Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1482 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 1482 conjugacy classes of subgroups — too many to draw. Only its 200 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 | C3×#5945 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#5927 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | C3×#5924 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C3×#5923 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | C2×C3×#984 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #87499 | C3 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 7 | C3×#3586 | — | 3 | 1 | no | maximal |
| 8 | C3×#1010 | — | 4 | 1 | no | maximal |
| 9 | C3×2−1+4⋊C3 | C22 | 1 | 3 | yes | complemented |
| 10 | C3×#994 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C2×C3×#41⋊C3 | C22 | 1 | 3 | yes | — |
| 12 | C3×#986 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C3×#985 | C22 | 1 | 6 | yes | complemented |
| 14 | C3×#984 | C22 | 1 | 3 | yes | complemented |
| 15 | C3×#984 | C22 | 1 | 6 | yes | complemented |
| 16 | C3×#983 | C22 | 1 | 6 | yes | complemented |
| 17 | C2×C3×#226 | C22 | 1 | 6 | yes | complemented |
| 18 | C3×#585 | D3 | 1 | 1 | yes | characteristic, complemented |
| 19 | C2×C3×2−1+4 | — | 3 | 1 | no | — |
| 20 | #5945 | — | 2 | 1 | no | — |
| 21 | #5945 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 22 | #5927 | C2×C3 | 1 | 6 | yes | complemented |
| 23 | #5924 | C2×C3 | 1 | 2 | yes | complemented |
| 24 | #5923 | C2×C3 | 1 | 3 | yes | complemented |
| 25 | C2×#984 | C2×C3 | 1 | 3 | yes | complemented |
| 26 | C3×#578 | — | 3 | 2 | no | — |
| 27 | C3×#578 | — | 3 | 6 | no | — |
| 28 | C3×#577 | — | 3 | 6 | no | — |
| 29 | C3×#577 | — | 3 | 2 | no | — |
| 30 | C3×#575 | — | 3 | 3 | no | — |
| 31 | C3×#575 | — | 3 | 3 | no | — |
| 32 | C2×C3×#137 | — | 3 | 3 | no | — |
| 33 | C2×C3×#137 | — | 3 | 3 | no | — |
| 34 | C3×#568 | — | 3 | 1 | no | — |
| 35 | C32×#41 | — | 4 | 1 | no | — |
| 36 | C3×D3×Q8 | — | 4 | 2 | no | — |
| 37 | C3×#237 | — | 4 | 6 | no | — |
| 38 | C3×#235 | — | 4 | 3 | no | — |
| 39 | C2×C3×Dic6 | — | 4 | 3 | no | — |
| 40 | C3×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 41 | C3×#41⋊C3 | C23 | 1 | 3 | yes | — |
| 42 | C2×C3×SL(2,𝔽3) | C23 | 1 | 3 | yes | — |
| 43 | C3×GL(2,𝔽3) | C23 | 1 | 2 | yes | — |
| 44 | C3×#226 | C23 | 1 | 6 | yes | — |
| 45 | #3586 | — | 3 | 1 | no | Sylow |
| 46 | C3×2−1+4 | — | 3 | 1 | no | — |
| 47 | C3×2−1+4 | — | 3 | 6 | no | — |
| 48 | C3×2−1+4 | — | 3 | 2 | no | — |
| 49 | C3×2−1+4 | — | 6 | 3 | no | — |
| 50 | C3×2−1+4 | — | 6 | 1 | no | — |
| 51 | C3×2−1+4 | C2×D3 | 1 | 3 | yes | — |
| 52 | C3×H(5,𝔽2) | — | 3 | 3 | no | — |
