | 4 | no | — |
| 70 | C2×#239 | D4 | 1 | 8 | yes | — |
| 71 | C2×#239 | D4 | 1 | 1 | yes | characteristic |
| 72 | C2×D3×Q8 | D4 | 1 | 1 | yes | characteristic |
| 73 | C2×#237 | — | 2 | 1 | no | — |
| 74 | C2×#237 | D4 | 1 | 1 | yes | characteristic |
| 75 | C2×D3×D4 | — | 2 | 1 | no | — |
| 76 | C2×D3×D4 | D4 | 1 | 1 | yes | characteristic |
| 77 | C2×#235 | — | 2 | 1 | no | — |
| 78 | C2×#235 | C23 | 1 | 1 | yes | characteristic |
| 79 | C22×D12 | — | 2 | 2 | no | — |
| 80 | C22×D12 | C23 | 1 | 2 | yes | — |
| 81 | C22×C4×D3 | — | 2 | 2 | no | — |
| 82 | C22×C4×D3 | — | 2 | 1 | no | — |
| 83 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 84 | C3×#137 | — | 2 | 4 | no | — |
| 85 | C3×#137 | — | 2 | 4 | no | — |
| 86 | C2×C3×Q16 | — | 2 | 4 | no | — |
| 87 | C2×C3×Q16 | — | 2 | 2 | no | — |
| 88 | C2×C3×Q16 | — | 2 | 2 | no | — |
| 89 | C2×C3×SD16 | — | 2 | 2 | no | — |
| 90 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 91 | C2×C3×M16 | C23 | 1 | 2 | yes | — |
| 92 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 93 | #949 | — | 2 | 4 | no | — |
| 94 | #949 | — | 2 | 4 | no | — |
| 95 | C2×#216 | — | 2 | 2 | no | — |
| 96 | #942 | — | 2 | 4 | no | — |
| 97 | #942 | — | 2 | 4 | no | — |
| 98 | C2×#215 | — | 2 | 2 | no | — |
| 99 | C2×#215 | — | 2 | 4 | no | — |
| 100 | C2×#215 | — | 2 | 2 | no | — |
| 101 | C2×#215 | — | 2 | 4 | no | — |
| 102 | C2×#215 | — | 2 | 4 | no | — |
| 103 | C2×#213 | — | 2 | 2 | no | — |
| 104 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 105 | C2×#208 | C23 | 1 | 2 | yes | — |
| 106 | C22×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 107 | #919 | — | 2 | 16 | no | — |
| 108 | #919 | — | 2 | 16 | no | — |
| 109 | #919 | — | 2 | 16 | no | — |
| 110 | #918 | — | 2 | 16 | no | — |
| 111 | #916 | — | 2 | 16 | no | — |
| 112 | #914 | — | 2 | 16 | no | — |
| 113 | #908 | — | 2 | 4 | no | — |
| 114 | #908 | — | 2 | 4 | no | — |
| 115 | D3×M16 | — | 2 | 4 | no | — |
| 116 | D3×M16 | — | 2 | 4 | no | — |
| 117 | D3×M16 | D4 | 1 | 8 | yes | — |
| 118 | C2×D24 | — | 2 | 4 | no | — |
| 119 | C2×D24 | — | 2 | 2 | no | — |
| 120 | C2×D24 | — | 2 | 2 | no | — |
| 121 | C2×#204 | — | 2 | 2 | no | — |
| 122 | C2×ΓL(1,𝔽25) | — | 2 | 2 | no | — |
| 123 | C2×ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 124 | C2×D3×C8 | — | 2 | 4 | no | — |
| 125 | C2×D3×C8 | — | 2 | 2 | no | — |
| 126 | C2×D3×C8 | — | 2 | 1 | no | — |
| 127 | C2×D3×C8 | D4 | 1 | 2 | yes | — |
| 128 | C2×D3×C8 | D4 | 1 | 2 | yes | — |
| 129 | C3×#101 | — | 2 | 4 | no | — |
| 130 | C3×C22⋊C8 | — | 2 | 2 | no | — |
| 131 | #836 | — | 2 | 4 | no | — |
| 132 | #830 | — | 2 | 2 | no | — |
| 133 | #823 | — | 2 | 4 | no | — |
| 134 | #823 | — | 2 | 4 | no | — |
| 135 | (C2×D3)⋊C8 | — | 2 | 2 | no | — |
| 136 | (C2×D3)⋊C8 | — | 2 | 2 | no | — |
| 137 | C22×#41 | — | 3 | 1 | no | — |
| 138 | C22×#41 | — | 3 | 2 | no | — |
| 139 | #575 | — | 6 | 8 | no | — |
| 140 | #575 | — | 6 | 8 | no | — |
| 141 | C2×#137 | — | 3 | 2 | no | — |
| 142 | C2×#137 | — | 6 | 2 | no | — |
