Finite Group DatabasebetaFinite Group DatabasebetaOrder 6912.
900 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 900 conjugacy classes of subgroups — too many to draw. Only its 60 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 | #72220456 | — | 3 | 1 | no | maximal |
| 2 | C4×(PSU(3,𝔽2)⋊C3)⋊C4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #41×PSU(3,𝔽2)⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #72220123 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | Q8×PSU(3,𝔽2)⋊C3 | C4 | 1 | 1 | yes | characteristic, complemented |
| 6 | D4×PSU(3,𝔽2)⋊C3 | — | 2 | 1 | no | — |
| 7 | D4×PSU(3,𝔽2)⋊C3 | C4 | 1 | 1 | yes | characteristic, complemented |
| 8 | C2×C4×PSU(3,𝔽2)⋊C3 | — | 2 | 1 | no | — |
| 9 | C2×C4×PSU(3,𝔽2)⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×(PSU(3,𝔽2)⋊C3)⋊C4 | — | 2 | 1 | no | — |
| 11 | (PSU(3,𝔽2)⋊C3)⋊C8 | — | 2 | 1 | no | — |
| 12 | #13141059 | — | 4 | 1 | no | maximal |
| 13 | #41×PSU(3,𝔽2) | D3 | 1 | 1 | yes | characteristic |
| 14 | #11785332 | — | 3 | 1 | no | — |
| 15 | C4×PSU(3,𝔽2)⋊C4 | — | 3 | 1 | no | — |
| 16 | #11775099 | — | 3 | 1 | no | — |
| 17 | #11774783 | — | 3 | 1 | no | — |
| 18 | #11774597 | — | 3 | 1 | no | — |
| 19 | #11774254 | — | 3 | 1 | no | — |
| 20 | C22×PSU(3,𝔽2)⋊C3 | — | 2 | 1 | no | — |
| 21 | C22×PSU(3,𝔽2)⋊C3 | D4 | 1 | 1 | yes | characteristic |
| 22 | C4×PSU(3,𝔽2)⋊C3 | — | 2 | 1 | no | — |
| 23 | C4×PSU(3,𝔽2)⋊C3 | C2×C4 | 1 | 1 | yes | characteristic |
| 24 | C4×PSU(3,𝔽2)⋊C3 | D4 | 1 | 1 | yes | characteristic |
| 25 | (PSU(3,𝔽2)⋊C3)⋊C4 | — | 2 | 2 | no | — |
| 26 | #41×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 27 | C4×((C3⋊D3)⋊C3)⋊C4 | — | 4 | 1 | no | — |
| 28 | #11721053 | — | 4 | 1 | no | — |
| 29 | #11720586 | — | 4 | 1 | no | — |
| 30 | #63664⋊C3 | — | 4 | 1 | no | — |
| 31 | #11720322 | — | 4 | 1 | no | — |
| 32 | #11720305 | — | 4 | 1 | no | — |
| 33 | #11711050 | — | 9 | 1 | no | maximal |
| 34 | #41×#157 | — | 3 | 1 | no | — |
| 35 | #10596547 | — | 3 | 1 | no | — |
| 36 | Q8×PSU(3,𝔽2) | Dic3 | 1 | 1 | yes | characteristic, complemented |
| 37 | #10596545 | — | 3 | 1 | no | — |
| 38 | #10596545 | — | 6 | 1 | no | — |
| 39 | D4×PSU(3,𝔽2) | — | 2 | 1 | no | — |
| 40 | D4×PSU(3,𝔽2) | Dic3 | 1 | 1 | yes | characteristic, complemented |
| 41 | #10596542 | — | 3 | 1 | no | — |
| 42 | #10596542 | — | 6 | 1 | no | — |
| 43 | C2×C4×PSU(3,𝔽2) | — | 2 | 1 | no | — |
| 44 | C2×C4×PSU(3,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 45 | #10596484 | — | 3 | 1 | no | — |
| 46 | C2×C4×AGL(1,𝔽9) | — | 3 | 1 | no | — |
| 47 | C2×PSU(3,𝔽2)⋊C4 | — | 6 | 1 | no | — |
| 48 | C4×#3773 | — | 3 | 1 | no | — |
| 49 | #10593328 | — | 3 | 1 | no | — |
| 50 | Q8⋊AGL(1,𝔽9) | — | 6 | 1 | no | — |
| 51 | D4⋊AGL(1,𝔽9) | — | 6 | 1 | no | — |
| 52 | #10593166 | — | 6 | 1 | no | — |
| 53 | #10593165 | — | 6 | 2 | no | — |
| 54 | PSU(3,𝔽2)⋊C8 | — | 6 | 2 | no | — |
| 55 | PSU(3,𝔽2)⋊C8 | — | 6 | 1 | no | — |
| 56 | PSU(3,𝔽2)⋊C8 | — | 6 | 1 | no | — |
| 57 | #10591671 | — | 6 | 1 | no | — |
| 58 | D3×#837 | — | 12 | 1 | no | — |
| 59 | #10590048 | — | 6 | 1 | no | — |
| 60 | C2×PSU(3,𝔽2)⋊C3 | — | 2 | 1 | no | — |
| 61 | C2×PSU(3,𝔽2)⋊C3 | — | 4 | 1 | no | — |
| 62 | C2×PSU(3,𝔽2)⋊C3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 63 | #41×H(3,𝔽3) | — | 4 | 1 | no | — |
| 64 | #88722 | — | 4 | 1 | no | — |
| 65 | Q8×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 66 | #3830⋊C3 | — | 4 | 1 | no | — |
| 67 | #3830⋊C3 | — | 8 | 1 | no | — |
| 68 | D4×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 69 | D4×(C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 70 | #3828⋊C3 | — | 4 | 1 | no | — |
| 71 | #3828⋊C3 | — | 8 | 1 | no | — |
| 72 | C2×C4×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 73 | C2×C4×(C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 74 | C2×((C3⋊D3)⋊C3)⋊C4 | — | 8 | 1 | no | — |
| 75 | C4×#1084 | — | 4 | 1 | no | — |
| 76 | #88538 | — | 4 | 1 | no | — |
| 77 | C4×(C3⋊Dic3)⋊C3 | — | 4 | 1 | no | — |
| 78 | #3748⋊C3 | — | 4 | 1 | no | — |
| 79 | #88447 | — | 8 | 1 | no | — |
| 80 | #88430 | — | 8 | 1 | no | — |
| 81 | ((C3⋊D3)⋊C3)⋊C8 | — | 8 | 1 | no | — |
| 82 | #41×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 83 | C4×#859 | — | 9 | 1 | no | — |
| 84 | #73055 | — | 9 | 1 | no | — |
| 85 | C22×PSU(3,𝔽2) | — | 2 | 1 | no | — |
| 86 | C22×PSU(3,𝔽2) | #67 | 1 | 1 | yes | characteristic |
| 87 | C22×AGL(1,𝔽9) | — | 6 | 1 | no | — |
| 88 | #41×C3⋊D3 | S4 | 1 | 1 | yes | characteristic |
| 89 | C3×D3×#41 | — | 12 | 1 | no | — |
| 90 | Q8×#157 | — | 3 | 1 | no | — |
| 91 | Q8×#157 | — | 3 | 1 | no | — |
