Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
587 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 587 conjugacy classes of subgroups — too many to draw. Only its 53 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 | C2×C3×#985 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#64198 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #5834⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10593661 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10593215 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10593203 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | Dic3×#226 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #85402 | — | 3 | 1 | no | maximal |
| 9 | #83924 | — | 3 | 1 | no | maximal |
| 10 | C2×C3×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C3⋊(#41⋊C3) | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C3⋊GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 13 | C3×#985 | — | 2 | 2 | no | — |
| 14 | C2×C3×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C3×#226 | C22 | 1 | 1 | yes | characteristic |
| 16 | #64198 | — | 2 | 2 | no | — |
| 17 | #63904 | — | 4 | 1 | no | maximal |
| 18 | Dic3×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 19 | C3⋊#859 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#985 | — | 3 | 1 | no | — |
| 21 | C2×#985 | D3 | 1 | 1 | yes | characteristic, complemented |
| 22 | C2×C3×#135 | — | 3 | 1 | no | — |
| 23 | #5834 | — | 3 | 1 | no | — |
| 24 | #5834 | D3 | 1 | 1 | yes | characteristic, complemented |
| 25 | C2×#919 | — | 3 | 1 | no | — |
| 26 | C4⋊(#41⋊C3) | — | 3 | 1 | no | — |
| 27 | #5427 | — | 3 | 1 | no | — |
| 28 | #5427 | — | 3 | 1 | no | — |
| 29 | #5427 | — | 6 | 1 | no | — |
| 30 | C4⋊GL(2,𝔽3) | — | 3 | 1 | no | — |
| 31 | C4×#226 | — | 3 | 1 | no | — |
| 32 | #5238 | — | 3 | 1 | no | — |
| 33 | #5238 | — | 3 | 1 | no | — |
| 34 | Dic3×Q16 | — | 3 | 1 | no | — |
| 35 | #5172 | — | 3 | 1 | no | — |
| 36 | #5172 | — | 3 | 1 | no | — |
| 37 | #5163 | — | 3 | 1 | no | — |
| 38 | #5163 | — | 3 | 1 | no | — |
| 39 | #5157 | — | 3 | 1 | no | — |
| 40 | #5151 | — | 3 | 1 | no | — |
| 41 | #5115 | — | 3 | 1 | no | — |
| 42 | C8×#67 | — | 3 | 1 | no | — |
| 43 | C2×C3×C4×D3 | — | 4 | 1 | no | — |
| 44 | C3×#41⋊C3 | — | 2 | 1 | no | — |
| 45 | C2×C3×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 46 | C2×#626 | — | 4 | 1 | no | — |
| 47 | C2×#624 | — | 4 | 1 | no | — |
| 48 | C3⋊(#41⋊C3) | — | 2 | 1 | no | — |
| 49 | C3⋊GL(2,𝔽3) | — | 2 | 1 | no | — |
| 50 | C3×GL(2,𝔽3) | — | 2 | 1 | no | — |
| 51 | C3×#226 | D4 | 1 | 2 | yes | complemented |
| 52 | #3752 | — | 4 | 1 | no | — |
