Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2630 conjugacy classes of subgroups.
The subgroup lattice has 382 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C3×#576 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #87277 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #87160 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #84100 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #83963 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | #83928 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | C2×#5160 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #83789 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #60471 | — | 3 | 1 | no | maximal, Sylow |
| 10 | C2×C3×H(5,𝔽2) | C22 | 1 | 2 | yes | — |
| 11 | #5964 | C22 | 1 | 1 | yes | characteristic |
| 12 | C3×#576 | — | 2 | 4 | no | — |
| 13 | C3×#576 | — | 2 | 4 | no | — |
| 14 | C2×C3×AGL(1,ℤ/8) | C22 | 1 | 6 | yes | complemented |
| 15 | C2×C3×#135 | C22 | 1 | 3 | yes | complemented |
| 16 | C22×C3×D8 | C22 | 1 | 3 | yes | complemented |
| 17 | C2×C3×#131 | C22 | 1 | 1 | yes | characteristic |
| 18 | #5836 | — | 2 | 8 | no | — |
| 19 | #5835 | — | 2 | 8 | no | — |
| 20 | #5822 | C22 | 1 | 12 | yes | complemented |
| 21 | #5819 | C22 | 1 | 2 | yes | — |
| 22 | #5819 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#932 | C22 | 1 | 12 | yes | complemented |
| 24 | #5750 | — | 2 | 4 | no | — |
| 25 | D3×#131 | — | 2 | 4 | no | — |
| 26 | #5745 | C22 | 1 | 6 | yes | complemented |
| 27 | C2×#901 | C22 | 1 | 6 | yes | complemented |
| 28 | #5237 | C22 | 1 | 12 | yes | complemented |
| 29 | C2×#833 | C22 | 1 | 12 | yes | complemented |
| 30 | #5192 | C22 | 1 | 4 | yes | complemented |
| 31 | #5177 | C22 | 1 | 24 | yes | complemented |
| 32 | #5160 | C22 | 1 | 12 | yes | complemented |
| 33 | #5160 | C22 | 1 | 24 | yes | complemented |
| 34 | #5125 | C22 | 1 | 6 | yes | complemented |
| 35 | C2×#819 | C22 | 1 | 6 | yes | complemented |
| 36 | #3585 | — | 3 | 2 | no | — |
| 37 | C2×#576 | D3 | 1 | 1 | yes | characteristic, complemented |
| 38 | #3573 | — | 3 | 1 | no | — |
| 39 | #3068 | — | 3 | 12 | no | — |
| 40 | #3067 | — | 3 | 6 | no | — |
| 41 | C2×#472 | — | 3 | 6 | no | — |
| 42 | #2916 | — | 3 | 1 | no | — |
| 43 | #2888 | — | 3 | 2 | no | — |
| 44 | C3×H(5,𝔽2) | — | 2 | 8 | no | — |
| 45 | C3×H(5,𝔽2) | — | 2 | 8 | no | — |
| 46 | C2×C3×#41 | — | 2 | 2 | no | — |
