Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
636 conjugacy classes of subgroups.
The subgroup lattice has 410 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #82028 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #82015 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #80947 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C3×#2222 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #71499 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #71452 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #71099 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #69362 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #69357 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #69273 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #69269 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #33860 | — | 3 | 1 | no | maximal, Sylow |
| 13 | #5779 | — | 2 | 2 | no | — |
| 14 | #5766 | C22 | 1 | 2 | yes | — |
| 15 | #5753 | C22 | 1 | 2 | yes | — |
| 16 | C2×C3×Q32 | C22 | 1 | 1 | yes | characteristic |
| 17 | C3×#504 | C22 | 1 | 1 | yes | characteristic |
| 18 | C3×#473 | C22 | 1 | 2 | yes | — |
| 19 | #5205 | — | 2 | 2 | no | — |
| 20 | #5183 | C22 | 1 | 2 | yes | — |
| 21 | C2×#829 | C22 | 1 | 2 | yes | — |
| 22 | #5179 | C22 | 1 | 2 | yes | — |
| 23 | #5144 | C22 | 1 | 1 | yes | characteristic |
| 24 | #4919 | — | 2 | 1 | no | — |
| 25 | #4918 | — | 2 | 2 | no | — |
| 26 | D3×Q32 | — | 2 | 1 | no | — |
| 27 | #4909 | — | 2 | 2 | no | — |
| 28 | #4909 | C22 | 1 | 2 | yes | — |
| 29 | C2×Dic24 | — | 2 | 1 | no | — |
| 30 | C2×Dic24 | C22 | 1 | 1 | yes | characteristic |
| 31 | #4904 | — | 2 | 1 | no | — |
| 32 | #4904 | C22 | 1 | 1 | yes | characteristic |
| 33 | #4901 | C22 | 1 | 1 | yes | characteristic |
| 34 | #4896 | C22 | 1 | 2 | yes | — |
| 35 | #4895 | C22 | 1 | 2 | yes | — |
| 36 | #4755 | — | 2 | 2 | no | — |
| 37 | #4752 | — | 2 | 2 | no | — |
| 38 | C3×#368 | C22 | 1 | 1 | yes | characteristic |
| 39 | C3×#362 | C22 | 1 | 2 | yes | — |
| 40 | #4561 | C22 | 1 | 1 | yes | characteristic |
| 41 | #4515 | C22 | 1 | 1 | yes | characteristic |
| 42 | #4511 | C22 | 1 | 1 | yes | characteristic |
| 43 | Dic3×C16 | C22 | 1 | 1 | yes | characteristic |
| 44 | #4497 | C22 | 1 | 2 | yes | — |
| 45 | #4496 | C22 | 1 | 2 | yes | — |
| 46 | #3417 | — | 3 | 1 | no | — |
| 47 | #3417 | — | 3 | 1 | no | — |
| 48 | #3293 | — | 3 | 2 | no | — |
| 49 | #2247 | — | 3 | 1 | no | — |
| 50 | #2222 | — | 3 | 1 | no | — |
| 51 | #2222 | D3 | 1 | 1 | yes | characteristic, complemented |
| 52 | #2214 | — | 3 | 2 | no | — |
| 53 | #2195 | — | 3 | 2 | no | — |
| 54 | #2195 | — | 3 | 2 | no | — |
| 55 | #2178 | — | 3 | 1 | no | — |
| 56 | #2170 | — | 3 | 1 | no | — |
| 57 | #1010 | — | 2 | 2 | no | — |
| 58 | #1007 | — | 2 | 2 | no | — |
| 59 | C3×#137 | — | 2 | 2 | no | — |
| 60 | C2×C3×Q16 | C23 | 1 | 2 | yes | — |