| 53 | C3×Dic3⋊C4 | — | 4 | 1 | no | — |
| 54 | (C2×D3)⋊Dic3 | — | 4 | 1 | no | — |
| 55 | Dic32 | — | 4 | 1 | no | — |
| 56 | #3287 | — | 9 | 1 | no | Sylow |
| 57 | C2×C3×#41 | — | 3 | 1 | no | — |
| 58 | C2×C3×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 59 | C2×#239 | — | 3 | 1 | no | — |
| 60 | C2×#239 | C2×D3 | 1 | 1 | yes | characteristic |
| 61 | C2×#41⋊C3 | — | 2 | 1 | no | — |
| 62 | C2×#41⋊C3 | — | 3 | 1 | no | — |
| 63 | C2×#41⋊C3 | C2×D3 | 1 | 1 | yes | characteristic |
| 64 | #985 | — | 2 | 2 | no | — |
| 65 | #985 | — | 6 | 2 | no | — |
| 66 | C2×GL(2,𝔽3) | — | 3 | 1 | no | — |
| 67 | C2×GL(2,𝔽3) | — | 6 | 1 | no | — |
| 68 | C2×GL(2,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic |
| 69 | C2×#226 | C2×D3 | 1 | 1 | yes | characteristic |
| 70 | C3×#135 | — | 6 | 2 | no | — |
| 71 | C3×#135 | — | 6 | 2 | no | — |
| 72 | C2×C3×Q16 | — | 3 | 1 | no | — |
| 73 | C2×C3×SD16 | — | 3 | 1 | no | — |
| 74 | C2×C3×SD16 | — | 3 | 1 | no | — |
| 75 | C2×C3×D8 | — | 3 | 1 | no | — |
| 76 | C22×C3×C8 | — | 3 | 1 | no | — |
| 77 | Q8×Dic3 | — | 3 | 1 | no | — |
| 78 | Q8×Dic3 | C2×D3 | 1 | 1 | yes | characteristic |
| 79 | C2×#215 | — | 3 | 1 | no | — |
| 80 | C2×#215 | — | 3 | 1 | no | — |
| 81 | #940 | — | 3 | 1 | no | — |
| 82 | #940 | — | 3 | 1 | no | — |
| 83 | #940 | — | 6 | 1 | no | — |
| 84 | #938 | — | 3 | 1 | no | — |
| 85 | #938 | — | 3 | 1 | no | — |
| 86 | #938 | — | 6 | 1 | no | — |
| 87 | C2×#213 | — | 3 | 1 | no | — |
| 88 | C2×#213 | — | 3 | 1 | no | — |
| 89 | #930 | — | 3 | 1 | no | — |
| 90 | #930 | — | 3 | 1 | no | — |
| 91 | #930 | — | 6 | 1 | no | — |
| 92 | C4×#67 | — | 3 | 1 | no | — |
| 93 | C4×#67 | — | 6 | 1 | no | — |
| 94 | #919 | — | 6 | 2 | no | — |
| 95 | #919 | — | 6 | 2 | no | — |
| 96 | C2×D24 | — | 3 | 1 | no | — |
| 97 | C2×D3×C8 | — | 3 | 1 | no | — |
| 98 | #893 | — | 12 | 1 | no | — |
| 99 | C4×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 100 | #859 | — | 3 | 1 | no | — |
| 101 | #859 | — | 6 | 1 | no | — |
| 102 | #835 | — | 3 | 1 | no | — |
| 103 | #835 | — | 3 | 1 | no | — |
| 104 | #832 | — | 3 | 1 | no | — |
| 105 | #832 | — | 3 | 1 | no | — |
| 106 | #830 | — | 3 | 1 | no | — |
| 107 | #821 | — | 3 | 1 | no | — |
| 108 | #821 | — | 3 | 1 | no | — |
| 109 | (C2×D3)⋊C8 | — | 3 | 1 | no | — |
| 110 | #818 | — | 3 | 1 | no | — |
| 111 | Dic3⋊C8 | — | 3 | 1 | no | — |
| 112 | C8×Dic3 | — | 3 | 1 | no | — |
| 113 | C22×C3⋊D3 | — | 4 | 1 | no | — |
| 114 | C22×C3×D3 | — | 4 | 1 | no | — |
| 115 | C2×C32×C4 | — | 4 | 1 | no | — |
| 116 | C2×C3⋊Dic3 | — | 4 | 1 | no | — |
