Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
519 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 519 conjugacy classes of subgroups — too many to draw. Only its 64 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×#5927 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#5926 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#578⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#5431 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#5430 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#5406 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C3×#5405 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #85474 | C3 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 9 | C3×#3289 | — | 3 | 1 | no | maximal |
| 10 | C3×2−1+4⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 11 | C3×2−1+4⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C3×#986 | C22 | 1 | 1 | yes | characteristic |
| 13 | C3×#985 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×#984 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C3×#983 | — | 2 | 1 | no | — |
| 16 | C3×#983 | — | 2 | 1 | no | — |
| 17 | C2×C3×GL(2,𝔽3) | — | 2 | 1 | no | — |
| 18 | C2×C3×#226 | — | 2 | 1 | no | — |
| 19 | C3×#911 | — | 4 | 1 | no | maximal |
| 20 | C3×#131⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C3×GU(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #5927 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 23 | #5926 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 24 | C3×#578 | — | 3 | 1 | no | — |
| 25 | C3×#578 | D3 | 1 | 1 | yes | characteristic, complemented |
| 26 | C3×#577 | — | 3 | 1 | no | — |
| 27 | C3×#577 | — | 3 | 1 | no | — |
| 28 | #578⋊C3 | — | 2 | 1 | no | — |
| 29 | #578⋊C3 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 30 | #5431 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 31 | #5430 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 32 | #5406 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 33 | #5405 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 34 | C3×#497 | — | 3 | 1 | no | — |
| 35 | C3×#473 | — | 3 | 1 | no | — |
| 36 | C3×#473 | — | 3 | 1 | no | — |
| 37 | C3×#471 | — | 3 | 1 | no | — |
| 38 | C3×#471 | — | 3 | 1 | no | — |
| 39 | C3×#456 | — | 3 | 1 | no | — |
| 40 | C3×#456 | — | 3 | 1 | no | — |
| 41 | C3×#455 | — | 3 | 1 | no | — |
| 42 | C3×#454 | — | 3 | 1 | no | — |
| 43 | C3×#444 | — | 3 | 1 | no | — |
| 44 | C3×#444 | — | 3 | 1 | no | — |
| 45 | C3×#237 | — | 4 | 1 | no | — |
| 46 | C3×D3×D4 | — | 4 | 1 | no | — |
| 47 | C3×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 48 | C2×C3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 49 | C2×C3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 50 | C3×GL(2,𝔽3) | — | 2 | 1 | no | — |
| 51 | C3×GL(2,𝔽3) | D4 | 1 | 1 | yes | characteristic |
| 52 | C3×#226 | — | 2 | 1 | no | — |
