Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
994 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 167 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 | #81783 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #81777 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #81761 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #81560 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C3×#1721 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #71279 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #71276 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #71254 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #71185 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #68091 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #68075 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #19745 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C2×#914 | — | 2 | 2 | no | — |
| 14 | C2×#911 | — | 2 | 4 | no | — |
| 15 | #5725 | C22 | 1 | 1 | yes | characteristic |
| 16 | #5716 | C22 | 1 | 2 | yes | — |
| 17 | D3×#127 | C22 | 1 | 1 | yes | characteristic |
| 18 | C3×#493 | C22 | 1 | 2 | yes | — |
| 19 | C3×#493 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C3×#492 | C22 | 1 | 1 | yes | characteristic |
| 21 | C3×#486 | C22 | 1 | 2 | yes | complemented |
| 22 | #5176 | — | 2 | 2 | no | — |
| 23 | #5159 | — | 2 | 2 | no | — |
| 24 | #5154 | — | 2 | 4 | no | — |
| 25 | #5152 | — | 2 | 2 | no | — |
| 26 | #5085 | C22 | 1 | 1 | yes | characteristic |
| 27 | #5080 | C22 | 1 | 2 | yes | complemented |
| 28 | #5076 | C22 | 1 | 2 | yes | — |
| 29 | #5073 | C22 | 1 | 2 | yes | — |
| 30 | #5073 | C22 | 1 | 1 | yes | characteristic |
| 31 | #5073 | C22 | 1 | 2 | yes | complemented |
| 32 | #5070 | C22 | 1 | 2 | yes | complemented |
| 33 | #4785 | — | 2 | 4 | no | — |
| 34 | #4782 | — | 2 | 4 | no | — |
| 35 | #4695 | C22 | 1 | 1 | yes | characteristic |
| 36 | #4694 | C22 | 1 | 2 | yes | complemented |
| 37 | #4693 | C22 | 1 | 2 | yes | — |
| 38 | C4×ΓL(1,𝔽25) | C22 | 1 | 1 | yes | characteristic |
| 39 | C4×ΓL(1,𝔽25) | C22 | 1 | 2 | yes | — |
| 40 | #4680 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | C3×#322 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #4454 | C22 | 1 | 2 | yes | complemented |
| 43 | C8×C3⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | #3184 | — | 3 | 1 | no | — |
| 45 | #3184 | — | 3 | 2 | no | — |
| 46 | #3151 | — | 3 | 2 | no | — |
| 47 | #3151 | — | 3 | 1 | no | — |
| 48 | #1721 | — | 3 | 2 | no | — |
| 49 | #1721 | D3 | 1 | 1 | yes | characteristic, complemented |
| 50 | #1715 | — | 3 | 2 | no | — |
| 51 | #1715 | — | 3 | 1 | no | — |
| 52 | #1712 | — | 3 | 1 | no | — |
| 53 | #1705 | — | 3 | 1 | no | — |
| 54 | #1455 | — | 3 | 1 | no | — |
| 55 | C2×#239 | — | 2 | 1 | no | — |
| 56 | C2×#237 | — | 2 | 2 | no | — |
| 57 | C2×D3×D4 | — | 2 | 2 | no | — |
| 58 | C2×D3×D4 | — | 2 | 1 | no | — |
| 59 | C2×C3×SD16 | — | 2 | 2 | no | — |
| 60 | C2×C3×D8 | — | 2 | 2 | no | — |
