Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
849 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 849 conjugacy classes of subgroups — too many to draw. Only its 61 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 | C22×C3⋊GL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×D3×GL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | SL(2,𝔽3)×#67 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#5421 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10593218 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10593215 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10593214 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | D4×GL(2,𝔽3) | — | 3 | 1 | no | maximal |
| 9 | #80063 | — | 3 | 1 | no | maximal |
| 10 | C22×C3×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C2×#3811 | — | 4 | 1 | no | maximal |
| 12 | C2×D3×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C2×C3⋊GL(2,𝔽3) | — | 2 | 2 | no | — |
| 14 | C2×C3⋊GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C3⋊GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C2×C3×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | D3×GL(2,𝔽3) | — | 2 | 2 | no | — |
| 18 | Dic3×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C3×#859 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C22×GL(2,𝔽3) | — | 3 | 1 | no | — |
| 21 | C22×GL(2,𝔽3) | — | 3 | 1 | no | — |
| 22 | C22×GL(2,𝔽3) | — | 6 | 1 | no | — |
| 23 | Q8×#67 | D3 | 1 | 1 | yes | characteristic, complemented |
| 24 | C22×#215 | — | 3 | 1 | no | — |
| 25 | C2×D3×SD16 | — | 3 | 1 | no | — |
| 26 | #5609 | — | 3 | 1 | no | — |
| 27 | D4×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 28 | #5421 | — | 3 | 1 | no | — |
| 29 | #5421 | D3 | 1 | 1 | yes | characteristic, complemented |
| 30 | C4⋊GL(2,𝔽3) | — | 3 | 1 | no | — |
| 31 | C4×GL(2,𝔽3) | — | 3 | 1 | no | — |
| 32 | C3×#448 | — | 3 | 1 | no | — |
| 33 | #5175 | — | 3 | 1 | no | — |
| 34 | #5169 | — | 3 | 1 | no | — |
| 35 | #5163 | — | 3 | 1 | no | — |
| 36 | #5041 | — | 3 | 1 | no | — |
| 37 | #4818 | — | 3 | 1 | no | — |
| 38 | #4807 | — | 3 | 1 | no | — |
| 39 | #4806 | — | 3 | 1 | no | — |
| 40 | #4788 | — | 3 | 1 | no | — |
| 41 | #4731 | — | 3 | 1 | no | — |
| 42 | #67⋊C8 | — | 3 | 1 | no | — |
| 43 | C23×C3⋊D3 | — | 4 | 1 | no | — |
| 44 | C22×D32 | — | 4 | 1 | no | — |
| 45 | C2×C3×#67 | — | 4 | 1 | no | — |
| 46 | C2×C3×#67 | — | 4 | 1 | no | — |
| 47 | C2×C3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 48 | C2×C3×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 49 | #3811 | — | 4 | 8 | no | — |
| 50 | C2×#626 | — | 4 | 1 | no | — |
| 51 | C2×#626 | — | 4 | 1 | no | — |
| 52 | C2×#624 | — | 4 | 1 | no | — |
| 53 | D3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 54 | C3⋊GL(2,𝔽3) | — | 2 | 1 | no | — |
| 55 | C3⋊GL(2,𝔽3) | D4 | 1 | 2 | yes | complemented |
| 56 | C3×GL(2,𝔽3) | — | 2 | 1 | no | — |
| 57 | D4×SD16 | — | 9 | 1 | no | Sylow |
| 58 | C22×C3×Q8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 59 | C2×D3×Q8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 60 | C2×D3×D4 | — | 3 | 1 | no | — |
| 61 | C2×D3×D4 | — | 6 | 1 | no | — |
