Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1320 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 117 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 | #87499 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #3584⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #85542 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #85475 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #85471 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #85466 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #85448 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#5403 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #61108 | — | 3 | 1 | no | maximal, Sylow |
| 10 | #5945 | C22 | 1 | 2 | yes | — |
| 11 | #5927 | — | 2 | 4 | no | — |
| 12 | #5927 | C22 | 1 | 4 | yes | complemented |
| 13 | #5924 | C22 | 1 | 4 | yes | complemented |
| 14 | #5923 | — | 2 | 2 | no | — |
| 15 | #5923 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#984 | — | 2 | 2 | no | — |
| 17 | C2×#984 | C22 | 1 | 2 | yes | — |
| 18 | #5771 | — | 4 | 1 | no | maximal |
| 19 | #578⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #577⋊C3 | C22 | 1 | 2 | yes | complemented |
| 21 | #576⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C2×#131⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 23 | #5430 | C22 | 1 | 4 | yes | complemented |
| 24 | #5428 | C22 | 1 | 4 | yes | complemented |
| 25 | #5423 | C22 | 1 | 1 | yes | characteristic |
| 26 | #5405 | C22 | 1 | 2 | yes | complemented |
| 27 | #5404 | C22 | 1 | 2 | yes | complemented |
| 28 | #5403 | C22 | 1 | 2 | yes | complemented |
| 29 | #5403 | C22 | 1 | 2 | yes | complemented |
| 30 | #3586 | — | 3 | 2 | no | — |
| 31 | #3584 | D3 | 1 | 1 | yes | characteristic, complemented |
| 32 | C2×#578 | — | 3 | 1 | no | — |
| 33 | #3293 | — | 3 | 2 | no | — |
| 34 | #3293 | — | 3 | 2 | no | — |
| 35 | #3290 | — | 3 | 2 | no | — |
| 36 | #3290 | — | 3 | 2 | no | — |
| 37 | #3289 | — | 3 | 4 | no | — |
| 38 | #3289 | — | 3 | 4 | no | — |
| 39 | #3156 | — | 3 | 1 | no | — |
| 40 | #3069 | — | 3 | 2 | no | — |
| 41 | #3067 | — | 3 | 1 | no | — |
| 42 | C2×#473 | — | 3 | 1 | no | — |
| 43 | #3022 | — | 3 | 2 | no | — |
| 44 | #3020 | — | 3 | 2 | no | — |
| 45 | #2957 | — | 3 | 1 | no | — |
| 46 | #2955 | — | 3 | 1 | no | — |
| 47 | #1010 | — | 4 | 2 | no | — |
| 48 | 2−1+4⋊C3 | — | 2 | 2 | no | — |
| 49 | 2−1+4⋊C3 | C23 | 1 | 2 | yes | — |
| 50 | #994 | C23 | 1 | 2 | yes | — |
| 51 | C2×#41⋊C3 | — | 2 | 2 | no | — |
| 52 | C2×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 53 | #986 | D4 | 1 | 1 | yes | characteristic |
| 54 | #985 | — | 2 | 4 | no | — |
| 55 | #985 | C23 | 1 | 2 | yes | — |
| 56 | #984 | — | 2 | 2 | no | — |
| 57 | #984 | — | 2 | 4 | no | — |
| 58 | #984 | D4 | 1 | 1 | yes | characteristic |
| 59 | #984 | C23 | 1 | 4 | yes | — |
| 60 | #983 | — | 2 | 4 | no | — |
| 61 | #983 | D4 | 1 | 2 | yes | — |
| 62 | C2×#226 | — | 2 | 2 | no | — |
| 63 | C2×#226 | — | 2 | 4 | no | — |
| 64 | C3×#135 | — | 4 | 1 | no | — |
