Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
704 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #78639 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #78600 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #69960 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #69944 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #69921 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#1298 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #67684 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #9347 | — | 3 | 1 | no | maximal, Sylow |
| 9 | C22×#235 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#930 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#908 | C4 | 1 | 1 | yes | characteristic, complemented |
| 12 | C2×#908 | C4 | 1 | 1 | yes | characteristic, complemented |
| 13 | C2×#901 | — | 2 | 1 | no | — |
| 14 | C3×#407 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C3×C22⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×C3×C22⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 17 | #5212 | C22 | 1 | 1 | yes | characteristic |
| 18 | #5207 | C22 | 1 | 1 | yes | characteristic |
| 19 | #5133 | C4 | 1 | 1 | yes | characteristic, complemented |
| 20 | #5133 | C4 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×#821 | — | 2 | 1 | no | — |
| 22 | #5110 | — | 2 | 1 | no | — |
| 23 | C2×#816 | — | 2 | 1 | no | — |
| 24 | #4738 | — | 2 | 1 | no | — |
| 25 | #4734 | — | 2 | 1 | no | — |
| 26 | #4734 | — | 2 | 1 | no | — |
| 27 | #4732 | — | 2 | 1 | no | — |
| 28 | #4727 | — | 2 | 2 | no | — |
| 29 | #4726 | — | 2 | 1 | no | — |
| 30 | D3×C22⋊C8 | — | 2 | 1 | no | — |
| 31 | #4470 | — | 2 | 1 | no | — |
| 32 | #4470 | — | 2 | 1 | no | — |
| 33 | #4468 | — | 2 | 2 | no | — |
| 34 | #3006 | — | 3 | 1 | no | — |
| 35 | #2880 | — | 3 | 1 | no | — |
| 36 | #1788 | — | 3 | 1 | no | — |
| 37 | #1519 | — | 3 | 1 | no | — |
| 38 | #1471 | — | 3 | 1 | no | — |
| 39 | #1305 | — | 3 | 1 | no | — |
| 40 | #1298 | D3 | 1 | 1 | yes | characteristic, complemented |
| 41 | C23×C3×C4 | C23 | 1 | 1 | yes | characteristic |
| 42 | C22×#67 | — | 2 | 1 | no | — |
| 43 | C22×#67 | — | 2 | 1 | no | — |
| 44 | C2×#235 | — | 2 | 1 | no | — |
| 45 | C2×#235 | — | 2 | 1 | no | — |
| 46 | C2×#235 | — | 4 | 2 | no | — |
| 47 | C2×#235 | — | 4 | 2 | no | — |
| 48 | C2×#235 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | C2×#235 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | C2×#235 | D4 | 1 | 1 | yes | characteristic |
| 51 | C2×#235 | D4 | 1 | 1 | yes | characteristic |
| 52 | C22×D12 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | C22×D12 | D4 | 1 | 1 | yes | characteristic |
| 54 | C22×C4×D3 | — | 2 | 1 | no | — |
| 55 | C22×Dic6 | D4 | 1 | 1 | yes | characteristic |
| 56 | C2×C3×M16 | C2×C4 | 1 | 1 | yes | characteristic |
| 57 | C2×C3×M16 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | C22×C3×C8 | — | 2 | 1 | no | — |
| 59 | C22×C3×C8 | — | 2 | 1 | no | — |