| 62 | C2×D3×D4 | — | 12 | 1 | no | — |
| 63 | C22×D12 | — | 3 | 1 | no | — |
| 64 | C22×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 65 | C22×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 66 | C22×SL(2,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 67 | C2×GL(2,𝔽3) | — | 3 | 1 | no | — |
| 68 | C2×GL(2,𝔽3) | — | 3 | 1 | no | — |
| 69 | C2×GL(2,𝔽3) | — | 6 | 1 | no | — |
| 70 | C2×GL(2,𝔽3) | — | 6 | 1 | no | — |
| 71 | C2×GL(2,𝔽3) | — | 6 | 2 | no | — |
| 72 | C2×GL(2,𝔽3) | — | 6 | 2 | no | — |
| 73 | C2×GL(2,𝔽3) | — | 6 | 4 | no | — |
| 74 | C2×GL(2,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 75 | C2×C3×SD16 | — | 3 | 1 | no | — |
| 76 | C2×C3×SD16 | — | 3 | 1 | no | — |
| 77 | C3×#121 | — | 3 | 1 | no | — |
| 78 | #946 | — | 3 | 1 | no | — |
| 79 | Q8×Dic3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 80 | #944 | — | 3 | 1 | no | — |
| 81 | C2×#215 | — | 3 | 1 | no | — |
| 82 | C2×#215 | — | 3 | 1 | no | — |
| 83 | C2×#215 | — | 3 | 1 | no | — |
| 84 | C2×#215 | — | 3 | 1 | no | — |
| 85 | C2×#215 | — | 6 | 2 | no | — |
| 86 | C2×#215 | — | 6 | 2 | no | — |
| 87 | #940 | — | 3 | 1 | no | — |
| 88 | #937 | — | 6 | 1 | no | — |
| 89 | C2×#214 | — | 3 | 1 | no | — |
| 90 | C4×#67 | — | 3 | 1 | no | — |
| 91 | #924 | — | 3 | 1 | no | — |
| 92 | C22×C3⋊C8 | — | 3 | 1 | no | — |
| 93 | D3×SD16 | — | 6 | 2 | no | — |
| 94 | D3×SD16 | — | 6 | 2 | no | — |
| 95 | C2×#204 | — | 3 | 1 | no | — |
| 96 | C2×#204 | — | 3 | 1 | no | — |
| 97 | C2×D3×C8 | — | 3 | 1 | no | — |
| 98 | #895 | — | 3 | 1 | no | — |
| 99 | #893 | — | 3 | 1 | no | — |
| 100 | #884 | — | 6 | 1 | no | — |
| 101 | #882 | — | 6 | 1 | no | — |
| 102 | C4×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 103 | #859 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 104 | C3×#103 | — | 3 | 1 | no | — |
| 105 | C3×#103 | — | 3 | 1 | no | — |
| 106 | C3×C22⋊C8 | — | 3 | 1 | no | — |
| 107 | #832 | — | 3 | 1 | no | — |
| 108 | #821 | — | 3 | 1 | no | — |
| 109 | #821 | — | 3 | 1 | no | — |
| 110 | (C2×D3)⋊C8 | — | 3 | 1 | no | — |
| 111 | Dic3⋊C8 | — | 3 | 1 | no | — |
| 112 | C8×Dic3 | — | 3 | 1 | no | — |
| 113 | #810 | — | 3 | 1 | no | — |
| 114 | #808 | — | 3 | 1 | no | — |
| 115 | C23×C32 | — | 4 | 1 | no | — |
| 116 | C22×C3⋊D3 | — | 4 | 1 | no | — |
| 117 | C22×C3⋊D3 | — | 4 | 1 | no | — |
| 118 | C22×C3⋊D3 | — | 4 | 4 | no | — |
| 119 | C22×C3⋊D3 | — | 8 | 2 | no | — |
| 120 | C22×C3⋊D3 | — | 8 | 2 | no | — |
| 121 | C22×C3×D3 | — | 4 | 1 | no | — |
| 122 | C22×C3×D3 | — | 4 | 1 | no | — |
| 123 | C2×D32 | — | 4 | 4 | no | — |
| 124 | C2×D32 | — | 8 | 2 | no | — |
| 125 | C2×D32 | — | 8 | 2 | no | — |
| 126 | C3×#67 | — | 4 | 4 | no | — |
| 127 | C3×#67 | — | 4 | 4 | no | — |
| 128 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 129 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 130 | C3×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic, complemented |
| 131 | #626 | — | 4 | 4 | no | — |
| 132 | #626 | — | 4 | 4 | no | — |
| 133 | #624 | — | 4 | 4 | no | — |
| 134 | C22×SD16 | — | 9 | 1 | no | — |
| 135 | C22×SD16 | — | 9 | 1 | no | — |
| 136 | D4×Q8 | — | 3 | 1 | no | — |
| 137 | D42 | — | 9 | 1 | no | — |
