Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2600 conjugacy classes of subgroups.
The subgroup lattice has 474 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #87197 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | C3×#3152 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #83998 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #83322 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C2×#5095 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #81885 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #81808 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #81774 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #78541 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #61111 | — | 3 | 1 | no | maximal, Sylow |
| 11 | #5964 | C22 | 1 | 2 | yes | complemented |
| 12 | C2×#1007 | C22 | 1 | 2 | yes | — |
| 13 | C2×C3×#137 | C22 | 1 | 4 | yes | complemented |
| 14 | C3×#532 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C3×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | #5822 | C22 | 1 | 4 | yes | — |
| 17 | C2×#942 | C22 | 1 | 4 | yes | complemented |
| 18 | #5779 | — | 2 | 8 | no | — |
| 19 | #5778 | — | 2 | 8 | no | — |
| 20 | #5777 | — | 2 | 8 | no | — |
| 21 | D3×#137 | — | 2 | 8 | no | — |
| 22 | #5766 | C22 | 1 | 16 | yes | complemented |
| 23 | #5762 | C22 | 1 | 16 | yes | complemented |
| 24 | #5748 | C22 | 1 | 2 | yes | — |
| 25 | #5745 | C22 | 1 | 4 | yes | complemented |
| 26 | C3×#497 | C22 | 1 | 4 | yes | complemented |
| 27 | C3×#494 | C22 | 1 | 2 | yes | complemented |
| 28 | C3×#492 | C22 | 1 | 2 | yes | complemented |
| 29 | C3×C4×M16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | #5237 | C22 | 1 | 2 | yes | complemented |
| 31 | C2×#836 | C22 | 1 | 2 | yes | complemented |
| 32 | #5192 | C22 | 1 | 16 | yes | complemented |
| 33 | #5177 | C22 | 1 | 16 | yes | complemented |
| 34 | #5125 | C22 | 1 | 2 | yes | complemented |
| 35 | #5095 | C22 | 1 | 8 | yes | complemented |
| 36 | #5095 | C22 | 1 | 8 | yes | complemented |
| 37 | #5095 | C22 | 1 | 4 | yes | complemented |
| 38 | #5077 | C22 | 1 | 4 | yes | complemented |
| 39 | #5062 | C22 | 1 | 4 | yes | complemented |
| 40 | #5061 | C22 | 1 | 4 | yes | complemented |
| 41 | C2×#805 | C22 | 1 | 4 | yes | complemented |
| 42 | #4717 | C22 | 1 | 8 | yes | complemented |
| 43 | #4700 | C22 | 1 | 8 | yes | complemented |
| 44 | #3586 | — | 3 | 4 | no | — |
| 45 | #3293 | — | 3 | 4 | no | — |
| 46 | #3291 | — | 3 | 4 | no | — |
| 47 | #3289 | — | 3 | 8 | no | — |
| 48 | #3152 | D3 | 1 | 1 | yes | characteristic, complemented |
| 49 | #3069 | — | 3 | 4 | no | — |