| 60 | C2×#217 | — | 2 | 1 | no | — |
| 61 | #930 | — | 2 | 1 | no | — |
| 62 | #930 | — | 2 | 1 | no | — |
| 63 | #930 | — | 2 | 1 | no | — |
| 64 | #930 | — | 2 | 1 | no | — |
| 65 | C2×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 66 | C2×C4⋊Dic3 | — | 2 | 1 | no | — |
| 67 | C2×C4⋊Dic3 | C2×C4 | 1 | 1 | yes | characteristic |
| 68 | C2×#208 | — | 2 | 1 | no | — |
| 69 | #908 | — | 4 | 2 | no | — |
| 70 | #908 | — | 4 | 2 | no | — |
| 71 | C2×D24 | — | 2 | 1 | no | — |
| 72 | C2×D24 | — | 2 | 1 | no | — |
| 73 | C2×#204 | — | 2 | 1 | no | — |
| 74 | C2×#204 | — | 2 | 1 | no | — |
| 75 | #901 | — | 4 | 2 | no | — |
| 76 | #901 | — | 4 | 2 | no | — |
| 77 | C2×ΓL(1,𝔽25) | — | 2 | 2 | no | — |
| 78 | C2×D3×C8 | — | 2 | 2 | no | — |
| 79 | C3×C22⋊C8 | — | 2 | 1 | no | — |
| 80 | C3×C22⋊C8 | — | 2 | 1 | no | — |
| 81 | C3×C22⋊C8 | — | 2 | 1 | no | — |
| 82 | C3×C22⋊C8 | — | 2 | 1 | no | — |
| 83 | C3×C22⋊C8 | — | 2 | 1 | no | — |
| 84 | C3×C22⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 85 | C3×C22⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 86 | C3⋊#95 | — | 2 | 1 | no | — |
| 87 | #830 | — | 2 | 1 | no | — |
| 88 | #830 | D4 | 1 | 2 | yes | — |
| 89 | #821 | — | 2 | 1 | no | — |
| 90 | #821 | — | 2 | 1 | no | — |
| 91 | #821 | — | 4 | 2 | no | — |
| 92 | (C2×D3)⋊C8 | — | 2 | 2 | no | — |
| 93 | (C2×D3)⋊C8 | — | 2 | 2 | no | — |
| 94 | #816 | — | 2 | 1 | no | — |
| 95 | #816 | — | 2 | 1 | no | — |
| 96 | #816 | — | 4 | 2 | no | — |
| 97 | C22×#41 | — | 3 | 1 | no | — |
| 98 | C2×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 99 | C2×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 100 | C2×#131 | — | 6 | 1 | no | — |
| 101 | C2×#121 | — | 3 | 1 | no | — |
| 102 | #449 | — | 6 | 1 | no | — |
| 103 | #449 | — | 6 | 1 | no | — |
| 104 | #448 | — | 6 | 1 | no | — |
| 105 | #447 | — | 6 | 1 | no | — |
| 106 | #417 | — | 3 | 1 | no | — |
| 107 | #417 | — | 3 | 1 | no | — |
| 108 | C2×#103 | — | 6 | 1 | no | — |
| 109 | C2×#102 | — | 6 | 1 | no | — |
| 110 | #408 | — | 6 | 2 | no | — |
| 111 | #408 | — | 6 | 1 | no | — |
| 112 | #407 | — | 3 | 1 | no | — |
| 113 | #407 | — | 6 | 1 | no | — |
| 114 | #407 | C2×D3 | 1 | 1 | yes | characteristic |
| 115 | C2×C22⋊C8 | — | 6 | 1 | no | — |
| 116 | C2×C22⋊C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 117 | C2×C22⋊C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 118 | #380 | — | 3 | 1 | no | — |
| 119 | #327 | — | 6 | 1 | no | — |
| 120 | #327 | — | 6 | 1 | no | — |
| 121 | #323 | — | 6 | 2 | no | — |
| 122 | C24×C3 | #41 | 1 | 1 | yes | characteristic |
| 123 | C23×D3 | — | 2 | 1 | no | — |
| 124 | C23×D3 | — | 2 | 1 | no | — |
| 125 | C22×C3×C4 | — | 4 | 1 | no | — |
| 126 | C22×C3×C4 | — | 4 | 1 | no | — |
| 127 | C22×C3×C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 128 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 130 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 131 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 132 | C22×C3×C4 | #41 | 1 | 1 | yes | characteristic |