| 143 | C2×#137 | C2×D3 | 1 | 2 | yes | — |
| 144 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 145 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 146 | C2×AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 147 | C2×#135 | — | 6 | 2 | no | — |
| 148 | C2×#135 | — | 6 | 2 | no | — |
| 149 | C2×#135 | — | 6 | 2 | no | — |
| 150 | C2×#135 | — | 6 | 8 | no | — |
| 151 | C2×#135 | — | 6 | 2 | no | — |
| 152 | C22×Q16 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 153 | C22×SD16 | — | 3 | 2 | no | — |
| 154 | C22×D8 | — | 3 | 1 | no | — |
| 155 | C22×M16 | — | 3 | 2 | no | — |
| 156 | C22×M16 | — | 3 | 1 | no | — |
| 157 | C23×C8 | — | 3 | 1 | no | — |
| 158 | #413 | — | 6 | 8 | no | — |
| 159 | C2×#101 | — | 3 | 2 | no | — |
| 160 | C2×#101 | C2×D3 | 1 | 2 | yes | complemented |
| 161 | C2×#100 | — | 3 | 2 | no | — |
| 162 | C2×#100 | — | 3 | 2 | no | — |
| 163 | #408 | — | 3 | 1 | no | — |
| 164 | #408 | — | 3 | 1 | no | — |
| 165 | #408 | — | 3 | 1 | no | — |
| 166 | #408 | — | 6 | 2 | no | — |
| 167 | #408 | C2×D3 | 1 | 1 | yes | characteristic |
| 168 | C2×C22⋊C8 | — | 6 | 2 | no | — |
| 169 | #341 | — | 3 | 2 | no | — |
| 170 | #341 | — | 3 | 1 | no | — |
| 171 | #341 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 172 | C23×D3 | — | 2 | 2 | no | — |
| 173 | C23×D3 | — | 2 | 1 | no | — |
| 174 | C23×D3 | #41 | 1 | 1 | yes | characteristic |
| 175 | C3×#41 | — | 2 | 2 | no | — |
| 176 | C3×#41 | — | 2 | 2 | no | — |
| 177 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 178 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 179 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 180 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 181 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 182 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 183 | C2×C3×Q8 | C2×D4 | 1 | 4 | yes | — |
| 184 | C2×C3×D4 | — | 2 | 1 | no | — |
| 185 | C2×C3×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 186 | C22×C3×C4 | — | 2 | 2 | no | — |
| 187 | C22×C3×C4 | — | 2 | 1 | no | — |
| 188 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 189 | C2×#67 | — | 2 | 1 | no | — |
| 190 | C2×#67 | — | 2 | 1 | no | — |
| 191 | C2×#67 | — | 2 | 1 | no | — |
| 192 | C22×Dic3 | — | 2 | 1 | no | — |
| 193 | C22×Dic3 | #41 | 1 | 1 | yes | characteristic |
| 194 | #239 | — | 2 | 8 | no | — |
| 195 | #239 | — | 2 | 8 | no | — |
| 196 | #239 | — | 2 | 8 | no | — |
| 197 | #239 | — | 2 | 8 | no | — |
| 198 | #239 | — | 2 | 4 | no | — |
| 199 | #239 | — | 4 | 4 | no | — |
| 200 | #239 | — | 4 | 4 | no | — |
| 201 | #239 | — | 4 | 4 | no | — |
| 202 | #239 | — | 4 | 4 | no | — |
| 203 | D3×Q8 | — | 2 | 4 | no | — |
| 204 | #237 | — | 2 | 4 | no | — |
| 205 | #237 | — | 4 | 4 | no | — |
| 206 | D3×D4 | — | 2 | 4 | no | — |
| 207 | D3×D4 | — | 4 | 4 | no | — |
| 208 | #235 | — | 2 | 2 | no | — |
| 209 | #235 | — | 2 | 2 | no | — |
| 210 | #235 | — | 4 | 2 | no | — |
| 211 | #235 | — | 4 | 2 | no | — |
| 212 | C2×D12 | — | 2 | 2 | no | — |
| 213 | C2×D12 | — | 2 | 2 | no | — |