| 92 | D4×#157 | — | 3 | 1 | no | — |
| 93 | D4×#157 | — | 3 | 1 | no | — |
| 94 | D4×#157 | — | 6 | 1 | no | — |
| 95 | D4×#157 | — | 6 | 1 | no | — |
| 96 | #64286 | — | 3 | 1 | no | — |
| 97 | #64286 | — | 6 | 1 | no | — |
| 98 | C2×C4×#157 | — | 3 | 1 | no | — |
| 99 | C2×C4×#157 | — | 6 | 1 | no | — |
| 100 | C22⋊PSU(3,𝔽2) | — | 3 | 2 | no | — |
| 101 | C22⋊PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 102 | C22⋊PSU(3,𝔽2) | — | 6 | 2 | no | — |
| 103 | C22⋊PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 104 | C22⋊PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 105 | C2×#3777 | — | 3 | 1 | no | — |
| 106 | C2×#3777 | — | 6 | 1 | no | — |
| 107 | C4⋊PSU(3,𝔽2) | — | 3 | 1 | no | — |
| 108 | C4⋊PSU(3,𝔽2) | — | 3 | 1 | no | — |
| 109 | C4⋊PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 110 | C4⋊PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 111 | C4×PSU(3,𝔽2) | — | 2 | 1 | no | — |
| 112 | C4×PSU(3,𝔽2) | — | 3 | 1 | no | — |
| 113 | C4×PSU(3,𝔽2) | — | 3 | 1 | no | — |
| 114 | C4×PSU(3,𝔽2) | — | 3 | 2 | no | — |
| 115 | C4×PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 116 | C4×PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 117 | C4×PSU(3,𝔽2) | C2×Dic3 | 1 | 1 | yes | characteristic |
| 118 | C4×PSU(3,𝔽2) | #67 | 1 | 1 | yes | characteristic |
| 119 | #64243 | — | 6 | 2 | no | — |
| 120 | #64243 | — | 6 | 1 | no | — |
| 121 | C2×#3773 | — | 6 | 1 | no | — |
| 122 | C22⋊AGL(1,𝔽9) | — | 6 | 1 | no | — |
| 123 | C4⋊AGL(1,𝔽9) | — | 6 | 1 | no | — |
| 124 | C4×AGL(1,𝔽9) | — | 6 | 1 | no | — |
| 125 | C4×AGL(1,𝔽9) | — | 6 | 1 | no | — |
| 126 | C4×AGL(1,𝔽9) | — | 6 | 1 | no | — |
| 127 | PSU(3,𝔽2)⋊C4 | — | 6 | 2 | no | — |
| 128 | PSU(3,𝔽2)⋊C4 | — | 6 | 2 | no | — |
| 129 | C4×#624 | — | 6 | 1 | no | — |
| 130 | C4×D3×Dic3 | — | 12 | 1 | no | — |
| 131 | #63818 | — | 6 | 1 | no | — |
| 132 | D3×#208 | — | 12 | 1 | no | — |
| 133 | #63737 | — | 6 | 1 | no | — |
| 134 | #63732 | — | 6 | 1 | no | — |
| 135 | #63732 | — | 6 | 1 | no | — |
| 136 | #63664 | — | 4 | 1 | no | — |
| 137 | C3×#837 | — | 12 | 1 | no | — |
| 138 | C3×#837 | — | 12 | 1 | no | — |
| 139 | C3×#837 | — | 24 | 1 | no | — |
| 140 | #63570 | — | 12 | 1 | no | — |
| 141 | #63569 | — | 12 | 1 | no | — |
| 142 | #63568 | — | 12 | 1 | no | — |
| 143 | #8439 | — | 27 | 1 | no | Sylow |
| 144 | PSU(3,𝔽2)⋊C3 | #104 | 1 | 1 | yes | characteristic, complemented |
| 145 | C22×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 146 | C22×(C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 147 | Q8×H(3,𝔽3) | — | 4 | 1 | no | — |
| 148 | D4×H(3,𝔽3) | — | 4 | 1 | no | — |
| 149 | D4×H(3,𝔽3) | — | 8 | 1 | no | — |
| 150 | C2×C4×H(3,𝔽3) | — | 4 | 1 | no | — |
| 151 | C2×C4×H(3,𝔽3) | — | 8 | 1 | no | — |
| 152 | C2×#1084 | — | 8 | 1 | no | — |
| 153 | #638⋊C3 | — | 8 | 1 | no | — |
| 154 | #638⋊C3 | — | 8 | 1 | no | — |
| 155 | #638⋊C3 | — | 8 | 1 | no | — |
| 156 | C2×(C3⋊Dic3)⋊C3 | — | 4 | 1 | no | — |
| 157 | C2×(C3⋊Dic3)⋊C3 | — | 8 | 1 | no | — |
| 158 | C2×(C3⋊Dic3)⋊C3 | — | 8 | 1 | no | — |
| 159 | C4⋊((C3⋊D3)⋊C3) | — | 4 | 1 | no | — |
| 160 | C4⋊((C3⋊D3)⋊C3) | — | 8 | 1 | no | — |
| 161 | C4×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 162 | C4×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 163 | C4×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 164 | C4×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 165 | C4×(C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 166 | C4×(C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 167 | C4×(C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 168 | #634⋊C3 | — | 4 | 1 | no | — |
| 169 | #634⋊C3 | — | 8 | 1 | no | — |
| 170 | ((C3⋊D3)⋊C3)⋊C4 | — | 8 | 2 | no | — |
| 171 | ((C3⋊D3)⋊C3)⋊C4 | — | 8 | 2 | no | — |
| 172 | #6180 | — | 8 | 1 | no | — |
| 173 | (C3⋊(C3⋊C8))⋊C3 | — | 8 | 1 | no | — |
| 174 | Q8×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 175 | D4×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 176 | D4×SL(2,𝔽3) | — | 18 | 1 | no | — |
| 177 | C2×C4×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 178 | C2×C4×SL(2,𝔽3) | — | 18 | 1 | no | — |
| 179 | C2×#859 | — | 18 | 1 | no | — |
| 180 | C2×#837 | — | 36 | 1 | no | — |
| 181 | D3×#104 | — | 36 | 1 | no | — |
| 182 | SL(2,𝔽3)⋊C8 | — | 18 | 1 | no | — |
| 183 | C22×#157 | — | 3 | 1 | no | — |
| 184 | C22×#157 | — | 3 | 1 | no | — |
| 185 | C22×#157 | — | 6 | 1 | no | — |
| 186 | C22×#157 | — | 6 | 1 | no | — |
| 187 | C2×PSU(3,𝔽2) | — | 2 | 1 | no | — |
| 188 | C2×PSU(3,𝔽2) | — | 3 | 1 | no | — |
| 189 | C2×PSU(3,𝔽2) | — | 3 | 2 | no | — |
