Finite Group DatabasebetaFinite Group DatabasebetaOrder 3456.
834 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 41 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 | D3×Ω+(4,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3⋊(#226⋊A4) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×GL(2,𝔽3)⋊A4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11923602 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #983⋊A4 | — | 3 | 1 | no | maximal |
| 6 | #87207⋊C3 | — | 3 | 1 | no | maximal |
| 7 | C3×Ω+(4,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 8 | #64316⋊C3 | — | 4 | 1 | no | maximal |
| 9 | C3×#64201 | — | 4 | 1 | no | maximal |
| 10 | D3×#997 | — | 2 | 1 | no | — |
| 11 | #5968⋊C3 | — | 3 | 1 | no | — |
| 12 | D3×#994 | D3 | 1 | 1 | yes | characteristic, complemented |
| 13 | D3×#994 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 14 | #10596588 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 15 | C3×#5924 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 16 | C2×Ω+(4,𝔽3) | — | 3 | 1 | no | — |
| 17 | #10596456 | — | 3 | 1 | no | — |
| 18 | #10596454 | — | 3 | 1 | no | — |
| 19 | #10596450 | — | 3 | 1 | no | — |
| 20 | #10596449 | — | 3 | 1 | no | — |
| 21 | GL(2,𝔽3)⋊A4 | — | 2 | 1 | no | — |
| 22 | GL(2,𝔽3)⋊A4 | D3 | 1 | 1 | yes | characteristic, complemented |
| 23 | #226⋊A4 | — | 3 | 1 | no | — |
| 24 | #226⋊A4 | — | 6 | 1 | no | — |
| 25 | C3×#577⋊C3 | — | 3 | 1 | no | — |
| 26 | #5837⋊C3 | — | 3 | 1 | no | — |
| 27 | #5835⋊C3 | — | 3 | 1 | no | — |
| 28 | #5752⋊C3 | — | 3 | 1 | no | — |
| 29 | #5750⋊C3 | — | 3 | 1 | no | — |
| 30 | C3⋊(C3⋊(#41⋊C3)) | — | 4 | 1 | no | — |
| 31 | C3×D3×SL(2,𝔽3) | — | 4 | 1 | no | — |
| 32 | C3×D3×SL(2,𝔽3) | — | 4 | 1 | no | — |
| 33 | C3×D3×SL(2,𝔽3) | — | 4 | 1 | no | — |
| 34 | C3×C3⋊#226 | — | 4 | 1 | no | — |
| 35 | C32×GL(2,𝔽3) | — | 4 | 1 | no | — |
| 36 | #87493 | — | 3 | 1 | no | — |
| 37 | #87207 | — | 3 | 1 | no | — |
| 38 | #3585⋊C3 | — | 9 | 1 | no | — |
| 39 | C3×#997 | — | 2 | 1 | no | — |
| 40 | C3×2−1+4⋊C3 | — | 3 | 1 | no | — |
| 41 | C3×#994 | C2×D3 | 1 | 1 | yes | characteristic |
| 42 | C3×#994 | C22×C3 | 1 | 1 | yes | characteristic |
| 43 | #64316 | — | 4 | 1 | no | — |
| 44 | D3×#41⋊C3 | — | 3 | 1 | no | — |
| 45 | D3×#41⋊C3 | — | 3 | 1 | no | — |
| 46 | C3⋊#994 | — | 3 | 1 | no | — |
| 47 | C3⋊#994 | — | 3 | 1 | no | — |
| 48 | C3⋊#994 | — | 3 | 1 | no | — |
| 49 | #1007⋊C3 | — | 6 | 1 | no | — |
| 50 | #1007⋊C3 | — | 12 | 1 | no | — |
| 51 | C2×C3⋊(#41⋊C3) | — | 6 | 1 | no | — |
| 52 | #64267 | — | 3 | 1 | no | — |
| 53 | #64266 | — | 3 | 1 | no | — |
| 54 | C3×#985 | — | 3 | 1 | no | — |
| 55 | C3×#984 | — | 3 | 1 | no | — |
| 56 | C3×#983 | — | 12 | 1 | no | — |
| 57 | Ω+(4,𝔽3) | — | 2 | 1 | no | — |
| 58 | Ω+(4,𝔽3) | — | 2 | 1 | no | — |
| 59 | Ω+(4,𝔽3) | — | 4 | 1 | no | — |
| 60 | Ω+(4,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 61 | #64202 | — | 3 | 1 | no | — |
| 62 | #64201 | A4 | 1 | 1 | yes | characteristic, complemented |
| 63 | #64199 | — | 3 | 1 | no | — |
| 64 | #64198 | — | 3 | 2 | no | — |
| 65 | #64196 | — | 3 | 1 | no | — |
| 66 | C3×#915 | — | 12 | 1 | no | — |
| 67 | C3×#131⋊C3 | — | 3 | 1 | no | — |
| 68 | C3⋊(#131⋊C3) | — | 3 | 1 | no | — |
| 69 | C32×SL(2,𝔽3) | — | 4 | 1 | no | — |
| 70 | C32×SL(2,𝔽3) | — | 4 | 1 | no | — |
| 71 | C3×#625 | — | 16 | 1 | no | — |
| 72 | #5968 | — | 3 | 1 | no | — |
| 73 | D3×H(5,𝔽2) | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 74 | C2×#997 | — | 6 | 1 | no | — |
| 75 | #5945 | — | 9 | 1 | no | — |
| 76 | C2×#994 | — | 3 | 1 | no | — |
| 77 | C2×#994 | — | 3 | 1 | no | — |
| 78 | #5925 | — | 3 | 1 | no | — |
| 79 | #5925 | — | 6 | 1 | no | — |
| 80 | #5925 | — | 9 | 1 | no | — |
| 81 | #5924 | — | 9 | 1 | no | — |
| 82 | #5924 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 83 | #5923 | — | 9 | 1 | no | — |
| 84 | #5923 | — | 9 | 1 | no | — |
| 85 | C3×#577 | — | 3 | 1 | no | — |
| 86 | #5837 | — | 3 | 1 | no | — |
| 87 | #5835 | — | 3 | 1 | no | — |
| 88 | #5778 | — | 9 | 1 | no | — |
| 89 | #5777 | — | 9 | 1 | no | — |