| 214 | C2×D12 | — | 2 | 2 | no | — |
| 215 | C2×D12 | — | 2 | 2 | no | — |
| 216 | C2×D12 | — | 2 | 8 | no | — |
| 217 | C2×D12 | — | 2 | 1 | no | — |
| 218 | C2×D12 | — | 2 | 2 | no | — |
| 219 | C2×D12 | — | 4 | 2 | no | — |
| 220 | C2×D12 | — | 4 | 2 | no | — |
| 221 | C2×D12 | — | 4 | 4 | no | — |
| 222 | C2×D12 | C2×D4 | 1 | 1 | yes | characteristic |
| 223 | C2×D12 | C2×D4 | 1 | 4 | yes | — |
| 224 | C2×C4×D3 | — | 2 | 1 | no | — |
| 225 | C2×C4×D3 | — | 2 | 1 | no | — |
| 226 | C2×C4×D3 | — | 2 | 1 | no | — |
| 227 | C2×C4×D3 | — | 2 | 8 | no | — |
| 228 | C2×C4×D3 | — | 4 | 2 | no | — |
| 229 | C2×C4×D3 | — | 4 | 4 | no | — |
| 230 | C2×C4×D3 | — | 4 | 2 | no | — |
| 231 | C2×C4×D3 | — | 4 | 2 | no | — |
| 232 | C2×C4×D3 | — | 4 | 2 | no | — |
| 233 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 234 | C2×C4×D3 | C2×D4 | 1 | 4 | yes | — |
| 235 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 236 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 237 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 238 | C2×C4×D3 | C2×D4 | 1 | 4 | yes | — |
| 239 | C2×Dic6 | — | 2 | 1 | no | — |
| 240 | C2×Dic6 | C2×D4 | 1 | 1 | yes | characteristic |
| 241 | C3×Q16 | — | 2 | 8 | no | — |
| 242 | C3×Q16 | — | 2 | 8 | no | — |
| 243 | C3×SD16 | — | 2 | 8 | no | — |
| 244 | C3×M16 | — | 2 | 2 | no | — |
| 245 | C3×M16 | — | 2 | 2 | no | — |
| 246 | C3×M16 | C2×D4 | 1 | 4 | yes | — |
| 247 | C2×C3×C8 | — | 2 | 2 | no | — |
| 248 | C2×C3×C8 | — | 2 | 2 | no | — |
| 249 | C2×C3×C8 | — | 2 | 1 | no | — |
| 250 | C2×C3×C8 | C2×D4 | 1 | 2 | yes | — |
| 251 | #216 | — | 2 | 8 | no | — |
| 252 | #215 | — | 2 | 8 | no | — |
| 253 | #215 | — | 2 | 8 | no | — |
| 254 | #215 | — | 2 | 16 | no | — |
| 255 | #213 | — | 2 | 8 | no | — |
| 256 | #208 | — | 2 | 2 | no | — |
| 257 | #208 | — | 2 | 2 | no | — |
| 258 | #208 | C2×D4 | 1 | 4 | yes | — |
| 259 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 260 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 261 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 262 | C2×C3⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 263 | D24 | — | 2 | 8 | no | — |
| 264 | D24 | — | 2 | 8 | no | — |
| 265 | #204 | — | 2 | 8 | no | — |
| 266 | ΓL(1,𝔽25) | — | 2 | 8 | no | — |
| 267 | ΓL(1,𝔽25) | — | 4 | 2 | no | — |
| 268 | D3×C8 | — | 2 | 4 | no | — |
| 269 | D3×C8 | — | 2 | 4 | no | — |
| 270 | D3×C8 | — | 2 | 8 | no | — |
| 271 | D3×C8 | — | 4 | 2 | no | — |
| 272 | C2×#41 | — | 3 | 1 | no | — |
| 273 | C2×#41 | — | 3 | 8 | no | — |
| 274 | C2×#41 | — | 3 | 1 | no | — |
| 275 | C2×#41 | — | 3 | 1 | no | — |
| 276 | C2×#41 | — | 6 | 1 | no | — |
| 277 | C2×#41 | — | 6 | 1 | no | — |
| 278 | C2×#41 | — | 6 | 4 | no | — |
| 279 | C2×#41 | — | 6 | 2 | no | — |
| 280 | C2×#41 | — | 6 | 2 | no | — |
| 281 | C2×#41 | — | 6 | 2 | no | — |
| 282 | C2×#41 | — | 6 | 4 | no | — |
| 283 | C2×#41 | — | 6 | 2 | no | — |
| 284 | C2×#41 | — | 6 | 4 | no | — |
| 285 | C2×#41 | — | 6 | 4 | no | — |
| 286 | C2×#41 | — | 6 | 4 | no | — |