| 53 | C3×#226 | D4 | 1 | 1 | yes | characteristic |
| 54 | C32×D8 | — | 4 | 1 | no | — |
| 55 | C3×#214 | — | 4 | 1 | no | — |
| 56 | C3×#213 | — | 4 | 1 | no | — |
| 57 | C3×#204 | — | 4 | 1 | no | — |
| 58 | C3×ΓL(1,𝔽25) | — | 4 | 1 | no | — |
| 59 | #3289 | — | 3 | 1 | no | Sylow |
| 60 | C3×2−1+4 | — | 3 | 1 | no | — |
| 61 | C3×2−1+4 | C2×D3 | 1 | 1 | yes | characteristic |
| 62 | C3×2−1+4 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 63 | C3×H(5,𝔽2) | — | 3 | 1 | no | — |
| 64 | 2−1+4⋊C3 | — | 2 | 1 | no | — |
| 65 | 2−1+4⋊C3 | — | 2 | 1 | no | — |
| 66 | 2−1+4⋊C3 | C22×C3 | 1 | 1 | yes | characteristic |
| 67 | 2−1+4⋊C3 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 68 | #986 | C22×C3 | 1 | 1 | yes | characteristic |
| 69 | #985 | C22×C3 | 1 | 1 | yes | characteristic |
| 70 | #984 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 71 | #983 | — | 2 | 1 | no | — |
| 72 | #983 | — | 2 | 1 | no | — |
| 73 | C2×GL(2,𝔽3) | — | 2 | 1 | no | — |
| 74 | C2×#226 | — | 2 | 1 | no | — |
| 75 | C3×#137 | — | 3 | 1 | no | — |
| 76 | C3×#137 | — | 3 | 1 | no | — |
| 77 | C3×#137 | — | 3 | 1 | no | — |
| 78 | C3×#137 | — | 3 | 1 | no | — |
| 79 | C3×#137 | — | 3 | 1 | no | — |
| 80 | C3×#137 | — | 3 | 1 | no | — |
| 81 | C3×#137 | — | 6 | 1 | no | — |
| 82 | C3×#137 | — | 6 | 1 | no | — |
| 83 | C3×#137 | — | 6 | 1 | no | — |
| 84 | C3×#137 | — | 6 | 1 | no | — |
| 85 | C3×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 86 | C3×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 87 | C3×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 88 | C3×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 89 | C3×#135 | — | 3 | 1 | no | — |
| 90 | C3×#135 | — | 3 | 1 | no | — |
| 91 | C3×#135 | — | 6 | 1 | no | — |
| 92 | C3×#135 | — | 6 | 1 | no | — |
| 93 | C3×#135 | — | 6 | 1 | no | — |
| 94 | C2×C3×Q16 | — | 3 | 1 | no | — |
| 95 | C2×C3×Q16 | — | 3 | 1 | no | — |
| 96 | C2×C3×Q16 | — | 6 | 1 | no | — |
| 97 | C2×C3×SD16 | — | 3 | 1 | no | — |
| 98 | C2×C3×SD16 | — | 3 | 1 | no | — |
| 99 | C2×C3×SD16 | — | 6 | 1 | no | — |
| 100 | C2×C3×SD16 | — | 6 | 1 | no | — |
| 101 | C3×#131 | — | 3 | 1 | no | — |
| 102 | C3×#131 | — | 3 | 1 | no | — |
| 103 | C3×#131 | — | 3 | 1 | no | — |
| 104 | C3×#131 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 105 | C3×C4⋊Q8 | — | 3 | 1 | no | — |
| 106 | C3×#124 | — | 3 | 1 | no | — |
| 107 | #911 | — | 4 | 1 | no | — |
| 108 | #131⋊C3 | — | 2 | 1 | no | — |
| 109 | #131⋊C3 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 110 | GU(2,𝔽3) | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 111 | C3×#108 | — | 3 | 1 | no | — |
| 112 | C3×#108 | — | 3 | 1 | no | — |
| 113 | C3×#104 | — | 3 | 1 | no | — |
| 114 | C3×#104 | — | 3 | 1 | no | — |
| 115 | C3×#104 | — | 3 | 1 | no | — |
| 116 | C3×#104 | — | 3 | 1 | no | — |
| 117 | C3×#101 | — | 3 | 1 | no | — |
