Finite Group DatabasebetaFinite Group DatabasebetaOrder 6912.
828 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 48 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 | #72220467 | — | 3 | 1 | no | maximal |
| 2 | C4×(PSU(3,𝔽2)⋊C3)⋊C4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72220138 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | M16×PSU(3,𝔽2)⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×C4×PSU(3,𝔽2)⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 6 | #13180131 | — | 2 | 1 | no | — |
| 7 | C2×(PSU(3,𝔽2)⋊C3)⋊C4 | — | 2 | 1 | no | — |
| 8 | C4⋊AGL(2,𝔽3) | C4 | 1 | 1 | yes | characteristic, complemented |
| 9 | C4×AGL(2,𝔽3) | — | 2 | 1 | no | — |
| 10 | (PSU(3,𝔽2)⋊C3)⋊Q8 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | C8×PSU(3,𝔽2)⋊C3 | — | 2 | 1 | no | — |
| 12 | #13139205 | — | 4 | 1 | no | maximal |
| 13 | #11870763 | — | 3 | 1 | no | — |
| 14 | M16×PSU(3,𝔽2) | D3 | 1 | 1 | yes | characteristic, complemented |
| 15 | #11791414 | — | 3 | 1 | no | — |
| 16 | C4×PSU(3,𝔽2)⋊C4 | — | 3 | 1 | no | — |
| 17 | #11774754 | — | 3 | 1 | no | — |
| 18 | #11771214 | — | 3 | 1 | no | — |
| 19 | #11770776 | — | 3 | 1 | no | — |
| 20 | C22×PSU(3,𝔽2)⋊C3 | D4 | 1 | 1 | yes | characteristic |
| 21 | C2×AGL(2,𝔽3) | — | 2 | 1 | no | — |
| 22 | C4×PSU(3,𝔽2)⋊C3 | C2×C4 | 1 | 1 | yes | characteristic |
| 23 | C4×PSU(3,𝔽2)⋊C3 | D4 | 1 | 1 | yes | characteristic |
| 24 | (PSU(3,𝔽2)⋊C3)⋊C4 | — | 2 | 2 | no | — |
| 25 | (PSU(3,𝔽2)⋊C3)⋊C4 | — | 2 | 1 | no | — |
| 26 | #11722490 | — | 4 | 1 | no | — |
| 27 | M16×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 28 | C4×((C3⋊D3)⋊C3)⋊C4 | — | 4 | 1 | no | — |
| 29 | #11720562 | — | 4 | 1 | no | — |
| 30 | #63652⋊C3 | — | 4 | 1 | no | — |
| 31 | #11720328 | — | 4 | 1 | no | — |
| 32 | #11720305 | — | 4 | 1 | no | — |
| 33 | #11711123 | — | 9 | 1 | no | maximal |
| 34 | C2×C4×PSU(3,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 35 | #10596511 | — | 3 | 1 | no | — |
| 36 | #10596484 | — | 3 | 1 | no | — |
| 37 | C2×C4×AGL(1,𝔽9) | — | 3 | 1 | no | — |
| 38 | #10596418 | — | 6 | 1 | no | — |
| 39 | C2×PSU(3,𝔽2)⋊C4 | — | 6 | 1 | no | — |
| 40 | #10596412 | — | 6 | 1 | no | — |
| 41 | #10596410 | — | 3 | 1 | no | — |
| 42 | #10596410 | — | 3 | 1 | no | — |
| 43 | C4×AΓL(1,𝔽9) | — | 6 | 1 | no | — |
| 44 | C4×AΓL(1,𝔽9) | — | 6 | 1 | no | — |
| 45 | PSU(3,𝔽2)⋊Q8 | — | 3 | 1 | no | — |
| 46 | PSU(3,𝔽2)⋊Q8 | — | 3 | 1 | no | — |
| 47 | M16×#157 | — | 3 | 1 | no | — |
| 48 | #10593539 | — | 3 | 1 | no | — |
| 49 | #10593532 | — | 6 | 1 | no | — |
| 50 | C8×PSU(3,𝔽2) | — | 2 | 1 | no | — |
| 51 | C4×#3773 | — | 3 | 1 | no | — |
| 52 | #10593380 | — | 6 | 1 | no | — |
| 53 | #10593166 | — | 6 | 1 | no | — |
| 54 | GO+(4,𝔽2)⋊C8 | — | 6 | 2 | no | — |
| 55 | #10591008 | — | 6 | 1 | no | — |
| 56 | D3×#825 | — | 12 | 1 | no | — |
| 57 | C2×PSU(3,𝔽2)⋊C3 | — | 2 | 1 | no | — |
| 58 | C2×PSU(3,𝔽2)⋊C3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 59 | AGL(2,𝔽3) | — | 4 | 1 | no | — |
| 60 | #88740 | — | 4 | 1 | no | — |
| 61 | #3828⋊C3 | — | 4 | 1 | no | — |
| 62 | C2×C4×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 63 | #88676 | — | 8 | 1 | no | — |
| 64 | #88671 | — | 8 | 1 | no | — |
| 65 | C2×((C3⋊D3)⋊C3)⋊C4 | — | 8 | 1 | no | — |
| 66 | #88654 | — | 4 | 1 | no | — |
| 67 | C4×((C3⋊D3)⋊C3)⋊C2 | — | 8 | 1 | no | — |
| 68 | #88652 | — | 4 | 1 | no | — |
| 69 | #88650 | — | 8 | 1 | no | — |
| 70 | #88648 | — | 4 | 1 | no | — |
| 71 | ((C3⋊D3)⋊C3)⋊Q8 | — | 4 | 1 | no | — |
| 72 | M16×H(3,𝔽3) | — | 4 | 1 | no | — |
| 73 | C4×#1084 | — | 4 | 1 | no | — |
| 74 | C4×(C3⋊Dic3)⋊C3 | — | 4 | 1 | no | — |
| 75 | #3748⋊C3 | — | 4 | 1 | no | — |
| 76 | #3743⋊C3 | — | 8 | 1 | no | — |
| 77 | C8×(C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 78 | #88447 | — | 8 | 1 | no | — |
| 79 | #85325 | — | 9 | 1 | no | — |
| 80 | M16×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 81 | C4×#859 | — | 9 | 1 | no | — |
| 82 | C22×PSU(3,𝔽2) | D12 | 1 | 1 | yes | characteristic |
| 83 | C22×AGL(1,𝔽9) | — | 6 | 1 | no | — |
| 84 | C2×AΓL(1,𝔽9) | — | 6 | 1 | no | — |
| 85 | C2×AΓL(1,𝔽9) | — | 6 | 1 | no | — |