| 287 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 288 | C22×Q8 | — | 3 | 1 | no | — |
| 289 | C22×Q8 | C22×D3 | 1 | 2 | yes | — |
| 290 | C22×D4 | — | 3 | 1 | no | — |
| 291 | C22×D4 | — | 3 | 2 | no | — |
| 292 | C22×D4 | — | 6 | 2 | no | — |
| 293 | C22×D4 | — | 6 | 1 | no | — |
| 294 | C23×C4 | — | 3 | 1 | no | — |
| 295 | C23×C4 | — | 6 | 1 | no | — |
| 296 | C23×C4 | — | 6 | 2 | no | — |
| 297 | #137 | — | 2 | 4 | no | — |
| 298 | #137 | — | 2 | 4 | no | — |
| 299 | #137 | — | 6 | 4 | no | — |
| 300 | #137 | — | 6 | 16 | no | — |
| 301 | #137 | — | 6 | 4 | no | — |
| 302 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 303 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 304 | AGL(1,ℤ/8) | — | 6 | 16 | no | — |
| 305 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 306 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 307 | #135 | — | 6 | 16 | no | — |
| 308 | #135 | — | 6 | 16 | no | — |
| 309 | #135 | — | 6 | 16 | no | — |
| 310 | #135 | — | 6 | 16 | no | — |
| 311 | C2×Q16 | — | 2 | 4 | no | — |
| 312 | C2×Q16 | — | 2 | 2 | no | — |
| 313 | C2×Q16 | — | 2 | 2 | no | — |
| 314 | C2×Q16 | — | 6 | 2 | no | — |
| 315 | C2×SD16 | — | 2 | 2 | no | — |
| 316 | C2×SD16 | — | 6 | 2 | no | — |
| 317 | C2×SD16 | — | 6 | 4 | no | — |
| 318 | C2×SD16 | — | 6 | 4 | no | — |
| 319 | C2×SD16 | — | 6 | 2 | no | — |
| 320 | C2×SD16 | — | 6 | 4 | no | — |
| 321 | C2×SD16 | — | 6 | 2 | no | — |
| 322 | C2×D8 | — | 6 | 4 | no | — |
| 323 | C2×D8 | — | 6 | 2 | no | — |
| 324 | C2×D8 | — | 6 | 2 | no | — |
| 325 | C2×D8 | — | 6 | 2 | no | — |
| 326 | C2×M16 | — | 3 | 2 | no | — |
| 327 | C2×M16 | — | 3 | 8 | no | — |
| 328 | C2×M16 | — | 3 | 1 | no | — |
| 329 | C2×M16 | — | 6 | 2 | no | — |
| 330 | C2×M16 | — | 6 | 1 | no | — |
| 331 | C2×M16 | — | 6 | 4 | no | — |
| 332 | C2×M16 | — | 6 | 4 | no | — |
| 333 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 334 | C2×M16 | C22×D3 | 1 | 2 | yes | — |
| 335 | C22×C8 | — | 3 | 1 | no | — |
| 336 | C22×C8 | — | 3 | 2 | no | — |
| 337 | C22×C8 | — | 3 | 2 | no | — |
| 338 | C22×C8 | — | 6 | 4 | no | — |
| 339 | C22×C8 | — | 6 | 2 | no | — |
| 340 | C22×C8 | — | 6 | 1 | no | — |
| 341 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 342 | #101 | — | 2 | 4 | no | — |
| 343 | #101 | — | 6 | 4 | no | — |
| 344 | #100 | — | 6 | 4 | no | — |
| 345 | #100 | — | 6 | 4 | no | — |
| 346 | C22⋊C8 | — | 2 | 2 | no | — |
| 347 | C22⋊C8 | — | 6 | 2 | no | — |
| 348 | C22⋊C8 | — | 6 | 2 | no | — |
| 349 | C22⋊C8 | — | 6 | 2 | no | — |
| 350 | C23×C3 | — | 2 | 1 | no | — |
| 351 | C23×C3 | C2×#41 | 1 | 1 | yes | characteristic |
| 352 | C22×D3 | — | 2 | 1 | no | — |
| 353 | C22×D3 | — | 2 | 4 | no | — |
| 354 | C22×D3 | — | 4 | 2 | no | — |
| 355 | C22×D3 | — | 4 | 4 | no | — |
| 356 | C22×D3 | — | 4 | 2 | no | — |
| 357 | C22×D3 | — | 4 | 2 | no | — |
| 358 | C22×D3 | — | 4 | 2 | no | — |
| 359 | C22×D3 | — | 8 | 4 | no | — |
| 360 | C22×D3 | #121 | 1 | 1 | yes | characteristic |
| 361 | C22×D3 | #121 | 1 | 1 | yes | characteristic |
