Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1561 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 1561 conjugacy classes of subgroups — too many to draw. Only its 127 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, complemented |
| 2 | C2×#64267 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#5923 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10596459 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | D3×#986 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10596456 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10596449 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10596446 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #87498 | — | 3 | 1 | no | maximal |
| 10 | #87200 | — | 3 | 1 | no | maximal |
| 11 | C2×C3×#41⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | #64308 | — | 4 | 1 | no | maximal |
| 13 | #1010⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | D3×#41⋊C3 | C22 | 1 | 2 | yes | complemented |
| 15 | C3⋊#994 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | #1007⋊C3 | C22 | 1 | 2 | yes | complemented |
| 17 | #64267 | C22 | 1 | 2 | yes | complemented |
| 18 | #64267 | C22 | 1 | 2 | yes | complemented |
| 19 | C2×C3⋊GL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 20 | C3×#986 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C3×#985 | C22 | 1 | 2 | yes | complemented |
| 22 | C3×#984 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C3×#983 | C22 | 1 | 2 | yes | complemented |
| 24 | D3×GL(2,𝔽3) | C22 | 1 | 4 | yes | complemented |
| 25 | #64202 | C22 | 1 | 4 | yes | complemented |
| 26 | #64199 | C22 | 1 | 4 | yes | complemented |
| 27 | #64198 | C22 | 1 | 4 | yes | complemented |
| 28 | #5964 | D3 | 1 | 1 | yes | characteristic, complemented |
| 29 | C2×#1009 | — | 3 | 1 | no | — |
| 30 | #5945 | — | 3 | 1 | no | — |
| 31 | #5926 | — | 3 | 2 | no | — |
| 32 | #5926 | — | 3 | 4 | no | — |
| 33 | #5925 | — | 3 | 2 | no | — |
| 34 | #5923 | — | 3 | 2 | no | — |
| 35 | #5923 | D3 | 1 | 1 | yes | characteristic, complemented |
| 36 | C2×#986 | — | 3 | 1 | no | — |
| 37 | C2×#986 | — | 3 | 2 | no | — |
| 38 | C2×#986 | — | 6 | 1 | no | — |
| 39 | C3×#575 | — | 3 | 1 | no | — |
| 40 | #5822 | — | 3 | 1 | no | — |
| 41 | C2×#949 | — | 3 | 1 | no | — |
| 42 | #5778 | — | 3 | 4 | no | — |
| 43 | #5777 | — | 3 | 2 | no | — |
| 44 | #5777 | — | 3 | 2 | no | — |
| 45 | #5774 | — | 3 | 4 | no | — |
| 46 | D3×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 47 | D3×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 48 | #5770 | — | 3 | 2 | no | — |
| 49 | #5770 | — | 3 | 2 | no | — |
| 50 | #5769 | — | 3 | 2 | no | — |
| 51 | #5769 | — | 3 | 2 | no | — |
| 52 | C2×#908 | — | 3 | 1 | no | — |
| 53 | #5745 | — | 3 | 1 | no | — |
| 54 | C2×C4⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 55 | C3×#235 | — | 4 | 1 | no | — |
| 56 | C3×#235 | — | 4 | 1 | no | — |
| 57 | C3×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 58 | C3×#41⋊C3 | C23 | 1 | 1 | yes | characteristic, complemented |
| 59 | C2×C3×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic, complemented |
| 60 | #3811 | — | 4 | 4 | no | — |
| 61 | D3×D12 | — | 4 | 2 | no | — |
| 62 | D3×D12 | — | 4 | 2 | no | — |
| 63 | #3799 | — | 4 | 2 | no | — |
| 64 | #3799 | — | 4 | 2 | no | — |
| 65 | D3×SL(2,𝔽3) | C23 | 1 | 2 | yes | complemented |
| 66 | C3⋊(#41⋊C3) | C23 | 1 | 2 | yes | complemented |
| 67 | C3⋊GL(2,𝔽3) | C23 | 1 | 4 | yes | complemented |
| 68 | C3×GL(2,𝔽3) | C23 | 1 | 2 | yes | complemented |
| 69 | C3×#226 | C23 | 1 | 2 | yes | complemented |
| 70 | #3585 | — | 9 | 1 | no | Sylow |
| 71 | C2×C3×#41 | — | 3 | 1 | no | — |
| 72 | C2×C3×#41 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 73 | #1010 | — | 3 | 1 | no | — |
| 74 | #1010 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 75 | #1009 | — | 3 | 1 | no | — |
| 76 | #1009 | — | 3 | 2 | no | — |
| 77 | #1009 | — | 3 | 2 | no | — |
| 78 | #1009 | — | 3 | 4 | no | — |
| 79 | #1009 | — | 6 | 2 | no | — |
| 80 | #1009 | — | 6 | 1 | no | — |
