Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
627 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 627 conjugacy classes of subgroups — too many to draw. Only its 79 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 | #5964⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C3⋊GU(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#5423 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10593228 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | D3×GU(2,𝔽3) | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #85541 | — | 3 | 1 | no | maximal |
| 7 | #78992 | — | 3 | 1 | no | maximal |
| 8 | C2×C3×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 9 | #1010⋊C3 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | D3×#41⋊C3 | C22 | 1 | 2 | yes | — |
| 11 | C3⋊#994 | C4 | 1 | 1 | yes | characteristic, complemented |
| 12 | #1007⋊C3 | C4 | 1 | 2 | yes | complemented |
| 13 | #63815 | — | 4 | 1 | no | maximal |
| 14 | C3⋊GU(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C3⋊GU(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C3×GU(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 17 | #5964 | D3 | 1 | 1 | yes | characteristic |
| 18 | #5945 | — | 3 | 1 | no | — |
| 19 | #5745 | — | 3 | 1 | no | — |
| 20 | #5522 | — | 3 | 1 | no | — |
| 21 | #5423 | — | 3 | 2 | no | — |
| 22 | #5423 | D3 | 1 | 1 | yes | characteristic, complemented |
| 23 | C2×GU(2,𝔽3) | — | 3 | 1 | no | — |
| 24 | C2×GU(2,𝔽3) | — | 3 | 2 | no | — |
| 25 | C2×GU(2,𝔽3) | — | 6 | 1 | no | — |
| 26 | C3×#421 | — | 3 | 1 | no | — |
| 27 | C2×#837 | — | 3 | 1 | no | — |
| 28 | C2×#825 | — | 3 | 1 | no | — |
| 29 | #5005 | — | 3 | 1 | no | — |
| 30 | #4821 | — | 3 | 2 | no | — |
| 31 | #4821 | — | 3 | 2 | no | — |
| 32 | D3×#104 | — | 3 | 2 | no | — |
| 33 | D3×#104 | — | 3 | 2 | no | — |
| 34 | C3×#235 | — | 4 | 1 | no | — |
| 35 | C3×#41⋊C3 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 36 | C3×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 37 | C2×C3×SL(2,𝔽3) | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 38 | D3×SL(2,𝔽3) | C2×C4 | 1 | 2 | yes | complemented |
| 39 | C3⋊(#41⋊C3) | C2×C4 | 1 | 2 | yes | complemented |
| 40 | C2×C3⋊(C3⋊C8) | — | 4 | 1 | no | — |
| 41 | C3×#208 | — | 4 | 1 | no | — |
| 42 | #3711 | — | 4 | 2 | no | — |
| 43 | D3×C3⋊C8 | — | 4 | 2 | no | — |
| 44 | #2901 | — | 9 | 1 | no | Sylow |
| 45 | C2×C3×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 46 | #1010 | — | 3 | 1 | no | — |
| 47 | #1010 | Dic3 | 1 | 1 | yes | characteristic |
| 48 | #1009 | — | 3 | 1 | no | — |
| 49 | #1009 | Dic3 | 1 | 1 | yes | characteristic |
| 50 | D3×#41 | — | 3 | 2 | no | — |
| 51 | D3×#41 | C2×D3 | 1 | 2 | yes | — |