| 133 | C2×#67 | — | 2 | 1 | no | — |
| 134 | C2×#67 | — | 2 | 1 | no | — |
| 135 | C2×#67 | — | 2 | 1 | no | — |
| 136 | C2×#67 | — | 2 | 1 | no | — |
| 137 | C2×#67 | — | 4 | 4 | no | — |
| 138 | C2×#67 | — | 4 | 1 | no | — |
| 139 | C2×#67 | — | 4 | 1 | no | — |
| 140 | C2×#67 | — | 8 | 1 | no | — |
| 141 | C2×#67 | — | 8 | 1 | no | — |
| 142 | C22×Dic3 | — | 2 | 1 | no | — |
| 143 | C22×Dic3 | — | 2 | 1 | no | — |
| 144 | C22×Dic3 | — | 4 | 1 | no | — |
| 145 | #235 | — | 2 | 2 | no | — |
| 146 | #235 | — | 2 | 2 | no | — |
| 147 | #235 | — | 2 | 2 | no | — |
| 148 | #235 | — | 2 | 2 | no | — |
| 149 | #235 | — | 4 | 1 | no | — |
| 150 | #235 | — | 4 | 1 | no | — |
| 151 | #235 | — | 4 | 1 | no | — |
| 152 | #235 | — | 4 | 1 | no | — |
| 153 | #235 | — | 4 | 4 | no | — |
| 154 | #235 | — | 4 | 4 | no | — |
| 155 | C2×D12 | — | 2 | 2 | no | — |
| 156 | C2×D12 | — | 2 | 1 | no | — |
| 157 | C2×D12 | — | 2 | 1 | no | — |
| 158 | C2×D12 | — | 2 | 1 | no | — |
| 159 | C2×D12 | — | 4 | 1 | no | — |
| 160 | C2×D12 | — | 4 | 1 | no | — |
| 161 | C2×D12 | — | 4 | 1 | no | — |
| 162 | C2×D12 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 163 | C2×D12 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 164 | C2×C4×D3 | — | 2 | 1 | no | — |
| 165 | C2×C4×D3 | — | 2 | 1 | no | — |
| 166 | C2×C4×D3 | — | 2 | 1 | no | — |
| 167 | C2×C4×D3 | — | 2 | 1 | no | — |
| 168 | C2×C4×D3 | — | 4 | 4 | no | — |
| 169 | C2×Dic6 | — | 2 | 2 | no | — |
| 170 | C2×Dic6 | — | 2 | 1 | no | — |
| 171 | C2×Dic6 | — | 4 | 1 | no | — |
| 172 | C2×Dic6 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 173 | C2×Dic6 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 174 | C3×M16 | — | 4 | 1 | no | — |
| 175 | C3×M16 | — | 4 | 1 | no | — |
| 176 | C2×C3×C8 | — | 2 | 1 | no | — |
| 177 | C2×C3×C8 | — | 2 | 1 | no | — |
| 178 | C2×C3×C8 | — | 2 | 1 | no | — |
| 179 | C2×C3×C8 | — | 2 | 1 | no | — |
| 180 | C2×C3×C8 | — | 4 | 1 | no | — |
| 181 | C2×C3×C8 | — | 4 | 1 | no | — |
| 182 | C2×C3×C8 | — | 4 | 1 | no | — |
| 183 | C2×C3×C8 | — | 4 | 1 | no | — |
| 184 | C2×C3×C8 | — | 4 | 1 | no | — |
| 185 | #217 | — | 8 | 1 | no | — |
| 186 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 187 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 188 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 189 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 190 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 191 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 192 | #208 | — | 4 | 1 | no | — |
| 193 | #208 | — | 4 | 1 | no | — |
| 194 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 195 | D24 | — | 4 | 2 | no | — |
| 196 | D24 | — | 4 | 2 | no | — |
| 197 | #204 | — | 4 | 2 | no | — |
| 198 | #204 | — | 4 | 2 | no | — |
| 199 | ΓL(1,𝔽25) | — | 4 | 4 | no | — |
| 200 | D3×C8 | — | 4 | 4 | no | — |
