Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
600 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 73 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 | #3585⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C2×#576⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #85629 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #2916⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #2888⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #60471 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Sylow |
| 7 | #5945 | C22 | 1 | 1 | yes | characteristic |
| 8 | C2×#994 | C22 | 1 | 2 | yes | — |
| 9 | #577⋊C3 | — | 2 | 2 | no | — |
| 10 | #576⋊C3 | — | 2 | 2 | no | — |
| 11 | #576⋊C3 | — | 2 | 1 | no | — |
| 12 | #576⋊C3 | — | 2 | 1 | no | — |
| 13 | #568⋊C3 | — | 2 | 1 | no | — |
| 14 | #568⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 15 | #568⋊C3 | C22 | 1 | 2 | yes | — |
| 16 | C2×#131⋊C3 | — | 2 | 1 | no | — |
| 17 | C2×#131⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 18 | C3×#473 | — | 4 | 1 | no | maximal |
| 19 | #3585 | C2×C3 | 1 | 2 | yes | — |
| 20 | C2×#576 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 21 | #3573 | C2×C3 | 1 | 1 | yes | characteristic |
| 22 | #3068 | — | 3 | 2 | no | — |
| 23 | #3068 | — | 3 | 2 | no | — |
| 24 | #3067 | — | 3 | 1 | no | — |
| 25 | #3067 | — | 3 | 1 | no | — |
| 26 | C2×#472 | — | 3 | 1 | no | — |
| 27 | C2×#472 | — | 3 | 1 | no | — |
| 28 | #2916 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 29 | #2888 | C2×C3 | 1 | 2 | yes | complemented |
| 30 | 2−1+4⋊C3 | — | 2 | 1 | no | — |
| 31 | 2−1+4⋊C3 | D4 | 1 | 1 | yes | characteristic |
| 32 | #994 | — | 2 | 2 | no | — |
| 33 | #994 | — | 2 | 2 | no | — |
| 34 | #994 | D4 | 1 | 1 | yes | characteristic |
| 35 | C2×#41⋊C3 | — | 2 | 1 | no | — |
| 36 | C2×#41⋊C3 | — | 2 | 2 | no | — |
| 37 | C2×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 38 | C3×#137 | — | 4 | 2 | no | — |
| 39 | C2×C3×Q16 | — | 4 | 1 | no | — |
| 40 | C3×#131 | — | 4 | 1 | no | — |
| 41 | #131⋊C3 | — | 2 | 1 | no | — |
| 42 | #131⋊C3 | — | 2 | 2 | no | — |
| 43 | #131⋊C3 | D4 | 1 | 1 | yes | characteristic |
| 44 | #131⋊C3 | D4 | 1 | 1 | yes | characteristic |
| 45 | C3×#108 | — | 4 | 1 | no | — |
| 46 | C3×#101 | — | 4 | 2 | no | — |
| 47 | #585 | C22×C3 | 1 | 1 | yes | characteristic |
| 48 | C2×H(5,𝔽2) | C22×C3 | 1 | 2 | yes | — |
| 49 | #577 | — | 2 | 2 | no | — |
| 50 | #577 | — | 6 | 2 | no | — |
| 51 | #576 | — | 2 | 2 | no | — |
| 52 | #576 | — | 2 | 1 | no | — |
| 53 | #576 | — | 2 | 1 | no | — |
| 54 | #576 | — | 6 | 1 | no | — |
| 55 | #576 | — | 6 | 1 | no | — |
| 56 | #576 | — | 6 | 2 | no | — |
| 57 | #575 | — | 3 | 2 | no | — |
| 58 | #575 | — | 3 | 2 | no | — |
| 59 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 60 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 61 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 62 | C2×#135 | — | 3 | 1 | no | — |