| 52 | #1007 | Dic3 | 1 | 2 | yes | — |
| 53 | #1004 | — | 3 | 2 | no | — |
| 54 | C2×#235 | — | 3 | 1 | no | — |
| 55 | C2×#235 | — | 3 | 1 | no | — |
| 56 | 2−1+4⋊C3 | — | 3 | 1 | no | — |
| 57 | 2−1+4⋊C3 | — | 3 | 2 | no | — |
| 58 | #994 | — | 3 | 1 | no | — |
| 59 | C2×#41⋊C3 | — | 2 | 1 | no | — |
| 60 | C2×#41⋊C3 | — | 3 | 2 | no | — |
| 61 | C2×#41⋊C3 | C2×D3 | 1 | 1 | yes | characteristic |
| 62 | C2×C3×M16 | — | 3 | 1 | no | — |
| 63 | C3×#117 | — | 3 | 1 | no | — |
| 64 | #948 | — | 12 | 1 | no | — |
| 65 | C2×C4×Dic3 | — | 3 | 1 | no | — |
| 66 | C2×#208 | — | 3 | 1 | no | — |
| 67 | #907 | — | 6 | 1 | no | — |
| 68 | #907 | — | 6 | 1 | no | — |
| 69 | D3×M16 | — | 3 | 2 | no | — |
| 70 | D3×M16 | — | 3 | 2 | no | — |
| 71 | #901 | — | 6 | 2 | no | — |
| 72 | #893 | — | 6 | 1 | no | — |
| 73 | #887 | — | 6 | 1 | no | — |
| 74 | #67⋊C4 | — | 6 | 2 | no | — |
| 75 | #872 | — | 3 | 2 | no | — |
| 76 | C42×D3 | — | 3 | 2 | no | — |
| 77 | GU(2,𝔽3) | — | 3 | 1 | no | — |
| 78 | GU(2,𝔽3) | — | 3 | 1 | no | — |
| 79 | GU(2,𝔽3) | — | 6 | 1 | no | — |
| 80 | GU(2,𝔽3) | — | 6 | 1 | no | — |
| 81 | GU(2,𝔽3) | C2×D3 | 1 | 2 | yes | complemented |
| 82 | C3×#104 | — | 3 | 2 | no | — |
| 83 | C3×#104 | — | 3 | 2 | no | — |
| 84 | #837 | — | 3 | 1 | no | — |
| 85 | #837 | — | 3 | 1 | no | — |
| 86 | #837 | — | 3 | 1 | no | — |
| 87 | #837 | — | 3 | 1 | no | — |
| 88 | #825 | — | 3 | 2 | no | — |
| 89 | #825 | — | 3 | 2 | no | — |
| 90 | #805 | — | 3 | 2 | no | — |
| 91 | #805 | — | 3 | 2 | no | — |
| 92 | C2×C32×C4 | — | 4 | 1 | no | — |
| 93 | C3×#67 | — | 4 | 2 | no | — |
| 94 | C3×D12 | — | 4 | 1 | no | — |
| 95 | C3×C4×D3 | — | 4 | 2 | no | — |
| 96 | C3×Dic6 | — | 4 | 1 | no | — |
| 97 | C3×SL(2,𝔽3) | C22×C4 | 1 | 1 | yes | characteristic |
| 98 | C3⋊(C3⋊C8) | — | 4 | 1 | no | — |
| 99 | C3⋊(C3⋊C8) | — | 4 | 1 | no | — |
| 100 | C3×C3⋊C8 | — | 4 | 2 | no | — |
| 101 | #585 | — | 3 | 1 | no | — |
| 102 | #568 | — | 9 | 1 | no | — |
| 103 | C4×#41 | — | 9 | 1 | no | — |
| 104 | #421 | — | 3 | 1 | no | — |
| 105 | #421 | — | 9 | 2 | no | — |
| 106 | #421 | — | 9 | 2 | no | — |
| 107 | #421 | — | 9 | 1 | no | — |
| 108 | C2×#104 | — | 9 | 2 | no | — |
| 109 | C2×#104 | — | 9 | 2 | no | — |
| 110 | C2×#104 | — | 9 | 1 | no | — |
| 111 | C2×#104 | — | 9 | 1 | no | — |
| 112 | C3×#41 | — | 3 | 1 | no | — |
| 113 | C3×#41 | — | 3 | 1 | no | — |
| 114 | C3×#41 | — | 12 | 1 | no | — |
| 115 | C3×#41 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 116 | C3×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 117 | C2×C3×Q8 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 118 | C2×C3×D4 | — | 3 | 1 | no | — |
| 119 | C22×C3×C4 | — | 3 | 1 | no | — |
| 120 | C2×#67 | — | 3 | 2 | no | — |
