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 | #5968⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10596589 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#5926 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | D3×#986 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10596454 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10596449 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10596448 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10596446 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10596445 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C2×#64199 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #10596435 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #87498 | — | 3 | 1 | no | maximal |
| 13 | #87207 | — | 3 | 1 | no | maximal |
| 14 | C3×2−1+4⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #64314 | — | 4 | 1 | no | maximal |
| 16 | D3×#41⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C3⋊#994 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | #1007⋊C3 | C22 | 1 | 2 | yes | complemented |
| 19 | C2×C3⋊(#41⋊C3) | C22 | 1 | 2 | yes | complemented |
| 20 | #64267 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #64266 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #64264 | C22 | 1 | 2 | yes | complemented |
| 23 | C2×C3⋊GL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 24 | C3×#986 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C3×#985 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C3×#983 | C22 | 1 | 2 | yes | complemented |
| 27 | C2×C3×GL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 28 | D3×GL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 29 | #64202 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | #64201 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #64199 | C22 | 1 | 2 | yes | complemented |
| 32 | #64199 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #64199 | C22 | 1 | 2 | yes | complemented |
| 34 | #64199 | C22 | 1 | 2 | yes | complemented |
| 35 | #64198 | C22 | 1 | 2 | yes | complemented |
| 36 | #64197 | C22 | 1 | 2 | yes | complemented |
| 37 | #64196 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | #5968 | D3 | 1 | 1 | yes | characteristic, complemented |
| 39 | D3×H(5,𝔽2) | — | 3 | 1 | no | — |
| 40 | #5945 | — | 3 | 1 | no | — |
| 41 | #5926 | — | 3 | 1 | no | — |
| 42 | #5926 | — | 3 | 2 | no | — |
| 43 | #5926 | — | 3 | 2 | no | — |
| 44 | #5926 | — | 6 | 1 | no | — |
| 45 | #5926 | D3 | 1 | 1 | yes | characteristic, complemented |
| 46 | #5925 | — | 3 | 1 | no | — |
| 47 | #5925 | — | 3 | 1 | no | — |
| 48 | #5923 | — | 3 | 1 | no | — |
| 49 | #5923 | — | 3 | 2 | no | — |
| 50 | C2×#986 | — | 3 | 1 | no | — |
| 51 | C2×#986 | — | 3 | 2 | no | — |
| 52 | C3×#577 | — | 3 | 1 | no | — |
| 53 | #5837 | — | 3 | 1 | no | — |
| 54 | #5835 | — | 3 | 1 | no | — |
| 55 | #5778 | — | 3 | 1 | no | — |
| 56 | #5778 | — | 3 | 2 | no | — |
| 57 | #5777 | — | 3 | 1 | no | — |
| 58 | #5777 | — | 3 | 2 | no | — |
| 59 | #5774 | — | 3 | 2 | no | — |
| 60 | #5774 | — | 3 | 1 | no | — |
| 61 | D3×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 62 | D3×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 63 | #5769 | — | 3 | 2 | no | — |
| 64 | #5769 | — | 3 | 1 | no | — |
| 65 | #5768 | — | 3 | 2 | no | — |
| 66 | #5768 | — | 3 | 1 | no | — |
| 67 | #5762 | — | 3 | 1 | no | — |
| 68 | #5762 | — | 3 | 2 | no | — |
| 69 | C2×#914 | — | 3 | 1 | no | — |
| 70 | C2×#914 | — | 3 | 2 | no | — |
| 71 | #5752 | — | 3 | 1 | no | — |
| 72 | #5750 | — | 3 | 1 | no | — |
| 73 | D4×C3⋊D3 | — | 4 | 1 | no | — |
| 74 | C3×#237 | — | 4 | 1 | no | — |
| 75 | C3×D3×D4 | — | 4 | 1 | no | — |
| 76 | C3×#41⋊C3 | C23 | 1 | 1 | yes | characteristic, complemented |
| 77 | C2×C3×SL(2,𝔽3) | C23 | 1 | 2 | yes | complemented |
| 78 | #3811 | — | 4 | 2 | no | — |
| 79 | D3×#67 | — | 4 | 2 | no | — |
| 80 | C2×#626 | — | 4 | 2 | no | — |
| 81 | #3804 | — | 4 | 2 | no | — |
| 82 | D3×D12 | — | 4 | 1 | no | — |
| 83 | #3799 | — | 4 | 1 | no | — |
| 84 | #3798 | — | 4 | 1 | no | — |
| 85 | #3796 | — | 4 | 1 | no | — |
| 86 | D3×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic, complemented |
| 87 | C3⋊(#41⋊C3) | C23 | 1 | 1 | yes | characteristic |
| 88 | C3⋊(#41⋊C3) | C23 | 1 | 2 | yes | complemented |
| 89 | C3⋊GL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic, complemented |
| 90 | C3⋊GL(2,𝔽3) | C23 | 1 | 2 | yes | complemented |
| 91 | C3⋊#226 | C23 | 1 | 1 | yes | characteristic, complemented |
| 92 | C3×GL(2,𝔽3) | C23 | 1 | 2 | yes | complemented |
| 93 | C3×GL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic, complemented |
| 94 | C3×#226 | C23 | 1 | 1 | yes | characteristic, complemented |
| 95 | #3585 | — | 9 | 1 | no | Sylow |
| 96 | C3×2−1+4 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 97 | C3×H(5,𝔽2) | — | 3 | 1 | no | — |
| 98 | #1009 | — | 3 | 1 | no | — |
| 99 | #1009 | — | 3 | 1 | no | — |
| 100 | #1009 | — | 3 | 2 | no | — |
| 101 | #1009 | — | 3 | 2 | no | — |
| 102 | #1009 | — | 3 | 1 | no | — |
| 103 | #1009 | — | 6 | 1 | no | — |
| 104 | #1009 | — | 12 | 1 | no | — |
| 105 | #1009 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 106 | D3×#41 | — | 3 | 1 | no | — |
| 107 | D3×#41 | — | 3 | 2 | no | — |
| 108 | D3×#41 | — | 3 | 2 | no | — |
| 109 | D3×#41 | — | 3 | 1 | no | — |
| 110 | D3×#41 | — | 6 | 1 | no | — |
| 111 | D3×#41 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 112 | #1007 | — | 3 | 1 | no | — |
| 113 | #1007 | C2×D3 | 1 | 2 | yes | complemented |