| 118 | C3×#101 | — | 3 | 1 | no | — |
| 119 | C3×#101 | — | 3 | 1 | no | — |
| 120 | C3×#100 | — | 3 | 1 | no | — |
| 121 | C3×#97 | — | 3 | 1 | no | — |
| 122 | C22×C3×D3 | — | 8 | 1 | no | — |
| 123 | C32×D4 | — | 4 | 1 | no | — |
| 124 | C32×D4 | — | 4 | 1 | no | — |
| 125 | C3×#67 | — | 8 | 1 | no | — |
| 126 | C3×#67 | — | 8 | 1 | no | — |
| 127 | C2×C3×Dic3 | — | 8 | 1 | no | — |
| 128 | C3×D12 | — | 4 | 1 | no | — |
| 129 | C3×C4×D3 | — | 4 | 1 | no | — |
| 130 | C3×Dic6 | — | 4 | 1 | no | — |
| 131 | C3×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 132 | C32×C8 | — | 4 | 1 | no | — |
| 133 | C3×C3⋊C8 | — | 4 | 1 | no | — |
| 134 | #578 | — | 3 | 1 | no | — |
| 135 | #578 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 136 | #577 | — | 3 | 1 | no | — |
| 137 | #577 | — | 3 | 1 | no | — |
| 138 | #497 | — | 3 | 1 | no | — |
| 139 | #473 | — | 3 | 1 | no | — |
| 140 | #473 | — | 3 | 1 | no | — |
| 141 | #471 | — | 3 | 1 | no | — |
| 142 | #471 | — | 3 | 1 | no | — |
| 143 | #456 | — | 3 | 1 | no | — |
| 144 | #456 | — | 3 | 1 | no | — |
| 145 | #455 | — | 3 | 1 | no | — |
| 146 | #454 | — | 3 | 1 | no | — |
| 147 | #444 | — | 3 | 1 | no | — |
| 148 | #444 | — | 3 | 1 | no | — |
| 149 | C3×#41 | — | 3 | 1 | no | — |
| 150 | C3×#41 | — | 3 | 1 | no | — |
| 151 | C3×#41 | — | 3 | 1 | no | — |
| 152 | C3×#41 | — | 6 | 1 | no | — |
| 153 | C3×#41 | — | 6 | 1 | no | — |
| 154 | C3×#41 | — | 6 | 1 | no | — |
| 155 | C3×#41 | — | 6 | 1 | no | — |
| 156 | C3×#41 | — | 6 | 1 | no | — |
| 157 | C3×#41 | — | 6 | 1 | no | — |
| 158 | C3×#41 | — | 12 | 1 | no | — |
| 159 | C3×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 160 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 161 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 162 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 163 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 164 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 165 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 166 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 167 | C2×C3×D4 | — | 3 | 1 | no | — |
| 168 | C2×C3×D4 | — | 6 | 1 | no | — |
| 169 | C2×C3×D4 | — | 6 | 1 | no | — |
| 170 | C2×C3×D4 | — | 12 | 1 | no | — |
| 171 | #237 | — | 4 | 1 | no | — |
| 172 | D3×D4 | — | 4 | 1 | no | — |
| 173 | #41⋊C3 | — | 2 | 1 | no | — |
| 174 | #41⋊C3 | C23×C3 | 1 | 1 | yes | characteristic |
| 175 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 176 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 177 | C2×SL(2,𝔽3) | — | 4 | 1 | no | — |
| 178 | C2×SL(2,𝔽3) | — | 4 | 1 | no | — |
| 179 | GL(2,𝔽3) | — | 2 | 1 | no | — |
| 180 | GL(2,𝔽3) | C3×D4 | 1 | 1 | yes | characteristic |
| 181 | #226 | — | 2 | 1 | no | — |
| 182 | #226 | C3×D4 | 1 | 1 | yes | characteristic |
| 183 | C3×Q16 | — | 3 | 1 | no | — |
| 184 | C3×Q16 | — | 3 | 1 | no | — |