| 117 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 118 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 119 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 120 | C3×C4×D3 | — | 8 | 2 | no | — |
| 121 | C3×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | #626 | — | 4 | 4 | no | — |
| 123 | #624 | — | 8 | 2 | no | — |
| 124 | C2×#135 | — | 3 | 1 | no | — |
| 125 | C2×#135 | — | 9 | 1 | no | — |
| 126 | #550 | — | 3 | 1 | no | — |
| 127 | #550 | — | 9 | 1 | no | — |
| 128 | #493 | — | 9 | 1 | no | — |
| 129 | #466 | — | 9 | 1 | no | — |
| 130 | #466 | — | 9 | 1 | no | — |
| 131 | #460 | — | 9 | 1 | no | — |
| 132 | #460 | — | 9 | 1 | no | — |
| 133 | #449 | — | 9 | 1 | no | — |
| 134 | #449 | — | 9 | 1 | no | — |
| 135 | #449 | — | 9 | 1 | no | — |
| 136 | #449 | — | 9 | 1 | no | — |
| 137 | C4×Q16 | — | 9 | 1 | no | — |
| 138 | C8×D4 | — | 9 | 1 | no | — |
| 139 | C3×#41 | — | 2 | 1 | no | — |
| 140 | C3×#41 | — | 6 | 1 | no | — |
| 141 | C3×#41 | — | 6 | 2 | no | — |
| 142 | C3×#41 | — | 12 | 1 | no | — |
| 143 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 144 | C2×C3×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 145 | C2×C3×D4 | — | 3 | 1 | no | — |
| 146 | C2×C3×D4 | — | 3 | 1 | no | — |
| 147 | C2×C3×D4 | — | 6 | 1 | no | — |
| 148 | C22×C3×C4 | — | 3 | 1 | no | — |
| 149 | C22×C3×C4 | — | 6 | 1 | no | — |
| 150 | C2×#67 | — | 3 | 1 | no | — |
| 151 | C2×#67 | — | 6 | 1 | no | — |
| 152 | C2×#67 | — | 6 | 1 | no | — |
| 153 | C2×#67 | — | 6 | 1 | no | — |
| 154 | C2×#67 | — | 6 | 1 | no | — |
| 155 | C2×#67 | — | 6 | 1 | no | — |
| 156 | #239 | — | 2 | 1 | no | — |
| 157 | #239 | — | 6 | 1 | no | — |
| 158 | #239 | — | 6 | 2 | no | — |
| 159 | #239 | — | 12 | 1 | no | — |
| 160 | C2×D12 | — | 3 | 1 | no | — |
| 161 | C2×D12 | — | 3 | 1 | no | — |
| 162 | C2×D12 | — | 6 | 1 | no | — |
| 163 | C2×D12 | — | 12 | 1 | no | — |
| 164 | C2×C4×D3 | — | 3 | 1 | no | — |
| 165 | C2×C4×D3 | — | 4 | 1 | no | — |
| 166 | C2×C4×D3 | — | 6 | 1 | no | — |
| 167 | C2×C4×D3 | — | 12 | 1 | no | — |
| 168 | #41⋊C3 | — | 2 | 1 | no | — |
| 169 | #41⋊C3 | — | 4 | 1 | no | — |
| 170 | #41⋊C3 | — | 6 | 1 | no | — |
| 171 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 172 | C2×SL(2,𝔽3) | C22×D3 | 1 | 1 | yes | characteristic |
| 173 | GL(2,𝔽3) | — | 2 | 1 | no | — |
| 174 | GL(2,𝔽3) | — | 6 | 1 | no | — |
| 175 | GL(2,𝔽3) | — | 12 | 1 | no | — |
| 176 | #226 | #67 | 1 | 2 | yes | complemented |
| 177 | C3×Q16 | — | 3 | 2 | no | — |
| 178 | C3×Q16 | — | 3 | 2 | no | — |
| 179 | C3×SD16 | — | 6 | 2 | no | — |
| 180 | C3×SD16 | — | 6 | 1 | no | — |
| 181 | C3×SD16 | — | 6 | 1 | no | — |
| 182 | C3×D8 | — | 6 | 2 | no | — |
| 183 | C2×C3×C8 | — | 3 | 1 | no | — |