| 114 | C2×#239 | — | 3 | 1 | no | — |
| 115 | C2×#239 | C2×D3 | 1 | 2 | yes | complemented |
| 116 | #1004 | — | 3 | 2 | no | — |
| 117 | #1004 | — | 3 | 1 | no | — |
| 118 | #1004 | — | 6 | 2 | no | — |
| 119 | #1004 | — | 6 | 1 | no | — |
| 120 | C2×D3×D4 | — | 3 | 2 | no | — |
| 121 | C2×D3×D4 | — | 3 | 1 | no | — |
| 122 | C2×D3×D4 | — | 6 | 1 | no | — |
| 123 | C2×D3×D4 | — | 6 | 2 | no | — |
| 124 | 2−1+4⋊C3 | — | 2 | 1 | no | — |
| 125 | 2−1+4⋊C3 | — | 3 | 2 | no | — |
| 126 | 2−1+4⋊C3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 127 | #994 | — | 3 | 1 | no | — |
| 128 | C2×#41⋊C3 | — | 3 | 1 | no | — |
| 129 | C2×#41⋊C3 | — | 3 | 2 | no | — |
| 130 | #986 | — | 3 | 1 | no | — |
| 131 | #986 | — | 3 | 2 | no | — |
| 132 | #986 | — | 3 | 1 | no | — |
| 133 | #986 | — | 3 | 2 | no | — |
| 134 | #986 | — | 3 | 2 | no | — |
| 135 | #986 | — | 6 | 1 | no | — |
| 136 | #986 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 137 | #985 | — | 3 | 1 | no | — |
| 138 | #985 | — | 3 | 2 | no | — |
| 139 | #985 | — | 3 | 2 | no | — |
| 140 | #985 | — | 6 | 1 | no | — |
| 141 | #985 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 142 | #984 | — | 3 | 1 | no | — |
| 143 | #983 | — | 3 | 2 | no | — |
| 144 | #983 | — | 3 | 1 | no | — |
| 145 | #983 | — | 3 | 1 | no | — |
| 146 | #983 | — | 6 | 2 | no | — |
| 147 | #983 | C2×D3 | 1 | 2 | yes | complemented |
| 148 | C2×GL(2,𝔽3) | — | 3 | 2 | no | — |
| 149 | C2×GL(2,𝔽3) | — | 3 | 2 | no | — |
| 150 | C2×GL(2,𝔽3) | — | 6 | 2 | no | — |
| 151 | C2×GL(2,𝔽3) | C2×D3 | 1 | 2 | yes | complemented |
| 152 | C3×#137 | — | 3 | 1 | no | — |
| 153 | C3×#137 | — | 3 | 2 | no | — |
| 154 | C3×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 155 | C3×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 156 | C3×#135 | — | 3 | 2 | no | — |
| 157 | C3×#135 | — | 3 | 1 | no | — |
| 158 | C2×C3×SD16 | — | 3 | 1 | no | — |
| 159 | C2×C3×SD16 | — | 3 | 2 | no | — |
| 160 | C3×#131 | — | 3 | 1 | no | — |
| 161 | #950 | — | 3 | 2 | no | — |
| 162 | #950 | — | 3 | 1 | no | — |
| 163 | #950 | — | 3 | 2 | no | — |
| 164 | #950 | — | 3 | 1 | no | — |
| 165 | #949 | — | 3 | 2 | no | — |
| 166 | #949 | — | 3 | 1 | no | — |
| 167 | #949 | — | 3 | 2 | no | — |
| 168 | #949 | — | 3 | 1 | no | — |
| 169 | #948 | — | 3 | 1 | no | — |
| 170 | #942 | — | 3 | 1 | no | — |
| 171 | #942 | — | 3 | 2 | no | — |
| 172 | C2×#215 | — | 3 | 1 | no | — |
| 173 | C2×#215 | — | 3 | 2 | no | — |
| 174 | #932 | — | 3 | 1 | no | — |
| 175 | #932 | — | 3 | 2 | no | — |
| 176 | C2×#213 | — | 3 | 1 | no | — |
| 177 | C2×#213 | — | 3 | 2 | no | — |
| 178 | #919 | — | 3 | 2 | no | — |
| 179 | #919 | — | 3 | 2 | no | — |
| 180 | #919 | — | 3 | 2 | no | — |
| 181 | #918 | — | 3 | 2 | no | — |
| 182 | #918 | — | 3 | 2 | no | — |
| 183 | #918 | — | 3 | 1 | no | — |
| 184 | #918 | — | 3 | 1 | no | — |
| 185 | #916 | — | 3 | 2 | no | — |
| 186 | #916 | — | 3 | 2 | no | — |
| 187 | #916 | — | 3 | 2 | no | — |
| 188 | #915 | — | 3 | 2 | no | — |
| 189 | #915 | — | 3 | 1 | no | — |
| 190 | #915 | — | 3 | 1 | no | — |
| 191 | #914 | — | 3 | 2 | no | — |
| 192 | #914 | — | 3 | 2 | no | — |
| 193 | #914 | — | 3 | 2 | no | — |
| 194 | #914 | — | 3 | 2 | no | — |
| 195 | #914 | — | 3 | 2 | no | — |
| 196 | #914 | — | 3 | 2 | no | — |
| 197 | #914 | — | 3 | 2 | no | — |
| 198 | #914 | — | 3 | 2 | no | — |
| 199 | #914 | — | 3 | 1 | no | — |
| 200 | #914 | — | 3 | 1 | no | — |
| 201 | #914 | — | 3 | 2 | no | — |
| 202 | #914 | — | 3 | 2 | no | — |
| 203 | #914 | — | 3 | 2 | no | — |
| 204 | D3×SD16 | — | 3 | 2 | no | — |
| 205 | D3×SD16 | — | 3 | 2 | no | — |
| 206 | D3×SD16 | — | 3 | 2 | no | — |
| 207 | #911 | — | 3 | 2 | no | — |
| 208 | #911 | — | 3 | 1 | no | — |
| 209 | #911 | — | 3 | 2 | no | — |
| 210 | #911 | — | 3 | 1 | no | — |
| 211 | D3×D8 | — | 3 | 2 | no | — |
| 212 | D3×D8 | — | 3 | 2 | no | — |
| 213 | D3×D8 | — | 3 | 2 | no | — |
| 214 | #908 | — | 3 | 1 | no | — |
| 215 | #908 | — | 3 | 2 | no | — |
| 216 | #908 | — | 3 | 1 | no | — |
| 217 | #908 | — | 3 | 2 | no | — |
| 218 | #907 | — | 3 | 2 | no | — |
| 219 | #907 | — | 3 | 1 | no | — |
| 220 | D3×M16 | — | 3 | 2 | no | — |
| 221 | D3×M16 | — | 3 | 1 | no | — |
| 222 | #904 | — | 3 | 1 | no | — |
| 223 | #904 | — | 3 | 2 | no | — |
| 224 | C2×D24 | — | 3 | 1 | no | — |
| 225 | C2×D24 | — | 3 | 2 | no | — |
| 226 | #901 | — | 3 | 2 | no | — |
| 227 | #901 | — | 3 | 1 | no | — |
| 228 | C2×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 229 | C2×ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 230 | C22×C3⋊D3 | — | 4 | 2 | no | — |
| 231 | C22×C3×D3 | — | 4 | 2 | no | — |
| 232 | C2×D32 | — | 4 | 2 | no | — |
| 233 | C32×D4 | — | 4 | 1 | no | — |
| 234 | #638 | — | 4 | 2 | no | — |
| 235 | C4⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 236 | C4×C3⋊D3 | — | 4 | 1 | no | — |
| 237 | C3×#67 | — | 4 | 2 | no | — |
| 238 | C3×#67 | — | 4 | 2 | no | — |
| 239 | C2×C3×Dic3 | — | 4 | 2 | no | — |
| 240 | C3×D12 | — | 4 | 1 | no | — |
| 241 | C3×C4×D3 | — | 4 | 1 | no | — |
| 242 | C3×C4×D3 | — | 4 | 1 | no | — |
| 243 | C3×Dic6 | — | 4 | 1 | no | — |
| 244 | C3×SL(2,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 245 | #627 | — | 4 | 1 | no | — |
| 246 | #626 | — | 4 | 1 | no | — |
| 247 | #626 | — | 4 | 2 | no | — |
| 248 | #626 | — | 4 | 1 | no | — |
| 249 | #626 | — | 4 | 2 | no | — |
| 250 | #626 | — | 4 | 2 | no | — |
| 251 | #625 | — | 4 | 1 | no | — |
| 252 | #624 | — | 4 | 2 | no | — |
| 253 | D3×Dic3 | — | 4 | 2 | no | — |
