Finite Group DatabasebetaFinite Group Databasebeta← GL(2,𝔽3)×((C3⋊D3)⋊C3)⋊C2 #72244581
Order 5184.
1810 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 1810 conjugacy classes of subgroups — too many to draw. Only its 71 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 | #72244580 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | GL(2,𝔽3)×#272 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | GL(2,𝔽3)×(C3⋊D3)⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | SL(2,𝔽3)×((C3⋊D3)⋊C3)⋊C2 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72220376 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | D32×GL(2,𝔽3) | — | 3 | 2 | no | maximal |
| 7 | SD16×((C3⋊D3)⋊C3)⋊C2 | — | 3 | 1 | no | maximal |
| 8 | C2×D3×((C3⋊D3)⋊C3)⋊C2 | — | 4 | 1 | no | maximal |
| 9 | SL(2,𝔽3)×#272 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | SL(2,𝔽3)×(C3⋊D3)⋊C3 | C22 | 1 | 2 | yes | complemented |
| 11 | #13048417 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | #13048389 | C22 | 1 | 2 | yes | complemented |
| 13 | H(3,𝔽3)×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | D32×SL(2,𝔽3) | — | 3 | 2 | no | — |
| 15 | #11724211 | — | 3 | 2 | no | — |
| 16 | D3×C3⋊GL(2,𝔽3) | — | 3 | 2 | no | — |
| 17 | D3×C3⋊GL(2,𝔽3) | — | 3 | 2 | no | — |
| 18 | C3⋊D3×GL(2,𝔽3) | D3 | 1 | 2 | yes | complemented |
| 19 | C3×D3×GL(2,𝔽3) | — | 3 | 2 | no | — |
| 20 | C3×D3×GL(2,𝔽3) | — | 3 | 2 | no | — |
| 21 | C3×D3×GL(2,𝔽3) | — | 6 | 1 | no | — |
| 22 | Q8×((C3⋊D3)⋊C3)⋊C2 | D3 | 1 | 1 | yes | characteristic, complemented |
| 23 | D4×((C3⋊D3)⋊C3)⋊C2 | — | 3 | 1 | no | — |
| 24 | #11722260 | — | 6 | 2 | no | — |
| 25 | SD16×#272 | — | 3 | 1 | no | — |
| 26 | SD16×(C3⋊D3)⋊C3 | — | 3 | 2 | no | — |
| 27 | #11721232 | — | 3 | 2 | no | — |
| 28 | #11721228 | — | 3 | 1 | no | — |
| 29 | #11721198 | — | 3 | 2 | no | — |
| 30 | #11721188 | — | 3 | 1 | no | — |
| 31 | #11720846 | — | 3 | 2 | no | — |
| 32 | #11720837 | — | 3 | 1 | no | — |
| 33 | C8×((C3⋊D3)⋊C3)⋊C2 | — | 3 | 1 | no | — |
| 34 | C2×#66432 | — | 4 | 1 | no | — |
| 35 | C2×D3×#272 | — | 4 | 1 | no | — |
| 36 | C2×((C3⋊D3)⋊C3)⋊D3 | — | 4 | 2 | no | — |
| 37 | C2×C3×((C3⋊D3)⋊C3)⋊C2 | — | 4 | 1 | no | — |
| 38 | C2×D3×(C3⋊D3)⋊C3 | — | 4 | 2 | no | — |
| 39 | D3×((C3⋊D3)⋊C3)⋊C2 | — | 4 | 8 | no | — |
| 40 | SL(2,𝔽3)×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic, complemented |
| 41 | C2×D3×GL(2,𝔽3) | — | 9 | 1 | no | — |
| 42 | C2×D3×GL(2,𝔽3) | — | 9 | 2 | no | — |
| 43 | D32×SD16 | — | 9 | 2 | no | — |