| 184 | C2×C3×C8 | — | 3 | 1 | no | — |
| 185 | C2×C3×C8 | — | 6 | 2 | no | — |
| 186 | C3×C4⋊C4 | — | 12 | 1 | no | — |
| 187 | #217 | — | 3 | 1 | no | — |
| 188 | #217 | — | 6 | 1 | no | — |
| 189 | #215 | — | 6 | 2 | no | — |
| 190 | #215 | — | 6 | 1 | no | — |
| 191 | #215 | — | 6 | 1 | no | — |
| 192 | #213 | — | 12 | 1 | no | — |
| 193 | #213 | — | 12 | 1 | no | — |
| 194 | (C2×D3)⋊C4 | — | 3 | 1 | no | — |
| 195 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 196 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 197 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 198 | (C2×D3)⋊C4 | — | 24 | 1 | no | — |
| 199 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 200 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 201 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 202 | Dic3⋊C4 | S4 | 1 | 1 | yes | characteristic |
| 203 | C4×Dic3 | — | 3 | 1 | no | — |
| 204 | C4×Dic3 | — | 6 | 1 | no | — |
| 205 | C4×Dic3 | — | 12 | 1 | no | — |
| 206 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 207 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 208 | D24 | — | 6 | 2 | no | — |
| 209 | D3×C8 | — | 6 | 2 | no | — |
| 210 | C22×C32 | — | 4 | 1 | no | — |
| 211 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 212 | C2×C3⋊D3 | — | 8 | 1 | no | — |
| 213 | C2×C3⋊D3 | — | 8 | 1 | no | — |
| 214 | C2×C3×D3 | — | 4 | 2 | no | — |
| 215 | C2×C3×D3 | — | 8 | 1 | no | — |
| 216 | C2×C3×D3 | — | 8 | 1 | no | — |
| 217 | C32×C4 | — | 8 | 1 | no | — |
| 218 | C3⋊Dic3 | — | 8 | 1 | no | — |
| 219 | C3×Dic3 | — | 4 | 2 | no | — |
| 220 | C3×Dic3 | — | 4 | 2 | no | — |
| 221 | C3×Dic3 | — | 8 | 1 | no | — |
| 222 | C2×#41 | — | 3 | 1 | no | — |
| 223 | C2×#41 | — | 3 | 1 | no | — |
| 224 | C2×#41 | — | 9 | 1 | no | — |
| 225 | C2×#41 | D32 | 1 | 1 | yes | characteristic |
| 226 | #135 | — | 6 | 2 | no | — |
| 227 | #135 | — | 6 | 2 | no | — |
| 228 | #135 | — | 18 | 2 | no | — |
| 229 | #135 | — | 18 | 2 | no | — |
| 230 | C2×Q16 | — | 3 | 1 | no | — |
| 231 | C2×SD16 | — | 3 | 1 | no | — |
| 232 | C2×SD16 | — | 3 | 1 | no | — |
| 233 | C2×SD16 | — | 9 | 1 | no | — |
| 234 | C2×SD16 | — | 9 | 1 | no | — |
| 235 | C2×D8 | — | 3 | 1 | no | — |
| 236 | C2×D8 | — | 9 | 1 | no | — |
| 237 | C2×D8 | — | 9 | 1 | no | — |
| 238 | C2×D8 | — | 9 | 1 | no | — |
| 239 | C22×C8 | — | 3 | 1 | no | — |
| 240 | C22×C8 | — | 9 | 1 | no | — |
| 241 | #127 | — | 9 | 1 | no | — |
| 242 | #127 | — | 9 | 1 | no | — |
| 243 | #127 | — | 18 | 1 | no | — |
| 244 | #121 | — | 9 | 1 | no | — |
| 245 | #121 | — | 9 | 1 | no | — |
| 246 | #121 | — | 9 | 1 | no | — |
| 247 | #121 | — | 9 | 1 | no | — |