| 138 | #492 | — | 9 | 1 | no | — |
| 139 | #465 | — | 9 | 1 | no | — |
| 140 | #465 | — | 9 | 1 | no | — |
| 141 | #461 | — | 9 | 1 | no | — |
| 142 | #460 | — | 9 | 1 | no | — |
| 143 | #450 | — | 9 | 1 | no | — |
| 144 | #450 | — | 9 | 1 | no | — |
| 145 | #448 | — | 3 | 1 | no | — |
| 146 | #448 | — | 9 | 1 | no | — |
| 147 | C4×SD16 | — | 9 | 1 | no | — |
| 148 | C8×D4 | — | 9 | 1 | no | — |
| 149 | C23×D3 | — | 6 | 1 | no | — |
| 150 | C23×D3 | — | 6 | 1 | no | — |
| 151 | C23×D3 | — | 12 | 1 | no | — |
| 152 | C23×D3 | — | 12 | 1 | no | — |
| 153 | C23×D3 | — | 24 | 1 | no | — |
| 154 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 155 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 156 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 157 | C2×C3×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 158 | C2×C3×D4 | — | 3 | 1 | no | — |
| 159 | C2×C3×D4 | — | 6 | 1 | no | — |
| 160 | C2×C3×D4 | — | 12 | 1 | no | — |
| 161 | C22×C3×C4 | — | 3 | 1 | no | — |
| 162 | C2×#67 | — | 4 | 1 | no | — |
| 163 | C2×#67 | — | 6 | 1 | no | — |
| 164 | C2×#67 | — | 6 | 1 | no | — |
| 165 | C2×#67 | — | 6 | 1 | no | — |
| 166 | C2×#67 | — | 12 | 1 | no | — |
| 167 | C2×#67 | S4 | 1 | 1 | yes | characteristic |
| 168 | D3×Q8 | — | 2 | 1 | no | — |
| 169 | D3×Q8 | — | 6 | 1 | no | — |
| 170 | D3×D4 | — | 6 | 2 | no | — |
| 171 | D3×D4 | — | 12 | 1 | no | — |
| 172 | D3×D4 | — | 12 | 8 | no | — |
| 173 | D3×D4 | — | 12 | 4 | no | — |
| 174 | C2×D12 | — | 3 | 1 | no | — |
| 175 | C2×D12 | — | 3 | 1 | no | — |
| 176 | C2×D12 | — | 6 | 2 | no | — |
| 177 | C2×D12 | — | 6 | 1 | no | — |
| 178 | C2×D12 | — | 6 | 1 | no | — |
| 179 | C2×D12 | — | 12 | 1 | no | — |
| 180 | C2×D12 | — | 12 | 1 | no | — |
| 181 | C2×C4×D3 | — | 3 | 1 | no | — |
| 182 | C2×C4×D3 | — | 6 | 1 | no | — |
| 183 | C2×C4×D3 | — | 12 | 1 | no | — |
| 184 | C2×Dic6 | — | 3 | 1 | no | — |
| 185 | C2×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 186 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 187 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 188 | C2×SL(2,𝔽3) | — | 6 | 1 | no | — |
| 189 | C2×SL(2,𝔽3) | C22×D3 | 1 | 1 | yes | characteristic |
| 190 | GL(2,𝔽3) | — | 2 | 1 | no | — |
| 191 | GL(2,𝔽3) | — | 3 | 2 | no | — |
| 192 | GL(2,𝔽3) | — | 6 | 2 | no | — |
| 193 | GL(2,𝔽3) | — | 6 | 2 | no | — |
| 194 | GL(2,𝔽3) | — | 6 | 1 | no | — |
| 195 | C3×SD16 | — | 6 | 1 | no | — |
| 196 | C3×SD16 | — | 6 | 1 | no | — |
| 197 | C3×SD16 | — | 12 | 1 | no | — |
| 198 | C2×C3×C8 | — | 3 | 1 | no | — |
| 199 | C2×C3×C8 | — | 3 | 1 | no | — |
| 200 | C3×C4⋊C4 | — | 3 | 1 | no | — |
| 201 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 202 | #217 | — | 3 | 1 | no | — |
| 203 | #215 | — | 3 | 2 | no | — |
| 204 | #215 | — | 3 | 2 | no | — |
| 205 | #215 | — | 6 | 2 | no | — |
| 206 | #215 | — | 6 | 2 | no | — |
| 207 | #215 | — | 6 | 1 | no | — |
| 208 | #215 | — | 6 | 1 | no | — |
| 209 | #214 | — | 6 | 2 | no | — |
| 210 | (C2×D3)⋊C4 | — | 3 | 1 | no | — |
| 211 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 212 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 213 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 214 | Dic3⋊C4 | — | 3 | 1 | no | — |