| 81 | #1009 | — | 6 | 1 | no | — |
| 82 | #1009 | — | 12 | 1 | no | — |
| 83 | #1009 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 84 | D3×#41 | — | 3 | 2 | no | — |
| 85 | D3×#41 | C2×D3 | 1 | 2 | yes | complemented |
| 86 | #1007 | C2×D3 | 1 | 2 | yes | complemented |
| 87 | C2×#239 | — | 3 | 2 | no | — |
| 88 | #1004 | — | 3 | 2 | no | — |
| 89 | C2×D3×D4 | — | 3 | 2 | no | — |
| 90 | C2×D3×D4 | — | 6 | 2 | no | — |
| 91 | C2×#235 | — | 3 | 1 | no | — |
| 92 | C2×#235 | — | 3 | 1 | no | — |
| 93 | C2×#235 | — | 6 | 1 | no | — |
| 94 | C22×D12 | — | 3 | 1 | no | — |
| 95 | C22×D12 | — | 6 | 1 | no | — |
| 96 | 2−1+4⋊C3 | — | 3 | 1 | no | — |
| 97 | 2−1+4⋊C3 | — | 3 | 2 | no | — |
| 98 | #994 | — | 3 | 1 | no | — |
| 99 | C2×#41⋊C3 | — | 2 | 1 | no | — |
| 100 | C2×#41⋊C3 | — | 3 | 2 | no | — |
| 101 | C2×#41⋊C3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 102 | #986 | — | 3 | 2 | no | — |
| 103 | #986 | — | 3 | 2 | no | — |
| 104 | #986 | — | 3 | 4 | no | — |
| 105 | #986 | — | 6 | 2 | no | — |
| 106 | #986 | — | 6 | 2 | no | — |
| 107 | #986 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 108 | #985 | — | 3 | 4 | no | — |
| 109 | #985 | C2×D3 | 1 | 2 | yes | complemented |
| 110 | #984 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 111 | #983 | — | 3 | 4 | no | — |
| 112 | #983 | C2×D3 | 1 | 2 | yes | complemented |
| 113 | C2×GL(2,𝔽3) | — | 3 | 2 | no | — |
| 114 | C2×GL(2,𝔽3) | — | 3 | 4 | no | — |
| 115 | C2×GL(2,𝔽3) | — | 6 | 2 | no | — |
| 116 | C3×#137 | — | 3 | 1 | no | — |
| 117 | C3×#137 | — | 3 | 1 | no | — |
| 118 | C3×#137 | — | 3 | 2 | no | — |
| 119 | C3×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 120 | C3×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 121 | C3×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 122 | C3×#135 | — | 3 | 2 | no | — |
| 123 | C3×#135 | — | 3 | 2 | no | — |
| 124 | C2×C3×M16 | — | 3 | 1 | no | — |
| 125 | #951 | — | 3 | 2 | no | — |
| 126 | #950 | — | 3 | 4 | no | — |
| 127 | #949 | — | 3 | 2 | no | — |
| 128 | #949 | — | 3 | 2 | no | — |
| 129 | #949 | — | 3 | 2 | no | — |
| 130 | #949 | — | 3 | 2 | no | — |
| 131 | #949 | — | 3 | 2 | no | — |
| 132 | #942 | — | 3 | 2 | no | — |
| 133 | C2×#215 | — | 3 | 2 | no | — |
| 134 | #932 | — | 3 | 2 | no | — |
| 135 | C2×#213 | — | 3 | 2 | no | — |
| 136 | C2×#208 | — | 3 | 1 | no | — |
| 137 | #919 | — | 3 | 4 | no | — |
| 138 | #919 | — | 3 | 4 | no | — |
| 139 | #918 | — | 3 | 4 | no | — |
| 140 | #918 | — | 3 | 4 | no | — |
| 141 | #916 | — | 3 | 4 | no | — |
| 142 | #916 | — | 3 | 4 | no | — |
| 143 | #914 | — | 3 | 4 | no | — |
| 144 | #914 | — | 3 | 4 | no | — |
| 145 | #914 | — | 3 | 4 | no | — |
| 146 | #914 | — | 3 | 4 | no | — |
| 147 | D3×SD16 | — | 3 | 4 | no | — |
| 148 | D3×SD16 | — | 3 | 4 | no | — |
| 149 | #911 | — | 3 | 4 | no | — |
| 150 | #911 | — | 3 | 4 | no | — |
| 151 | D3×D8 | — | 3 | 4 | no | — |
| 152 | D3×D8 | — | 3 | 4 | no | — |
| 153 | #908 | — | 3 | 2 | no | — |
| 154 | #908 | — | 3 | 2 | no | — |
| 155 | #908 | — | 3 | 4 | no | — |
| 156 | #907 | — | 3 | 4 | no | — |
| 157 | D3×M16 | — | 3 | 2 | no | — |
| 158 | D3×M16 | — | 3 | 2 | no | — |
| 159 | C2×D24 | — | 3 | 2 | no | — |
| 160 | C2×#204 | — | 3 | 2 | no | — |
| 161 | #901 | — | 3 | 2 | no | — |
| 162 | #901 | — | 3 | 2 | no | — |
| 163 | C22×C3⋊D3 | — | 4 | 2 | no | — |
| 164 | C2×D32 | — | 4 | 4 | no | — |
| 165 | C2×C32×C4 | — | 4 | 1 | no | — |
| 166 | C4⋊(C3⋊D3) | — | 4 | 2 | no | — |
| 167 | C4⋊(C3⋊D3) | — | 4 | 2 | no | — |
| 168 | C3×#67 | — | 4 | 2 | no | — |
| 169 | C3×#67 | — | 4 | 2 | no | — |
| 170 | C3×D12 | — | 4 | 1 | no | — |
| 171 | C3×D12 | — | 4 | 1 | no | — |
| 172 | C3×C4×D3 | — | 4 | 2 | no | — |
| 173 | C3×C4×D3 | — | 4 | 2 | no | — |
| 174 | C3×Dic6 | — | 4 | 1 | no | — |
| 175 | C3×Dic6 | — | 4 | 1 | no | — |
| 176 | C3×SL(2,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 177 | #626 | — | 4 | 4 | no | — |
| 178 | #626 | — | 4 | 4 | no | — |
| 179 | #624 | — | 4 | 4 | no | — |
| 180 | #585 | — | 3 | 1 | no | — |