| 50 | #3018 | — | 3 | 2 | no | — |
| 51 | C2×#456 | — | 3 | 2 | no | — |
| 52 | #2956 | — | 3 | 2 | no | — |
| 53 | C2×C3×#41 | C23 | 1 | 2 | yes | — |
| 54 | C22×C3×Q8 | C23 | 1 | 2 | yes | — |
| 55 | #1010 | — | 2 | 4 | no | — |
| 56 | #1009 | — | 2 | 4 | no | — |
| 57 | D3×#41 | — | 2 | 8 | no | — |
| 58 | #1007 | — | 2 | 8 | no | — |
| 59 | #1007 | — | 4 | 2 | no | — |
| 60 | #1007 | C23 | 1 | 8 | yes | — |
| 61 | #1007 | C23 | 1 | 4 | yes | — |
| 62 | C2×#239 | — | 2 | 4 | no | — |
| 63 | C2×D3×Q8 | — | 2 | 4 | no | — |
| 64 | #1004 | — | 4 | 2 | no | — |
| 65 | #1004 | C23 | 1 | 4 | yes | — |
| 66 | C2×#235 | — | 4 | 2 | no | — |
| 67 | C2×#235 | — | 4 | 2 | no | — |
| 68 | C2×#235 | C23 | 1 | 4 | yes | — |
| 69 | C3×#137 | — | 2 | 8 | no | — |
| 70 | C3×#137 | — | 2 | 8 | no | — |
| 71 | C2×C3×Q16 | C23 | 1 | 8 | yes | — |
| 72 | C2×C3×SD16 | C23 | 1 | 8 | yes | — |
| 73 | C2×C3×M16 | C23 | 1 | 2 | yes | — |
| 74 | C3×C4⋊Q8 | — | 4 | 1 | no | — |
| 75 | C3×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 76 | C3×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 77 | C3×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 78 | C3×#127 | C23 | 1 | 1 | yes | characteristic |
| 79 | C3×#124 | C23 | 1 | 2 | yes | — |
| 80 | C3×#121 | — | 4 | 1 | no | — |
| 81 | C3×C4×D4 | — | 4 | 1 | no | — |
| 82 | C2×C3×C4⋊C4 | — | 4 | 1 | no | — |
| 83 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 84 | #951 | — | 2 | 4 | no | — |
| 85 | #950 | — | 2 | 8 | no | — |
| 86 | #949 | — | 2 | 4 | no | — |
| 87 | C2×#216 | — | 2 | 4 | no | — |
| 88 | #942 | — | 2 | 8 | no | — |
| 89 | #942 | C23 | 1 | 16 | yes | — |
| 90 | #942 | C23 | 1 | 8 | yes | — |
| 91 | C2×#215 | — | 2 | 4 | no | — |
| 92 | #932 | C23 | 1 | 8 | yes | — |
| 93 | C2×#208 | C23 | 1 | 4 | yes | — |
| 94 | #919 | — | 2 | 16 | no | — |
| 95 | #918 | — | 2 | 16 | no | — |
| 96 | #918 | — | 2 | 16 | no | — |
| 97 | D3×Q16 | — | 2 | 16 | no | — |
| 98 | #916 | — | 2 | 16 | no | — |
| 99 | #915 | — | 2 | 16 | no | — |
| 100 | #914 | — | 2 | 16 | no | — |
| 101 | D3×SD16 | — | 2 | 16 | no | — |
| 102 | #909 | D4 | 1 | 8 | yes | complemented |
| 103 | #908 | D4 | 1 | 8 | yes | complemented |
| 104 | #907 | — | 2 | 8 | no | — |
| 105 | D3×M16 | — | 2 | 8 | no | — |
| 106 | #904 | C23 | 1 | 8 | yes | — |
| 107 | #901 | C23 | 1 | 16 | yes | — |
| 108 | C3×#97 | C23 | 1 | 2 | yes | — |
| 109 | C3×C4×C8 | C23 | 1 | 2 | yes | — |
| 110 | #836 | C23 | 1 | 8 | yes | — |
| 111 | #836 | C23 | 1 | 4 | yes | — |
| 112 | #833 | C23 | 1 | 4 | yes | — |
| 113 | #819 | C23 | 1 | 8 | yes | — |
| 114 | #805 | C23 | 1 | 8 | yes | — |
| 115 | #805 | C23 | 1 | 8 | yes | — |