| 65 | #951 | — | 4 | 2 | no | — |
| 66 | D3×Q16 | — | 4 | 2 | no | — |
| 67 | #915 | — | 4 | 4 | no | — |
| 68 | #912 | — | 4 | 2 | no | — |
| 69 | C2×Dic12 | — | 4 | 1 | no | — |
| 70 | #901 | — | 4 | 1 | no | — |
| 71 | #131⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 72 | #131⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 73 | GU(2,𝔽3) | C23 | 1 | 2 | yes | — |
| 74 | #585 | C2×D3 | 1 | 2 | yes | — |
| 75 | C2×2−1+4 | — | 3 | 2 | no | — |
| 76 | #578 | — | 3 | 1 | no | — |
| 77 | #578 | — | 3 | 4 | no | — |
| 78 | #578 | — | 3 | 4 | no | — |
| 79 | #578 | — | 3 | 2 | no | — |
| 80 | #578 | — | 3 | 2 | no | — |
| 81 | #578 | — | 3 | 4 | no | — |
| 82 | #578 | — | 6 | 2 | no | — |
| 83 | #578 | — | 6 | 1 | no | — |
| 84 | #578 | — | 6 | 4 | no | — |
| 85 | #578 | — | 6 | 1 | no | — |
| 86 | #578 | C2×D3 | 1 | 1 | yes | characteristic |
| 87 | #577 | — | 3 | 2 | no | — |
| 88 | #577 | — | 3 | 4 | no | — |
| 89 | #577 | — | 3 | 4 | no | — |
| 90 | #577 | — | 6 | 4 | no | — |
| 91 | #577 | C2×D3 | 1 | 2 | yes | — |
| 92 | #576 | — | 3 | 1 | no | — |
| 93 | #576 | C2×D3 | 1 | 1 | yes | characteristic |
| 94 | #575 | — | 3 | 1 | no | — |
| 95 | #575 | — | 3 | 2 | no | — |
| 96 | #575 | — | 3 | 2 | no | — |
| 97 | #575 | — | 6 | 2 | no | — |
| 98 | #575 | — | 6 | 2 | no | — |
| 99 | C2×#137 | — | 3 | 2 | no | — |
| 100 | C2×#137 | — | 3 | 2 | no | — |
| 101 | C2×#137 | — | 3 | 2 | no | — |
| 102 | C2×#137 | — | 6 | 2 | no | — |
| 103 | C2×#137 | — | 6 | 2 | no | — |
| 104 | C2×#137 | — | 6 | 2 | no | — |
| 105 | C2×#135 | — | 3 | 1 | no | — |
| 106 | C2×#135 | — | 3 | 1 | no | — |
| 107 | C2×#135 | — | 6 | 1 | no | — |
| 108 | C22×Q16 | — | 3 | 1 | no | — |
| 109 | C22×Q16 | — | 6 | 1 | no | — |
| 110 | #568 | — | 3 | 2 | no | — |
| 111 | C2×#131 | — | 3 | 1 | no | — |
| 112 | C2×#131 | C2×D3 | 1 | 1 | yes | characteristic |
| 113 | #536 | — | 3 | 2 | no | — |
| 114 | #497 | — | 3 | 4 | no | — |
| 115 | #495 | — | 3 | 2 | no | — |
| 116 | #494 | — | 3 | 2 | no | — |
| 117 | #473 | — | 3 | 2 | no | — |
| 118 | #473 | — | 3 | 4 | no | — |
| 119 | #473 | — | 3 | 4 | no | — |
| 120 | #473 | — | 3 | 2 | no | — |
| 121 | #473 | — | 3 | 2 | no | — |
| 122 | #473 | — | 3 | 2 | no | — |
| 123 | #473 | — | 3 | 2 | no | — |
| 124 | #472 | — | 3 | 2 | no | — |
| 125 | #471 | — | 3 | 4 | no | — |
| 126 | #471 | — | 3 | 4 | no | — |
| 127 | #471 | — | 3 | 4 | no | — |
| 128 | #456 | — | 3 | 4 | no | — |
| 129 | #456 | — | 3 | 4 | no | — |
| 130 | #456 | — | 3 | 4 | no | — |
| 131 | #456 | — | 3 | 4 | no | — |
| 132 | #455 | — | 3 | 4 | no | — |
| 133 | #455 | — | 3 | 4 | no | — |
| 134 | #454 | — | 3 | 4 | no | — |
| 135 | #454 | — | 3 | 4 | no | — |
| 136 | #444 | — | 3 | 2 | no | — |
| 137 | #444 | — | 3 | 4 | no | — |
| 138 | #444 | — | 3 | 2 | no | — |
| 139 | #443 | — | 3 | 2 | no | — |
| 140 | #443 | — | 3 | 2 | no | — |
| 141 | #443 | — | 3 | 2 | no | — |
| 142 | #443 | — | 3 | 2 | no | — |
| 143 | #430 | — | 3 | 1 | no | — |
| 144 | C2×#108 | — | 3 | 1 | no | — |