| 362 | C22×D3 | #121 | 1 | 4 | yes | — |
| 363 | C3×Q8 | — | 2 | 2 | no | — |
| 364 | C3×Q8 | — | 2 | 4 | no | — |
| 365 | C3×Q8 | — | 2 | 4 | no | — |
| 366 | C3×Q8 | — | 4 | 2 | no | — |
| 367 | C3×Q8 | — | 4 | 2 | no | — |
| 368 | C3×D4 | — | 2 | 2 | no | — |
| 369 | C3×D4 | — | 4 | 2 | no | — |
| 370 | C2×C3×C4 | — | 2 | 1 | no | — |
| 371 | C2×C3×C4 | — | 2 | 4 | no | — |
| 372 | C2×C3×C4 | — | 4 | 2 | no | — |
| 373 | C2×C3×C4 | — | 4 | 2 | no | — |
| 374 | C2×C3×C4 | — | 4 | 1 | no | — |
| 375 | C2×C3×C4 | — | 4 | 1 | no | — |
| 376 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 377 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 378 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 379 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 380 | #67 | — | 4 | 2 | no | — |
| 381 | #67 | — | 4 | 2 | no | — |
| 382 | #67 | — | 4 | 2 | no | — |
| 383 | C2×Dic3 | — | 2 | 1 | no | — |
| 384 | C2×Dic3 | — | 4 | 2 | no | — |
| 385 | C2×Dic3 | #121 | 1 | 1 | yes | characteristic |
| 386 | C2×Dic3 | #121 | 1 | 4 | yes | — |
| 387 | C2×Dic3 | #121 | 1 | 1 | yes | characteristic |
| 388 | D12 | — | 2 | 4 | no | — |
| 389 | D12 | — | 2 | 4 | no | — |
| 390 | D12 | — | 2 | 2 | no | — |
| 391 | D12 | — | 4 | 8 | no | — |
| 392 | D12 | — | 4 | 8 | no | — |
| 393 | D12 | — | 4 | 2 | no | — |
| 394 | D12 | — | 4 | 2 | no | — |
| 395 | D12 | — | 4 | 2 | no | — |
| 396 | C4×D3 | — | 4 | 2 | no | — |
| 397 | C4×D3 | — | 4 | 1 | no | — |
| 398 | C4×D3 | — | 4 | 1 | no | — |
| 399 | C4×D3 | — | 4 | 2 | no | — |
| 400 | C4×D3 | — | 4 | 8 | no | — |
| 401 | C4×D3 | — | 4 | 8 | no | — |
| 402 | C4×D3 | #120 | 1 | 2 | yes | — |
| 403 | C4×D3 | #120 | 1 | 2 | yes | — |
| 404 | C4×D3 | #120 | 1 | 4 | yes | — |
| 405 | C4×D3 | #120 | 1 | 4 | yes | — |
| 406 | C4×D3 | #127 | 1 | 2 | yes | — |
| 407 | C4×D3 | #127 | 1 | 2 | yes | — |
| 408 | Dic6 | — | 2 | 2 | no | — |
| 409 | Dic6 | — | 4 | 2 | no | — |
| 410 | C3×C8 | — | 2 | 2 | no | — |
| 411 | C3×C8 | — | 2 | 4 | no | — |
| 412 | C3×C8 | — | 4 | 1 | no | — |
| 413 | C3⋊C8 | — | 2 | 2 | no | — |
| 414 | C3⋊C8 | — | 2 | 4 | no | — |
| 415 | C3⋊C8 | — | 4 | 1 | no | — |
| 416 | C24 | — | 3 | 1 | no | — |
| 417 | C24 | — | 6 | 1 | no | — |
| 418 | C24 | — | 6 | 2 | no | — |
| 419 | #41 | — | 2 | 2 | no | — |
| 420 | #41 | — | 2 | 2 | no | — |
| 421 | #41 | — | 6 | 4 | no | — |
| 422 | #41 | — | 6 | 8 | no | — |
| 423 | #41 | — | 6 | 8 | no | — |
| 424 | #41 | — | 6 | 8 | no | — |
| 425 | #41 | — | 6 | 4 | no | — |
| 426 | #41 | — | 6 | 8 | no | — |
| 427 | #41 | — | 6 | 2 | no | — |
| 428 | #41 | — | 6 | 2 | no | — |
| 429 | #41 | — | 12 | 2 | no | — |
| 430 | #41 | — | 12 | 2 | no | — |
| 431 | #41 | — | 12 | 4 | no | — |
| 432 | #41 | — | 12 | 4 | no | — |
| 433 | #41 | — | 12 | 4 | no | — |
| 434 | #41 | — | 12 | 4 | no | — |
| 435 | #41 | — | 12 | 4 | no | — |
| 436 | C2×Q8 | — | 2 | 2 | no | — |
| 437 | C2×Q8 | — | 2 | 2 | no | — |
| 438 | C2×Q8 | — | 2 | 2 | no | — |
| 439 | C2×Q8 | — | 2 | 2 | no | — |
| 440 | C2×Q8 | — | 2 | 2 | no | — |