| 185 | C3×Q16 | — | 6 | 1 | no | — |
| 186 | C3×Q16 | — | 6 | 1 | no | — |
| 187 | C3×Q16 | — | 6 | 1 | no | — |
| 188 | C3×Q16 | — | 6 | 1 | no | — |
| 189 | C3×Q16 | — | 6 | 1 | no | — |
| 190 | C3×Q16 | — | 6 | 1 | no | — |
| 191 | C3×Q16 | — | 6 | 1 | no | — |
| 192 | C3×SD16 | — | 3 | 1 | no | — |
| 193 | C3×SD16 | — | 3 | 1 | no | — |
| 194 | C3×SD16 | — | 3 | 1 | no | — |
| 195 | C3×SD16 | — | 3 | 1 | no | — |
| 196 | C3×SD16 | — | 6 | 1 | no | — |
| 197 | C3×SD16 | — | 6 | 1 | no | — |
| 198 | C3×SD16 | — | 6 | 1 | no | — |
| 199 | C3×SD16 | — | 6 | 1 | no | — |
| 200 | C3×SD16 | — | 6 | 1 | no | — |
| 201 | C3×SD16 | — | 6 | 1 | no | — |
| 202 | C3×SD16 | — | 6 | 1 | no | — |
| 203 | C3×SD16 | — | 6 | 1 | no | — |
| 204 | C3×SD16 | — | 6 | 1 | no | — |
| 205 | C3×SD16 | — | 6 | 1 | no | — |
| 206 | C3×D8 | — | 3 | 1 | no | — |
| 207 | C3×D8 | — | 4 | 1 | no | — |
| 208 | C3×D8 | — | 6 | 1 | no | — |
| 209 | C3×D8 | — | 6 | 1 | no | — |
| 210 | C3×D8 | — | 8 | 1 | no | — |
| 211 | C3×D8 | S4 | 1 | 1 | yes | characteristic |
| 212 | C3×M16 | — | 3 | 1 | no | — |
| 213 | C3×M16 | — | 3 | 1 | no | — |
| 214 | C3×M16 | — | 3 | 1 | no | — |
| 215 | C3×M16 | — | 3 | 1 | no | — |
| 216 | C3×M16 | — | 6 | 1 | no | — |
| 217 | C3×M16 | — | 6 | 1 | no | — |
| 218 | C3×M16 | — | 6 | 1 | no | — |
| 219 | C2×C3×C8 | — | 3 | 1 | no | — |
| 220 | C2×C3×C8 | — | 3 | 1 | no | — |
| 221 | C2×C3×C8 | — | 6 | 1 | no | — |
| 222 | C2×C3×C8 | — | 6 | 1 | no | — |
| 223 | C2×C3×C8 | — | 6 | 1 | no | — |
| 224 | C3×C4⋊C4 | — | 12 | 1 | no | — |
| 225 | C3×C22⋊C4 | — | 12 | 1 | no | — |
| 226 | C3×C42 | — | 3 | 1 | no | — |
| 227 | #214 | — | 4 | 1 | no | — |
| 228 | #213 | — | 4 | 1 | no | — |
| 229 | #204 | — | 4 | 1 | no | — |
| 230 | ΓL(1,𝔽25) | — | 4 | 1 | no | — |
| 231 | C22×C32 | — | 8 | 1 | no | — |
| 232 | C22×C32 | — | 8 | 1 | no | — |
| 233 | C2×C3×D3 | — | 4 | 1 | no | — |
| 234 | C2×C3×D3 | — | 8 | 1 | no | — |
| 235 | C2×C3×D3 | — | 16 | 2 | no | — |
| 236 | C32×C4 | — | 4 | 1 | no | — |
| 237 | C3×Dic3 | — | 4 | 1 | no | — |
| 238 | C3×Dic3 | — | 8 | 1 | no | — |
| 239 | 2−1+4 | — | 3 | 1 | no | — |
| 240 | 2−1+4 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 241 | 2−1+4 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 242 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 243 | #137 | — | 3 | 1 | no | — |
| 244 | #137 | — | 3 | 1 | no | — |
| 245 | #137 | — | 3 | 1 | no | — |
| 246 | #137 | — | 3 | 1 | no | — |
| 247 | #137 | — | 3 | 1 | no | — |
| 248 | #137 | — | 3 | 1 | no | — |
| 249 | #137 | — | 6 | 1 | no | — |
| 250 | #137 | — | 6 | 1 | no | — |
| 251 | #137 | — | 6 | 1 | no | — |
| 252 | #137 | — | 6 | 1 | no | — |
| 253 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 254 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 255 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 256 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 257 | #135 | — | 3 | 1 | no | — |