| 53 | C3×H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 54 | C2×C3×#41 | — | 3 | 1 | no | — |
| 55 | C2×C3×#41 | — | 3 | 3 | no | — |
| 56 | C2×C3×#41 | — | 3 | 3 | no | — |
| 57 | C2×C3×#41 | — | 6 | 3 | no | — |
| 58 | C2×C3×#41 | C2×D3 | 1 | 3 | yes | — |
| 59 | C22×C3×Q8 | — | 3 | 3 | no | — |
| 60 | C22×C3×Q8 | — | 6 | 1 | no | — |
| 61 | #1010 | — | 4 | 1 | no | — |
| 62 | 2−1+4⋊C3 | — | 2 | 3 | no | — |
| 63 | 2−1+4⋊C3 | C22×C3 | 1 | 3 | yes | complemented |
| 64 | #994 | — | 2 | 1 | no | — |
| 65 | #994 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 66 | C2×#41⋊C3 | — | 2 | 3 | no | — |
| 67 | C2×#41⋊C3 | C22×C3 | 1 | 3 | yes | — |
| 68 | #986 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 69 | #985 | C22×C3 | 1 | 6 | yes | complemented |
| 70 | #984 | C22×C3 | 1 | 3 | yes | complemented |
| 71 | #984 | C22×C3 | 1 | 6 | yes | complemented |
| 72 | #983 | C22×C3 | 1 | 6 | yes | complemented |
| 73 | C2×#226 | C22×C3 | 1 | 6 | yes | complemented |
| 74 | C3×#137 | — | 3 | 3 | no | — |
| 75 | C3×#137 | — | 3 | 6 | no | — |
| 76 | C3×#137 | — | 3 | 6 | no | — |
| 77 | C3×#137 | — | 3 | 12 | no | — |
| 78 | C3×#137 | — | 3 | 6 | no | — |
| 79 | C3×#137 | — | 3 | 3 | no | — |
| 80 | C3×#137 | — | 3 | 6 | no | — |
| 81 | C3×#137 | — | 3 | 6 | no | — |
| 82 | C3×AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 83 | C3×AGL(1,ℤ/8) | — | 3 | 6 | no | — |
| 84 | C3×AGL(1,ℤ/8) | — | 3 | 6 | no | — |
| 85 | C3×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 86 | C3×#135 | — | 3 | 6 | no | — |
| 87 | C3×#135 | — | 3 | 12 | no | — |
| 88 | C3×#135 | — | 3 | 6 | no | — |
| 89 | C2×C3×Q16 | — | 3 | 6 | no | — |
| 90 | C2×C3×Q16 | — | 3 | 6 | no | — |
| 91 | C2×C3×SD16 | — | 3 | 6 | no | — |
| 92 | C2×C3×SD16 | — | 3 | 6 | no | — |
| 93 | C3×#131 | — | 3 | 2 | no | — |
| 94 | C3×#131 | — | 3 | 6 | no | — |
| 95 | C2×C3×M16 | — | 3 | 3 | no | — |
| 96 | C2×C3×M16 | — | 3 | 3 | no | — |
| 97 | C32×Q8 | — | 4 | 1 | no | — |
| 98 | C32×D4 | — | 4 | 3 | no | — |
| 99 | C2×C32×C4 | — | 4 | 3 | no | — |
| 100 | C3×#67 | — | 4 | 6 | no | — |
| 101 | C2×C3×Dic3 | — | 4 | 6 | no | — |
| 102 | C3×D12 | — | 4 | 1 | no | — |
| 103 | C3×C4×D3 | — | 4 | 6 | no | — |
| 104 | C3×Dic6 | — | 4 | 3 | no | — |
| 105 | C3×Dic6 | — | 4 | 6 | no | — |
| 106 | C3×SL(2,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 107 | #585 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 108 | C2×2−1+4 | — | 3 | 1 | no | — |
| 109 | #578 | — | 3 | 2 | no | — |
| 110 | #578 | — | 3 | 6 | no | — |
| 111 | #577 | — | 3 | 6 | no | — |
| 112 | #577 | — | 3 | 2 | no | — |
| 113 | #575 | — | 3 | 3 | no | — |
| 114 | #575 | — | 3 | 3 | no | — |