| 86 | #64306 | — | 6 | 1 | no | — |
| 87 | D3×#235 | — | 12 | 1 | no | — |
| 88 | C2×C4×#157 | — | 3 | 1 | no | — |
| 89 | #64283 | — | 3 | 1 | no | — |
| 90 | C2×#3777 | — | 3 | 1 | no | — |
| 91 | C4×PSU(3,𝔽2) | — | 3 | 1 | no | — |
| 92 | C4×PSU(3,𝔽2) | — | 3 | 1 | no | — |
| 93 | C4×PSU(3,𝔽2) | C4×D3 | 1 | 1 | yes | characteristic |
| 94 | C4×PSU(3,𝔽2) | #67 | 1 | 1 | yes | characteristic |
| 95 | #64242 | — | 6 | 1 | no | — |
| 96 | #64242 | — | 6 | 1 | no | — |
| 97 | C2×#3773 | — | 6 | 1 | no | — |
| 98 | #64231 | — | 3 | 1 | no | — |
| 99 | C4×GO+(4,𝔽2) | — | 6 | 1 | no | — |
| 100 | C4×GO+(4,𝔽2) | — | 6 | 1 | no | — |
| 101 | #64222 | — | 3 | 1 | no | — |
| 102 | #64221 | — | 6 | 1 | no | — |
| 103 | C22⋊AGL(1,𝔽9) | — | 6 | 1 | no | — |
| 104 | C4⋊AGL(1,𝔽9) | — | 3 | 1 | no | — |
| 105 | C4⋊AGL(1,𝔽9) | — | 3 | 1 | no | — |
| 106 | C4×AGL(1,𝔽9) | — | 6 | 1 | no | — |
| 107 | C4×AGL(1,𝔽9) | — | 6 | 1 | no | — |
| 108 | C4×AGL(1,𝔽9) | — | 6 | 1 | no | — |
| 109 | AGL(1,𝔽9)⋊C4 | — | 6 | 1 | no | — |
| 110 | AGL(1,𝔽9)⋊C4 | — | 6 | 1 | no | — |
| 111 | PSU(3,𝔽2)⋊C4 | — | 6 | 2 | no | — |
| 112 | PSU(3,𝔽2)⋊C4 | — | 6 | 1 | no | — |
| 113 | PSU(3,𝔽2)⋊C4 | — | 6 | 2 | no | — |
| 114 | PSU(3,𝔽2)⋊C4 | — | 6 | 1 | no | — |
| 115 | GO+(4,𝔽2)⋊C4 | — | 6 | 1 | no | — |
| 116 | GO+(4,𝔽2)⋊C4 | — | 6 | 1 | no | — |
| 117 | M16×C3⋊D3 | S4 | 1 | 1 | yes | characteristic |
| 118 | C3×D3×M16 | — | 12 | 1 | no | — |
| 119 | C4×#624 | — | 6 | 1 | no | — |
| 120 | C4×D3×Dic3 | — | 12 | 1 | no | — |
| 121 | #63767 | — | 6 | 1 | no | — |
| 122 | C8×#157 | — | 6 | 1 | no | — |
| 123 | #63744 | — | 3 | 2 | no | — |
| 124 | #63744 | — | 6 | 1 | no | — |
| 125 | #63741 | — | 12 | 2 | no | — |
| 126 | #63737 | — | 6 | 1 | no | — |
| 127 | #63652 | — | 4 | 1 | no | — |
| 128 | C3×#825 | — | 12 | 1 | no | — |
| 129 | C3×#825 | — | 12 | 1 | no | — |
| 130 | C3×#825 | — | 24 | 1 | no | — |
| 131 | #63570 | — | 12 | 1 | no | — |
| 132 | #63569 | — | 12 | 1 | no | — |
| 133 | #63568 | — | 12 | 1 | no | — |
| 134 | #8992 | — | 27 | 1 | no | Sylow |
| 135 | PSU(3,𝔽2)⋊C3 | #104 | 1 | 1 | yes | characteristic, complemented |
| 136 | C22×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 137 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 8 | 1 | no | — |
| 138 | C2×C4×H(3,𝔽3) | — | 4 | 1 | no | — |
| 139 | #6235 | — | 8 | 1 | no | — |
| 140 | C2×#1084 | — | 8 | 1 | no | — |
| 141 | C4⋊#272 | — | 4 | 1 | no | — |
| 142 | C4×#272 | — | 8 | 1 | no | — |
| 143 | #6229 | — | 4 | 1 | no | — |
| 144 | #638⋊C3 | — | 8 | 1 | no | — |
| 145 | C2×(C3⋊Dic3)⋊C3 | — | 4 | 1 | no | — |
| 146 | C2×(C3⋊Dic3)⋊C3 | — | 8 | 1 | no | — |
| 147 | C4⋊((C3⋊D3)⋊C3) | — | 4 | 1 | no | — |
| 148 | C4×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 149 | C4×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 150 | C4×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 151 | C4×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 152 | C4×(C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 153 | #634⋊C3 | — | 4 | 1 | no | — |
| 154 | #6200 | — | 8 | 1 | no | — |
| 155 | #6200 | — | 8 | 1 | no | — |
| 156 | #6199 | — | 8 | 1 | no | — |
| 157 | #6198 | — | 8 | 1 | no | — |
| 158 | ((C3⋊D3)⋊C3)⋊C4 | — | 8 | 1 | no | — |
| 159 | ((C3⋊D3)⋊C3)⋊C4 | — | 8 | 1 | no | — |
| 160 | ((C3⋊D3)⋊C3)⋊C4 | — | 8 | 2 | no | — |
| 161 | ((C3⋊D3)⋊C3)⋊C4 | — | 8 | 2 | no | — |
| 162 | #6196 | — | 8 | 1 | no | — |
| 163 | C8×H(3,𝔽3) | — | 8 | 1 | no | — |
| 164 | (C3⋊(C3⋊C8))⋊C3 | — | 8 | 1 | no | — |
| 165 | C2×C4×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 166 | #5421 | — | 18 | 1 | no | — |
| 167 | C2×#859 | — | 18 | 1 | no | — |
| 168 | C4⋊GL(2,𝔽3) | — | 9 | 1 | no | — |
| 169 | C4×GL(2,𝔽3) | — | 18 | 1 | no | — |
| 170 | #5386 | — | 9 | 1 | no | — |
| 171 | C2×#825 | — | 36 | 1 | no | — |
| 172 | D3×#104 | — | 36 | 1 | no | — |
| 173 | C8×SL(2,𝔽3) | — | 18 | 1 | no | — |
| 174 | C22×#157 | — | 3 | 1 | no | — |
| 175 | C22×#157 | — | 3 | 1 | no | — |
| 176 | C2×PSU(3,𝔽2) | — | 2 | 1 | no | — |
| 177 | C2×PSU(3,𝔽2) | — | 3 | 1 | no | — |
| 178 | C2×PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 179 | C2×PSU(3,𝔽2) | (C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 180 | C2×GO+(4,𝔽2) | — | 6 | 1 | no | — |