| 116 | #585 | — | 3 | 2 | no | — |
| 117 | C2×2−1+4 | — | 3 | 2 | no | — |
| 118 | #578 | — | 3 | 16 | no | — |
| 119 | #578 | — | 6 | 8 | no | — |
| 120 | #577 | — | 3 | 16 | no | — |
| 121 | #577 | — | 6 | 8 | no | — |
| 122 | #575 | — | 3 | 4 | no | — |
| 123 | #575 | — | 3 | 2 | no | — |
| 124 | #575 | — | 6 | 8 | no | — |
| 125 | C2×#137 | — | 3 | 4 | no | — |
| 126 | C2×#137 | — | 6 | 8 | no | — |
| 127 | C2×#137 | C2×D3 | 1 | 4 | yes | complemented |
| 128 | #568 | — | 3 | 4 | no | — |
| 129 | #532 | C2×D3 | 1 | 1 | yes | characteristic |
| 130 | C2×C4⋊Q8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 131 | #497 | C2×D3 | 1 | 4 | yes | complemented |
| 132 | #494 | C2×D3 | 1 | 2 | yes | complemented |
| 133 | #492 | C2×D3 | 1 | 2 | yes | complemented |
| 134 | #473 | — | 3 | 16 | no | — |
| 135 | #471 | — | 3 | 16 | no | — |
| 136 | #456 | — | 3 | 8 | no | — |
| 137 | #456 | — | 3 | 8 | no | — |
| 138 | #456 | — | 3 | 4 | no | — |
| 139 | #455 | — | 3 | 4 | no | — |
| 140 | #454 | — | 3 | 4 | no | — |
| 141 | #453 | — | 3 | 4 | no | — |
| 142 | #444 | — | 3 | 8 | no | — |
| 143 | #443 | — | 3 | 8 | no | — |
| 144 | #430 | — | 3 | 2 | no | — |
| 145 | C2×#104 | — | 3 | 4 | no | — |
| 146 | #413 | — | 3 | 2 | no | — |
| 147 | C2×#101 | — | 3 | 2 | no | — |
| 148 | C4×M16 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 149 | C3×#41 | — | 2 | 4 | no | — |
| 150 | C3×#41 | — | 2 | 4 | no | — |
| 151 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 152 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 153 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 154 | C2×C3×Q8 | C24 | 1 | 2 | yes | — |
| 155 | C2×C3×Q8 | C24 | 1 | 4 | yes | — |
| 156 | C2×C3×D4 | — | 2 | 2 | no | — |
| 157 | C2×C3×D4 | — | 4 | 1 | no | — |
| 158 | C2×C3×D4 | C24 | 1 | 2 | yes | — |
| 159 | C22×C3×C4 | — | 2 | 1 | no | — |
| 160 | C22×C3×C4 | — | 2 | 2 | no | — |
| 161 | C22×C3×C4 | — | 2 | 2 | no | — |
| 162 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 163 | C2×#67 | — | 2 | 4 | no | — |
| 164 | C2×#67 | — | 4 | 4 | no | — |
| 165 | #239 | — | 2 | 16 | no | — |
| 166 | #239 | — | 2 | 8 | no | — |
| 167 | #239 | — | 4 | 8 | no | — |
| 168 | D3×Q8 | — | 2 | 16 | no | — |
| 169 | D3×Q8 | — | 2 | 8 | no | — |
| 170 | D3×Q8 | — | 4 | 8 | no | — |
| 171 | #237 | — | 2 | 8 | no | — |
| 172 | #237 | — | 4 | 8 | no | — |
| 173 | D3×D4 | — | 2 | 8 | no | — |
| 174 | D3×D4 | — | 4 | 8 | no | — |
| 175 | #235 | — | 2 | 4 | no | — |
| 176 | #235 | — | 2 | 4 | no | — |
| 177 | #235 | — | 4 | 4 | no | — |
| 178 | #235 | — | 4 | 4 | no | — |
| 179 | #235 | — | 4 | 4 | no | — |