| 115 | C2×#137 | — | 3 | 3 | no | — |
| 116 | C2×#137 | — | 3 | 3 | no | — |
| 117 | #568 | — | 3 | 1 | no | — |
| 118 | C3×#41 | — | 3 | 1 | no | — |
| 119 | C3×#41 | — | 3 | 3 | no | — |
| 120 | C3×#41 | — | 3 | 3 | no | — |
| 121 | C3×#41 | — | 3 | 3 | no | — |
| 122 | C3×#41 | — | 3 | 3 | no | — |
| 123 | C3×#41 | — | 3 | 6 | no | — |
| 124 | C3×#41 | — | 3 | 6 | no | — |
| 125 | C3×#41 | — | 3 | 6 | no | — |
| 126 | C3×#41 | — | 4 | 1 | no | — |
| 127 | C3×#41 | — | 6 | 3 | no | — |
| 128 | C3×#41 | — | 6 | 3 | no | — |
| 129 | C3×#41 | — | 6 | 12 | no | — |
| 130 | C3×#41 | — | 6 | 6 | no | — |
| 131 | C3×#41 | — | 6 | 6 | no | — |
| 132 | C3×#41 | — | 6 | 3 | no | — |
| 133 | C3×#41 | — | 8 | 1 | no | — |
| 134 | C3×#41 | S4 | 1 | 1 | yes | characteristic |
| 135 | C3×#41 | C22×D3 | 1 | 3 | yes | — |
| 136 | C3×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 137 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 138 | C2×C3×Q8 | — | 3 | 3 | no | — |
| 139 | C2×C3×Q8 | — | 3 | 6 | no | — |
| 140 | C2×C3×Q8 | — | 3 | 6 | no | — |
| 141 | C2×C3×Q8 | — | 3 | 3 | no | — |
| 142 | C2×C3×Q8 | — | 6 | 3 | no | — |
| 143 | C2×C3×Q8 | — | 6 | 3 | no | — |
| 144 | C2×C3×Q8 | — | 6 | 6 | no | — |
| 145 | C2×C3×Q8 | — | 6 | 2 | no | — |
| 146 | C2×C3×Q8 | — | 6 | 3 | no | — |
| 147 | C2×C3×Q8 | C22×D3 | 1 | 3 | yes | — |
| 148 | C2×C3×D4 | — | 3 | 3 | no | — |
| 149 | C2×C3×D4 | — | 3 | 3 | no | — |
| 150 | C2×C3×D4 | — | 3 | 3 | no | — |
| 151 | C2×C3×D4 | — | 3 | 1 | no | — |
| 152 | C2×C3×D4 | — | 6 | 3 | no | — |
| 153 | C2×C3×D4 | — | 6 | 3 | no | — |
| 154 | C22×C3×C4 | — | 3 | 3 | no | — |
| 155 | C22×C3×C4 | — | 6 | 1 | no | — |
| 156 | C22×C3×C4 | — | 6 | 3 | no | — |
| 157 | C22×C3×C4 | — | 6 | 3 | no | — |
| 158 | D3×Q8 | — | 4 | 2 | no | — |
| 159 | #237 | — | 4 | 6 | no | — |
| 160 | #235 | — | 4 | 3 | no | — |
| 161 | C2×Dic6 | — | 4 | 3 | no | — |
| 162 | #41⋊C3 | — | 2 | 1 | no | — |
| 163 | #41⋊C3 | — | 2 | 3 | no | — |
| 164 | #41⋊C3 | C23×C3 | 1 | 1 | yes | characteristic |
| 165 | #41⋊C3 | C23×C3 | 1 | 3 | yes | — |
| 166 | C2×SL(2,𝔽3) | — | 2 | 3 | no | — |
| 167 | C2×SL(2,𝔽3) | C23×C3 | 1 | 3 | yes | — |
| 168 | GL(2,𝔽3) | C23×C3 | 1 | 2 | yes | — |
| 169 | #226 | C23×C3 | 1 | 6 | yes | — |
| 170 | C3×Q16 | — | 3 | 6 | no | — |
| 171 | C3×Q16 | — | 3 | 12 | no | — |
| 172 | C3×Q16 | — | 3 | 6 | no | — |
| 173 | C3×SD16 | — | 3 | 12 | no | — |
| 174 | C3×SD16 | — | 3 | 6 | no | — |
| 175 | C3×SD16 | — | 3 | 6 | no | — |
| 176 | C3×SD16 | — | 3 | 6 | no | — |
| 177 | C3×SD16 | — | 3 | 2 | no | — |
| 178 | C3×D8 | — | 3 | 2 | no | — |
| 179 | C3×D8 | — | 3 | 6 | no | — |
| 180 | C3×M16 | — | 3 | 3 | no | — |