| 145 | #421 | — | 3 | 1 | no | — |
| 146 | #421 | — | 3 | 2 | no | — |
| 147 | #421 | — | 3 | 1 | no | — |
| 148 | #413 | — | 3 | 2 | no | — |
| 149 | C2×#101 | — | 3 | 2 | no | — |
| 150 | #405 | — | 3 | 1 | no | — |
| 151 | C3×#41 | — | 4 | 2 | no | — |
| 152 | D3×Q8 | — | 4 | 4 | no | — |
| 153 | #237 | — | 4 | 4 | no | — |
| 154 | #237 | — | 8 | 4 | no | — |
| 155 | #235 | — | 4 | 1 | no | — |
| 156 | #235 | — | 8 | 2 | no | — |
| 157 | C2×Dic6 | — | 4 | 2 | no | — |
| 158 | C2×Dic6 | — | 8 | 2 | no | — |
| 159 | #41⋊C3 | — | 2 | 2 | no | — |
| 160 | #41⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 161 | #41⋊C3 | C24 | 1 | 1 | yes | characteristic |
| 162 | C2×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 163 | C2×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | GL(2,𝔽3) | C2×D4 | 1 | 2 | yes | — |
| 165 | #226 | — | 2 | 4 | no | — |
| 166 | #226 | C2×D4 | 1 | 2 | yes | — |
| 167 | C3×Q16 | — | 4 | 1 | no | — |
| 168 | C3×SD16 | — | 4 | 2 | no | — |
| 169 | C3×D8 | — | 4 | 1 | no | — |
| 170 | C2×C3×C8 | — | 4 | 1 | no | — |
| 171 | #216 | — | 4 | 4 | no | — |
| 172 | #214 | — | 4 | 4 | no | — |
| 173 | #208 | — | 4 | 1 | no | — |
| 174 | Dic12 | — | 4 | 2 | no | — |
| 175 | Dic12 | — | 4 | 2 | no | — |
| 176 | ΓL(1,𝔽25) | — | 4 | 2 | no | — |
| 177 | D3×C8 | — | 4 | 2 | no | — |
| 178 | 2−1+4 | — | 2 | 2 | no | — |
| 179 | 2−1+4 | — | 3 | 2 | no | — |
| 180 | 2−1+4 | — | 3 | 4 | no | — |
| 181 | 2−1+4 | — | 3 | 4 | no | — |
| 182 | 2−1+4 | — | 6 | 4 | no | — |
| 183 | 2−1+4 | — | 6 | 2 | no | — |
| 184 | 2−1+4 | — | 6 | 2 | no | — |
| 185 | 2−1+4 | — | 12 | 2 | no | — |
| 186 | 2−1+4 | C22×D3 | 1 | 2 | yes | — |
| 187 | H(5,𝔽2) | — | 3 | 2 | no | — |
| 188 | H(5,𝔽2) | — | 6 | 2 | no | — |
| 189 | H(5,𝔽2) | C22×D3 | 1 | 2 | yes | — |
| 190 | C2×#41 | — | 2 | 2 | no | — |
| 191 | C2×#41 | — | 3 | 1 | no | — |
| 192 | C2×#41 | — | 3 | 2 | no | — |
| 193 | C2×#41 | — | 3 | 2 | no | — |
| 194 | C2×#41 | — | 6 | 2 | no | — |
| 195 | C2×#41 | — | 6 | 2 | no | — |
| 196 | C2×#41 | — | 6 | 2 | no | — |
| 197 | C2×#41 | — | 12 | 2 | no | — |
| 198 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 199 | C22×Q8 | — | 3 | 2 | no | — |
| 200 | C22×Q8 | — | 6 | 2 | no | — |
| 201 | C22×Q8 | — | 6 | 2 | no | — |
| 202 | #137 | — | 3 | 1 | no | — |
| 203 | #137 | — | 3 | 1 | no | — |
| 204 | #137 | — | 3 | 2 | no | — |
| 205 | #137 | — | 3 | 2 | no | — |
| 206 | #137 | — | 3 | 2 | no | — |
| 207 | #137 | — | 3 | 4 | no | — |
| 208 | #137 | — | 3 | 4 | no | — |
| 209 | #137 | — | 3 | 4 | no | — |
| 210 | #137 | — | 3 | 4 | no | — |
| 211 | #137 | — | 3 | 4 | no | — |
| 212 | #137 | — | 6 | 2 | no | — |
| 213 | #137 | — | 6 | 2 | no | — |
| 214 | #137 | — | 6 | 4 | no | — |
| 215 | #137 | — | 6 | 2 | no | — |
| 216 | #137 | — | 6 | 4 | no | — |
| 217 | #137 | — | 6 | 4 | no | — |
| 218 | #137 | — | 6 | 4 | no | — |
| 219 | #137 | — | 6 | 4 | no | — |
| 220 | #137 | — | 6 | 4 | no | — |
| 221 | #137 | — | 6 | 4 | no | — |
| 222 | #137 | — | 6 | 4 | no | — |
| 223 | #137 | — | 6 | 4 | no | — |