| 44 | C2×D33 | — | 12 | 2 | no | — |
| 45 | C3⋊D3×SL(2,𝔽3) | C2×D3 | 1 | 2 | yes | complemented |
| 46 | C3×D3×SL(2,𝔽3) | — | 3 | 2 | no | — |
| 47 | C3×D3×SL(2,𝔽3) | — | 3 | 2 | no | — |
| 48 | C3×D3×SL(2,𝔽3) | — | 6 | 1 | no | — |
| 49 | C3⋊(C3⋊GL(2,𝔽3)) | C2×D3 | 1 | 2 | yes | complemented |
| 50 | C3×C3⋊GL(2,𝔽3) | — | 3 | 2 | no | — |
| 51 | C3×C3⋊GL(2,𝔽3) | — | 3 | 2 | no | — |
| 52 | C3×C3⋊GL(2,𝔽3) | — | 6 | 1 | no | — |
| 53 | C32×GL(2,𝔽3) | — | 2 | 1 | no | — |
| 54 | C32×GL(2,𝔽3) | C2×D3 | 1 | 2 | yes | complemented |
| 55 | C22×((C3⋊D3)⋊C3)⋊C2 | — | 6 | 1 | no | — |
| 56 | Q8×#272 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 57 | D4×#272 | — | 3 | 1 | no | — |
| 58 | Q8×(C3⋊D3)⋊C3 | C2×D3 | 1 | 2 | yes | complemented |
| 59 | D4×(C3⋊D3)⋊C3 | — | 3 | 2 | no | — |
| 60 | #88677 | — | 6 | 1 | no | — |
| 61 | #88676 | — | 6 | 2 | no | — |
| 62 | #88655 | — | 3 | 1 | no | — |
| 63 | #88654 | — | 3 | 2 | no | — |
| 64 | C4×((C3⋊D3)⋊C3)⋊C2 | — | 3 | 1 | no | — |
| 65 | #88651 | — | 3 | 1 | no | — |
| 66 | ((C3⋊D3)⋊C3)⋊Q8 | — | 3 | 2 | no | — |
| 67 | #88623 | — | 2 | 2 | no | — |
| 68 | #88611 | — | 6 | 2 | no | — |
| 69 | #88611 | — | 12 | 1 | no | — |
| 70 | (C3⋊GL(2,𝔽3))⋊C3 | — | 6 | 2 | no | — |
| 71 | SD16×H(3,𝔽3) | — | 3 | 1 | no | — |
| 72 | #88549 | — | 3 | 1 | no | — |
| 73 | #88546 | — | 3 | 1 | no | — |
| 74 | #88528 | — | 3 | 1 | no | — |
| 75 | C8×#272 | — | 3 | 1 | no | — |
| 76 | #3755⋊C3 | — | 3 | 2 | no | — |
| 77 | #3754⋊C3 | — | 3 | 2 | no | — |
| 78 | #3744⋊C3 | — | 3 | 2 | no | — |
| 79 | C8×(C3⋊D3)⋊C3 | — | 3 | 2 | no | — |
| 80 | #88438 | — | 3 | 2 | no | — |
| 81 | #88437 | — | 3 | 2 | no | — |
| 82 | #88434 | — | 3 | 1 | no | — |
| 83 | #88431 | — | 3 | 2 | no | — |
| 84 | ((C3⋊D3)⋊C3)⋊C8 | — | 3 | 2 | no | — |
| 85 | C2×C3⋊#272 | — | 4 | 1 | no | — |
| 86 | C2×C3×#272 | — | 4 | 1 | no | — |
| 87 | C2×C3⋊((C3⋊D3)⋊C3) | — | 4 | 2 | no | — |
| 88 | C2×D3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 89 | C2×C3×(C3⋊D3)⋊C3 | — | 4 | 2 | no | — |
| 90 | #66432 | — | 4 | 4 | no | — |
| 91 | D3×#272 | — | 4 | 4 | no | — |
| 92 | ((C3⋊D3)⋊C3)⋊D3 | — | 4 | 8 | no | — |
| 93 | C3×((C3⋊D3)⋊C3)⋊C2 | — | 4 | 4 | no | — |
| 94 | D3×(C3⋊D3)⋊C3 | — | 4 | 8 | no | — |
| 95 | D32×Q8 | — | 3 | 2 | no | — |
| 96 | D32×D4 | — | 9 | 2 | no | — |
| 97 | C2×D3×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 98 | C2×D3×SL(2,𝔽3) | — | 9 | 2 | no | — |
| 99 | C2×C3⋊GL(2,𝔽3) | — | 9 | 1 | no | — |
| 100 | C2×C3⋊GL(2,𝔽3) | — | 9 | 2 | no | — |
| 101 | C2×C3×GL(2,𝔽3) | — | 9 | 2 | no | — |