| 121 | C2×#67 | — | 6 | 1 | no | — |
| 122 | C22×Dic3 | — | 6 | 1 | no | — |
| 123 | #239 | — | 3 | 2 | no | — |
| 124 | #239 | C2×Dic3 | 1 | 2 | yes | — |
| 125 | D3×Q8 | — | 3 | 2 | no | — |
| 126 | D3×Q8 | C2×Dic3 | 1 | 2 | yes | — |
| 127 | #237 | — | 3 | 2 | no | — |
| 128 | #237 | — | 3 | 2 | no | — |
| 129 | #237 | — | 6 | 2 | no | — |
| 130 | D3×D4 | — | 3 | 2 | no | — |
| 131 | D3×D4 | — | 3 | 2 | no | — |
| 132 | D3×D4 | — | 6 | 2 | no | — |
| 133 | #235 | — | 3 | 1 | no | — |
| 134 | #235 | — | 3 | 2 | no | — |
| 135 | #235 | — | 3 | 1 | no | — |
| 136 | #235 | — | 3 | 2 | no | — |
| 137 | #235 | — | 3 | 2 | no | — |
| 138 | #235 | — | 3 | 2 | no | — |
| 139 | #235 | — | 3 | 1 | no | — |
| 140 | #235 | — | 6 | 1 | no | — |
| 141 | #235 | S4 | 1 | 1 | yes | characteristic |
| 142 | C2×D12 | — | 3 | 1 | no | — |
| 143 | C2×D12 | — | 3 | 1 | no | — |
| 144 | C2×C4×D3 | — | 3 | 2 | no | — |
| 145 | C2×C4×D3 | — | 6 | 1 | no | — |
| 146 | C2×C4×D3 | — | 6 | 2 | no | — |
| 147 | C2×Dic6 | — | 3 | 1 | no | — |
| 148 | C2×Dic6 | — | 3 | 1 | no | — |
| 149 | #41⋊C3 | — | 2 | 1 | no | — |
| 150 | #41⋊C3 | — | 2 | 1 | no | — |
| 151 | #41⋊C3 | — | 3 | 2 | no | — |
| 152 | #41⋊C3 | C4×D3 | 1 | 1 | yes | characteristic, complemented |
| 153 | #41⋊C3 | C22×D3 | 1 | 1 | yes | characteristic |
| 154 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 155 | C2×SL(2,𝔽3) | — | 3 | 2 | no | — |
| 156 | C2×SL(2,𝔽3) | C4×D3 | 1 | 1 | yes | characteristic, complemented |
| 157 | C3×M16 | — | 3 | 2 | no | — |
| 158 | C3×M16 | — | 6 | 1 | no | — |
| 159 | C2×C3×C8 | — | 6 | 1 | no | — |
| 160 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 161 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 162 | C3×C42 | — | 3 | 2 | no | — |
| 163 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 164 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 165 | C4×Dic3 | — | 3 | 1 | no | — |
| 166 | C4×Dic3 | — | 3 | 1 | no | — |
| 167 | C4×Dic3 | — | 6 | 2 | no | — |
| 168 | C4×Dic3 | — | 6 | 1 | no | — |
| 169 | #208 | — | 3 | 1 | no | — |
| 170 | #208 | — | 3 | 1 | no | — |
| 171 | #208 | — | 4 | 1 | no | — |
| 172 | #208 | — | 6 | 1 | no | — |
| 173 | #208 | — | 12 | 2 | no | — |
| 174 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 175 | C2×C3⋊C8 | — | 12 | 2 | no | — |
| 176 | C2×C3⋊C8 | — | 12 | 1 | no | — |
| 177 | C2×C3⋊C8 | — | 24 | 1 | no | — |
| 178 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 179 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 180 | D3×C8 | — | 6 | 2 | no | — |
| 181 | D3×C8 | — | 6 | 2 | no | — |
| 182 | C22×C32 | — | 4 | 1 | no | — |
| 183 | C2×C3×D3 | — | 4 | 2 | no | — |
| 184 | C32×C4 | — | 4 | 1 | no | — |