| 181 | C2×GO+(4,𝔽2) | — | 6 | 1 | no | — |
| 182 | C2×AGL(1,𝔽9) | — | 6 | 1 | no | — |
| 183 | C2×AGL(1,𝔽9) | — | 6 | 1 | no | — |
| 184 | C2×AGL(1,𝔽9) | — | 6 | 2 | no | — |
| 185 | C2×AGL(1,𝔽9) | — | 12 | 1 | no | — |
| 186 | C2×AGL(1,𝔽9) | — | 12 | 1 | no | — |
| 187 | AΓL(1,𝔽9) | — | 12 | 1 | no | — |
| 188 | AΓL(1,𝔽9) | — | 12 | 2 | no | — |
| 189 | AΓL(1,𝔽9) | — | 12 | 1 | no | — |
| 190 | #3828 | — | 4 | 1 | no | — |
| 191 | C2×C4×C3⋊D3 | C2×S4 | 1 | 1 | yes | characteristic |
| 192 | C3×#235 | — | 12 | 1 | no | — |
| 193 | C3×#235 | — | 12 | 1 | no | — |
| 194 | C3×#235 | — | 24 | 1 | no | — |
| 195 | C2×C3×C4×D3 | — | 12 | 1 | no | — |
| 196 | #3811 | — | 12 | 1 | no | — |
| 197 | D3×#67 | — | 24 | 1 | no | — |
| 198 | C2×#624 | — | 12 | 1 | no | — |
| 199 | #3805 | — | 12 | 1 | no | — |
| 200 | #3804 | — | 24 | 1 | no | — |
| 201 | C2×D3×Dic3 | — | 24 | 1 | no | — |
| 202 | #3802 | — | 6 | 1 | no | — |
| 203 | D3×D12 | — | 12 | 1 | no | — |
| 204 | C4×D32 | — | 12 | 1 | no | — |
| 205 | C4×D32 | — | 24 | 1 | no | — |
| 206 | #3799 | — | 12 | 1 | no | — |
| 207 | #3798 | — | 12 | 1 | no | — |
| 208 | #3798 | — | 24 | 1 | no | — |
| 209 | #3797 | — | 6 | 1 | no | — |
| 210 | #3796 | — | 12 | 1 | no | — |
| 211 | #3795 | — | 12 | 1 | no | — |
| 212 | D3×Dic6 | — | 12 | 1 | no | — |
| 213 | #3792 | — | 6 | 1 | no | — |
| 214 | C4×#157 | — | 3 | 1 | no | — |
| 215 | C4×#157 | — | 3 | 1 | no | — |
| 216 | C4×#157 | — | 3 | 1 | no | — |
| 217 | C4×#157 | — | 3 | 1 | no | — |
| 218 | #3788 | — | 6 | 1 | no | — |
| 219 | #3787 | — | 6 | 1 | no | — |
| 220 | #3777 | — | 3 | 1 | no | — |
| 221 | #3777 | — | 3 | 1 | no | — |
| 222 | #3777 | — | 6 | 1 | no | — |
| 223 | #3773 | — | 6 | 1 | no | — |
| 224 | #3773 | — | 6 | 1 | no | — |
| 225 | #3773 | — | 6 | 2 | no | — |
| 226 | #3773 | — | 12 | 1 | no | — |
| 227 | D32⋊C4 | — | 12 | 1 | no | — |
| 228 | D32⋊C4 | — | 12 | 1 | no | — |
| 229 | C32×M16 | — | 4 | 1 | no | — |
| 230 | C32×M16 | — | 8 | 1 | no | — |
| 231 | C32×M16 | GL(2,𝔽3) | 1 | 1 | yes | characteristic, complemented |
| 232 | C4×C3⋊Dic3 | — | 4 | 1 | no | — |
| 233 | #3748 | GL(2,𝔽3) | 1 | 1 | yes | characteristic, complemented |
| 234 | #3743 | — | 2 | 1 | no | — |
| 235 | C8×C3⋊D3 | — | 2 | 1 | no | — |
| 236 | C3×C4×Dic3 | — | 12 | 1 | no | — |
| 237 | C3×C4×Dic3 | — | 12 | 1 | no | — |
| 238 | C3×C4×Dic3 | — | 24 | 1 | no | — |
| 239 | C3×#208 | — | 12 | 1 | no | — |
| 240 | C3×ΓL(1,𝔽25) | — | 24 | 1 | no | — |
| 241 | C3×D3×C8 | — | 24 | 1 | no | — |
| 242 | Dic32 | — | 12 | 1 | no | — |
| 243 | Dic32 | — | 24 | 1 | no | — |
| 244 | #3103 | — | 27 | 1 | no | — |
| 245 | Q8×M16 | — | 9 | 1 | no | — |
| 246 | #1980 | — | 27 | 1 | no | — |
| 247 | C4×#103 | — | 27 | 1 | no | — |
| 248 | #1492 | — | 27 | 1 | no | — |
| 249 | #1303 | — | 27 | 1 | no | — |
| 250 | #1278 | — | 27 | 1 | no | — |
| 251 | C22×H(3,𝔽3) | — | 4 | 1 | no | — |
| 252 | C2×#272 | — | 8 | 1 | no | — |
| 253 | C2×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 254 | C2×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 255 | C2×(C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 256 | C2×(C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 257 | C2×(C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 258 | ((C3⋊D3)⋊C3)⋊C2 | — | 16 | 1 | no | — |
| 259 | ((C3⋊D3)⋊C3)⋊C2 | — | 16 | 1 | no | — |
| 260 | C4×H(3,𝔽3) | — | 4 | 1 | no | — |
| 261 | C4×H(3,𝔽3) | — | 4 | 1 | no | — |
| 262 | #1084 | — | 8 | 1 | no | — |
| 263 | #1084 | — | 8 | 2 | no | — |
| 264 | (C3⋊Dic3)⋊C3 | — | 4 | 1 | no | — |
| 265 | (C3⋊Dic3)⋊C3 | — | 4 | 1 | no | — |
| 266 | (C3⋊Dic3)⋊C3 | — | 8 | 1 | no | — |
| 267 | (C3⋊Dic3)⋊C3 | — | 8 | 2 | no | — |
| 268 | D3×#41 | — | 36 | 1 | no | — |
| 269 | C2×#235 | — | 36 | 1 | no | — |
| 270 | C22×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 271 | C2×GL(2,𝔽3) | — | 18 | 1 | no | — |
| 272 | C2×C3×M16 | — | 36 | 1 | no | — |
| 273 | C2×C4×Dic3 | — | 36 | 1 | no | — |
| 274 | D3×M16 | — | 12 | 1 | no | — |
| 275 | C42×D3 | — | 36 | 1 | no | — |