| 47 | C2×C3×#41 | C23 | 1 | 6 | yes | — |
| 48 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 49 | C22×C3×D4 | — | 2 | 6 | no | — |
| 50 | C22×C3×D4 | C23 | 1 | 6 | yes | — |
| 51 | #1010 | D4 | 1 | 4 | yes | — |
| 52 | #1009 | D4 | 1 | 4 | yes | — |
| 53 | D3×#41 | — | 2 | 4 | no | — |
| 54 | #1007 | — | 2 | 1 | no | — |
| 55 | #1004 | — | 2 | 3 | no | — |
| 56 | C2×#235 | C23 | 1 | 6 | yes | — |
| 57 | C3×AGL(1,ℤ/8) | — | 2 | 24 | no | — |
| 58 | C3×#135 | — | 2 | 6 | no | — |
| 59 | C3×#135 | — | 2 | 6 | no | — |
| 60 | C2×C3×Q16 | C23 | 1 | 1 | yes | characteristic |
| 61 | C2×C3×SD16 | C23 | 1 | 6 | yes | — |
| 62 | C2×C3×D8 | — | 2 | 6 | no | — |
| 63 | C2×C3×D8 | — | 2 | 6 | no | — |
| 64 | C2×C3×D8 | C23 | 1 | 3 | yes | — |
| 65 | C2×C3×D8 | C23 | 1 | 6 | yes | — |
| 66 | C3×#131 | D4 | 1 | 4 | yes | — |
| 67 | C3×#131 | D4 | 1 | 4 | yes | — |
| 68 | C2×C3×M16 | C23 | 1 | 3 | yes | — |
| 69 | C22×C3×C8 | C23 | 1 | 3 | yes | — |
| 70 | #951 | — | 2 | 12 | no | — |
| 71 | #950 | — | 2 | 24 | no | — |
| 72 | #949 | — | 2 | 12 | no | — |
| 73 | #948 | — | 2 | 4 | no | — |
| 74 | #948 | — | 2 | 8 | no | — |
| 75 | #942 | C23 | 1 | 8 | yes | — |
| 76 | C2×#214 | — | 2 | 12 | no | — |
| 77 | #932 | — | 2 | 24 | no | — |
| 78 | #932 | C23 | 1 | 24 | yes | — |
| 79 | C2×#213 | — | 2 | 12 | no | — |
| 80 | C2×#208 | C23 | 1 | 12 | yes | — |
| 81 | C2×#208 | C23 | 1 | 6 | yes | — |
| 82 | #907 | — | 2 | 12 | no | — |
| 83 | D3×M16 | — | 2 | 12 | no | — |
| 84 | #901 | — | 2 | 6 | no | — |
| 85 | #901 | — | 2 | 6 | no | — |
| 86 | #901 | C23 | 1 | 4 | yes | — |
| 87 | #901 | C23 | 1 | 12 | yes | — |
| 88 | C2×ΓL(1,𝔽25) | — | 2 | 6 | no | — |
| 89 | C2×D3×C8 | — | 2 | 6 | no | — |
| 90 | #836 | C23 | 1 | 8 | yes | — |
| 91 | #833 | C23 | 1 | 24 | yes | — |
| 92 | #819 | C23 | 1 | 12 | yes | — |
| 93 | #819 | C23 | 1 | 4 | yes | — |
| 94 | #585 | — | 3 | 1 | no | — |
| 95 | C2×H(5,𝔽2) | C2×D3 | 1 | 2 | yes | — |
| 96 | #577 | — | 6 | 8 | no | — |
| 97 | #576 | — | 2 | 4 | no | — |
| 98 | #576 | — | 2 | 4 | no | — |
| 99 | #576 | — | 6 | 8 | no | — |
| 100 | #575 | — | 3 | 12 | no | — |
| 101 | C2×AGL(1,ℤ/8) | — | 3 | 12 | no | — |
| 102 | C2×AGL(1,ℤ/8) | C2×D3 | 1 | 6 | yes | complemented |
| 103 | C2×#135 | C2×D3 | 1 | 3 | yes | complemented |
| 104 | C22×D8 | C2×D3 | 1 | 3 | yes | complemented |
| 105 | #568 | — | 3 | 2 | no | — |
| 106 | #568 | — | 3 | 1 | no | — |
| 107 | #568 | — | 3 | 6 | no | — |