| 201 | C2×#41 | — | 3 | 1 | no | — |
| 202 | C2×#41 | — | 3 | 1 | no | — |
| 203 | C2×#41 | — | 3 | 1 | no | — |
| 204 | C2×#41 | — | 3 | 1 | no | — |
| 205 | C2×#41 | — | 6 | 1 | no | — |
| 206 | C2×#41 | — | 6 | 1 | no | — |
| 207 | C2×#41 | — | 12 | 2 | no | — |
| 208 | C2×#41 | — | 12 | 2 | no | — |
| 209 | C22×Q8 | — | 3 | 1 | no | — |
| 210 | C22×D4 | — | 3 | 1 | no | — |
| 211 | C22×D4 | — | 3 | 1 | no | — |
| 212 | C22×D4 | — | 6 | 1 | no | — |
| 213 | C22×D4 | — | 6 | 1 | no | — |
| 214 | C23×C4 | — | 6 | 1 | no | — |
| 215 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 216 | AGL(1,ℤ/8) | — | 12 | 2 | no | — |
| 217 | AGL(1,ℤ/8) | — | 12 | 2 | no | — |
| 218 | C2×SD16 | — | 6 | 1 | no | — |
| 219 | C2×SD16 | — | 6 | 1 | no | — |
| 220 | C2×D8 | — | 6 | 1 | no | — |
| 221 | C2×D8 | — | 6 | 1 | no | — |
| 222 | #131 | — | 12 | 2 | no | — |
| 223 | #131 | — | 12 | 2 | no | — |
| 224 | C2×M16 | — | 6 | 2 | no | — |
| 225 | C2×M16 | — | 6 | 1 | no | — |
| 226 | C2×M16 | C4×D3 | 1 | 1 | yes | characteristic |
| 227 | C2×M16 | C4×D3 | 1 | 1 | yes | characteristic |
| 228 | C22×C8 | — | 2 | 1 | no | — |
| 229 | C22×C8 | — | 2 | 1 | no | — |
| 230 | C22×C8 | — | 6 | 2 | no | — |
| 231 | #121 | — | 6 | 1 | no | — |
| 232 | #121 | — | 6 | 1 | no | — |
| 233 | #121 | — | 6 | 1 | no | — |
| 234 | #121 | — | 6 | 1 | no | — |
| 235 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 236 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 237 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 238 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 239 | #103 | — | 6 | 1 | no | — |
| 240 | #103 | — | 6 | 1 | no | — |
| 241 | #103 | — | 12 | 2 | no | — |
| 242 | #102 | — | 6 | 1 | no | — |
| 243 | #102 | — | 6 | 1 | no | — |
| 244 | #102 | — | 12 | 2 | no | — |
| 245 | C22⋊C8 | — | 2 | 1 | no | — |
| 246 | C22⋊C8 | — | 2 | 1 | no | — |
| 247 | C22⋊C8 | — | 2 | 1 | no | — |
| 248 | C22⋊C8 | — | 2 | 1 | no | — |
| 249 | C22⋊C8 | — | 2 | 1 | no | — |
| 250 | C22⋊C8 | — | 3 | 2 | no | — |
| 251 | C22⋊C8 | — | 6 | 2 | no | — |
| 252 | C22⋊C8 | — | 6 | 2 | no | — |
| 253 | C22⋊C8 | — | 6 | 1 | no | — |
| 254 | C22⋊C8 | D12 | 1 | 1 | yes | characteristic |
| 255 | C22⋊C8 | D12 | 1 | 1 | yes | characteristic |
| 256 | #95 | — | 6 | 1 | no | — |
| 257 | C23×C3 | — | 2 | 1 | no | — |
| 258 | C23×C3 | — | 2 | 1 | no | — |
| 259 | C23×C3 | — | 4 | 1 | no | — |
| 260 | C23×C3 | — | 4 | 1 | no | — |
| 261 | C23×C3 | C4×D4 | 1 | 1 | yes | characteristic |
| 262 | C23×C3 | #121 | 1 | 1 | yes | characteristic |
| 263 | C23×C3 | #123 | 1 | 1 | yes | characteristic |
| 264 | C22×D3 | — | 2 | 1 | no | — |
| 265 | C22×D3 | — | 2 | 1 | no | — |
| 266 | C22×D3 | — | 4 | 2 | no | — |
| 267 | C22×D3 | — | 4 | 1 | no | — |
| 268 | C22×D3 | — | 4 | 1 | no | — |
| 269 | C22×D3 | — | 4 | 1 | no | — |
| 270 | C22×D3 | — | 4 | 2 | no | — |
| 271 | C22×D3 | — | 8 | 1 | no | — |
| 272 | C22×D3 | — | 8 | 1 | no | — |