| 441 | C2×Q8 | — | 3 | 1 | no | — |
| 442 | C2×Q8 | — | 6 | 1 | no | — |
| 443 | C2×Q8 | — | 6 | 4 | no | — |
| 444 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 445 | C2×Q8 | D3×D4 | 1 | 4 | yes | — |
| 446 | C2×D4 | — | 2 | 1 | no | — |
| 447 | C2×D4 | — | 3 | 1 | no | — |
| 448 | C2×D4 | — | 3 | 4 | no | — |
| 449 | C2×D4 | — | 6 | 8 | no | — |
| 450 | C2×D4 | — | 6 | 1 | no | — |
| 451 | C2×D4 | — | 6 | 4 | no | — |
| 452 | C2×D4 | — | 6 | 1 | no | — |
| 453 | C2×D4 | — | 6 | 1 | no | — |
| 454 | C2×D4 | — | 6 | 1 | no | — |
| 455 | C2×D4 | — | 6 | 2 | no | — |
| 456 | C2×D4 | — | 6 | 2 | no | — |
| 457 | C2×D4 | — | 6 | 2 | no | — |
| 458 | C2×D4 | — | 6 | 2 | no | — |
| 459 | C2×D4 | — | 6 | 2 | no | — |
| 460 | C2×D4 | — | 12 | 4 | no | — |
| 461 | C2×D4 | — | 12 | 2 | no | — |
| 462 | C2×D4 | — | 12 | 2 | no | — |
| 463 | C2×D4 | — | 12 | 4 | no | — |
| 464 | C2×D4 | D3×D4 | 1 | 1 | yes | characteristic |
| 465 | C22×C4 | — | 2 | 2 | no | — |
| 466 | C22×C4 | — | 2 | 1 | no | — |
| 467 | C22×C4 | — | 3 | 1 | no | — |
| 468 | C22×C4 | — | 3 | 1 | no | — |
| 469 | C22×C4 | — | 3 | 1 | no | — |
| 470 | C22×C4 | — | 3 | 1 | no | — |
| 471 | C22×C4 | — | 3 | 4 | no | — |
| 472 | C22×C4 | — | 3 | 4 | no | — |
| 473 | C22×C4 | — | 3 | 1 | no | — |
| 474 | C22×C4 | — | 6 | 8 | no | — |
| 475 | C22×C4 | — | 6 | 1 | no | — |
| 476 | C22×C4 | — | 6 | 1 | no | — |
| 477 | C22×C4 | — | 6 | 1 | no | — |
| 478 | C22×C4 | — | 6 | 1 | no | — |
| 479 | C22×C4 | — | 12 | 4 | no | — |
| 480 | C22×C4 | — | 12 | 2 | no | — |
| 481 | C22×C4 | — | 12 | 2 | no | — |
| 482 | C22×C4 | — | 12 | 2 | no | — |
| 483 | C22×C4 | — | 12 | 2 | no | — |
| 484 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 485 | Q16 | — | 2 | 8 | no | — |
| 486 | Q16 | — | 2 | 8 | no | — |
| 487 | Q16 | — | 6 | 8 | no | — |
| 488 | SD16 | — | 2 | 8 | no | — |
| 489 | SD16 | — | 6 | 8 | no | — |
| 490 | SD16 | — | 6 | 16 | no | — |
| 491 | SD16 | — | 6 | 8 | no | — |
| 492 | SD16 | — | 6 | 8 | no | — |
| 493 | D8 | — | 6 | 8 | no | — |
| 494 | D8 | — | 6 | 8 | no | — |
| 495 | D8 | — | 6 | 8 | no | — |
| 496 | M16 | — | 2 | 2 | no | — |
| 497 | M16 | — | 2 | 2 | no | — |
| 498 | M16 | — | 3 | 4 | no | — |
| 499 | M16 | — | 6 | 8 | no | — |
| 500 | M16 | — | 6 | 2 | no | — |
| 501 | M16 | — | 6 | 2 | no | — |
| 502 | M16 | — | 12 | 2 | no | — |
| 503 | M16 | D3×D4 | 1 | 4 | yes | — |
| 504 | C2×C8 | — | 2 | 2 | no | — |
| 505 | C2×C8 | — | 2 | 2 | no | — |
| 506 | C2×C8 | — | 2 | 1 | no | — |
| 507 | C2×C8 | — | 3 | 2 | no | — |
| 508 | C2×C8 | — | 6 | 4 | no | — |
| 509 | C2×C8 | — | 6 | 4 | no | — |
| 510 | C2×C8 | — | 6 | 8 | no | — |
| 511 | C2×C8 | — | 6 | 2 | no | — |
| 512 | C2×C8 | — | 6 | 2 | no | — |
| 513 | C2×C8 | — | 6 | 1 | no | — |
| 514 | C2×C8 | — | 12 | 2 | no | — |
| 515 | C2×C8 | D3×D4 | 1 | 2 | yes | — |
| 516 | C22×C3 | — | 2 | 2 | no | — |
| 517 | C22×C3 | — | 4 | 1 | no | — |
| 518 | C22×C3 | — | 4 | 2 | no | — |
| 519 | C22×C3 | C2×#121 | 1 | 2 | yes | — |