| 181 | C2×H(5,𝔽2) | — | 9 | 1 | no | — |
| 182 | #577 | — | 9 | 2 | no | — |
| 183 | #577 | — | 9 | 2 | no | — |
| 184 | #577 | — | 9 | 4 | no | — |
| 185 | #576 | — | 9 | 2 | no | — |
| 186 | #576 | — | 9 | 2 | no | — |
| 187 | #576 | — | 9 | 4 | no | — |
| 188 | #575 | — | 3 | 1 | no | — |
| 189 | #575 | — | 9 | 2 | no | — |
| 190 | #575 | — | 9 | 2 | no | — |
| 191 | #575 | — | 9 | 1 | no | — |
| 192 | C2×AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 193 | C2×AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 194 | C2×AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 195 | C2×AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 196 | #568 | — | 9 | 1 | no | — |
| 197 | C23×D3 | — | 6 | 2 | no | — |
| 198 | C23×D3 | — | 6 | 1 | no | — |
| 199 | C3×#41 | — | 3 | 1 | no | — |
| 200 | C3×#41 | — | 3 | 1 | no | — |
| 201 | C3×#41 | — | 3 | 2 | no | — |
| 202 | C3×#41 | — | 3 | 2 | no | — |
| 203 | C3×#41 | — | 6 | 1 | no | — |
| 204 | C3×#41 | — | 6 | 1 | no | — |
| 205 | C3×#41 | — | 12 | 1 | no | — |
| 206 | C3×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 207 | C3×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 208 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 209 | C2×C3×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 210 | C2×C3×D4 | — | 3 | 1 | no | — |
| 211 | C2×C3×D4 | — | 3 | 1 | no | — |
| 212 | C2×C3×D4 | — | 6 | 1 | no | — |
| 213 | C22×C3×C4 | — | 3 | 1 | no | — |
| 214 | C22×C3×C4 | — | 6 | 1 | no | — |
| 215 | C2×#67 | — | 3 | 2 | no | — |
| 216 | C2×#67 | — | 6 | 2 | no | — |
| 217 | C2×#67 | — | 6 | 1 | no | — |
| 218 | #239 | — | 3 | 2 | no | — |
| 219 | #239 | — | 3 | 4 | no | — |
| 220 | #239 | — | 3 | 4 | no | — |
| 221 | #239 | — | 6 | 2 | no | — |
| 222 | #239 | — | 6 | 2 | no | — |
| 223 | #239 | — | 12 | 2 | no | — |
| 224 | #239 | C22×D3 | 1 | 2 | yes | — |
| 225 | D3×Q8 | — | 3 | 2 | no | — |
| 226 | D3×Q8 | C22×D3 | 1 | 2 | yes | — |
| 227 | #237 | — | 3 | 2 | no | — |
| 228 | #237 | — | 3 | 2 | no | — |
| 229 | #237 | — | 6 | 2 | no | — |
| 230 | D3×D4 | — | 3 | 2 | no | — |
| 231 | D3×D4 | — | 3 | 2 | no | — |
| 232 | D3×D4 | — | 3 | 4 | no | — |
| 233 | D3×D4 | — | 3 | 4 | no | — |
| 234 | D3×D4 | — | 6 | 2 | no | — |
| 235 | D3×D4 | — | 6 | 2 | no | — |
| 236 | D3×D4 | — | 6 | 4 | no | — |
| 237 | D3×D4 | — | 6 | 4 | no | — |
| 238 | D3×D4 | — | 6 | 4 | no | — |
| 239 | D3×D4 | — | 6 | 4 | no | — |
| 240 | D3×D4 | — | 6 | 2 | no | — |
| 241 | D3×D4 | — | 12 | 2 | no | — |
| 242 | D3×D4 | — | 12 | 4 | no | — |
| 243 | #235 | — | 3 | 1 | no | — |
| 244 | #235 | — | 3 | 2 | no | — |
| 245 | #235 | — | 3 | 1 | no | — |
| 246 | #235 | — | 3 | 2 | no | — |
| 247 | #235 | — | 3 | 2 | no | — |
| 248 | #235 | — | 3 | 2 | no | — |
| 249 | #235 | — | 3 | 1 | no | — |
| 250 | #235 | — | 4 | 1 | no | — |
| 251 | #235 | — | 6 | 1 | no | — |
| 252 | #235 | — | 6 | 2 | no | — |
| 253 | #235 | — | 6 | 4 | no | — |
| 254 | #235 | — | 6 | 2 | no | — |
| 255 | #235 | — | 12 | 2 | no | — |
| 256 | #235 | S4 | 1 | 1 | yes | characteristic |
| 257 | C2×D12 | — | 3 | 1 | no | — |
| 258 | C2×D12 | — | 3 | 1 | no | — |
| 259 | C2×D12 | — | 3 | 2 | no | — |
| 260 | C2×D12 | — | 3 | 2 | no | — |
| 261 | C2×D12 | — | 3 | 2 | no | — |
| 262 | C2×D12 | — | 6 | 4 | no | — |
| 263 | C2×D12 | — | 6 | 2 | no | — |
| 264 | C2×D12 | — | 6 | 1 | no | — |
| 265 | C2×D12 | — | 6 | 1 | no | — |
| 266 | C2×D12 | — | 6 | 2 | no | — |
| 267 | C2×D12 | — | 6 | 1 | no | — |
| 268 | C2×D12 | — | 6 | 2 | no | — |
| 269 | C2×D12 | — | 12 | 2 | no | — |
| 270 | C2×D12 | — | 12 | 1 | no | — |
| 271 | C2×D12 | — | 24 | 1 | no | — |
| 272 | C2×C4×D3 | — | 3 | 2 | no | — |
| 273 | C2×C4×D3 | — | 6 | 1 | no | — |
| 274 | C2×C4×D3 | — | 6 | 2 | no | — |
| 275 | C2×Dic6 | — | 3 | 1 | no | — |
| 276 | C2×Dic6 | — | 3 | 1 | no | — |
| 277 | #41⋊C3 | — | 2 | 1 | no | — |
| 278 | #41⋊C3 | — | 2 | 1 | no | — |
| 279 | #41⋊C3 | — | 3 | 2 | no | — |
| 280 | #41⋊C3 | C22×D3 | 1 | 1 | yes | characteristic |
| 281 | #41⋊C3 | C22×D3 | 1 | 1 | yes | characteristic, complemented |