| 190 | C2×PSU(3,𝔽2) | — | 4 | 1 | no | — |
| 191 | C2×PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 192 | C2×PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 193 | C2×PSU(3,𝔽2) | — | 12 | 1 | no | — |
| 194 | C2×PSU(3,𝔽2) | #217 | 1 | 1 | yes | characteristic |
| 195 | C2×AGL(1,𝔽9) | — | 6 | 2 | no | — |
| 196 | C2×AGL(1,𝔽9) | — | 12 | 1 | no | — |
| 197 | C2×AGL(1,𝔽9) | — | 12 | 1 | no | — |
| 198 | C2×AGL(1,𝔽9) | — | 12 | 1 | no | — |
| 199 | C32×#41 | — | 4 | 1 | no | — |
| 200 | C32×#41 | — | 8 | 1 | no | — |
| 201 | C32×#41 | GL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 202 | #3832 | #226 | 1 | 1 | yes | characteristic |
| 203 | Q8×C3⋊D3 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 204 | #3830 | — | 2 | 1 | no | — |
| 205 | #3830 | #226 | 1 | 1 | yes | characteristic |
| 206 | D4×C3⋊D3 | — | 2 | 1 | no | — |
| 207 | D4×C3⋊D3 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 208 | #3828 | — | 2 | 1 | no | — |
| 209 | #3828 | GL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 210 | C2×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 211 | C2×C4×C3⋊D3 | C2×S4 | 1 | 1 | yes | characteristic |
| 212 | C3×#239 | — | 12 | 1 | no | — |
| 213 | C3×D3×Q8 | — | 12 | 1 | no | — |
| 214 | C3×#237 | — | 12 | 1 | no | — |
| 215 | C3×#237 | — | 24 | 1 | no | — |
| 216 | C3×D3×D4 | — | 12 | 1 | no | — |
| 217 | C3×D3×D4 | — | 24 | 1 | no | — |
| 218 | C3×#235 | — | 12 | 1 | no | — |
| 219 | C3×#235 | — | 24 | 1 | no | — |
| 220 | C2×C3×C4×D3 | — | 12 | 1 | no | — |
| 221 | C2×C3×C4×D3 | — | 24 | 1 | no | — |
| 222 | C2×#624 | — | 12 | 1 | no | — |
| 223 | C2×D3×Dic3 | — | 24 | 1 | no | — |
| 224 | C22⋊#157 | — | 6 | 1 | no | — |
| 225 | C22⋊#157 | — | 6 | 1 | no | — |
| 226 | C22⋊#157 | — | 6 | 1 | no | — |
| 227 | C4⋊#157 | — | 3 | 1 | no | — |
| 228 | C4⋊#157 | — | 3 | 1 | no | — |
| 229 | C4⋊#157 | — | 6 | 1 | no | — |
| 230 | C4⋊#157 | — | 6 | 1 | no | — |
| 231 | C4×#157 | — | 3 | 1 | no | — |
| 232 | C4×#157 | — | 3 | 1 | no | — |
| 233 | C4×#157 | — | 3 | 1 | no | — |
| 234 | C4×#157 | — | 3 | 1 | no | — |
| 235 | C4×#157 | — | 6 | 1 | no | — |
| 236 | C4×#157 | — | 6 | 1 | no | — |
| 237 | C4×#157 | — | 6 | 1 | no | — |
| 238 | #3777 | — | 3 | 1 | no | — |
| 239 | #3777 | — | 3 | 1 | no | — |
| 240 | #3777 | — | 3 | 2 | no | — |
| 241 | #3777 | — | 6 | 1 | no | — |
| 242 | #3777 | — | 6 | 1 | no | — |
| 243 | #3777 | — | 6 | 2 | no | — |
| 244 | #3777 | — | 6 | 2 | no | — |
| 245 | #3773 | — | 6 | 2 | no | — |
| 246 | #3773 | — | 12 | 1 | no | — |
| 247 | C4×C3⋊Dic3 | — | 4 | 1 | no | — |
| 248 | #3748 | — | 4 | 1 | no | — |
| 249 | C3×C4×Dic3 | — | 12 | 1 | no | — |
| 250 | C3×C4×Dic3 | — | 12 | 1 | no | — |
| 251 | C3×C4×Dic3 | — | 24 | 1 | no | — |
| 252 | C3×#208 | — | 12 | 1 | no | — |
| 253 | C3×#208 | — | 12 | 1 | no | — |
| 254 | C3×#208 | — | 24 | 1 | no | — |
| 255 | Dic32 | — | 12 | 1 | no | — |
| 256 | Dic32 | — | 24 | 1 | no | — |
| 257 | #3712 | — | 12 | 1 | no | — |
| 258 | #3711 | — | 24 | 1 | no | — |
| 259 | #3710 | — | 12 | 1 | no | — |
| 260 | D3×C3⋊C8 | — | 24 | 1 | no | — |
| 261 | Q8×#41 | — | 9 | 1 | no | — |
| 262 | #1806 | — | 27 | 1 | no | — |
| 263 | C4×#103 | — | 27 | 1 | no | — |
| 264 | #1503 | — | 27 | 1 | no | — |
| 265 | #1493 | — | 27 | 1 | no | — |
| 266 | #1487 | — | 27 | 1 | no | — |
| 267 | #1476 | — | 27 | 1 | no | — |
| 268 | C22×H(3,𝔽3) | — | 4 | 1 | no | — |
| 269 | C22×H(3,𝔽3) | — | 8 | 1 | no | — |
| 270 | C2×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 271 | C2×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 272 | C2×(C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 273 | C2×(C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 274 | C2×(C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 275 | C2×(C3⋊D3)⋊C3 | — | 16 | 1 | no | — |
| 276 | C2×(C3⋊D3)⋊C3 | — | 16 | 1 | no | — |
| 277 | C4×H(3,𝔽3) | — | 4 | 1 | no | — |
| 278 | C4×H(3,𝔽3) | — | 4 | 1 | no | — |
| 279 | C4×H(3,𝔽3) | — | 8 | 1 | no | — |
| 280 | #1084 | — | 8 | 2 | no | — |
| 281 | (C3⋊Dic3)⋊C3 | — | 4 | 1 | no | — |
| 282 | (C3⋊Dic3)⋊C3 | — | 4 | 1 | no | — |
| 283 | (C3⋊Dic3)⋊C3 | — | 8 | 1 | no | — |
| 284 | (C3⋊Dic3)⋊C3 | — | 8 | 2 | no | — |
| 285 | C2×C3×#41 | — | 36 | 1 | no | — |
| 286 | D3×#41 | — | 12 | 1 | no | — |
| 287 | C22×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 288 | C22×SL(2,𝔽3) | — | 18 | 1 | no | — |
| 289 | C2×C4×Dic3 | — | 36 | 1 | no | — |
| 290 | C2×#208 | — | 36 | 1 | no | — |
| 291 | D3×M16 | — | 36 | 1 | no | — |
| 292 | C42×D3 | — | 36 | 1 | no | — |