| 215 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 216 | C4×Dic3 | — | 3 | 1 | no | — |
| 217 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 218 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 219 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 220 | #204 | — | 6 | 2 | no | — |
| 221 | #204 | — | 12 | 1 | no | — |
| 222 | D3×C8 | — | 6 | 2 | no | — |
| 223 | C22×C32 | — | 4 | 2 | no | — |
| 224 | C22×C32 | — | 4 | 1 | no | — |
| 225 | C22×C32 | — | 8 | 1 | no | — |
| 226 | C22×C32 | — | 8 | 1 | no | — |
| 227 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 228 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 229 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 230 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 231 | C2×C3⋊D3 | — | 8 | 1 | no | — |
| 232 | C2×C3⋊D3 | — | 8 | 1 | no | — |
| 233 | C2×C3⋊D3 | — | 8 | 8 | no | — |
| 234 | C2×C3×D3 | — | 4 | 2 | no | — |
| 235 | C2×C3×D3 | — | 4 | 2 | no | — |
| 236 | C2×C3×D3 | — | 8 | 1 | no | — |
| 237 | C2×C3×D3 | — | 8 | 1 | no | — |
| 238 | C2×C3×D3 | — | 8 | 1 | no | — |
| 239 | C2×C3×D3 | — | 8 | 1 | no | — |
| 240 | D32 | — | 8 | 8 | no | — |
| 241 | C3×Dic3 | — | 4 | 2 | no | — |
| 242 | C3×Dic3 | — | 4 | 2 | no | — |
| 243 | C22×Q8 | — | 3 | 1 | no | — |
| 244 | C22×Q8 | D32 | 1 | 1 | yes | characteristic, complemented |
| 245 | C22×D4 | — | 9 | 1 | no | — |
| 246 | C22×D4 | — | 9 | 1 | no | — |
| 247 | C22×D4 | — | 18 | 1 | no | — |
| 248 | C2×SD16 | — | 3 | 1 | no | — |
| 249 | C2×SD16 | — | 3 | 1 | no | — |
| 250 | C2×SD16 | — | 9 | 1 | no | — |
| 251 | C2×SD16 | — | 9 | 1 | no | — |
| 252 | C2×SD16 | — | 9 | 1 | no | — |
| 253 | C2×SD16 | — | 9 | 1 | no | — |
| 254 | C2×SD16 | — | 9 | 1 | no | — |
| 255 | C2×SD16 | — | 9 | 1 | no | — |
| 256 | C2×SD16 | — | 9 | 1 | no | — |
| 257 | C2×SD16 | — | 18 | 2 | no | — |
| 258 | C2×SD16 | — | 18 | 2 | no | — |
| 259 | C2×SD16 | — | 18 | 2 | no | — |
| 260 | C2×SD16 | — | 18 | 2 | no | — |
| 261 | C22×C8 | — | 9 | 1 | no | — |
| 262 | C22×C8 | — | 9 | 1 | no | — |
| 263 | C4⋊Q8 | — | 9 | 1 | no | — |
| 264 | #127 | — | 9 | 1 | no | — |
| 265 | C22⋊Q8 | — | 9 | 1 | no | — |
| 266 | C22⋊Q8 | — | 9 | 1 | no | — |
| 267 | #121 | — | 3 | 1 | no | — |
| 268 | #121 | — | 9 | 1 | no | — |
| 269 | #121 | — | 18 | 1 | no | — |
| 270 | #120 | — | 18 | 1 | no | — |
| 271 | #120 | — | 18 | 1 | no | — |
| 272 | C4×Q8 | — | 3 | 1 | no | — |
| 273 | C4×D4 | — | 9 | 1 | no | — |
| 274 | C4×D4 | — | 9 | 1 | no | — |
| 275 | #106 | — | 9 | 1 | no | — |
| 276 | C4⋊C8 | — | 9 | 1 | no | — |
| 277 | #103 | — | 3 | 1 | no | — |
| 278 | #103 | — | 3 | 1 | no | — |
| 279 | #103 | — | 9 | 1 | no | — |
| 280 | #102 | — | 9 | 1 | no | — |
| 281 | #102 | — | 9 | 1 | no | — |
| 282 | #102 | — | 9 | 1 | no | — |
| 283 | C22⋊C8 | — | 3 | 1 | no | — |
| 284 | C22⋊C8 | — | 9 | 1 | no | — |
| 285 | C4×C8 | — | 9 | 1 | no | — |
| 286 | C23×C3 | — | 4 | 1 | no | — |
| 287 | C23×C3 | — | 6 | 1 | no | — |
| 288 | C23×C3 | — | 8 | 1 | no | — |
| 289 | C23×C3 | — | 12 | 1 | no | — |
| 290 | C23×C3 | C2×S4 | 1 | 1 | yes | characteristic |