| 61 | C3×#131 | C23 | 1 | 1 | yes | characteristic |
| 62 | #950 | D4 | 1 | 1 | yes | characteristic |
| 63 | #944 | — | 2 | 2 | no | — |
| 64 | C2×#216 | — | 2 | 2 | no | — |
| 65 | #942 | — | 2 | 2 | no | — |
| 66 | #919 | — | 2 | 2 | no | — |
| 67 | #918 | — | 4 | 2 | no | — |
| 68 | #918 | — | 4 | 2 | no | — |
| 69 | D3×Q16 | — | 2 | 2 | no | — |
| 70 | D3×Q16 | — | 4 | 2 | no | — |
| 71 | #916 | — | 4 | 2 | no | — |
| 72 | #915 | — | 4 | 2 | no | — |
| 73 | #909 | — | 2 | 2 | no | — |
| 74 | #909 | — | 2 | 2 | no | — |
| 75 | #909 | — | 4 | 2 | no | — |
| 76 | #907 | — | 2 | 2 | no | — |
| 77 | C2×Dic12 | — | 2 | 2 | no | — |
| 78 | C2×Dic12 | C23 | 1 | 2 | yes | — |
| 79 | #904 | — | 2 | 2 | no | — |
| 80 | #904 | C23 | 1 | 2 | yes | — |
| 81 | #901 | C23 | 1 | 1 | yes | characteristic |
| 82 | C3×Q32 | — | 2 | 1 | no | — |
| 83 | C3×Q32 | — | 2 | 1 | no | — |
| 84 | C3×M32 | — | 2 | 1 | no | — |
| 85 | C3×M32 | C23 | 1 | 1 | yes | characteristic |
| 86 | C2×C3×C16 | — | 2 | 1 | no | — |
| 87 | C2×C3×C16 | C23 | 1 | 1 | yes | characteristic |
| 88 | C3×#108 | C23 | 1 | 2 | yes | — |
| 89 | C3×#101 | — | 2 | 2 | no | — |
| 90 | #837 | D4 | 1 | 1 | yes | characteristic |
| 91 | #829 | — | 2 | 2 | no | — |
| 92 | #829 | — | 4 | 2 | no | — |
| 93 | #828 | — | 2 | 2 | no | — |
| 94 | #825 | — | 2 | 2 | no | — |
| 95 | #825 | D4 | 1 | 1 | yes | characteristic |
| 96 | #824 | — | 2 | 2 | no | — |
| 97 | #822 | D4 | 1 | 1 | yes | characteristic |
| 98 | C8×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 99 | #812 | C23 | 1 | 1 | yes | characteristic |
| 100 | C2×C3⋊C16 | C23 | 1 | 1 | yes | characteristic |
| 101 | Dic24 | — | 2 | 2 | no | — |
| 102 | Dic24 | — | 2 | 1 | no | — |
| 103 | Dic24 | — | 2 | 1 | no | — |
| 104 | Dic24 | D4 | 1 | 1 | yes | characteristic |
| 105 | #800 | — | 2 | 2 | no | — |
| 106 | #800 | D4 | 1 | 2 | yes | — |
| 107 | D48 | D4 | 1 | 1 | yes | characteristic |
| 108 | #798 | — | 2 | 1 | no | — |
| 109 | D3×C16 | — | 2 | 1 | no | — |
| 110 | #578 | — | 3 | 2 | no | — |
| 111 | #578 | — | 3 | 2 | no | — |
| 112 | #578 | — | 6 | 2 | no | — |
| 113 | #510 | — | 3 | 2 | no | — |
| 114 | #510 | — | 3 | 2 | no | — |
| 115 | #510 | — | 6 | 2 | no | — |
| 116 | #510 | — | 6 | 2 | no | — |
| 117 | #508 | — | 3 | 1 | no | — |
| 118 | #508 | — | 6 | 1 | no | — |
| 119 | #508 | — | 6 | 1 | no | — |
| 120 | C2×Q32 | — | 3 | 2 | no | — |
| 121 | C2×Q32 | — | 3 | 1 | no | — |
| 122 | C2×Q32 | — | 6 | 1 | no | — |
| 123 | C2×Q32 | — | 6 | 1 | no | — |
| 124 | C2×Q32 | C2×D3 | 1 | 1 | yes | characteristic |
| 125 | #504 | — | 3 | 1 | no | — |
| 126 | #504 | C2×D3 | 1 | 1 | yes | characteristic |
| 127 | #494 | — | 3 | 2 | no | — |
| 128 | #473 | — | 3 | 2 | no | — |
| 129 | #473 | — | 6 | 2 | no | — |
| 130 | #473 | C2×D3 | 1 | 2 | yes | — |
| 131 | #456 | — | 6 | 2 | no | — |
| 132 | #456 | — | 6 | 2 | no | — |
| 133 | #443 | — | 3 | 1 | no | — |