| 102 | C2×C3×GL(2,𝔽3) | — | 9 | 1 | no | — |
| 103 | D3×GL(2,𝔽3) | — | 3 | 2 | no | — |
| 104 | D3×GL(2,𝔽3) | — | 3 | 2 | no | — |
| 105 | D3×GL(2,𝔽3) | — | 6 | 1 | no | — |
| 106 | D3×GL(2,𝔽3) | — | 9 | 2 | no | — |
| 107 | D3×GL(2,𝔽3) | — | 9 | 2 | no | — |
| 108 | D3×GL(2,𝔽3) | — | 9 | 2 | no | — |
| 109 | D3×GL(2,𝔽3) | — | 9 | 2 | no | — |
| 110 | D3×GL(2,𝔽3) | — | 18 | 2 | no | — |
| 111 | D3×GL(2,𝔽3) | — | 18 | 2 | no | — |
| 112 | SD16×C3⋊D3 | — | 3 | 2 | no | — |
| 113 | C3×D3×SD16 | — | 9 | 2 | no | — |
| 114 | C3×D3×SD16 | — | 9 | 2 | no | — |
| 115 | C3×D3×SD16 | — | 18 | 1 | no | — |
| 116 | #63940 | — | 9 | 2 | no | — |
| 117 | D3×#215 | — | 9 | 2 | no | — |
| 118 | D3×#215 | — | 9 | 2 | no | — |
| 119 | #63930 | — | 9 | 2 | no | — |
| 120 | D3×#214 | — | 9 | 2 | no | — |
| 121 | D3×#214 | — | 9 | 2 | no | — |
| 122 | #63796 | — | 9 | 2 | no | — |
| 123 | D3×#204 | — | 9 | 2 | no | — |
| 124 | D3×#204 | — | 9 | 2 | no | — |
| 125 | D32×C8 | — | 9 | 2 | no | — |
| 126 | C2×#1113 | — | 12 | 2 | no | — |
| 127 | C2×D3×C3⋊D3 | — | 4 | 2 | no | — |
| 128 | C2×D3×C3⋊D3 | — | 12 | 2 | no | — |
| 129 | C2×D3×C3⋊D3 | — | 12 | 2 | no | — |
| 130 | C2×C3×D32 | — | 12 | 2 | no | — |
| 131 | C2×C3×D32 | — | 12 | 2 | no | — |
| 132 | C2×C3×D32 | — | 12 | 2 | no | — |
| 133 | C2×C3×D32 | — | 24 | 1 | no | — |
| 134 | D33 | — | 12 | 16 | no | — |
| 135 | C32×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 136 | C32×SL(2,𝔽3) | C22×D3 | 1 | 2 | yes | complemented |
| 137 | C22×#272 | — | 6 | 1 | no | — |
| 138 | C22×(C3⋊D3)⋊C3 | — | 6 | 2 | no | — |
| 139 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 6 | 1 | no | — |
| 140 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 6 | 2 | no | — |
| 141 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 12 | 4 | no | — |
| 142 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 24 | 2 | no | — |
| 143 | C2×((C3⋊D3)⋊C3)⋊C2 | S4 | 1 | 1 | yes | characteristic |
| 144 | Q8×H(3,𝔽3) | C22×D3 | 1 | 1 | yes | characteristic, complemented |
| 145 | D4×H(3,𝔽3) | — | 3 | 1 | no | — |
| 146 | #6235 | — | 6 | 1 | no | — |
| 147 | C4⋊#272 | — | 3 | 1 | no | — |
| 148 | C4×#272 | — | 3 | 1 | no | — |
| 149 | #6229 | — | 3 | 1 | no | — |
| 150 | #638⋊C3 | — | 6 | 2 | no | — |
| 151 | C4⋊((C3⋊D3)⋊C3) | — | 3 | 2 | no | — |
| 152 | C4×(C3⋊D3)⋊C3 | — | 3 | 2 | no | — |
| 153 | #634⋊C3 | — | 3 | 2 | no | — |
| 154 | Q8⋊H(3,𝔽3) | — | 2 | 2 | no | — |
| 155 | Q8⋊H(3,𝔽3) | — | 4 | 1 | no | — |
| 156 | #6200 | — | 6 | 2 | no | — |