| 291 | C22×D3 | — | 4 | 1 | no | — |
| 292 | C22×D3 | — | 6 | 1 | no | — |
| 293 | C22×D3 | — | 6 | 1 | no | — |
| 294 | C22×D3 | — | 12 | 1 | no | — |
| 295 | C22×D3 | — | 12 | 1 | no | — |
| 296 | C22×D3 | — | 12 | 2 | no | — |
| 297 | C22×D3 | — | 12 | 4 | no | — |
| 298 | C22×D3 | — | 12 | 2 | no | — |
| 299 | C22×D3 | — | 12 | 4 | no | — |
| 300 | C22×D3 | — | 12 | 2 | no | — |
| 301 | C22×D3 | — | 12 | 2 | no | — |
| 302 | C22×D3 | — | 24 | 1 | no | — |
| 303 | C22×D3 | — | 24 | 1 | no | — |
| 304 | C22×D3 | — | 24 | 2 | no | — |
| 305 | C22×D3 | — | 24 | 2 | no | — |
| 306 | C22×D3 | — | 24 | 4 | no | — |
| 307 | C22×D3 | — | 24 | 4 | no | — |
| 308 | C22×D3 | — | 24 | 1 | no | — |
| 309 | C22×D3 | — | 24 | 2 | no | — |
| 310 | C22×D3 | — | 24 | 1 | no | — |
| 311 | C22×D3 | — | 24 | 2 | no | — |
| 312 | C22×D3 | — | 24 | 4 | no | — |
| 313 | C22×D3 | C2×S4 | 1 | 1 | yes | characteristic |
| 314 | C3×Q8 | — | 3 | 1 | no | — |
| 315 | C3×Q8 | — | 6 | 1 | no | — |
| 316 | C3×Q8 | — | 6 | 1 | no | — |
| 317 | C3×Q8 | D3×D4 | 1 | 1 | yes | characteristic, complemented |
| 318 | C3×D4 | — | 6 | 1 | no | — |
| 319 | C3×D4 | — | 6 | 1 | no | — |
| 320 | C3×D4 | — | 12 | 4 | no | — |
| 321 | C3×D4 | — | 12 | 2 | no | — |
| 322 | C2×C3×C4 | — | 3 | 1 | no | — |
| 323 | C2×C3×C4 | — | 3 | 1 | no | — |
| 324 | C2×C3×C4 | — | 6 | 1 | no | — |
| 325 | C2×C3×C4 | — | 6 | 1 | no | — |
| 326 | C2×C3×C4 | — | 6 | 1 | no | — |
| 327 | C2×C3×C4 | — | 12 | 1 | no | — |
| 328 | #67 | — | 4 | 4 | no | — |
| 329 | #67 | — | 12 | 4 | no | — |
| 330 | #67 | — | 12 | 2 | no | — |
| 331 | #67 | — | 12 | 2 | no | — |
| 332 | #67 | — | 24 | 1 | no | — |
| 333 | #67 | GL(2,𝔽3) | 1 | 4 | yes | complemented |
| 334 | C2×Dic3 | — | 3 | 1 | no | — |
| 335 | C2×Dic3 | — | 3 | 1 | no | — |
| 336 | C2×Dic3 | — | 4 | 1 | no | — |
| 337 | C2×Dic3 | C2×S4 | 1 | 1 | yes | characteristic |
| 338 | D12 | — | 3 | 2 | no | — |
| 339 | D12 | — | 6 | 1 | no | — |
| 340 | D12 | — | 6 | 1 | no | — |
| 341 | D12 | — | 6 | 1 | no | — |
| 342 | D12 | — | 12 | 2 | no | — |
| 343 | D12 | — | 12 | 4 | no | — |
| 344 | D12 | — | 12 | 2 | no | — |
| 345 | C4×D3 | — | 6 | 1 | no | — |
| 346 | C4×D3 | — | 6 | 1 | no | — |
| 347 | C4×D3 | — | 12 | 4 | no | — |
| 348 | C4×D3 | — | 12 | 2 | no | — |
| 349 | Dic6 | — | 6 | 1 | no | — |
| 350 | Dic6 | — | 6 | 1 | no | — |
| 351 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 352 | SL(2,𝔽3) | D3×D4 | 1 | 1 | yes | characteristic, complemented |
| 353 | C3×C8 | — | 6 | 1 | no | — |
| 354 | C3×C8 | — | 6 | 1 | no | — |
| 355 | C3⋊C8 | — | 3 | 2 | no | — |
| 356 | C3⋊C8 | — | 6 | 1 | no | — |
| 357 | C2×C32 | — | 4 | 1 | no | — |
| 358 | C2×C32 | — | 4 | 1 | no | — |
| 359 | C2×C32 | — | 4 | 1 | no | — |
| 360 | C2×C32 | — | 8 | 2 | no | — |
| 361 | C3⋊D3 | — | 4 | 4 | no | — |
| 362 | C3⋊D3 | — | 8 | 2 | no | — |
| 363 | C3×D3 | — | 8 | 2 | no | — |
| 364 | C3×D3 | — | 8 | 2 | no | — |
| 365 | C24 | — | 18 | 1 | no | — |
| 366 | C24 | — | 18 | 1 | no | — |
| 367 | C2×Q8 | — | 2 | 1 | no | — |
| 368 | C2×Q8 | — | 3 | 1 | no | — |
| 369 | C2×Q8 | — | 6 | 1 | no | — |
| 370 | C2×Q8 | — | 6 | 1 | no | — |
| 371 | C2×Q8 | — | 9 | 1 | no | — |