| 282 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 283 | C2×SL(2,𝔽3) | — | 3 | 2 | no | — |
| 284 | C2×SL(2,𝔽3) | C22×D3 | 1 | 1 | yes | characteristic, complemented |
| 285 | GL(2,𝔽3) | — | 3 | 4 | no | — |
| 286 | GL(2,𝔽3) | — | 6 | 4 | no | — |
| 287 | GL(2,𝔽3) | C22×D3 | 1 | 2 | yes | complemented |
| 288 | #226 | C22×D3 | 1 | 2 | yes | complemented |
| 289 | C3×Q16 | — | 3 | 2 | no | — |
| 290 | C3×Q16 | — | 3 | 2 | no | — |
| 291 | C3×SD16 | — | 3 | 2 | no | — |
| 292 | C3×SD16 | — | 3 | 2 | no | — |
| 293 | C3×SD16 | — | 3 | 2 | no | — |
| 294 | C3×SD16 | — | 3 | 2 | no | — |
| 295 | C3×D8 | — | 3 | 2 | no | — |
| 296 | C3×D8 | — | 3 | 2 | no | — |
| 297 | C3×M16 | — | 3 | 1 | no | — |
| 298 | C3×M16 | — | 3 | 1 | no | — |
| 299 | C3×M16 | — | 3 | 2 | no | — |
| 300 | C2×C3×C8 | — | 3 | 2 | no | — |
| 301 | #216 | — | 3 | 4 | no | — |
| 302 | #215 | — | 3 | 4 | no | — |
| 303 | #215 | — | 3 | 4 | no | — |
| 304 | #215 | — | 3 | 4 | no | — |
| 305 | #214 | — | 3 | 4 | no | — |
| 306 | #213 | — | 3 | 4 | no | — |
| 307 | #213 | — | 3 | 4 | no | — |
| 308 | #213 | — | 3 | 4 | no | — |
| 309 | #208 | — | 3 | 2 | no | — |
| 310 | #208 | — | 3 | 2 | no | — |
| 311 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 312 | D24 | — | 3 | 4 | no | — |
| 313 | D24 | — | 3 | 4 | no | — |
| 314 | #204 | — | 3 | 4 | no | — |
| 315 | #204 | — | 3 | 4 | no | — |
| 316 | ΓL(1,𝔽25) | — | 3 | 4 | no | — |
| 317 | ΓL(1,𝔽25) | — | 3 | 4 | no | — |
| 318 | D3×C8 | — | 3 | 4 | no | — |
| 319 | D3×C8 | — | 3 | 4 | no | — |
| 320 | C22×C32 | — | 4 | 1 | no | — |
| 321 | C2×C3⋊D3 | — | 4 | 4 | no | — |
| 322 | C2×C3⋊D3 | — | 16 | 2 | no | — |
| 323 | C2×C3×D3 | — | 4 | 2 | no | — |
| 324 | C2×C3×D3 | — | 4 | 2 | no | — |
| 325 | D32 | — | 16 | 4 | no | — |
| 326 | C32×C4 | — | 4 | 1 | no | — |
| 327 | C32×C4 | — | 4 | 1 | no | — |
| 328 | C3×Dic3 | — | 4 | 2 | no | — |
| 329 | C3×Dic3 | — | 4 | 2 | no | — |
| 330 | 2−1+4 | — | 3 | 1 | no | — |
| 331 | 2−1+4 | — | 3 | 2 | no | — |
| 332 | 2−1+4 | — | 9 | 1 | no | — |
| 333 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 334 | H(5,𝔽2) | — | 9 | 2 | no | — |
| 335 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 336 | H(5,𝔽2) | — | 9 | 2 | no | — |
| 337 | H(5,𝔽2) | — | 9 | 4 | no | — |
| 338 | H(5,𝔽2) | — | 9 | 2 | no | — |
| 339 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 340 | H(5,𝔽2) | — | 18 | 2 | no | — |
| 341 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 342 | C2×#41 | — | 3 | 1 | no | — |
| 343 | C2×#41 | — | 3 | 2 | no | — |
| 344 | C2×#41 | — | 9 | 1 | no | — |
| 345 | C2×#41 | — | 9 | 1 | no | — |
| 346 | C2×#41 | — | 9 | 2 | no | — |
| 347 | C2×#41 | — | 9 | 2 | no | — |
| 348 | C2×#41 | — | 18 | 1 | no | — |
| 349 | C2×#41 | D32 | 1 | 1 | yes | characteristic, complemented |
| 350 | C22×D4 | — | 9 | 1 | no | — |
| 351 | C22×D4 | — | 9 | 2 | no | — |
| 352 | C22×D4 | — | 18 | 1 | no | — |
| 353 | C22×D4 | — | 18 | 2 | no | — |
| 354 | #137 | — | 3 | 1 | no | — |
| 355 | #137 | — | 3 | 1 | no | — |
| 356 | #137 | — | 3 | 2 | no | — |
| 357 | #137 | — | 9 | 4 | no | — |
| 358 | #137 | — | 9 | 4 | no | — |
| 359 | #137 | — | 9 | 2 | no | — |
| 360 | #137 | — | 9 | 2 | no | — |
| 361 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 362 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 363 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 364 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 365 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 366 | AGL(1,ℤ/8) | — | 9 | 4 | no | — |
| 367 | AGL(1,ℤ/8) | — | 9 | 4 | no | — |
| 368 | AGL(1,ℤ/8) | — | 9 | 4 | no | — |
| 369 | AGL(1,ℤ/8) | — | 9 | 4 | no | — |
| 370 | AGL(1,ℤ/8) | — | 9 | 4 | no | — |
| 371 | AGL(1,ℤ/8) | — | 9 | 4 | no | — |
| 372 | AGL(1,ℤ/8) | — | 9 | 4 | no | — |
| 373 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 374 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 375 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 376 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 377 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 378 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 379 | #135 | — | 3 | 2 | no | — |