| 108 | #568 | — | 6 | 4 | no | — |
| 109 | C2×#131 | — | 3 | 6 | no | — |
| 110 | C2×#131 | — | 6 | 4 | no | — |
| 111 | C2×#131 | C2×D3 | 1 | 1 | yes | characteristic |
| 112 | #473 | — | 3 | 4 | no | — |
| 113 | #472 | — | 3 | 12 | no | — |
| 114 | #472 | — | 3 | 24 | no | — |
| 115 | #471 | — | 3 | 24 | no | — |
| 116 | #430 | — | 3 | 6 | no | — |
| 117 | C2×#108 | — | 3 | 6 | no | — |
| 118 | #413 | — | 3 | 12 | no | — |
| 119 | C2×#100 | — | 3 | 12 | no | — |
| 120 | C24×C3 | — | 2 | 6 | no | — |
| 121 | C3×#41 | — | 2 | 12 | no | — |
| 122 | C3×#41 | — | 2 | 12 | no | — |
| 123 | C3×#41 | — | 4 | 8 | no | — |
| 124 | C3×#41 | C2×D4 | 1 | 4 | yes | — |
| 125 | C3×#41 | C2×D4 | 1 | 4 | yes | — |
| 126 | C2×C3×Q8 | #41 | 1 | 1 | yes | characteristic |
| 127 | C2×C3×Q8 | C24 | 1 | 2 | yes | — |
| 128 | C2×C3×D4 | — | 2 | 6 | no | — |
| 129 | C2×C3×D4 | — | 2 | 12 | no | — |
| 130 | C2×C3×D4 | — | 2 | 12 | no | — |
| 131 | C2×C3×D4 | — | 2 | 6 | no | — |
| 132 | C2×C3×D4 | — | 4 | 24 | no | — |
| 133 | C2×C3×D4 | #41 | 1 | 3 | yes | — |
| 134 | C2×C3×D4 | C24 | 1 | 6 | yes | — |
| 135 | C22×C3×C4 | — | 2 | 6 | no | — |
| 136 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 137 | C2×#67 | — | 2 | 6 | no | — |
| 138 | #239 | — | 2 | 4 | no | — |
| 139 | D3×Q8 | — | 2 | 4 | no | — |
| 140 | #237 | — | 2 | 12 | no | — |
| 141 | D3×D4 | — | 2 | 12 | no | — |
| 142 | #235 | — | 2 | 6 | no | — |
| 143 | #235 | — | 2 | 6 | no | — |
| 144 | #235 | C2×D4 | 1 | 12 | yes | — |
| 145 | #235 | C24 | 1 | 4 | yes | — |
| 146 | C2×D12 | C2×D4 | 1 | 6 | yes | — |
| 147 | C2×C4×D3 | — | 2 | 6 | no | — |
| 148 | C2×Dic6 | C2×D4 | 1 | 6 | yes | — |
| 149 | C3×Q16 | — | 2 | 1 | no | — |
| 150 | C3×Q16 | — | 2 | 1 | no | — |
| 151 | C3×SD16 | — | 2 | 12 | no | — |
| 152 | C3×D8 | — | 2 | 3 | no | — |
| 153 | C3×D8 | — | 2 | 3 | no | — |
| 154 | C3×D8 | — | 2 | 12 | no | — |
| 155 | C3×M16 | C2×D4 | 1 | 12 | yes | — |
| 156 | C2×C3×C8 | C2×D4 | 1 | 6 | yes | — |
| 157 | C2×C3×C8 | C2×D4 | 1 | 6 | yes | — |
| 158 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 159 | C2×C3×C8 | C24 | 1 | 3 | yes | — |
| 160 | #216 | — | 2 | 8 | no | — |
| 161 | #215 | — | 2 | 8 | no | — |
| 162 | #214 | — | 2 | 24 | no | — |
| 163 | #213 | — | 2 | 24 | no | — |
| 164 | #208 | — | 2 | 6 | no | — |
| 165 | #208 | — | 2 | 12 | no | — |
| 166 | #208 | C24 | 1 | 8 | yes | — |