| 90 | #5774 | — | 9 | 1 | no | — |
| 91 | D3×AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 92 | #5769 | — | 9 | 1 | no | — |
| 93 | #5768 | — | 9 | 1 | no | — |
| 94 | #5762 | — | 9 | 1 | no | — |
| 95 | C2×#914 | — | 9 | 1 | no | — |
| 96 | #5752 | — | 3 | 1 | no | — |
| 97 | #5750 | — | 3 | 1 | no | — |
| 98 | #577⋊C3 | — | 3 | 1 | no | — |
| 99 | #577⋊C3 | — | 6 | 1 | no | — |
| 100 | #577⋊C3 | — | 9 | 1 | no | — |
| 101 | #576⋊C3 | — | 9 | 1 | no | — |
| 102 | #576⋊C3 | — | 9 | 1 | no | — |
| 103 | #568⋊C3 | — | 9 | 1 | no | — |
| 104 | C2×D3×A4 | — | 24 | 1 | no | — |
| 105 | #3832 | — | 4 | 1 | no | — |
| 106 | C3×D3×Q8 | — | 4 | 1 | no | — |
| 107 | C3×D3×Q8 | — | 4 | 1 | no | — |
| 108 | C3×D3×Q8 | — | 4 | 1 | no | — |
| 109 | C3×#237 | — | 12 | 1 | no | — |
| 110 | C3×#41⋊C3 | — | 3 | 1 | no | — |
| 111 | C3×#41⋊C3 | — | 3 | 1 | no | — |
| 112 | C2×C3×SL(2,𝔽3) | — | 6 | 1 | no | — |
| 113 | C2×C3×SL(2,𝔽3) | — | 12 | 1 | no | — |
| 114 | C2×C3×SL(2,𝔽3) | — | 12 | 1 | no | — |
| 115 | #3799 | — | 12 | 1 | no | — |
| 116 | #3799 | — | 12 | 1 | no | — |
| 117 | #3798 | — | 12 | 1 | no | — |
| 118 | #3797 | — | 12 | 1 | no | — |
| 119 | D3×SL(2,𝔽3) | — | 4 | 1 | no | — |
| 120 | D3×SL(2,𝔽3) | — | 8 | 1 | no | — |
| 121 | D3×SL(2,𝔽3) | — | 8 | 1 | no | — |
| 122 | D3×SL(2,𝔽3) | — | 8 | 1 | no | — |
| 123 | D3×SL(2,𝔽3) | S4 | 1 | 1 | yes | characteristic |
| 124 | D3×SL(2,𝔽3) | C2×A4 | 1 | 1 | yes | characteristic |
| 125 | C3⋊(#41⋊C3) | — | 3 | 1 | no | — |
| 126 | C3⋊(#41⋊C3) | — | 3 | 1 | no | — |
| 127 | C3⋊(#41⋊C3) | — | 6 | 1 | no | — |
| 128 | C3⋊(#41⋊C3) | — | 12 | 1 | no | — |
| 129 | C3⋊(#41⋊C3) | — | 24 | 1 | no | — |
| 130 | C3⋊GL(2,𝔽3) | — | 3 | 1 | no | — |
| 131 | C3⋊#226 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 132 | C3×GL(2,𝔽3) | — | 4 | 1 | no | — |
| 133 | C3×GL(2,𝔽3) | — | 8 | 1 | no | — |
| 134 | C3×GL(2,𝔽3) | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 135 | C3×#226 | — | 3 | 1 | no | — |
| 136 | C3×#226 | — | 12 | 1 | no | — |
| 137 | C3×#226 | — | 24 | 1 | no | — |
| 138 | C32×SD16 | — | 12 | 1 | no | — |
| 139 | C3×#216 | — | 12 | 1 | no | — |
| 140 | C3×#214 | — | 12 | 1 | no | — |
| 141 | C3×Dic12 | — | 12 | 1 | no | — |
| 142 | C3×ΓL(1,𝔽25) | — | 12 | 1 | no | — |
| 143 | #3585 | — | 9 | 1 | no | Sylow |
| 144 | C2×C32×D3 | — | 16 | 1 | no | — |
| 145 | C2×C32×D3 | — | 16 | 1 | no | — |
| 146 | C3×C3⋊Dic3 | — | 16 | 1 | no | — |
| 147 | C3×2−1+4 | — | 3 | 1 | no | — |
| 148 | C3×H(5,𝔽2) | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 149 | #1009 | — | 3 | 1 | no | — |
| 150 | #1009 | — | 3 | 1 | no | — |
| 151 | #1009 | — | 3 | 1 | no | — |
| 152 | #1009 | — | 9 | 1 | no | — |
| 153 | #1009 | — | 18 | 1 | no | — |
| 154 | D3×#41 | — | 3 | 1 | no | — |
| 155 | D3×#41 | — | 3 | 1 | no | — |
| 156 | D3×#41 | — | 9 | 1 | no | — |
| 157 | D3×#41 | — | 18 | 1 | no | — |
| 158 | #1007 | — | 6 | 1 | no | — |
| 159 | #1007 | — | 9 | 1 | no | — |
| 160 | #1007 | — | 12 | 1 | no | — |
| 161 | C2×#239 | — | 6 | 1 | no | — |
| 162 | C2×#239 | — | 9 | 1 | no | — |
| 163 | #1004 | — | 9 | 1 | no | — |
| 164 | C2×D3×D4 | — | 9 | 1 | no | — |
| 165 | #997 | — | 2 | 1 | no | — |
| 166 | #997 | — | 4 | 1 | no | — |
| 167 | 2−1+4⋊C3 | — | 3 | 1 | no | — |
| 168 | 2−1+4⋊C3 | — | 6 | 1 | no | — |
| 169 | 2−1+4⋊C3 | — | 18 | 1 | no | — |
| 170 | #994 | — | 2 | 1 | no | — |
| 171 | #994 | — | 2 | 1 | no | — |
| 172 | #994 | — | 9 | 1 | no | — |
| 173 | #994 | — | 9 | 1 | no | — |
| 174 | #994 | — | 9 | 1 | no | — |
| 175 | #994 | D32 | 1 | 1 | yes | characteristic |
| 176 | #994 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 177 | C2×#41⋊C3 | — | 9 | 1 | no | — |
| 178 | C2×#41⋊C3 | — | 9 | 1 | no | — |
| 179 | C2×#41⋊C3 | — | 18 | 1 | no | — |
| 180 | #986 | — | 9 | 1 | no | — |
| 181 | #986 | — | 9 | 1 | no | — |
| 182 | #986 | — | 18 | 1 | no | — |
| 183 | #985 | — | 3 | 1 | no | — |
| 184 | #985 | — | 9 | 1 | no | — |
| 185 | #985 | — | 9 | 2 | no | — |
| 186 | #985 | — | 18 | 1 | no | — |
| 187 | #984 | — | 3 | 1 | no | — |