| 157 | #6199 | — | 3 | 1 | no | — |
| 158 | #6198 | — | 6 | 1 | no | — |
| 159 | ((C3⋊D3)⋊C3)⋊C4 | — | 3 | 2 | no | — |
| 160 | #6196 | — | 6 | 1 | no | — |
| 161 | C8×H(3,𝔽3) | — | 3 | 1 | no | — |
| 162 | #6180 | — | 3 | 1 | no | — |
| 163 | (C3⋊(C3⋊C8))⋊C3 | — | 3 | 2 | no | — |
| 164 | C22×GL(2,𝔽3) | — | 27 | 1 | no | — |
| 165 | C2×D3×SD16 | — | 27 | 1 | no | — |
| 166 | C2×D3×SD16 | — | 27 | 2 | no | — |
| 167 | C2×C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 168 | C3⋊#272 | — | 4 | 2 | no | — |
| 169 | C3×#272 | — | 4 | 2 | no | — |
| 170 | C3⋊((C3⋊D3)⋊C3) | — | 4 | 4 | no | — |
| 171 | D3×H(3,𝔽3) | — | 4 | 2 | no | — |
| 172 | C3×(C3⋊D3)⋊C3 | — | 4 | 4 | no | — |
| 173 | C22×D32 | — | 18 | 2 | no | — |
| 174 | C22×D32 | — | 36 | 1 | no | — |
| 175 | C22×D32 | — | 36 | 2 | no | — |
| 176 | Q8×C3⋊D3 | D32 | 1 | 2 | yes | complemented |
| 177 | D4×C3⋊D3 | — | 3 | 2 | no | — |
| 178 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 179 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 180 | C3×D3×Q8 | — | 6 | 1 | no | — |
| 181 | C3×D3×D4 | — | 9 | 2 | no | — |
| 182 | C3×D3×D4 | — | 9 | 2 | no | — |
| 183 | C3×D3×D4 | — | 18 | 1 | no | — |
| 184 | C2×C3×SL(2,𝔽3) | — | 9 | 2 | no | — |
| 185 | C2×C3×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 186 | #3811 | — | 18 | 2 | no | — |
| 187 | D3×#67 | — | 18 | 2 | no | — |
| 188 | D3×#67 | — | 18 | 2 | no | — |
| 189 | #3802 | — | 9 | 2 | no | — |
| 190 | D3×D12 | — | 9 | 2 | no | — |
| 191 | D3×D12 | — | 9 | 2 | no | — |
| 192 | C4×D32 | — | 9 | 2 | no | — |
| 193 | #3797 | — | 9 | 2 | no | — |
| 194 | D3×Dic6 | — | 9 | 2 | no | — |
| 195 | D3×Dic6 | — | 9 | 2 | no | — |
| 196 | D3×SL(2,𝔽3) | — | 3 | 2 | no | — |
| 197 | D3×SL(2,𝔽3) | — | 3 | 2 | no | — |
| 198 | D3×SL(2,𝔽3) | — | 6 | 2 | no | — |
| 199 | D3×SL(2,𝔽3) | — | 6 | 1 | no | — |
| 200 | D3×SL(2,𝔽3) | — | 6 | 2 | no | — |
| 201 | D3×SL(2,𝔽3) | — | 9 | 2 | no | — |
| 202 | D3×SL(2,𝔽3) | — | 12 | 1 | no | — |
| 203 | C3⋊GL(2,𝔽3) | — | 3 | 2 | no | — |
| 204 | C3⋊GL(2,𝔽3) | — | 3 | 2 | no | — |
| 205 | C3⋊GL(2,𝔽3) | — | 6 | 2 | no | — |
| 206 | C3⋊GL(2,𝔽3) | — | 6 | 1 | no | — |
| 207 | C3⋊GL(2,𝔽3) | — | 9 | 2 | no | — |
| 208 | C3⋊GL(2,𝔽3) | — | 18 | 2 | no | — |
| 209 | C3×GL(2,𝔽3) | — | 3 | 2 | no | — |
| 210 | C3×GL(2,𝔽3) | — | 6 | 1 | no | — |
| 211 | C3×GL(2,𝔽3) | — | 9 | 2 | no | — |
| 212 | C3×GL(2,𝔽3) | — | 9 | 1 | no | — |
| 213 | C3×GL(2,𝔽3) | — | 18 | 2 | no | — |
| 214 | C3×GL(2,𝔽3) | — | 18 | 2 | no | — |