| 293 | C4×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 294 | C4×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 295 | C4×SL(2,𝔽3) | — | 18 | 1 | no | — |
| 296 | #859 | — | 18 | 2 | no | — |
| 297 | C3×#104 | — | 36 | 1 | no | — |
| 298 | #837 | — | 12 | 1 | no | — |
| 299 | #837 | — | 12 | 1 | no | — |
| 300 | #837 | — | 24 | 1 | no | — |
| 301 | #837 | — | 36 | 1 | no | — |
| 302 | #837 | — | 36 | 1 | no | — |
| 303 | #837 | — | 36 | 1 | no | — |
| 304 | #825 | — | 36 | 1 | no | — |
| 305 | #805 | — | 36 | 1 | no | — |
| 306 | C22×C3⋊D3 | — | 2 | 1 | no | — |
| 307 | C22×C3⋊D3 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 308 | C22×C3×D3 | — | 12 | 1 | no | — |
| 309 | C22×C3×D3 | — | 24 | 1 | no | — |
| 310 | C2×#157 | — | 3 | 1 | no | — |
| 311 | C2×#157 | — | 3 | 1 | no | — |
| 312 | C2×#157 | — | 3 | 1 | no | — |
| 313 | C2×#157 | — | 3 | 1 | no | — |
| 314 | C2×#157 | — | 6 | 1 | no | — |
| 315 | C2×#157 | — | 6 | 1 | no | — |
| 316 | C2×#157 | — | 6 | 1 | no | — |
| 317 | C2×#157 | — | 6 | 1 | no | — |
| 318 | C2×#157 | — | 12 | 1 | no | — |
| 319 | C2×#157 | — | 12 | 1 | no | — |
| 320 | C2×#157 | — | 12 | 1 | no | — |
| 321 | C2×#157 | — | 24 | 1 | no | — |
| 322 | PSU(3,𝔽2) | — | 3 | 1 | no | — |
| 323 | PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 324 | PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 325 | PSU(3,𝔽2) | — | 12 | 1 | no | — |
| 326 | PSU(3,𝔽2) | — | 12 | 1 | no | — |
| 327 | PSU(3,𝔽2) | — | 12 | 2 | no | — |
| 328 | PSU(3,𝔽2) | #837 | 1 | 1 | yes | characteristic, complemented |
| 329 | AGL(1,𝔽9) | — | 12 | 2 | no | — |
| 330 | AGL(1,𝔽9) | — | 24 | 1 | no | — |
| 331 | C32×Q8 | — | 4 | 1 | no | — |
| 332 | C32×Q8 | — | 8 | 1 | no | — |
| 333 | C32×Q8 | #859 | 1 | 1 | yes | characteristic, complemented |
| 334 | C32×D4 | — | 2 | 1 | no | — |
| 335 | C32×D4 | — | 4 | 1 | no | — |
| 336 | C32×D4 | — | 8 | 1 | no | — |
| 337 | C32×D4 | — | 8 | 1 | no | — |
| 338 | C32×D4 | — | 16 | 1 | no | — |
| 339 | C32×D4 | #859 | 1 | 1 | yes | characteristic, complemented |
| 340 | C2×C32×C4 | — | 2 | 1 | no | — |
| 341 | C2×C32×C4 | — | 4 | 1 | no | — |
| 342 | C2×C32×C4 | — | 8 | 1 | no | — |
| 343 | C2×C32×C4 | — | 8 | 1 | no | — |
| 344 | C2×C32×C4 | — | 16 | 1 | no | — |
| 345 | C2×C32×C4 | C2×GL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 346 | #638 | — | 2 | 1 | no | — |
| 347 | #638 | — | 2 | 1 | no | — |
| 348 | #638 | — | 2 | 1 | no | — |
| 349 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 350 | C2×C3⋊Dic3 | — | 8 | 1 | no | — |
| 351 | C2×C3⋊Dic3 | #983 | 1 | 1 | yes | characteristic |
| 352 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 353 | C4⋊(C3⋊D3) | #859 | 1 | 1 | yes | characteristic, complemented |
| 354 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 355 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 356 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 357 | C4×C3⋊D3 | C2×#226 | 1 | 1 | yes | characteristic |
| 358 | C4×C3⋊D3 | #983 | 1 | 1 | yes | characteristic |
| 359 | C4×C3⋊D3 | C2×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 360 | C4×C3⋊D3 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 361 | #634 | — | 2 | 1 | no | — |
| 362 | #634 | #859 | 1 | 1 | yes | characteristic, complemented |
| 363 | C3×#67 | — | 24 | 1 | no | — |
| 364 | C3×#67 | — | 24 | 1 | no | — |
| 365 | C3×#67 | — | 24 | 1 | no | — |
| 366 | C2×C3×Dic3 | — | 12 | 1 | no | — |
| 367 | C2×C3×Dic3 | — | 24 | 1 | no | — |
| 368 | C2×C3×Dic3 | — | 24 | 1 | no | — |
| 369 | C2×C3×Dic3 | — | 24 | 1 | no | — |
| 370 | C2×C3×Dic3 | — | 48 | 1 | no | — |
| 371 | C3×D12 | — | 12 | 1 | no | — |
| 372 | C3×D12 | — | 24 | 1 | no | — |
| 373 | C3×C4×D3 | — | 12 | 1 | no | — |
| 374 | C3×C4×D3 | — | 12 | 1 | no | — |
| 375 | C3×C4×D3 | — | 12 | 1 | no | — |
| 376 | C3×C4×D3 | — | 12 | 1 | no | — |
| 377 | C3×C4×D3 | — | 24 | 1 | no | — |
| 378 | C3×C4×D3 | — | 24 | 1 | no | — |
| 379 | C3×C4×D3 | — | 24 | 1 | no | — |
| 380 | C3×Dic6 | — | 12 | 1 | no | — |
| 381 | C3×Dic6 | — | 24 | 1 | no | — |
| 382 | #624 | — | 12 | 2 | no | — |
| 383 | #624 | — | 24 | 1 | no | — |
| 384 | D3×Dic3 | — | 24 | 2 | no | — |
| 385 | D3×Dic3 | — | 24 | 2 | no | — |
| 386 | C3⋊(C3⋊C8) | — | 8 | 1 | no | — |
| 387 | C3×C3⋊C8 | — | 24 | 1 | no | — |
| 388 | C3×C3⋊C8 | — | 24 | 1 | no | — |
| 389 | C3×C3⋊C8 | — | 48 | 1 | no | — |
| 390 | Q82 | — | 9 | 1 | no | — |
| 391 | #557 | — | 27 | 1 | no | — |
| 392 | #554 | — | 27 | 1 | no | — |
| 393 | #554 | — | 54 | 1 | no | — |
| 394 | D4×Q8 | — | 9 | 1 | no | — |
| 395 | D4×Q8 | — | 18 | 1 | no | — |
| 396 | #533 | — | 27 | 1 | no | — |