| 276 | C4×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 277 | C4×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 278 | #859 | — | 18 | 1 | no | — |
| 279 | #859 | — | 18 | 2 | no | — |
| 280 | C3×#104 | — | 36 | 1 | no | — |
| 281 | #837 | — | 36 | 1 | no | — |
| 282 | #825 | — | 12 | 1 | no | — |
| 283 | #825 | — | 12 | 1 | no | — |
| 284 | #825 | — | 24 | 1 | no | — |
| 285 | #825 | — | 36 | 1 | no | — |
| 286 | #825 | — | 36 | 1 | no | — |
| 287 | #825 | — | 36 | 1 | no | — |
| 288 | #805 | — | 36 | 1 | no | — |
| 289 | C22×C3⋊D3 | C4⋊S4 | 1 | 1 | yes | characteristic |
| 290 | C22×C3×D3 | — | 12 | 1 | no | — |
| 291 | C2×D32 | — | 12 | 1 | no | — |
| 292 | C2×D32 | — | 24 | 1 | no | — |
| 293 | C2×#157 | — | 3 | 1 | no | — |
| 294 | C2×#157 | — | 3 | 1 | no | — |
| 295 | C2×#157 | — | 3 | 1 | no | — |
| 296 | C2×#157 | — | 3 | 1 | no | — |
| 297 | C2×#157 | — | 6 | 1 | no | — |
| 298 | C2×#157 | — | 6 | 1 | no | — |
| 299 | C2×#157 | — | 12 | 1 | no | — |
| 300 | PSU(3,𝔽2) | — | 3 | 1 | no | — |
| 301 | PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 302 | PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 303 | PSU(3,𝔽2) | #825 | 1 | 1 | yes | characteristic, complemented |
| 304 | GO+(4,𝔽2) | — | 12 | 1 | no | — |
| 305 | GO+(4,𝔽2) | — | 12 | 1 | no | — |
| 306 | GO+(4,𝔽2) | — | 12 | 2 | no | — |
| 307 | AGL(1,𝔽9) | — | 12 | 1 | no | — |
| 308 | AGL(1,𝔽9) | — | 12 | 1 | no | — |
| 309 | AGL(1,𝔽9) | — | 12 | 2 | no | — |
| 310 | C2×C32×C4 | — | 4 | 1 | no | — |
| 311 | C2×C32×C4 | — | 8 | 1 | no | — |
| 312 | C2×C32×C4 | C2×GL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 313 | #638 | — | 8 | 1 | no | — |
| 314 | C2×C3⋊Dic3 | — | 8 | 1 | no | — |
| 315 | C2×C3⋊Dic3 | #986 | 1 | 1 | yes | characteristic |
| 316 | C4⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 317 | C4×C3⋊D3 | — | 8 | 1 | no | — |
| 318 | C4×C3⋊D3 | C4×S4 | 1 | 1 | yes | characteristic |
| 319 | C4×C3⋊D3 | #983 | 1 | 1 | yes | characteristic |
| 320 | C4×C3⋊D3 | #985 | 1 | 1 | yes | characteristic |
| 321 | C4×C3⋊D3 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 322 | #634 | — | 4 | 1 | no | — |
| 323 | C3×#67 | — | 24 | 1 | no | — |
| 324 | C3×#67 | — | 24 | 1 | no | — |
| 325 | C3×#67 | — | 48 | 1 | no | — |
| 326 | C2×C3×Dic3 | — | 12 | 1 | no | — |
| 327 | C2×C3×Dic3 | — | 24 | 1 | no | — |
| 328 | C2×C3×Dic3 | — | 24 | 1 | no | — |
| 329 | C2×C3×Dic3 | — | 48 | 1 | no | — |
| 330 | C3×D12 | — | 12 | 1 | no | — |
| 331 | C3×D12 | — | 12 | 1 | no | — |
| 332 | C3×D12 | — | 24 | 1 | no | — |
| 333 | C3×C4×D3 | — | 12 | 1 | no | — |
| 334 | C3×C4×D3 | — | 12 | 1 | no | — |
| 335 | C3×C4×D3 | — | 12 | 1 | no | — |
| 336 | C3×C4×D3 | — | 12 | 1 | no | — |
| 337 | C3×C4×D3 | — | 24 | 1 | no | — |
| 338 | C3×C4×D3 | — | 24 | 1 | no | — |
| 339 | C3×C4×D3 | — | 48 | 1 | no | — |
| 340 | C3×Dic6 | — | 12 | 1 | no | — |
| 341 | C3×Dic6 | — | 12 | 1 | no | — |
| 342 | C3×Dic6 | — | 24 | 1 | no | — |
| 343 | #627 | — | 12 | 1 | no | — |
| 344 | #627 | — | 24 | 1 | no | — |
| 345 | #626 | — | 24 | 1 | no | — |
| 346 | #626 | — | 24 | 1 | no | — |
| 347 | #626 | — | 24 | 1 | no | — |
| 348 | #625 | — | 12 | 1 | no | — |
| 349 | #625 | — | 24 | 1 | no | — |
| 350 | #624 | — | 12 | 2 | no | — |
| 351 | #624 | — | 12 | 1 | no | — |
| 352 | #624 | — | 24 | 1 | no | — |
| 353 | #624 | — | 24 | 1 | no | — |
| 354 | D3×Dic3 | — | 24 | 1 | no | — |
| 355 | D3×Dic3 | — | 24 | 1 | no | — |
| 356 | D3×Dic3 | — | 24 | 2 | no | — |
| 357 | D3×Dic3 | — | 24 | 2 | no | — |
| 358 | D3×Dic3 | — | 24 | 1 | no | — |
| 359 | #622 | — | 12 | 1 | no | — |
| 360 | C32×C8 | — | 2 | 1 | no | — |
| 361 | C32×C8 | — | 8 | 1 | no | — |
| 362 | C32×C8 | — | 16 | 1 | no | — |
| 363 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 364 | C3×C3⋊C8 | — | 24 | 1 | no | — |
| 365 | #532 | — | 27 | 1 | no | — |
| 366 | C2×C4×Q8 | — | 9 | 1 | no | — |
| 367 | #481 | — | 54 | 1 | no | — |
| 368 | #475 | — | 27 | 1 | no | — |
| 369 | #475 | — | 27 | 1 | no | — |
| 370 | #460 | — | 27 | 1 | no | — |
| 371 | #460 | — | 27 | 1 | no | — |
| 372 | #448 | — | 54 | 1 | no | — |
| 373 | #446 | — | 54 | 1 | no | — |
| 374 | C8×Q8 | — | 18 | 1 | no | — |