| 63 | C22×D8 | — | 3 | 1 | no | — |
| 64 | #568 | — | 2 | 1 | no | — |
| 65 | #568 | — | 3 | 1 | no | — |
| 66 | #568 | — | 3 | 1 | no | — |
| 67 | #568 | — | 6 | 1 | no | — |
| 68 | #568 | C22×C3 | 1 | 2 | yes | — |
| 69 | #568 | C22×C3 | 1 | 1 | yes | characteristic |
| 70 | C2×#131 | — | 2 | 1 | no | — |
| 71 | C2×#131 | — | 3 | 1 | no | — |
| 72 | C2×#131 | — | 3 | 1 | no | — |
| 73 | C2×#131 | — | 6 | 1 | no | — |
| 74 | C2×#131 | C22×C3 | 1 | 1 | yes | characteristic |
| 75 | #473 | — | 3 | 1 | no | — |
| 76 | #473 | A4 | 1 | 1 | yes | characteristic |
| 77 | #472 | — | 3 | 2 | no | — |
| 78 | #472 | — | 3 | 2 | no | — |
| 79 | #472 | — | 3 | 4 | no | — |
| 80 | #472 | — | 3 | 2 | no | — |
| 81 | #472 | — | 3 | 1 | no | — |
| 82 | #472 | — | 3 | 1 | no | — |
| 83 | #471 | — | 3 | 4 | no | — |
| 84 | #471 | — | 3 | 2 | no | — |
| 85 | #471 | — | 3 | 2 | no | — |
| 86 | #430 | — | 3 | 2 | no | — |
| 87 | C2×#108 | — | 3 | 1 | no | — |
| 88 | C2×#108 | — | 3 | 1 | no | — |
| 89 | #413 | — | 3 | 2 | no | — |
| 90 | #413 | — | 3 | 2 | no | — |
| 91 | C2×#100 | — | 3 | 2 | no | — |
| 92 | C2×#100 | — | 3 | 2 | no | — |
| 93 | C3×#41 | — | 4 | 1 | no | — |
| 94 | C2×C3×Q8 | — | 4 | 2 | no | — |
| 95 | #41⋊C3 | — | 2 | 1 | no | — |
| 96 | #41⋊C3 | — | 4 | 2 | no | — |
| 97 | #41⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 98 | #41⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 99 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 100 | C2×SL(2,𝔽3) | #41 | 1 | 1 | yes | characteristic |
| 101 | C3×Q16 | — | 8 | 1 | no | — |
| 102 | C3×Q16 | — | 8 | 1 | no | — |
| 103 | C3×Q16 | — | 8 | 2 | no | — |
| 104 | C3×SD16 | — | 8 | 2 | no | — |
| 105 | C3×M16 | — | 4 | 1 | no | — |
| 106 | C3×M16 | — | 4 | 2 | no | — |
| 107 | C3×M16 | — | 8 | 1 | no | — |
| 108 | C2×C3×C8 | — | 4 | 1 | no | — |
| 109 | C2×C3×C8 | — | 8 | 1 | no | — |
| 110 | 2−1+4 | — | 2 | 1 | no | — |
| 111 | 2−1+4 | — | 3 | 1 | no | — |
| 112 | 2−1+4 | C3×D4 | 1 | 1 | yes | characteristic |
| 113 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 114 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 115 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 116 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 117 | H(5,𝔽2) | — | 6 | 2 | no | — |
| 118 | H(5,𝔽2) | — | 6 | 2 | no | — |
| 119 | H(5,𝔽2) | C3×D4 | 1 | 1 | yes | characteristic |
| 120 | C2×#41 | — | 2 | 1 | no | — |
| 121 | C2×#41 | — | 2 | 2 | no | — |
| 122 | C2×#41 | — | 3 | 1 | no | — |
| 123 | C2×#41 | — | 3 | 1 | no | — |
| 124 | C2×#41 | — | 3 | 2 | no | — |
| 125 | C2×#41 | — | 6 | 1 | no | — |
| 126 | C2×#41 | C23×C3 | 1 | 1 | yes | characteristic |
| 127 | C22×D4 | — | 3 | 2 | no | — |
| 128 | C22×D4 | — | 6 | 2 | no | — |
| 129 | #137 | — | 3 | 2 | no | — |