| 188 | #984 | — | 9 | 1 | no | — |
| 189 | #983 | — | 3 | 1 | no | — |
| 190 | #983 | — | 9 | 1 | no | — |
| 191 | C3×#137 | — | 9 | 1 | no | — |
| 192 | C3×#137 | — | 36 | 1 | no | — |
| 193 | C3×AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 194 | C3×#135 | — | 9 | 1 | no | — |
| 195 | C2×C3×SD16 | — | 9 | 1 | no | — |
| 196 | C3×#131 | — | 3 | 1 | no | — |
| 197 | #950 | — | 9 | 1 | no | — |
| 198 | #950 | — | 9 | 1 | no | — |
| 199 | #949 | — | 9 | 1 | no | — |
| 200 | #949 | — | 9 | 1 | no | — |
| 201 | #948 | — | 3 | 1 | no | — |
| 202 | #942 | — | 9 | 1 | no | — |
| 203 | C2×#215 | — | 9 | 1 | no | — |
| 204 | #932 | — | 9 | 1 | no | — |
| 205 | C2×#213 | — | 9 | 1 | no | — |
| 206 | #919 | — | 9 | 2 | no | — |
| 207 | #918 | — | 9 | 1 | no | — |
| 208 | #918 | — | 9 | 1 | no | — |
| 209 | #916 | — | 9 | 2 | no | — |
| 210 | #915 | — | 3 | 1 | no | — |
| 211 | #915 | — | 9 | 1 | no | — |
| 212 | #914 | — | 9 | 1 | no | — |
| 213 | #914 | — | 9 | 1 | no | — |
| 214 | #914 | — | 9 | 2 | no | — |
| 215 | #914 | — | 9 | 2 | no | — |
| 216 | #914 | — | 9 | 2 | no | — |
| 217 | D3×SD16 | — | 9 | 2 | no | — |
| 218 | #911 | — | 9 | 1 | no | — |
| 219 | #911 | — | 9 | 1 | no | — |
| 220 | D3×D8 | — | 9 | 2 | no | — |
| 221 | #908 | — | 9 | 1 | no | — |
| 222 | #908 | — | 9 | 1 | no | — |
| 223 | #907 | — | 9 | 1 | no | — |
| 224 | D3×M16 | — | 9 | 1 | no | — |
| 225 | #904 | — | 9 | 1 | no | — |
| 226 | C2×D24 | — | 9 | 1 | no | — |
| 227 | #901 | — | 9 | 1 | no | — |
| 228 | C2×ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 229 | #131⋊C3 | — | 3 | 1 | no | — |
| 230 | #131⋊C3 | — | 6 | 1 | no | — |
| 231 | #131⋊C3 | — | 9 | 1 | no | — |
| 232 | C2×C3×A4 | — | 24 | 1 | no | — |
| 233 | D3×A4 | — | 24 | 2 | no | — |
| 234 | C32×Q8 | — | 4 | 1 | no | — |
| 235 | C32×Q8 | — | 4 | 1 | no | — |
| 236 | C32×D4 | — | 12 | 1 | no | — |
| 237 | C4⋊(C3⋊D3) | — | 12 | 1 | no | — |
| 238 | C4×C3⋊D3 | — | 12 | 1 | no | — |
| 239 | C3×#67 | — | 24 | 1 | no | — |
| 240 | C3×#67 | — | 48 | 1 | no | — |
| 241 | C2×C3×Dic3 | — | 24 | 1 | no | — |
| 242 | C3×C4×D3 | — | 12 | 1 | no | — |
| 243 | C3×C4×D3 | — | 12 | 1 | no | — |
| 244 | C3×C4×D3 | — | 12 | 1 | no | — |
| 245 | C3×Dic6 | — | 12 | 1 | no | — |
| 246 | C3×Dic6 | — | 12 | 1 | no | — |
| 247 | C3×Dic6 | — | 12 | 1 | no | — |
| 248 | C3×Dic6 | — | 12 | 1 | no | — |
| 249 | C3×SL(2,𝔽3) | — | 4 | 1 | no | — |
| 250 | C3×SL(2,𝔽3) | — | 4 | 1 | no | — |
| 251 | C3×SL(2,𝔽3) | — | 8 | 1 | no | — |
| 252 | C3×SL(2,𝔽3) | — | 8 | 1 | no | — |
| 253 | C3×SL(2,𝔽3) | — | 8 | 1 | no | — |
| 254 | C3×SL(2,𝔽3) | — | 8 | 1 | no | — |
| 255 | C3×SL(2,𝔽3) | — | 8 | 1 | no | — |
| 256 | C3×SL(2,𝔽3) | — | 8 | 1 | no | — |
| 257 | C3×SL(2,𝔽3) | — | 16 | 1 | no | — |
| 258 | C3×SL(2,𝔽3) | — | 16 | 1 | no | — |
| 259 | C3×SL(2,𝔽3) | C2×S4 | 1 | 1 | yes | characteristic |
| 260 | C3×SL(2,𝔽3) | C22×A4 | 1 | 1 | yes | characteristic |
| 261 | #627 | — | 12 | 1 | no | — |
| 262 | #626 | — | 12 | 1 | no | — |
| 263 | #626 | — | 12 | 1 | no | — |
| 264 | #625 | — | 4 | 1 | no | — |
| 265 | #624 | — | 12 | 2 | no | — |
| 266 | C32×C8 | — | 12 | 1 | no | — |
| 267 | C3×C3⋊C8 | — | 12 | 1 | no | — |
| 268 | #585 | — | 9 | 1 | no | — |
| 269 | C2×H(5,𝔽2) | — | 3 | 1 | no | — |
| 270 | #577 | — | 3 | 1 | no | — |
| 271 | #577 | — | 9 | 1 | no | — |
| 272 | #577 | — | 27 | 1 | no | — |
| 273 | #577 | — | 27 | 1 | no | — |
| 274 | #576 | — | 9 | 1 | no | — |
| 275 | #576 | — | 9 | 1 | no | — |
| 276 | #576 | — | 27 | 1 | no | — |
| 277 | #576 | — | 27 | 1 | no | — |
| 278 | #575 | — | 27 | 1 | no | — |
| 279 | #575 | — | 27 | 1 | no | — |
| 280 | C2×AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 281 | C2×AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 282 | #568 | — | 9 | 1 | no | — |
| 283 | C2×C33 | — | 16 | 1 | no | — |
| 284 | C32×D3 | — | 32 | 1 | no | — |
| 285 | C32×D3 | — | 32 | 1 | no | — |
| 286 | C23×D3 | — | 6 | 1 | no | — |
| 287 | C22×A4 | — | 72 | 1 | no | — |
| 288 | C3×#41 | — | 3 | 1 | no | — |
| 289 | C3×#41 | — | 3 | 1 | no | — |