| 61 | C2×C3×D8 | — | 2 | 4 | no | — |
| 62 | C3×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 63 | C3×#127 | C23 | 1 | 1 | yes | characteristic |
| 64 | C3×#127 | C23 | 1 | 2 | yes | — |
| 65 | #947 | — | 2 | 1 | no | — |
| 66 | C2×#215 | — | 2 | 2 | no | — |
| 67 | #940 | — | 2 | 2 | no | — |
| 68 | #940 | — | 2 | 1 | no | — |
| 69 | #938 | — | 2 | 2 | no | — |
| 70 | #938 | — | 2 | 2 | no | — |
| 71 | #936 | — | 2 | 2 | no | — |
| 72 | D4×Dic3 | — | 2 | 2 | no | — |
| 73 | D4×Dic3 | — | 2 | 2 | no | — |
| 74 | C2×#214 | — | 2 | 4 | no | — |
| 75 | C2×#213 | — | 2 | 4 | no | — |
| 76 | C2×#213 | — | 2 | 2 | no | — |
| 77 | C2×#213 | — | 2 | 4 | no | — |
| 78 | #914 | — | 4 | 8 | no | — |
| 79 | #911 | — | 4 | 16 | no | — |
| 80 | C2×D24 | — | 2 | 2 | no | — |
| 81 | C2×#204 | — | 2 | 4 | no | — |
| 82 | C2×ΓL(1,𝔽25) | D4 | 1 | 2 | yes | — |
| 83 | C2×ΓL(1,𝔽25) | D4 | 1 | 4 | yes | — |
| 84 | #895 | — | 2 | 2 | no | — |
| 85 | #893 | — | 2 | 2 | no | — |
| 86 | #874 | C23 | 1 | 1 | yes | characteristic |
| 87 | #874 | C23 | 1 | 1 | yes | characteristic |
| 88 | C42×D3 | C23 | 1 | 1 | yes | characteristic |
| 89 | #869 | C23 | 1 | 2 | yes | — |
| 90 | C3×#102 | — | 2 | 4 | no | — |
| 91 | C3×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 92 | C3×C4×C8 | C23 | 1 | 2 | yes | — |
| 93 | #832 | — | 2 | 4 | no | — |
| 94 | #821 | — | 2 | 4 | no | — |
| 95 | #817 | — | 2 | 2 | no | — |
| 96 | #815 | D4 | 1 | 2 | yes | — |
| 97 | #815 | D4 | 1 | 4 | yes | — |
| 98 | #808 | — | 2 | 4 | no | — |
| 99 | C4×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 100 | C4×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 101 | C2×AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 102 | C2×AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 103 | #532 | — | 3 | 1 | no | — |
| 104 | #532 | — | 3 | 2 | no | — |
| 105 | C2×#127 | — | 3 | 1 | no | — |
| 106 | #498 | — | 3 | 2 | no | — |
| 107 | #498 | — | 3 | 1 | no | — |
| 108 | #496 | — | 6 | 4 | no | — |
| 109 | #496 | — | 6 | 2 | no | — |
| 110 | #493 | — | 3 | 2 | no | — |
| 111 | #493 | — | 3 | 1 | no | — |
| 112 | #493 | — | 3 | 2 | no | — |
| 113 | #493 | — | 3 | 1 | no | — |
| 114 | #493 | C2×D3 | 1 | 2 | yes | — |
| 115 | #493 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 116 | #492 | — | 3 | 1 | no | — |
| 117 | #492 | — | 3 | 2 | no | — |
| 118 | #492 | — | 3 | 2 | no | — |
| 119 | #492 | C2×D3 | 1 | 1 | yes | characteristic |
| 120 | #486 | — | 3 | 2 | no | — |
| 121 | #486 | — | 3 | 2 | no | — |
| 122 | #486 | C2×D3 | 1 | 2 | yes | complemented |
| 123 | #469 | — | 6 | 4 | no | — |
| 124 | #469 | — | 6 | 2 | no | — |
| 125 | #442 | — | 6 | 4 | no | — |
| 126 | #442 | — | 6 | 2 | no | — |
| 127 | C4×M16 | — | 3 | 2 | no | — |
| 128 | C4×M16 | — | 3 | 1 | no | — |
| 129 | #322 | — | 3 | 2 | no | — |
| 130 | #322 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 131 | C82 | — | 3 | 1 | no | — |
| 132 | C23×D3 | — | 4 | 1 | no | — |
| 133 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 134 | C2×C3×D4 | — | 2 | 2 | no | — |