| 397 | #533 | — | 54 | 1 | no | — |
| 398 | C4×#41 | — | 27 | 1 | no | — |
| 399 | C2×C4×Q8 | — | 9 | 1 | no | — |
| 400 | C2×C4×Q8 | — | 18 | 1 | no | — |
| 401 | #431 | — | 27 | 1 | no | — |
| 402 | #423 | — | 27 | 1 | no | — |
| 403 | C2×#104 | — | 54 | 1 | no | — |
| 404 | C2×#103 | — | 54 | 1 | no | — |
| 405 | C2×C4×C8 | — | 27 | 1 | no | — |
| 406 | C4×C4⋊C4 | — | 27 | 1 | no | — |
| 407 | #340 | — | 54 | 1 | no | — |
| 408 | #339 | — | 54 | 1 | no | — |
| 409 | #328 | — | 54 | 2 | no | — |
| 410 | Q8⋊C8 | — | 54 | 1 | no | — |
| 411 | Q8⋊C8 | — | 54 | 1 | no | — |
| 412 | Q8⋊C8 | — | 54 | 2 | no | — |
| 413 | Q8⋊C8 | — | 54 | 1 | no | — |
| 414 | D4⋊C8 | — | 54 | 1 | no | — |
| 415 | C2×H(3,𝔽3) | — | 4 | 1 | no | — |
| 416 | C2×H(3,𝔽3) | — | 8 | 1 | no | — |
| 417 | C2×H(3,𝔽3) | — | 16 | 1 | no | — |
| 418 | (C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 419 | (C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 420 | (C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 421 | (C3⋊D3)⋊C3 | — | 16 | 1 | no | — |
| 422 | C3×#41 | — | 4 | 1 | no | — |
| 423 | C3×#41 | — | 12 | 1 | no | — |
| 424 | C3×#41 | — | 24 | 1 | no | — |
| 425 | C3×#41 | — | 36 | 1 | no | — |
| 426 | C3×#41 | — | 36 | 1 | no | — |
| 427 | C3×#41 | — | 36 | 1 | no | — |
| 428 | C3×#41 | — | 72 | 1 | no | — |
| 429 | C3×#41 | — | 72 | 1 | no | — |
| 430 | C2×C3×Q8 | — | 36 | 1 | no | — |
| 431 | C2×C3×D4 | — | 36 | 1 | no | — |
| 432 | C2×C3×D4 | — | 72 | 1 | no | — |
| 433 | C22×C3×C4 | — | 36 | 1 | no | — |
| 434 | C22×C3×C4 | — | 72 | 1 | no | — |
| 435 | C22×Dic3 | — | 72 | 1 | no | — |
| 436 | #239 | — | 12 | 1 | no | — |
| 437 | D3×Q8 | — | 12 | 1 | no | — |
| 438 | #237 | — | 12 | 1 | no | — |
| 439 | #237 | — | 24 | 1 | no | — |
| 440 | D3×D4 | — | 12 | 1 | no | — |
| 441 | D3×D4 | — | 24 | 1 | no | — |
| 442 | #235 | — | 12 | 1 | no | — |
| 443 | #235 | — | 24 | 1 | no | — |
| 444 | C2×C4×D3 | — | 12 | 1 | no | — |
| 445 | C2×C4×D3 | — | 24 | 1 | no | — |
| 446 | C2×C4×D3 | — | 72 | 1 | no | — |
| 447 | C2×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 448 | C2×SL(2,𝔽3) | — | 18 | 1 | no | — |
| 449 | C2×SL(2,𝔽3) | — | 36 | 1 | no | — |
| 450 | C3×M16 | — | 36 | 1 | no | — |
| 451 | C3×C42 | — | 36 | 1 | no | — |
| 452 | C4×Dic3 | — | 12 | 1 | no | — |
| 453 | C4×Dic3 | — | 12 | 1 | no | — |
| 454 | C4×Dic3 | — | 24 | 1 | no | — |
| 455 | C4×Dic3 | — | 36 | 1 | no | — |
| 456 | C4×Dic3 | — | 72 | 1 | no | — |
| 457 | C4×Dic3 | — | 72 | 1 | no | — |
| 458 | #208 | — | 12 | 1 | no | — |
| 459 | #208 | — | 12 | 1 | no | — |
| 460 | #208 | — | 24 | 1 | no | — |
| 461 | #208 | — | 36 | 1 | no | — |
| 462 | #208 | — | 72 | 1 | no | — |
| 463 | C2×C3⋊C8 | — | 72 | 1 | no | — |
| 464 | ΓL(1,𝔽25) | — | 72 | 1 | no | — |
| 465 | D3×C8 | — | 72 | 1 | no | — |
| 466 | C22×C32 | — | 2 | 1 | no | — |
| 467 | C22×C32 | — | 4 | 1 | no | — |
| 468 | C22×C32 | — | 8 | 1 | no | — |
| 469 | C22×C32 | — | 8 | 1 | no | — |
| 470 | C22×C32 | — | 16 | 1 | no | — |
| 471 | C22×C32 | #5421 | 1 | 1 | yes | characteristic |
| 472 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 473 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 474 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 475 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 476 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 477 | C2×C3⋊D3 | #5419 | 1 | 1 | yes | characteristic |
| 478 | C2×C3⋊D3 | #5432 | 1 | 1 | yes | characteristic |
| 479 | C2×C3×D3 | — | 12 | 1 | no | — |
| 480 | C2×C3×D3 | — | 12 | 1 | no | — |
| 481 | C2×C3×D3 | — | 24 | 1 | no | — |
| 482 | C2×C3×D3 | — | 24 | 1 | no | — |
| 483 | C2×C3×D3 | — | 24 | 1 | no | — |
| 484 | C2×C3×D3 | — | 48 | 1 | no | — |
| 485 | C2×C3×D3 | — | 48 | 1 | no | — |
| 486 | #157 | — | 3 | 1 | no | — |
| 487 | #157 | — | 3 | 1 | no | — |
| 488 | #157 | — | 6 | 1 | no | — |
| 489 | #157 | — | 6 | 1 | no | — |
| 490 | #157 | — | 6 | 1 | no | — |
| 491 | #157 | — | 12 | 1 | no | — |
| 492 | #157 | — | 12 | 1 | no | — |
| 493 | C32×C4 | — | 2 | 1 | no | — |
| 494 | C32×C4 | — | 4 | 1 | no | — |
| 495 | C32×C4 | — | 4 | 1 | no | — |
| 496 | C32×C4 | — | 8 | 1 | no | — |
| 497 | C32×C4 | — | 8 | 1 | no | — |
| 498 | C32×C4 | — | 8 | 1 | no | — |
| 499 | C32×C4 | — | 16 | 1 | no | — |
| 500 | C32×C4 | C2×#859 | 1 | 1 | yes | characteristic |
| 501 | C32×C4 | #5421 | 1 | 1 | yes | characteristic |
| 502 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 503 | C3⋊Dic3 | — | 8 | 2 | no | — |
| 504 | C3⋊Dic3 | #5419 | 1 | 1 | yes | characteristic |
| 505 | C3⋊Dic3 | #5420 | 1 | 1 | yes | characteristic |