| 254 | #585 | — | 3 | 1 | no | — |
| 255 | C2×H(5,𝔽2) | — | 9 | 1 | no | — |
| 256 | #577 | — | 3 | 1 | no | — |
| 257 | #577 | — | 9 | 2 | no | — |
| 258 | #577 | — | 9 | 1 | no | — |
| 259 | #577 | — | 9 | 2 | no | — |
| 260 | #577 | — | 9 | 1 | no | — |
| 261 | #577 | — | 9 | 1 | no | — |
| 262 | #576 | — | 9 | 1 | no | — |
| 263 | #576 | — | 9 | 1 | no | — |
| 264 | #576 | — | 9 | 2 | no | — |
| 265 | #576 | — | 9 | 1 | no | — |
| 266 | #576 | — | 9 | 2 | no | — |
| 267 | #576 | — | 9 | 1 | no | — |
| 268 | #575 | — | 9 | 1 | no | — |
| 269 | #575 | — | 9 | 2 | no | — |
| 270 | #575 | — | 9 | 2 | no | — |
| 271 | #575 | — | 9 | 1 | no | — |
| 272 | C2×AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 273 | C2×AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 274 | C2×AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 275 | C2×AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 276 | #568 | — | 9 | 1 | no | — |
| 277 | C23×D3 | — | 6 | 2 | no | — |
| 278 | C23×D3 | — | 6 | 1 | no | — |
| 279 | C3×#41 | — | 3 | 1 | no | — |
| 280 | C3×#41 | — | 3 | 2 | no | — |
| 281 | C3×#41 | — | 3 | 2 | no | — |
| 282 | C3×#41 | — | 3 | 1 | no | — |
| 283 | C3×#41 | — | 6 | 1 | no | — |
| 284 | C3×#41 | — | 12 | 1 | no | — |
| 285 | C3×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 286 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 287 | C2×C3×Q8 | C22×D3 | 1 | 2 | yes | — |
| 288 | C2×C3×D4 | — | 3 | 2 | no | — |
| 289 | C2×C3×D4 | — | 3 | 1 | no | — |
| 290 | C2×C3×D4 | — | 6 | 2 | no | — |
| 291 | C2×C3×D4 | — | 6 | 1 | no | — |
| 292 | C2×#67 | — | 6 | 1 | no | — |
| 293 | C2×#67 | — | 6 | 2 | no | — |
| 294 | C2×#67 | — | 6 | 2 | no | — |
| 295 | C2×#67 | — | 6 | 2 | no | — |
| 296 | C2×#67 | — | 6 | 2 | no | — |
| 297 | #239 | — | 3 | 1 | no | — |
| 298 | #239 | — | 3 | 2 | no | — |
| 299 | #239 | — | 3 | 2 | no | — |
| 300 | #239 | — | 3 | 2 | no | — |
| 301 | #239 | — | 3 | 1 | no | — |
| 302 | #239 | — | 3 | 2 | no | — |
| 303 | #239 | — | 6 | 1 | no | — |
| 304 | #239 | — | 6 | 1 | no | — |
| 305 | #239 | — | 12 | 1 | no | — |
| 306 | #239 | — | 12 | 1 | no | — |
| 307 | #239 | C22×D3 | 1 | 1 | yes | characteristic |
| 308 | #239 | C22×D3 | 1 | 2 | yes | — |
| 309 | D3×Q8 | — | 3 | 1 | no | — |
| 310 | D3×Q8 | — | 3 | 2 | no | — |
| 311 | D3×Q8 | — | 3 | 1 | no | — |
| 312 | D3×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 313 | #237 | — | 3 | 2 | no | — |
| 314 | #237 | — | 3 | 1 | no | — |
| 315 | #237 | — | 3 | 1 | no | — |
| 316 | #237 | — | 3 | 2 | no | — |
| 317 | #237 | — | 6 | 2 | no | — |
| 318 | #237 | — | 6 | 1 | no | — |
| 319 | #237 | — | 6 | 2 | no | — |
| 320 | #237 | — | 6 | 1 | no | — |
| 321 | #237 | S4 | 1 | 1 | yes | characteristic |
| 322 | D3×D4 | — | 3 | 1 | no | — |
| 323 | D3×D4 | — | 3 | 2 | no | — |
| 324 | D3×D4 | — | 3 | 2 | no | — |
| 325 | D3×D4 | — | 3 | 1 | no | — |
| 326 | D3×D4 | — | 3 | 2 | no | — |
| 327 | D3×D4 | — | 3 | 2 | no | — |
| 328 | D3×D4 | — | 3 | 2 | no | — |
| 329 | D3×D4 | — | 3 | 2 | no | — |
| 330 | D3×D4 | — | 3 | 1 | no | — |
| 331 | D3×D4 | — | 4 | 1 | no | — |
| 332 | D3×D4 | — | 6 | 1 | no | — |
| 333 | D3×D4 | — | 6 | 2 | no | — |
| 334 | D3×D4 | — | 6 | 2 | no | — |
| 335 | D3×D4 | — | 6 | 2 | no | — |
| 336 | D3×D4 | — | 6 | 1 | no | — |
| 337 | D3×D4 | — | 6 | 2 | no | — |
| 338 | D3×D4 | — | 6 | 2 | no | — |
| 339 | D3×D4 | — | 6 | 2 | no | — |
| 340 | D3×D4 | — | 6 | 2 | no | — |
| 341 | D3×D4 | — | 6 | 2 | no | — |
| 342 | D3×D4 | — | 6 | 1 | no | — |
| 343 | D3×D4 | — | 6 | 1 | no | — |
| 344 | D3×D4 | — | 6 | 2 | no | — |
| 345 | D3×D4 | — | 6 | 1 | no | — |
| 346 | D3×D4 | — | 12 | 2 | no | — |
| 347 | D3×D4 | — | 12 | 1 | no | — |
| 348 | D3×D4 | — | 12 | 2 | no | — |
| 349 | D3×D4 | — | 24 | 1 | no | — |
| 350 | #235 | — | 3 | 2 | no | — |
| 351 | #235 | — | 3 | 1 | no | — |
| 352 | #235 | — | 3 | 2 | no | — |
| 353 | #235 | — | 3 | 2 | no | — |
| 354 | #235 | — | 3 | 1 | no | — |
| 355 | #235 | — | 3 | 1 | no | — |
| 356 | #235 | — | 6 | 2 | no | — |
| 357 | #235 | — | 6 | 2 | no | — |
| 358 | #235 | — | 6 | 2 | no | — |
| 359 | #235 | — | 6 | 1 | no | — |
| 360 | #235 | — | 6 | 1 | no | — |
| 361 | #235 | — | 12 | 1 | no | — |
| 362 | #235 | — | 12 | 2 | no | — |
| 363 | C2×D12 | — | 3 | 1 | no | — |
| 364 | C2×D12 | — | 3 | 2 | no | — |
| 365 | C2×D12 | — | 3 | 2 | no | — |
| 366 | C2×D12 | — | 3 | 1 | no | — |
| 367 | C2×D12 | — | 6 | 1 | no | — |
| 368 | C2×D12 | — | 6 | 2 | no | — |
| 369 | C2×D12 | — | 6 | 1 | no | — |
| 370 | C2×D12 | — | 12 | 1 | no | — |
| 371 | C2×D12 | — | 12 | 2 | no | — |
| 372 | C2×C4×D3 | — | 3 | 2 | no | — |
| 373 | C2×C4×D3 | — | 3 | 1 | no | — |
| 374 | C2×C4×D3 | — | 6 | 1 | no | — |
| 375 | C2×C4×D3 | — | 6 | 1 | no | — |
| 376 | C2×C4×D3 | — | 6 | 2 | no | — |
| 377 | #41⋊C3 | — | 2 | 1 | no | — |
| 378 | #41⋊C3 | — | 3 | 1 | no | — |
| 379 | #41⋊C3 | — | 3 | 2 | no | — |
| 380 | #41⋊C3 | C22×D3 | 1 | 1 | yes | characteristic, complemented |
| 381 | C2×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 382 | C2×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 383 | C2×SL(2,𝔽3) | C22×D3 | 1 | 2 | yes | complemented |
| 384 | GL(2,𝔽3) | — | 3 | 1 | no | — |
| 385 | GL(2,𝔽3) | — | 3 | 2 | no | — |
| 386 | GL(2,𝔽3) | — | 6 | 1 | no | — |
| 387 | GL(2,𝔽3) | — | 6 | 2 | no | — |
| 388 | GL(2,𝔽3) | C22×D3 | 1 | 2 | yes | complemented |
| 389 | GL(2,𝔽3) | C22×D3 | 1 | 1 | yes | characteristic, complemented |
| 390 | #226 | — | 3 | 1 | no | — |
| 391 | #226 | — | 6 | 1 | no | — |