| 134 | #443 | — | 3 | 2 | no | — |
| 135 | #368 | C2×D3 | 1 | 1 | yes | characteristic |
| 136 | #364 | — | 3 | 1 | no | — |
| 137 | #362 | — | 3 | 2 | no | — |
| 138 | #362 | C2×D3 | 1 | 2 | yes | — |
| 139 | #359 | — | 3 | 2 | no | — |
| 140 | #350 | — | 3 | 1 | no | — |
| 141 | #350 | — | 3 | 1 | no | — |
| 142 | C4×C16 | — | 3 | 1 | no | — |
| 143 | C3×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 144 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 145 | #239 | — | 4 | 2 | no | — |
| 146 | #239 | — | 4 | 2 | no | — |
| 147 | D3×Q8 | — | 4 | 2 | no | — |
| 148 | D3×Q8 | — | 4 | 2 | no | — |
| 149 | D3×Q8 | — | 4 | 2 | no | — |
| 150 | #237 | — | 4 | 2 | no | — |
| 151 | #237 | — | 8 | 2 | no | — |
| 152 | #235 | — | 2 | 2 | no | — |
| 153 | #235 | — | 4 | 2 | no | — |
| 154 | #235 | — | 8 | 2 | no | — |
| 155 | #235 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | C2×Dic6 | — | 2 | 2 | no | — |
| 157 | C2×Dic6 | — | 4 | 2 | no | — |
| 158 | C3×Q16 | — | 2 | 2 | no | — |
| 159 | C3×Q16 | — | 2 | 2 | no | — |
| 160 | C3×Q16 | — | 4 | 2 | no | — |
| 161 | C3×SD16 | — | 4 | 2 | no | — |
| 162 | C3×M16 | — | 2 | 1 | no | — |
| 163 | C3×M16 | — | 2 | 2 | no | — |
| 164 | C3×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 165 | C2×C3×C8 | — | 2 | 1 | no | — |
| 166 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 167 | #216 | — | 4 | 2 | no | — |
| 168 | #216 | — | 4 | 2 | no | — |
| 169 | #216 | — | 4 | 2 | no | — |
| 170 | #216 | D8 | 1 | 1 | yes | characteristic |
| 171 | #215 | — | 4 | 2 | no | — |
| 172 | #215 | D8 | 1 | 1 | yes | characteristic |
| 173 | #214 | D8 | 1 | 1 | yes | characteristic |
| 174 | #213 | D8 | 1 | 1 | yes | characteristic |
| 175 | Dic3⋊C4 | — | 8 | 2 | no | — |
| 176 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 177 | #208 | C2×D4 | 1 | 1 | yes | characteristic |
| 178 | C2×C3⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 179 | Dic12 | — | 2 | 2 | no | — |
| 180 | Dic12 | — | 2 | 2 | no | — |
| 181 | Dic12 | — | 4 | 2 | no | — |
| 182 | Dic12 | — | 4 | 2 | no | — |
| 183 | Dic12 | C2×D4 | 1 | 2 | yes | — |
| 184 | D24 | C2×D4 | 1 | 2 | yes | — |
| 185 | #204 | — | 2 | 2 | no | — |
| 186 | #204 | — | 4 | 2 | no | — |
| 187 | #204 | — | 4 | 2 | no | — |
| 188 | ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 189 | ΓL(1,𝔽25) | — | 4 | 2 | no | — |
| 190 | D3×C8 | — | 2 | 1 | no | — |
| 191 | D3×C8 | — | 4 | 2 | no | — |
| 192 | C3×C16 | — | 2 | 1 | no | — |
| 193 | C3×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 194 | C3×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 195 | C3⋊C16 | — | 2 | 1 | no | — |
| 196 | C3⋊C16 | — | 2 | 1 | no | — |
| 197 | 2−1+4 | — | 6 | 2 | no | — |
| 198 | 2−1+4 | — | 6 | 2 | no | — |
| 199 | #137 | — | 2 | 2 | no | — |
| 200 | #137 | — | 6 | 2 | no | — |
| 201 | #137 | — | 6 | 2 | no | — |
| 202 | #137 | — | 6 | 2 | no | — |
| 203 | #137 | — | 12 | 2 | no | — |