| 224 | #137 | — | 6 | 4 | no | — |
| 225 | #137 | — | 6 | 2 | no | — |
| 226 | #137 | — | 6 | 2 | no | — |
| 227 | #137 | — | 6 | 2 | no | — |
| 228 | #137 | — | 6 | 2 | no | — |
| 229 | #137 | — | 6 | 2 | no | — |
| 230 | #137 | — | 6 | 4 | no | — |
| 231 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 232 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 233 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 234 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 235 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 236 | AGL(1,ℤ/8) | — | 3 | 4 | no | — |
| 237 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 238 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 239 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 240 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 241 | #135 | — | 3 | 2 | no | — |
| 242 | #135 | — | 3 | 2 | no | — |
| 243 | #135 | — | 3 | 2 | no | — |
| 244 | #135 | — | 3 | 1 | no | — |
| 245 | #135 | — | 3 | 2 | no | — |
| 246 | #135 | — | 3 | 1 | no | — |
| 247 | #135 | — | 3 | 1 | no | — |
| 248 | #135 | — | 6 | 1 | no | — |
| 249 | #135 | — | 6 | 1 | no | — |
| 250 | #135 | — | 6 | 1 | no | — |
| 251 | #135 | — | 6 | 4 | no | — |
| 252 | #135 | — | 6 | 2 | no | — |
| 253 | #135 | — | 6 | 4 | no | — |
| 254 | #135 | — | 6 | 4 | no | — |
| 255 | #135 | — | 6 | 4 | no | — |
| 256 | #135 | — | 6 | 4 | no | — |
| 257 | #135 | — | 6 | 4 | no | — |
| 258 | #135 | — | 6 | 2 | no | — |
| 259 | #135 | S4 | 1 | 1 | yes | characteristic |
| 260 | C2×Q16 | — | 3 | 1 | no | — |
| 261 | C2×Q16 | — | 3 | 1 | no | — |
| 262 | C2×Q16 | — | 3 | 2 | no | — |
| 263 | C2×Q16 | — | 3 | 2 | no | — |
| 264 | C2×Q16 | — | 3 | 4 | no | — |
| 265 | C2×Q16 | — | 6 | 1 | no | — |
| 266 | C2×Q16 | — | 6 | 1 | no | — |
| 267 | C2×Q16 | — | 6 | 1 | no | — |
| 268 | C2×Q16 | — | 6 | 4 | no | — |
| 269 | C2×Q16 | — | 6 | 4 | no | — |
| 270 | C2×Q16 | — | 6 | 2 | no | — |
| 271 | C2×Q16 | — | 6 | 4 | no | — |
| 272 | C2×Q16 | — | 6 | 2 | no | — |
| 273 | C2×Q16 | — | 6 | 2 | no | — |
| 274 | C2×Q16 | — | 6 | 2 | no | — |
| 275 | C2×Q16 | — | 6 | 1 | no | — |
| 276 | C2×SD16 | — | 3 | 2 | no | — |
| 277 | C2×SD16 | — | 3 | 2 | no | — |
| 278 | C2×SD16 | — | 3 | 4 | no | — |
| 279 | C2×SD16 | — | 6 | 4 | no | — |
| 280 | C2×SD16 | — | 6 | 4 | no | — |
| 281 | C2×SD16 | — | 6 | 2 | no | — |
| 282 | C2×SD16 | — | 6 | 2 | no | — |
| 283 | C2×D8 | — | 3 | 1 | no | — |
| 284 | C2×D8 | — | 3 | 1 | no | — |
| 285 | #131 | — | 3 | 1 | no | — |
| 286 | #131 | — | 3 | 1 | no | — |
| 287 | #131 | — | 3 | 2 | no | — |
| 288 | #131 | — | 3 | 2 | no | — |
| 289 | #131 | — | 3 | 4 | no | — |
| 290 | #131 | — | 3 | 4 | no | — |
| 291 | #131 | — | 6 | 1 | no | — |
| 292 | #131 | — | 6 | 4 | no | — |
| 293 | #131 | — | 6 | 1 | no | — |
| 294 | #131 | C22×D3 | 1 | 1 | yes | characteristic |
| 295 | #131 | C22×D3 | 1 | 1 | yes | characteristic |
| 296 | C2×M16 | — | 3 | 1 | no | — |
| 297 | C2×M16 | — | 3 | 1 | no | — |
| 298 | C2×M16 | — | 3 | 1 | no | — |