| 180 | #235 | — | 4 | 8 | no | — |
| 181 | #235 | — | 4 | 8 | no | — |
| 182 | #235 | C2×D4 | 1 | 8 | yes | — |
| 183 | #235 | C24 | 1 | 8 | yes | — |
| 184 | C2×D12 | — | 4 | 2 | no | — |
| 185 | C2×D12 | — | 4 | 2 | no | — |
| 186 | C2×D12 | C2×D4 | 1 | 4 | yes | — |
| 187 | C2×C4×D3 | — | 2 | 4 | no | — |
| 188 | C2×C4×D3 | — | 4 | 4 | no | — |
| 189 | C2×C4×D3 | — | 4 | 4 | no | — |
| 190 | C2×Dic6 | — | 4 | 2 | no | — |
| 191 | C2×Dic6 | — | 4 | 2 | no | — |
| 192 | C2×Dic6 | C2×D4 | 1 | 4 | yes | — |
| 193 | C3×Q16 | — | 2 | 16 | no | — |
| 194 | C3×SD16 | — | 2 | 16 | no | — |
| 195 | C3×M16 | C2×D4 | 1 | 8 | yes | — |
| 196 | C2×C3×C8 | C24 | 1 | 4 | yes | — |
| 197 | C3×C4⋊C4 | — | 4 | 2 | no | — |
| 198 | C3×C4⋊C4 | — | 4 | 2 | no | — |
| 199 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 200 | C3×C22⋊C4 | — | 4 | 2 | no | — |
| 201 | C3×C42 | — | 2 | 1 | no | — |
| 202 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 203 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 204 | #216 | — | 2 | 16 | no | — |
| 205 | #216 | — | 2 | 8 | no | — |
| 206 | #215 | — | 2 | 16 | no | — |
| 207 | #215 | — | 2 | 8 | no | — |
| 208 | #214 | — | 2 | 8 | no | — |
| 209 | #213 | — | 2 | 8 | no | — |
| 210 | #208 | — | 2 | 4 | no | — |
| 211 | #208 | C24 | 1 | 8 | yes | — |
| 212 | C2×C3⋊C8 | — | 2 | 4 | no | — |
| 213 | Dic12 | C2×D4 | 1 | 8 | yes | — |
| 214 | D24 | C2×D4 | 1 | 8 | yes | — |
| 215 | #204 | C2×D4 | 1 | 16 | yes | — |
| 216 | ΓL(1,𝔽25) | — | 2 | 16 | no | — |
| 217 | D3×C8 | — | 2 | 16 | no | — |
| 218 | 2−1+4 | — | 3 | 8 | no | — |
| 219 | 2−1+4 | — | 3 | 4 | no | — |
| 220 | 2−1+4 | — | 6 | 8 | no | — |
| 221 | 2−1+4 | — | 6 | 4 | no | — |
| 222 | 2−1+4 | — | 12 | 2 | no | — |
| 223 | H(5,𝔽2) | — | 3 | 4 | no | — |
| 224 | H(5,𝔽2) | — | 6 | 4 | no | — |
| 225 | H(5,𝔽2) | — | 12 | 2 | no | — |
| 226 | C2×#41 | — | 3 | 4 | no | — |
| 227 | C2×#41 | — | 6 | 4 | no | — |
| 228 | C2×#41 | — | 6 | 8 | no | — |
| 229 | C2×#41 | — | 12 | 2 | no | — |
| 230 | C2×#41 | — | 12 | 2 | no | — |
| 231 | C2×#41 | C22×D3 | 1 | 2 | yes | — |
| 232 | C22×Q8 | — | 6 | 4 | no | — |
| 233 | C22×Q8 | C22×D3 | 1 | 2 | yes | — |
| 234 | #137 | — | 2 | 8 | no | — |
| 235 | #137 | — | 2 | 8 | no | — |
| 236 | #137 | — | 3 | 16 | no | — |
| 237 | #137 | — | 3 | 8 | no | — |
| 238 | #137 | — | 3 | 8 | no | — |
| 239 | #137 | — | 6 | 16 | no | — |
| 240 | #137 | — | 6 | 16 | no | — |
| 241 | #137 | — | 6 | 16 | no | — |
| 242 | #137 | — | 6 | 8 | no | — |
| 243 | #137 | — | 6 | 4 | no | — |
| 244 | AGL(1,ℤ/8) | — | 3 | 8 | no | — |
| 245 | AGL(1,ℤ/8) | — | 3 | 8 | no | — |
| 246 | AGL(1,ℤ/8) | — | 6 | 16 | no | — |