| 181 | C3×M16 | — | 3 | 1 | no | — |
| 182 | C3×M16 | — | 3 | 6 | no | — |
| 183 | C3×M16 | — | 3 | 6 | no | — |
| 184 | C2×C3×C8 | — | 3 | 6 | no | — |
| 185 | C2×C3×C8 | — | 3 | 6 | no | — |
| 186 | C22×C32 | — | 4 | 3 | no | — |
| 187 | C2×C3×D3 | — | 4 | 2 | no | — |
| 188 | C32×C4 | — | 4 | 1 | no | — |
| 189 | C32×C4 | — | 4 | 3 | no | — |
| 190 | C3×Dic3 | — | 4 | 6 | no | — |
| 191 | 2−1+4 | — | 3 | 1 | no | — |
| 192 | 2−1+4 | — | 3 | 6 | no | — |
| 193 | 2−1+4 | — | 3 | 2 | no | — |
| 194 | 2−1+4 | — | 6 | 3 | no | — |
| 195 | 2−1+4 | — | 6 | 1 | no | — |
| 196 | 2−1+4 | C2×C3×D3 | 1 | 3 | yes | — |
| 197 | H(5,𝔽2) | — | 3 | 3 | no | — |
| 198 | H(5,𝔽2) | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 199 | C2×#41 | — | 3 | 1 | no | — |
| 200 | C2×#41 | — | 3 | 3 | no | — |
| 201 | C2×#41 | — | 3 | 3 | no | — |
| 202 | C2×#41 | — | 6 | 3 | no | — |
| 203 | C2×#41 | C2×C3×D3 | 1 | 3 | yes | — |
| 204 | C22×Q8 | — | 3 | 3 | no | — |
| 205 | C22×Q8 | — | 6 | 1 | no | — |
| 206 | #137 | — | 3 | 3 | no | — |
| 207 | #137 | — | 3 | 6 | no | — |
| 208 | #137 | — | 3 | 6 | no | — |
| 209 | #137 | — | 3 | 12 | no | — |
| 210 | #137 | — | 3 | 6 | no | — |
| 211 | #137 | — | 3 | 3 | no | — |
| 212 | #137 | — | 3 | 6 | no | — |
| 213 | #137 | — | 3 | 6 | no | — |
| 214 | AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 215 | AGL(1,ℤ/8) | — | 3 | 6 | no | — |
| 216 | AGL(1,ℤ/8) | — | 3 | 6 | no | — |
| 217 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 218 | #135 | — | 3 | 6 | no | — |
| 219 | #135 | — | 3 | 12 | no | — |
| 220 | #135 | — | 3 | 6 | no | — |
| 221 | C2×Q16 | — | 3 | 6 | no | — |
| 222 | C2×Q16 | — | 3 | 6 | no | — |
| 223 | C2×SD16 | — | 3 | 6 | no | — |
| 224 | C2×SD16 | — | 3 | 6 | no | — |
| 225 | #131 | — | 3 | 2 | no | — |
| 226 | #131 | — | 3 | 6 | no | — |
| 227 | C2×M16 | — | 3 | 3 | no | — |
| 228 | C2×M16 | — | 3 | 3 | no | — |
| 229 | C23×C3 | — | 3 | 3 | no | — |
| 230 | C23×C3 | — | 6 | 1 | no | — |
| 231 | C23×C3 | — | 6 | 1 | no | — |
| 232 | C3×Q8 | — | 3 | 3 | no | — |
| 233 | C3×Q8 | — | 3 | 3 | no | — |
| 234 | C3×Q8 | — | 3 | 6 | no | — |
| 235 | C3×Q8 | — | 4 | 1 | no | — |
| 236 | C3×Q8 | — | 6 | 6 | no | — |
| 237 | C3×Q8 | — | 6 | 3 | no | — |
| 238 | C3×Q8 | — | 6 | 6 | no | — |
| 239 | C3×Q8 | — | 8 | 1 | no | — |
| 240 | C3×Q8 | C2×S4 | 1 | 1 | yes | characteristic |
| 241 | C3×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 242 | C3×D4 | — | 3 | 1 | no | — |
| 243 | C3×D4 | — | 3 | 3 | no | — |
| 244 | C3×D4 | — | 3 | 6 | no | — |
| 245 | C3×D4 | — | 3 | 2 | no | — |
| 246 | C3×D4 | — | 3 | 3 | no | — |
| 247 | C3×D4 | — | 4 | 3 | no | — |
| 248 | C3×D4 | — | 6 | 3 | no | — |