| 520 | C22×C3 | C2×#121 | 1 | 1 | yes | characteristic |
| 521 | C2×D3 | — | 2 | 2 | no | — |
| 522 | C2×D3 | — | 2 | 2 | no | — |
| 523 | C2×D3 | — | 4 | 4 | no | — |
| 524 | C2×D3 | — | 4 | 4 | no | — |
| 525 | C2×D3 | — | 4 | 1 | no | — |
| 526 | C2×D3 | — | 4 | 2 | no | — |
| 527 | C2×D3 | — | 8 | 4 | no | — |
| 528 | C2×D3 | — | 8 | 4 | no | — |
| 529 | C2×D3 | — | 8 | 4 | no | — |
| 530 | C2×D3 | — | 8 | 4 | no | — |
| 531 | C2×D3 | #392 | 1 | 2 | yes | — |
| 532 | C2×D3 | #392 | 1 | 2 | yes | — |
| 533 | C3×C4 | — | 4 | 1 | no | — |
| 534 | C3×C4 | — | 4 | 4 | no | — |
| 535 | C3×C4 | C2×#120 | 1 | 2 | yes | — |
| 536 | C3×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 537 | C3×C4 | C2×#127 | 1 | 1 | yes | characteristic |
| 538 | Dic3 | — | 4 | 1 | no | — |
| 539 | Dic3 | #392 | 1 | 2 | yes | — |
| 540 | Dic3 | #392 | 1 | 2 | yes | — |
| 541 | C23 | — | 2 | 1 | no | — |
| 542 | C23 | — | 3 | 1 | no | — |
| 543 | C23 | — | 3 | 1 | no | — |
| 544 | C23 | — | 3 | 4 | no | — |
| 545 | C23 | — | 6 | 1 | no | — |
| 546 | C23 | — | 6 | 4 | no | — |
| 547 | C23 | — | 12 | 2 | no | — |
| 548 | C23 | — | 12 | 2 | no | — |
| 549 | C23 | — | 12 | 4 | no | — |
| 550 | C23 | — | 12 | 2 | no | — |
| 551 | C23 | — | 12 | 2 | no | — |
| 552 | C23 | — | 24 | 4 | no | — |
| 553 | C23 | D3×#41 | 1 | 1 | yes | characteristic |
| 554 | Q8 | — | 2 | 4 | no | — |
| 555 | Q8 | — | 2 | 4 | no | — |
| 556 | Q8 | — | 2 | 2 | no | — |
| 557 | Q8 | — | 4 | 2 | no | — |
| 558 | Q8 | — | 4 | 2 | no | — |
| 559 | Q8 | — | 6 | 2 | no | — |
| 560 | Q8 | — | 12 | 2 | no | — |
| 561 | D4 | — | 2 | 2 | no | — |
| 562 | D4 | — | 4 | 2 | no | — |
| 563 | D4 | — | 6 | 4 | no | — |
| 564 | D4 | — | 6 | 2 | no | — |
| 565 | D4 | — | 6 | 4 | no | — |
| 566 | D4 | — | 12 | 2 | no | — |
| 567 | D4 | — | 12 | 2 | no | — |
| 568 | D4 | — | 12 | 8 | no | — |
| 569 | D4 | — | 12 | 8 | no | — |
| 570 | D4 | — | 12 | 2 | no | — |
| 571 | D4 | — | 12 | 2 | no | — |
| 572 | D4 | — | 12 | 2 | no | — |
| 573 | D4 | — | 12 | 2 | no | — |
| 574 | C2×C4 | — | 2 | 4 | no | — |
| 575 | C2×C4 | — | 2 | 1 | no | — |
| 576 | C2×C4 | — | 3 | 4 | no | — |
| 577 | C2×C4 | — | 3 | 1 | no | — |
| 578 | C2×C4 | — | 3 | 1 | no | — |
| 579 | C2×C4 | — | 3 | 2 | no | — |
| 580 | C2×C4 | — | 3 | 2 | no | — |
| 581 | C2×C4 | — | 3 | 2 | no | — |
| 582 | C2×C4 | — | 3 | 4 | no | — |
| 583 | C2×C4 | — | 3 | 2 | no | — |
| 584 | C2×C4 | — | 3 | 4 | no | — |
| 585 | C2×C4 | — | 4 | 2 | no | — |
| 586 | C2×C4 | — | 4 | 2 | no | — |
| 587 | C2×C4 | — | 4 | 1 | no | — |
| 588 | C2×C4 | — | 4 | 1 | no | — |
| 589 | C2×C4 | — | 6 | 1 | no | — |
| 590 | C2×C4 | — | 12 | 2 | no | — |
| 591 | C2×C4 | — | 12 | 8 | no | — |
| 592 | C2×C4 | — | 12 | 8 | no | — |
| 593 | C2×C4 | — | 12 | 2 | no | — |
| 594 | C2×C4 | — | 12 | 2 | no | — |
| 595 | C2×C4 | — | 12 | 1 | no | — |
| 596 | C2×C4 | — | 12 | 1 | no | — |
| 597 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 598 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 599 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 600 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 601 | C8 | — | 2 | 2 | no | — |