| 299 | C2×M16 | — | 3 | 2 | no | — |
| 300 | C2×M16 | — | 6 | 1 | no | — |
| 301 | C2×M16 | — | 6 | 2 | no | — |
| 302 | C2×M16 | — | 6 | 2 | no | — |
| 303 | C22×C8 | — | 3 | 1 | no | — |
| 304 | C22×C8 | — | 6 | 1 | no | — |
| 305 | C4⋊Q8 | — | 3 | 4 | no | — |
| 306 | #124 | — | 3 | 4 | no | — |
| 307 | #123 | — | 12 | 2 | no | — |
| 308 | C22⋊Q8 | — | 12 | 2 | no | — |
| 309 | #117 | — | 3 | 1 | no | — |
| 310 | #108 | — | 3 | 2 | no | — |
| 311 | #108 | — | 3 | 2 | no | — |
| 312 | #108 | — | 3 | 2 | no | — |
| 313 | #108 | — | 3 | 2 | no | — |
| 314 | #104 | — | 3 | 2 | no | — |
| 315 | #104 | — | 3 | 2 | no | — |
| 316 | #104 | — | 3 | 4 | no | — |
| 317 | #104 | — | 3 | 4 | no | — |
| 318 | #104 | — | 3 | 2 | no | — |
| 319 | #104 | — | 3 | 2 | no | — |
| 320 | #101 | — | 3 | 4 | no | — |
| 321 | #101 | — | 3 | 4 | no | — |
| 322 | #101 | — | 3 | 4 | no | — |
| 323 | #100 | — | 3 | 4 | no | — |
| 324 | #97 | — | 3 | 2 | no | — |
| 325 | C4×C8 | — | 3 | 2 | no | — |
| 326 | C3×Q8 | — | 4 | 2 | no | — |
| 327 | C3×D4 | — | 4 | 2 | no | — |
| 328 | C3×D4 | — | 8 | 2 | no | — |
| 329 | C2×C3×C4 | — | 4 | 1 | no | — |
| 330 | C2×C3×C4 | — | 8 | 2 | no | — |
| 331 | #67 | — | 4 | 2 | no | — |
| 332 | #67 | — | 8 | 4 | no | — |
| 333 | C2×Dic3 | — | 8 | 4 | no | — |
| 334 | C2×Dic3 | — | 8 | 2 | no | — |
| 335 | D12 | — | 4 | 1 | no | — |
| 336 | C4×D3 | — | 4 | 2 | no | — |
| 337 | C4×D3 | — | 8 | 4 | no | — |
| 338 | Dic6 | — | 4 | 1 | no | — |
| 339 | Dic6 | — | 4 | 4 | no | — |
| 340 | Dic6 | — | 8 | 4 | no | — |
| 341 | Dic6 | — | 8 | 2 | no | — |
| 342 | SL(2,𝔽3) | C22×D4 | 1 | 1 | yes | characteristic |
| 343 | C3×C8 | — | 4 | 1 | no | — |
| 344 | C3×C8 | — | 4 | 1 | no | — |
| 345 | C3⋊C8 | — | 4 | 2 | no | — |
| 346 | #41 | — | 2 | 2 | no | — |
| 347 | #41 | — | 3 | 1 | no | — |
| 348 | #41 | — | 3 | 1 | no | — |
| 349 | #41 | — | 3 | 2 | no | — |
| 350 | #41 | — | 3 | 2 | no | — |
| 351 | #41 | — | 3 | 2 | no | — |
| 352 | #41 | — | 3 | 2 | no | — |
| 353 | #41 | — | 3 | 2 | no | — |
| 354 | #41 | — | 6 | 2 | no | — |
| 355 | #41 | — | 6 | 2 | no | — |
| 356 | #41 | — | 6 | 1 | no | — |
| 357 | #41 | — | 6 | 2 | no | — |
| 358 | #41 | — | 6 | 2 | no | — |
| 359 | #41 | — | 6 | 2 | no | — |
| 360 | #41 | — | 6 | 1 | no | — |
| 361 | #41 | — | 6 | 2 | no | — |
| 362 | #41 | — | 6 | 2 | no | — |
| 363 | #41 | — | 6 | 4 | no | — |
| 364 | #41 | — | 6 | 4 | no | — |
| 365 | #41 | — | 6 | 4 | no | — |
| 366 | #41 | — | 6 | 2 | no | — |
| 367 | #41 | — | 6 | 4 | no | — |
| 368 | #41 | — | 12 | 2 | no | — |
| 369 | #41 | — | 12 | 2 | no | — |
| 370 | #41 | — | 12 | 4 | no | — |
| 371 | #41 | — | 12 | 4 | no | — |
| 372 | #41 | — | 12 | 4 | no | — |
| 373 | #41 | — | 12 | 2 | no | — |
| 374 | #41 | — | 12 | 4 | no | — |
| 375 | #41 | — | 12 | 4 | no | — |
| 376 | #41 | D3×D4 | 1 | 1 | yes | characteristic |
| 377 | #41 | C2×S4 | 1 | 2 | yes | — |
| 378 | #41 | C23×D3 | 1 | 1 | yes | characteristic |
| 379 | C2×Q8 | — | 2 | 2 | no | — |
| 380 | C2×Q8 | — | 3 | 1 | no | — |
| 381 | C2×Q8 | — | 3 | 2 | no | — |