| 372 | C2×Q8 | — | 18 | 1 | no | — |
| 373 | C2×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 374 | C2×D4 | — | 3 | 1 | no | — |
| 375 | C2×D4 | — | 3 | 1 | no | — |
| 376 | C2×D4 | — | 6 | 1 | no | — |
| 377 | C2×D4 | — | 9 | 1 | no | — |
| 378 | C2×D4 | — | 9 | 1 | no | — |
| 379 | C2×D4 | — | 18 | 1 | no | — |
| 380 | C2×D4 | — | 18 | 1 | no | — |
| 381 | C2×D4 | — | 18 | 2 | no | — |
| 382 | C2×D4 | — | 18 | 1 | no | — |
| 383 | C2×D4 | — | 18 | 1 | no | — |
| 384 | C2×D4 | — | 18 | 1 | no | — |
| 385 | C2×D4 | — | 18 | 2 | no | — |
| 386 | C2×D4 | — | 36 | 1 | no | — |
| 387 | C2×D4 | — | 36 | 1 | no | — |
| 388 | C2×D4 | — | 36 | 4 | no | — |
| 389 | C22×C4 | — | 3 | 1 | no | — |
| 390 | C22×C4 | — | 9 | 1 | no | — |
| 391 | C22×C4 | — | 18 | 1 | no | — |
| 392 | SD16 | — | 6 | 1 | no | — |
| 393 | SD16 | — | 6 | 1 | no | — |
| 394 | SD16 | — | 9 | 2 | no | — |
| 395 | SD16 | — | 9 | 2 | no | — |
| 396 | SD16 | — | 12 | 1 | no | — |
| 397 | SD16 | — | 18 | 2 | no | — |
| 398 | SD16 | — | 18 | 2 | no | — |
| 399 | SD16 | — | 18 | 2 | no | — |
| 400 | SD16 | — | 18 | 2 | no | — |
| 401 | SD16 | — | 18 | 1 | no | — |
| 402 | SD16 | — | 18 | 1 | no | — |
| 403 | SD16 | — | 36 | 1 | no | — |
| 404 | C2×C8 | — | 3 | 1 | no | — |
| 405 | C2×C8 | — | 3 | 1 | no | — |
| 406 | C2×C8 | — | 9 | 1 | no | — |
| 407 | C2×C8 | — | 9 | 1 | no | — |
| 408 | C2×C8 | — | 18 | 2 | no | — |
| 409 | C2×C8 | — | 18 | 2 | no | — |
| 410 | C4⋊C4 | — | 3 | 1 | no | — |
| 411 | C4⋊C4 | — | 9 | 1 | no | — |
| 412 | C4⋊C4 | — | 9 | 1 | no | — |
| 413 | C4⋊C4 | — | 18 | 1 | no | — |
| 414 | C22⋊C4 | — | 6 | 1 | no | — |
| 415 | C22⋊C4 | — | 9 | 1 | no | — |
| 416 | C22⋊C4 | — | 9 | 1 | no | — |
| 417 | C22⋊C4 | — | 18 | 1 | no | — |
| 418 | C22⋊C4 | — | 18 | 1 | no | — |
| 419 | C42 | — | 9 | 1 | no | — |
| 420 | C22×C3 | — | 2 | 1 | no | — |
| 421 | C22×C3 | — | 2 | 1 | no | — |
| 422 | C22×C3 | — | 4 | 1 | no | — |
| 423 | C22×C3 | — | 4 | 2 | no | — |
| 424 | C22×C3 | — | 8 | 1 | no | — |
| 425 | C22×C3 | — | 8 | 1 | no | — |
| 426 | C22×C3 | — | 8 | 2 | no | — |
| 427 | C22×C3 | — | 8 | 2 | no | — |
| 428 | C22×C3 | — | 8 | 1 | no | — |
| 429 | C22×C3 | — | 8 | 2 | no | — |
| 430 | C22×C3 | — | 12 | 2 | no | — |
| 431 | C22×C3 | — | 12 | 1 | no | — |
| 432 | C22×C3 | — | 12 | 1 | no | — |
| 433 | C22×C3 | — | 12 | 1 | no | — |
| 434 | C22×C3 | — | 24 | 1 | no | — |
| 435 | C22×C3 | — | 24 | 1 | no | — |
| 436 | C22×C3 | C2×GL(2,𝔽3) | 1 | 2 | yes | complemented |
| 437 | C22×C3 | C22×S4 | 1 | 1 | yes | characteristic |
| 438 | C2×D3 | — | 2 | 1 | no | — |
| 439 | C2×D3 | — | 2 | 1 | no | — |
| 440 | C2×D3 | — | 4 | 2 | no | — |
| 441 | C2×D3 | — | 6 | 2 | no | — |
| 442 | C2×D3 | — | 8 | 1 | no | — |
| 443 | C2×D3 | — | 8 | 1 | no | — |
| 444 | C2×D3 | — | 12 | 2 | no | — |
| 445 | C2×D3 | — | 12 | 2 | no | — |
| 446 | C2×D3 | — | 12 | 2 | no | — |
| 447 | C2×D3 | — | 12 | 1 | no | — |
| 448 | C2×D3 | — | 12 | 1 | no | — |
| 449 | C2×D3 | — | 12 | 2 | no | — |
| 450 | C2×D3 | — | 12 | 1 | no | — |
| 451 | C2×D3 | — | 12 | 1 | no | — |
| 452 | C2×D3 | — | 12 | 1 | no | — |
| 453 | C2×D3 | — | 24 | 2 | no | — |