| 380 | #135 | — | 3 | 2 | no | — |
| 381 | #135 | — | 9 | 4 | no | — |
| 382 | #135 | — | 9 | 4 | no | — |
| 383 | #135 | — | 9 | 4 | no | — |
| 384 | #135 | — | 9 | 4 | no | — |
| 385 | #135 | — | 9 | 4 | no | — |
| 386 | C2×SD16 | — | 9 | 2 | no | — |
| 387 | C2×SD16 | — | 9 | 4 | no | — |
| 388 | C2×SD16 | — | 9 | 4 | no | — |
| 389 | C2×SD16 | — | 9 | 2 | no | — |
| 390 | C2×D8 | — | 9 | 2 | no | — |
| 391 | C2×D8 | — | 9 | 4 | no | — |
| 392 | C2×D8 | — | 9 | 4 | no | — |
| 393 | C2×D8 | — | 9 | 2 | no | — |
| 394 | #131 | — | 9 | 2 | no | — |
| 395 | #131 | — | 9 | 2 | no | — |
| 396 | #131 | — | 9 | 4 | no | — |
| 397 | C2×M16 | — | 3 | 1 | no | — |
| 398 | C2×M16 | — | 9 | 2 | no | — |
| 399 | C2×M16 | — | 9 | 2 | no | — |
| 400 | C2×M16 | — | 9 | 1 | no | — |
| 401 | C23×C3 | — | 3 | 1 | no | — |
| 402 | C23×C3 | — | 6 | 1 | no | — |
| 403 | C22×D3 | — | 3 | 2 | no | — |
| 404 | C22×D3 | — | 6 | 1 | no | — |
| 405 | C22×D3 | — | 6 | 4 | no | — |
| 406 | C22×D3 | — | 6 | 2 | no | — |
| 407 | C22×D3 | — | 6 | 2 | no | — |
| 408 | C22×D3 | — | 6 | 2 | no | — |
| 409 | C22×D3 | — | 6 | 4 | no | — |
| 410 | C22×D3 | — | 12 | 4 | no | — |
| 411 | C22×D3 | — | 12 | 2 | no | — |
| 412 | C22×D3 | — | 24 | 2 | no | — |
| 413 | C22×D3 | — | 24 | 4 | no | — |
| 414 | C22×D3 | — | 24 | 2 | no | — |
| 415 | C3×Q8 | — | 3 | 1 | no | — |
| 416 | C3×Q8 | — | 3 | 2 | no | — |
| 417 | C3×Q8 | — | 6 | 1 | no | — |
| 418 | C3×Q8 | — | 12 | 1 | no | — |
| 419 | C3×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 420 | C3×D4 | — | 3 | 1 | no | — |
| 421 | C3×D4 | — | 3 | 1 | no | — |
| 422 | C3×D4 | — | 3 | 2 | no | — |
| 423 | C3×D4 | — | 6 | 1 | no | — |
| 424 | C3×D4 | — | 6 | 2 | no | — |
| 425 | C3×D4 | — | 6 | 2 | no | — |
| 426 | C3×D4 | — | 6 | 1 | no | — |
| 427 | C3×D4 | — | 12 | 1 | no | — |
| 428 | C3×D4 | — | 12 | 2 | no | — |
| 429 | C2×C3×C4 | — | 3 | 1 | no | — |
| 430 | C2×C3×C4 | — | 3 | 1 | no | — |
| 431 | C2×C3×C4 | — | 3 | 1 | no | — |
| 432 | C2×C3×C4 | — | 3 | 1 | no | — |
| 433 | C2×C3×C4 | — | 3 | 1 | no | — |
| 434 | C2×C3×C4 | — | 4 | 1 | no | — |
| 435 | C2×C3×C4 | — | 6 | 2 | no | — |
| 436 | C2×C3×C4 | — | 6 | 1 | no | — |
| 437 | C2×C3×C4 | — | 6 | 2 | no | — |
| 438 | C2×C3×C4 | — | 8 | 1 | no | — |
| 439 | C2×C3×C4 | — | 12 | 2 | no | — |
| 440 | C2×C3×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 441 | #67 | — | 3 | 2 | no | — |
| 442 | #67 | — | 3 | 2 | no | — |
| 443 | #67 | — | 3 | 2 | no | — |
| 444 | #67 | — | 4 | 2 | no | — |
| 445 | #67 | — | 6 | 2 | no | — |
| 446 | #67 | — | 6 | 4 | no | — |
| 447 | #67 | — | 6 | 4 | no | — |
| 448 | #67 | — | 12 | 4 | no | — |
| 449 | #67 | C2×S4 | 1 | 2 | yes | — |
| 450 | C2×Dic3 | — | 3 | 2 | no | — |
| 451 | C2×Dic3 | — | 6 | 1 | no | — |
| 452 | D12 | — | 3 | 2 | no | — |
| 453 | D12 | — | 3 | 2 | no | — |
| 454 | D12 | — | 3 | 4 | no | — |
| 455 | D12 | — | 3 | 1 | no | — |
| 456 | D12 | — | 4 | 1 | no | — |
| 457 | D12 | — | 6 | 2 | no | — |
| 458 | D12 | — | 6 | 4 | no | — |
| 459 | D12 | — | 6 | 4 | no | — |
| 460 | D12 | — | 6 | 2 | no | — |
| 461 | D12 | — | 6 | 2 | no | — |
| 462 | D12 | — | 12 | 2 | no | — |
| 463 | D12 | — | 12 | 2 | no | — |
| 464 | D12 | — | 12 | 4 | no | — |
| 465 | D12 | — | 24 | 2 | no | — |
| 466 | D12 | — | 24 | 2 | no | — |
| 467 | D12 | C2×S4 | 1 | 1 | yes | characteristic |
| 468 | C4×D3 | — | 3 | 2 | no | — |
| 469 | C4×D3 | — | 3 | 2 | no | — |
| 470 | C4×D3 | — | 3 | 2 | no | — |
| 471 | C4×D3 | — | 4 | 2 | no | — |
| 472 | C4×D3 | — | 6 | 2 | no | — |
| 473 | C4×D3 | — | 6 | 4 | no | — |
| 474 | C4×D3 | — | 6 | 4 | no | — |
| 475 | C4×D3 | — | 12 | 4 | no | — |
| 476 | C4×D3 | C2×S4 | 1 | 2 | yes | — |
| 477 | Dic6 | — | 3 | 1 | no | — |
| 478 | Dic6 | — | 3 | 2 | no | — |
| 479 | Dic6 | — | 3 | 2 | no | — |
| 480 | Dic6 | — | 4 | 1 | no | — |
| 481 | Dic6 | C2×S4 | 1 | 1 | yes | characteristic |