| 135 | C2×C3×D4 | — | 2 | 2 | no | — |
| 136 | C2×C3×D4 | — | 2 | 2 | no | — |
| 137 | C2×C3×D4 | — | 2 | 1 | no | — |
| 138 | C2×C3×D4 | — | 2 | 2 | no | — |
| 139 | C2×#67 | — | 4 | 2 | no | — |
| 140 | C2×#67 | — | 4 | 2 | no | — |
| 141 | C2×#67 | — | 4 | 1 | no | — |
| 142 | C22×Dic3 | — | 4 | 2 | no | — |
| 143 | #239 | — | 4 | 4 | no | — |
| 144 | #237 | — | 4 | 8 | no | — |
| 145 | D3×D4 | — | 4 | 8 | no | — |
| 146 | D3×D4 | — | 4 | 4 | no | — |
| 147 | C2×D12 | — | 2 | 2 | no | — |
| 148 | C2×D12 | — | 2 | 2 | no | — |
| 149 | C2×D12 | — | 2 | 1 | no | — |
| 150 | C2×D12 | — | 2 | 1 | no | — |
| 151 | C2×D12 | — | 4 | 1 | no | — |
| 152 | C2×C4×D3 | — | 4 | 1 | no | — |
| 153 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 154 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C2×Dic6 | — | 2 | 2 | no | — |
| 156 | C3×SD16 | — | 4 | 4 | no | — |
| 157 | C3×D8 | — | 4 | 8 | no | — |
| 158 | C3×D8 | — | 4 | 4 | no | — |
| 159 | C2×C3×C8 | C2×D4 | 1 | 4 | yes | — |
| 160 | C2×C3×C8 | C2×D4 | 1 | 2 | yes | — |
| 161 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 162 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 163 | #217 | — | 4 | 2 | no | — |
| 164 | #217 | — | 4 | 2 | no | — |
| 165 | #215 | — | 4 | 4 | no | — |
| 166 | #214 | — | 4 | 8 | no | — |
| 167 | #213 | — | 4 | 4 | no | — |
| 168 | #213 | — | 4 | 8 | no | — |
| 169 | #213 | — | 4 | 8 | no | — |
| 170 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 171 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 172 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 173 | C4×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 174 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | C2×C3⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 176 | C2×C3⋊C8 | C2×D4 | 1 | 4 | yes | — |
| 177 | D24 | — | 4 | 4 | no | — |
| 178 | #204 | — | 4 | 8 | no | — |
| 179 | ΓL(1,𝔽25) | — | 2 | 4 | no | — |
| 180 | ΓL(1,𝔽25) | — | 2 | 8 | no | — |
| 181 | C2×#41 | — | 6 | 2 | no | — |
| 182 | C2×#41 | — | 6 | 1 | no | — |
| 183 | C22×D4 | — | 6 | 2 | no | — |
| 184 | C22×D4 | — | 6 | 1 | no | — |
| 185 | AGL(1,ℤ/8) | — | 12 | 16 | no | — |
| 186 | AGL(1,ℤ/8) | — | 12 | 8 | no | — |
| 187 | C2×SD16 | — | 2 | 2 | no | — |
| 188 | C2×SD16 | — | 6 | 4 | no | — |
| 189 | C2×SD16 | — | 6 | 2 | no | — |
| 190 | C2×SD16 | — | 6 | 4 | no | — |
| 191 | C2×D8 | — | 2 | 4 | no | — |
| 192 | C2×D8 | — | 2 | 2 | no | — |
| 193 | C2×D8 | — | 6 | 4 | no | — |
| 194 | C2×D8 | — | 6 | 2 | no | — |
| 195 | C2×D8 | — | 6 | 4 | no | — |
| 196 | C2×D8 | — | 6 | 2 | no | — |
| 197 | C2×M16 | — | 3 | 4 | no | — |
| 198 | C2×M16 | — | 3 | 2 | no | — |
| 199 | C4⋊Q8 | — | 3 | 2 | no | — |
| 200 | C4⋊Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 201 | #127 | — | 3 | 1 | no | — |
| 202 | #127 | — | 3 | 1 | no | — |
| 203 | #127 | — | 6 | 2 | no | — |
| 204 | #127 | — | 6 | 1 | no | — |
| 205 | #127 | C22×D3 | 1 | 1 | yes | characteristic |
| 206 | #127 | C22×D3 | 1 | 2 | yes | — |