| 273 | C22×D3 | — | 8 | 1 | no | — |
| 274 | C2×C3×C4 | — | 2 | 1 | no | — |
| 275 | C2×C3×C4 | — | 2 | 1 | no | — |
| 276 | C2×C3×C4 | — | 2 | 1 | no | — |
| 277 | C2×C3×C4 | — | 2 | 1 | no | — |
| 278 | C2×C3×C4 | — | 2 | 1 | no | — |
| 279 | C2×C3×C4 | — | 2 | 1 | no | — |
| 280 | C2×C3×C4 | — | 4 | 1 | no | — |
| 281 | C2×C3×C4 | — | 4 | 1 | no | — |
| 282 | C2×C3×C4 | — | 4 | 1 | no | — |
| 283 | C2×C3×C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 284 | C2×C3×C4 | C4×D4 | 1 | 1 | yes | characteristic |
| 285 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 286 | C2×C3×C4 | #121 | 1 | 1 | yes | characteristic |
| 287 | #67 | — | 2 | 4 | no | — |
| 288 | #67 | — | 4 | 2 | no | — |
| 289 | #67 | — | 4 | 2 | no | — |
| 290 | #67 | — | 4 | 2 | no | — |
| 291 | #67 | — | 8 | 2 | no | — |
| 292 | #67 | — | 8 | 1 | no | — |
| 293 | #67 | — | 8 | 1 | no | — |
| 294 | C2×Dic3 | — | 2 | 1 | no | — |
| 295 | C2×Dic3 | — | 2 | 1 | no | — |
| 296 | C2×Dic3 | — | 4 | 2 | no | — |
| 297 | C2×Dic3 | — | 4 | 1 | no | — |
| 298 | C2×Dic3 | — | 8 | 1 | no | — |
| 299 | C2×Dic3 | — | 8 | 1 | no | — |
| 300 | C2×Dic3 | — | 8 | 1 | no | — |
| 301 | C2×Dic3 | — | 8 | 1 | no | — |
| 302 | D12 | — | 2 | 1 | no | — |
| 303 | D12 | — | 2 | 1 | no | — |
| 304 | D12 | — | 2 | 1 | no | — |
| 305 | D12 | — | 4 | 2 | no | — |
| 306 | D12 | — | 4 | 1 | no | — |
| 307 | D12 | — | 4 | 1 | no | — |
| 308 | D12 | — | 8 | 1 | no | — |
| 309 | D12 | #99 | 1 | 2 | yes | — |
| 310 | C4×D3 | — | 2 | 4 | no | — |
| 311 | C4×D3 | — | 4 | 2 | no | — |
| 312 | C4×D3 | — | 4 | 2 | no | — |
| 313 | C4×D3 | — | 4 | 2 | no | — |
| 314 | Dic6 | — | 2 | 1 | no | — |
| 315 | Dic6 | — | 2 | 1 | no | — |
| 316 | Dic6 | — | 2 | 1 | no | — |
| 317 | Dic6 | — | 4 | 2 | no | — |
| 318 | Dic6 | #99 | 1 | 2 | yes | — |
| 319 | C3×C8 | — | 4 | 1 | no | — |
| 320 | C3×C8 | — | 4 | 1 | no | — |
| 321 | C3×C8 | — | 4 | 1 | no | — |
| 322 | C3×C8 | — | 4 | 1 | no | — |
| 323 | C3×C8 | — | 8 | 1 | no | — |
| 324 | C3⋊C8 | — | 4 | 2 | no | — |
| 325 | C24 | — | 6 | 1 | no | — |
| 326 | C24 | — | 6 | 1 | no | — |
| 327 | C24 | #239 | 1 | 1 | yes | characteristic |
| 328 | #41 | — | 6 | 2 | no | — |
| 329 | #41 | — | 6 | 2 | no | — |
| 330 | #41 | — | 6 | 2 | no | — |
| 331 | #41 | — | 6 | 2 | no | — |
| 332 | #41 | — | 12 | 1 | no | — |
| 333 | #41 | — | 12 | 1 | no | — |
| 334 | #41 | — | 12 | 1 | no | — |
| 335 | #41 | — | 12 | 1 | no | — |
| 336 | #41 | — | 12 | 4 | no | — |
| 337 | #41 | — | 12 | 4 | no | — |
| 338 | C2×Q8 | — | 3 | 1 | no | — |
| 339 | C2×Q8 | — | 3 | 1 | no | — |
| 340 | C2×Q8 | — | 6 | 2 | no | — |
| 341 | C2×Q8 | — | 6 | 1 | no | — |
| 342 | C2×Q8 | — | 12 | 1 | no | — |
| 343 | C2×D4 | — | 3 | 1 | no | — |
| 344 | C2×D4 | — | 3 | 1 | no | — |
| 345 | C2×D4 | — | 6 | 2 | no | — |
| 346 | C2×D4 | — | 6 | 1 | no | — |
| 347 | C2×D4 | — | 6 | 1 | no | — |
| 348 | C2×D4 | — | 6 | 1 | no | — |