| 454 | C2×D3 | — | 24 | 1 | no | — |
| 455 | C2×D3 | — | 24 | 1 | no | — |
| 456 | C2×D3 | — | 24 | 2 | no | — |
| 457 | C2×D3 | — | 24 | 2 | no | — |
| 458 | C2×D3 | — | 24 | 2 | no | — |
| 459 | C2×D3 | — | 24 | 2 | no | — |
| 460 | C2×D3 | — | 24 | 2 | no | — |
| 461 | C2×D3 | — | 24 | 4 | no | — |
| 462 | C2×D3 | — | 24 | 8 | no | — |
| 463 | C2×D3 | — | 24 | 4 | no | — |
| 464 | C2×D3 | — | 24 | 8 | no | — |
| 465 | C2×D3 | — | 24 | 16 | no | — |
| 466 | C2×D3 | C2×GL(2,𝔽3) | 1 | 2 | yes | complemented |
| 467 | C3×C4 | — | 3 | 1 | no | — |
| 468 | C3×C4 | — | 3 | 1 | no | — |
| 469 | C3×C4 | — | 6 | 1 | no | — |
| 470 | C3×C4 | — | 12 | 2 | no | — |
| 471 | C3×C4 | — | 12 | 1 | no | — |
| 472 | Dic3 | — | 4 | 2 | no | — |
| 473 | Dic3 | — | 6 | 1 | no | — |
| 474 | Dic3 | — | 6 | 1 | no | — |
| 475 | Dic3 | C2×GL(2,𝔽3) | 1 | 2 | yes | complemented |
| 476 | C32 | — | 4 | 1 | no | Sylow |
| 477 | C23 | — | 3 | 1 | no | — |
| 478 | C23 | — | 6 | 1 | no | — |
| 479 | C23 | — | 18 | 1 | no | — |
| 480 | C23 | — | 18 | 1 | no | — |
| 481 | C23 | — | 36 | 2 | no | — |
| 482 | C23 | — | 36 | 2 | no | — |
| 483 | C23 | — | 36 | 2 | no | — |
| 484 | C23 | — | 36 | 2 | no | — |
| 485 | C23 | — | 72 | 1 | no | — |
| 486 | C23 | — | 72 | 1 | no | — |
| 487 | C23 | D3×S4 | 1 | 1 | yes | characteristic |
| 488 | Q8 | — | 3 | 1 | no | — |
| 489 | Q8 | — | 6 | 1 | no | — |
| 490 | Q8 | — | 6 | 1 | no | — |
| 491 | Q8 | — | 18 | 1 | no | — |
| 492 | Q8 | — | 18 | 1 | no | — |
| 493 | Q8 | #3811 | 1 | 1 | yes | characteristic, complemented |
| 494 | D4 | — | 3 | 4 | no | — |
| 495 | D4 | — | 6 | 1 | no | — |
| 496 | D4 | — | 6 | 1 | no | — |
| 497 | D4 | — | 9 | 2 | no | — |
| 498 | D4 | — | 12 | 2 | no | — |
| 499 | D4 | — | 18 | 1 | no | — |
| 500 | D4 | — | 18 | 1 | no | — |
| 501 | D4 | — | 18 | 1 | no | — |
| 502 | D4 | — | 36 | 2 | no | — |
| 503 | D4 | — | 36 | 2 | no | — |
| 504 | D4 | — | 36 | 2 | no | — |
| 505 | D4 | — | 36 | 2 | no | — |
| 506 | D4 | — | 72 | 1 | no | — |
| 507 | C2×C4 | — | 3 | 1 | no | — |
| 508 | C2×C4 | — | 3 | 1 | no | — |
| 509 | C2×C4 | — | 3 | 1 | no | — |
| 510 | C2×C4 | — | 6 | 1 | no | — |
| 511 | C2×C4 | — | 6 | 1 | no | — |
| 512 | C2×C4 | — | 6 | 1 | no | — |
| 513 | C2×C4 | — | 9 | 1 | no | — |
| 514 | C2×C4 | — | 9 | 1 | no | — |
| 515 | C2×C4 | — | 18 | 1 | no | — |
| 516 | C2×C4 | — | 18 | 1 | no | — |
| 517 | C2×C4 | — | 36 | 2 | no | — |
| 518 | C8 | — | 6 | 1 | no | — |
| 519 | C8 | — | 6 | 1 | no | — |
| 520 | C8 | — | 9 | 2 | no | — |
| 521 | C8 | — | 18 | 1 | no | — |
| 522 | C2×C3 | — | 2 | 2 | no | — |
| 523 | C2×C3 | — | 4 | 1 | no | — |
| 524 | C2×C3 | — | 4 | 1 | no | — |
| 525 | C2×C3 | — | 4 | 1 | no | — |
| 526 | C2×C3 | — | 8 | 2 | no | — |
| 527 | C2×C3 | — | 8 | 4 | no | — |
| 528 | C2×C3 | — | 8 | 1 | no | — |
| 529 | C2×C3 | — | 8 | 1 | no | — |
| 530 | C2×C3 | — | 8 | 1 | no | — |
| 531 | C2×C3 | — | 24 | 2 | no | — |
| 532 | C2×C3 | — | 24 | 1 | no | — |
| 533 | C2×C3 | D4×S4 | 1 | 1 | yes | characteristic |
| 534 | C2×C3 | C22×GL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 535 | C2×C3 | #5926 | 1 | 1 | yes | characteristic |
| 536 | D3 | — | 2 | 2 | no | — |