| 247 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 248 | #135 | — | 3 | 8 | no | — |
| 249 | #135 | — | 6 | 16 | no | — |
| 250 | #135 | — | 6 | 16 | no | — |
| 251 | #135 | — | 6 | 8 | no | — |
| 252 | C2×Q16 | — | 6 | 16 | no | — |
| 253 | C2×Q16 | — | 6 | 4 | no | — |
| 254 | C2×Q16 | C22×D3 | 1 | 8 | yes | — |
| 255 | C2×SD16 | — | 6 | 16 | no | — |
| 256 | C2×SD16 | — | 6 | 4 | no | — |
| 257 | C2×SD16 | C22×D3 | 1 | 8 | yes | — |
| 258 | #131 | — | 3 | 16 | no | — |
| 259 | #131 | — | 6 | 8 | no | — |
| 260 | C2×M16 | — | 3 | 4 | no | — |
| 261 | C2×M16 | — | 6 | 8 | no | — |
| 262 | C2×M16 | C22×D3 | 1 | 2 | yes | — |
| 263 | C4⋊Q8 | — | 4 | 1 | no | — |
| 264 | C4⋊Q8 | C22×D3 | 1 | 2 | yes | — |
| 265 | C4⋊Q8 | C22×D3 | 1 | 2 | yes | — |
| 266 | C4⋊Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 267 | #127 | C22×D3 | 1 | 1 | yes | characteristic |
| 268 | #124 | C22×D3 | 1 | 2 | yes | — |
| 269 | #121 | — | 4 | 1 | no | — |
| 270 | C4×D4 | — | 4 | 1 | no | — |
| 271 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 272 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 273 | #108 | — | 3 | 8 | no | — |
| 274 | #104 | — | 3 | 8 | no | — |
| 275 | #104 | — | 3 | 8 | no | — |
| 276 | #101 | — | 3 | 8 | no | — |
| 277 | #101 | — | 3 | 4 | no | — |
| 278 | #100 | — | 3 | 4 | no | — |
| 279 | #97 | C22×D3 | 1 | 2 | yes | — |
| 280 | C4×C8 | C22×D3 | 1 | 2 | yes | — |
| 281 | C23×C3 | — | 2 | 2 | no | — |
| 282 | C23×C3 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 283 | C22×D3 | — | 2 | 4 | no | — |
| 284 | C22×D3 | — | 4 | 4 | no | — |
| 285 | C3×Q8 | — | 2 | 8 | no | — |
| 286 | C3×Q8 | — | 2 | 4 | no | — |
| 287 | C3×Q8 | — | 4 | 4 | no | — |
| 288 | C3×D4 | — | 2 | 4 | no | — |
| 289 | C3×D4 | — | 4 | 4 | no | — |
| 290 | C3×D4 | — | 8 | 2 | no | — |
| 291 | C2×C3×C4 | — | 2 | 1 | no | — |
| 292 | C2×C3×C4 | — | 2 | 1 | no | — |
| 293 | C2×C3×C4 | — | 2 | 2 | no | — |
| 294 | C2×C3×C4 | — | 2 | 4 | no | — |
| 295 | C2×C3×C4 | — | 4 | 2 | no | — |
| 296 | C2×C3×C4 | — | 4 | 2 | no | — |
| 297 | C2×C3×C4 | — | 4 | 2 | no | — |
| 298 | C2×C3×C4 | — | 4 | 2 | no | — |
| 299 | C2×C3×C4 | — | 4 | 2 | no | — |
| 300 | C2×C3×C4 | C22×D4 | 1 | 4 | yes | — |
| 301 | C2×C3×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 302 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 303 | #67 | — | 2 | 8 | no | — |
| 304 | #67 | — | 2 | 8 | no | — |
| 305 | #67 | — | 4 | 8 | no | — |
| 306 | C2×Dic3 | — | 2 | 4 | no | — |
| 307 | C2×Dic3 | — | 4 | 4 | no | — |
| 308 | D12 | — | 2 | 4 | no | — |
| 309 | D12 | — | 4 | 4 | no | — |
| 310 | D12 | — | 4 | 8 | no | — |