| 204 | #137 | — | 12 | 2 | no | — |
| 205 | #137 | — | 12 | 2 | no | — |
| 206 | #137 | — | 12 | 2 | no | — |
| 207 | #135 | — | 3 | 1 | no | — |
| 208 | #135 | — | 3 | 2 | no | — |
| 209 | #135 | — | 6 | 2 | no | — |
| 210 | #135 | — | 6 | 2 | no | — |
| 211 | #135 | — | 12 | 2 | no | — |
| 212 | C2×Q16 | — | 3 | 2 | no | — |
| 213 | C2×Q16 | — | 6 | 2 | no | — |
| 214 | C2×Q16 | — | 6 | 2 | no | — |
| 215 | C2×Q16 | — | 6 | 2 | no | — |
| 216 | C2×Q16 | — | 12 | 2 | no | — |
| 217 | C2×Q16 | C22×D3 | 1 | 2 | yes | — |
| 218 | #131 | — | 3 | 1 | no | — |
| 219 | #131 | — | 6 | 2 | no | — |
| 220 | #131 | C22×D3 | 1 | 1 | yes | characteristic |
| 221 | C4⋊Q8 | — | 6 | 2 | no | — |
| 222 | Q32 | — | 2 | 1 | no | — |
| 223 | Q32 | — | 2 | 1 | no | — |
| 224 | Q32 | — | 3 | 1 | no | — |
| 225 | Q32 | — | 6 | 2 | no | — |
| 226 | Q32 | — | 6 | 2 | no | — |
| 227 | Q32 | — | 6 | 1 | no | — |
| 228 | Q32 | — | 6 | 1 | no | — |
| 229 | Q32 | — | 12 | 2 | no | — |
| 230 | SD32 | — | 3 | 2 | no | — |
| 231 | SD32 | — | 6 | 2 | no | — |
| 232 | SD32 | — | 6 | 2 | no | — |
| 233 | D16 | — | 3 | 1 | no | — |
| 234 | M32 | — | 2 | 1 | no | — |
| 235 | M32 | — | 3 | 1 | no | — |
| 236 | M32 | — | 6 | 1 | no | — |
| 237 | M32 | C22×D3 | 1 | 1 | yes | characteristic |
| 238 | C2×C16 | — | 2 | 1 | no | — |
| 239 | C2×C16 | — | 3 | 1 | no | — |
| 240 | C2×C16 | — | 6 | 1 | no | — |
| 241 | C2×C16 | C22×D3 | 1 | 1 | yes | characteristic |
| 242 | #108 | — | 3 | 1 | no | — |
| 243 | #108 | C22×D3 | 1 | 2 | yes | — |
| 244 | #104 | — | 3 | 1 | no | — |
| 245 | #104 | — | 3 | 1 | no | — |
| 246 | #104 | — | 6 | 2 | no | — |
| 247 | #101 | — | 2 | 2 | no | — |
| 248 | #101 | — | 6 | 2 | no | — |
| 249 | C4×C8 | — | 3 | 1 | no | — |
| 250 | C3×Q8 | — | 4 | 2 | no | — |
| 251 | C3×Q8 | — | 4 | 2 | no | — |
| 252 | C3×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 253 | C3×D4 | — | 2 | 1 | no | — |
| 254 | C3×D4 | C2×D8 | 1 | 1 | yes | characteristic |
| 255 | C2×C3×C4 | — | 2 | 1 | no | — |
| 256 | C2×C3×C4 | — | 4 | 2 | no | — |
| 257 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 258 | #67 | — | 2 | 1 | no | — |
| 259 | #67 | — | 4 | 2 | no | — |
| 260 | #67 | — | 8 | 2 | no | — |
| 261 | C2×Dic3 | — | 2 | 1 | no | — |
| 262 | C2×Dic3 | — | 4 | 2 | no | — |
| 263 | C2×Dic3 | — | 8 | 2 | no | — |
| 264 | D12 | — | 2 | 2 | no | — |
| 265 | D12 | — | 8 | 2 | no | — |
| 266 | D12 | C2×D8 | 1 | 1 | yes | characteristic |
| 267 | C4×D3 | — | 2 | 1 | no | — |
| 268 | C4×D3 | — | 4 | 2 | no | — |
| 269 | C4×D3 | — | 8 | 2 | no | — |
| 270 | C4×D3 | — | 8 | 2 | no | — |
| 271 | C4×D3 | — | 8 | 2 | no | — |
| 272 | Dic6 | — | 2 | 2 | no | — |
| 273 | Dic6 | — | 4 | 2 | no | — |
| 274 | Dic6 | — | 4 | 2 | no | — |
| 275 | Dic6 | — | 8 | 2 | no | — |
| 276 | Dic6 | — | 8 | 2 | no | — |
| 277 | Dic6 | C2×D8 | 1 | 1 | yes | characteristic |