| 258 | #135 | — | 3 | 1 | no | — |
| 259 | #135 | — | 6 | 1 | no | — |
| 260 | #135 | — | 6 | 1 | no | — |
| 261 | #135 | — | 6 | 1 | no | — |
| 262 | C2×Q16 | — | 3 | 1 | no | — |
| 263 | C2×Q16 | — | 3 | 1 | no | — |
| 264 | C2×Q16 | — | 6 | 1 | no | — |
| 265 | C2×SD16 | — | 3 | 1 | no | — |
| 266 | C2×SD16 | — | 3 | 1 | no | — |
| 267 | C2×SD16 | — | 6 | 1 | no | — |
| 268 | C2×SD16 | — | 6 | 1 | no | — |
| 269 | #131 | — | 3 | 1 | no | — |
| 270 | #131 | — | 3 | 1 | no | — |
| 271 | #131 | — | 3 | 1 | no | — |
| 272 | #131 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 273 | C4⋊Q8 | — | 3 | 1 | no | — |
| 274 | #124 | — | 3 | 1 | no | — |
| 275 | #108 | — | 3 | 1 | no | — |
| 276 | #108 | — | 3 | 1 | no | — |
| 277 | #104 | — | 3 | 1 | no | — |
| 278 | #104 | — | 3 | 1 | no | — |
| 279 | #104 | — | 3 | 1 | no | — |
| 280 | #104 | — | 3 | 1 | no | — |
| 281 | #101 | — | 3 | 1 | no | — |
| 282 | #101 | — | 3 | 1 | no | — |
| 283 | #101 | — | 3 | 1 | no | — |
| 284 | #100 | — | 3 | 1 | no | — |
| 285 | #97 | — | 3 | 1 | no | — |
| 286 | C23×C3 | — | 6 | 1 | no | — |
| 287 | C23×C3 | — | 12 | 1 | no | — |
| 288 | C22×D3 | — | 8 | 1 | no | — |
| 289 | C3×Q8 | — | 3 | 1 | no | — |
| 290 | C3×Q8 | — | 3 | 1 | no | — |
| 291 | C3×Q8 | — | 3 | 1 | no | — |
| 292 | C3×Q8 | — | 6 | 1 | no | — |
| 293 | C3×Q8 | — | 6 | 1 | no | — |
| 294 | C3×Q8 | — | 6 | 1 | no | — |
| 295 | C3×Q8 | — | 6 | 1 | no | — |
| 296 | C3×Q8 | — | 12 | 1 | no | — |
| 297 | C3×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 298 | C3×D4 | — | 3 | 1 | no | — |
| 299 | C3×D4 | — | 3 | 1 | no | — |
| 300 | C3×D4 | — | 4 | 1 | no | — |
| 301 | C3×D4 | — | 4 | 1 | no | — |
| 302 | C3×D4 | — | 6 | 1 | no | — |
| 303 | C3×D4 | — | 6 | 1 | no | — |
| 304 | C3×D4 | — | 6 | 1 | no | — |
| 305 | C3×D4 | — | 6 | 1 | no | — |
| 306 | C3×D4 | — | 6 | 1 | no | — |
| 307 | C3×D4 | — | 8 | 1 | no | — |
| 308 | C3×D4 | — | 8 | 1 | no | — |
| 309 | C3×D4 | — | 12 | 1 | no | — |
| 310 | C3×D4 | — | 12 | 1 | no | — |
| 311 | C3×D4 | — | 12 | 1 | no | — |
| 312 | C3×D4 | C2×S4 | 1 | 1 | yes | characteristic |
| 313 | C3×D4 | C2×S4 | 1 | 1 | yes | characteristic |
| 314 | C2×C3×C4 | — | 3 | 1 | no | — |
| 315 | C2×C3×C4 | — | 6 | 1 | no | — |
| 316 | C2×C3×C4 | — | 6 | 1 | no | — |
| 317 | C2×C3×C4 | — | 6 | 1 | no | — |
| 318 | C2×C3×C4 | — | 6 | 1 | no | — |
| 319 | C2×C3×C4 | — | 6 | 1 | no | — |
| 320 | C2×C3×C4 | — | 6 | 1 | no | — |
| 321 | C2×C3×C4 | — | 6 | 1 | no | — |
| 322 | C2×C3×C4 | — | 12 | 1 | no | — |
| 323 | C2×C3×C4 | — | 12 | 1 | no | — |
| 324 | C2×C3×C4 | — | 12 | 1 | no | — |
| 325 | #67 | — | 8 | 1 | no | — |
| 326 | #67 | — | 8 | 1 | no | — |
| 327 | C2×Dic3 | — | 8 | 1 | no | — |
| 328 | D12 | — | 4 | 1 | no | — |
| 329 | C4×D3 | — | 4 | 1 | no | — |