| 185 | C32×C4 | — | 4 | 1 | no | — |
| 186 | C3×Dic3 | — | 4 | 2 | no | — |
| 187 | 2−1+4 | — | 3 | 1 | no | — |
| 188 | 2−1+4 | — | 3 | 2 | no | — |
| 189 | 2−1+4 | — | 9 | 1 | no | — |
| 190 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 191 | H(5,𝔽2) | — | 9 | 2 | no | — |
| 192 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 193 | C2×#41 | — | 3 | 2 | no | — |
| 194 | C2×#41 | — | 9 | 1 | no | — |
| 195 | C2×#41 | — | 9 | 1 | no | — |
| 196 | C2×#41 | — | 9 | 2 | no | — |
| 197 | C2×#41 | D32 | 1 | 1 | yes | characteristic |
| 198 | #131 | — | 18 | 2 | no | — |
| 199 | #131 | — | 18 | 1 | no | — |
| 200 | #131 | — | 18 | 1 | no | — |
| 201 | C2×M16 | — | 3 | 1 | no | — |
| 202 | C2×M16 | — | 9 | 2 | no | — |
| 203 | C2×M16 | — | 9 | 2 | no | — |
| 204 | C2×M16 | — | 9 | 1 | no | — |
| 205 | C4×Q8 | — | 18 | 1 | no | — |
| 206 | C4×D4 | — | 18 | 2 | no | — |
| 207 | C4×D4 | — | 18 | 1 | no | — |
| 208 | #117 | — | 3 | 1 | no | — |
| 209 | #117 | — | 9 | 2 | no | — |
| 210 | C2×C42 | — | 9 | 2 | no | — |
| 211 | C2×C42 | — | 9 | 1 | no | — |
| 212 | #104 | — | 3 | 2 | no | — |
| 213 | #104 | — | 3 | 2 | no | — |
| 214 | #104 | — | 9 | 2 | no | — |
| 215 | #104 | — | 9 | 2 | no | — |
| 216 | #104 | — | 9 | 2 | no | — |
| 217 | #104 | — | 9 | 2 | no | — |
| 218 | #104 | — | 9 | 1 | no | — |
| 219 | #104 | — | 9 | 1 | no | — |
| 220 | #104 | — | 9 | 1 | no | — |
| 221 | #104 | — | 9 | 1 | no | — |
| 222 | C23×C3 | — | 3 | 1 | no | — |
| 223 | C22×D3 | — | 3 | 2 | no | — |
| 224 | C22×D3 | — | 6 | 1 | no | — |
| 225 | C3×Q8 | — | 3 | 1 | no | — |
| 226 | C3×Q8 | — | 12 | 1 | no | — |
| 227 | C3×Q8 | C22×Dic3 | 1 | 1 | yes | characteristic |
| 228 | C3×D4 | — | 3 | 1 | no | — |
| 229 | C3×D4 | — | 3 | 1 | no | — |
| 230 | C3×D4 | — | 6 | 1 | no | — |
| 231 | C3×D4 | — | 12 | 1 | no | — |
| 232 | C3×D4 | — | 12 | 2 | no | — |
| 233 | C2×C3×C4 | — | 3 | 1 | no | — |
| 234 | C2×C3×C4 | — | 3 | 1 | no | — |
| 235 | C2×C3×C4 | — | 3 | 1 | no | — |
| 236 | C2×C3×C4 | — | 3 | 1 | no | — |
| 237 | C2×C3×C4 | — | 3 | 1 | no | — |
| 238 | C2×C3×C4 | — | 4 | 1 | no | — |
| 239 | C2×C3×C4 | — | 6 | 2 | no | — |
| 240 | C2×C3×C4 | — | 8 | 1 | no | — |
| 241 | C2×C3×C4 | — | 12 | 2 | no | — |
| 242 | C2×C3×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 243 | #67 | — | 3 | 2 | no | — |
| 244 | #67 | — | 3 | 2 | no | — |
| 245 | #67 | — | 3 | 2 | no | — |
| 246 | #67 | — | 6 | 2 | no | — |
| 247 | #67 | SL(2,ℤ/4) | 1 | 2 | yes | — |
| 248 | C2×Dic3 | — | 3 | 2 | no | — |
| 249 | C2×Dic3 | — | 6 | 1 | no | — |
| 250 | C2×Dic3 | — | 6 | 1 | no | — |
| 251 | C2×Dic3 | — | 6 | 1 | no | — |
| 252 | C2×Dic3 | — | 12 | 2 | no | — |
| 253 | D12 | — | 3 | 2 | no | — |
| 254 | D12 | — | 3 | 2 | no | — |