| 290 | C3×#41 | — | 9 | 1 | no | — |
| 291 | C3×#41 | — | 18 | 1 | no | — |
| 292 | C3×#41 | — | 36 | 1 | no | — |
| 293 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 294 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 295 | C2×C3×Q8 | — | 12 | 1 | no | — |
| 296 | C2×C3×Q8 | — | 12 | 1 | no | — |
| 297 | C2×C3×D4 | — | 9 | 1 | no | — |
| 298 | C2×#67 | — | 18 | 1 | no | — |
| 299 | #239 | — | 3 | 1 | no | — |
| 300 | #239 | — | 3 | 1 | no | — |
| 301 | #239 | — | 6 | 1 | no | — |
| 302 | #239 | — | 9 | 1 | no | — |
| 303 | #239 | — | 9 | 2 | no | — |
| 304 | #239 | — | 12 | 1 | no | — |
| 305 | #239 | — | 18 | 1 | no | — |
| 306 | #239 | — | 18 | 1 | no | — |
| 307 | #239 | — | 18 | 1 | no | — |
| 308 | #239 | — | 24 | 1 | no | — |
| 309 | #239 | — | 36 | 1 | no | — |
| 310 | D3×Q8 | — | 4 | 1 | no | — |
| 311 | D3×Q8 | — | 9 | 1 | no | — |
| 312 | D3×Q8 | — | 18 | 1 | no | — |
| 313 | D3×Q8 | — | 36 | 1 | no | — |
| 314 | D3×Q8 | C3×S4 | 1 | 1 | yes | characteristic |
| 315 | D3×Q8 | D3×A4 | 1 | 1 | yes | characteristic |
| 316 | #237 | — | 3 | 1 | no | — |
| 317 | #237 | — | 9 | 1 | no | — |
| 318 | #237 | — | 9 | 1 | no | — |
| 319 | #237 | — | 18 | 1 | no | — |
| 320 | D3×D4 | — | 9 | 1 | no | — |
| 321 | D3×D4 | — | 9 | 1 | no | — |
| 322 | D3×D4 | — | 9 | 2 | no | — |
| 323 | D3×D4 | — | 9 | 1 | no | — |
| 324 | D3×D4 | — | 18 | 1 | no | — |
| 325 | D3×D4 | — | 18 | 1 | no | — |
| 326 | D3×D4 | — | 18 | 2 | no | — |
| 327 | D3×D4 | — | 18 | 1 | no | — |
| 328 | #235 | — | 9 | 1 | no | — |
| 329 | #235 | — | 9 | 1 | no | — |
| 330 | #235 | — | 9 | 1 | no | — |
| 331 | #235 | — | 18 | 1 | no | — |
| 332 | #235 | — | 18 | 1 | no | — |
| 333 | #235 | — | 18 | 2 | no | — |
| 334 | #235 | — | 36 | 1 | no | — |
| 335 | #235 | — | 36 | 1 | no | — |
| 336 | C2×D12 | — | 9 | 1 | no | — |
| 337 | C2×D12 | — | 9 | 1 | no | — |
| 338 | C2×D12 | — | 18 | 1 | no | — |
| 339 | C2×D12 | — | 18 | 1 | no | — |
| 340 | C2×C4×D3 | — | 9 | 1 | no | — |
| 341 | C2×C4×D3 | — | 18 | 1 | no | — |
| 342 | C2×C4×D3 | — | 18 | 1 | no | — |
| 343 | #41⋊C3 | — | 3 | 1 | no | — |
| 344 | #41⋊C3 | — | 3 | 1 | no | — |
| 345 | #41⋊C3 | — | 6 | 1 | no | — |
| 346 | #41⋊C3 | — | 6 | 1 | no | — |
| 347 | #41⋊C3 | — | 9 | 1 | no | — |
| 348 | #41⋊C3 | — | 9 | 1 | no | — |
| 349 | #41⋊C3 | — | 18 | 1 | no | — |
| 350 | C2×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 351 | C2×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 352 | C2×SL(2,𝔽3) | — | 6 | 1 | no | — |
| 353 | C2×SL(2,𝔽3) | — | 12 | 1 | no | — |
| 354 | C2×SL(2,𝔽3) | — | 24 | 1 | no | — |
| 355 | C2×SL(2,𝔽3) | — | 24 | 1 | no | — |
| 356 | GL(2,𝔽3) | — | 9 | 1 | no | — |
| 357 | GL(2,𝔽3) | — | 18 | 1 | no | — |
| 358 | GL(2,𝔽3) | D3×A4 | 1 | 1 | yes | characteristic, complemented |
| 359 | #226 | — | 3 | 1 | no | — |
| 360 | #226 | — | 3 | 1 | no | — |
| 361 | #226 | — | 6 | 1 | no | — |
| 362 | C3×Q16 | — | 9 | 1 | no | — |
| 363 | C3×Q16 | — | 36 | 1 | no | — |
| 364 | C3×Q16 | — | 36 | 1 | no | — |
| 365 | C3×SD16 | — | 3 | 1 | no | — |
| 366 | C3×SD16 | — | 9 | 1 | no | — |
| 367 | C3×SD16 | — | 9 | 2 | no | — |
| 368 | C3×SD16 | — | 12 | 1 | no | — |
| 369 | C3×SD16 | — | 24 | 1 | no | — |
| 370 | C3×SD16 | — | 36 | 1 | no | — |
| 371 | C3×D8 | — | 9 | 1 | no | — |
| 372 | C3×M16 | — | 9 | 1 | no | — |
| 373 | C3×M16 | — | 36 | 1 | no | — |
| 374 | C2×C3×C8 | — | 9 | 1 | no | — |
| 375 | #216 | — | 3 | 1 | no | — |
| 376 | #216 | — | 9 | 1 | no | — |
| 377 | #215 | — | 9 | 1 | no | — |
| 378 | #215 | — | 9 | 2 | no | — |
| 379 | #215 | — | 9 | 1 | no | — |
| 380 | #214 | — | 3 | 1 | no | — |
| 381 | #214 | — | 9 | 1 | no | — |
| 382 | #213 | — | 9 | 1 | no | — |
| 383 | #213 | — | 9 | 1 | no | — |
| 384 | #213 | — | 9 | 2 | no | — |
| 385 | #208 | — | 9 | 1 | no | — |
| 386 | C2×C3⋊C8 | — | 9 | 1 | no | — |
| 387 | Dic12 | — | 3 | 1 | no | — |
| 388 | D24 | — | 9 | 1 | no | — |
| 389 | D24 | — | 9 | 2 | no | — |
| 390 | #204 | — | 9 | 1 | no | — |
| 391 | #204 | — | 9 | 1 | no | — |