| 375 | C4×SD16 | — | 54 | 1 | no | — |
| 376 | C4×SD16 | — | 54 | 1 | no | — |
| 377 | #431 | — | 27 | 1 | no | — |
| 378 | #423 | — | 27 | 1 | no | — |
| 379 | C2×#104 | — | 54 | 1 | no | — |
| 380 | C2×#104 | — | 54 | 1 | no | — |
| 381 | C2×#103 | — | 54 | 1 | no | — |
| 382 | C4×M16 | — | 27 | 1 | no | — |
| 383 | C2×C4×C8 | — | 27 | 1 | no | — |
| 384 | C4×C4⋊C4 | — | 27 | 1 | no | — |
| 385 | #340 | — | 54 | 1 | no | — |
| 386 | D4⋊C8 | — | 54 | 2 | no | — |
| 387 | C2×H(3,𝔽3) | — | 4 | 1 | no | — |
| 388 | C2×H(3,𝔽3) | — | 8 | 1 | no | — |
| 389 | #272 | — | 16 | 1 | no | — |
| 390 | (C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 391 | (C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 392 | (C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 393 | (C3⋊D3)⋊C3 | — | 16 | 1 | no | — |
| 394 | C3×#41 | — | 36 | 1 | no | — |
| 395 | C22×C3×C4 | — | 36 | 1 | no | — |
| 396 | C2×#67 | — | 72 | 1 | no | — |
| 397 | C22×Dic3 | — | 72 | 1 | no | — |
| 398 | #239 | — | 36 | 1 | no | — |
| 399 | D3×Q8 | — | 36 | 1 | no | — |
| 400 | #237 | — | 36 | 1 | no | — |
| 401 | #237 | — | 72 | 1 | no | — |
| 402 | D3×D4 | — | 36 | 1 | no | — |
| 403 | D3×D4 | — | 72 | 1 | no | — |
| 404 | #235 | — | 12 | 1 | no | — |
| 405 | #235 | — | 12 | 1 | no | — |
| 406 | #235 | — | 24 | 1 | no | — |
| 407 | #235 | — | 36 | 1 | no | — |
| 408 | #235 | — | 36 | 1 | no | — |
| 409 | #235 | — | 36 | 1 | no | — |
| 410 | #235 | — | 72 | 1 | no | — |
| 411 | #235 | — | 72 | 1 | no | — |
| 412 | #235 | — | 72 | 1 | no | — |
| 413 | C2×D12 | — | 36 | 1 | no | — |
| 414 | C2×C4×D3 | — | 12 | 1 | no | — |
| 415 | C2×C4×D3 | — | 72 | 1 | no | — |
| 416 | C2×C4×D3 | — | 72 | 1 | no | — |
| 417 | C2×C4×D3 | — | 72 | 1 | no | — |
| 418 | C2×Dic6 | — | 36 | 1 | no | — |
| 419 | C2×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 420 | C2×SL(2,𝔽3) | — | 18 | 1 | no | — |
| 421 | GL(2,𝔽3) | — | 36 | 1 | no | — |
| 422 | C3×M16 | — | 4 | 1 | no | — |
| 423 | C3×M16 | — | 12 | 1 | no | — |
| 424 | C3×M16 | — | 24 | 1 | no | — |
| 425 | C3×M16 | — | 36 | 1 | no | — |
| 426 | C3×M16 | — | 72 | 1 | no | — |
| 427 | C2×C3×C8 | — | 72 | 1 | no | — |
| 428 | C3×C42 | — | 36 | 1 | no | — |
| 429 | C4×Dic3 | — | 12 | 1 | no | — |
| 430 | C4×Dic3 | — | 12 | 1 | no | — |
| 431 | C4×Dic3 | — | 24 | 1 | no | — |
| 432 | C4×Dic3 | — | 36 | 1 | no | — |
| 433 | C4×Dic3 | — | 72 | 1 | no | — |
| 434 | C4×Dic3 | — | 72 | 1 | no | — |
| 435 | #208 | — | 12 | 1 | no | — |
| 436 | ΓL(1,𝔽25) | — | 24 | 1 | no | — |
| 437 | D3×C8 | — | 24 | 1 | no | — |
| 438 | C22×C32 | — | 4 | 1 | no | — |
| 439 | C22×C32 | — | 8 | 1 | no | — |
| 440 | C22×C32 | C4⋊GL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 441 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 442 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 443 | C2×C3⋊D3 | — | 8 | 1 | no | — |
| 444 | C2×C3⋊D3 | #5395 | 1 | 1 | yes | characteristic |
| 445 | C2×C3⋊D3 | (C2×S4)⋊C4 | 1 | 1 | yes | characteristic |
| 446 | C2×C3×D3 | — | 12 | 1 | no | — |
| 447 | C2×C3×D3 | — | 12 | 1 | no | — |
| 448 | C2×C3×D3 | — | 24 | 1 | no | — |
| 449 | C2×C3×D3 | — | 24 | 1 | no | — |
| 450 | C2×C3×D3 | — | 24 | 1 | no | — |
| 451 | C2×C3×D3 | — | 24 | 1 | no | — |
| 452 | C2×C3×D3 | — | 48 | 1 | no | — |
| 453 | D32 | — | 24 | 1 | no | — |
| 454 | D32 | — | 24 | 1 | no | — |
| 455 | D32 | — | 48 | 1 | no | — |
| 456 | D32 | — | 48 | 1 | no | — |
| 457 | #157 | — | 3 | 1 | no | — |
| 458 | #157 | — | 3 | 1 | no | — |
| 459 | #157 | — | 6 | 1 | no | — |
| 460 | #157 | — | 6 | 1 | no | — |
| 461 | #157 | — | 6 | 1 | no | — |
| 462 | C32×C4 | — | 4 | 1 | no | — |
| 463 | C32×C4 | — | 4 | 1 | no | — |
| 464 | C32×C4 | — | 8 | 1 | no | — |
| 465 | C32×C4 | — | 8 | 1 | no | — |
| 466 | C32×C4 | C4×GL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 467 | C32×C4 | #5421 | 1 | 1 | yes | characteristic |
| 468 | C3⋊Dic3 | — | 8 | 1 | no | — |
| 469 | C3⋊Dic3 | — | 8 | 2 | no | — |
| 470 | C3⋊Dic3 | #5394 | 1 | 1 | yes | characteristic |
| 471 | C3⋊Dic3 | #5427 | 1 | 1 | yes | characteristic |
| 472 | C3×Dic3 | — | 12 | 1 | no | — |
| 473 | C3×Dic3 | — | 12 | 1 | no | — |