| 248 | #121 | — | 18 | 1 | no | — |
| 249 | #121 | — | 18 | 1 | no | — |
| 250 | C4×Q8 | — | 3 | 1 | no | — |
| 251 | C4×Q8 | — | 9 | 1 | no | — |
| 252 | C4×D4 | — | 9 | 1 | no | — |
| 253 | C4×D4 | — | 18 | 1 | no | — |
| 254 | #107 | — | 9 | 1 | no | — |
| 255 | C4⋊C8 | — | 9 | 1 | no | — |
| 256 | #103 | — | 9 | 1 | no | — |
| 257 | #103 | — | 9 | 1 | no | — |
| 258 | #102 | — | 9 | 1 | no | — |
| 259 | #102 | — | 9 | 1 | no | — |
| 260 | #102 | — | 9 | 1 | no | — |
| 261 | #102 | — | 9 | 1 | no | — |
| 262 | C22⋊C8 | — | 9 | 1 | no | — |
| 263 | C22⋊C8 | — | 9 | 1 | no | — |
| 264 | C4×C8 | — | 9 | 1 | no | — |
| 265 | C23×C3 | — | 3 | 1 | no | — |
| 266 | C23×C3 | — | 6 | 1 | no | — |
| 267 | C22×D3 | — | 3 | 1 | no | — |
| 268 | C22×D3 | — | 4 | 1 | no | — |
| 269 | C22×D3 | — | 6 | 1 | no | — |
| 270 | C22×D3 | — | 12 | 1 | no | — |
| 271 | C22×D3 | — | 24 | 1 | no | — |
| 272 | C3×Q8 | — | 3 | 1 | no | — |
| 273 | C3×Q8 | — | 3 | 2 | no | — |
| 274 | C3×Q8 | — | 6 | 1 | no | — |
| 275 | C3×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 276 | C3×D4 | — | 6 | 1 | no | — |
| 277 | C3×D4 | — | 6 | 1 | no | — |
| 278 | C3×D4 | — | 6 | 1 | no | — |
| 279 | C3×D4 | — | 6 | 1 | no | — |
| 280 | C3×D4 | — | 12 | 2 | no | — |
| 281 | C2×C3×C4 | — | 3 | 1 | no | — |
| 282 | C2×C3×C4 | — | 4 | 1 | no | — |
| 283 | C2×C3×C4 | — | 6 | 1 | no | — |
| 284 | C2×C3×C4 | — | 6 | 1 | no | — |
| 285 | C2×C3×C4 | — | 6 | 1 | no | — |
| 286 | C2×C3×C4 | — | 8 | 1 | no | — |
| 287 | C2×C3×C4 | — | 12 | 1 | no | — |
| 288 | C2×C3×C4 | — | 12 | 1 | no | — |
| 289 | C2×C3×C4 | — | 12 | 2 | no | — |
| 290 | C2×C3×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 291 | #67 | — | 6 | 2 | no | — |
| 292 | #67 | — | 12 | 2 | no | — |
| 293 | #67 | — | 24 | 1 | no | — |
| 294 | #67 | — | 24 | 1 | no | — |
| 295 | #67 | — | 24 | 1 | no | — |
| 296 | #67 | — | 24 | 1 | no | — |
| 297 | C2×Dic3 | — | 3 | 1 | no | — |
| 298 | C2×Dic3 | — | 4 | 1 | no | — |
| 299 | C2×Dic3 | — | 6 | 1 | no | — |
| 300 | C2×Dic3 | — | 12 | 1 | no | — |
| 301 | C2×Dic3 | — | 24 | 1 | no | — |
| 302 | C2×Dic3 | C2×S4 | 1 | 1 | yes | characteristic |
| 303 | C2×Dic3 | C2×S4 | 1 | 1 | yes | characteristic |
| 304 | D12 | — | 6 | 1 | no | — |
| 305 | D12 | — | 6 | 1 | no | — |
| 306 | D12 | — | 6 | 1 | no | — |
| 307 | D12 | — | 6 | 1 | no | — |
| 308 | D12 | — | 12 | 2 | no | — |
| 309 | D12 | — | 12 | 4 | no | — |
| 310 | C4×D3 | — | 6 | 1 | no | — |
| 311 | C4×D3 | — | 6 | 1 | no | — |
| 312 | C4×D3 | — | 8 | 2 | no | — |
| 313 | C4×D3 | — | 12 | 2 | no | — |
| 314 | C4×D3 | — | 24 | 2 | no | — |