| 207 | #124 | — | 6 | 2 | no | — |
| 208 | #124 | — | 6 | 1 | no | — |
| 209 | #121 | — | 6 | 2 | no | — |
| 210 | #121 | — | 6 | 2 | no | — |
| 211 | #121 | — | 6 | 2 | no | — |
| 212 | C4×D4 | — | 6 | 2 | no | — |
| 213 | C4×D4 | — | 6 | 2 | no | — |
| 214 | C4×D4 | — | 6 | 2 | no | — |
| 215 | C2×C42 | — | 3 | 1 | no | — |
| 216 | #106 | — | 6 | 4 | no | — |
| 217 | #106 | — | 6 | 2 | no | — |
| 218 | #102 | — | 2 | 4 | no | — |
| 219 | #102 | — | 6 | 4 | no | — |
| 220 | #102 | — | 6 | 4 | no | — |
| 221 | #97 | — | 3 | 4 | no | — |
| 222 | #97 | — | 3 | 2 | no | — |
| 223 | C4×C8 | — | 3 | 2 | no | — |
| 224 | C4×C8 | — | 3 | 1 | no | — |
| 225 | C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 226 | C4×C8 | C22×D3 | 1 | 2 | yes | — |
| 227 | C23×C3 | — | 4 | 2 | no | — |
| 228 | C23×C3 | — | 4 | 1 | no | — |
| 229 | C22×D3 | — | 4 | 1 | no | — |
| 230 | C22×D3 | — | 4 | 1 | no | — |
| 231 | C22×D3 | — | 8 | 2 | no | — |
| 232 | C22×D3 | — | 8 | 4 | no | — |
| 233 | C22×D3 | #127 | 1 | 1 | yes | characteristic |
| 234 | C3×Q8 | — | 4 | 2 | no | — |
| 235 | C3×D4 | — | 4 | 4 | no | — |
| 236 | C3×D4 | — | 4 | 2 | no | — |
| 237 | C3×D4 | — | 4 | 4 | no | — |
| 238 | C3×D4 | — | 4 | 4 | no | — |
| 239 | C3×D4 | — | 4 | 4 | no | — |
| 240 | C2×C3×C4 | — | 4 | 1 | no | — |
| 241 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 242 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 243 | #67 | — | 8 | 2 | no | — |
| 244 | #67 | — | 8 | 4 | no | — |
| 245 | #67 | — | 8 | 4 | no | — |
| 246 | C2×Dic3 | — | 4 | 2 | no | — |
| 247 | C2×Dic3 | — | 8 | 4 | no | — |
| 248 | C2×Dic3 | #127 | 1 | 2 | yes | — |
| 249 | C2×Dic3 | #127 | 1 | 1 | yes | characteristic |
| 250 | D12 | — | 4 | 4 | no | — |
| 251 | D12 | — | 4 | 2 | no | — |
| 252 | D12 | — | 4 | 2 | no | — |
| 253 | D12 | — | 4 | 4 | no | — |
| 254 | D12 | — | 8 | 2 | no | — |
| 255 | C4×D3 | — | 2 | 4 | no | — |
| 256 | C4×D3 | — | 2 | 2 | no | — |
| 257 | C4×D3 | — | 8 | 2 | no | — |
| 258 | Dic6 | — | 4 | 4 | no | — |
| 259 | C3×C8 | — | 2 | 4 | no | — |
| 260 | C3×C8 | AGL(1,ℤ/8) | 1 | 4 | yes | complemented |
| 261 | C3⋊C8 | — | 2 | 2 | no | — |
| 262 | C3⋊C8 | AGL(1,ℤ/8) | 1 | 8 | yes | complemented |
| 263 | C24 | — | 12 | 1 | no | — |
| 264 | #41 | — | 12 | 8 | no | — |
| 265 | #41 | — | 12 | 4 | no | — |
| 266 | C2×Q8 | — | 2 | 1 | no | — |
| 267 | C2×Q8 | — | 6 | 2 | no | — |
| 268 | C2×D4 | — | 2 | 2 | no | — |
| 269 | C2×D4 | — | 2 | 2 | no | — |
| 270 | C2×D4 | — | 2 | 2 | no | — |
| 271 | C2×D4 | — | 2 | 2 | no | — |
| 272 | C2×D4 | — | 2 | 1 | no | — |
| 273 | C2×D4 | — | 6 | 2 | no | — |
| 274 | C2×D4 | — | 6 | 1 | no | — |
| 275 | C2×D4 | — | 6 | 1 | no | — |
| 276 | C2×D4 | — | 6 | 2 | no | — |
| 277 | C2×D4 | — | 12 | 1 | no | — |
| 278 | C2×D4 | — | 12 | 2 | no | — |
| 279 | C2×D4 | — | 12 | 1 | no | — |
| 280 | C2×D4 | — | 12 | 4 | no | — |
| 281 | C2×D4 | — | 12 | 8 | no | — |
| 282 | C2×D4 | — | 12 | 2 | no | — |
| 283 | C22×C4 | — | 3 | 1 | no | — |
| 284 | C22×C4 | — | 3 | 2 | no | — |