| 255 | D12 | — | 3 | 1 | no | — |
| 256 | D12 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 257 | C4×D3 | — | 3 | 2 | no | — |
| 258 | C4×D3 | — | 3 | 2 | no | — |
| 259 | C4×D3 | — | 3 | 2 | no | — |
| 260 | C4×D3 | — | 6 | 2 | no | — |
| 261 | C4×D3 | — | 12 | 4 | no | — |
| 262 | C4×D3 | C2×S4 | 1 | 2 | yes | — |
| 263 | Dic6 | — | 3 | 1 | no | — |
| 264 | Dic6 | — | 3 | 2 | no | — |
| 265 | Dic6 | — | 3 | 2 | no | — |
| 266 | Dic6 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 267 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 268 | SL(2,𝔽3) | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 269 | C3×C8 | — | 6 | 2 | no | — |
| 270 | C3⋊C8 | — | 4 | 2 | no | — |
| 271 | C3⋊C8 | — | 6 | 1 | no | — |
| 272 | C3⋊C8 | — | 6 | 1 | no | — |
| 273 | C3⋊C8 | — | 12 | 1 | no | — |
| 274 | C3⋊C8 | — | 12 | 1 | no | — |
| 275 | C3⋊C8 | — | 24 | 1 | no | — |
| 276 | C3⋊C8 | — | 24 | 1 | no | — |
| 277 | C2×C32 | — | 4 | 1 | no | — |
| 278 | C2×C32 | — | 8 | 1 | no | — |
| 279 | C3×D3 | — | 8 | 2 | no | — |
| 280 | #41 | — | 3 | 1 | no | — |
| 281 | #41 | — | 3 | 1 | no | — |
| 282 | #41 | — | 3 | 1 | no | — |
| 283 | #41 | — | 3 | 2 | no | — |
| 284 | #41 | — | 9 | 2 | no | — |
| 285 | #41 | — | 9 | 2 | no | — |
| 286 | #41 | — | 9 | 1 | no | — |
| 287 | #41 | — | 9 | 1 | no | — |
| 288 | #41 | — | 9 | 2 | no | — |
| 289 | #41 | — | 9 | 2 | no | — |
| 290 | #41 | — | 9 | 1 | no | — |
| 291 | #41 | — | 9 | 2 | no | — |
| 292 | #41 | — | 9 | 2 | no | — |
| 293 | #41 | — | 9 | 2 | no | — |
| 294 | #41 | — | 18 | 1 | no | — |
| 295 | #41 | — | 18 | 2 | no | — |
| 296 | #41 | D3×Dic3 | 1 | 1 | yes | characteristic |
| 297 | #41 | C2×D32 | 1 | 1 | yes | characteristic |
| 298 | C2×Q8 | — | 3 | 2 | no | — |
| 299 | C2×Q8 | — | 9 | 1 | no | — |
| 300 | C2×Q8 | — | 9 | 1 | no | — |
| 301 | C2×Q8 | — | 9 | 2 | no | — |
| 302 | C2×Q8 | D3×Dic3 | 1 | 1 | yes | characteristic |
| 303 | C2×D4 | — | 3 | 1 | no | — |
| 304 | C2×D4 | — | 9 | 1 | no | — |
| 305 | C2×D4 | — | 9 | 1 | no | — |
| 306 | C2×D4 | — | 9 | 2 | no | — |
| 307 | C2×D4 | — | 9 | 2 | no | — |
| 308 | C2×D4 | — | 9 | 2 | no | — |
| 309 | C2×D4 | — | 18 | 2 | no | — |
| 310 | C2×D4 | — | 18 | 1 | no | — |
| 311 | C22×C4 | — | 3 | 1 | no | — |
| 312 | C22×C4 | — | 9 | 2 | no | — |
| 313 | C22×C4 | — | 18 | 1 | no | — |
| 314 | C22×C4 | — | 18 | 2 | no | — |
| 315 | C22×C4 | — | 18 | 1 | no | — |
| 316 | M16 | — | 3 | 2 | no | — |
| 317 | M16 | — | 6 | 1 | no | — |
| 318 | M16 | — | 9 | 1 | no | — |
| 319 | M16 | — | 9 | 1 | no | — |
| 320 | M16 | — | 18 | 2 | no | — |
| 321 | M16 | — | 18 | 2 | no | — |
| 322 | M16 | — | 18 | 1 | no | — |
| 323 | C2×C8 | — | 6 | 1 | no | — |