| 167 | #208 | C24 | 1 | 4 | yes | — |
| 168 | C2×C3⋊C8 | — | 2 | 6 | no | — |
| 169 | C2×C3⋊C8 | — | 2 | 12 | no | — |
| 170 | ΓL(1,𝔽25) | — | 2 | 4 | no | — |
| 171 | ΓL(1,𝔽25) | — | 2 | 12 | no | — |
| 172 | D3×C8 | — | 2 | 4 | no | — |
| 173 | D3×C8 | — | 2 | 12 | no | — |
| 174 | 2−1+4 | — | 3 | 4 | no | — |
| 175 | 2−1+4 | — | 6 | 1 | no | — |
| 176 | H(5,𝔽2) | — | 2 | 8 | no | — |
| 177 | H(5,𝔽2) | — | 2 | 8 | no | — |
| 178 | H(5,𝔽2) | — | 3 | 4 | no | — |
| 179 | H(5,𝔽2) | — | 6 | 3 | no | — |
| 180 | C2×#41 | — | 2 | 2 | no | — |
| 181 | C2×#41 | — | 3 | 6 | no | — |
| 182 | C2×#41 | — | 6 | 4 | no | — |
| 183 | C2×#41 | C22×D3 | 1 | 6 | yes | — |
| 184 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 185 | C22×D4 | — | 2 | 6 | no | — |
| 186 | C22×D4 | C22×D3 | 1 | 6 | yes | — |
| 187 | #137 | — | 3 | 8 | no | — |
| 188 | #137 | — | 6 | 12 | no | — |
| 189 | AGL(1,ℤ/8) | — | 2 | 24 | no | — |
| 190 | AGL(1,ℤ/8) | — | 3 | 24 | no | — |
| 191 | AGL(1,ℤ/8) | — | 6 | 24 | no | — |
| 192 | AGL(1,ℤ/8) | — | 6 | 12 | no | — |
| 193 | #135 | — | 2 | 6 | no | — |
| 194 | #135 | — | 2 | 6 | no | — |
| 195 | #135 | — | 6 | 24 | no | — |
| 196 | C2×Q16 | C22×D3 | 1 | 1 | yes | characteristic |
| 197 | C2×SD16 | — | 6 | 12 | no | — |
| 198 | C2×SD16 | C22×D3 | 1 | 6 | yes | — |
| 199 | C2×D8 | — | 2 | 6 | no | — |
| 200 | C2×D8 | — | 2 | 6 | no | — |
| 201 | C2×D8 | — | 6 | 12 | no | — |
| 202 | C2×D8 | C22×D3 | 1 | 3 | yes | — |
| 203 | C2×D8 | C22×D3 | 1 | 6 | yes | — |
| 204 | #131 | — | 3 | 4 | no | — |
| 205 | #131 | — | 3 | 12 | no | — |
| 206 | #131 | — | 6 | 8 | no | — |
| 207 | #131 | — | 6 | 4 | no | — |
| 208 | #131 | — | 6 | 12 | no | — |
| 209 | #131 | — | 6 | 6 | no | — |
| 210 | #131 | — | 6 | 6 | no | — |
| 211 | #131 | #67 | 1 | 4 | yes | — |
| 212 | #131 | #67 | 1 | 4 | yes | — |
| 213 | C2×M16 | — | 3 | 6 | no | — |
| 214 | C2×M16 | — | 3 | 12 | no | — |
| 215 | C2×M16 | — | 6 | 12 | no | — |
| 216 | C2×M16 | — | 6 | 6 | no | — |
| 217 | C2×M16 | C22×D3 | 1 | 3 | yes | — |
| 218 | C22×C8 | — | 6 | 6 | no | — |
| 219 | C22×C8 | C22×D3 | 1 | 3 | yes | — |
| 220 | #108 | — | 3 | 4 | no | — |
| 221 | #108 | — | 3 | 12 | no | — |
| 222 | #101 | — | 3 | 8 | no | — |
| 223 | #100 | — | 3 | 24 | no | — |
| 224 | C23×C3 | — | 2 | 6 | no | — |
| 225 | C23×C3 | — | 4 | 12 | no | — |
| 226 | C23×C3 | — | 16 | 6 | no | — |
| 227 | C23×C3 | C2×#41 | 1 | 3 | yes | — |