| 382 | C2×Q8 | — | 3 | 2 | no | — |
| 383 | C2×Q8 | — | 3 | 4 | no | — |
| 384 | C2×Q8 | — | 6 | 2 | no | — |
| 385 | C2×Q8 | — | 6 | 2 | no | — |
| 386 | C2×Q8 | — | 6 | 2 | no | — |
| 387 | C2×Q8 | — | 6 | 2 | no | — |
| 388 | C2×Q8 | — | 6 | 2 | no | — |
| 389 | C2×Q8 | — | 6 | 4 | no | — |
| 390 | C2×Q8 | — | 6 | 4 | no | — |
| 391 | C2×Q8 | — | 6 | 4 | no | — |
| 392 | C2×Q8 | — | 6 | 4 | no | — |
| 393 | C2×Q8 | — | 6 | 2 | no | — |
| 394 | C2×Q8 | — | 12 | 2 | no | — |
| 395 | C2×Q8 | — | 12 | 2 | no | — |
| 396 | C2×Q8 | — | 12 | 4 | no | — |
| 397 | C2×Q8 | — | 12 | 2 | no | — |
| 398 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 399 | C2×D4 | — | 3 | 1 | no | — |
| 400 | C2×D4 | — | 3 | 1 | no | — |
| 401 | C2×D4 | — | 3 | 2 | no | — |
| 402 | C2×D4 | — | 3 | 2 | no | — |
| 403 | C2×D4 | — | 6 | 2 | no | — |
| 404 | C2×D4 | — | 6 | 2 | no | — |
| 405 | C2×D4 | — | 6 | 2 | no | — |
| 406 | C2×D4 | — | 6 | 1 | no | — |
| 407 | C2×D4 | — | 6 | 2 | no | — |
| 408 | C2×D4 | — | 12 | 2 | no | — |
| 409 | C2×D4 | — | 12 | 2 | no | — |
| 410 | C22×C4 | — | 3 | 1 | no | — |
| 411 | C22×C4 | — | 6 | 2 | no | — |
| 412 | C22×C4 | — | 6 | 1 | no | — |
| 413 | C22×C4 | — | 6 | 2 | no | — |
| 414 | C22×C4 | — | 6 | 2 | no | — |
| 415 | C22×C4 | — | 12 | 2 | no | — |
| 416 | C22×C4 | — | 12 | 2 | no | — |
| 417 | Q16 | — | 3 | 2 | no | — |
| 418 | Q16 | — | 3 | 2 | no | — |
| 419 | Q16 | — | 3 | 2 | no | — |
| 420 | Q16 | — | 3 | 1 | no | — |
| 421 | Q16 | — | 6 | 1 | no | — |
| 422 | Q16 | — | 6 | 2 | no | — |
| 423 | Q16 | — | 6 | 2 | no | — |
| 424 | Q16 | — | 6 | 4 | no | — |
| 425 | Q16 | — | 6 | 4 | no | — |
| 426 | Q16 | — | 6 | 4 | no | — |
| 427 | Q16 | — | 6 | 4 | no | — |
| 428 | Q16 | — | 6 | 4 | no | — |
| 429 | Q16 | — | 6 | 4 | no | — |
| 430 | Q16 | — | 6 | 4 | no | — |
| 431 | Q16 | — | 6 | 2 | no | — |
| 432 | Q16 | — | 6 | 2 | no | — |
| 433 | Q16 | C2×S4 | 1 | 1 | yes | characteristic |
| 434 | SD16 | — | 3 | 2 | no | — |
| 435 | SD16 | — | 3 | 2 | no | — |
| 436 | SD16 | — | 3 | 2 | no | — |
| 437 | SD16 | — | 3 | 2 | no | — |
| 438 | SD16 | — | 3 | 2 | no | — |
| 439 | SD16 | — | 3 | 2 | no | — |
| 440 | SD16 | — | 3 | 2 | no | — |
| 441 | SD16 | — | 6 | 2 | no | — |
| 442 | SD16 | — | 6 | 4 | no | — |
| 443 | SD16 | — | 6 | 4 | no | — |
| 444 | SD16 | — | 6 | 4 | no | — |
| 445 | SD16 | — | 6 | 4 | no | — |
| 446 | SD16 | — | 6 | 4 | no | — |
| 447 | SD16 | — | 6 | 4 | no | — |
| 448 | SD16 | — | 6 | 4 | no | — |
| 449 | SD16 | — | 6 | 4 | no | — |
| 450 | SD16 | C2×S4 | 1 | 2 | yes | — |
| 451 | D8 | — | 3 | 2 | no | — |
| 452 | D8 | — | 3 | 2 | no | — |
| 453 | D8 | — | 3 | 2 | no | — |
| 454 | D8 | — | 3 | 1 | no | — |
| 455 | D8 | — | 6 | 1 | no | — |
| 456 | D8 | — | 6 | 4 | no | — |
| 457 | D8 | C2×S4 | 1 | 1 | yes | characteristic |
| 458 | M16 | — | 3 | 1 | no | — |
| 459 | M16 | — | 3 | 1 | no | — |
| 460 | M16 | — | 3 | 2 | no | — |
| 461 | M16 | — | 3 | 1 | no | — |
| 462 | M16 | — | 3 | 1 | no | — |
| 463 | M16 | — | 3 | 2 | no | — |