| 311 | D12 | C22×D4 | 1 | 8 | yes | — |
| 312 | C4×D3 | — | 2 | 8 | no | — |
| 313 | C4×D3 | — | 2 | 8 | no | — |
| 314 | C4×D3 | — | 4 | 8 | no | — |
| 315 | C4×D3 | — | 4 | 16 | no | — |
| 316 | Dic6 | — | 2 | 4 | no | — |
| 317 | Dic6 | — | 4 | 4 | no | — |
| 318 | Dic6 | — | 4 | 8 | no | — |
| 319 | Dic6 | C22×D4 | 1 | 8 | yes | — |
| 320 | C3×C8 | C22×D4 | 1 | 8 | yes | — |
| 321 | C3⋊C8 | — | 2 | 8 | no | — |
| 322 | #41 | — | 2 | 4 | no | — |
| 323 | #41 | — | 2 | 4 | no | — |
| 324 | #41 | — | 3 | 8 | no | — |
| 325 | #41 | — | 3 | 8 | no | — |
| 326 | #41 | — | 6 | 4 | no | — |
| 327 | #41 | — | 6 | 4 | no | — |
| 328 | #41 | — | 6 | 8 | no | — |
| 329 | #41 | — | 6 | 16 | no | — |
| 330 | #41 | — | 6 | 8 | no | — |
| 331 | #41 | — | 12 | 4 | no | — |
| 332 | #41 | — | 12 | 8 | no | — |
| 333 | #41 | — | 12 | 4 | no | — |
| 334 | #41 | — | 12 | 8 | no | — |
| 335 | #41 | — | 12 | 4 | no | — |
| 336 | #41 | — | 12 | 8 | no | — |
| 337 | #41 | — | 12 | 8 | no | — |
| 338 | C2×Q8 | — | 2 | 2 | no | — |
| 339 | C2×Q8 | — | 2 | 4 | no | — |
| 340 | C2×Q8 | — | 2 | 4 | no | — |
| 341 | C2×Q8 | — | 3 | 4 | no | — |
| 342 | C2×Q8 | — | 6 | 16 | no | — |
| 343 | C2×Q8 | — | 6 | 8 | no | — |
| 344 | C2×Q8 | — | 12 | 2 | no | — |
| 345 | C2×Q8 | — | 12 | 2 | no | — |
| 346 | C2×Q8 | — | 12 | 8 | no | — |
| 347 | C2×Q8 | C23×D3 | 1 | 2 | yes | — |
| 348 | C2×Q8 | C23×D3 | 1 | 4 | yes | — |
| 349 | C2×D4 | — | 2 | 2 | no | — |
| 350 | C2×D4 | — | 3 | 4 | no | — |
| 351 | C2×D4 | — | 4 | 1 | no | — |
| 352 | C2×D4 | — | 6 | 8 | no | — |
| 353 | C2×D4 | — | 6 | 4 | no | — |
| 354 | C2×D4 | — | 12 | 2 | no | — |
| 355 | C2×D4 | — | 12 | 2 | no | — |
| 356 | C2×D4 | — | 12 | 8 | no | — |
| 357 | C2×D4 | — | 12 | 4 | no | — |
| 358 | C2×D4 | C23×D3 | 1 | 2 | yes | — |
| 359 | C22×C4 | — | 2 | 1 | no | — |
| 360 | C22×C4 | — | 2 | 2 | no | — |
| 361 | C22×C4 | — | 2 | 2 | no | — |
| 362 | C22×C4 | — | 6 | 4 | no | — |
| 363 | C22×C4 | — | 12 | 4 | no | — |
| 364 | C22×C4 | — | 12 | 4 | no | — |
| 365 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 366 | Q16 | — | 2 | 16 | no | — |
| 367 | Q16 | — | 3 | 8 | no | — |
| 368 | Q16 | — | 6 | 16 | no | — |
| 369 | Q16 | — | 6 | 8 | no | — |
| 370 | SD16 | — | 2 | 16 | no | — |
| 371 | SD16 | — | 3 | 16 | no | — |
| 372 | SD16 | — | 6 | 8 | no | — |
| 373 | SD16 | — | 6 | 16 | no | — |
| 374 | SD16 | — | 6 | 8 | no | — |
| 375 | D8 | — | 3 | 8 | no | — |
| 376 | D8 | — | 6 | 8 | no | — |
| 377 | M16 | — | 3 | 8 | no | — |
| 378 | M16 | — | 6 | 4 | no | — |
| 379 | M16 | — | 6 | 16 | no | — |
| 380 | M16 | D3×D4 | 1 | 8 | yes | — |