| 506 | C3×Dic3 | — | 12 | 1 | no | — |
| 507 | C3×Dic3 | — | 12 | 1 | no | — |
| 508 | C3×Dic3 | — | 24 | 2 | no | — |
| 509 | C3×Dic3 | — | 24 | 1 | no | — |
| 510 | C3×Dic3 | — | 24 | 2 | no | — |
| 511 | C3×Dic3 | — | 48 | 2 | no | — |
| 512 | C2×#41 | — | 9 | 1 | no | — |
| 513 | C22×Q8 | — | 9 | 1 | no | — |
| 514 | C22×Q8 | — | 18 | 1 | no | — |
| 515 | C2×M16 | — | 54 | 1 | no | — |
| 516 | C22×C8 | — | 54 | 1 | no | — |
| 517 | C4⋊Q8 | — | 27 | 1 | no | — |
| 518 | C4⋊Q8 | — | 27 | 1 | no | — |
| 519 | C4⋊Q8 | — | 54 | 1 | no | — |
| 520 | C4⋊Q8 | — | 54 | 1 | no | — |
| 521 | #125 | — | 54 | 1 | no | — |
| 522 | #125 | — | 54 | 2 | no | — |
| 523 | C22⋊Q8 | — | 27 | 2 | no | — |
| 524 | C22⋊Q8 | — | 54 | 2 | no | — |
| 525 | C22⋊Q8 | — | 54 | 1 | no | — |
| 526 | C22⋊Q8 | — | 54 | 1 | no | — |
| 527 | C22⋊Q8 | — | 54 | 1 | no | — |
| 528 | C4×Q8 | — | 9 | 1 | no | — |
| 529 | C4×Q8 | — | 9 | 1 | no | — |
| 530 | C4×Q8 | — | 18 | 1 | no | — |
| 531 | C4×Q8 | — | 27 | 1 | no | — |
| 532 | C4×Q8 | — | 27 | 1 | no | — |
| 533 | C4×Q8 | — | 27 | 1 | no | — |
| 534 | C4×Q8 | — | 27 | 1 | no | — |
| 535 | C4×Q8 | — | 27 | 2 | no | — |
| 536 | C4×Q8 | — | 54 | 1 | no | — |
| 537 | C4×Q8 | — | 54 | 1 | no | — |
| 538 | C4×D4 | — | 27 | 1 | no | — |
| 539 | C4×D4 | — | 27 | 1 | no | — |
| 540 | C4×D4 | — | 54 | 1 | no | — |
| 541 | C4×D4 | — | 54 | 1 | no | — |
| 542 | #117 | — | 27 | 1 | no | — |
| 543 | #117 | — | 54 | 1 | no | — |
| 544 | C2×C4⋊C4 | — | 27 | 1 | no | — |
| 545 | C2×C4⋊C4 | — | 54 | 1 | no | — |
| 546 | C2×C4⋊C4 | — | 54 | 1 | no | — |
| 547 | C2×C42 | — | 27 | 1 | no | — |
| 548 | C2×C42 | — | 54 | 1 | no | — |
| 549 | C2×C42 | — | 54 | 1 | no | — |
| 550 | C4⋊C8 | — | 54 | 1 | no | — |
| 551 | C4⋊C8 | — | 54 | 1 | no | — |
| 552 | C4⋊C8 | — | 54 | 1 | no | — |
| 553 | #104 | — | 36 | 1 | no | — |
| 554 | #104 | — | 108 | 1 | no | — |
| 555 | #103 | — | 54 | 2 | no | — |
| 556 | #103 | — | 54 | 2 | no | — |
| 557 | C22⋊C8 | — | 54 | 1 | no | — |
| 558 | C4×C8 | — | 54 | 1 | no | — |
| 559 | C4×C8 | — | 54 | 1 | no | — |
| 560 | C4×C8 | — | 54 | 1 | no | — |
| 561 | #95 | — | 54 | 1 | no | — |
| 562 | H(3,𝔽3) | — | 4 | 1 | no | Sylow |
| 563 | C23×C3 | — | 36 | 1 | no | — |
| 564 | C23×C3 | — | 72 | 1 | no | — |
| 565 | C22×D3 | — | 12 | 1 | no | — |
| 566 | C22×D3 | — | 24 | 1 | no | — |
| 567 | C3×Q8 | — | 4 | 1 | no | — |
| 568 | C3×Q8 | — | 12 | 1 | no | — |
| 569 | C3×Q8 | — | 24 | 1 | no | — |
| 570 | C3×Q8 | — | 36 | 1 | no | — |
| 571 | C3×Q8 | — | 72 | 1 | no | — |
| 572 | C3×D4 | — | 4 | 1 | no | — |
| 573 | C3×D4 | — | 8 | 1 | no | — |
| 574 | C3×D4 | — | 12 | 1 | no | — |
| 575 | C3×D4 | — | 24 | 1 | no | — |
| 576 | C3×D4 | — | 24 | 1 | no | — |
| 577 | C3×D4 | — | 36 | 1 | no | — |
| 578 | C3×D4 | — | 48 | 1 | no | — |
| 579 | C3×D4 | — | 72 | 1 | no | — |
| 580 | C3×D4 | — | 72 | 1 | no | — |
| 581 | C3×D4 | — | 72 | 1 | no | — |
| 582 | C3×D4 | — | 72 | 1 | no | — |
| 583 | C2×C3×C4 | — | 4 | 1 | no | — |
| 584 | C2×C3×C4 | — | 8 | 1 | no | — |
| 585 | C2×C3×C4 | — | 12 | 1 | no | — |
| 586 | C2×C3×C4 | — | 24 | 1 | no | — |
| 587 | C2×C3×C4 | — | 24 | 1 | no | — |
| 588 | C2×C3×C4 | — | 36 | 1 | no | — |
| 589 | C2×C3×C4 | — | 36 | 1 | no | — |
| 590 | C2×C3×C4 | — | 36 | 1 | no | — |
| 591 | C2×C3×C4 | — | 36 | 1 | no | — |
| 592 | C2×C3×C4 | — | 36 | 1 | no | — |
| 593 | C2×C3×C4 | — | 48 | 1 | no | — |
| 594 | C2×C3×C4 | — | 72 | 1 | no | — |
| 595 | C2×C3×C4 | — | 72 | 1 | no | — |
| 596 | C2×C3×C4 | — | 72 | 1 | no | — |
| 597 | C2×C3×C4 | — | 72 | 1 | no | — |
| 598 | C2×C3×C4 | — | 72 | 1 | no | — |
| 599 | #67 | — | 24 | 1 | no | — |
| 600 | #67 | — | 24 | 1 | no | — |
| 601 | #67 | — | 24 | 1 | no | — |
| 602 | C2×Dic3 | — | 12 | 1 | no | — |
| 603 | C2×Dic3 | — | 24 | 1 | no | — |
| 604 | C2×Dic3 | — | 24 | 1 | no | — |
| 605 | C2×Dic3 | — | 24 | 1 | no | — |
| 606 | C2×Dic3 | — | 48 | 1 | no | — |
| 607 | C2×Dic3 | — | 72 | 1 | no | — |
| 608 | C2×Dic3 | — | 72 | 2 | no | — |
| 609 | C2×Dic3 | — | 72 | 2 | no | — |
| 610 | D12 | — | 12 | 1 | no | — |
| 611 | D12 | — | 24 | 1 | no | — |
| 612 | C4×D3 | — | 12 | 1 | no | — |
| 613 | C4×D3 | — | 12 | 1 | no | — |
| 614 | C4×D3 | — | 12 | 1 | no | — |
| 615 | C4×D3 | — | 12 | 1 | no | — |
| 616 | C4×D3 | — | 24 | 1 | no | — |
| 617 | C4×D3 | — | 24 | 1 | no | — |
| 618 | C4×D3 | — | 24 | 1 | no | — |
| 619 | C4×D3 | — | 72 | 2 | no | — |
| 620 | C4×D3 | — | 72 | 2 | no | — |
| 621 | Dic6 | — | 12 | 1 | no | — |
| 622 | Dic6 | — | 24 | 1 | no | — |
| 623 | SL(2,𝔽3) | — | 9 | 1 | no | — |