| 464 | M16 | — | 3 | 4 | no | — |
| 465 | M16 | — | 6 | 1 | no | — |
| 466 | M16 | — | 6 | 4 | no | — |
| 467 | M16 | — | 6 | 4 | no | — |
| 468 | M16 | — | 6 | 2 | no | — |
| 469 | M16 | — | 6 | 2 | no | — |
| 470 | M16 | — | 6 | 1 | no | — |
| 471 | M16 | — | 6 | 2 | no | — |
| 472 | C2×C8 | — | 3 | 2 | no | — |
| 473 | C2×C8 | — | 3 | 1 | no | — |
| 474 | C2×C8 | — | 3 | 1 | no | — |
| 475 | C2×C8 | — | 3 | 1 | no | — |
| 476 | C2×C8 | — | 3 | 1 | no | — |
| 477 | C2×C8 | — | 3 | 1 | no | — |
| 478 | C2×C8 | — | 6 | 2 | no | — |
| 479 | C2×C8 | — | 6 | 4 | no | — |
| 480 | C2×C8 | — | 6 | 4 | no | — |
| 481 | C2×C8 | — | 6 | 1 | no | — |
| 482 | C2×C8 | — | 6 | 2 | no | — |
| 483 | C2×C8 | — | 6 | 2 | no | — |
| 484 | C2×C8 | C2×S4 | 1 | 1 | yes | characteristic |
| 485 | C4⋊C4 | — | 6 | 1 | no | — |
| 486 | C4⋊C4 | — | 12 | 4 | no | — |
| 487 | C22⋊C4 | — | 6 | 1 | no | — |
| 488 | C22⋊C4 | — | 12 | 4 | no | — |
| 489 | C42 | — | 3 | 2 | no | — |
| 490 | C22×C3 | — | 4 | 1 | no | — |
| 491 | C22×C3 | — | 8 | 2 | no | — |
| 492 | C2×D3 | — | 4 | 2 | no | — |
| 493 | C3×C4 | — | 4 | 1 | no | — |
| 494 | C3×C4 | — | 4 | 1 | no | — |
| 495 | C3×C4 | — | 8 | 2 | no | — |
| 496 | Dic3 | — | 4 | 2 | no | — |
| 497 | Dic3 | — | 8 | 4 | no | — |
| 498 | C23 | — | 3 | 1 | no | — |
| 499 | C23 | — | 6 | 2 | no | — |
| 500 | C23 | — | 6 | 1 | no | — |
| 501 | C23 | — | 6 | 2 | no | — |
| 502 | Q8 | — | 3 | 1 | no | — |
| 503 | Q8 | — | 3 | 2 | no | — |
| 504 | Q8 | — | 3 | 2 | no | — |
| 505 | Q8 | — | 6 | 2 | no | — |
| 506 | Q8 | — | 6 | 2 | no | — |
| 507 | Q8 | — | 6 | 4 | no | — |
| 508 | Q8 | — | 6 | 1 | no | — |
| 509 | Q8 | — | 6 | 4 | no | — |
| 510 | Q8 | — | 12 | 4 | no | — |
| 511 | Q8 | — | 12 | 2 | no | — |
| 512 | Q8 | — | 12 | 4 | no | — |
| 513 | Q8 | — | 12 | 2 | no | — |
| 514 | Q8 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 515 | Q8 | C22×S4 | 1 | 2 | yes | — |
| 516 | D4 | — | 2 | 2 | no | — |
| 517 | D4 | — | 3 | 1 | no | — |
| 518 | D4 | — | 3 | 1 | no | — |
| 519 | D4 | — | 3 | 2 | no | — |
| 520 | D4 | — | 3 | 2 | no | — |
| 521 | D4 | — | 6 | 2 | no | — |
| 522 | D4 | — | 6 | 2 | no | — |
| 523 | D4 | — | 6 | 1 | no | — |
| 524 | D4 | — | 6 | 2 | no | — |
| 525 | D4 | — | 6 | 2 | no | — |
| 526 | D4 | — | 6 | 2 | no | — |
| 527 | D4 | — | 6 | 2 | no | — |
| 528 | D4 | — | 6 | 2 | no | — |
| 529 | D4 | — | 6 | 1 | no | — |
| 530 | D4 | — | 12 | 2 | no | — |
| 531 | D4 | — | 12 | 4 | no | — |
| 532 | D4 | — | 12 | 4 | no | — |
| 533 | D4 | C22×S4 | 1 | 2 | yes | — |
| 534 | C2×C4 | — | 2 | 2 | no | — |
| 535 | C2×C4 | — | 3 | 1 | no | — |
| 536 | C2×C4 | — | 3 | 1 | no | — |
| 537 | C2×C4 | — | 3 | 1 | no | — |
| 538 | C2×C4 | — | 3 | 1 | no | — |
| 539 | C2×C4 | — | 3 | 1 | no | — |
| 540 | C2×C4 | — | 6 | 2 | no | — |
| 541 | C2×C4 | — | 6 | 2 | no | — |
| 542 | C2×C4 | — | 6 | 2 | no | — |
| 543 | C2×C4 | — | 6 | 2 | no | — |
| 544 | C2×C4 | — | 6 | 1 | no | — |
| 545 | C2×C4 | — | 6 | 2 | no | — |
| 546 | C2×C4 | — | 6 | 2 | no | — |
| 547 | C2×C4 | — | 6 | 2 | no | — |