| 330 | Dic6 | — | 4 | 1 | no | — |
| 331 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 332 | SL(2,𝔽3) | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 333 | C3×C8 | — | 3 | 1 | no | — |
| 334 | C3×C8 | — | 3 | 1 | no | — |
| 335 | C3×C8 | — | 3 | 1 | no | — |
| 336 | C3×C8 | — | 4 | 1 | no | — |
| 337 | C3×C8 | — | 6 | 1 | no | — |
| 338 | C3×C8 | — | 6 | 1 | no | — |
| 339 | C3×C8 | — | 6 | 1 | no | — |
| 340 | C3×C8 | — | 8 | 1 | no | — |
| 341 | C3×C8 | C2×S4 | 1 | 1 | yes | characteristic |
| 342 | C3⋊C8 | — | 4 | 1 | no | — |
| 343 | C2×C32 | — | 4 | 1 | no | — |
| 344 | C2×C32 | — | 16 | 1 | no | — |
| 345 | C2×C32 | — | 16 | 1 | no | — |
| 346 | C3×D3 | — | 8 | 1 | no | — |
| 347 | C3×D3 | — | 16 | 1 | no | — |
| 348 | #41 | — | 3 | 1 | no | — |
| 349 | #41 | — | 3 | 1 | no | — |
| 350 | #41 | — | 3 | 1 | no | — |
| 351 | #41 | — | 6 | 1 | no | — |
| 352 | #41 | — | 6 | 1 | no | — |
| 353 | #41 | — | 6 | 1 | no | — |
| 354 | #41 | — | 6 | 1 | no | — |
| 355 | #41 | — | 6 | 1 | no | — |
| 356 | #41 | — | 6 | 1 | no | — |
| 357 | #41 | — | 12 | 1 | no | — |
| 358 | #41 | C22×C3×D3 | 1 | 1 | yes | characteristic |
| 359 | C2×Q8 | — | 2 | 1 | no | — |
| 360 | C2×Q8 | — | 2 | 1 | no | — |
| 361 | C2×Q8 | — | 3 | 1 | no | — |
| 362 | C2×Q8 | — | 3 | 1 | no | — |
| 363 | C2×Q8 | — | 3 | 1 | no | — |
| 364 | C2×Q8 | — | 6 | 1 | no | — |
| 365 | C2×Q8 | — | 6 | 1 | no | — |
| 366 | C2×D4 | — | 3 | 1 | no | — |
| 367 | C2×D4 | — | 6 | 1 | no | — |
| 368 | C2×D4 | — | 6 | 1 | no | — |
| 369 | C2×D4 | — | 12 | 1 | no | — |
| 370 | Q16 | — | 3 | 1 | no | — |
| 371 | Q16 | — | 3 | 1 | no | — |
| 372 | Q16 | — | 6 | 1 | no | — |
| 373 | Q16 | — | 6 | 1 | no | — |
| 374 | Q16 | — | 6 | 1 | no | — |
| 375 | Q16 | — | 6 | 1 | no | — |
| 376 | Q16 | — | 6 | 1 | no | — |
| 377 | Q16 | — | 6 | 1 | no | — |
| 378 | Q16 | — | 6 | 1 | no | — |
| 379 | SD16 | — | 3 | 1 | no | — |
| 380 | SD16 | — | 3 | 1 | no | — |
| 381 | SD16 | — | 3 | 1 | no | — |
| 382 | SD16 | — | 3 | 1 | no | — |
| 383 | SD16 | — | 6 | 1 | no | — |
| 384 | SD16 | — | 6 | 1 | no | — |
| 385 | SD16 | — | 6 | 1 | no | — |
| 386 | SD16 | — | 6 | 1 | no | — |
| 387 | SD16 | — | 6 | 1 | no | — |
| 388 | SD16 | — | 6 | 1 | no | — |
| 389 | SD16 | — | 6 | 1 | no | — |
| 390 | SD16 | — | 6 | 1 | no | — |
| 391 | SD16 | — | 6 | 1 | no | — |
| 392 | SD16 | — | 6 | 1 | no | — |
| 393 | D8 | — | 3 | 1 | no | — |
| 394 | D8 | — | 6 | 1 | no | — |
| 395 | D8 | — | 6 | 1 | no | — |
| 396 | D8 | C3×S4 | 1 | 1 | yes | characteristic |
| 397 | M16 | — | 3 | 1 | no | — |
| 398 | M16 | — | 3 | 1 | no | — |
| 399 | M16 | — | 3 | 1 | no | — |
| 400 | M16 | — | 3 | 1 | no | — |
| 401 | M16 | — | 6 | 1 | no | — |
| 402 | M16 | — | 6 | 1 | no | — |
| 403 | M16 | — | 6 | 1 | no | — |
| 404 | C2×C8 | — | 3 | 1 | no | — |
| 405 | C2×C8 | — | 3 | 1 | no | — |
| 406 | C2×C8 | — | 6 | 1 | no | — |