| 392 | ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 393 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 394 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 395 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 396 | D3×C8 | — | 9 | 2 | no | — |
| 397 | C22×C32 | — | 24 | 1 | no | — |
| 398 | C22×C32 | — | 48 | 1 | no | — |
| 399 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 400 | C2×C3×D3 | — | 4 | 1 | no | — |
| 401 | C2×C3×D3 | — | 4 | 1 | no | — |
| 402 | C2×C3×D3 | — | 4 | 1 | no | — |
| 403 | C2×C3×D3 | — | 16 | 1 | no | — |
| 404 | C2×C3×D3 | — | 32 | 1 | no | — |
| 405 | C2×C3×D3 | — | 32 | 1 | no | — |
| 406 | C3×A4 | — | 24 | 1 | no | — |
| 407 | C32×C4 | — | 12 | 1 | no | — |
| 408 | C32×C4 | — | 12 | 1 | no | — |
| 409 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 410 | C3×Dic3 | — | 12 | 1 | no | — |
| 411 | C3×Dic3 | — | 12 | 1 | no | — |
| 412 | C3×Dic3 | — | 12 | 1 | no | — |
| 413 | C3×Dic3 | — | 24 | 1 | no | — |
| 414 | C3×Dic3 | — | 48 | 1 | no | — |
| 415 | C3×Dic3 | — | 96 | 1 | no | — |
| 416 | 2−1+4 | — | 3 | 1 | no | — |
| 417 | 2−1+4 | — | 18 | 1 | no | — |
| 418 | 2−1+4 | — | 27 | 1 | no | — |
| 419 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 420 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 421 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 422 | H(5,𝔽2) | — | 27 | 1 | no | — |
| 423 | H(5,𝔽2) | — | 27 | 1 | no | — |
| 424 | H(5,𝔽2) | — | 54 | 1 | no | — |
| 425 | H(5,𝔽2) | C3×D32 | 1 | 1 | yes | characteristic |
| 426 | C2×#41 | — | 9 | 1 | no | — |
| 427 | C2×#41 | — | 9 | 1 | no | — |
| 428 | C2×#41 | — | 18 | 1 | no | — |
| 429 | C2×#41 | — | 27 | 1 | no | — |
| 430 | C2×#41 | — | 27 | 1 | no | — |
| 431 | C2×#41 | — | 54 | 1 | no | — |
| 432 | C22×D4 | — | 27 | 1 | no | — |
| 433 | #137 | — | 9 | 1 | no | — |
| 434 | #137 | — | 9 | 1 | no | — |
| 435 | #137 | — | 27 | 1 | no | — |
| 436 | #137 | — | 27 | 1 | no | — |
| 437 | #137 | — | 27 | 1 | no | — |
| 438 | #137 | — | 27 | 1 | no | — |
| 439 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 440 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 441 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 442 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 443 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 444 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 445 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 446 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 447 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 448 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 449 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 450 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 451 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 452 | #135 | — | 9 | 1 | no | — |
| 453 | #135 | — | 27 | 1 | no | — |
| 454 | #135 | — | 27 | 1 | no | — |
| 455 | #135 | — | 27 | 2 | no | — |
| 456 | #135 | — | 27 | 1 | no | — |
| 457 | #135 | — | 27 | 2 | no | — |
| 458 | C2×SD16 | — | 9 | 1 | no | — |
| 459 | C2×SD16 | — | 27 | 2 | no | — |
| 460 | C2×SD16 | — | 27 | 1 | no | — |
| 461 | C2×D8 | — | 27 | 1 | no | — |
| 462 | C2×D8 | — | 27 | 2 | no | — |
| 463 | C2×D8 | — | 27 | 1 | no | — |
| 464 | #131 | — | 3 | 1 | no | — |
| 465 | #131 | — | 9 | 1 | no | — |
| 466 | #131 | — | 27 | 1 | no | — |
| 467 | #131 | — | 27 | 1 | no | — |
| 468 | C2×M16 | — | 27 | 1 | no | — |
| 469 | C2×M16 | — | 27 | 1 | no | — |
| 470 | C33 | — | 16 | 1 | no | Sylow |
| 471 | C23×C3 | — | 6 | 1 | no | — |
| 472 | C22×D3 | — | 9 | 1 | no | — |
| 473 | C22×D3 | — | 18 | 1 | no | — |
| 474 | C22×D3 | — | 18 | 1 | no | — |
| 475 | C22×D3 | — | 18 | 1 | no | — |
| 476 | C22×D3 | — | 24 | 2 | no | — |
| 477 | C2×A4 | — | 24 | 1 | no | — |
| 478 | C2×A4 | — | 48 | 1 | no | — |
| 479 | C2×A4 | — | 72 | 2 | no | — |
| 480 | C3×Q8 | — | 4 | 1 | no | — |
| 481 | C3×Q8 | — | 4 | 1 | no | — |
| 482 | C3×Q8 | — | 8 | 1 | no | — |
| 483 | C3×Q8 | — | 8 | 1 | no | — |
| 484 | C3×Q8 | — | 9 | 1 | no | — |
| 485 | C3×Q8 | — | 18 | 1 | no | — |
| 486 | C3×Q8 | — | 36 | 1 | no | — |
| 487 | C3×Q8 | — | 36 | 1 | no | — |