| 381 | C2×C8 | — | 6 | 4 | no | — |
| 382 | C2×C8 | — | 6 | 16 | no | — |
| 383 | C2×C8 | C23×D3 | 1 | 4 | yes | — |
| 384 | C4⋊C4 | — | 4 | 2 | no | — |
| 385 | C4⋊C4 | — | 4 | 2 | no | — |
| 386 | C4⋊C4 | — | 4 | 1 | no | — |
| 387 | C22⋊C4 | — | 4 | 2 | no | — |
| 388 | C42 | — | 2 | 1 | no | — |
| 389 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 390 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 391 | C22×C3 | — | 4 | 1 | no | — |
| 392 | C22×C3 | — | 4 | 2 | no | — |
| 393 | C22×C3 | — | 8 | 2 | no | — |
| 394 | C22×C3 | D42 | 1 | 2 | yes | — |
| 395 | C22×C3 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 396 | C2×D3 | — | 2 | 8 | no | — |
| 397 | C2×D3 | — | 8 | 4 | no | — |
| 398 | C2×D3 | — | 16 | 4 | no | — |
| 399 | C3×C4 | — | 2 | 2 | no | — |
| 400 | C3×C4 | — | 4 | 1 | no | — |
| 401 | C3×C4 | — | 4 | 2 | no | — |
| 402 | C3×C4 | — | 4 | 4 | no | — |
| 403 | C3×C4 | D42 | 1 | 2 | yes | — |
| 404 | C3×C4 | C23×D4 | 1 | 2 | yes | — |
| 405 | Dic3 | — | 2 | 8 | no | — |
| 406 | C23 | — | 2 | 2 | no | — |
| 407 | C23 | — | 6 | 4 | no | — |
| 408 | C23 | — | 12 | 4 | no | — |
| 409 | C23 | #1004 | 1 | 1 | yes | characteristic |
| 410 | Q8 | — | 2 | 8 | no | — |
| 411 | Q8 | — | 2 | 4 | no | — |
| 412 | Q8 | — | 3 | 8 | no | — |
| 413 | Q8 | — | 4 | 4 | no | — |
| 414 | Q8 | — | 6 | 4 | no | — |
| 415 | Q8 | — | 12 | 8 | no | — |
| 416 | Q8 | — | 12 | 4 | no | — |
| 417 | D4 | — | 2 | 4 | no | — |
| 418 | D4 | — | 3 | 8 | no | — |
| 419 | D4 | — | 4 | 4 | no | — |
| 420 | D4 | — | 6 | 8 | no | — |
| 421 | D4 | — | 6 | 8 | no | — |
| 422 | D4 | — | 6 | 4 | no | — |
| 423 | D4 | — | 8 | 2 | no | — |
| 424 | D4 | — | 12 | 4 | no | — |
| 425 | D4 | — | 12 | 8 | no | — |
| 426 | D4 | — | 12 | 8 | no | — |
| 427 | C2×C4 | — | 2 | 1 | no | — |
| 428 | C2×C4 | — | 2 | 1 | no | — |
| 429 | C2×C4 | — | 2 | 2 | no | — |
| 430 | C2×C4 | — | 2 | 4 | no | — |
| 431 | C2×C4 | — | 4 | 2 | no | — |
| 432 | C2×C4 | — | 4 | 2 | no | — |
| 433 | C2×C4 | — | 4 | 2 | no | — |
| 434 | C2×C4 | — | 4 | 2 | no | — |
| 435 | C2×C4 | — | 4 | 2 | no | — |
| 436 | C2×C4 | — | 6 | 4 | no | — |
| 437 | C2×C4 | — | 6 | 8 | no | — |
| 438 | C2×C4 | — | 6 | 8 | no | — |
| 439 | C2×C4 | — | 12 | 8 | no | — |
| 440 | C2×C4 | — | 12 | 16 | no | — |
| 441 | C2×C4 | — | 12 | 4 | no | — |
| 442 | C2×C4 | C2×D3×D4 | 1 | 4 | yes | — |
| 443 | C2×C4 | #1004 | 1 | 1 | yes | characteristic |
| 444 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 445 | C8 | — | 6 | 8 | no | — |
| 446 | C8 | C2×D3×D4 | 1 | 8 | yes | — |
| 447 | C2×C3 | — | 2 | 1 | no | — |
| 448 | C2×C3 | — | 2 | 2 | no | — |