| 624 | C3×C8 | — | 72 | 1 | no | — |
| 625 | C3⋊C8 | — | 24 | 1 | no | — |
| 626 | C3⋊C8 | — | 24 | 1 | no | — |
| 627 | C3⋊C8 | — | 48 | 1 | no | — |
| 628 | C3⋊C8 | — | 72 | 1 | no | — |
| 629 | C2×C32 | — | 2 | 1 | no | — |
| 630 | C2×C32 | — | 4 | 1 | no | — |
| 631 | C2×C32 | — | 4 | 1 | no | — |
| 632 | C2×C32 | — | 8 | 1 | no | — |
| 633 | C2×C32 | — | 8 | 1 | no | — |
| 634 | C2×C32 | — | 16 | 1 | no | — |
| 635 | C2×C32 | — | 16 | 1 | no | — |
| 636 | C2×C32 | — | 32 | 1 | no | — |
| 637 | C2×C32 | #73148 | 1 | 1 | yes | characteristic |
| 638 | C3⋊D3 | — | 2 | 1 | no | — |
| 639 | C3⋊D3 | — | 4 | 1 | no | — |
| 640 | C3⋊D3 | #73150 | 1 | 1 | yes | characteristic |
| 641 | C3⋊D3 | #73157 | 1 | 1 | yes | characteristic |
| 642 | C3×D3 | — | 12 | 1 | no | — |
| 643 | C3×D3 | — | 12 | 1 | no | — |
| 644 | C3×D3 | — | 24 | 1 | no | — |
| 645 | C3×D3 | — | 48 | 1 | no | — |
| 646 | #41 | — | 9 | 1 | no | — |
| 647 | #41 | — | 9 | 1 | no | — |
| 648 | #41 | — | 9 | 1 | no | — |
| 649 | #41 | — | 18 | 1 | no | — |
| 650 | #41 | — | 18 | 1 | no | — |
| 651 | #41 | AGL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 652 | C2×Q8 | — | 9 | 1 | no | — |
| 653 | C2×Q8 | — | 9 | 1 | no | — |
| 654 | C2×Q8 | — | 18 | 1 | no | — |
| 655 | C2×Q8 | — | 27 | 1 | no | — |
| 656 | C2×Q8 | — | 27 | 2 | no | — |
| 657 | C2×Q8 | — | 36 | 1 | no | — |
| 658 | C2×Q8 | — | 54 | 1 | no | — |
| 659 | C2×Q8 | — | 54 | 1 | no | — |
| 660 | C2×Q8 | — | 108 | 1 | no | — |
| 661 | C2×D4 | — | 9 | 1 | no | — |
| 662 | C2×D4 | — | 18 | 1 | no | — |
| 663 | C22×C4 | — | 9 | 1 | no | — |
| 664 | C22×C4 | — | 18 | 1 | no | — |
| 665 | C22×C4 | — | 27 | 1 | no | — |
| 666 | C22×C4 | — | 27 | 1 | no | — |
| 667 | C22×C4 | — | 54 | 1 | no | — |
| 668 | C22×C4 | — | 54 | 1 | no | — |
| 669 | C22×C4 | — | 108 | 1 | no | — |
| 670 | M16 | — | 36 | 1 | no | — |
| 671 | M16 | — | 108 | 1 | no | — |
| 672 | C2×C8 | — | 54 | 2 | no | — |
| 673 | C2×C8 | — | 108 | 1 | no | — |
| 674 | C2×C8 | — | 108 | 1 | no | — |
| 675 | C2×C8 | — | 108 | 1 | no | — |
| 676 | C2×C8 | — | 108 | 1 | no | — |
| 677 | C4⋊C4 | — | 27 | 1 | no | — |
| 678 | C4⋊C4 | — | 27 | 1 | no | — |
| 679 | C4⋊C4 | — | 27 | 1 | no | — |
| 680 | C4⋊C4 | — | 27 | 1 | no | — |
| 681 | C4⋊C4 | — | 27 | 2 | no | — |
| 682 | C4⋊C4 | — | 54 | 1 | no | — |
| 683 | C4⋊C4 | — | 54 | 1 | no | — |
| 684 | C4⋊C4 | — | 54 | 1 | no | — |
| 685 | C4⋊C4 | — | 54 | 1 | no | — |
| 686 | C4⋊C4 | — | 54 | 2 | no | — |
| 687 | C4⋊C4 | — | 54 | 2 | no | — |
| 688 | C4⋊C4 | — | 54 | 2 | no | — |
| 689 | C4⋊C4 | — | 108 | 1 | no | — |
| 690 | C22⋊C4 | — | 54 | 1 | no | — |
| 691 | C22⋊C4 | — | 54 | 1 | no | — |
| 692 | C22⋊C4 | — | 54 | 1 | no | — |
| 693 | C42 | — | 27 | 1 | no | — |
| 694 | C42 | — | 27 | 1 | no | — |
| 695 | C42 | — | 27 | 1 | no | — |
| 696 | C42 | — | 27 | 1 | no | — |
| 697 | C42 | — | 36 | 1 | no | — |
| 698 | C42 | — | 54 | 1 | no | — |
| 699 | C42 | — | 54 | 1 | no | — |
| 700 | C42 | — | 54 | 1 | no | — |
| 701 | C42 | — | 108 | 1 | no | — |
| 702 | C22×C3 | — | 4 | 1 | no | — |
| 703 | C22×C3 | — | 8 | 1 | no | — |
| 704 | C22×C3 | — | 12 | 1 | no | — |
| 705 | C22×C3 | — | 24 | 1 | no | — |
| 706 | C22×C3 | — | 24 | 1 | no | — |
| 707 | C22×C3 | — | 36 | 1 | no | — |
| 708 | C22×C3 | — | 36 | 1 | no | — |
| 709 | C22×C3 | — | 48 | 1 | no | — |
| 710 | C22×C3 | — | 72 | 1 | no | — |
| 711 | C22×C3 | — | 72 | 1 | no | — |
| 712 | C22×C3 | — | 72 | 1 | no | — |
| 713 | C22×C3 | — | 144 | 1 | no | — |
| 714 | C22×C3 | — | 144 | 1 | no | — |
| 715 | C2×D3 | — | 12 | 1 | no | — |
| 716 | C2×D3 | — | 12 | 1 | no | — |
| 717 | C2×D3 | — | 24 | 1 | no | — |
| 718 | C2×D3 | — | 24 | 1 | no | — |
| 719 | C2×D3 | — | 24 | 1 | no | — |
| 720 | C2×D3 | — | 48 | 1 | no | — |
| 721 | C2×D3 | — | 48 | 1 | no | — |
| 722 | C3×C4 | — | 4 | 1 | no | — |
| 723 | C3×C4 | — | 4 | 1 | no | — |
| 724 | C3×C4 | — | 8 | 1 | no | — |
| 725 | C3×C4 | — | 12 | 1 | no | — |
| 726 | C3×C4 | — | 12 | 1 | no | — |
| 727 | C3×C4 | — | 24 | 1 | no | — |
| 728 | C3×C4 | — | 24 | 1 | no | — |
| 729 | C3×C4 | — | 24 | 1 | no | — |
| 730 | C3×C4 | — | 36 | 1 | no | — |
| 731 | C3×C4 | — | 36 | 1 | no | — |
| 732 | C3×C4 | — | 48 | 1 | no | — |
| 733 | C3×C4 | — | 72 | 1 | no | — |
| 734 | C3×C4 | — | 72 | 2 | no | — |
| 735 | Dic3 | — | 12 | 1 | no | — |
| 736 | Dic3 | — | 12 | 1 | no | — |
| 737 | Dic3 | — | 24 | 1 | no | — |
| 738 | Dic3 | — | 24 | 2 | no | — |
| 739 | Dic3 | — | 24 | 2 | no | — |
| 740 | Dic3 | — | 48 | 2 | no | — |
| 741 | Dic3 | — | 72 | 2 | no | — |
| 742 | C32 | — | 4 | 1 | no | — |