| 488 | C3×Q8 | — | 36 | 1 | no | — |
| 489 | C3×Q8 | C2×C3×S4 | 1 | 1 | yes | characteristic |
| 490 | C3×Q8 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 491 | C3×D4 | — | 3 | 1 | no | — |
| 492 | C3×D4 | — | 9 | 1 | no | — |
| 493 | C3×D4 | — | 9 | 1 | no | — |
| 494 | C3×D4 | — | 12 | 1 | no | — |
| 495 | C3×D4 | — | 18 | 1 | no | — |
| 496 | C3×D4 | — | 24 | 1 | no | — |
| 497 | C3×D4 | — | 72 | 1 | no | — |
| 498 | C2×C3×C4 | — | 9 | 1 | no | — |
| 499 | C2×C3×C4 | — | 18 | 1 | no | — |
| 500 | C2×C3×C4 | — | 18 | 1 | no | — |
| 501 | C2×C3×C4 | — | 36 | 1 | no | — |
| 502 | C2×C3×C4 | — | 36 | 1 | no | — |
| 503 | C2×C3×C4 | — | 72 | 1 | no | — |
| 504 | #67 | — | 6 | 1 | no | — |
| 505 | #67 | — | 9 | 2 | no | — |
| 506 | #67 | — | 12 | 1 | no | — |
| 507 | #67 | — | 18 | 1 | no | — |
| 508 | #67 | — | 18 | 1 | no | — |
| 509 | #67 | — | 18 | 1 | no | — |
| 510 | #67 | — | 36 | 1 | no | — |
| 511 | C2×Dic3 | — | 6 | 1 | no | — |
| 512 | C2×Dic3 | — | 9 | 1 | no | — |
| 513 | D12 | — | 9 | 1 | no | — |
| 514 | D12 | — | 9 | 1 | no | — |
| 515 | D12 | — | 9 | 1 | no | — |
| 516 | D12 | — | 18 | 1 | no | — |
| 517 | D12 | — | 18 | 2 | no | — |
| 518 | D12 | — | 18 | 1 | no | — |
| 519 | D12 | — | 36 | 1 | no | — |
| 520 | D12 | — | 36 | 1 | no | — |
| 521 | D12 | — | 72 | 1 | no | — |
| 522 | C4×D3 | — | 3 | 1 | no | — |
| 523 | C4×D3 | — | 3 | 1 | no | — |
| 524 | C4×D3 | — | 9 | 1 | no | — |
| 525 | C4×D3 | — | 9 | 1 | no | — |
| 526 | C4×D3 | — | 12 | 1 | no | — |
| 527 | C4×D3 | — | 18 | 2 | no | — |
| 528 | C4×D3 | — | 18 | 1 | no | — |
| 529 | C4×D3 | — | 18 | 1 | no | — |
| 530 | C4×D3 | — | 18 | 1 | no | — |
| 531 | C4×D3 | — | 36 | 1 | no | — |
| 532 | C4×D3 | — | 36 | 2 | no | — |
| 533 | C4×D3 | — | 72 | 1 | no | — |
| 534 | Dic6 | — | 3 | 1 | no | — |
| 535 | Dic6 | — | 3 | 1 | no | — |
| 536 | Dic6 | — | 3 | 1 | no | — |
| 537 | Dic6 | — | 12 | 1 | no | — |
| 538 | Dic6 | — | 18 | 1 | no | — |
| 539 | Dic6 | — | 36 | 1 | no | — |
| 540 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 541 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 542 | SL(2,𝔽3) | — | 8 | 1 | no | — |
| 543 | SL(2,𝔽3) | — | 8 | 1 | no | — |
| 544 | SL(2,𝔽3) | — | 16 | 1 | no | — |
| 545 | SL(2,𝔽3) | — | 16 | 1 | no | — |
| 546 | SL(2,𝔽3) | D3×S4 | 1 | 1 | yes | characteristic |
| 547 | SL(2,𝔽3) | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 548 | C3×C8 | — | 3 | 1 | no | — |
| 549 | C3×C8 | — | 9 | 1 | no | — |
| 550 | C3×C8 | — | 12 | 1 | no | — |
| 551 | C3×C8 | — | 24 | 1 | no | — |
| 552 | C3×C8 | — | 36 | 1 | no | — |
| 553 | C3⋊C8 | — | 3 | 1 | no | — |
| 554 | C3⋊C8 | — | 9 | 1 | no | — |
| 555 | C2×C32 | — | 4 | 1 | no | — |
| 556 | C2×C32 | — | 4 | 1 | no | — |
| 557 | C2×C32 | — | 16 | 1 | no | — |
| 558 | C2×C32 | — | 32 | 1 | no | — |
| 559 | C2×C32 | — | 32 | 1 | no | — |
| 560 | C2×C32 | — | 32 | 1 | no | — |
| 561 | C2×C32 | — | 48 | 1 | no | — |
| 562 | C2×C32 | — | 64 | 1 | no | — |
| 563 | C2×C32 | — | 96 | 1 | no | — |
| 564 | C3⋊D3 | — | 24 | 1 | no | — |
| 565 | C3×D3 | — | 8 | 1 | no | — |
| 566 | C3×D3 | — | 8 | 1 | no | — |
| 567 | C3×D3 | — | 8 | 1 | no | — |
| 568 | C3×D3 | — | 32 | 2 | no | — |
| 569 | C3×D3 | — | 32 | 1 | no | — |
| 570 | C3×D3 | — | 32 | 2 | no | — |
| 571 | C24 | — | 18 | 1 | no | — |
| 572 | #41 | — | 3 | 1 | no | — |
| 573 | #41 | — | 3 | 1 | no | — |
| 574 | #41 | — | 9 | 1 | no | — |
| 575 | #41 | — | 9 | 1 | no | — |
| 576 | #41 | — | 9 | 1 | no | — |
| 577 | #41 | — | 9 | 1 | no | — |
| 578 | #41 | — | 18 | 1 | no | — |
| 579 | #41 | — | 18 | 1 | no | — |
| 580 | #41 | — | 27 | 1 | no | — |
| 581 | #41 | — | 27 | 1 | no | — |
| 582 | #41 | — | 27 | 1 | no | — |
| 583 | #41 | — | 27 | 1 | no | — |
| 584 | #41 | — | 27 | 1 | no | — |
| 585 | #41 | — | 27 | 1 | no | — |
| 586 | #41 | — | 27 | 2 | no | — |
| 587 | #41 | — | 54 | 1 | no | — |
| 588 | #41 | — | 54 | 1 | no | — |
| 589 | #41 | — | 54 | 1 | no | — |
| 590 | #41 | — | 54 | 2 | no | — |
| 591 | #41 | — | 54 | 1 | no | — |
| 592 | #41 | — | 54 | 1 | no | — |