| 482 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 483 | SL(2,𝔽3) | C23×D3 | 1 | 1 | yes | characteristic |
| 484 | C3×C8 | — | 3 | 2 | no | — |
| 485 | C3×C8 | — | 3 | 2 | no | — |
| 486 | C3⋊C8 | — | 3 | 4 | no | — |
| 487 | C2×C32 | — | 4 | 1 | no | — |
| 488 | C2×C32 | — | 8 | 1 | no | — |
| 489 | C3⋊D3 | — | 8 | 4 | no | — |
| 490 | C3×D3 | — | 8 | 2 | no | — |
| 491 | C3×D3 | — | 8 | 2 | no | — |
| 492 | C24 | — | 18 | 1 | no | — |
| 493 | C24 | — | 18 | 2 | no | — |
| 494 | #41 | — | 3 | 1 | no | — |
| 495 | #41 | — | 3 | 1 | no | — |
| 496 | #41 | — | 3 | 1 | no | — |
| 497 | #41 | — | 3 | 2 | no | — |
| 498 | #41 | — | 3 | 2 | no | — |
| 499 | #41 | — | 3 | 2 | no | — |
| 500 | #41 | — | 6 | 1 | no | — |
| 501 | #41 | — | 6 | 1 | no | — |
| 502 | #41 | — | 9 | 2 | no | — |
| 503 | #41 | — | 9 | 2 | no | — |
| 504 | #41 | — | 9 | 1 | no | — |
| 505 | #41 | — | 9 | 1 | no | — |
| 506 | #41 | — | 9 | 2 | no | — |
| 507 | #41 | — | 9 | 2 | no | — |
| 508 | #41 | — | 9 | 1 | no | — |
| 509 | #41 | — | 9 | 2 | no | — |
| 510 | #41 | — | 9 | 2 | no | — |
| 511 | #41 | — | 9 | 2 | no | — |
| 512 | #41 | — | 9 | 4 | no | — |
| 513 | #41 | — | 9 | 4 | no | — |
| 514 | #41 | — | 18 | 1 | no | — |
| 515 | #41 | — | 18 | 2 | no | — |
| 516 | #41 | — | 18 | 2 | no | — |
| 517 | #41 | — | 18 | 4 | no | — |
| 518 | #41 | — | 18 | 2 | no | — |
| 519 | #41 | — | 18 | 2 | no | — |
| 520 | #41 | — | 18 | 2 | no | — |
| 521 | #41 | C2×D32 | 1 | 1 | yes | characteristic |
| 522 | #41 | C2×D32 | 1 | 1 | yes | characteristic |
| 523 | C2×Q8 | — | 3 | 1 | no | — |
| 524 | C2×Q8 | — | 3 | 2 | no | — |
| 525 | C2×Q8 | — | 9 | 1 | no | — |
| 526 | C2×Q8 | — | 9 | 1 | no | — |
| 527 | C2×Q8 | — | 9 | 2 | no | — |
| 528 | C2×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 529 | C2×D4 | — | 3 | 1 | no | — |
| 530 | C2×D4 | — | 3 | 1 | no | — |
| 531 | C2×D4 | — | 6 | 1 | no | — |
| 532 | C2×D4 | — | 9 | 1 | no | — |
| 533 | C2×D4 | — | 9 | 1 | no | — |
| 534 | C2×D4 | — | 9 | 2 | no | — |
| 535 | C2×D4 | — | 9 | 2 | no | — |
| 536 | C2×D4 | — | 9 | 2 | no | — |
| 537 | C2×D4 | — | 9 | 2 | no | — |
| 538 | C2×D4 | — | 9 | 2 | no | — |
| 539 | C2×D4 | — | 9 | 2 | no | — |
| 540 | C2×D4 | — | 9 | 4 | no | — |
| 541 | C2×D4 | — | 9 | 4 | no | — |
| 542 | C2×D4 | — | 18 | 2 | no | — |
| 543 | C2×D4 | — | 18 | 1 | no | — |
| 544 | C2×D4 | — | 18 | 1 | no | — |
| 545 | C2×D4 | — | 18 | 2 | no | — |
| 546 | C2×D4 | — | 18 | 4 | no | — |
| 547 | C2×D4 | — | 18 | 2 | no | — |
| 548 | C2×D4 | — | 18 | 2 | no | — |
| 549 | C2×D4 | — | 18 | 2 | no | — |
| 550 | C2×D4 | — | 18 | 2 | no | — |
| 551 | C2×D4 | — | 18 | 4 | no | — |
| 552 | C2×D4 | — | 18 | 2 | no | — |
| 553 | C2×D4 | — | 18 | 4 | no | — |
| 554 | C2×D4 | — | 18 | 4 | no | — |
| 555 | C2×D4 | — | 18 | 4 | no | — |
| 556 | C2×D4 | — | 18 | 1 | no | — |
| 557 | C2×D4 | — | 18 | 1 | no | — |
| 558 | C22×C4 | — | 3 | 1 | no | — |
| 559 | C22×C4 | — | 6 | 1 | no | — |
| 560 | C22×C4 | — | 9 | 2 | no | — |
| 561 | C22×C4 | — | 18 | 1 | no | — |
| 562 | C22×C4 | — | 18 | 2 | no | — |
| 563 | Q16 | — | 3 | 2 | no | — |
| 564 | Q16 | — | 3 | 2 | no | — |
| 565 | Q16 | — | 9 | 4 | no | — |
| 566 | SD16 | — | 3 | 2 | no | — |
| 567 | SD16 | — | 3 | 2 | no | — |
| 568 | SD16 | — | 3 | 2 | no | — |
| 569 | SD16 | — | 3 | 2 | no | — |
| 570 | SD16 | — | 9 | 4 | no | — |
| 571 | SD16 | — | 9 | 4 | no | — |
| 572 | SD16 | — | 9 | 4 | no | — |
| 573 | SD16 | — | 9 | 4 | no | — |
| 574 | SD16 | — | 9 | 4 | no | — |
| 575 | SD16 | — | 9 | 4 | no | — |
| 576 | D8 | — | 3 | 2 | no | — |
| 577 | D8 | — | 3 | 2 | no | — |
| 578 | D8 | — | 9 | 4 | no | — |
| 579 | D8 | — | 9 | 4 | no | — |
| 580 | D8 | — | 9 | 4 | no | — |
| 581 | D8 | — | 9 | 4 | no | — |
| 582 | D8 | — | 9 | 4 | no | — |
| 583 | M16 | — | 3 | 1 | no | — |
| 584 | M16 | — | 3 | 1 | no | — |
| 585 | M16 | — | 3 | 2 | no | — |
| 586 | M16 | — | 9 | 4 | no | — |
| 587 | M16 | — | 9 | 4 | no | — |
| 588 | M16 | — | 9 | 2 | no | — |
| 589 | M16 | — | 9 | 2 | no | — |
| 590 | C2×C8 | — | 3 | 2 | no | — |