| 349 | C2×D4 | — | 6 | 1 | no | — |
| 350 | C2×D4 | — | 6 | 1 | no | — |
| 351 | C2×D4 | — | 6 | 1 | no | — |
| 352 | C2×D4 | — | 6 | 1 | no | — |
| 353 | C2×D4 | — | 12 | 1 | no | — |
| 354 | C2×D4 | — | 12 | 1 | no | — |
| 355 | C2×D4 | — | 12 | 1 | no | — |
| 356 | C2×D4 | — | 12 | 4 | no | — |
| 357 | C2×D4 | — | 12 | 1 | no | — |
| 358 | C2×D4 | — | 12 | 1 | no | — |
| 359 | C2×D4 | — | 24 | 1 | no | — |
| 360 | C2×D4 | — | 24 | 1 | no | — |
| 361 | C22×C4 | — | 4 | 1 | no | — |
| 362 | C22×C4 | — | 4 | 1 | no | — |
| 363 | C22×C4 | — | 6 | 1 | no | — |
| 364 | C22×C4 | — | 6 | 1 | no | — |
| 365 | C22×C4 | — | 6 | 1 | no | — |
| 366 | C22×C4 | — | 6 | 1 | no | — |
| 367 | C22×C4 | — | 6 | 1 | no | — |
| 368 | C22×C4 | — | 6 | 1 | no | — |
| 369 | C22×C4 | — | 12 | 4 | no | — |
| 370 | C22×C4 | — | 12 | 1 | no | — |
| 371 | C22×C4 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 372 | C22×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 373 | C22×C4 | #235 | 1 | 1 | yes | characteristic |
| 374 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 375 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 376 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 377 | SD16 | — | 12 | 2 | no | — |
| 378 | SD16 | — | 12 | 2 | no | — |
| 379 | D8 | — | 12 | 2 | no | — |
| 380 | D8 | — | 12 | 2 | no | — |
| 381 | M16 | — | 4 | 1 | no | — |
| 382 | M16 | — | 4 | 1 | no | — |
| 383 | M16 | — | 12 | 4 | no | — |
| 384 | M16 | — | 12 | 1 | no | — |
| 385 | M16 | — | 12 | 1 | no | — |
| 386 | C2×C8 | — | 2 | 1 | no | — |
| 387 | C2×C8 | — | 2 | 1 | no | — |
| 388 | C2×C8 | — | 2 | 1 | no | — |
| 389 | C2×C8 | — | 2 | 1 | no | — |
| 390 | C2×C8 | — | 4 | 1 | no | — |
| 391 | C2×C8 | — | 4 | 1 | no | — |
| 392 | C2×C8 | — | 4 | 1 | no | — |
| 393 | C2×C8 | — | 4 | 1 | no | — |
| 394 | C2×C8 | — | 4 | 1 | no | — |
| 395 | C2×C8 | — | 6 | 2 | no | — |
| 396 | C2×C8 | — | 12 | 4 | no | — |
| 397 | C4⋊C4 | — | 6 | 1 | no | — |
| 398 | C4⋊C4 | — | 6 | 1 | no | — |
| 399 | C4⋊C4 | — | 12 | 1 | no | — |
| 400 | C4⋊C4 | — | 12 | 1 | no | — |
| 401 | C22⋊C4 | — | 12 | 1 | no | — |
| 402 | C22⋊C4 | — | 12 | 1 | no | — |
| 403 | C22⋊C4 | — | 24 | 1 | no | — |
| 404 | C22×C3 | — | 2 | 1 | no | — |
| 405 | C22×C3 | — | 2 | 1 | no | — |
| 406 | C22×C3 | — | 2 | 1 | no | — |
| 407 | C22×C3 | — | 2 | 1 | no | — |
| 408 | C22×C3 | — | 2 | 1 | no | — |
| 409 | C22×C3 | — | 2 | 1 | no | — |
| 410 | C22×C3 | — | 2 | 1 | no | — |
| 411 | C22×C3 | — | 2 | 1 | no | — |
| 412 | C22×C3 | — | 8 | 1 | no | — |
| 413 | C22×C3 | — | 8 | 1 | no | — |
| 414 | C22×C3 | #386 | 1 | 1 | yes | characteristic |
| 415 | C22×C3 | #471 | 1 | 1 | yes | characteristic |
| 416 | C22×C3 | #472 | 1 | 1 | yes | characteristic |
| 417 | C2×D3 | — | 2 | 2 | no | — |
| 418 | C2×D3 | — | 4 | 1 | no | — |
| 419 | C2×D3 | — | 4 | 1 | no | — |
| 420 | C2×D3 | — | 4 | 1 | no | — |
| 421 | C2×D3 | — | 4 | 1 | no | — |
| 422 | C2×D3 | — | 4 | 1 | no | — |