| 593 | #41 | — | 54 | 1 | no | — |
| 594 | C2×Q8 | — | 3 | 1 | no | — |
| 595 | C2×Q8 | — | 3 | 1 | no | — |
| 596 | C2×Q8 | — | 6 | 1 | no | — |
| 597 | C2×Q8 | — | 9 | 1 | no | — |
| 598 | C2×Q8 | — | 27 | 1 | no | — |
| 599 | C2×Q8 | — | 54 | 1 | no | — |
| 600 | C2×D4 | — | 9 | 1 | no | — |
| 601 | C2×D4 | — | 27 | 1 | no | — |
| 602 | C2×D4 | — | 27 | 1 | no | — |
| 603 | C2×D4 | — | 27 | 1 | no | — |
| 604 | C2×D4 | — | 27 | 1 | no | — |
| 605 | C2×D4 | — | 27 | 1 | no | — |
| 606 | C2×D4 | — | 27 | 2 | no | — |
| 607 | C2×D4 | — | 54 | 1 | no | — |
| 608 | C2×D4 | — | 54 | 1 | no | — |
| 609 | C2×D4 | — | 54 | 1 | no | — |
| 610 | C2×D4 | — | 54 | 1 | no | — |
| 611 | C2×D4 | — | 54 | 1 | no | — |
| 612 | C2×D4 | — | 54 | 1 | no | — |
| 613 | C2×D4 | — | 54 | 2 | no | — |
| 614 | C22×C4 | — | 27 | 1 | no | — |
| 615 | C22×C4 | — | 54 | 1 | no | — |
| 616 | C22×C4 | — | 54 | 1 | no | — |
| 617 | Q16 | — | 9 | 1 | no | — |
| 618 | Q16 | — | 9 | 1 | no | — |
| 619 | Q16 | — | 9 | 1 | no | — |
| 620 | Q16 | — | 27 | 1 | no | — |
| 621 | SD16 | — | 3 | 1 | no | — |
| 622 | SD16 | — | 9 | 1 | no | — |
| 623 | SD16 | — | 9 | 1 | no | — |
| 624 | SD16 | — | 9 | 2 | no | — |
| 625 | SD16 | — | 27 | 1 | no | — |
| 626 | SD16 | — | 27 | 1 | no | — |
| 627 | SD16 | — | 27 | 1 | no | — |
| 628 | SD16 | — | 27 | 1 | no | — |
| 629 | SD16 | — | 27 | 2 | no | — |
| 630 | SD16 | — | 27 | 1 | no | — |
| 631 | D8 | — | 9 | 1 | no | — |
| 632 | D8 | — | 27 | 1 | no | — |
| 633 | D8 | — | 27 | 1 | no | — |
| 634 | D8 | — | 27 | 2 | no | — |
| 635 | D8 | — | 27 | 1 | no | — |
| 636 | D8 | — | 27 | 2 | no | — |
| 637 | M16 | — | 9 | 1 | no | — |
| 638 | M16 | — | 9 | 1 | no | — |
| 639 | M16 | — | 27 | 1 | no | — |
| 640 | M16 | — | 27 | 1 | no | — |
| 641 | M16 | — | 27 | 1 | no | — |
| 642 | M16 | — | 27 | 1 | no | — |
| 643 | C2×C8 | — | 9 | 1 | no | — |
| 644 | C2×C8 | — | 27 | 1 | no | — |
| 645 | C2×C8 | — | 27 | 2 | no | — |
| 646 | C22×C3 | — | 6 | 1 | no | — |
| 647 | C22×C3 | — | 9 | 1 | no | — |
| 648 | C22×C3 | — | 12 | 1 | no | — |
| 649 | C22×C3 | — | 12 | 1 | no | — |
| 650 | C22×C3 | — | 24 | 1 | no | — |
| 651 | C22×C3 | — | 24 | 1 | no | — |
| 652 | C22×C3 | — | 48 | 1 | no | — |
| 653 | C22×C3 | — | 96 | 1 | no | — |
| 654 | C2×D3 | — | 4 | 1 | no | — |
| 655 | C2×D3 | — | 9 | 1 | no | — |
| 656 | C2×D3 | — | 18 | 1 | no | — |
| 657 | C2×D3 | — | 36 | 1 | no | — |
| 658 | C2×D3 | — | 36 | 1 | no | — |
| 659 | C2×D3 | — | 72 | 1 | no | — |
| 660 | C2×D3 | — | 72 | 1 | no | — |
| 661 | C2×D3 | — | 72 | 1 | no | — |
| 662 | C2×D3 | — | 72 | 1 | no | — |
| 663 | C2×D3 | A4×S4 | 1 | 1 | yes | characteristic |
| 664 | A4 | — | 24 | 1 | no | — |
| 665 | A4 | — | 48 | 1 | no | — |
| 666 | C3×C4 | — | 3 | 1 | no | — |
| 667 | C3×C4 | — | 3 | 1 | no | — |
| 668 | C3×C4 | — | 12 | 1 | no | — |
| 669 | C3×C4 | — | 12 | 1 | no | — |
| 670 | C3×C4 | — | 18 | 1 | no | — |
| 671 | C3×C4 | — | 24 | 1 | no | — |
| 672 | C3×C4 | — | 24 | 1 | no | — |
| 673 | C3×C4 | — | 36 | 1 | no | — |
| 674 | C3×C4 | — | 36 | 1 | no | — |
| 675 | C3×C4 | — | 72 | 1 | no | — |
| 676 | Dic3 | — | 3 | 1 | no | — |
| 677 | Dic3 | — | 3 | 1 | no | — |
| 678 | Dic3 | — | 6 | 1 | no | — |
| 679 | Dic3 | — | 12 | 1 | no | — |
| 680 | Dic3 | — | 12 | 1 | no | — |
| 681 | Dic3 | — | 24 | 1 | no | — |
| 682 | C32 | — | 4 | 1 | no | — |
| 683 | C32 | — | 4 | 1 | no | — |
| 684 | C32 | — | 16 | 1 | no | — |
| 685 | C32 | — | 32 | 1 | no | — |
| 686 | C32 | — | 32 | 1 | no | — |
| 687 | C32 | — | 32 | 1 | no | — |
| 688 | C32 | — | 64 | 1 | no | — |
| 689 | C23 | — | 6 | 1 | no | — |
| 690 | C23 | — | 27 | 1 | no | — |
| 691 | C23 | — | 54 | 1 | no | — |
| 692 | C23 | — | 54 | 1 | no | — |
| 693 | C23 | — | 54 | 1 | no | — |
| 694 | C23 | — | 72 | 2 | no | — |
| 695 | Q8 | — | 9 | 1 | no | — |
| 696 | Q8 | — | 9 | 1 | no | — |
| 697 | Q8 | — | 9 | 1 | no | — |
| 698 | Q8 | — | 9 | 1 | no | — |
| 699 | Q8 | — | 18 | 1 | no | — |
| 700 | Q8 | — | 54 | 1 | no | — |
| 701 | Q8 | C3×D3×S4 | 1 | 1 | yes | characteristic |
| 702 | Q8 | D32×A4 | 1 | 1 | yes | characteristic |