| 249 | C3×D4 | — | 6 | 6 | no | — |
| 250 | C3×D4 | — | 6 | 6 | no | — |
| 251 | C3×D4 | — | 6 | 1 | no | — |
| 252 | C3×D4 | — | 8 | 3 | no | — |
| 253 | C3×D4 | C2×S4 | 1 | 3 | yes | — |
| 254 | C2×C3×C4 | — | 3 | 3 | no | — |
| 255 | C2×C3×C4 | — | 3 | 3 | no | — |
| 256 | C2×C3×C4 | — | 3 | 1 | no | — |
| 257 | C2×C3×C4 | — | 3 | 3 | no | — |
| 258 | C2×C3×C4 | — | 3 | 3 | no | — |
| 259 | C2×C3×C4 | — | 4 | 3 | no | — |
| 260 | C2×C3×C4 | — | 6 | 3 | no | — |
| 261 | C2×C3×C4 | — | 6 | 6 | no | — |
| 262 | C2×C3×C4 | — | 6 | 3 | no | — |
| 263 | C2×C3×C4 | — | 6 | 6 | no | — |
| 264 | C2×C3×C4 | — | 6 | 6 | no | — |
| 265 | C2×C3×C4 | — | 6 | 6 | no | — |
| 266 | C2×C3×C4 | — | 8 | 3 | no | — |
| 267 | C2×C3×C4 | C2×S4 | 1 | 3 | yes | — |
| 268 | #67 | — | 4 | 6 | no | — |
| 269 | C2×Dic3 | — | 4 | 6 | no | — |
| 270 | D12 | — | 4 | 1 | no | — |
| 271 | C4×D3 | — | 4 | 6 | no | — |
| 272 | Dic6 | — | 4 | 3 | no | — |
| 273 | Dic6 | — | 4 | 6 | no | — |
| 274 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 275 | SL(2,𝔽3) | C24×C3 | 1 | 1 | yes | characteristic |
| 276 | C3×C8 | — | 3 | 6 | no | — |
| 277 | C3×C8 | — | 3 | 2 | no | — |
| 278 | C2×C32 | — | 4 | 1 | no | — |
| 279 | C2×C32 | — | 8 | 3 | no | — |
| 280 | C3×D3 | — | 8 | 2 | no | — |
| 281 | #41 | — | 3 | 1 | no | — |
| 282 | #41 | — | 3 | 3 | no | — |
| 283 | #41 | — | 3 | 3 | no | — |
| 284 | #41 | — | 3 | 3 | no | — |
| 285 | #41 | — | 3 | 3 | no | — |
| 286 | #41 | — | 3 | 6 | no | — |
| 287 | #41 | — | 3 | 6 | no | — |
| 288 | #41 | — | 3 | 6 | no | — |
| 289 | #41 | — | 6 | 3 | no | — |
| 290 | #41 | — | 6 | 3 | no | — |
| 291 | #41 | — | 6 | 12 | no | — |
| 292 | #41 | — | 6 | 6 | no | — |
| 293 | #41 | — | 6 | 6 | no | — |
| 294 | #41 | — | 6 | 3 | no | — |
| 295 | #41 | C3×S4 | 1 | 1 | yes | characteristic |
| 296 | #41 | C22×C3×D3 | 1 | 3 | yes | — |
| 297 | #41 | C22×C3×D3 | 1 | 1 | yes | characteristic |
| 298 | C2×Q8 | — | 3 | 1 | no | — |
| 299 | C2×Q8 | — | 3 | 3 | no | — |
| 300 | C2×Q8 | — | 3 | 6 | no | — |
| 301 | C2×Q8 | — | 3 | 6 | no | — |
| 302 | C2×Q8 | — | 3 | 3 | no | — |
| 303 | C2×Q8 | — | 6 | 3 | no | — |
| 304 | C2×Q8 | — | 6 | 3 | no | — |
| 305 | C2×Q8 | — | 6 | 6 | no | — |
| 306 | C2×Q8 | — | 6 | 2 | no | — |
| 307 | C2×Q8 | — | 6 | 3 | no | — |
| 308 | C2×Q8 | C22×C3×D3 | 1 | 3 | yes | — |
| 309 | C2×D4 | — | 3 | 3 | no | — |
| 310 | C2×D4 | — | 3 | 3 | no | — |
| 311 | C2×D4 | — | 3 | 3 | no | — |
| 312 | C2×D4 | — | 3 | 1 | no | — |
| 313 | C2×D4 | — | 6 | 3 | no | — |
| 314 | C2×D4 | — | 6 | 3 | no | — |
| 315 | C22×C4 | — | 3 | 3 | no | — |
| 316 | C22×C4 | — | 6 | 1 | no | — |
| 317 | C22×C4 | — | 6 | 3 | no | — |
| 318 | C22×C4 | — | 6 | 3 | no | — |