| 474 | C3×Dic3 | — | 24 | 2 | no | — |
| 475 | C3×Dic3 | — | 24 | 1 | no | — |
| 476 | C3×Dic3 | — | 24 | 2 | no | — |
| 477 | C3×Dic3 | — | 24 | 1 | no | — |
| 478 | C3×Dic3 | — | 48 | 1 | no | — |
| 479 | C3×Dic3 | — | 48 | 2 | no | — |
| 480 | C2×#41 | — | 54 | 1 | no | — |
| 481 | C22×Q8 | — | 9 | 1 | no | — |
| 482 | C2×SD16 | — | 54 | 1 | no | — |
| 483 | C2×SD16 | — | 54 | 1 | no | — |
| 484 | C2×M16 | — | 9 | 1 | no | — |
| 485 | C2×M16 | — | 27 | 1 | no | — |
| 486 | C22×C8 | — | 54 | 1 | no | — |
| 487 | C4⋊Q8 | — | 27 | 1 | no | — |
| 488 | #127 | — | 27 | 1 | no | — |
| 489 | #124 | — | 54 | 1 | no | — |
| 490 | #121 | — | 54 | 1 | no | — |
| 491 | #121 | — | 54 | 1 | no | — |
| 492 | C4×Q8 | — | 9 | 1 | no | — |
| 493 | C4×Q8 | — | 9 | 1 | no | — |
| 494 | C4×Q8 | — | 27 | 1 | no | — |
| 495 | C4×Q8 | — | 27 | 1 | no | — |
| 496 | C4×D4 | — | 54 | 1 | no | — |
| 497 | C4×D4 | — | 54 | 1 | no | — |
| 498 | C2×C4⋊C4 | — | 27 | 1 | no | — |
| 499 | C2×C4⋊C4 | — | 54 | 1 | no | — |
| 500 | C2×C42 | — | 27 | 1 | no | — |
| 501 | C2×C42 | — | 54 | 1 | no | — |
| 502 | #106 | — | 54 | 1 | no | — |
| 503 | #106 | — | 54 | 1 | no | — |
| 504 | C4⋊C8 | — | 27 | 2 | no | — |
| 505 | C4⋊C8 | — | 27 | 1 | no | — |
| 506 | C4⋊C8 | — | 27 | 1 | no | — |
| 507 | C4⋊C8 | — | 54 | 1 | no | — |
| 508 | #104 | — | 36 | 1 | no | — |
| 509 | #104 | — | 108 | 1 | no | — |
| 510 | #104 | — | 108 | 2 | no | — |
| 511 | #103 | — | 54 | 1 | no | — |
| 512 | #103 | — | 54 | 2 | no | — |
| 513 | #103 | — | 54 | 1 | no | — |
| 514 | #103 | — | 54 | 2 | no | — |
| 515 | #102 | — | 54 | 1 | no | — |
| 516 | #102 | — | 54 | 1 | no | — |
| 517 | C22⋊C8 | — | 54 | 1 | no | — |
| 518 | #97 | — | 54 | 1 | no | — |
| 519 | C4×C8 | — | 54 | 1 | no | — |
| 520 | C4×C8 | — | 54 | 1 | no | — |
| 521 | C4×C8 | — | 54 | 1 | no | — |
| 522 | C4×C8 | — | 54 | 1 | no | — |
| 523 | #95 | — | 54 | 1 | no | — |
| 524 | H(3,𝔽3) | — | 4 | 1 | no | Sylow |
| 525 | C23×C3 | — | 36 | 1 | no | — |
| 526 | C22×D3 | — | 12 | 1 | no | — |
| 527 | C22×D3 | — | 72 | 1 | no | — |
| 528 | C22×D3 | — | 72 | 1 | no | — |
| 529 | C3×Q8 | — | 36 | 1 | no | — |
| 530 | C3×D4 | — | 36 | 1 | no | — |
| 531 | C3×D4 | — | 72 | 1 | no | — |
| 532 | C2×C3×C4 | — | 4 | 1 | no | — |
| 533 | C2×C3×C4 | — | 12 | 1 | no | — |
| 534 | C2×C3×C4 | — | 24 | 1 | no | — |
| 535 | C2×C3×C4 | — | 36 | 1 | no | — |
| 536 | C2×C3×C4 | — | 36 | 1 | no | — |
| 537 | C2×C3×C4 | — | 36 | 1 | no | — |
| 538 | C2×C3×C4 | — | 36 | 1 | no | — |
| 539 | C2×C3×C4 | — | 36 | 1 | no | — |
| 540 | C2×C3×C4 | — | 72 | 1 | no | — |
| 541 | C2×C3×C4 | — | 72 | 1 | no | — |
| 542 | #67 | — | 24 | 1 | no | — |
| 543 | #67 | — | 24 | 1 | no | — |
| 544 | #67 | — | 48 | 1 | no | — |
| 545 | #67 | — | 72 | 1 | no | — |
| 546 | #67 | — | 72 | 1 | no | — |
| 547 | #67 | — | 72 | 1 | no | — |
| 548 | #67 | — | 72 | 1 | no | — |
| 549 | #67 | — | 72 | 1 | no | — |
| 550 | C2×Dic3 | — | 12 | 1 | no | — |
| 551 | C2×Dic3 | — | 24 | 1 | no | — |
| 552 | C2×Dic3 | — | 24 | 1 | no | — |
| 553 | C2×Dic3 | — | 48 | 1 | no | — |
| 554 | C2×Dic3 | — | 72 | 1 | no | — |
| 555 | C2×Dic3 | — | 72 | 1 | no | — |
| 556 | C2×Dic3 | — | 72 | 2 | no | — |
| 557 | C2×Dic3 | — | 72 | 1 | no | — |
| 558 | C2×Dic3 | — | 72 | 2 | no | — |
| 559 | D12 | — | 12 | 1 | no | — |
| 560 | D12 | — | 12 | 1 | no | — |
| 561 | D12 | — | 24 | 1 | no | — |
| 562 | D12 | — | 36 | 1 | no | — |
| 563 | D12 | — | 72 | 1 | no | — |
| 564 | D12 | — | 72 | 1 | no | — |
| 565 | C4×D3 | — | 12 | 1 | no | — |
| 566 | C4×D3 | — | 12 | 1 | no | — |
| 567 | C4×D3 | — | 12 | 1 | no | — |
| 568 | C4×D3 | — | 12 | 1 | no | — |
| 569 | C4×D3 | — | 24 | 1 | no | — |
| 570 | C4×D3 | — | 24 | 1 | no | — |
| 571 | C4×D3 | — | 48 | 1 | no | — |
| 572 | C4×D3 | — | 72 | 1 | no | — |
| 573 | C4×D3 | — | 72 | 1 | no | — |
| 574 | C4×D3 | — | 72 | 2 | no | — |
| 575 | C4×D3 | — | 72 | 1 | no | — |
| 576 | C4×D3 | — | 72 | 1 | no | — |
| 577 | C4×D3 | — | 72 | 2 | no | — |
| 578 | C4×D3 | — | 72 | 1 | no | — |
| 579 | Dic6 | — | 12 | 1 | no | — |
| 580 | Dic6 | — | 12 | 1 | no | — |
| 581 | Dic6 | — | 24 | 1 | no | — |
| 582 | Dic6 | — | 36 | 1 | no | — |