| 392 | #226 | C22×D3 | 1 | 1 | yes | characteristic, complemented |
| 393 | C3×Q16 | — | 3 | 2 | no | — |
| 394 | C3×Q16 | — | 3 | 1 | no | — |
| 395 | C3×SD16 | — | 3 | 2 | no | — |
| 396 | C3×SD16 | — | 3 | 2 | no | — |
| 397 | C3×SD16 | — | 3 | 2 | no | — |
| 398 | C3×SD16 | — | 3 | 1 | no | — |
| 399 | C3×SD16 | — | 3 | 2 | no | — |
| 400 | C3×SD16 | — | 3 | 1 | no | — |
| 401 | C3×D8 | — | 3 | 2 | no | — |
| 402 | C3×D8 | — | 3 | 1 | no | — |
| 403 | C3×M16 | — | 3 | 2 | no | — |
| 404 | C3×M16 | — | 3 | 1 | no | — |
| 405 | C2×C3×C8 | — | 3 | 2 | no | — |
| 406 | C2×C3×C8 | — | 3 | 1 | no | — |
| 407 | #216 | — | 3 | 2 | no | — |
| 408 | #216 | — | 3 | 1 | no | — |
| 409 | #216 | — | 3 | 1 | no | — |
| 410 | #215 | — | 3 | 2 | no | — |
| 411 | #215 | — | 3 | 2 | no | — |
| 412 | #215 | — | 3 | 2 | no | — |
| 413 | #215 | — | 3 | 2 | no | — |
| 414 | #215 | — | 3 | 1 | no | — |
| 415 | #215 | — | 3 | 2 | no | — |
| 416 | #215 | — | 3 | 1 | no | — |
| 417 | #214 | — | 3 | 1 | no | — |
| 418 | #214 | — | 3 | 1 | no | — |
| 419 | #214 | — | 3 | 2 | no | — |
| 420 | #213 | — | 3 | 1 | no | — |
| 421 | #213 | — | 3 | 2 | no | — |
| 422 | #213 | — | 3 | 2 | no | — |
| 423 | #213 | — | 3 | 2 | no | — |
| 424 | #213 | — | 3 | 2 | no | — |
| 425 | #213 | — | 3 | 2 | no | — |
| 426 | #213 | — | 3 | 1 | no | — |
| 427 | #208 | — | 3 | 2 | no | — |
| 428 | #208 | — | 3 | 1 | no | — |
| 429 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 430 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 431 | Dic12 | — | 3 | 1 | no | — |
| 432 | D24 | — | 3 | 2 | no | — |
| 433 | D24 | — | 3 | 1 | no | — |
| 434 | D24 | — | 3 | 2 | no | — |
| 435 | D24 | — | 3 | 2 | no | — |
| 436 | D24 | — | 3 | 2 | no | — |
| 437 | #204 | — | 3 | 1 | no | — |
| 438 | #204 | — | 3 | 2 | no | — |
| 439 | #204 | — | 3 | 1 | no | — |
| 440 | #204 | — | 3 | 2 | no | — |
| 441 | ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 442 | ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 443 | ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 444 | ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 445 | ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 446 | ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 447 | ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 448 | D3×C8 | — | 3 | 2 | no | — |
| 449 | D3×C8 | — | 3 | 2 | no | — |
| 450 | D3×C8 | — | 3 | 2 | no | — |
| 451 | C22×C32 | — | 4 | 2 | no | — |
| 452 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 453 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 454 | C2×C3⋊D3 | — | 16 | 2 | no | — |
| 455 | C2×C3×D3 | — | 4 | 2 | no | — |
| 456 | C2×C3×D3 | — | 4 | 1 | no | — |
| 457 | C2×C3×D3 | — | 4 | 1 | no | — |
| 458 | C2×C3×D3 | — | 16 | 2 | no | — |
| 459 | D32 | — | 16 | 2 | no | — |
| 460 | C32×C4 | — | 4 | 1 | no | — |
| 461 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 462 | C3×Dic3 | — | 4 | 1 | no | — |
| 463 | C3×Dic3 | — | 4 | 2 | no | — |
| 464 | C3×Dic3 | — | 4 | 1 | no | — |
| 465 | 2−1+4 | — | 3 | 2 | no | — |
| 466 | 2−1+4 | — | 9 | 1 | no | — |
| 467 | 2−1+4 | D32 | 1 | 1 | yes | characteristic, complemented |
| 468 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 469 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 470 | H(5,𝔽2) | — | 9 | 2 | no | — |
| 471 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 472 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 473 | H(5,𝔽2) | — | 9 | 2 | no | — |
| 474 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 475 | H(5,𝔽2) | — | 9 | 2 | no | — |
| 476 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 477 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 478 | H(5,𝔽2) | — | 18 | 2 | no | — |
| 479 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 480 | C2×#41 | — | 3 | 1 | no | — |
| 481 | C2×#41 | — | 3 | 2 | no | — |
| 482 | C2×#41 | — | 9 | 1 | no | — |
| 483 | C2×#41 | — | 9 | 1 | no | — |
| 484 | C2×#41 | — | 9 | 2 | no | — |
| 485 | C2×#41 | — | 9 | 1 | no | — |
| 486 | C2×#41 | — | 9 | 2 | no | — |
| 487 | C2×#41 | — | 18 | 1 | no | — |
| 488 | C22×D4 | — | 9 | 1 | no | — |
| 489 | C22×D4 | — | 9 | 2 | no | — |
| 490 | C22×D4 | — | 18 | 2 | no | — |
| 491 | C22×D4 | — | 18 | 1 | no | — |
| 492 | #137 | — | 3 | 1 | no | — |
| 493 | #137 | — | 3 | 2 | no | — |
| 494 | #137 | — | 9 | 1 | no | — |
| 495 | #137 | — | 9 | 1 | no | — |
| 496 | #137 | — | 9 | 2 | no | — |
| 497 | #137 | — | 9 | 1 | no | — |
| 498 | #137 | — | 9 | 1 | no | — |
| 499 | #137 | — | 9 | 2 | no | — |
| 500 | #137 | — | 9 | 2 | no | — |
| 501 | #137 | — | 9 | 1 | no | — |
| 502 | #137 | — | 9 | 2 | no | — |
| 503 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 504 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 505 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 506 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 507 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 508 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 509 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 510 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 511 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 512 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 513 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 514 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 515 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 516 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 517 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 518 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 519 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 520 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 521 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 522 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 523 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 524 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 525 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 526 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 527 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 528 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 529 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 530 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 531 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 532 | #135 | — | 3 | 2 | no | — |