| 703 | D4 | — | 3 | 1 | no | — |
| 704 | D4 | — | 9 | 1 | no | — |
| 705 | D4 | — | 9 | 1 | no | — |
| 706 | D4 | — | 18 | 1 | no | — |
| 707 | D4 | — | 18 | 1 | no | — |
| 708 | D4 | — | 27 | 1 | no | — |
| 709 | D4 | — | 27 | 1 | no | — |
| 710 | D4 | — | 27 | 1 | no | — |
| 711 | D4 | — | 27 | 2 | no | — |
| 712 | D4 | — | 54 | 1 | no | — |
| 713 | D4 | — | 54 | 1 | no | — |
| 714 | D4 | — | 54 | 1 | no | — |
| 715 | D4 | — | 54 | 1 | no | — |
| 716 | D4 | — | 54 | 1 | no | — |
| 717 | D4 | — | 54 | 2 | no | — |
| 718 | C2×C4 | — | 9 | 1 | no | — |
| 719 | C2×C4 | — | 9 | 1 | no | — |
| 720 | C2×C4 | — | 9 | 1 | no | — |
| 721 | C2×C4 | — | 18 | 1 | no | — |
| 722 | C2×C4 | — | 18 | 1 | no | — |
| 723 | C2×C4 | — | 18 | 1 | no | — |
| 724 | C2×C4 | — | 27 | 1 | no | — |
| 725 | C2×C4 | — | 27 | 1 | no | — |
| 726 | C2×C4 | — | 27 | 1 | no | — |
| 727 | C2×C4 | — | 54 | 1 | no | — |
| 728 | C2×C4 | — | 54 | 1 | no | — |
| 729 | C2×C4 | — | 54 | 2 | no | — |
| 730 | C2×C4 | — | 54 | 1 | no | — |
| 731 | C8 | — | 3 | 1 | no | — |
| 732 | C8 | — | 9 | 1 | no | — |
| 733 | C8 | — | 9 | 1 | no | — |
| 734 | C8 | — | 27 | 1 | no | — |
| 735 | C2×C3 | — | 4 | 1 | no | — |
| 736 | C2×C3 | — | 4 | 1 | no | — |
| 737 | C2×C3 | — | 8 | 1 | no | — |
| 738 | C2×C3 | — | 8 | 1 | no | — |
| 739 | C2×C3 | — | 12 | 1 | no | — |
| 740 | C2×C3 | — | 18 | 1 | no | — |
| 741 | C2×C3 | — | 24 | 1 | no | — |
| 742 | C2×C3 | — | 24 | 1 | no | — |
| 743 | C2×C3 | — | 32 | 1 | no | — |
| 744 | C2×C3 | — | 48 | 1 | no | — |
| 745 | C2×C3 | — | 64 | 1 | no | — |
| 746 | C2×C3 | — | 96 | 2 | no | — |
| 747 | C2×C3 | — | 96 | 1 | no | — |
| 748 | C2×C3 | C2×A4×S4 | 1 | 1 | yes | characteristic |
| 749 | D3 | — | 2 | 1 | no | — |
| 750 | D3 | — | 8 | 1 | no | — |
| 751 | D3 | — | 18 | 1 | no | — |
| 752 | D3 | — | 36 | 1 | no | — |
| 753 | D3 | — | 72 | 1 | no | — |
| 754 | D3 | — | 144 | 1 | no | — |
| 755 | C22 | — | 3 | 1 | no | — |
| 756 | C22 | — | 6 | 1 | no | — |
| 757 | C22 | — | 9 | 1 | no | — |
| 758 | C22 | — | 24 | 1 | no | — |
| 759 | C22 | — | 27 | 1 | no | — |
| 760 | C22 | — | 54 | 1 | no | — |
| 761 | C22 | — | 108 | 1 | no | — |
| 762 | C22 | — | 216 | 1 | no | — |
| 763 | C22 | — | 216 | 1 | no | — |
| 764 | C22 | — | 216 | 1 | no | — |
| 765 | C4 | — | 3 | 1 | no | — |
| 766 | C4 | — | 3 | 1 | no | — |
| 767 | C4 | — | 9 | 1 | no | — |
| 768 | C4 | — | 9 | 1 | no | — |
| 769 | C4 | — | 18 | 1 | no | — |
| 770 | C4 | — | 18 | 1 | no | — |
| 771 | C3 | — | 4 | 1 | no | — |
| 772 | C3 | — | 4 | 1 | no | — |
| 773 | C3 | — | 8 | 1 | no | — |
| 774 | C3 | — | 8 | 1 | no | — |
| 775 | C3 | — | 32 | 1 | no | — |
| 776 | C3 | — | 64 | 1 | no | — |
| 777 | C3 | #983⋊A4 | 1 | 1 | yes | characteristic, complemented |
| 778 | C2 | — | 6 | 1 | no | — |
| 779 | C2 | — | 12 | 1 | no | — |
| 780 | C2 | — | 18 | 1 | no | — |
| 781 | C2 | — | 54 | 1 | no | — |
| 782 | C2 | — | 108 | 1 | no | — |
| 783 | C2 | D3×A4×S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×A4×S4 |
| commutator, cosocle, hypocenter | C3×#994 | C22×C3 |
| Fitting | C3×H(5,𝔽2) | C2×C3×D3 |
| socle | C2×C3 | C2×A4×S4 |
| LCS | G ▷ C3×#994 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D3×Ω+(4,𝔽3) | C2 | semidirect |
| 2. C3⋊(#226⋊A4) | C2 | semidirect |
| 3. C3×GL(2,𝔽3)⋊A4 | C2 | semidirect |
| 4. #11923602 | C3 | semidirect |
| 7. C3×Ω+(4,𝔽3) | C22 | semidirect |
| 12. D3×#994 | D3 | semidirect |
| 13. D3×#994 | C2×C3 | semidirect |
| 14. #10596588 | C2×C3 | semidirect |
| 15. C3×#5924 | C2×C3 | semidirect |
| 22. GL(2,𝔽3)⋊A4 | D3 | semidirect |
| 60. Ω+(4,𝔽3) | C2×D3 | semidirect |
| 62. #64201 | A4 | semidirect |
| 73. D3×H(5,𝔽2) | C3×D3 | semidirect |
| 82. #5924 | C3×D3 | semidirect |
| 131. C3⋊#226 | C2×A4 | semidirect |
| 134. C3×GL(2,𝔽3) | C2×A4 | semidirect |
| 358. GL(2,𝔽3) | D3×A4 | semidirect |
| 777. C3 | #983⋊A4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×Ω+(4,𝔽3) | 2 |
| C3⋊(#226⋊A4) | 2 |
| C3×GL(2,𝔽3)⋊A4 | 2 |
| #11923602 | 3 |
| #983⋊A4 | 3 |
| #87207⋊C3 | 3 |
| #64316⋊C3 | 4 |
| C3×#64201 | 4 |