| 583 | Dic6 | — | 72 | 1 | no | — |
| 584 | Dic6 | — | 72 | 1 | no | — |
| 585 | SL(2,𝔽3) | — | 9 | 1 | no | — |
| 586 | C3×C8 | — | 8 | 1 | no | — |
| 587 | C3×C8 | — | 24 | 1 | no | — |
| 588 | C3×C8 | — | 48 | 1 | no | — |
| 589 | C3×C8 | — | 72 | 1 | no | — |
| 590 | C3⋊C8 | — | 24 | 1 | no | — |
| 591 | C2×C32 | — | 2 | 1 | no | — |
| 592 | C2×C32 | — | 4 | 1 | no | — |
| 593 | C2×C32 | — | 8 | 1 | no | — |
| 594 | C2×C32 | — | 8 | 1 | no | — |
| 595 | C2×C32 | — | 16 | 1 | no | — |
| 596 | C2×C32 | #73065 | 1 | 1 | yes | characteristic |
| 597 | C3⋊D3 | — | 2 | 1 | no | — |
| 598 | C3⋊D3 | — | 16 | 1 | no | — |
| 599 | C3⋊D3 | #73117 | 1 | 1 | yes | characteristic |
| 600 | C3⋊D3 | #73132 | 1 | 1 | yes | characteristic |
| 601 | C3×D3 | — | 12 | 1 | no | — |
| 602 | C3×D3 | — | 12 | 1 | no | — |
| 603 | C3×D3 | — | 24 | 1 | no | — |
| 604 | C3×D3 | — | 48 | 1 | no | — |
| 605 | C3×D3 | — | 48 | 1 | no | — |
| 606 | C3×D3 | — | 96 | 1 | no | — |
| 607 | #41 | — | 36 | 1 | no | — |
| 608 | #41 | — | 108 | 1 | no | — |
| 609 | #41 | — | 108 | 1 | no | — |
| 610 | #41 | — | 108 | 1 | no | — |
| 611 | C2×Q8 | — | 9 | 1 | no | — |
| 612 | C2×Q8 | — | 18 | 1 | no | — |
| 613 | C2×Q8 | — | 27 | 1 | no | — |
| 614 | C2×Q8 | — | 54 | 1 | no | — |
| 615 | C2×Q8 | — | 54 | 1 | no | — |
| 616 | C2×D4 | — | 54 | 1 | no | — |
| 617 | C2×D4 | — | 54 | 1 | no | — |
| 618 | C2×D4 | — | 54 | 1 | no | — |
| 619 | C2×D4 | — | 108 | 1 | no | — |
| 620 | C22×C4 | — | 9 | 1 | no | — |
| 621 | C22×C4 | — | 27 | 1 | no | — |
| 622 | C22×C4 | — | 27 | 1 | no | — |
| 623 | C22×C4 | — | 108 | 1 | no | — |
| 624 | C22×C4 | — | 108 | 1 | no | — |
| 625 | SD16 | — | 108 | 1 | no | — |
| 626 | SD16 | — | 108 | 1 | no | — |
| 627 | SD16 | — | 108 | 2 | no | — |
| 628 | M16 | — | 9 | 1 | no | — |
| 629 | M16 | — | 18 | 1 | no | — |
| 630 | M16 | — | 54 | 1 | no | — |
| 631 | M16 | — | 54 | 1 | no | — |
| 632 | M16 | AGL(2,𝔽3) | 1 | 1 | yes | characteristic, complemented |
| 633 | C2×C8 | — | 18 | 1 | no | — |
| 634 | C2×C8 | — | 54 | 1 | no | — |
| 635 | C2×C8 | — | 54 | 1 | no | — |
| 636 | C2×C8 | — | 54 | 1 | no | — |
| 637 | C2×C8 | — | 54 | 2 | no | — |
| 638 | C2×C8 | — | 108 | 1 | no | — |
| 639 | C2×C8 | — | 108 | 1 | no | — |
| 640 | C4⋊C4 | — | 27 | 1 | no | — |
| 641 | C4⋊C4 | — | 27 | 1 | no | — |
| 642 | C4⋊C4 | — | 54 | 1 | no | — |
| 643 | C4⋊C4 | — | 54 | 1 | no | — |
| 644 | C4⋊C4 | — | 54 | 1 | no | — |
| 645 | C4⋊C4 | — | 54 | 2 | no | — |
| 646 | C4⋊C4 | — | 108 | 1 | no | — |
| 647 | C22⋊C4 | — | 108 | 1 | no | — |
| 648 | C22⋊C4 | — | 108 | 1 | no | — |
| 649 | C42 | — | 27 | 1 | no | — |
| 650 | C42 | — | 27 | 1 | no | — |
| 651 | C42 | — | 27 | 1 | no | — |
| 652 | C42 | — | 27 | 1 | no | — |
| 653 | C42 | — | 36 | 1 | no | — |
| 654 | C42 | — | 108 | 1 | no | — |
| 655 | C22×C3 | — | 4 | 1 | no | — |
| 656 | C22×C3 | — | 12 | 1 | no | — |
| 657 | C22×C3 | — | 24 | 1 | no | — |
| 658 | C22×C3 | — | 36 | 1 | no | — |
| 659 | C22×C3 | — | 36 | 1 | no | — |
| 660 | C22×C3 | — | 72 | 1 | no | — |
| 661 | C22×C3 | — | 72 | 1 | no | — |
| 662 | C22×C3 | — | 72 | 1 | no | — |
| 663 | C2×D3 | — | 12 | 1 | no | — |
| 664 | C2×D3 | — | 12 | 1 | no | — |
| 665 | C2×D3 | — | 24 | 1 | no | — |
| 666 | C2×D3 | — | 24 | 1 | no | — |
| 667 | C2×D3 | — | 24 | 1 | no | — |
| 668 | C2×D3 | — | 24 | 1 | no | — |
| 669 | C2×D3 | — | 48 | 1 | no | — |
| 670 | C2×D3 | — | 72 | 1 | no | — |
| 671 | C2×D3 | — | 144 | 1 | no | — |
| 672 | C2×D3 | — | 144 | 1 | no | — |
| 673 | C2×D3 | — | 144 | 1 | no | — |
| 674 | C2×D3 | — | 144 | 1 | no | — |
| 675 | C3×C4 | — | 4 | 1 | no | — |
| 676 | C3×C4 | — | 4 | 1 | no | — |
| 677 | C3×C4 | — | 12 | 1 | no | — |
| 678 | C3×C4 | — | 12 | 1 | no | — |
| 679 | C3×C4 | — | 24 | 1 | no | — |
| 680 | C3×C4 | — | 24 | 1 | no | — |
| 681 | C3×C4 | — | 36 | 1 | no | — |
| 682 | C3×C4 | — | 36 | 1 | no | — |
| 683 | C3×C4 | — | 72 | 1 | no | — |
| 684 | C3×C4 | — | 72 | 2 | no | — |
| 685 | Dic3 | — | 12 | 1 | no | — |
| 686 | Dic3 | — | 12 | 1 | no | — |
| 687 | Dic3 | — | 24 | 1 | no | — |
| 688 | Dic3 | — | 24 | 2 | no | — |
| 689 | Dic3 | — | 24 | 1 | no | — |