| 548 | C2×C4 | — | 6 | 2 | no | — |
| 549 | C2×C4 | — | 6 | 4 | no | — |
| 550 | C2×C4 | — | 12 | 4 | no | — |
| 551 | C2×C4 | — | 12 | 2 | no | — |
| 552 | C2×C4 | — | 12 | 4 | no | — |
| 553 | C2×C4 | — | 12 | 4 | no | — |
| 554 | C2×C4 | — | 12 | 4 | no | — |
| 555 | C2×C4 | — | 12 | 2 | no | — |
| 556 | C2×C4 | — | 12 | 2 | no | — |
| 557 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 558 | C8 | — | 3 | 2 | no | — |
| 559 | C8 | — | 3 | 2 | no | — |
| 560 | C8 | — | 3 | 1 | no | — |
| 561 | C8 | — | 3 | 1 | no | — |
| 562 | C8 | — | 6 | 4 | no | — |
| 563 | C8 | — | 6 | 2 | no | — |
| 564 | C8 | C22×S4 | 1 | 1 | yes | characteristic |
| 565 | C8 | C22×S4 | 1 | 1 | yes | characteristic |
| 566 | C2×C3 | — | 4 | 1 | no | — |
| 567 | C2×C3 | — | 8 | 1 | no | — |
| 568 | C2×C3 | — | 16 | 2 | no | — |
| 569 | D3 | — | 8 | 2 | no | — |
| 570 | C22 | — | 2 | 2 | no | — |
| 571 | C22 | — | 3 | 1 | no | — |
| 572 | C22 | — | 3 | 1 | no | — |
| 573 | C22 | — | 6 | 2 | no | — |
| 574 | C22 | — | 6 | 2 | no | — |
| 575 | C22 | — | 12 | 1 | no | — |
| 576 | C22 | — | 12 | 2 | no | — |
| 577 | C22 | — | 24 | 2 | no | — |
| 578 | C22 | — | 24 | 2 | no | — |
| 579 | C22 | D4×S4 | 1 | 1 | yes | characteristic |
| 580 | C4 | — | 2 | 2 | no | — |
| 581 | C4 | — | 3 | 1 | no | — |
| 582 | C4 | — | 3 | 1 | no | — |
| 583 | C4 | — | 6 | 2 | no | — |
| 584 | C4 | — | 6 | 2 | no | — |
| 585 | C4 | — | 12 | 2 | no | — |
| 586 | C4 | — | 12 | 4 | no | — |
| 587 | C4 | D4×S4 | 1 | 1 | yes | characteristic |
| 588 | C4 | C23×S4 | 1 | 1 | yes | characteristic |
| 589 | C3 | — | 4 | 1 | no | Sylow |
| 590 | C2 | — | 2 | 1 | no | — |
| 591 | C2 | — | 4 | 2 | no | — |
| 592 | C2 | — | 6 | 1 | no | — |
| 593 | C2 | — | 6 | 1 | no | — |
| 594 | C2 | — | 12 | 2 | no | — |
| 595 | C2 | — | 12 | 2 | no | — |
| 596 | C2 | C2×D4×S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | C2×D4×S4 |
| commutator, cosocle | #41⋊C3 | C24 |
| Frattini | C4 | C23×S4 |
| Fitting | #3584 | D3 |
| hypercenter | #135 | S4 |
| hypocenter | SL(2,𝔽3) | C22×D4 |
| LCS | G ▷ #41⋊C3 ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #135 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #87499 | C2 | semidirect |
| 2. #3584⋊C3 | C2 | semidirect |
| 3. #85542 | C2 | semidirect |
| 4. #85475 | C2 | semidirect |
| 5. #85471 | C2 | semidirect |
| 6. #85466 | C2 | semidirect |
| 7. #85448 | C2 | semidirect |
| 8. C2×#5403 | C2 | semidirect |
| 12. #5927 | C22 | semidirect |
| 13. #5924 | C22 | semidirect |
| 19. #578⋊C3 | C22 | semidirect |
| 20. #577⋊C3 | C22 | semidirect |
| 21. #576⋊C3 | C22 | semidirect |
| 23. #5430 | C22 | semidirect |
| 24. #5428 | C22 | semidirect |
| 26. #5405 | C22 | semidirect |
| 27. #5404 | C22 | semidirect |
| 28. #5403 | C22 | semidirect |
| 29. #5403 | C22 | semidirect |
| 31. #3584 | D3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #87499 | 2 |
| #3584⋊C3 | 2 |
| #85542 | 2 |
| #85475 | 2 |
| #85471 | 2 |
| #85466 | 2 |
| #85448 | 2 |
| C2×#5403 | 2 |
| #61108 | 3 |
| #5771 | 4 |