| 449 | C2×C3 | — | 8 | 2 | no | — |
| 450 | C2×C3 | C2×D42 | 1 | 1 | yes | characteristic |
| 451 | D3 | — | 4 | 8 | no | — |
| 452 | C22 | — | 4 | 1 | no | — |
| 453 | C22 | — | 4 | 2 | no | — |
| 454 | C22 | — | 6 | 8 | no | — |
| 455 | C22 | — | 8 | 2 | no | — |
| 456 | C22 | — | 24 | 4 | no | — |
| 457 | C22 | — | 48 | 4 | no | — |
| 458 | C22 | #5717 | 1 | 2 | yes | — |
| 459 | C22 | C2×#1004 | 1 | 1 | yes | characteristic |
| 460 | C4 | — | 2 | 2 | no | — |
| 461 | C4 | — | 4 | 1 | no | — |
| 462 | C4 | — | 4 | 2 | no | — |
| 463 | C4 | — | 4 | 4 | no | — |
| 464 | C4 | — | 6 | 8 | no | — |
| 465 | C4 | #5717 | 1 | 2 | yes | — |
| 466 | C4 | C22×D3×D4 | 1 | 2 | yes | — |
| 467 | C3 | #61111 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 468 | C2 | — | 2 | 1 | no | — |
| 469 | C2 | — | 2 | 2 | no | — |
| 470 | C2 | — | 8 | 2 | no | — |
| 471 | C2 | — | 12 | 8 | no | — |
| 472 | C2 | C2×#5717 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #87197 | C2 | semidirect |
| 2. C3×#3152 | C2 | semidirect |
| 3. #83998 | C2 | semidirect |
| 4. #83322 | C2 | semidirect |
| 5. C2×#5095 | C2 | semidirect |
| 6. #81885 | C2 | semidirect |
| 7. #81808 | C2 | semidirect |
| 8. #81774 | C2 | semidirect |
| 9. #78541 | C2 | semidirect |
| 11. #5964 | C22 | semidirect |
| 13. C2×C3×#137 | C22 | semidirect |
| 15. C2×C3×C4⋊Q8 | C22 | semidirect |
| 17. C2×#942 | C22 | semidirect |
| 22. #5766 | C22 | semidirect |
| 23. #5762 | C22 | semidirect |
| 25. #5745 | C22 | semidirect |
| 26. C3×#497 | C22 | semidirect |
| 27. C3×#494 | C22 | semidirect |
| 28. C3×#492 | C22 | semidirect |
| 29. C3×C4×M16 | C22 | semidirect |
| 30. #5237 | C22 | semidirect |
| 31. C2×#836 | C22 | semidirect |
| 32. #5192 | C22 | semidirect |
| 33. #5177 | C22 | semidirect |
| 34. #5125 | C22 | semidirect |
| 35. #5095 | C22 | semidirect |
| 36. #5095 | C22 | semidirect |
| 37. #5095 | C22 | semidirect |
| 38. #5077 | C22 | semidirect |
| 39. #5062 | C22 | semidirect |
| 40. #5061 | C22 | semidirect |
| 41. C2×#805 | C22 | semidirect |
| 42. #4717 | C22 | semidirect |
| 43. #4700 | C22 | semidirect |
| 48. #3152 | D3 | semidirect |
| 102. #909 | D4 | semidirect |
| 103. #908 | D4 | semidirect |
| 127. C2×#137 | C2×D3 | semidirect |
| 130. C2×C4⋊Q8 | C2×D3 | semidirect |
| 131. #497 | C2×D3 | semidirect |
| 132. #494 | C2×D3 | semidirect |
| 133. #492 | C2×D3 | semidirect |
| 148. C4×M16 | C2×D3 | semidirect |
| 467. C3 | #61111 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #87197 | 2 |
| C3×#3152 | 2 |
| #83998 | 2 |
| #83322 | 2 |
| C2×#5095 | 2 |
| #81885 | 2 |
| #81808 | 2 |
| #81774 | 2 |
| #78541 | 2 |
| #61111 | 3 |