| 423 | C2×D3 | — | 8 | 2 | no | — |
| 424 | C2×D3 | — | 8 | 2 | no | — |
| 425 | C2×D3 | — | 8 | 1 | no | — |
| 426 | C2×D3 | — | 8 | 1 | no | — |
| 427 | C2×D3 | — | 8 | 1 | no | — |
| 428 | C2×D3 | — | 16 | 2 | no | — |
| 429 | C3×C4 | — | 2 | 1 | no | — |
| 430 | C3×C4 | — | 2 | 1 | no | — |
| 431 | C3×C4 | — | 2 | 1 | no | — |
| 432 | C3×C4 | C2×#99 | 1 | 1 | yes | characteristic |
| 433 | C3×C4 | C2×#99 | 1 | 1 | yes | characteristic |
| 434 | Dic3 | — | 2 | 2 | no | — |
| 435 | Dic3 | — | 4 | 1 | no | — |
| 436 | Dic3 | — | 8 | 1 | no | — |
| 437 | Dic3 | — | 16 | 1 | no | — |
| 438 | C23 | — | 2 | 1 | no | — |
| 439 | C23 | — | 2 | 1 | no | — |
| 440 | C23 | — | 4 | 1 | no | — |
| 441 | C23 | — | 4 | 1 | no | — |
| 442 | C23 | — | 6 | 1 | no | — |
| 443 | C23 | — | 6 | 1 | no | — |
| 444 | C23 | — | 12 | 2 | no | — |
| 445 | C23 | — | 12 | 2 | no | — |
| 446 | C23 | — | 12 | 1 | no | — |
| 447 | C23 | — | 12 | 1 | no | — |
| 448 | C23 | — | 12 | 1 | no | — |
| 449 | C23 | — | 24 | 1 | no | — |
| 450 | C23 | — | 24 | 1 | no | — |
| 451 | C23 | — | 24 | 1 | no | — |
| 452 | C23 | #893 | 1 | 1 | yes | characteristic |
| 453 | C23 | #894 | 1 | 1 | yes | characteristic |
| 454 | C23 | #895 | 1 | 1 | yes | characteristic |
| 455 | Q8 | — | 3 | 2 | no | — |
| 456 | Q8 | — | 6 | 1 | no | — |
| 457 | Q8 | — | 6 | 1 | no | — |
| 458 | Q8 | — | 6 | 1 | no | — |
| 459 | Q8 | — | 12 | 2 | no | — |
| 460 | D4 | — | 3 | 2 | no | — |
| 461 | D4 | — | 6 | 4 | no | — |
| 462 | D4 | — | 6 | 1 | no | — |
| 463 | D4 | — | 6 | 1 | no | — |
| 464 | D4 | — | 6 | 1 | no | — |
| 465 | D4 | — | 12 | 2 | no | — |
| 466 | D4 | — | 12 | 2 | no | — |
| 467 | D4 | — | 12 | 2 | no | — |
| 468 | D4 | — | 12 | 2 | no | — |
| 469 | D4 | — | 12 | 1 | no | — |
| 470 | D4 | — | 12 | 1 | no | — |
| 471 | D4 | — | 24 | 1 | no | — |
| 472 | D4 | — | 24 | 2 | no | — |
| 473 | D4 | — | 24 | 1 | no | — |
| 474 | D4 | — | 24 | 1 | no | — |
| 475 | C2×C4 | — | 2 | 1 | no | — |
| 476 | C2×C4 | — | 2 | 1 | no | — |
| 477 | C2×C4 | — | 2 | 1 | no | — |
| 478 | C2×C4 | — | 2 | 1 | no | — |
| 479 | C2×C4 | — | 2 | 1 | no | — |
| 480 | C2×C4 | — | 2 | 1 | no | — |
| 481 | C2×C4 | — | 4 | 1 | no | — |
| 482 | C2×C4 | — | 4 | 1 | no | — |
| 483 | C2×C4 | — | 4 | 1 | no | — |
| 484 | C2×C4 | — | 6 | 4 | no | — |
| 485 | C2×C4 | — | 6 | 1 | no | — |
| 486 | C2×C4 | — | 6 | 1 | no | — |
| 487 | C2×C4 | — | 12 | 2 | no | — |
| 488 | C2×C4 | — | 12 | 2 | no | — |
| 489 | C2×C4 | — | 12 | 2 | no | — |
| 490 | C2×C4 | — | 12 | 2 | no | — |
| 491 | C2×C4 | — | 12 | 1 | no | — |
| 492 | C2×C4 | — | 24 | 1 | no | — |
| 493 | C2×C4 | — | 24 | 1 | no | — |
| 494 | C2×C4 | — | 24 | 1 | no | — |
| 495 | C2×C4 | — | 24 | 1 | no | — |
| 496 | C2×C4 | C4×D12 | 1 | 1 | yes | characteristic |
| 497 | C2×C4 | D3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 498 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 499 | C2×C4 | #884 | 1 | 1 | yes | characteristic |