| 130 | #137 | — | 6 | 2 | no | — |
| 131 | #137 | — | 6 | 2 | no | — |
| 132 | #137 | C2×A4 | 1 | 2 | yes | — |
| 133 | AGL(1,ℤ/8) | — | 3 | 4 | no | — |
| 134 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 135 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 136 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 137 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 138 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 139 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 140 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 141 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 142 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 143 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 144 | #135 | — | 6 | 1 | no | — |
| 145 | #135 | — | 6 | 1 | no | — |
| 146 | #135 | — | 6 | 1 | no | — |
| 147 | #135 | — | 6 | 1 | no | — |
| 148 | #135 | — | 6 | 2 | no | — |
| 149 | #135 | — | 6 | 2 | no | — |
| 150 | #135 | — | 6 | 4 | no | — |
| 151 | C2×Q16 | C2×A4 | 1 | 1 | yes | characteristic |
| 152 | C2×SD16 | — | 3 | 2 | no | — |
| 153 | C2×SD16 | — | 6 | 2 | no | — |
| 154 | C2×SD16 | — | 6 | 2 | no | — |
| 155 | C2×D8 | — | 3 | 2 | no | — |
| 156 | C2×D8 | — | 3 | 1 | no | — |
| 157 | C2×D8 | — | 6 | 1 | no | — |
| 158 | C2×D8 | — | 6 | 1 | no | — |
| 159 | C2×D8 | — | 6 | 1 | no | — |
| 160 | C2×D8 | — | 6 | 1 | no | — |
| 161 | C2×D8 | — | 6 | 2 | no | — |
| 162 | C2×D8 | — | 6 | 2 | no | — |
| 163 | #131 | — | 2 | 1 | no | — |
| 164 | #131 | — | 2 | 2 | no | — |
| 165 | #131 | — | 3 | 1 | no | — |
| 166 | #131 | — | 3 | 1 | no | — |
| 167 | #131 | — | 3 | 2 | no | — |
| 168 | #131 | — | 3 | 1 | no | — |
| 169 | #131 | — | 3 | 1 | no | — |
| 170 | #131 | — | 3 | 1 | no | — |
| 171 | #131 | — | 6 | 1 | no | — |
| 172 | #131 | — | 6 | 1 | no | — |
| 173 | #131 | — | 6 | 1 | no | — |
| 174 | #131 | — | 6 | 1 | no | — |
| 175 | #131 | — | 6 | 2 | no | — |
| 176 | #131 | — | 6 | 1 | no | — |
| 177 | #131 | — | 6 | 1 | no | — |
| 178 | #131 | — | 6 | 1 | no | — |
| 179 | #131 | — | 6 | 2 | no | — |
| 180 | #131 | C3×D4 | 1 | 1 | yes | characteristic |
| 181 | #131 | C3×D4 | 1 | 1 | yes | characteristic |
| 182 | #131 | C2×A4 | 1 | 1 | yes | characteristic |
| 183 | C2×M16 | — | 3 | 1 | no | — |
| 184 | C2×M16 | — | 3 | 1 | no | — |
| 185 | C2×M16 | — | 3 | 2 | no | — |
| 186 | C2×M16 | — | 3 | 1 | no | — |
| 187 | C2×M16 | — | 3 | 2 | no | — |
| 188 | C2×M16 | — | 6 | 1 | no | — |
| 189 | C2×M16 | — | 6 | 1 | no | — |
| 190 | C2×M16 | — | 6 | 2 | no | — |
| 191 | C2×M16 | — | 6 | 1 | no | — |
| 192 | C2×M16 | — | 6 | 1 | no | — |
| 193 | C22×C8 | — | 3 | 1 | no | — |
| 194 | C22×C8 | — | 6 | 1 | no | — |
| 195 | C22×C8 | — | 6 | 1 | no | — |
| 196 | #108 | — | 3 | 2 | no | — |
| 197 | #108 | — | 3 | 2 | no | — |
| 198 | #108 | — | 3 | 1 | no | — |
| 199 | #108 | C2×A4 | 1 | 1 | yes | characteristic |