| 407 | C2×C8 | — | 6 | 1 | no | — |
| 408 | C2×C8 | — | 6 | 1 | no | — |
| 409 | C4⋊C4 | — | 12 | 1 | no | — |
| 410 | C22⋊C4 | — | 12 | 1 | no | — |
| 411 | C42 | — | 3 | 1 | no | — |
| 412 | C22×C3 | — | 2 | 1 | no | — |
| 413 | C22×C3 | — | 2 | 1 | no | — |
| 414 | C22×C3 | — | 3 | 1 | no | — |
| 415 | C22×C3 | — | 6 | 1 | no | — |
| 416 | C22×C3 | — | 8 | 1 | no | — |
| 417 | C22×C3 | — | 8 | 1 | no | — |
| 418 | C22×C3 | — | 12 | 1 | no | — |
| 419 | C22×C3 | — | 16 | 1 | no | — |
| 420 | C22×C3 | — | 16 | 1 | no | — |
| 421 | C22×C3 | — | 24 | 1 | no | — |
| 422 | C22×C3 | — | 48 | 1 | no | — |
| 423 | C2×D3 | — | 4 | 1 | no | — |
| 424 | C2×D3 | — | 8 | 1 | no | — |
| 425 | C2×D3 | — | 16 | 2 | no | — |
| 426 | C3×C4 | — | 3 | 1 | no | — |
| 427 | C3×C4 | — | 4 | 1 | no | — |
| 428 | C3×C4 | — | 6 | 1 | no | — |
| 429 | C3×C4 | — | 6 | 1 | no | — |
| 430 | C3×C4 | — | 6 | 1 | no | — |
| 431 | C3×C4 | — | 8 | 1 | no | — |
| 432 | C3×C4 | — | 12 | 1 | no | — |
| 433 | C3×C4 | — | 12 | 1 | no | — |
| 434 | C3×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 435 | Dic3 | — | 4 | 1 | no | — |
| 436 | Dic3 | — | 8 | 1 | no | — |
| 437 | C32 | — | 4 | 1 | no | Sylow |
| 438 | C23 | — | 6 | 1 | no | — |
| 439 | C23 | — | 12 | 1 | no | — |
| 440 | Q8 | — | 3 | 1 | no | — |
| 441 | Q8 | — | 3 | 1 | no | — |
| 442 | Q8 | — | 3 | 1 | no | — |
| 443 | Q8 | — | 6 | 1 | no | — |
| 444 | Q8 | — | 6 | 1 | no | — |
| 445 | Q8 | — | 6 | 1 | no | — |
| 446 | Q8 | — | 6 | 1 | no | — |
| 447 | Q8 | — | 12 | 1 | no | — |
| 448 | Q8 | C3×D3×D4 | 1 | 1 | yes | characteristic |
| 449 | D4 | — | 3 | 1 | no | — |
| 450 | D4 | — | 3 | 1 | no | — |
| 451 | D4 | — | 6 | 1 | no | — |
| 452 | D4 | — | 6 | 1 | no | — |
| 453 | D4 | — | 6 | 1 | no | — |
| 454 | D4 | — | 6 | 1 | no | — |
| 455 | D4 | — | 6 | 1 | no | — |
| 456 | D4 | — | 12 | 1 | no | — |
| 457 | D4 | — | 12 | 1 | no | — |
| 458 | D4 | — | 12 | 1 | no | — |
| 459 | D4 | C2×C3×S4 | 1 | 1 | yes | characteristic |
| 460 | D4 | C2×C3×S4 | 1 | 1 | yes | characteristic |
| 461 | C2×C4 | — | 3 | 1 | no | — |
| 462 | C2×C4 | — | 6 | 1 | no | — |
| 463 | C2×C4 | — | 6 | 1 | no | — |
| 464 | C2×C4 | — | 6 | 1 | no | — |
| 465 | C2×C4 | — | 6 | 1 | no | — |
| 466 | C2×C4 | — | 6 | 1 | no | — |
| 467 | C2×C4 | — | 6 | 1 | no | — |
| 468 | C2×C4 | — | 6 | 1 | no | — |
| 469 | C2×C4 | — | 12 | 1 | no | — |
| 470 | C2×C4 | — | 12 | 1 | no | — |
| 471 | C2×C4 | — | 12 | 1 | no | — |
| 472 | C8 | — | 3 | 1 | no | — |
| 473 | C8 | — | 3 | 1 | no | — |
| 474 | C8 | — | 3 | 1 | no | — |
| 475 | C8 | — | 6 | 1 | no | — |
| 476 | C8 | — | 6 | 1 | no | — |
| 477 | C8 | — | 6 | 1 | no | — |
| 478 | C8 | C2×C3×S4 | 1 | 1 | yes | characteristic |
| 479 | C2×C3 | — | 4 | 1 | no | — |
| 480 | C2×C3 | — | 4 | 1 | no | — |
| 481 | C2×C3 | — | 4 | 1 | no | — |
| 482 | C2×C3 | — | 6 | 1 | no | — |