| 537 | D3 | — | 8 | 2 | no | — |
| 538 | D3 | — | 12 | 4 | no | — |
| 539 | D3 | — | 12 | 2 | no | — |
| 540 | D3 | — | 24 | 4 | no | — |
| 541 | D3 | — | 24 | 2 | no | — |
| 542 | D3 | — | 24 | 4 | no | — |
| 543 | D3 | — | 24 | 1 | no | — |
| 544 | C22 | — | 2 | 1 | no | — |
| 545 | C22 | — | 2 | 1 | no | — |
| 546 | C22 | — | 3 | 2 | no | — |
| 547 | C22 | — | 6 | 1 | no | — |
| 548 | C22 | — | 6 | 1 | no | — |
| 549 | C22 | — | 12 | 1 | no | — |
| 550 | C22 | — | 12 | 1 | no | — |
| 551 | C22 | — | 12 | 1 | no | — |
| 552 | C22 | — | 18 | 2 | no | — |
| 553 | C22 | — | 36 | 1 | no | — |
| 554 | C22 | — | 36 | 1 | no | — |
| 555 | C22 | — | 36 | 1 | no | — |
| 556 | C22 | — | 36 | 1 | no | — |
| 557 | C22 | — | 36 | 1 | no | — |
| 558 | C22 | — | 72 | 4 | no | — |
| 559 | C22 | — | 72 | 4 | no | — |
| 560 | C22 | D3×GL(2,𝔽3) | 1 | 2 | yes | complemented |
| 561 | C22 | C2×D3×S4 | 1 | 1 | yes | characteristic |
| 562 | C4 | — | 3 | 2 | no | — |
| 563 | C4 | — | 3 | 1 | no | — |
| 564 | C4 | — | 3 | 1 | no | — |
| 565 | C4 | — | 6 | 1 | no | — |
| 566 | C4 | — | 12 | 1 | no | — |
| 567 | C4 | — | 18 | 1 | no | — |
| 568 | C4 | — | 18 | 1 | no | — |
| 569 | C3 | — | 4 | 1 | no | — |
| 570 | C3 | — | 8 | 1 | no | — |
| 571 | C3 | D4×GL(2,𝔽3) | 1 | 1 | yes | characteristic, complemented |
| 572 | C2 | — | 2 | 2 | no | — |
| 573 | C2 | — | 6 | 2 | no | — |
| 574 | C2 | — | 24 | 1 | no | — |
| 575 | C2 | — | 36 | 2 | no | — |
| 576 | C2 | — | 72 | 1 | no | — |
| 577 | C2 | C2×D3×GL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 578 | C2 | #10596446 | 1 | 1 | yes | characteristic |
| 579 | C2 | #10596473 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C3⋊GL(2,𝔽3) | C2 | semidirect |
| 2. C2×D3×GL(2,𝔽3) | C2 | semidirect |
| 3. SL(2,𝔽3)×#67 | C2 | semidirect |
| 4. C3×#5421 | C2 | semidirect |
| 5. #10593218 | C2 | semidirect |
| 6. #10593215 | C2 | semidirect |
| 7. #10593214 | C2 | semidirect |
| 10. C22×C3×SL(2,𝔽3) | C22 | semidirect |
| 12. C2×D3×SL(2,𝔽3) | C22 | semidirect |
| 15. C2×C3⋊GL(2,𝔽3) | C22 | semidirect |
| 16. C2×C3×GL(2,𝔽3) | C22 | semidirect |
| 18. Dic3×SL(2,𝔽3) | C22 | semidirect |
| 19. C3×#859 | C22 | semidirect |
| 23. Q8×#67 | D3 | semidirect |
| 29. #5421 | D3 | semidirect |
| 55. C3⋊GL(2,𝔽3) | D4 | semidirect |
| 58. C22×C3×Q8 | C2×D3 | semidirect |
| 59. C2×D3×Q8 | C2×D3 | semidirect |
| 66. C22×SL(2,𝔽3) | C2×D3 | semidirect |
| 74. C2×GL(2,𝔽3) | C2×D3 | semidirect |
| 79. Q8×Dic3 | C2×D3 | semidirect |
| 103. #859 | C2×D3 | semidirect |
| 130. C3×SL(2,𝔽3) | C2×D4 | semidirect |
| 244. C22×Q8 | D32 | semidirect |
| 317. C3×Q8 | D3×D4 | semidirect |
| 333. #67 | GL(2,𝔽3) | semidirect |
| 352. SL(2,𝔽3) | D3×D4 | semidirect |
| 436. C22×C3 | C2×GL(2,𝔽3) | semidirect |
| 466. C2×D3 | C2×GL(2,𝔽3) | semidirect |
| 475. Dic3 | C2×GL(2,𝔽3) | semidirect |
| 493. Q8 | #3811 | semidirect |
| 560. C22 | D3×GL(2,𝔽3) | semidirect |
| 571. C3 | D4×GL(2,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊GL(2,𝔽3) | 2 |
| C2×D3×GL(2,𝔽3) | 2 |
| SL(2,𝔽3)×#67 | 2 |
| C3×#5421 | 2 |
| #10593218 | 2 |
| #10593215 | 2 |
| #10593214 | 2 |
| D4×GL(2,𝔽3) | 3 |
| #80063 | 3 |
| C2×#3811 | 4 |