| 228 | C22×D3 | — | 2 | 6 | no | — |
| 229 | C3×Q8 | — | 2 | 2 | no | — |
| 230 | C3×Q8 | — | 2 | 2 | no | — |
| 231 | C3×Q8 | #121 | 1 | 4 | yes | — |
| 232 | C3×D4 | — | 2 | 6 | no | — |
| 233 | C3×D4 | — | 2 | 6 | no | — |
| 234 | C3×D4 | — | 4 | 12 | no | — |
| 235 | C3×D4 | — | 4 | 12 | no | — |
| 236 | C3×D4 | #121 | 1 | 12 | yes | — |
| 237 | C2×C3×C4 | — | 2 | 2 | no | — |
| 238 | C2×C3×C4 | — | 4 | 12 | no | — |
| 239 | C2×C3×C4 | C22×D4 | 1 | 6 | yes | — |
| 240 | C2×C3×C4 | C22×D4 | 1 | 6 | yes | — |
| 241 | C2×C3×C4 | C2×#41 | 1 | 3 | yes | — |
| 242 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 243 | #67 | — | 2 | 12 | no | — |
| 244 | #67 | — | 2 | 4 | no | — |
| 245 | C2×Dic3 | — | 2 | 6 | no | — |
| 246 | D12 | — | 2 | 6 | no | — |
| 247 | D12 | C22×D4 | 1 | 4 | yes | — |
| 248 | C4×D3 | — | 2 | 12 | no | — |
| 249 | C4×D3 | — | 2 | 4 | no | — |
| 250 | Dic6 | — | 2 | 6 | no | — |
| 251 | Dic6 | C22×D4 | 1 | 4 | yes | — |
| 252 | C3×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 253 | C3×C8 | C22×D4 | 1 | 6 | yes | — |
| 254 | C3×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 255 | C3⋊C8 | — | 2 | 4 | no | — |
| 256 | C3⋊C8 | — | 2 | 8 | no | — |
| 257 | C24 | — | 2 | 6 | no | — |
| 258 | #41 | — | 2 | 12 | no | — |
| 259 | #41 | — | 2 | 12 | no | — |
| 260 | #41 | — | 3 | 12 | no | — |
| 261 | #41 | — | 3 | 4 | no | — |
| 262 | #41 | — | 4 | 8 | no | — |
| 263 | #41 | — | 6 | 4 | no | — |
| 264 | #41 | — | 6 | 12 | no | — |
| 265 | #41 | — | 6 | 6 | no | — |
| 266 | #41 | — | 6 | 6 | no | — |
| 267 | #41 | D3×D4 | 1 | 4 | yes | — |
| 268 | #41 | C2×#67 | 1 | 4 | yes | — |
| 269 | C2×Q8 | — | 3 | 6 | no | — |
| 270 | C2×Q8 | — | 6 | 4 | no | — |
| 271 | C2×Q8 | #237 | 1 | 1 | yes | characteristic |
| 272 | C2×Q8 | C23×D3 | 1 | 2 | yes | — |
| 273 | C2×D4 | — | 2 | 6 | no | — |
| 274 | C2×D4 | — | 2 | 12 | no | — |
| 275 | C2×D4 | — | 2 | 6 | no | — |
| 276 | C2×D4 | — | 2 | 12 | no | — |
| 277 | C2×D4 | — | 3 | 6 | no | — |
| 278 | C2×D4 | — | 4 | 24 | no | — |
| 279 | C2×D4 | — | 6 | 6 | no | — |
| 280 | C2×D4 | — | 6 | 12 | no | — |
| 281 | C2×D4 | #237 | 1 | 3 | yes | — |
| 282 | C2×D4 | C23×D3 | 1 | 6 | yes | — |
| 283 | C22×C4 | — | 2 | 6 | no | — |
| 284 | C22×C4 | — | 6 | 6 | no | — |
| 285 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 286 | Q16 | — | 2 | 1 | no | — |
| 287 | Q16 | — | 2 | 1 | no | — |
| 288 | Q16 | — | 6 | 8 | no | — |