| 483 | C2×C3 | — | 8 | 1 | no | — |
| 484 | C2×C3 | — | 12 | 1 | no | — |
| 485 | C2×C3 | — | 16 | 1 | no | — |
| 486 | C2×C3 | — | 16 | 1 | no | — |
| 487 | C2×C3 | — | 24 | 1 | no | — |
| 488 | C2×C3 | — | 32 | 1 | no | — |
| 489 | C2×C3 | — | 32 | 1 | no | — |
| 490 | C2×C3 | D4×S4 | 1 | 1 | yes | characteristic |
| 491 | D3 | — | 8 | 1 | no | — |
| 492 | D3 | — | 16 | 1 | no | — |
| 493 | C22 | — | 2 | 1 | no | — |
| 494 | C22 | — | 2 | 1 | no | — |
| 495 | C22 | — | 3 | 1 | no | — |
| 496 | C22 | — | 6 | 1 | no | — |
| 497 | C22 | — | 12 | 1 | no | — |
| 498 | C22 | — | 24 | 1 | no | — |
| 499 | C22 | — | 48 | 1 | no | — |
| 500 | C4 | — | 3 | 1 | no | — |
| 501 | C4 | — | 6 | 1 | no | — |
| 502 | C4 | — | 6 | 1 | no | — |
| 503 | C4 | — | 6 | 1 | no | — |
| 504 | C4 | — | 12 | 1 | no | — |
| 505 | C4 | — | 12 | 1 | no | — |
| 506 | C4 | C22×C3×S4 | 1 | 1 | yes | characteristic |
| 507 | C3 | — | 4 | 1 | no | — |
| 508 | C3 | — | 8 | 1 | no | — |
| 509 | C3 | #85474 | 1 | 1 | yes | characteristic, direct product factor |
| 510 | C2 | — | 4 | 1 | no | — |
| 511 | C2 | — | 4 | 1 | no | — |
| 512 | C2 | — | 6 | 1 | no | — |
| 513 | C2 | — | 12 | 1 | no | — |
| 514 | C2 | — | 24 | 1 | no | — |
| 515 | C2 | C3×D4×S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | D4×S4 |
| commutator, cosocle | #41⋊C3 | C23×C3 |
| Frattini | C4 | C22×C3×S4 |
| Fitting | C3×#578 | D3 |
| hypercenter | C3×D8 | S4 |
| hypocenter | SL(2,𝔽3) | C2×C3×D4 |
| LCS | G ▷ #41⋊C3 ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C2×C3 ◁ C3×C4 ◁ C3×D8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#5927 | C2 | semidirect |
| 2. C3×#5926 | C2 | semidirect |
| 3. C3×#578⋊C3 | C2 | semidirect |
| 4. C3×#5431 | C2 | semidirect |
| 5. C3×#5430 | C2 | semidirect |
| 6. C3×#5406 | C2 | semidirect |
| 7. C3×#5405 | C2 | semidirect |
| 8. #85474 | C3 | direct (N × H) |
| 11. C3×2−1+4⋊C3 | C22 | semidirect |
| 14. C3×#984 | C22 | semidirect |
| 20. C3×#131⋊C3 | C22 | semidirect |
| 21. C3×GU(2,𝔽3) | C22 | semidirect |
| 22. #5927 | C2×C3 | semidirect |
| 23. #5926 | C2×C3 | semidirect |
| 25. C3×#578 | D3 | semidirect |
| 29. #578⋊C3 | C2×C3 | semidirect |
| 30. #5431 | C2×C3 | semidirect |
| 31. #5430 | C2×C3 | semidirect |
| 32. #5406 | C2×C3 | semidirect |
| 33. #5405 | C2×C3 | semidirect |
| 62. C3×2−1+4 | C2×D3 | semidirect |
| 67. 2−1+4⋊C3 | C22×C3 | semidirect |
| 70. #984 | C22×C3 | semidirect |
| 104. C3×#131 | C2×D3 | semidirect |
| 109. #131⋊C3 | C22×C3 | semidirect |
| 110. GU(2,𝔽3) | C22×C3 | semidirect |
| 135. #578 | C3×D3 | semidirect |
| 241. 2−1+4 | C2×C3×D3 | semidirect |
| 272. #131 | C2×C3×D3 | semidirect |
| 509. C3 | #85474 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5927 | 2 |
| C3×#5926 | 2 |
| C3×#578⋊C3 | 2 |
| C3×#5431 | 2 |
| C3×#5430 | 2 |
| C3×#5406 | 2 |
| C3×#5405 | 2 |
| #85474 | 3 |
| C3×#3289 | 3 |
| C3×#911 | 4 |