| 200 | #101 | — | 3 | 2 | no | — |
| 201 | #101 | C2×A4 | 1 | 2 | yes | — |
| 202 | #100 | — | 3 | 4 | no | — |
| 203 | #100 | — | 3 | 2 | no | — |
| 204 | #100 | — | 3 | 2 | no | — |
| 205 | C3×Q8 | — | 4 | 1 | no | — |
| 206 | C3×Q8 | — | 8 | 2 | no | — |
| 207 | C3×Q8 | — | 8 | 2 | no | — |
| 208 | C3×D4 | — | 4 | 1 | no | — |
| 209 | C3×D4 | — | 8 | 1 | no | — |
| 210 | C2×C3×C4 | — | 4 | 1 | no | — |
| 211 | C2×C3×C4 | — | 8 | 1 | no | — |
| 212 | C2×C3×C4 | — | 8 | 2 | no | — |
| 213 | SL(2,𝔽3) | #121 | 1 | 1 | yes | characteristic |
| 214 | C3×C8 | — | 4 | 1 | no | — |
| 215 | C3×C8 | — | 4 | 1 | no | — |
| 216 | C3×C8 | — | 8 | 1 | no | — |
| 217 | C3×C8 | — | 8 | 2 | no | — |
| 218 | C24 | — | 6 | 2 | no | — |
| 219 | #41 | — | 2 | 1 | no | — |
| 220 | #41 | — | 3 | 1 | no | — |
| 221 | #41 | — | 3 | 1 | no | — |
| 222 | #41 | — | 3 | 2 | no | — |
| 223 | #41 | — | 3 | 1 | no | — |
| 224 | #41 | — | 3 | 1 | no | — |
| 225 | #41 | — | 3 | 1 | no | — |
| 226 | #41 | — | 4 | 2 | no | — |
| 227 | #41 | — | 6 | 1 | no | — |
| 228 | #41 | — | 6 | 1 | no | — |
| 229 | #41 | — | 6 | 1 | no | — |
| 230 | #41 | — | 6 | 1 | no | — |
| 231 | #41 | — | 6 | 2 | no | — |
| 232 | #41 | — | 6 | 2 | no | — |
| 233 | #41 | — | 6 | 2 | no | — |
| 234 | #41 | — | 6 | 2 | no | — |
| 235 | #41 | — | 6 | 2 | no | — |
| 236 | #41 | — | 6 | 1 | no | — |
| 237 | #41 | — | 6 | 1 | no | — |
| 238 | #41 | — | 6 | 1 | no | — |
| 239 | #41 | — | 12 | 2 | no | — |
| 240 | #41 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 241 | #41 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 242 | #41 | C22×A4 | 1 | 1 | yes | characteristic |
| 243 | C2×Q8 | — | 2 | 1 | no | — |
| 244 | C2×Q8 | — | 3 | 1 | no | — |
| 245 | C2×Q8 | — | 3 | 1 | no | — |
| 246 | C2×Q8 | — | 6 | 1 | no | — |
| 247 | C2×Q8 | C3×#41 | 1 | 1 | yes | characteristic |
| 248 | C2×Q8 | C22×A4 | 1 | 2 | yes | — |
| 249 | C2×D4 | — | 3 | 1 | no | — |
| 250 | C2×D4 | — | 3 | 1 | no | — |
| 251 | C2×D4 | — | 3 | 1 | no | — |
| 252 | C2×D4 | — | 3 | 2 | no | — |
| 253 | C2×D4 | — | 6 | 2 | no | — |
| 254 | C2×D4 | — | 6 | 2 | no | — |
| 255 | C2×D4 | — | 6 | 2 | no | — |
| 256 | C2×D4 | — | 6 | 2 | no | — |
| 257 | C2×D4 | — | 6 | 2 | no | — |
| 258 | C2×D4 | — | 6 | 2 | no | — |
| 259 | C2×D4 | — | 6 | 1 | no | — |
| 260 | C2×D4 | — | 6 | 1 | no | — |
| 261 | C2×D4 | — | 6 | 2 | no | — |
| 262 | C2×D4 | — | 6 | 1 | no | — |
| 263 | C2×D4 | — | 6 | 1 | no | — |
| 264 | C2×D4 | — | 12 | 4 | no | — |
| 265 | C2×D4 | — | 12 | 2 | no | — |
| 266 | C2×D4 | — | 12 | 2 | no | — |
| 267 | C22×C4 | — | 3 | 1 | no | — |
| 268 | C22×C4 | — | 6 | 1 | no | — |
| 269 | C22×C4 | — | 6 | 2 | no | — |
| 270 | C22×C4 | — | 6 | 1 | no | — |
| 271 | Q16 | — | 2 | 2 | no | — |
| 272 | Q16 | — | 2 | 1 | no | — |
| 273 | Q16 | — | 2 | 1 | no | — |
| 274 | Q16 | — | 6 | 2 | no | — |
| 275 | SD16 | — | 2 | 2 | no | — |