| 215 | C3×GL(2,𝔽3) | — | 36 | 1 | no | — |
| 216 | C3×GL(2,𝔽3) | D32 | 1 | 1 | yes | characteristic |
| 217 | C32×SD16 | — | 3 | 2 | no | — |
| 218 | C32×SD16 | — | 6 | 1 | no | — |
| 219 | #3755 | — | 3 | 2 | no | — |
| 220 | #3754 | — | 3 | 2 | no | — |
| 221 | #3744 | — | 3 | 2 | no | — |
| 222 | C8×C3⋊D3 | — | 3 | 2 | no | — |
| 223 | C3×#215 | — | 9 | 2 | no | — |
| 224 | C3×#215 | — | 9 | 2 | no | — |
| 225 | C3×#215 | — | 18 | 1 | no | — |
| 226 | C3×#214 | — | 9 | 2 | no | — |
| 227 | C3×#214 | — | 9 | 2 | no | — |
| 228 | C3×#214 | — | 18 | 1 | no | — |
| 229 | C3×#204 | — | 9 | 2 | no | — |
| 230 | C3×#204 | — | 9 | 2 | no | — |
| 231 | C3×#204 | — | 18 | 1 | no | — |
| 232 | C3×D3×C8 | — | 9 | 2 | no | — |
| 233 | C3×D3×C8 | — | 9 | 2 | no | — |
| 234 | C3×D3×C8 | — | 18 | 1 | no | — |
| 235 | #3717 | — | 9 | 2 | no | — |
| 236 | #3717 | — | 9 | 2 | no | — |
| 237 | #3716 | — | 9 | 2 | no | — |
| 238 | #3716 | — | 9 | 2 | no | — |
| 239 | #3715 | — | 9 | 2 | no | — |
| 240 | #3715 | — | 9 | 2 | no | — |
| 241 | #3710 | — | 9 | 2 | no | — |
| 242 | D3×C3⋊C8 | — | 9 | 2 | no | — |
| 243 | D3×C3⋊C8 | — | 9 | 2 | no | — |
| 244 | C2×C3⋊(C3⋊D3) | — | 4 | 2 | no | — |
| 245 | C2×C3×C3⋊D3 | — | 4 | 2 | no | — |
| 246 | C2×C3×C3⋊D3 | — | 12 | 2 | no | — |
| 247 | C2×C3×C3⋊D3 | — | 12 | 2 | no | — |
| 248 | C2×C3×C3⋊D3 | — | 24 | 1 | no | — |
| 249 | C2×C32×D3 | — | 4 | 2 | no | — |
| 250 | C2×C32×D3 | — | 8 | 1 | no | — |
| 251 | C2×C32×D3 | — | 12 | 2 | no | — |
| 252 | C2×C32×D3 | — | 12 | 2 | no | — |
| 253 | C2×C32×D3 | — | 24 | 1 | no | — |
| 254 | #1113 | — | 12 | 8 | no | — |
| 255 | D3×C3⋊D3 | — | 4 | 8 | no | — |
| 256 | D3×C3⋊D3 | — | 12 | 8 | no | — |
| 257 | D3×C3⋊D3 | — | 12 | 8 | no | — |
| 258 | C3×D32 | — | 12 | 8 | no | — |
| 259 | C3×D32 | — | 12 | 8 | no | — |
| 260 | C3×D32 | — | 12 | 8 | no | — |
| 261 | C3×D32 | — | 24 | 4 | no | — |
| 262 | C22×H(3,𝔽3) | — | 6 | 1 | no | — |
| 263 | C2×#272 | — | 6 | 1 | no | — |
| 264 | C2×#272 | — | 12 | 2 | no | — |
| 265 | C2×#272 | — | 24 | 2 | no | — |
| 266 | C2×#272 | — | 48 | 1 | no | — |
| 267 | C2×#272 | C2×S4 | 1 | 1 | yes | characteristic |
| 268 | C2×(C3⋊D3)⋊C3 | — | 6 | 2 | no | — |
| 269 | C2×(C3⋊D3)⋊C3 | — | 8 | 2 | no | — |
| 270 | C2×(C3⋊D3)⋊C3 | — | 12 | 4 | no | — |
| 271 | C2×(C3⋊D3)⋊C3 | — | 24 | 2 | no | — |
| 272 | C2×(C3⋊D3)⋊C3 | C2×S4 | 1 | 2 | yes | — |
| 273 | ((C3⋊D3)⋊C3)⋊C2 | — | 12 | 2 | no | — |
| 274 | ((C3⋊D3)⋊C3)⋊C2 | — | 12 | 4 | no | — |
| 275 | ((C3⋊D3)⋊C3)⋊C2 | — | 24 | 8 | no | — |