| 533 | #135 | — | 3 | 1 | no | — |
| 534 | #135 | — | 9 | 1 | no | — |
| 535 | #135 | — | 9 | 2 | no | — |
| 536 | #135 | — | 9 | 2 | no | — |
| 537 | #135 | — | 9 | 2 | no | — |
| 538 | #135 | — | 9 | 2 | no | — |
| 539 | #135 | — | 9 | 2 | no | — |
| 540 | #135 | — | 9 | 2 | no | — |
| 541 | #135 | — | 9 | 2 | no | — |
| 542 | #135 | — | 9 | 1 | no | — |
| 543 | #135 | — | 9 | 2 | no | — |
| 544 | #135 | — | 9 | 2 | no | — |
| 545 | #135 | — | 9 | 1 | no | — |
| 546 | C2×SD16 | — | 3 | 1 | no | — |
| 547 | C2×SD16 | — | 3 | 2 | no | — |
| 548 | C2×SD16 | — | 9 | 2 | no | — |
| 549 | C2×SD16 | — | 9 | 2 | no | — |
| 550 | C2×SD16 | — | 9 | 2 | no | — |
| 551 | C2×SD16 | — | 9 | 1 | no | — |
| 552 | C2×SD16 | — | 9 | 2 | no | — |
| 553 | C2×D8 | — | 9 | 1 | no | — |
| 554 | C2×D8 | — | 9 | 2 | no | — |
| 555 | C2×D8 | — | 9 | 2 | no | — |
| 556 | C2×D8 | — | 9 | 2 | no | — |
| 557 | C2×D8 | — | 9 | 2 | no | — |
| 558 | C2×D8 | — | 9 | 1 | no | — |
| 559 | C2×D8 | — | 9 | 2 | no | — |
| 560 | #131 | — | 3 | 1 | no | — |
| 561 | #131 | — | 9 | 2 | no | — |
| 562 | #131 | — | 9 | 1 | no | — |
| 563 | #131 | — | 9 | 2 | no | — |
| 564 | #131 | — | 9 | 1 | no | — |
| 565 | #131 | — | 9 | 1 | no | — |
| 566 | C2×M16 | — | 9 | 2 | no | — |
| 567 | C2×M16 | — | 9 | 1 | no | — |
| 568 | C2×M16 | — | 9 | 1 | no | — |
| 569 | C2×M16 | — | 9 | 2 | no | — |
| 570 | C23×C3 | — | 6 | 1 | no | — |
| 571 | C23×C3 | — | 6 | 2 | no | — |
| 572 | C22×D3 | — | 3 | 2 | no | — |
| 573 | C22×D3 | — | 3 | 1 | no | — |
| 574 | C22×D3 | — | 4 | 2 | no | — |
| 575 | C22×D3 | — | 6 | 1 | no | — |
| 576 | C22×D3 | — | 6 | 1 | no | — |
| 577 | C22×D3 | — | 6 | 2 | no | — |
| 578 | C22×D3 | — | 6 | 2 | no | — |
| 579 | C22×D3 | — | 6 | 2 | no | — |
| 580 | C22×D3 | — | 6 | 1 | no | — |
| 581 | C22×D3 | — | 6 | 2 | no | — |
| 582 | C22×D3 | — | 6 | 2 | no | — |
| 583 | C22×D3 | — | 12 | 2 | no | — |
| 584 | C22×D3 | — | 12 | 2 | no | — |
| 585 | C22×D3 | — | 24 | 2 | no | — |
| 586 | C22×D3 | — | 24 | 2 | no | — |
| 587 | C22×D3 | — | 24 | 4 | no | — |
| 588 | C3×Q8 | — | 3 | 2 | no | — |
| 589 | C3×Q8 | — | 3 | 1 | no | — |
| 590 | C3×Q8 | — | 3 | 1 | no | — |
| 591 | C3×Q8 | — | 12 | 1 | no | — |
| 592 | C3×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 593 | C3×D4 | — | 3 | 1 | no | — |
| 594 | C3×D4 | — | 3 | 2 | no | — |
| 595 | C3×D4 | — | 3 | 1 | no | — |
| 596 | C3×D4 | — | 3 | 2 | no | — |
| 597 | C3×D4 | — | 4 | 1 | no | — |
| 598 | C3×D4 | — | 6 | 2 | no | — |
| 599 | C3×D4 | — | 6 | 1 | no | — |
| 600 | C3×D4 | — | 6 | 2 | no | — |
| 601 | C3×D4 | — | 6 | 1 | no | — |
| 602 | C3×D4 | — | 8 | 1 | no | — |
| 603 | C3×D4 | — | 12 | 2 | no | — |
| 604 | C3×D4 | C2×S4 | 1 | 1 | yes | characteristic |
| 605 | C2×C3×C4 | — | 3 | 2 | no | — |
| 606 | C2×C3×C4 | — | 3 | 1 | no | — |
| 607 | C2×C3×C4 | — | 6 | 1 | no | — |
| 608 | C2×C3×C4 | — | 6 | 2 | no | — |
| 609 | C2×C3×C4 | — | 6 | 1 | no | — |
| 610 | C2×C3×C4 | — | 12 | 1 | no | — |
| 611 | C2×C3×C4 | — | 12 | 2 | no | — |
| 612 | #67 | — | 3 | 2 | no | — |
| 613 | #67 | — | 3 | 2 | no | — |
| 614 | #67 | — | 4 | 2 | no | — |
| 615 | #67 | — | 6 | 1 | no | — |
| 616 | #67 | — | 6 | 2 | no | — |
| 617 | #67 | — | 6 | 2 | no | — |
| 618 | #67 | — | 6 | 1 | no | — |
| 619 | #67 | — | 6 | 2 | no | — |
| 620 | #67 | — | 6 | 1 | no | — |
| 621 | #67 | — | 6 | 2 | no | — |
| 622 | #67 | — | 6 | 2 | no | — |
| 623 | #67 | — | 6 | 1 | no | — |
| 624 | #67 | — | 6 | 2 | no | — |
| 625 | #67 | — | 12 | 1 | no | — |
| 626 | #67 | — | 12 | 1 | no | — |
| 627 | #67 | — | 12 | 2 | no | — |
| 628 | #67 | — | 24 | 2 | no | — |
| 629 | #67 | C2×S4 | 1 | 2 | yes | — |
| 630 | C2×Dic3 | — | 3 | 1 | no | — |
| 631 | C2×Dic3 | — | 6 | 1 | no | — |
| 632 | C2×Dic3 | — | 6 | 2 | no | — |
| 633 | C2×Dic3 | C2×S4 | 1 | 2 | yes | — |
| 634 | D12 | — | 3 | 1 | no | — |
| 635 | D12 | — | 3 | 2 | no | — |
| 636 | D12 | — | 3 | 2 | no | — |
| 637 | D12 | — | 3 | 1 | no | — |
| 638 | D12 | — | 3 | 2 | no | — |
| 639 | D12 | — | 3 | 1 | no | — |
| 640 | D12 | — | 4 | 1 | no | — |
| 641 | D12 | — | 6 | 2 | no | — |
| 642 | D12 | — | 6 | 2 | no | — |
| 643 | D12 | — | 6 | 2 | no | — |
| 644 | D12 | — | 6 | 1 | no | — |
| 645 | D12 | — | 6 | 1 | no | — |
| 646 | D12 | — | 12 | 1 | no | — |
| 647 | D12 | — | 12 | 1 | no | — |
| 648 | D12 | — | 12 | 2 | no | — |
| 649 | D12 | — | 12 | 2 | no | — |
| 650 | D12 | — | 12 | 2 | no | — |
| 651 | D12 | — | 24 | 1 | no | — |
| 652 | C4×D3 | — | 3 | 1 | no | — |
| 653 | C4×D3 | — | 3 | 1 | no | — |
| 654 | C4×D3 | — | 3 | 2 | no | — |
| 655 | C4×D3 | — | 3 | 1 | no | — |
| 656 | C4×D3 | — | 3 | 2 | no | — |
| 657 | C4×D3 | — | 3 | 2 | no | — |
| 658 | C4×D3 | — | 4 | 1 | no | — |
| 659 | C4×D3 | — | 6 | 2 | no | — |