| 276 | SD16 | — | 6 | 2 | no | — |
| 277 | SD16 | — | 6 | 2 | no | — |
| 278 | SD16 | — | 6 | 2 | no | — |
| 279 | SD16 | — | 6 | 2 | no | — |
| 280 | SD16 | — | 6 | 4 | no | — |
| 281 | SD16 | — | 6 | 2 | no | — |
| 282 | D8 | — | 6 | 2 | no | — |
| 283 | D8 | — | 6 | 2 | no | — |
| 284 | D8 | — | 6 | 2 | no | — |
| 285 | D8 | — | 6 | 4 | no | — |
| 286 | D8 | — | 6 | 2 | no | — |
| 287 | D8 | — | 6 | 1 | no | — |
| 288 | D8 | — | 6 | 1 | no | — |
| 289 | M16 | — | 2 | 1 | no | — |
| 290 | M16 | — | 3 | 2 | no | — |
| 291 | M16 | — | 3 | 1 | no | — |
| 292 | M16 | — | 3 | 1 | no | — |
| 293 | M16 | — | 3 | 1 | no | — |
| 294 | M16 | — | 3 | 2 | no | — |
| 295 | M16 | — | 6 | 1 | no | — |
| 296 | M16 | — | 6 | 1 | no | — |
| 297 | M16 | — | 6 | 2 | no | — |
| 298 | M16 | — | 6 | 1 | no | — |
| 299 | M16 | — | 6 | 2 | no | — |
| 300 | M16 | — | 6 | 1 | no | — |
| 301 | M16 | — | 6 | 1 | no | — |
| 302 | M16 | — | 6 | 2 | no | — |
| 303 | M16 | C22×A4 | 1 | 1 | yes | characteristic |
| 304 | M16 | C22×A4 | 1 | 2 | yes | — |
| 305 | C2×C8 | — | 2 | 1 | no | — |
| 306 | C2×C8 | — | 3 | 1 | no | — |
| 307 | C2×C8 | — | 3 | 1 | no | — |
| 308 | C2×C8 | — | 3 | 1 | no | — |
| 309 | C2×C8 | — | 3 | 1 | no | — |
| 310 | C2×C8 | — | 3 | 1 | no | — |
| 311 | C2×C8 | — | 6 | 1 | no | — |
| 312 | C2×C8 | — | 6 | 1 | no | — |
| 313 | C2×C8 | — | 6 | 2 | no | — |
| 314 | C2×C8 | — | 6 | 1 | no | — |
| 315 | C2×C8 | — | 6 | 2 | no | — |
| 316 | C2×C8 | — | 6 | 1 | no | — |
| 317 | C2×C8 | — | 6 | 1 | no | — |
| 318 | C2×C8 | — | 6 | 2 | no | — |
| 319 | C2×C8 | C22×A4 | 1 | 1 | yes | characteristic |
| 320 | C22×C3 | — | 4 | 1 | no | — |
| 321 | C22×C3 | — | 8 | 1 | no | — |
| 322 | C3×C4 | — | 4 | 1 | no | — |
| 323 | C3×C4 | — | 4 | 1 | no | — |
| 324 | C3×C4 | — | 8 | 1 | no | — |
| 325 | C3×C4 | — | 16 | 2 | no | — |
| 326 | C23 | — | 3 | 1 | no | — |
| 327 | C23 | — | 6 | 1 | no | — |
| 328 | C23 | — | 6 | 1 | no | — |
| 329 | C23 | — | 6 | 2 | no | — |
| 330 | C23 | — | 12 | 2 | no | — |
| 331 | C23 | — | 12 | 2 | no | — |
| 332 | C23 | — | 48 | 2 | no | — |
| 333 | Q8 | — | 2 | 2 | no | — |
| 334 | Q8 | — | 2 | 2 | no | — |
| 335 | Q8 | — | 3 | 1 | no | — |
| 336 | Q8 | — | 3 | 1 | no | — |
| 337 | Q8 | — | 6 | 1 | no | — |
| 338 | Q8 | — | 6 | 1 | no | — |
| 339 | Q8 | C3×#121 | 1 | 1 | yes | characteristic |
| 340 | Q8 | D4×A4 | 1 | 1 | yes | characteristic |
| 341 | D4 | — | 2 | 1 | no | — |
| 342 | D4 | — | 3 | 1 | no | — |
| 343 | D4 | — | 3 | 1 | no | — |
| 344 | D4 | — | 3 | 2 | no | — |
| 345 | D4 | — | 3 | 1 | no | — |
| 346 | D4 | — | 6 | 1 | no | — |
| 347 | D4 | — | 6 | 1 | no | — |
| 348 | D4 | — | 6 | 1 | no | — |
| 349 | D4 | — | 6 | 1 | no | — |
| 350 | D4 | — | 6 | 2 | no | — |
| 351 | D4 | — | 6 | 1 | no | — |
| 352 | D4 | — | 6 | 2 | no | — |
| 353 | D4 | — | 6 | 2 | no | — |
| 354 | D4 | — | 12 | 2 | no | — |