| 315 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 316 | SL(2,𝔽3) | C2×#67 | 1 | 1 | yes | characteristic |
| 317 | C3×C8 | — | 3 | 2 | no | — |
| 318 | C3×C8 | — | 6 | 1 | no | — |
| 319 | C3⋊C8 | — | 6 | 1 | no | — |
| 320 | C3⋊C8 | — | 6 | 1 | no | — |
| 321 | C2×C32 | — | 4 | 1 | no | — |
| 322 | C2×C32 | — | 4 | 1 | no | — |
| 323 | C2×C32 | — | 4 | 1 | no | — |
| 324 | C3⋊D3 | — | 8 | 2 | no | — |
| 325 | C3×D3 | — | 8 | 2 | no | — |
| 326 | #41 | — | 2 | 1 | no | — |
| 327 | #41 | — | 6 | 1 | no | — |
| 328 | #41 | — | 6 | 2 | no | — |
| 329 | #41 | — | 6 | 1 | no | — |
| 330 | #41 | — | 12 | 1 | no | — |
| 331 | #41 | — | 18 | 1 | no | — |
| 332 | #41 | — | 18 | 2 | no | — |
| 333 | #41 | — | 36 | 1 | no | — |
| 334 | C2×Q8 | — | 3 | 1 | no | — |
| 335 | C2×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 336 | C2×D4 | — | 3 | 1 | no | — |
| 337 | C2×D4 | — | 3 | 1 | no | — |
| 338 | C2×D4 | — | 6 | 1 | no | — |
| 339 | C2×D4 | — | 9 | 1 | no | — |
| 340 | C2×D4 | — | 9 | 1 | no | — |
| 341 | C2×D4 | — | 9 | 1 | no | — |
| 342 | C2×D4 | — | 18 | 1 | no | — |
| 343 | C2×D4 | — | 18 | 1 | no | — |
| 344 | C2×D4 | — | 18 | 1 | no | — |
| 345 | C2×D4 | — | 18 | 1 | no | — |
| 346 | C2×D4 | — | 18 | 1 | no | — |
| 347 | C2×D4 | — | 18 | 1 | no | — |
| 348 | C22×C4 | — | 3 | 1 | no | — |
| 349 | C22×C4 | — | 6 | 1 | no | — |
| 350 | C22×C4 | — | 9 | 1 | no | — |
| 351 | C22×C4 | — | 18 | 1 | no | — |
| 352 | Q16 | — | 3 | 2 | no | — |
| 353 | Q16 | — | 3 | 2 | no | — |
| 354 | SD16 | — | 6 | 2 | no | — |
| 355 | SD16 | — | 6 | 1 | no | — |
| 356 | SD16 | — | 6 | 1 | no | — |
| 357 | SD16 | — | 18 | 2 | no | — |
| 358 | SD16 | — | 18 | 1 | no | — |
| 359 | SD16 | — | 18 | 1 | no | — |
| 360 | D8 | — | 6 | 2 | no | — |
| 361 | D8 | — | 18 | 2 | no | — |
| 362 | D8 | — | 36 | 1 | no | — |
| 363 | D8 | — | 36 | 1 | no | — |
| 364 | C2×C8 | — | 3 | 1 | no | — |
| 365 | C2×C8 | — | 3 | 1 | no | — |
| 366 | C2×C8 | — | 6 | 2 | no | — |
| 367 | C2×C8 | — | 9 | 1 | no | — |
| 368 | C2×C8 | — | 9 | 1 | no | — |
| 369 | C2×C8 | — | 18 | 2 | no | — |
| 370 | C4⋊C4 | — | 3 | 1 | no | — |
| 371 | C4⋊C4 | — | 9 | 1 | no | — |
| 372 | C4⋊C4 | — | 9 | 1 | no | — |
| 373 | C4⋊C4 | — | 18 | 1 | no | — |
| 374 | C22⋊C4 | — | 9 | 1 | no | — |
| 375 | C22⋊C4 | — | 9 | 1 | no | — |
| 376 | C22⋊C4 | — | 18 | 1 | no | — |
| 377 | C22⋊C4 | — | 18 | 1 | no | — |
| 378 | C42 | — | 9 | 1 | no | — |
| 379 | C42 | — | 18 | 1 | no | — |
| 380 | C22×C3 | — | 4 | 1 | no | — |
| 381 | C22×C3 | — | 6 | 1 | no | — |
| 382 | C22×C3 | — | 6 | 1 | no | — |
| 383 | C22×C3 | — | 6 | 1 | no | — |
| 384 | C22×C3 | — | 8 | 1 | no | — |
| 385 | C22×C3 | — | 12 | 1 | no | — |