| 602 | C8 | — | 2 | 4 | no | — |
| 603 | C8 | — | 4 | 1 | no | — |
| 604 | C8 | — | 6 | 2 | no | — |
| 605 | C8 | — | 6 | 4 | no | — |
| 606 | C8 | — | 12 | 1 | no | — |
| 607 | C2×C3 | — | 2 | 2 | no | — |
| 608 | C2×C3 | — | 8 | 1 | no | — |
| 609 | C2×C3 | C2×#392 | 1 | 1 | yes | characteristic |
| 610 | C2×C3 | #3067 | 1 | 2 | yes | — |
| 611 | D3 | — | 2 | 2 | no | — |
| 612 | D3 | — | 2 | 2 | no | — |
| 613 | D3 | — | 8 | 1 | no | — |
| 614 | D3 | — | 8 | 4 | no | — |
| 615 | C22 | — | 2 | 2 | no | — |
| 616 | C22 | — | 3 | 2 | no | — |
| 617 | C22 | — | 3 | 2 | no | — |
| 618 | C22 | — | 4 | 2 | no | — |
| 619 | C22 | — | 4 | 1 | no | — |
| 620 | C22 | — | 6 | 2 | no | — |
| 621 | C22 | — | 6 | 2 | no | — |
| 622 | C22 | — | 12 | 4 | no | — |
| 623 | C22 | — | 12 | 2 | no | — |
| 624 | C22 | — | 12 | 1 | no | — |
| 625 | C22 | — | 12 | 4 | no | — |
| 626 | C22 | — | 24 | 4 | no | — |
| 627 | C22 | — | 24 | 4 | no | — |
| 628 | C22 | — | 24 | 4 | no | — |
| 629 | C22 | — | 24 | 4 | no | — |
| 630 | C22 | D3×#121 | 1 | 2 | yes | — |
| 631 | C22 | D3×#121 | 1 | 1 | yes | characteristic |
| 632 | C4 | — | 3 | 2 | no | — |
| 633 | C4 | — | 3 | 2 | no | — |
| 634 | C4 | — | 4 | 1 | no | — |
| 635 | C4 | — | 4 | 4 | no | — |
| 636 | C4 | — | 12 | 1 | no | — |
| 637 | C4 | D3×#120 | 1 | 1 | yes | characteristic |
| 638 | C4 | D3×#120 | 1 | 2 | yes | — |
| 639 | C4 | D3×#127 | 1 | 1 | yes | characteristic |
| 640 | C3 | #23438 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 641 | C2 | — | 2 | 2 | no | — |
| 642 | C2 | — | 6 | 2 | no | — |
| 643 | C2 | — | 6 | 2 | no | — |
| 644 | C2 | — | 8 | 1 | no | — |
| 645 | C2 | — | 24 | 1 | no | — |
| 646 | C2 | — | 24 | 4 | no | — |
| 647 | C2 | D3×#392 | 1 | 1 | yes | characteristic |
| 648 | C2 | #80943 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#5777 | C2 | semidirect |
| 2. C22×#919 | C2 | semidirect |
| 3. C2×#4751 | C2 | semidirect |
| 4. D3×#408 | C2 | semidirect |
| 5. C3×#2020 | C2 | semidirect |
| 6. #72107 | C2 | semidirect |
| 7. #72074 | C2 | semidirect |
| 8. #70117 | C2 | semidirect |
| 9. #70006 | C2 | semidirect |
| 10. #68942 | C2 | semidirect |
| 11. D3×#341 | C2 | semidirect |
| 16. C22×C3×Q16 | C22 | semidirect |
| 19. C22×#215 | C22 | semidirect |
| 32. C22×D24 | C22 | semidirect |
| 34. C2×C3×#101 | C22 | semidirect |
| 37. C2×#836 | C22 | semidirect |
| 38. C2×#823 | C22 | semidirect |
| 39. C2×#823 | C22 | semidirect |
| 45. C3×#341 | C22 | semidirect |
| 46. #4558 | C22 | semidirect |
| 47. #4552 | C22 | semidirect |
| 53. #2020 | D3 | semidirect |
| 152. C22×Q16 | C2×D3 | semidirect |
| 160. C2×#101 | C2×D3 | semidirect |
| 171. #341 | C2×D3 | semidirect |
| 640. C3 | #23438 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5777 | 2 |
| C22×#919 | 2 |
| C2×#4751 | 2 |
| D3×#408 | 2 |
| C3×#2020 | 2 |
| #72107 | 2 |
| #72074 | 2 |
| #70117 | 2 |
| #70006 | 2 |
| #68942 | 2 |
| D3×#341 | 2 |
| #23438 | 3 |