| 285 | C22×C4 | — | 12 | 1 | no | — |
| 286 | C22×C4 | — | 12 | 2 | no | — |
| 287 | SD16 | — | 4 | 4 | no | — |
| 288 | SD16 | — | 12 | 8 | no | — |
| 289 | SD16 | — | 12 | 8 | no | — |
| 290 | SD16 | — | 12 | 4 | no | — |
| 291 | D8 | — | 4 | 8 | no | — |
| 292 | D8 | — | 4 | 4 | no | — |
| 293 | D8 | — | 12 | 8 | no | — |
| 294 | D8 | — | 12 | 8 | no | — |
| 295 | D8 | — | 12 | 4 | no | — |
| 296 | D8 | — | 12 | 4 | no | — |
| 297 | M16 | — | 6 | 8 | no | — |
| 298 | M16 | — | 6 | 4 | no | — |
| 299 | C2×C8 | — | 3 | 4 | no | — |
| 300 | C2×C8 | — | 3 | 2 | no | — |
| 301 | C2×C8 | D3×D4 | 1 | 4 | yes | — |
| 302 | C2×C8 | D3×D4 | 1 | 2 | yes | — |
| 303 | C4⋊C4 | — | 2 | 2 | no | — |
| 304 | C4⋊C4 | — | 6 | 2 | no | — |
| 305 | C4⋊C4 | — | 6 | 2 | no | — |
| 306 | C22⋊C4 | — | 12 | 2 | no | — |
| 307 | C22⋊C4 | — | 12 | 2 | no | — |
| 308 | C22⋊C4 | — | 12 | 2 | no | — |
| 309 | C42 | — | 3 | 1 | no | — |
| 310 | C42 | — | 3 | 2 | no | — |
| 311 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 312 | C22×C3 | — | 8 | 2 | no | — |
| 313 | C22×C3 | — | 8 | 1 | no | — |
| 314 | C22×C3 | — | 8 | 2 | no | — |
| 315 | C22×C3 | — | 8 | 2 | no | — |
| 316 | C22×C3 | — | 8 | 2 | no | — |
| 317 | C22×C3 | C2×#127 | 1 | 1 | yes | characteristic |
| 318 | C2×D3 | — | 2 | 1 | no | — |
| 319 | C2×D3 | — | 2 | 2 | no | — |
| 320 | C2×D3 | — | 8 | 1 | no | — |
| 321 | C2×D3 | — | 8 | 1 | no | — |
| 322 | C2×D3 | — | 8 | 2 | no | — |
| 323 | C2×D3 | — | 8 | 2 | no | — |
| 324 | C2×D3 | — | 16 | 4 | no | — |
| 325 | C3×C4 | — | 8 | 1 | no | — |
| 326 | C3×C4 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 327 | C3×C4 | C2×AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 328 | Dic3 | — | 2 | 1 | no | — |
| 329 | Dic3 | — | 2 | 2 | no | — |
| 330 | Dic3 | — | 8 | 2 | no | — |
| 331 | C23 | — | 3 | 1 | no | — |
| 332 | C23 | — | 4 | 2 | no | — |
| 333 | C23 | — | 4 | 1 | no | — |
| 334 | C23 | — | 12 | 1 | no | — |
| 335 | C23 | — | 12 | 1 | no | — |
| 336 | C23 | — | 24 | 2 | no | — |
| 337 | C23 | — | 24 | 4 | no | — |
| 338 | Q8 | — | 4 | 2 | no | — |
| 339 | Q8 | — | 12 | 4 | no | — |
| 340 | D4 | — | 4 | 4 | no | — |
| 341 | D4 | — | 4 | 2 | no | — |
| 342 | D4 | — | 4 | 4 | no | — |
| 343 | D4 | — | 4 | 4 | no | — |
| 344 | D4 | — | 4 | 4 | no | — |
| 345 | D4 | — | 12 | 2 | no | — |
| 346 | D4 | — | 12 | 2 | no | — |
| 347 | D4 | — | 12 | 4 | no | — |
| 348 | D4 | — | 12 | 4 | no | — |
| 349 | D4 | — | 24 | 2 | no | — |
| 350 | D4 | — | 24 | 4 | no | — |
| 351 | D4 | — | 24 | 2 | no | — |
| 352 | D4 | — | 24 | 4 | no | — |
| 353 | C2×C4 | — | 3 | 1 | no | — |
| 354 | C2×C4 | — | 3 | 2 | no | — |
| 355 | C2×C4 | — | 4 | 1 | no | — |
| 356 | C2×C4 | — | 6 | 2 | no | — |
| 357 | C2×C4 | — | 6 | 4 | no | — |
| 358 | C2×C4 | — | 12 | 2 | no | — |
| 359 | C2×C4 | — | 24 | 2 | no | — |
| 360 | C2×C4 | — | 24 | 4 | no | — |
| 361 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 362 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 363 | C8 | — | 2 | 4 | no | — |