| 278 | C3×C8 | — | 2 | 1 | no | — |
| 279 | C3×C8 | — | 4 | 2 | no | — |
| 280 | C3×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 281 | C3×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 282 | C3⋊C8 | — | 2 | 1 | no | — |
| 283 | C3⋊C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 284 | C3⋊C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 285 | #41 | — | 3 | 1 | no | — |
| 286 | #41 | — | 6 | 2 | no | — |
| 287 | #41 | — | 12 | 2 | no | — |
| 288 | #41 | — | 12 | 2 | no | — |
| 289 | #41 | — | 12 | 2 | no | — |
| 290 | #41 | — | 12 | 2 | no | — |
| 291 | #41 | — | 24 | 2 | no | — |
| 292 | #41 | — | 24 | 2 | no | — |
| 293 | #41 | D3×D4 | 1 | 1 | yes | characteristic |
| 294 | C2×Q8 | — | 2 | 2 | no | — |
| 295 | C2×Q8 | — | 6 | 2 | no | — |
| 296 | C2×Q8 | — | 12 | 2 | no | — |
| 297 | C2×Q8 | — | 12 | 2 | no | — |
| 298 | C2×Q8 | — | 12 | 2 | no | — |
| 299 | C2×Q8 | — | 12 | 2 | no | — |
| 300 | Q16 | — | 2 | 2 | no | — |
| 301 | Q16 | — | 2 | 2 | no | — |
| 302 | Q16 | — | 3 | 1 | no | — |
| 303 | Q16 | — | 3 | 2 | no | — |
| 304 | Q16 | — | 4 | 2 | no | — |
| 305 | Q16 | — | 6 | 2 | no | — |
| 306 | Q16 | — | 6 | 2 | no | — |
| 307 | Q16 | — | 12 | 2 | no | — |
| 308 | Q16 | — | 12 | 2 | no | — |
| 309 | Q16 | — | 12 | 2 | no | — |
| 310 | Q16 | — | 12 | 2 | no | — |
| 311 | Q16 | — | 12 | 2 | no | — |
| 312 | SD16 | — | 3 | 1 | no | — |
| 313 | SD16 | — | 3 | 1 | no | — |
| 314 | SD16 | — | 4 | 2 | no | — |
| 315 | SD16 | — | 6 | 2 | no | — |
| 316 | SD16 | — | 12 | 2 | no | — |
| 317 | SD16 | — | 12 | 2 | no | — |
| 318 | SD16 | — | 12 | 2 | no | — |
| 319 | D8 | — | 3 | 1 | no | — |
| 320 | D8 | — | 3 | 2 | no | — |
| 321 | M16 | — | 2 | 1 | no | — |
| 322 | M16 | — | 2 | 2 | no | — |
| 323 | M16 | — | 3 | 1 | no | — |
| 324 | M16 | — | 6 | 1 | no | — |
| 325 | M16 | — | 12 | 2 | no | — |
| 326 | M16 | D3×D4 | 1 | 1 | yes | characteristic |
| 327 | C2×C8 | — | 2 | 1 | no | — |
| 328 | C2×C8 | — | 3 | 1 | no | — |
| 329 | C2×C8 | — | 6 | 1 | no | — |
| 330 | C2×C8 | — | 12 | 2 | no | — |
| 331 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 332 | C4⋊C4 | — | 24 | 2 | no | — |
| 333 | C42 | — | 3 | 1 | no | — |
| 334 | C16 | — | 2 | 1 | no | — |
| 335 | C16 | — | 6 | 1 | no | — |
| 336 | C16 | — | 6 | 1 | no | — |
| 337 | C16 | D3×D4 | 1 | 1 | yes | characteristic |
| 338 | C16 | D3×D4 | 1 | 1 | yes | characteristic |
| 339 | C22×C3 | — | 2 | 1 | no | — |
| 340 | C22×C3 | #576 | 1 | 1 | yes | characteristic |
| 341 | C2×D3 | — | 2 | 1 | no | — |
| 342 | C2×D3 | — | 4 | 2 | no | — |
| 343 | C3×C4 | — | 2 | 1 | no | — |
| 344 | C3×C4 | — | 8 | 2 | no | — |
| 345 | C3×C4 | D42 | 1 | 1 | yes | characteristic |
| 346 | C3×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 347 | Dic3 | — | 2 | 2 | no | — |
| 348 | Dic3 | — | 2 | 1 | no | — |
| 349 | Dic3 | — | 4 | 2 | no | — |
| 350 | Dic3 | — | 8 | 2 | no | — |
| 351 | Q8 | — | 3 | 1 | no | — |