| 324 | C2×C8 | — | 18 | 2 | no | — |
| 325 | C2×C8 | — | 18 | 2 | no | — |
| 326 | C2×C8 | — | 18 | 1 | no | — |
| 327 | C4⋊C4 | — | 6 | 1 | no | — |
| 328 | C4⋊C4 | — | 18 | 2 | no | — |
| 329 | C22⋊C4 | — | 6 | 1 | no | — |
| 330 | C22⋊C4 | — | 18 | 2 | no | — |
| 331 | C42 | — | 3 | 2 | no | — |
| 332 | C42 | — | 9 | 1 | no | — |
| 333 | C42 | — | 9 | 1 | no | — |
| 334 | C42 | — | 18 | 1 | no | — |
| 335 | C42 | — | 18 | 2 | no | — |
| 336 | C22×C3 | — | 3 | 1 | no | — |
| 337 | C22×C3 | — | 3 | 1 | no | — |
| 338 | C22×C3 | — | 4 | 1 | no | — |
| 339 | C22×C3 | — | 8 | 1 | no | — |
| 340 | C22×C3 | — | 12 | 2 | no | — |
| 341 | C22×C3 | — | 12 | 1 | no | — |
| 342 | C22×C3 | C2×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 343 | C2×D3 | — | 3 | 2 | no | — |
| 344 | C2×D3 | — | 12 | 2 | no | — |
| 345 | C2×D3 | — | 24 | 1 | no | — |
| 346 | C2×D3 | C2×SL(2,ℤ/4) | 1 | 2 | yes | — |
| 347 | C3×C4 | — | 3 | 1 | no | — |
| 348 | C3×C4 | — | 3 | 1 | no | — |
| 349 | C3×C4 | — | 4 | 1 | no | — |
| 350 | C3×C4 | — | 4 | 1 | no | — |
| 351 | C3×C4 | — | 8 | 1 | no | — |
| 352 | C3×C4 | — | 8 | 1 | no | — |
| 353 | C3×C4 | — | 12 | 2 | no | — |
| 354 | C3×C4 | — | 12 | 2 | no | — |
| 355 | C3×C4 | C2×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 356 | C3×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 357 | Dic3 | — | 3 | 2 | no | — |
| 358 | Dic3 | — | 6 | 2 | no | — |
| 359 | Dic3 | — | 12 | 1 | no | — |
| 360 | Dic3 | C2×SL(2,ℤ/4) | 1 | 2 | yes | — |
| 361 | C32 | — | 4 | 1 | no | Sylow |
| 362 | C23 | — | 3 | 1 | no | — |
| 363 | C23 | — | 9 | 2 | no | — |
| 364 | C23 | — | 18 | 1 | no | — |
| 365 | Q8 | — | 3 | 1 | no | — |
| 366 | Q8 | — | 3 | 1 | no | — |
| 367 | Q8 | — | 9 | 2 | no | — |
| 368 | Q8 | — | 9 | 2 | no | — |
| 369 | Q8 | — | 9 | 1 | no | — |
| 370 | Q8 | C2×D3×Dic3 | 1 | 1 | yes | characteristic |
| 371 | D4 | — | 3 | 1 | no | — |
| 372 | D4 | — | 3 | 1 | no | — |
| 373 | D4 | — | 3 | 2 | no | — |
| 374 | D4 | — | 3 | 1 | no | — |
| 375 | D4 | — | 6 | 1 | no | — |
| 376 | D4 | — | 9 | 2 | no | — |
| 377 | D4 | — | 9 | 2 | no | — |
| 378 | D4 | — | 9 | 2 | no | — |
| 379 | D4 | — | 9 | 2 | no | — |
| 380 | D4 | — | 9 | 2 | no | — |
| 381 | D4 | — | 9 | 1 | no | — |
| 382 | D4 | — | 18 | 2 | no | — |
| 383 | C2×C4 | — | 3 | 1 | no | — |
| 384 | C2×C4 | — | 3 | 1 | no | — |
| 385 | C2×C4 | — | 3 | 1 | no | — |
| 386 | C2×C4 | — | 3 | 2 | no | — |
| 387 | C2×C4 | — | 3 | 1 | no | — |
| 388 | C2×C4 | — | 3 | 1 | no | — |
| 389 | C2×C4 | — | 6 | 2 | no | — |
| 390 | C2×C4 | — | 9 | 2 | no | — |
| 391 | C2×C4 | — | 9 | 2 | no | — |
| 392 | C2×C4 | — | 9 | 2 | no | — |
| 393 | C2×C4 | — | 9 | 2 | no | — |
| 394 | C2×C4 | — | 18 | 2 | no | — |