| 660 | C4×D3 | — | 6 | 1 | no | — |
| 661 | C4×D3 | — | 6 | 2 | no | — |
| 662 | C4×D3 | — | 6 | 1 | no | — |
| 663 | C4×D3 | — | 6 | 1 | no | — |
| 664 | C4×D3 | — | 6 | 2 | no | — |
| 665 | C4×D3 | — | 12 | 2 | no | — |
| 666 | C4×D3 | — | 12 | 1 | no | — |
| 667 | C4×D3 | — | 12 | 2 | no | — |
| 668 | C4×D3 | — | 24 | 1 | no | — |
| 669 | C4×D3 | C2×S4 | 1 | 1 | yes | characteristic |
| 670 | Dic6 | — | 3 | 2 | no | — |
| 671 | Dic6 | — | 3 | 1 | no | — |
| 672 | Dic6 | — | 3 | 1 | no | — |
| 673 | Dic6 | — | 6 | 1 | no | — |
| 674 | Dic6 | — | 12 | 1 | no | — |
| 675 | Dic6 | C2×S4 | 1 | 1 | yes | characteristic |
| 676 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 677 | SL(2,𝔽3) | C23×D3 | 1 | 1 | yes | characteristic |
| 678 | C3×C8 | — | 3 | 1 | no | — |
| 679 | C3×C8 | — | 3 | 2 | no | — |
| 680 | C3×C8 | — | 3 | 1 | no | — |
| 681 | C3⋊C8 | — | 3 | 1 | no | — |
| 682 | C3⋊C8 | — | 3 | 2 | no | — |
| 683 | C3⋊C8 | — | 3 | 1 | no | — |
| 684 | C2×C32 | — | 4 | 1 | no | — |
| 685 | C2×C32 | — | 8 | 2 | no | — |
| 686 | C3⋊D3 | — | 8 | 1 | no | — |
| 687 | C3⋊D3 | — | 8 | 2 | no | — |
| 688 | C3×D3 | — | 8 | 1 | no | — |
| 689 | C3×D3 | — | 8 | 2 | no | — |
| 690 | C3×D3 | — | 8 | 1 | no | — |
| 691 | C24 | — | 18 | 1 | no | — |
| 692 | C24 | — | 18 | 2 | no | — |
| 693 | #41 | — | 3 | 1 | no | — |
| 694 | #41 | — | 3 | 1 | no | — |
| 695 | #41 | — | 3 | 2 | no | — |
| 696 | #41 | — | 3 | 2 | no | — |
| 697 | #41 | — | 3 | 1 | no | — |
| 698 | #41 | — | 3 | 2 | no | — |
| 699 | #41 | — | 3 | 1 | no | — |
| 700 | #41 | — | 6 | 1 | no | — |
| 701 | #41 | — | 9 | 2 | no | — |
| 702 | #41 | — | 9 | 2 | no | — |
| 703 | #41 | — | 9 | 1 | no | — |
| 704 | #41 | — | 9 | 1 | no | — |
| 705 | #41 | — | 9 | 1 | no | — |
| 706 | #41 | — | 9 | 2 | no | — |
| 707 | #41 | — | 9 | 2 | no | — |
| 708 | #41 | — | 9 | 1 | no | — |
| 709 | #41 | — | 9 | 1 | no | — |
| 710 | #41 | — | 9 | 2 | no | — |
| 711 | #41 | — | 9 | 2 | no | — |
| 712 | #41 | — | 9 | 2 | no | — |
| 713 | #41 | — | 9 | 1 | no | — |
| 714 | #41 | — | 9 | 2 | no | — |
| 715 | #41 | — | 9 | 2 | no | — |
| 716 | #41 | — | 9 | 1 | no | — |
| 717 | #41 | — | 18 | 1 | no | — |
| 718 | #41 | — | 18 | 2 | no | — |
| 719 | #41 | — | 18 | 2 | no | — |
| 720 | #41 | — | 18 | 2 | no | — |
| 721 | #41 | — | 18 | 1 | no | — |
| 722 | #41 | — | 18 | 2 | no | — |
| 723 | #41 | — | 18 | 1 | no | — |
| 724 | #41 | — | 18 | 1 | no | — |
| 725 | #41 | — | 18 | 1 | no | — |
| 726 | #41 | — | 18 | 2 | no | — |
| 727 | #41 | — | 18 | 1 | no | — |
| 728 | #41 | C2×D32 | 1 | 1 | yes | characteristic |
| 729 | C2×Q8 | — | 3 | 1 | no | — |
| 730 | C2×Q8 | — | 3 | 1 | no | — |
| 731 | C2×Q8 | — | 9 | 1 | no | — |
| 732 | C2×Q8 | — | 9 | 2 | no | — |
| 733 | C2×Q8 | — | 9 | 1 | no | — |
| 734 | C2×Q8 | C2×D32 | 1 | 2 | yes | — |
| 735 | C2×D4 | — | 3 | 2 | no | — |
| 736 | C2×D4 | — | 3 | 1 | no | — |
| 737 | C2×D4 | — | 6 | 2 | no | — |
| 738 | C2×D4 | — | 6 | 1 | no | — |
| 739 | C2×D4 | — | 9 | 1 | no | — |
| 740 | C2×D4 | — | 9 | 2 | no | — |
| 741 | C2×D4 | — | 9 | 2 | no | — |
| 742 | C2×D4 | — | 9 | 1 | no | — |
| 743 | C2×D4 | — | 9 | 2 | no | — |
| 744 | C2×D4 | — | 9 | 2 | no | — |
| 745 | C2×D4 | — | 9 | 1 | no | — |
| 746 | C2×D4 | — | 9 | 2 | no | — |
| 747 | C2×D4 | — | 9 | 2 | no | — |
| 748 | C2×D4 | — | 9 | 2 | no | — |
| 749 | C2×D4 | — | 9 | 2 | no | — |
| 750 | C2×D4 | — | 9 | 1 | no | — |
| 751 | C2×D4 | — | 9 | 1 | no | — |
| 752 | C2×D4 | — | 18 | 1 | no | — |
| 753 | C2×D4 | — | 18 | 2 | no | — |
| 754 | C2×D4 | — | 18 | 1 | no | — |
| 755 | C2×D4 | — | 18 | 2 | no | — |
| 756 | C2×D4 | — | 18 | 1 | no | — |
| 757 | C2×D4 | — | 18 | 2 | no | — |
| 758 | C2×D4 | — | 18 | 1 | no | — |
| 759 | C2×D4 | — | 18 | 2 | no | — |
| 760 | C2×D4 | — | 18 | 1 | no | — |
| 761 | C2×D4 | — | 18 | 2 | no | — |
| 762 | C2×D4 | — | 18 | 2 | no | — |
| 763 | C2×D4 | — | 18 | 2 | no | — |
| 764 | C2×D4 | — | 18 | 2 | no | — |
| 765 | C2×D4 | — | 18 | 2 | no | — |
| 766 | C2×D4 | — | 18 | 2 | no | — |
| 767 | C2×D4 | — | 18 | 2 | no | — |
| 768 | C2×D4 | — | 18 | 1 | no | — |
| 769 | C2×D4 | — | 18 | 1 | no | — |
| 770 | C2×D4 | — | 18 | 2 | no | — |
| 771 | C2×D4 | — | 18 | 2 | no | — |
| 772 | C2×D4 | — | 18 | 2 | no | — |
| 773 | C2×D4 | — | 18 | 1 | no | — |
| 774 | C22×C4 | — | 9 | 2 | no | — |
| 775 | C22×C4 | — | 9 | 1 | no | — |
| 776 | C22×C4 | — | 18 | 1 | no | — |
| 777 | C22×C4 | — | 18 | 2 | no | — |
| 778 | C22×C4 | — | 18 | 1 | no | — |
| 779 | Q16 | — | 3 | 2 | no | — |
| 780 | Q16 | — | 3 | 1 | no | — |
| 781 | Q16 | — | 9 | 1 | no | — |
| 782 | Q16 | — | 9 | 2 | no | — |
| 783 | Q16 | — | 9 | 1 | no | — |
| 784 | Q16 | — | 9 | 1 | no | — |
| 785 | SD16 | — | 3 | 2 | no | — |
| 786 | SD16 | — | 3 | 2 | no | — |
| 787 | SD16 | — | 3 | 2 | no | — |
| 788 | SD16 | — | 3 | 1 | no | — |
| 789 | SD16 | — | 3 | 1 | no | — |
| 790 | SD16 | — | 3 | 2 | no | — |
| 791 | SD16 | — | 9 | 2 | no | — |
| 792 | SD16 | — | 9 | 1 | no | — |
| 793 | SD16 | — | 9 | 2 | no | — |
| 794 | SD16 | — | 9 | 1 | no | — |
| 795 | SD16 | — | 9 | 2 | no | — |
| 796 | SD16 | — | 9 | 1 | no | — |
| 797 | SD16 | — | 9 | 1 | no | — |
| 798 | SD16 | — | 9 | 2 | no | — |
| 799 | SD16 | — | 9 | 2 | no | — |
| 800 | SD16 | — | 9 | 2 | no | — |
| 801 | SD16 | — | 9 | 2 | no | — |
| 802 | SD16 | — | 9 | 1 | no | — |
| 803 | SD16 | — | 9 | 2 | no | — |
| 804 | SD16 | — | 9 | 1 | no | — |
| 805 | D8 | — | 3 | 2 | no | — |
| 806 | D8 | — | 3 | 1 | no | — |
| 807 | D8 | — | 9 | 1 | no | — |