| 743 | C32 | — | 8 | 1 | no | — |
| 744 | C32 | #11711050 | 1 | 1 | yes | characteristic, complemented |
| 745 | C23 | — | 9 | 1 | no | — |
| 746 | C23 | — | 18 | 1 | no | — |
| 747 | Q8 | — | 9 | 1 | no | — |
| 748 | Q8 | — | 9 | 1 | no | — |
| 749 | Q8 | — | 18 | 1 | no | — |
| 750 | Q8 | — | 27 | 1 | no | — |
| 751 | Q8 | — | 54 | 1 | no | — |
| 752 | Q8 | — | 54 | 1 | no | — |
| 753 | Q8 | — | 108 | 1 | no | — |
| 754 | Q8 | — | 108 | 1 | no | — |
| 755 | Q8 | — | 108 | 2 | no | — |
| 756 | Q8 | (PSU(3,𝔽2)⋊C3)⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 757 | D4 | — | 2 | 1 | no | — |
| 758 | D4 | — | 9 | 1 | no | — |
| 759 | D4 | — | 18 | 1 | no | — |
| 760 | D4 | — | 18 | 1 | no | — |
| 761 | D4 | — | 18 | 1 | no | — |
| 762 | D4 | — | 18 | 1 | no | — |
| 763 | D4 | (PSU(3,𝔽2)⋊C3)⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 764 | C2×C4 | — | 2 | 1 | no | — |
| 765 | C2×C4 | — | 9 | 1 | no | — |
| 766 | C2×C4 | — | 9 | 1 | no | — |
| 767 | C2×C4 | — | 9 | 1 | no | — |
| 768 | C2×C4 | — | 9 | 1 | no | — |
| 769 | C2×C4 | — | 9 | 1 | no | — |
| 770 | C2×C4 | — | 18 | 1 | no | — |
| 771 | C2×C4 | — | 18 | 1 | no | — |
| 772 | C2×C4 | — | 18 | 1 | no | — |
| 773 | C2×C4 | — | 18 | 1 | no | — |
| 774 | C2×C4 | — | 27 | 1 | no | — |
| 775 | C2×C4 | — | 27 | 1 | no | — |
| 776 | C2×C4 | — | 27 | 1 | no | — |
| 777 | C2×C4 | — | 27 | 1 | no | — |
| 778 | C2×C4 | — | 54 | 1 | no | — |
| 779 | C2×C4 | — | 54 | 1 | no | — |
| 780 | C2×C4 | — | 54 | 1 | no | — |
| 781 | C2×C4 | — | 54 | 1 | no | — |
| 782 | C2×C4 | — | 72 | 1 | no | — |
| 783 | C2×C4 | — | 108 | 1 | no | — |
| 784 | C2×C4 | — | 108 | 1 | no | — |
| 785 | C2×C4 | — | 108 | 1 | no | — |
| 786 | C2×C4 | — | 108 | 2 | no | — |
| 787 | C2×C4 | — | 216 | 1 | no | — |
| 788 | C2×C4 | — | 216 | 1 | no | — |
| 789 | C2×C4 | C2×AGL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 790 | C8 | — | 72 | 1 | no | — |
| 791 | C8 | — | 108 | 2 | no | — |
| 792 | C8 | — | 216 | 1 | no | — |
| 793 | C2×C3 | — | 4 | 1 | no | — |
| 794 | C2×C3 | — | 8 | 1 | no | — |
| 795 | C2×C3 | — | 12 | 1 | no | — |
| 796 | C2×C3 | — | 16 | 1 | no | — |
| 797 | C2×C3 | — | 24 | 1 | no | — |
| 798 | C2×C3 | — | 24 | 1 | no | — |
| 799 | C2×C3 | — | 36 | 1 | no | — |
| 800 | C2×C3 | — | 36 | 1 | no | — |
| 801 | C2×C3 | — | 48 | 1 | no | — |
| 802 | C2×C3 | — | 48 | 1 | no | — |
| 803 | C2×C3 | — | 72 | 1 | no | — |
| 804 | C2×C3 | — | 96 | 1 | no | — |
| 805 | C2×C3 | — | 144 | 1 | no | — |
| 806 | D3 | — | 12 | 1 | no | — |
| 807 | D3 | — | 12 | 1 | no | — |
| 808 | D3 | — | 24 | 1 | no | — |
| 809 | D3 | — | 48 | 1 | no | — |
| 810 | C22 | — | 2 | 1 | no | — |
| 811 | C22 | — | 9 | 1 | no | — |
| 812 | C22 | — | 9 | 1 | no | — |
| 813 | C22 | — | 18 | 1 | no | — |
| 814 | C22 | — | 18 | 1 | no | — |
| 815 | C22 | — | 18 | 1 | no | — |
| 816 | C22 | — | 36 | 1 | no | — |
| 817 | C22 | — | 36 | 1 | no | — |
| 818 | C22 | #13180131 | 1 | 1 | yes | characteristic |
| 819 | C4 | — | 2 | 1 | no | — |
| 820 | C4 | — | 9 | 1 | no | — |
| 821 | C4 | — | 9 | 1 | no | — |
| 822 | C4 | — | 18 | 1 | no | — |
| 823 | C4 | — | 27 | 1 | no | — |
| 824 | C4 | — | 27 | 1 | no | — |
| 825 | C4 | — | 54 | 1 | no | — |
| 826 | C4 | — | 54 | 1 | no | — |
| 827 | C4 | — | 54 | 1 | no | — |
| 828 | C4 | — | 72 | 2 | no | — |
| 829 | C4 | — | 108 | 1 | no | — |
| 830 | C4 | — | 108 | 1 | no | — |
| 831 | C4 | C2×(PSU(3,𝔽2)⋊C3)⋊C4 | 1 | 1 | yes | characteristic |
| 832 | C4 | #13180131 | 1 | 1 | yes | characteristic |
| 833 | C3 | — | 4 | 1 | no | — |
| 834 | C3 | — | 12 | 1 | no | — |
| 835 | C3 | — | 24 | 1 | no | — |
| 836 | C2 | — | 2 | 1 | no | — |
| 837 | C2 | — | 4 | 1 | no | — |
| 838 | C2 | — | 9 | 1 | no | — |
| 839 | C2 | — | 9 | 1 | no | — |
| 840 | C2 | — | 18 | 1 | no | — |
| 841 | C2 | — | 36 | 1 | no | — |
| 842 | C2 | #72220407 | 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. #72220123 | C2 | semidirect |
| 5. Q8×PSU(3,𝔽2)⋊C3 | C4 | semidirect |
| 7. D4×PSU(3,𝔽2)⋊C3 | C4 | semidirect |
| 36. Q8×PSU(3,𝔽2) | Dic3 | semidirect |
| 40. D4×PSU(3,𝔽2) | Dic3 | semidirect |
| 144. PSU(3,𝔽2)⋊C3 | #104 | semidirect |
| 328. PSU(3,𝔽2) | #837 | semidirect |
| 333. C32×Q8 | #859 | semidirect |
| 339. C32×D4 | #859 | semidirect |
| 353. C4⋊(C3⋊D3) | #859 | semidirect |
| 362. #634 | #859 | semidirect |
| 744. C32 | #11711050 | semidirect |
| 756. Q8 | (PSU(3,𝔽2)⋊C3)⋊C4 | semidirect |
| 763. D4 | (PSU(3,𝔽2)⋊C3)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72220456 | 3 |
| C4×(PSU(3,𝔽2)⋊C3)⋊C4 | 2 |
| #41×PSU(3,𝔽2)⋊C3 | 2 |
| #72220123 | 2 |
| #13141059 | 4 |
| #11711050 | 9 |