| 386 | C22×C3 | — | 12 | 1 | no | — |
| 387 | C22×C3 | — | 12 | 1 | no | — |
| 388 | C22×C3 | C22×S4 | 1 | 1 | yes | characteristic |
| 389 | C2×D3 | — | 4 | 2 | no | — |
| 390 | C2×D3 | — | 6 | 1 | no | — |
| 391 | C2×D3 | — | 6 | 1 | no | — |
| 392 | C2×D3 | — | 6 | 1 | no | — |
| 393 | C2×D3 | — | 8 | 1 | no | — |
| 394 | C2×D3 | — | 8 | 1 | no | — |
| 395 | C2×D3 | — | 12 | 2 | no | — |
| 396 | C2×D3 | — | 12 | 1 | no | — |
| 397 | C2×D3 | — | 12 | 1 | no | — |
| 398 | C2×D3 | — | 12 | 1 | no | — |
| 399 | C2×D3 | — | 24 | 1 | no | — |
| 400 | C2×D3 | — | 24 | 1 | no | — |
| 401 | C2×D3 | — | 24 | 2 | no | — |
| 402 | C2×D3 | — | 48 | 1 | no | — |
| 403 | C2×D3 | — | 48 | 1 | no | — |
| 404 | C3×C4 | — | 2 | 1 | no | — |
| 405 | C3×C4 | — | 3 | 1 | no | — |
| 406 | C3×C4 | — | 3 | 1 | no | — |
| 407 | C3×C4 | — | 6 | 2 | no | — |
| 408 | C3×C4 | — | 8 | 1 | no | — |
| 409 | C3×C4 | — | 12 | 2 | no | — |
| 410 | C3×C4 | — | 16 | 1 | no | — |
| 411 | C3×C4 | — | 24 | 1 | no | — |
| 412 | Dic3 | — | 2 | 1 | no | — |
| 413 | Dic3 | — | 4 | 2 | no | — |
| 414 | Dic3 | — | 6 | 1 | no | — |
| 415 | Dic3 | — | 12 | 1 | no | — |
| 416 | Dic3 | — | 24 | 1 | no | — |
| 417 | Dic3 | — | 48 | 1 | no | — |
| 418 | Dic3 | #985 | 1 | 2 | yes | complemented |
| 419 | C32 | — | 4 | 1 | no | Sylow |
| 420 | C23 | — | 3 | 1 | no | — |
| 421 | C23 | — | 6 | 1 | no | — |
| 422 | C23 | — | 9 | 1 | no | — |
| 423 | C23 | — | 18 | 1 | no | — |
| 424 | Q8 | — | 3 | 1 | no | — |
| 425 | Q8 | — | 3 | 2 | no | — |
| 426 | Q8 | — | 6 | 1 | no | — |
| 427 | Q8 | D3×#67 | 1 | 1 | yes | characteristic |
| 428 | D4 | — | 6 | 1 | no | — |
| 429 | D4 | — | 6 | 1 | no | — |
| 430 | D4 | — | 6 | 1 | no | — |
| 431 | D4 | — | 6 | 1 | no | — |
| 432 | D4 | — | 12 | 2 | no | — |
| 433 | D4 | — | 18 | 2 | no | — |
| 434 | D4 | — | 18 | 1 | no | — |
| 435 | D4 | — | 18 | 1 | no | — |
| 436 | D4 | — | 18 | 1 | no | — |
| 437 | D4 | — | 18 | 1 | no | — |
| 438 | D4 | — | 36 | 2 | no | — |
| 439 | D4 | — | 36 | 2 | no | — |
| 440 | D4 | — | 72 | 1 | no | — |
| 441 | D4 | — | 72 | 1 | no | — |
| 442 | D4 | — | 72 | 1 | no | — |
| 443 | D4 | — | 72 | 1 | no | — |
| 444 | C2×C4 | — | 3 | 1 | no | — |
| 445 | C2×C4 | — | 3 | 1 | no | — |
| 446 | C2×C4 | — | 3 | 1 | no | — |
| 447 | C2×C4 | — | 6 | 1 | no | — |
| 448 | C2×C4 | — | 6 | 1 | no | — |
| 449 | C2×C4 | — | 6 | 1 | no | — |
| 450 | C2×C4 | — | 9 | 1 | no | — |
| 451 | C2×C4 | — | 12 | 2 | no | — |
| 452 | C2×C4 | — | 18 | 1 | no | — |
| 453 | C2×C4 | — | 18 | 1 | no | — |
| 454 | C2×C4 | — | 18 | 1 | no | — |
| 455 | C2×C4 | — | 36 | 2 | no | — |
| 456 | C2×C4 | D3×S4 | 1 | 1 | yes | characteristic |