| 395 | C2×C4 | — | 18 | 1 | no | — |
| 396 | C2×C4 | — | 18 | 1 | no | — |
| 397 | C2×C4 | — | 18 | 1 | no | — |
| 398 | C2×C4 | — | 36 | 4 | no | — |
| 399 | C2×C4 | — | 36 | 2 | no | — |
| 400 | C2×C4 | D3×S4 | 1 | 1 | yes | characteristic |
| 401 | C8 | — | 6 | 2 | no | — |
| 402 | C8 | — | 18 | 1 | no | — |
| 403 | C8 | — | 18 | 1 | no | — |
| 404 | C2×C3 | — | 2 | 1 | no | — |
| 405 | C2×C3 | — | 4 | 1 | no | — |
| 406 | C2×C3 | — | 6 | 1 | no | — |
| 407 | C2×C3 | — | 6 | 1 | no | — |
| 408 | C2×C3 | — | 8 | 1 | no | — |
| 409 | C2×C3 | — | 8 | 2 | no | — |
| 410 | C2×C3 | — | 8 | 1 | no | — |
| 411 | C2×C3 | — | 24 | 2 | no | — |
| 412 | C2×C3 | C22×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 413 | D3 | — | 2 | 2 | no | — |
| 414 | D3 | — | 6 | 2 | no | — |
| 415 | C22 | — | 3 | 1 | no | — |
| 416 | C22 | — | 3 | 1 | no | — |
| 417 | C22 | — | 3 | 2 | no | — |
| 418 | C22 | — | 9 | 2 | no | — |
| 419 | C22 | — | 12 | 1 | no | — |
| 420 | C22 | — | 36 | 2 | no | — |
| 421 | C22 | — | 72 | 1 | no | — |
| 422 | C22 | D3×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 423 | C4 | — | 3 | 1 | no | — |
| 424 | C4 | — | 3 | 1 | no | — |
| 425 | C4 | — | 3 | 2 | no | — |
| 426 | C4 | — | 9 | 2 | no | — |
| 427 | C4 | — | 12 | 2 | no | — |
| 428 | C4 | — | 18 | 2 | no | — |
| 429 | C4 | — | 36 | 1 | no | — |
| 430 | C4 | D3×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 431 | C4 | C2×D3×S4 | 1 | 1 | yes | characteristic |
| 432 | C3 | — | 4 | 1 | no | — |
| 433 | C3 | — | 8 | 1 | no | — |
| 434 | C3 | #85541 | 1 | 1 | yes | characteristic, complemented |
| 435 | C2 | — | 2 | 1 | no | — |
| 436 | C2 | — | 6 | 1 | no | — |
| 437 | C2 | — | 6 | 1 | no | — |
| 438 | C2 | — | 6 | 2 | no | — |
| 439 | C2 | — | 18 | 2 | no | — |
| 440 | C2 | C2×D3×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3⋊GU(2,𝔽3) | C2 | semidirect |
| 3. C3×#5423 | C2 | semidirect |
| 4. #10593228 | C2 | semidirect |
| 5. D3×GU(2,𝔽3) | C2 | semidirect |
| 9. #1010⋊C3 | C4 | semidirect |
| 11. C3⋊#994 | C4 | semidirect |
| 12. #1007⋊C3 | C4 | semidirect |
| 14. C3⋊GU(2,𝔽3) | C22 | semidirect |
| 15. C3⋊GU(2,𝔽3) | C22 | semidirect |
| 16. C3×GU(2,𝔽3) | C22 | semidirect |
| 22. #5423 | D3 | semidirect |
| 35. C3×#41⋊C3 | C2×C4 | semidirect |
| 37. C2×C3×SL(2,𝔽3) | C2×C4 | semidirect |
| 38. D3×SL(2,𝔽3) | C2×C4 | semidirect |
| 39. C3⋊(#41⋊C3) | C2×C4 | semidirect |
| 81. GU(2,𝔽3) | C2×D3 | semidirect |
| 152. #41⋊C3 | C4×D3 | semidirect |
| 156. C2×SL(2,𝔽3) | C4×D3 | semidirect |
| 434. C3 | #85541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5964⋊C3 | 2 |
| C2×C3⋊GU(2,𝔽3) | 2 |
| C3×#5423 | 2 |
| #10593228 | 2 |
| D3×GU(2,𝔽3) | 2 |
| #85541 | 3 |
| #78992 | 3 |
| #63815 | 4 |