| 355 | D4 | — | 12 | 2 | no | — |
| 356 | D4 | — | 12 | 2 | no | — |
| 357 | D4 | — | 12 | 2 | no | — |
| 358 | D4 | D4×A4 | 1 | 1 | yes | characteristic |
| 359 | C2×C4 | — | 2 | 1 | no | — |
| 360 | C2×C4 | — | 2 | 2 | no | — |
| 361 | C2×C4 | — | 3 | 1 | no | — |
| 362 | C2×C4 | — | 3 | 1 | no | — |
| 363 | C2×C4 | — | 3 | 1 | no | — |
| 364 | C2×C4 | — | 3 | 1 | no | — |
| 365 | C2×C4 | — | 3 | 1 | no | — |
| 366 | C2×C4 | — | 6 | 1 | no | — |
| 367 | C2×C4 | — | 6 | 1 | no | — |
| 368 | C2×C4 | — | 6 | 1 | no | — |
| 369 | C2×C4 | — | 6 | 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 | C23×A4 | 1 | 1 | yes | characteristic |
| 375 | C8 | — | 2 | 1 | no | — |
| 376 | C8 | — | 2 | 2 | no | — |
| 377 | C8 | — | 3 | 1 | no | — |
| 378 | C8 | — | 3 | 1 | no | — |
| 379 | C8 | — | 6 | 1 | no | — |
| 380 | C8 | — | 6 | 2 | no | — |
| 381 | C8 | D4×A4 | 1 | 1 | yes | characteristic |
| 382 | C8 | D4×A4 | 1 | 1 | yes | characteristic |
| 383 | C2×C3 | — | 4 | 1 | no | — |
| 384 | C2×C3 | — | 8 | 1 | no | — |
| 385 | C2×C3 | — | 16 | 1 | no | — |
| 386 | C22 | — | 2 | 1 | no | — |
| 387 | C22 | — | 3 | 1 | no | — |
| 388 | C22 | — | 3 | 1 | no | — |
| 389 | C22 | — | 6 | 1 | no | — |
| 390 | C22 | — | 12 | 1 | no | — |
| 391 | C22 | — | 12 | 2 | no | — |
| 392 | C22 | — | 24 | 2 | no | — |
| 393 | C22 | — | 24 | 1 | no | — |
| 394 | C22 | — | 24 | 1 | no | — |
| 395 | C22 | — | 48 | 2 | no | — |
| 396 | C22 | — | 48 | 2 | no | — |
| 397 | C22 | A4×#41 | 1 | 1 | yes | characteristic |
| 398 | C4 | — | 2 | 1 | no | — |
| 399 | C4 | — | 3 | 1 | no | — |
| 400 | C4 | — | 3 | 1 | no | — |
| 401 | C4 | — | 4 | 2 | no | — |
| 402 | C4 | — | 6 | 1 | no | — |
| 403 | C4 | C2×D4×A4 | 1 | 1 | yes | characteristic |
| 404 | C4 | C2×D4×A4 | 1 | 1 | yes | characteristic |
| 405 | C3 | — | 4 | 1 | no | Sylow |
| 406 | C2 | — | 2 | 1 | no | — |
| 407 | C2 | — | 4 | 1 | no | — |
| 408 | C2 | — | 6 | 1 | no | — |
| 409 | C2 | — | 6 | 1 | no | — |
| 410 | C2 | — | 12 | 1 | no | — |
| 411 | C2 | — | 24 | 2 | no | — |
| 412 | C2 | A4×#121 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | A4×#121 |
| commutator, cosocle | C2×#41 | C23×C3 |
| Frattini | C2×C4 | C23×A4 |
| Fitting | #60471 | C3 |
| hypercenter | #473 | A4 |
| hypocenter | Q8 | C3×#121 |
| LCS | G ▷ C2×#41 ▷ Q8 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #473 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3585⋊C3 | C2 | semidirect |
| 2. C2×#576⋊C3 | C2 | semidirect |
| 3. #85629 | C2 | semidirect |
| 4. #2916⋊C3 | C2 | semidirect |
| 5. #2888⋊C3 | C2 | semidirect |
| 6. #60471 | C3 | semidirect |
| 20. C2×#576 | C2×C3 | semidirect |
| 28. #2916 | C2×C3 | semidirect |
| 29. #2888 | C2×C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3585⋊C3 | 2 |
| C2×#576⋊C3 | 2 |
| #85629 | 2 |
| #2916⋊C3 | 2 |
| #2888⋊C3 | 2 |
| #60471 | 3 |
| C3×#473 | 4 |