| 289 | SD16 | — | 2 | 12 | no | — |
| 290 | SD16 | — | 6 | 24 | no | — |
| 291 | SD16 | — | 6 | 8 | no | — |
| 292 | D8 | — | 2 | 3 | no | — |
| 293 | D8 | — | 2 | 3 | no | — |
| 294 | D8 | — | 2 | 12 | no | — |
| 295 | D8 | — | 6 | 24 | no | — |
| 296 | M16 | — | 3 | 4 | no | — |
| 297 | M16 | — | 3 | 8 | no | — |
| 298 | M16 | — | 6 | 12 | no | — |
| 299 | M16 | — | 6 | 6 | no | — |
| 300 | M16 | — | 6 | 12 | no | — |
| 301 | M16 | — | 6 | 4 | no | — |
| 302 | M16 | C2×#67 | 1 | 12 | yes | — |
| 303 | C2×C8 | — | 6 | 12 | no | — |
| 304 | C2×C8 | — | 6 | 6 | no | — |
| 305 | C2×C8 | — | 6 | 4 | no | — |
| 306 | C2×C8 | — | 6 | 12 | no | — |
| 307 | C2×C8 | C2×#67 | 1 | 6 | yes | — |
| 308 | C2×C8 | C2×#67 | 1 | 6 | yes | — |
| 309 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 310 | C2×C8 | C23×D3 | 1 | 3 | yes | — |
| 311 | C22×C3 | — | 4 | 3 | no | — |
| 312 | C22×C3 | — | 4 | 6 | no | — |
| 313 | C22×C3 | — | 8 | 6 | no | — |
| 314 | C22×C3 | — | 16 | 12 | no | — |
| 315 | C22×C3 | C2×#121 | 1 | 6 | yes | — |
| 316 | C22×C3 | C22×#41 | 1 | 1 | yes | characteristic |
| 317 | C2×D3 | — | 2 | 4 | no | — |
| 318 | C2×D3 | — | 8 | 6 | no | — |
| 319 | C3×C4 | — | 4 | 2 | no | — |
| 320 | C3×C4 | C2×#121 | 1 | 6 | yes | — |
| 321 | C3×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 322 | C3×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 323 | Dic3 | — | 2 | 4 | no | — |
| 324 | C23 | — | 2 | 6 | no | — |
| 325 | C23 | — | 4 | 12 | no | — |
| 326 | C23 | — | 6 | 6 | no | — |
| 327 | C23 | — | 16 | 6 | no | — |
| 328 | C23 | C2×#237 | 1 | 3 | yes | — |
| 329 | Q8 | — | 2 | 2 | no | — |
| 330 | Q8 | — | 2 | 2 | no | — |
| 331 | Q8 | — | 3 | 4 | no | — |
| 332 | Q8 | — | 6 | 6 | no | — |
| 333 | Q8 | #938 | 1 | 4 | yes | — |
| 334 | D4 | — | 2 | 6 | no | — |
| 335 | D4 | — | 2 | 6 | no | — |
| 336 | D4 | — | 3 | 4 | no | — |
| 337 | D4 | — | 4 | 12 | no | — |
| 338 | D4 | — | 4 | 12 | no | — |
| 339 | D4 | — | 6 | 4 | no | — |
| 340 | D4 | — | 6 | 12 | no | — |
| 341 | D4 | — | 6 | 6 | no | — |
| 342 | D4 | #938 | 1 | 12 | yes | — |
| 343 | C2×C4 | — | 2 | 2 | no | — |
| 344 | C2×C4 | — | 4 | 12 | no | — |
| 345 | C2×C4 | — | 6 | 6 | no | — |
| 346 | C2×C4 | — | 6 | 4 | no | — |
| 347 | C2×C4 | — | 6 | 12 | no | — |
| 348 | C2×C4 | C2×D3×D4 | 1 | 6 | yes | — |
| 349 | C2×C4 | C2×#237 | 1 | 3 | yes | — |
| 350 | C2×C4 | C22×#67 | 1 | 6 | yes | — |