| 808 | D8 | — | 9 | 2 | no | — |
| 809 | D8 | — | 9 | 2 | no | — |
| 810 | D8 | — | 9 | 2 | no | — |
| 811 | D8 | — | 9 | 2 | no | — |
| 812 | D8 | — | 9 | 2 | no | — |
| 813 | D8 | — | 9 | 1 | no | — |
| 814 | D8 | — | 9 | 2 | no | — |
| 815 | D8 | — | 9 | 2 | no | — |
| 816 | D8 | — | 9 | 2 | no | — |
| 817 | D8 | — | 9 | 1 | no | — |
| 818 | D8 | — | 9 | 2 | no | — |
| 819 | M16 | — | 3 | 2 | no | — |
| 820 | M16 | — | 3 | 1 | no | — |
| 821 | M16 | — | 9 | 1 | no | — |
| 822 | M16 | — | 9 | 2 | no | — |
| 823 | M16 | — | 9 | 1 | no | — |
| 824 | M16 | — | 9 | 2 | no | — |
| 825 | M16 | — | 9 | 1 | no | — |
| 826 | M16 | — | 9 | 2 | no | — |
| 827 | M16 | — | 9 | 1 | no | — |
| 828 | M16 | — | 9 | 2 | no | — |
| 829 | M16 | — | 9 | 1 | no | — |
| 830 | C2×C8 | — | 3 | 2 | no | — |
| 831 | C2×C8 | — | 3 | 1 | no | — |
| 832 | C2×C8 | — | 9 | 2 | no | — |
| 833 | C2×C8 | — | 9 | 2 | no | — |
| 834 | C2×C8 | — | 9 | 2 | no | — |
| 835 | C2×C8 | — | 9 | 2 | no | — |
| 836 | C2×C8 | — | 9 | 1 | no | — |
| 837 | C22×C3 | — | 3 | 1 | no | — |
| 838 | C22×C3 | — | 4 | 2 | no | — |
| 839 | C22×C3 | — | 6 | 1 | no | — |
| 840 | C22×C3 | — | 6 | 2 | no | — |
| 841 | C22×C3 | — | 8 | 2 | no | — |
| 842 | C22×C3 | — | 12 | 1 | no | — |
| 843 | C22×C3 | — | 24 | 2 | no | — |
| 844 | C22×C3 | — | 24 | 1 | no | — |
| 845 | C22×C3 | C22×S4 | 1 | 2 | yes | — |
| 846 | C2×D3 | — | 3 | 1 | no | — |
| 847 | C2×D3 | — | 3 | 2 | no | — |
| 848 | C2×D3 | — | 4 | 1 | no | — |
| 849 | C2×D3 | — | 4 | 2 | no | — |
| 850 | C2×D3 | — | 6 | 1 | no | — |
| 851 | C2×D3 | — | 6 | 2 | no | — |
| 852 | C2×D3 | — | 12 | 2 | no | — |
| 853 | C2×D3 | — | 12 | 1 | no | — |
| 854 | C2×D3 | — | 12 | 1 | no | — |
| 855 | C2×D3 | — | 12 | 2 | no | — |
| 856 | C2×D3 | — | 12 | 2 | no | — |
| 857 | C2×D3 | — | 12 | 4 | no | — |
| 858 | C2×D3 | — | 16 | 2 | no | — |
| 859 | C2×D3 | — | 24 | 1 | no | — |
| 860 | C2×D3 | — | 24 | 2 | no | — |
| 861 | C2×D3 | — | 24 | 2 | no | — |
| 862 | C2×D3 | — | 24 | 1 | no | — |
| 863 | C2×D3 | — | 24 | 2 | no | — |
| 864 | C2×D3 | — | 24 | 2 | no | — |
| 865 | C2×D3 | — | 24 | 2 | no | — |
| 866 | C2×D3 | — | 24 | 1 | no | — |
| 867 | C2×D3 | — | 48 | 2 | no | — |
| 868 | C2×D3 | — | 48 | 2 | no | — |
| 869 | C2×D3 | — | 48 | 4 | no | — |
| 870 | C2×D3 | C22×S4 | 1 | 1 | yes | characteristic |
| 871 | C3×C4 | — | 3 | 1 | no | — |
| 872 | C3×C4 | — | 3 | 2 | no | — |
| 873 | C3×C4 | — | 4 | 1 | no | — |
| 874 | C3×C4 | — | 6 | 1 | no | — |
| 875 | C3×C4 | — | 8 | 1 | no | — |
| 876 | C3×C4 | — | 12 | 1 | no | — |
| 877 | C3×C4 | — | 12 | 2 | no | — |
| 878 | C3×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 879 | Dic3 | — | 3 | 1 | no | — |
| 880 | Dic3 | — | 4 | 1 | no | — |
| 881 | Dic3 | — | 6 | 1 | no | — |
| 882 | Dic3 | — | 12 | 1 | no | — |
| 883 | Dic3 | — | 24 | 1 | no | — |
| 884 | Dic3 | C22×S4 | 1 | 2 | yes | — |
| 885 | Dic3 | C22×S4 | 1 | 1 | yes | characteristic |
| 886 | C32 | — | 4 | 1 | no | Sylow |
| 887 | C23 | — | 6 | 1 | no | — |
| 888 | C23 | — | 6 | 2 | no | — |
| 889 | C23 | — | 9 | 1 | no | — |
| 890 | C23 | — | 9 | 2 | no | — |
| 891 | C23 | — | 18 | 2 | no | — |
| 892 | C23 | — | 18 | 1 | no | — |
| 893 | C23 | — | 18 | 1 | no | — |
| 894 | C23 | — | 18 | 2 | no | — |
| 895 | C23 | — | 18 | 1 | no | — |
| 896 | C23 | — | 18 | 2 | no | — |
| 897 | C23 | — | 18 | 2 | no | — |
| 898 | C23 | — | 18 | 2 | no | — |
| 899 | C23 | — | 72 | 4 | no | — |
| 900 | C23 | — | 72 | 2 | no | — |
| 901 | Q8 | — | 3 | 2 | no | — |
| 902 | Q8 | — | 3 | 1 | no | — |
| 903 | Q8 | — | 3 | 1 | no | — |
| 904 | Q8 | — | 3 | 1 | no | — |
| 905 | Q8 | — | 9 | 2 | no | — |
| 906 | Q8 | — | 9 | 1 | no | — |
| 907 | Q8 | — | 9 | 1 | no | — |
| 908 | Q8 | — | 18 | 1 | no | — |
| 909 | Q8 | C22×D32 | 1 | 1 | yes | characteristic |
| 910 | D4 | — | 3 | 1 | no | — |
| 911 | D4 | — | 3 | 2 | no | — |
| 912 | D4 | — | 3 | 2 | no | — |
| 913 | D4 | — | 3 | 2 | no | — |
| 914 | D4 | — | 3 | 1 | no | — |
| 915 | D4 | — | 6 | 2 | no | — |
| 916 | D4 | — | 6 | 1 | no | — |
| 917 | D4 | — | 6 | 2 | no | — |
| 918 | D4 | — | 6 | 1 | no | — |
| 919 | D4 | — | 9 | 2 | no | — |
| 920 | D4 | — | 9 | 2 | no | — |
| 921 | D4 | — | 9 | 1 | no | — |
| 922 | D4 | — | 9 | 2 | no | — |
| 923 | D4 | — | 9 | 1 | no | — |
| 924 | D4 | — | 9 | 2 | no | — |
| 925 | D4 | — | 9 | 2 | no | — |
| 926 | D4 | — | 9 | 1 | no | — |
| 927 | D4 | — | 18 | 2 | no | — |
| 928 | D4 | — | 18 | 1 | no | — |
| 929 | D4 | — | 18 | 2 | no | — |
| 930 | D4 | — | 18 | 2 | no | — |
| 931 | D4 | — | 18 | 2 | no | — |
| 932 | D4 | — | 18 | 2 | no | — |
| 933 | D4 | — | 18 | 1 | no | — |
| 934 | D4 | — | 18 | 2 | no | — |
| 935 | D4 | — | 18 | 1 | no | — |
| 936 | D4 | — | 18 | 2 | no | — |
| 937 | D4 | — | 18 | 1 | no | — |
| 938 | D4 | — | 18 | 1 | no | — |
| 939 | D4 | — | 18 | 2 | no | — |
| 940 | D4 | — | 18 | 2 | no | — |
| 941 | D4 | — | 18 | 1 | no | — |
| 942 | D4 | D3×S4 | 1 | 1 | yes | characteristic |
| 943 | C2×C4 | — | 3 | 2 | no | — |
| 944 | C2×C4 | — | 3 | 2 | no | — |
| 945 | C2×C4 | — | 3 | 1 | no | — |
| 946 | C2×C4 | — | 3 | 1 | no | — |
| 947 | C2×C4 | — | 6 | 1 | no | — |
| 948 | C2×C4 | — | 6 | 2 | no | — |
| 949 | C2×C4 | — | 6 | 1 | no | — |
| 950 | C2×C4 | — | 9 | 2 | no | — |
| 951 | C2×C4 | — | 9 | 1 | no | — |
| 952 | C2×C4 | — | 9 | 2 | no | — |
| 953 | C2×C4 | — | 9 | 2 | no | — |
| 954 | C2×C4 | — | 9 | 1 | no | — |
| 955 | C2×C4 | — | 9 | 1 | no | — |
| 956 | C2×C4 | — | 9 | 1 | no | — |
| 957 | C2×C4 | — | 18 | 2 | no | — |
| 958 | C2×C4 | — | 18 | 2 | no | — |