| 352 | Q8 | — | 4 | 2 | no | — |
| 353 | Q8 | — | 4 | 2 | no | — |
| 354 | Q8 | — | 6 | 2 | no | — |
| 355 | Q8 | — | 12 | 2 | no | — |
| 356 | Q8 | — | 12 | 2 | no | — |
| 357 | Q8 | — | 24 | 2 | no | — |
| 358 | Q8 | — | 24 | 2 | no | — |
| 359 | Q8 | D3×D8 | 1 | 1 | yes | characteristic |
| 360 | D4 | — | 2 | 1 | no | — |
| 361 | D4 | — | 3 | 1 | no | — |
| 362 | D4 | — | 6 | 1 | no | — |
| 363 | D4 | — | 6 | 2 | no | — |
| 364 | D4 | — | 12 | 2 | no | — |
| 365 | D4 | — | 24 | 2 | no | — |
| 366 | D4 | — | 24 | 2 | no | — |
| 367 | D4 | D3×D8 | 1 | 1 | yes | characteristic |
| 368 | C2×C4 | — | 2 | 1 | no | — |
| 369 | C2×C4 | — | 4 | 2 | no | — |
| 370 | C2×C4 | — | 6 | 1 | no | — |
| 371 | C2×C4 | — | 6 | 1 | no | — |
| 372 | C2×C4 | — | 12 | 2 | no | — |
| 373 | C2×C4 | — | 12 | 2 | no | — |
| 374 | C2×C4 | — | 24 | 2 | no | — |
| 375 | C2×C4 | — | 24 | 2 | no | — |
| 376 | C2×C4 | — | 24 | 2 | no | — |
| 377 | C2×C4 | — | 24 | 2 | no | — |
| 378 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 379 | C8 | — | 2 | 1 | no | — |
| 380 | C8 | — | 3 | 1 | no | — |
| 381 | C8 | — | 3 | 1 | no | — |
| 382 | C8 | — | 4 | 2 | no | — |
| 383 | C8 | — | 6 | 1 | no | — |
| 384 | C8 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 385 | C8 | #1009 | 1 | 1 | yes | characteristic |
| 386 | C2×C3 | — | 2 | 1 | no | — |
| 387 | C2×C3 | — | 4 | 1 | no | — |
| 388 | C2×C3 | D4×D8 | 1 | 1 | yes | characteristic |
| 389 | D3 | — | 4 | 1 | no | — |
| 390 | D3 | — | 8 | 2 | no | — |
| 391 | C22 | — | 2 | 1 | no | — |
| 392 | C22 | — | 6 | 1 | no | — |
| 393 | C22 | — | 12 | 2 | no | — |
| 394 | C22 | #5769 | 1 | 1 | yes | characteristic |
| 395 | C4 | — | 2 | 1 | no | — |
| 396 | C4 | — | 6 | 2 | no | — |
| 397 | C4 | — | 6 | 1 | no | — |
| 398 | C4 | — | 8 | 2 | no | — |
| 399 | C4 | — | 12 | 2 | no | — |
| 400 | C4 | — | 24 | 2 | no | — |
| 401 | C4 | #5609 | 1 | 1 | yes | characteristic |
| 402 | C4 | C2×D3×D8 | 1 | 1 | yes | characteristic |
| 403 | C3 | #33860 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 404 | C2 | — | 2 | 1 | no | — |
| 405 | C2 | — | 4 | 1 | no | — |
| 406 | C2 | — | 12 | 1 | no | — |
| 407 | C2 | — | 24 | 2 | no | — |
| 408 | C2 | #80729 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #82028 | C2 | semidirect |
| 2. #82015 | C2 | semidirect |
| 3. #80947 | C2 | semidirect |
| 4. C3×#2222 | C2 | semidirect |
| 5. #71499 | C2 | semidirect |
| 6. #71452 | C2 | semidirect |
| 7. #71099 | C2 | semidirect |
| 8. #69362 | C2 | semidirect |
| 9. #69357 | C2 | semidirect |
| 10. #69273 | C2 | semidirect |
| 11. #69269 | C2 | semidirect |
| 51. #2222 | D3 | semidirect |
| 403. C3 | #33860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #82028 | 2 |
| #82015 | 2 |
| #80947 | 2 |
| C3×#2222 | 2 |
| #71499 | 2 |
| #71452 | 2 |
| #71099 | 2 |
| #69362 | 2 |
| #69357 | 2 |
| #69273 | 2 |
| #69269 | 2 |
| #33860 | 3 |