| 351 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 352 | C8 | — | 6 | 8 | no | — |
| 353 | C8 | — | 6 | 4 | no | — |
| 354 | C8 | C22×#67 | 1 | 1 | yes | characteristic |
| 355 | C8 | C22×#67 | 1 | 6 | yes | — |
| 356 | C8 | C22×#67 | 1 | 1 | yes | characteristic |
| 357 | C2×C3 | — | 2 | 6 | no | — |
| 358 | C2×C3 | — | 2 | 1 | no | — |
| 359 | C2×C3 | — | 8 | 6 | no | — |
| 360 | C2×C3 | C22×#121 | 1 | 1 | yes | characteristic |
| 361 | D3 | — | 4 | 4 | no | — |
| 362 | C22 | — | 4 | 3 | no | — |
| 363 | C22 | — | 4 | 6 | no | — |
| 364 | C22 | — | 6 | 4 | no | — |
| 365 | C22 | — | 8 | 6 | no | — |
| 366 | C22 | — | 16 | 12 | no | — |
| 367 | C22 | — | 24 | 6 | no | — |
| 368 | C22 | C2×#938 | 1 | 6 | yes | — |
| 369 | C22 | C22×#237 | 1 | 1 | yes | characteristic |
| 370 | C4 | — | 4 | 2 | no | — |
| 371 | C4 | — | 6 | 4 | no | — |
| 372 | C4 | C2×#938 | 1 | 6 | yes | — |
| 373 | C4 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 374 | C4 | C23×#67 | 1 | 1 | yes | characteristic |
| 375 | C3 | #60471 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 376 | C2 | — | 2 | 1 | no | — |
| 377 | C2 | — | 2 | 6 | no | — |
| 378 | C2 | — | 8 | 6 | no | — |
| 379 | C2 | — | 12 | 4 | no | — |
| 380 | C2 | C22×#938 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×#576 | C2 | semidirect |
| 2. #87277 | C2 | semidirect |
| 3. #87160 | C2 | semidirect |
| 4. #84100 | C2 | semidirect |
| 5. #83963 | C2 | semidirect |
| 6. #83928 | C2 | semidirect |
| 7. C2×#5160 | C2 | semidirect |
| 8. #83789 | C2 | semidirect |
| 14. C2×C3×AGL(1,ℤ/8) | C22 | semidirect |
| 15. C2×C3×#135 | C22 | semidirect |
| 16. C22×C3×D8 | C22 | semidirect |
| 20. #5822 | C22 | semidirect |
| 23. C2×#932 | C22 | semidirect |
| 26. #5745 | C22 | semidirect |
| 27. C2×#901 | C22 | semidirect |
| 28. #5237 | C22 | semidirect |
| 29. C2×#833 | C22 | semidirect |
| 30. #5192 | C22 | semidirect |
| 31. #5177 | C22 | semidirect |
| 32. #5160 | C22 | semidirect |
| 33. #5160 | C22 | semidirect |
| 34. #5125 | C22 | semidirect |
| 35. C2×#819 | C22 | semidirect |
| 37. C2×#576 | D3 | semidirect |
| 102. C2×AGL(1,ℤ/8) | C2×D3 | semidirect |
| 103. C2×#135 | C2×D3 | semidirect |
| 104. C22×D8 | C2×D3 | semidirect |
| 375. C3 | #60471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#576 | 2 |
| #87277 | 2 |
| #87160 | 2 |
| #84100 | 2 |
| #83963 | 2 |
| #83928 | 2 |
| C2×#5160 | 2 |
| #83789 | 2 |
| #60471 | 3 |