| 319 | Q16 | — | 3 | 6 | no | — |
| 320 | Q16 | — | 3 | 12 | no | — |
| 321 | Q16 | — | 3 | 6 | no | — |
| 322 | SD16 | — | 3 | 12 | no | — |
| 323 | SD16 | — | 3 | 6 | no | — |
| 324 | SD16 | — | 3 | 6 | no | — |
| 325 | SD16 | — | 3 | 6 | no | — |
| 326 | SD16 | — | 3 | 2 | no | — |
| 327 | D8 | — | 3 | 2 | no | — |
| 328 | D8 | — | 3 | 6 | no | — |
| 329 | M16 | — | 3 | 3 | no | — |
| 330 | M16 | — | 3 | 1 | no | — |
| 331 | M16 | — | 3 | 6 | no | — |
| 332 | M16 | — | 3 | 6 | no | — |
| 333 | C2×C8 | — | 3 | 6 | no | — |
| 334 | C2×C8 | — | 3 | 6 | no | — |
| 335 | C22×C3 | — | 3 | 1 | no | — |
| 336 | C22×C3 | — | 3 | 3 | no | — |
| 337 | C22×C3 | — | 4 | 3 | no | — |
| 338 | C22×C3 | — | 6 | 2 | no | — |
| 339 | C22×C3 | — | 8 | 3 | no | — |
| 340 | C22×C3 | — | 12 | 3 | no | — |
| 341 | C22×C3 | — | 12 | 2 | no | — |
| 342 | C22×C3 | — | 24 | 1 | no | — |
| 343 | C22×C3 | C22×S4 | 1 | 3 | yes | — |
| 344 | C2×D3 | — | 4 | 2 | no | — |
| 345 | C3×C4 | — | 3 | 1 | no | — |
| 346 | C3×C4 | — | 3 | 3 | no | — |
| 347 | C3×C4 | — | 4 | 1 | no | — |
| 348 | C3×C4 | — | 4 | 3 | no | — |
| 349 | C3×C4 | — | 6 | 6 | no | — |
| 350 | C3×C4 | — | 8 | 1 | no | — |
| 351 | C3×C4 | — | 8 | 3 | no | — |
| 352 | C3×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 353 | C3×C4 | C22×S4 | 1 | 3 | yes | — |
| 354 | Dic3 | — | 4 | 6 | no | — |
| 355 | C32 | — | 4 | 1 | no | Sylow |
| 356 | C23 | — | 3 | 3 | no | — |
| 357 | C23 | — | 6 | 1 | no | — |
| 358 | C23 | — | 6 | 1 | no | — |
| 359 | Q8 | — | 3 | 3 | no | — |
| 360 | Q8 | — | 3 | 3 | no | — |
| 361 | Q8 | — | 3 | 6 | no | — |
| 362 | Q8 | — | 6 | 6 | no | — |
| 363 | Q8 | — | 6 | 3 | no | — |
| 364 | Q8 | — | 6 | 6 | no | — |
| 365 | Q8 | C2×C3×S4 | 1 | 1 | yes | characteristic |
| 366 | Q8 | C23×C3×D3 | 1 | 1 | yes | characteristic |
| 367 | D4 | — | 3 | 1 | no | — |
| 368 | D4 | — | 3 | 3 | no | — |
| 369 | D4 | — | 3 | 6 | no | — |
| 370 | D4 | — | 3 | 2 | no | — |
| 371 | D4 | — | 3 | 3 | no | — |
| 372 | D4 | — | 6 | 3 | no | — |
| 373 | D4 | — | 6 | 6 | no | — |
| 374 | D4 | — | 6 | 6 | no | — |
| 375 | D4 | — | 6 | 1 | no | — |
| 376 | D4 | C2×C3×S4 | 1 | 3 | yes | — |
| 377 | C2×C4 | — | 3 | 3 | no | — |
| 378 | C2×C4 | — | 3 | 3 | no | — |
| 379 | C2×C4 | — | 3 | 1 | no | — |
| 380 | C2×C4 | — | 3 | 3 | no | — |
| 381 | C2×C4 | — | 3 | 3 | no | — |
| 382 | C2×C4 | — | 6 | 3 | no | — |
| 383 | C2×C4 | — | 6 | 6 | no | — |
| 384 | C2×C4 | — | 6 | 3 | no | — |
| 385 | C2×C4 | — | 6 | 6 | no | — |
| 386 | C2×C4 | — | 6 | 6 | no | — |
| 387 | C2×C4 | — | 6 | 6 | no | — |
| 388 | C2×C4 | C2×C3×S4 | 1 | 3 | yes | — |
| 389 | C8 | — | 3 | 6 | no | — |
| 390 | C8 | — | 3 | 2 | no | — |