| 364 | C8 | — | 3 | 8 | no | — |
| 365 | C8 | — | 6 | 2 | no | — |
| 366 | C8 | #911 | 1 | 4 | yes | complemented |
| 367 | C2×C3 | — | 16 | 1 | no | — |
| 368 | C2×C3 | — | 16 | 2 | no | — |
| 369 | C2×C3 | #3151 | 1 | 1 | yes | characteristic |
| 370 | C2×C3 | #3151 | 1 | 2 | yes | — |
| 371 | D3 | — | 4 | 1 | no | — |
| 372 | D3 | — | 16 | 1 | no | — |
| 373 | D3 | — | 16 | 1 | no | — |
| 374 | C22 | — | 6 | 1 | no | — |
| 375 | C22 | — | 6 | 2 | no | — |
| 376 | C22 | — | 8 | 1 | no | — |
| 377 | C22 | — | 8 | 2 | no | — |
| 378 | C22 | — | 8 | 2 | no | — |
| 379 | C22 | — | 8 | 2 | no | — |
| 380 | C22 | — | 8 | 2 | no | — |
| 381 | C22 | — | 24 | 1 | no | — |
| 382 | C22 | — | 24 | 1 | no | — |
| 383 | C22 | — | 24 | 2 | no | — |
| 384 | C22 | — | 24 | 2 | no | — |
| 385 | C22 | — | 48 | 4 | no | — |
| 386 | C22 | D3×#127 | 1 | 1 | yes | characteristic |
| 387 | C4 | — | 6 | 1 | no | — |
| 388 | C4 | — | 6 | 2 | no | — |
| 389 | C4 | — | 8 | 1 | no | — |
| 390 | C4 | — | 24 | 2 | no | — |
| 391 | C4 | C2×#911 | 1 | 2 | yes | — |
| 392 | C4 | D3×AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 393 | C3 | #19745 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 394 | C2 | — | 12 | 1 | no | — |
| 395 | C2 | — | 16 | 1 | no | — |
| 396 | C2 | — | 16 | 2 | no | — |
| 397 | C2 | — | 48 | 1 | no | — |
| 398 | C2 | — | 48 | 1 | no | — |
| 399 | C2 | #81783 | 1 | 1 | yes | characteristic |
| 400 | C2 | #81845 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D3×#127 |
| commutator, cosocle | C3×C42 | C24 |
| Frattini | C42 | C23×D3 |
| Fitting | C3×#1721 | C2 |
| socle | C22×C3 | C2×#127 |
| hypercenter | #1721 | D3 |
| hypocenter | C3 | #19745 |
| LCS | G ▷ C3×C42 ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #1721 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #81783 | C2 | semidirect |
| 2. #81777 | C2 | semidirect |
| 3. #81761 | C2 | semidirect |
| 4. #81560 | C2 | semidirect |
| 5. C3×#1721 | C2 | semidirect |
| 6. #71279 | C2 | semidirect |
| 7. #71276 | C2 | semidirect |
| 8. #71254 | C2 | semidirect |
| 9. #71185 | C2 | semidirect |
| 10. #68091 | C2 | semidirect |
| 11. #68075 | C2 | semidirect |
| 19. C3×#493 | C22 | semidirect |
| 21. C3×#486 | C22 | semidirect |
| 27. #5080 | C22 | semidirect |
| 31. #5073 | C22 | semidirect |
| 32. #5070 | C22 | semidirect |
| 36. #4694 | C22 | semidirect |
| 40. #4680 | C22 | semidirect |
| 41. C3×#322 | C22 | semidirect |
| 42. #4454 | C22 | semidirect |
| 43. C8×C3⋊C8 | C22 | semidirect |
| 49. #1721 | D3 | semidirect |
| 115. #493 | C2×D3 | semidirect |
| 122. #486 | C2×D3 | semidirect |
| 130. #322 | C2×D3 | semidirect |
| 260. C3×C8 | AGL(1,ℤ/8) | semidirect |
| 262. C3⋊C8 | AGL(1,ℤ/8) | semidirect |
| 366. C8 | #911 | semidirect |
| 393. C3 | #19745 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #81783 | 2 |
| #81777 | 2 |
| #81761 | 2 |
| #81560 | 2 |
| C3×#1721 | 2 |
| #71279 | 2 |
| #71276 | 2 |
| #71254 | 2 |
| #71185 | 2 |
| #68091 | 2 |
| #68075 | 2 |
| #19745 | 3 |