| 591 | C2×C8 | — | 9 | 4 | no | — |
| 592 | C2×C8 | — | 9 | 4 | no | — |
| 593 | C2×C8 | — | 9 | 2 | no | — |
| 594 | C22×C3 | — | 3 | 1 | no | — |
| 595 | C22×C3 | — | 3 | 1 | no | — |
| 596 | C22×C3 | — | 4 | 1 | no | — |
| 597 | C22×C3 | — | 6 | 2 | no | — |
| 598 | C22×C3 | — | 8 | 1 | no | — |
| 599 | C22×C3 | — | 12 | 2 | no | — |
| 600 | C22×C3 | — | 12 | 1 | no | — |
| 601 | C22×C3 | — | 12 | 2 | no | — |
| 602 | C22×C3 | C22×S4 | 1 | 1 | yes | characteristic |
| 603 | C2×D3 | — | 3 | 2 | no | — |
| 604 | C2×D3 | — | 4 | 2 | no | — |
| 605 | C2×D3 | — | 6 | 4 | no | — |
| 606 | C2×D3 | — | 12 | 4 | no | — |
| 607 | C2×D3 | — | 12 | 2 | no | — |
| 608 | C2×D3 | — | 12 | 4 | no | — |
| 609 | C2×D3 | — | 24 | 4 | no | — |
| 610 | C2×D3 | — | 24 | 4 | no | — |
| 611 | C2×D3 | — | 24 | 1 | no | — |
| 612 | C2×D3 | — | 24 | 4 | no | — |
| 613 | C2×D3 | — | 24 | 2 | no | — |
| 614 | C2×D3 | — | 24 | 2 | no | — |
| 615 | C2×D3 | — | 48 | 4 | no | — |
| 616 | C2×D3 | — | 48 | 2 | no | — |
| 617 | C2×D3 | — | 48 | 4 | no | — |
| 618 | C2×D3 | C22×S4 | 1 | 2 | yes | — |
| 619 | C3×C4 | — | 3 | 1 | no | — |
| 620 | C3×C4 | — | 3 | 1 | no | — |
| 621 | C3×C4 | — | 4 | 1 | no | — |
| 622 | C3×C4 | — | 4 | 1 | no | — |
| 623 | C3×C4 | — | 6 | 2 | no | — |
| 624 | C3×C4 | — | 8 | 1 | no | — |
| 625 | C3×C4 | — | 8 | 1 | no | — |
| 626 | C3×C4 | — | 12 | 2 | no | — |
| 627 | C3×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 628 | C3×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 629 | Dic3 | — | 3 | 2 | no | — |
| 630 | Dic3 | — | 4 | 2 | no | — |
| 631 | Dic3 | C22×S4 | 1 | 2 | yes | — |
| 632 | C32 | — | 4 | 1 | no | Sylow |
| 633 | C23 | — | 3 | 1 | no | — |
| 634 | C23 | — | 6 | 1 | no | — |
| 635 | C23 | — | 9 | 2 | no | — |
| 636 | C23 | — | 18 | 4 | no | — |
| 637 | C23 | — | 18 | 1 | no | — |
| 638 | C23 | — | 18 | 2 | no | — |
| 639 | C23 | — | 18 | 2 | no | — |
| 640 | C23 | — | 18 | 4 | no | — |
| 641 | C23 | — | 18 | 2 | no | — |
| 642 | C23 | — | 72 | 2 | no | — |
| 643 | C23 | — | 72 | 4 | no | — |
| 644 | Q8 | — | 3 | 1 | no | — |
| 645 | Q8 | — | 3 | 1 | no | — |
| 646 | Q8 | — | 3 | 2 | no | — |
| 647 | Q8 | — | 6 | 1 | no | — |
| 648 | Q8 | — | 9 | 2 | no | — |
| 649 | Q8 | — | 9 | 2 | no | — |
| 650 | Q8 | — | 9 | 1 | no | — |
| 651 | Q8 | C22×D32 | 1 | 1 | yes | characteristic |
| 652 | D4 | — | 3 | 1 | no | — |
| 653 | D4 | — | 3 | 1 | no | — |
| 654 | D4 | — | 3 | 2 | no | — |
| 655 | D4 | — | 3 | 2 | no | — |
| 656 | D4 | — | 3 | 1 | no | — |
| 657 | D4 | — | 6 | 1 | no | — |
| 658 | D4 | — | 6 | 2 | no | — |
| 659 | D4 | — | 6 | 2 | no | — |
| 660 | D4 | — | 6 | 1 | no | — |
| 661 | D4 | — | 9 | 2 | no | — |
| 662 | D4 | — | 9 | 2 | no | — |
| 663 | D4 | — | 9 | 2 | no | — |
| 664 | D4 | — | 9 | 4 | no | — |
| 665 | D4 | — | 9 | 2 | no | — |
| 666 | D4 | — | 9 | 2 | no | — |
| 667 | D4 | — | 9 | 1 | no | — |
| 668 | D4 | — | 18 | 4 | no | — |
| 669 | D4 | — | 18 | 2 | no | — |
| 670 | D4 | — | 18 | 4 | no | — |
| 671 | D4 | — | 18 | 4 | no | — |
| 672 | D4 | — | 18 | 2 | no | — |
| 673 | D4 | — | 18 | 4 | no | — |
| 674 | D4 | — | 18 | 2 | no | — |
| 675 | D4 | — | 18 | 2 | no | — |
| 676 | C2×C4 | — | 3 | 1 | no | — |
| 677 | C2×C4 | — | 3 | 1 | no | — |
| 678 | C2×C4 | — | 3 | 1 | no | — |
| 679 | C2×C4 | — | 3 | 1 | no | — |
| 680 | C2×C4 | — | 3 | 1 | no | — |
| 681 | C2×C4 | — | 3 | 2 | no | — |
| 682 | C2×C4 | — | 6 | 2 | no | — |
| 683 | C2×C4 | — | 6 | 1 | no | — |
| 684 | C2×C4 | — | 6 | 2 | no | — |
| 685 | C2×C4 | — | 9 | 2 | no | — |
| 686 | C2×C4 | — | 9 | 2 | no | — |
| 687 | C2×C4 | — | 9 | 2 | no | — |
| 688 | C2×C4 | — | 9 | 2 | no | — |
| 689 | C2×C4 | — | 18 | 4 | no | — |
| 690 | C2×C4 | — | 18 | 2 | no | — |
| 691 | C2×C4 | — | 18 | 4 | no | — |
| 692 | C2×C4 | — | 18 | 1 | no | — |
| 693 | C2×C4 | D3×S4 | 1 | 1 | yes | characteristic |
| 694 | C8 | — | 3 | 2 | no | — |
| 695 | C8 | — | 3 | 2 | no | — |
| 696 | C8 | — | 9 | 4 | no | — |
| 697 | C2×C3 | — | 2 | 1 | no | — |
| 698 | C2×C3 | — | 4 | 1 | no | — |
| 699 | C2×C3 | — | 6 | 1 | no | — |