| 690 | Dic3 | — | 24 | 2 | no | — |
| 691 | Dic3 | — | 48 | 1 | no | — |
| 692 | Dic3 | — | 48 | 2 | no | — |
| 693 | Dic3 | — | 72 | 1 | no | — |
| 694 | Dic3 | — | 72 | 2 | no | — |
| 695 | C32 | — | 4 | 1 | no | — |
| 696 | C32 | — | 8 | 1 | no | — |
| 697 | C32 | #11711123 | 1 | 1 | yes | characteristic, complemented |
| 698 | C23 | — | 9 | 1 | no | — |
| 699 | C23 | — | 108 | 1 | no | — |
| 700 | Q8 | — | 9 | 1 | no | — |
| 701 | Q8 | — | 27 | 1 | no | — |
| 702 | Q8 | — | 36 | 1 | no | — |
| 703 | Q8 | — | 54 | 1 | no | — |
| 704 | Q8 | — | 54 | 1 | no | — |
| 705 | Q8 | — | 108 | 1 | no | — |
| 706 | D4 | — | 36 | 1 | no | — |
| 707 | D4 | — | 72 | 1 | no | — |
| 708 | D4 | — | 108 | 1 | no | — |
| 709 | D4 | — | 108 | 1 | no | — |
| 710 | D4 | — | 108 | 1 | no | — |
| 711 | D4 | — | 108 | 2 | no | — |
| 712 | D4 | — | 216 | 1 | no | — |
| 713 | C2×C4 | — | 9 | 1 | no | — |
| 714 | C2×C4 | — | 9 | 1 | no | — |
| 715 | C2×C4 | — | 9 | 1 | no | — |
| 716 | C2×C4 | — | 9 | 1 | no | — |
| 717 | C2×C4 | — | 9 | 1 | no | — |
| 718 | C2×C4 | — | 27 | 1 | no | — |
| 719 | C2×C4 | — | 27 | 1 | no | — |
| 720 | C2×C4 | — | 27 | 1 | no | — |
| 721 | C2×C4 | — | 27 | 1 | no | — |
| 722 | C2×C4 | — | 54 | 1 | no | — |
| 723 | C2×C4 | — | 54 | 1 | no | — |
| 724 | C2×C4 | — | 72 | 1 | no | — |
| 725 | C2×C4 | — | 72 | 1 | no | — |
| 726 | C2×C4 | — | 108 | 1 | no | — |
| 727 | C2×C4 | — | 108 | 1 | no | — |
| 728 | C2×C4 | — | 108 | 2 | no | — |
| 729 | C2×C4 | — | 216 | 1 | no | — |
| 730 | C2×C4 | — | 216 | 1 | no | — |
| 731 | C2×C4 | C2×AGL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 732 | C8 | — | 2 | 1 | no | — |
| 733 | C8 | — | 18 | 1 | no | — |
| 734 | C8 | — | 108 | 1 | no | — |
| 735 | C8 | — | 108 | 1 | no | — |
| 736 | C8 | — | 108 | 1 | no | — |
| 737 | C8 | — | 108 | 2 | no | — |
| 738 | C2×C3 | — | 4 | 1 | no | — |
| 739 | C2×C3 | — | 8 | 1 | no | — |
| 740 | C2×C3 | — | 12 | 1 | no | — |
| 741 | C2×C3 | — | 24 | 1 | no | — |
| 742 | C2×C3 | — | 24 | 1 | no | — |
| 743 | C2×C3 | — | 36 | 1 | no | — |
| 744 | C2×C3 | — | 36 | 1 | no | — |
| 745 | C2×C3 | — | 48 | 1 | no | — |
| 746 | C2×C3 | — | 72 | 1 | no | — |
| 747 | C2×C3 | — | 144 | 1 | no | — |
| 748 | D3 | — | 12 | 1 | no | — |
| 749 | D3 | — | 12 | 1 | no | — |
| 750 | D3 | — | 24 | 1 | no | — |
| 751 | D3 | — | 48 | 1 | no | — |
| 752 | D3 | — | 48 | 1 | no | — |
| 753 | D3 | — | 96 | 1 | no | — |
| 754 | D3 | — | 144 | 1 | no | — |
| 755 | C22 | — | 9 | 1 | no | — |
| 756 | C22 | — | 9 | 1 | no | — |
| 757 | C22 | — | 18 | 1 | no | — |
| 758 | C22 | — | 18 | 1 | no | — |
| 759 | C22 | — | 72 | 1 | no | — |
| 760 | C22 | — | 216 | 1 | no | — |
| 761 | C22 | — | 216 | 1 | no | — |
| 762 | C22 | C4⋊AGL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 763 | C4 | — | 9 | 1 | no | — |
| 764 | C4 | — | 9 | 1 | no | — |
| 765 | C4 | — | 27 | 1 | no | — |
| 766 | C4 | — | 27 | 1 | no | — |
| 767 | C4 | — | 54 | 1 | no | — |
| 768 | C4 | — | 54 | 1 | no | — |
| 769 | C4 | — | 54 | 1 | no | — |
| 770 | C4 | — | 72 | 2 | no | — |
| 771 | C4 | — | 72 | 1 | no | — |
| 772 | C4 | C4×AGL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 773 | C4 | #13180131 | 1 | 1 | yes | characteristic |
| 774 | C3 | — | 4 | 1 | no | — |
| 775 | C3 | — | 12 | 1 | no | — |
| 776 | C3 | — | 24 | 1 | no | — |
| 777 | C2 | — | 2 | 1 | no | — |
| 778 | C2 | — | 9 | 1 | no | — |
| 779 | C2 | — | 9 | 1 | no | — |
| 780 | C2 | — | 18 | 1 | no | — |
| 781 | C2 | — | 144 | 1 | no | — |
| 782 | C2 | #72220441 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×(PSU(3,𝔽2)⋊C3)⋊C4 | C2 | semidirect |
| 4. M16×PSU(3,𝔽2)⋊C3 | C2 | semidirect |
| 8. C4⋊AGL(2,𝔽3) | C4 | semidirect |
| 10. (PSU(3,𝔽2)⋊C3)⋊Q8 | C4 | semidirect |
| 14. M16×PSU(3,𝔽2) | D3 | semidirect |
| 135. PSU(3,𝔽2)⋊C3 | #104 | semidirect |
| 231. C32×M16 | GL(2,𝔽3) | semidirect |
| 233. #3748 | GL(2,𝔽3) | semidirect |
| 303. PSU(3,𝔽2) | #825 | semidirect |
| 632. M16 | AGL(2,𝔽3) | semidirect |
| 697. C32 | #11711123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72220467 | 3 |
| C4×(PSU(3,𝔽2)⋊C3)⋊C4 | 2 |
| #72220138 | 2 |
| M16×PSU(3,𝔽2)⋊C3 | 2 |
| #13139205 | 4 |
| #11711123 | 9 |