| 500 | C8 | — | 4 | 1 | no | — |
| 501 | C8 | — | 4 | 1 | no | — |
| 502 | C8 | — | 4 | 1 | no | — |
| 503 | C8 | — | 4 | 1 | no | — |
| 504 | C8 | — | 8 | 1 | no | — |
| 505 | C8 | — | 12 | 2 | no | — |
| 506 | C2×C3 | — | 2 | 1 | no | — |
| 507 | C2×C3 | — | 2 | 1 | no | — |
| 508 | C2×C3 | — | 4 | 1 | no | — |
| 509 | C2×C3 | — | 4 | 1 | no | — |
| 510 | C2×C3 | #1881 | 1 | 1 | yes | characteristic |
| 511 | C2×C3 | #1898 | 1 | 1 | yes | characteristic |
| 512 | C2×C3 | #1907 | 1 | 1 | yes | characteristic |
| 513 | D3 | — | 4 | 2 | no | — |
| 514 | D3 | — | 8 | 1 | no | — |
| 515 | D3 | — | 16 | 1 | no | — |
| 516 | C22 | — | 2 | 1 | no | — |
| 517 | C22 | — | 2 | 1 | no | — |
| 518 | C22 | — | 2 | 1 | no | — |
| 519 | C22 | — | 2 | 1 | no | — |
| 520 | C22 | — | 2 | 1 | no | — |
| 521 | C22 | — | 2 | 1 | no | — |
| 522 | C22 | — | 2 | 1 | no | — |
| 523 | C22 | — | 2 | 1 | no | — |
| 524 | C22 | — | 6 | 2 | no | — |
| 525 | C22 | — | 8 | 1 | no | — |
| 526 | C22 | — | 8 | 1 | no | — |
| 527 | C22 | — | 12 | 1 | no | — |
| 528 | C22 | — | 12 | 1 | no | — |
| 529 | C22 | — | 12 | 1 | no | — |
| 530 | C22 | — | 12 | 1 | no | — |
| 531 | C22 | — | 12 | 1 | no | — |
| 532 | C22 | — | 24 | 2 | no | — |
| 533 | C22 | — | 24 | 2 | no | — |
| 534 | C22 | — | 24 | 1 | no | — |
| 535 | C22 | — | 24 | 1 | no | — |
| 536 | C22 | — | 24 | 1 | no | — |
| 537 | C22 | — | 48 | 2 | no | — |
| 538 | C22 | #4665 | 1 | 1 | yes | characteristic |
| 539 | C22 | #4897 | 1 | 1 | yes | characteristic |
| 540 | C22 | #4898 | 1 | 1 | yes | characteristic |
| 541 | C4 | — | 2 | 1 | no | — |
| 542 | C4 | — | 2 | 1 | no | — |
| 543 | C4 | — | 2 | 1 | no | — |
| 544 | C4 | — | 6 | 2 | no | — |
| 545 | C4 | — | 12 | 1 | no | — |
| 546 | C4 | — | 24 | 1 | no | — |
| 547 | C4 | — | 48 | 1 | no | — |
| 548 | C4 | D3×#99 | 1 | 1 | yes | characteristic |
| 549 | C4 | D3×#99 | 1 | 1 | yes | characteristic |
| 550 | C3 | #9347 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 551 | C2 | — | 2 | 1 | no | — |
| 552 | C2 | — | 2 | 1 | no | — |
| 553 | C2 | — | 4 | 1 | no | — |
| 554 | C2 | — | 4 | 1 | no | — |
| 555 | C2 | — | 12 | 2 | no | — |
| 556 | C2 | — | 24 | 1 | no | — |
| 557 | C2 | — | 48 | 1 | no | — |
| 558 | C2 | #68947 | 1 | 1 | yes | characteristic |
| 559 | C2 | #68948 | 1 | 1 | yes | characteristic |
| 560 | C2 | #68970 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #78600 | C2 | semidirect |
| 3. #69960 | C2 | semidirect |
| 4. #69944 | C2 | semidirect |
| 5. #69921 | C2 | semidirect |
| 6. C3×#1298 | C2 | semidirect |
| 7. #67684 | C2 | semidirect |
| 11. C2×#908 | C4 | semidirect |
| 12. C2×#908 | C4 | semidirect |
| 19. #5133 | C4 | semidirect |
| 20. #5133 | C4 | semidirect |
| 40. #1298 | D3 | semidirect |
| 550. C3 | #9347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78639 | 2 |
| #78600 | 2 |
| #69960 | 2 |
| #69944 | 2 |
| #69921 | 2 |
| C3×#1298 | 2 |
| #67684 | 2 |
| #9347 | 3 |