| 700 | C2×C3 | — | 6 | 1 | no | — |
| 701 | C2×C3 | — | 8 | 1 | no | — |
| 702 | C2×C3 | — | 8 | 2 | no | — |
| 703 | C2×C3 | — | 8 | 1 | no | — |
| 704 | C2×C3 | — | 12 | 2 | no | — |
| 705 | C2×C3 | — | 24 | 2 | no | — |
| 706 | C2×C3 | C23×S4 | 1 | 1 | yes | characteristic |
| 707 | D3 | — | 2 | 2 | no | — |
| 708 | D3 | — | 6 | 2 | no | — |
| 709 | D3 | — | 8 | 2 | no | — |
| 710 | D3 | — | 12 | 4 | no | — |
| 711 | D3 | — | 24 | 4 | no | — |
| 712 | D3 | — | 48 | 4 | no | — |
| 713 | C22 | — | 3 | 1 | no | — |
| 714 | C22 | — | 3 | 1 | no | — |
| 715 | C22 | — | 3 | 2 | no | — |
| 716 | C22 | — | 6 | 2 | no | — |
| 717 | C22 | — | 9 | 2 | no | — |
| 718 | C22 | — | 12 | 1 | no | — |
| 719 | C22 | — | 12 | 2 | no | — |
| 720 | C22 | — | 18 | 4 | no | — |
| 721 | C22 | — | 36 | 2 | no | — |
| 722 | C22 | — | 36 | 4 | no | — |
| 723 | C22 | — | 72 | 2 | no | — |
| 724 | C22 | — | 72 | 4 | no | — |
| 725 | C22 | — | 72 | 1 | no | — |
| 726 | C22 | — | 72 | 2 | no | — |
| 727 | C22 | — | 72 | 4 | no | — |
| 728 | C22 | C2×D3×S4 | 1 | 1 | yes | characteristic |
| 729 | C4 | — | 3 | 1 | no | — |
| 730 | C4 | — | 3 | 1 | no | — |
| 731 | C4 | — | 3 | 2 | no | — |
| 732 | C4 | — | 6 | 2 | no | — |
| 733 | C4 | — | 9 | 2 | no | — |
| 734 | C4 | C2×D3×S4 | 1 | 1 | yes | characteristic |
| 735 | C4 | C2×D3×S4 | 1 | 1 | yes | characteristic |
| 736 | C3 | — | 4 | 1 | no | — |
| 737 | C3 | — | 8 | 1 | no | — |
| 738 | C3 | #87498 | 1 | 1 | yes | characteristic, complemented |
| 739 | C2 | — | 2 | 1 | no | — |
| 740 | C2 | — | 6 | 1 | no | — |
| 741 | C2 | — | 6 | 1 | no | — |
| 742 | C2 | — | 6 | 2 | no | — |
| 743 | C2 | — | 12 | 2 | no | — |
| 744 | C2 | — | 18 | 2 | no | — |
| 745 | C2 | — | 36 | 4 | no | — |
| 746 | C2 | C22×D3×S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D3×S4 |
| commutator, cosocle, hypocenter | C3×SL(2,𝔽3) | C24 |
| Fitting | C2×C3×#41 | C2×D3 |
| socle | C2×C3 | C23×S4 |
| hypercenter | C2×C4 | D3×S4 |
| LCS | G ▷ C3×SL(2,𝔽3) | |
| UCS | C1 ◁ C2 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #5964⋊C3 | C2 | semidirect |
| 2. C2×#64267 | C2 | semidirect |
| 3. C3×#5923 | C2 | semidirect |
| 4. #10596459 | C2 | semidirect |
| 5. D3×#986 | C2 | semidirect |
| 6. #10596456 | C2 | semidirect |
| 7. #10596449 | C2 | semidirect |
| 8. #10596446 | C2 | semidirect |
| 11. C2×C3×#41⋊C3 | C22 | semidirect |
| 13. #1010⋊C3 | C22 | semidirect |
| 14. D3×#41⋊C3 | C22 | semidirect |
| 15. C3⋊#994 | C22 | semidirect |
| 16. #1007⋊C3 | C22 | semidirect |
| 17. #64267 | C22 | semidirect |
| 18. #64267 | C22 | semidirect |
| 19. C2×C3⋊GL(2,𝔽3) | C22 | semidirect |
| 20. C3×#986 | C22 | semidirect |
| 21. C3×#985 | C22 | semidirect |
| 22. C3×#984 | C22 | semidirect |
| 23. C3×#983 | C22 | semidirect |
| 24. D3×GL(2,𝔽3) | C22 | semidirect |
| 25. #64202 | C22 | semidirect |
| 26. #64199 | C22 | semidirect |
| 27. #64198 | C22 | semidirect |
| 28. #5964 | D3 | semidirect |
| 35. #5923 | D3 | semidirect |
| 58. C3×#41⋊C3 | C23 | semidirect |
| 59. C2×C3×SL(2,𝔽3) | C23 | semidirect |
| 65. D3×SL(2,𝔽3) | C23 | semidirect |
| 66. C3⋊(#41⋊C3) | C23 | semidirect |
| 67. C3⋊GL(2,𝔽3) | C23 | semidirect |
| 68. C3×GL(2,𝔽3) | C23 | semidirect |
| 69. C3×#226 | C23 | semidirect |
| 72. C2×C3×#41 | C2×D3 | semidirect |
| 74. #1010 | C2×D3 | semidirect |
| 83. #1009 | C2×D3 | semidirect |
| 85. D3×#41 | C2×D3 | semidirect |
| 86. #1007 | C2×D3 | semidirect |
| 101. C2×#41⋊C3 | C2×D3 | semidirect |
| 107. #986 | C2×D3 | semidirect |
| 109. #985 | C2×D3 | semidirect |
| 110. #984 | C2×D3 | semidirect |
| 112. #983 | C2×D3 | semidirect |
| 281. #41⋊C3 | C22×D3 | semidirect |
| 284. C2×SL(2,𝔽3) | C22×D3 | semidirect |
| 287. GL(2,𝔽3) | C22×D3 | semidirect |
| 288. #226 | C22×D3 | semidirect |
| 349. C2×#41 | D32 | semidirect |
| 738. C3 | #87498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5964⋊C3 | 2 |
| C2×#64267 | 2 |
| C3×#5923 | 2 |
| #10596459 | 2 |
| D3×#986 | 2 |
| #10596456 | 2 |
| #10596449 | 2 |
| #10596446 | 2 |
| #87498 | 3 |
| #87200 | 3 |
| #64308 | 4 |