| 391 | C2×C3 | — | 2 | 3 | no | — |
| 392 | C2×C3 | — | 4 | 1 | no | — |
| 393 | C2×C3 | — | 6 | 1 | no | — |
| 394 | C2×C3 | — | 6 | 3 | no | — |
| 395 | C2×C3 | — | 8 | 3 | no | — |
| 396 | C2×C3 | — | 8 | 1 | no | — |
| 397 | C2×C3 | — | 12 | 2 | no | — |
| 398 | C2×C3 | — | 16 | 3 | no | — |
| 399 | C2×C3 | C23×S4 | 1 | 1 | yes | characteristic |
| 400 | D3 | — | 8 | 2 | no | — |
| 401 | C22 | — | 3 | 1 | no | — |
| 402 | C22 | — | 3 | 3 | no | — |
| 403 | C22 | — | 6 | 2 | no | — |
| 404 | C22 | — | 12 | 3 | no | — |
| 405 | C22 | — | 12 | 2 | no | — |
| 406 | C22 | — | 24 | 1 | no | — |
| 407 | C22 | C22×C3×S4 | 1 | 3 | yes | — |
| 408 | C4 | — | 3 | 1 | no | — |
| 409 | C4 | — | 3 | 3 | no | — |
| 410 | C4 | — | 6 | 6 | no | — |
| 411 | C4 | C22×C3×S4 | 1 | 1 | yes | characteristic |
| 412 | C4 | C22×C3×S4 | 1 | 3 | yes | — |
| 413 | C3 | — | 4 | 1 | no | — |
| 414 | C3 | — | 8 | 1 | no | — |
| 415 | C3 | #87499 | 1 | 1 | yes | characteristic, direct product factor |
| 416 | C2 | — | 2 | 3 | no | — |
| 417 | C2 | — | 6 | 1 | no | — |
| 418 | C2 | — | 6 | 3 | no | — |
| 419 | C2 | — | 12 | 2 | no | — |
| 420 | C2 | C23×C3×S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | C23×S4 |
| commutator, cosocle, hypocenter | SL(2,𝔽3) | C24×C3 |
| Frattini | C2 | C23×C3×S4 |
| Fitting | C3×#585 | D3 |
| hypercenter | C3×#41 | S4 |
| LCS | G ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C2×C3 ◁ C3×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#5945 | C2 | semidirect |
| 2. C3×#5927 | C2 | semidirect |
| 3. C3×#5924 | C2 | semidirect |
| 4. C3×#5923 | C2 | semidirect |
| 5. C2×C3×#984 | C2 | semidirect |
| 6. #87499 | C3 | direct (N × H) |
| 9. C3×2−1+4⋊C3 | C22 | semidirect |
| 10. C3×#994 | C22 | semidirect |
| 12. C3×#986 | C22 | semidirect |
| 13. C3×#985 | C22 | semidirect |
| 14. C3×#984 | C22 | semidirect |
| 15. C3×#984 | C22 | semidirect |
| 16. C3×#983 | C22 | semidirect |
| 17. C2×C3×#226 | C22 | semidirect |
| 18. C3×#585 | D3 | semidirect |
| 21. #5945 | C2×C3 | semidirect |
| 22. #5927 | C2×C3 | semidirect |
| 23. #5924 | C2×C3 | semidirect |
| 24. #5923 | C2×C3 | semidirect |
| 25. C2×#984 | C2×C3 | semidirect |
| 63. 2−1+4⋊C3 | C22×C3 | semidirect |
| 65. #994 | C22×C3 | semidirect |
| 68. #986 | C22×C3 | semidirect |
| 69. #985 | C22×C3 | semidirect |
| 70. #984 | C22×C3 | semidirect |
| 71. #984 | C22×C3 | semidirect |
| 72. #983 | C22×C3 | semidirect |
| 73. C2×#226 | C22×C3 | semidirect |
| 107. #585 | C3×D3 | semidirect |
| 415. C3 | #87499 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5945 | 2 |
| C3×#5927 | 2 |
| C3×#5924 | 2 |
| C3×#5923 | 2 |
| C2×C3×#984 | 2 |
| #87499 | 3 |
| C3×#3586 | 3 |
| C3×#1010 | 4 |