| 959 | C2×C4 | — | 18 | 2 | no | — |
| 960 | C2×C4 | — | 18 | 2 | no | — |
| 961 | C2×C4 | — | 18 | 1 | no | — |
| 962 | C2×C4 | — | 18 | 1 | no | — |
| 963 | C2×C4 | — | 18 | 1 | no | — |
| 964 | C2×C4 | — | 18 | 1 | no | — |
| 965 | C8 | — | 3 | 1 | no | — |
| 966 | C8 | — | 3 | 1 | no | — |
| 967 | C8 | — | 3 | 2 | no | — |
| 968 | C8 | — | 9 | 1 | no | — |
| 969 | C8 | — | 9 | 2 | no | — |
| 970 | C8 | — | 9 | 1 | no | — |
| 971 | C2×C3 | — | 2 | 2 | no | — |
| 972 | C2×C3 | — | 4 | 1 | no | — |
| 973 | C2×C3 | — | 6 | 1 | no | — |
| 974 | C2×C3 | — | 8 | 2 | no | — |
| 975 | C2×C3 | — | 8 | 1 | no | — |
| 976 | C2×C3 | — | 12 | 2 | no | — |
| 977 | C2×C3 | — | 12 | 1 | no | — |
| 978 | C2×C3 | — | 16 | 2 | no | — |
| 979 | C2×C3 | — | 24 | 1 | no | — |
| 980 | C2×C3 | C23×S4 | 1 | 1 | yes | characteristic |
| 981 | D3 | — | 2 | 1 | no | — |
| 982 | D3 | — | 6 | 1 | no | — |
| 983 | D3 | — | 6 | 2 | no | — |
| 984 | D3 | — | 8 | 1 | no | — |
| 985 | D3 | — | 8 | 2 | no | — |
| 986 | D3 | — | 12 | 1 | no | — |
| 987 | D3 | — | 12 | 2 | no | — |
| 988 | D3 | — | 24 | 1 | no | — |
| 989 | D3 | — | 24 | 2 | no | — |
| 990 | D3 | — | 24 | 2 | no | — |
| 991 | D3 | — | 48 | 2 | no | — |
| 992 | C22 | — | 3 | 1 | no | — |
| 993 | C22 | — | 3 | 1 | no | — |
| 994 | C22 | — | 6 | 2 | no | — |
| 995 | C22 | — | 6 | 1 | no | — |
| 996 | C22 | — | 9 | 1 | no | — |
| 997 | C22 | — | 9 | 2 | no | — |
| 998 | C22 | — | 18 | 1 | no | — |
| 999 | C22 | — | 18 | 2 | no | — |
| 1000 | C22 | — | 24 | 2 | no | — |
| 1001 | C22 | — | 24 | 1 | no | — |
| 1002 | C22 | — | 36 | 2 | no | — |
| 1003 | C22 | — | 36 | 1 | no | — |
| 1004 | C22 | — | 36 | 2 | no | — |
| 1005 | C22 | — | 36 | 4 | no | — |
| 1006 | C22 | — | 72 | 2 | no | — |
| 1007 | C22 | — | 72 | 2 | no | — |
| 1008 | C22 | — | 72 | 1 | no | — |
| 1009 | C22 | — | 72 | 1 | no | — |
| 1010 | C22 | — | 72 | 2 | no | — |
| 1011 | C22 | — | 72 | 2 | no | — |
| 1012 | C22 | C2×D3×S4 | 1 | 2 | yes | — |
| 1013 | C4 | — | 3 | 1 | no | — |
| 1014 | C4 | — | 3 | 1 | no | — |
| 1015 | C4 | — | 3 | 2 | no | — |
| 1016 | C4 | — | 3 | 2 | no | — |
| 1017 | C4 | — | 6 | 1 | no | — |
| 1018 | C4 | — | 9 | 1 | no | — |
| 1019 | C4 | — | 18 | 1 | no | — |
| 1020 | C4 | C2×D3×S4 | 1 | 1 | yes | characteristic |
| 1021 | C3 | — | 4 | 1 | no | — |
| 1022 | C3 | — | 8 | 1 | no | — |
| 1023 | C3 | #87498 | 1 | 1 | yes | characteristic, complemented |
| 1024 | C2 | — | 2 | 2 | no | — |
| 1025 | C2 | — | 6 | 1 | no | — |
| 1026 | C2 | — | 6 | 1 | no | — |
| 1027 | C2 | — | 12 | 1 | no | — |
| 1028 | C2 | — | 12 | 2 | no | — |
| 1029 | C2 | — | 18 | 1 | no | — |
| 1030 | C2 | — | 18 | 2 | no | — |
| 1031 | C2 | — | 36 | 1 | no | — |
| 1032 | C2 | — | 36 | 2 | no | — |
| 1033 | 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 | C3×2−1+4 | C2×D3 |
| socle | C2×C3 | C23×S4 |
| hypercenter | D4 | D3×S4 |
| LCS | G ▷ C3×SL(2,𝔽3) | |
| UCS | C1 ◁ C2 ◁ D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #5968⋊C3 | C2 | semidirect |
| 2. #10596589 | C2 | semidirect |
| 3. C3×#5926 | C2 | semidirect |
| 4. D3×#986 | C2 | semidirect |
| 5. #10596454 | C2 | semidirect |
| 6. #10596449 | C2 | semidirect |
| 7. #10596448 | C2 | semidirect |
| 8. #10596446 | C2 | semidirect |
| 9. #10596445 | C2 | semidirect |
| 10. C2×#64199 | C2 | semidirect |
| 11. #10596435 | C2 | semidirect |
| 14. C3×2−1+4⋊C3 | C22 | semidirect |
| 16. D3×#41⋊C3 | C22 | semidirect |
| 17. C3⋊#994 | C22 | semidirect |
| 18. #1007⋊C3 | C22 | semidirect |
| 19. C2×C3⋊(#41⋊C3) | C22 | semidirect |
| 20. #64267 | C22 | semidirect |
| 21. #64266 | C22 | semidirect |
| 22. #64264 | C22 | semidirect |
| 23. C2×C3⋊GL(2,𝔽3) | C22 | semidirect |
| 24. C3×#986 | C22 | semidirect |
| 25. C3×#985 | C22 | semidirect |
| 26. C3×#983 | C22 | semidirect |
| 27. C2×C3×GL(2,𝔽3) | C22 | semidirect |
| 28. D3×GL(2,𝔽3) | C22 | semidirect |
| 29. #64202 | C22 | semidirect |
| 30. #64201 | C22 | semidirect |
| 31. #64199 | C22 | semidirect |
| 32. #64199 | C22 | semidirect |
| 33. #64199 | C22 | semidirect |
| 34. #64199 | C22 | semidirect |
| 35. #64198 | C22 | semidirect |
| 36. #64197 | C22 | semidirect |
| 37. #64196 | C22 | semidirect |
| 38. #5968 | D3 | semidirect |
| 45. #5926 | D3 | semidirect |
| 76. C3×#41⋊C3 | C23 | semidirect |
| 77. C2×C3×SL(2,𝔽3) | C23 | semidirect |
| 86. D3×SL(2,𝔽3) | C23 | semidirect |
| 88. C3⋊(#41⋊C3) | C23 | semidirect |
| 89. C3⋊GL(2,𝔽3) | C23 | semidirect |
| 90. C3⋊GL(2,𝔽3) | C23 | semidirect |
| 91. C3⋊#226 | C23 | semidirect |
| 92. C3×GL(2,𝔽3) | C23 | semidirect |
| 93. C3×GL(2,𝔽3) | C23 | semidirect |
| 94. C3×#226 | C23 | semidirect |
| 96. C3×2−1+4 | C2×D3 | semidirect |
| 105. #1009 | C2×D3 | semidirect |
| 111. D3×#41 | C2×D3 | semidirect |
| 113. #1007 | C2×D3 | semidirect |
| 115. C2×#239 | C2×D3 | semidirect |
| 126. 2−1+4⋊C3 | C2×D3 | semidirect |
| 136. #986 | C2×D3 | semidirect |
| 141. #985 | C2×D3 | semidirect |
| 147. #983 | C2×D3 | semidirect |
| 151. C2×GL(2,𝔽3) | C2×D3 | semidirect |
| 380. #41⋊C3 | C22×D3 | semidirect |
| 383. C2×SL(2,𝔽3) | C22×D3 | semidirect |
| 388. GL(2,𝔽3) | C22×D3 | semidirect |
| 389. GL(2,𝔽3) | C22×D3 | semidirect |
| 392. #226 | C22×D3 | semidirect |
| 467. 2−1+4 | D32 | semidirect |
| 1023. C3 | #87498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5968⋊C3 | 2 |
| #10596589 | 2 |
| C3×#5926 | 2 |
| D3×#986 | 2 |
| #10596454 | 2 |
| #10596449 | 2 |
| #10596448 | 2 |
| #10596446 | 2 |
| #10596445 | 2 |
| C2×#64199 | 2 |
| #10596435 | 2 |
| #87498 | 3 |
| #87207 | 3 |
| #64314 | 4 |