| 457 | C8 | — | 3 | 2 | no | — |
| 458 | C8 | — | 6 | 1 | no | — |
| 459 | C8 | — | 18 | 1 | no | — |
| 460 | C8 | — | 18 | 1 | no | — |
| 461 | C2×C3 | — | 4 | 1 | no | — |
| 462 | C2×C3 | — | 4 | 1 | no | — |
| 463 | C2×C3 | — | 4 | 1 | no | — |
| 464 | C2×C3 | — | 8 | 1 | no | — |
| 465 | C2×C3 | — | 8 | 1 | no | — |
| 466 | C2×C3 | — | 8 | 1 | no | — |
| 467 | C2×C3 | — | 12 | 1 | no | — |
| 468 | C2×C3 | — | 24 | 1 | no | — |
| 469 | C2×C3 | D4×S4 | 1 | 1 | yes | characteristic |
| 470 | C2×C3 | C2×#985 | 1 | 1 | yes | characteristic |
| 471 | C2×C3 | #5925 | 1 | 1 | yes | characteristic |
| 472 | D3 | — | 8 | 2 | no | — |
| 473 | D3 | — | 12 | 1 | no | — |
| 474 | D3 | — | 24 | 2 | no | — |
| 475 | D3 | — | 24 | 1 | no | — |
| 476 | D3 | — | 48 | 2 | no | — |
| 477 | C22 | — | 6 | 1 | no | — |
| 478 | C22 | — | 6 | 1 | no | — |
| 479 | C22 | — | 6 | 1 | no | — |
| 480 | C22 | — | 12 | 1 | no | — |
| 481 | C22 | — | 12 | 1 | no | — |
| 482 | C22 | — | 12 | 1 | no | — |
| 483 | C22 | — | 18 | 1 | no | — |
| 484 | C22 | — | 18 | 1 | no | — |
| 485 | C22 | — | 18 | 1 | no | — |
| 486 | C22 | — | 36 | 1 | no | — |
| 487 | C22 | — | 36 | 1 | no | — |
| 488 | C22 | — | 36 | 1 | no | — |
| 489 | C22 | C2×D3×S4 | 1 | 1 | yes | characteristic |
| 490 | C4 | — | 2 | 1 | no | — |
| 491 | C4 | — | 3 | 2 | no | — |
| 492 | C4 | — | 3 | 1 | no | — |
| 493 | C4 | — | 3 | 1 | no | — |
| 494 | C4 | — | 6 | 1 | no | — |
| 495 | C4 | — | 6 | 2 | no | — |
| 496 | C4 | — | 18 | 1 | no | — |
| 497 | C4 | — | 36 | 1 | no | — |
| 498 | C3 | — | 4 | 1 | no | — |
| 499 | C3 | — | 8 | 1 | no | — |
| 500 | C3 | #85402 | 1 | 1 | yes | characteristic, complemented |
| 501 | C2 | — | 12 | 1 | no | — |
| 502 | C2 | — | 24 | 1 | no | — |
| 503 | C2 | — | 36 | 1 | no | — |
| 504 | C2 | — | 72 | 1 | no | — |
| 505 | C2 | #10596449 | 1 | 1 | yes | characteristic |
| 506 | C2 | D3×#985 | 1 | 1 | yes | characteristic |
| 507 | C2 | #67×S4 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×#985 | C2 | semidirect |
| 2. C2×#64198 | C2 | semidirect |
| 3. #5834⋊C3 | C2 | semidirect |
| 4. #10593661 | C2 | semidirect |
| 5. #10593215 | C2 | semidirect |
| 6. #10593203 | C2 | semidirect |
| 7. Dic3×#226 | C2 | semidirect |
| 21. C2×#985 | D3 | semidirect |
| 24. #5834 | D3 | semidirect |
| 51. C3×#226 | D4 | semidirect |
| 176. #226 | #67 | semidirect |
| 418. Dic3 | #985 | semidirect |
| 500. C3 | #85402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#985 | 2 |
| C2×#64198 | 2 |
| #5834⋊C3 | 2 |
| #10593661 | 2 |
| #10593215 | 2 |
| #10593203 | 2 |
| Dic3×#226 | 2 |
| #85402 | 3 |
| #83924 | 3 |
| #63904 | 4 |