| 276 | ((C3⋊D3)⋊C3)⋊C2 | GL(2,𝔽3) | 1 | 4 | yes | direct product factor |
| 277 | C4×H(3,𝔽3) | — | 3 | 1 | no | — |
| 278 | #1084 | — | 3 | 1 | no | — |
| 279 | (C3⋊Dic3)⋊C3 | — | 3 | 2 | no | — |
| 280 | C2×D3×Q8 | — | 9 | 1 | no | — |
| 281 | C2×D3×Q8 | — | 9 | 2 | no | — |
| 282 | C2×D3×D4 | — | 27 | 1 | no | — |
| 283 | C2×D3×D4 | — | 27 | 2 | no | — |
| 284 | C22×SL(2,𝔽3) | — | 27 | 1 | no | — |
| 285 | C2×GL(2,𝔽3) | — | 9 | 1 | no | — |
| 286 | C2×GL(2,𝔽3) | — | 9 | 2 | no | — |
| 287 | C2×GL(2,𝔽3) | — | 27 | 2 | no | — |
| 288 | C2×GL(2,𝔽3) | — | 27 | 1 | no | — |
| 289 | C2×GL(2,𝔽3) | — | 54 | 1 | no | — |
| 290 | C2×GL(2,𝔽3) | — | 54 | 2 | no | — |
| 291 | C2×C3×SD16 | — | 27 | 1 | no | — |
| 292 | C2×C3×SD16 | — | 27 | 2 | no | — |
| 293 | C2×#215 | — | 27 | 1 | no | — |
| 294 | C2×#215 | — | 27 | 2 | no | — |
| 295 | C2×#214 | — | 27 | 1 | no | — |
| 296 | C2×#214 | — | 27 | 2 | no | — |
| 297 | D3×SD16 | — | 9 | 2 | no | — |
| 298 | D3×SD16 | — | 9 | 2 | no | — |
| 299 | D3×SD16 | — | 18 | 1 | no | — |
| 300 | D3×SD16 | — | 27 | 2 | no | — |
| 301 | D3×SD16 | — | 27 | 2 | no | — |
| 302 | D3×SD16 | — | 27 | 2 | no | — |
| 303 | D3×SD16 | — | 27 | 2 | no | — |
| 304 | D3×SD16 | — | 27 | 2 | no | — |
| 305 | D3×SD16 | — | 27 | 2 | no | — |
| 306 | D3×SD16 | — | 27 | 2 | no | — |
| 307 | D3×SD16 | — | 27 | 2 | no | — |
| 308 | D3×SD16 | — | 27 | 2 | no | — |
| 309 | D3×SD16 | — | 27 | 2 | no | — |
| 310 | C2×#204 | — | 27 | 1 | no | — |
| 311 | C2×#204 | — | 27 | 2 | no | — |
| 312 | C2×D3×C8 | — | 27 | 1 | no | — |
| 313 | C2×D3×C8 | — | 27 | 2 | no | — |
| 314 | C3×H(3,𝔽3) | — | 4 | 1 | no | Sylow |
| 315 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 316 | C22×C3⋊D3 | — | 36 | 1 | no | — |
| 317 | C22×C3⋊D3 | — | 36 | 2 | no | — |
| 318 | C22×C3×D3 | — | 18 | 2 | no | — |
| 319 | C22×C3×D3 | — | 18 | 2 | no | — |
| 320 | C22×C3×D3 | — | 36 | 1 | no | — |
| 321 | C22×C3×D3 | — | 36 | 2 | no | — |
| 322 | C22×C3×D3 | — | 36 | 1 | no | — |
| 323 | C22×C3×D3 | — | 36 | 1 | no | — |
| 324 | C22×C3×D3 | — | 36 | 2 | no | — |
| 325 | C2×D32 | — | 3 | 2 | no | — |
| 326 | C2×D32 | — | 12 | 2 | no | — |
| 327 | C2×D32 | — | 12 | 2 | no | — |
| 328 | C2×D32 | — | 18 | 2 | no | — |
| 329 | C2×D32 | — | 18 | 2 | no | — |
| 330 | C2×D32 | — | 18 | 2 | no | — |
| 331 | C2×D32 | — | 24 | 1 | no | — |
| 332 | C2×D32 | — | 36 | 2 | no | — |
| 333 | C2×D32 | — | 36 | 2 | no | — |
| 334 | C2×D32 | — | 36 | 2 | no | — |
| 335 | C2×D32 | — | 36 | 2 | no | — |
| 336 | C2×D32 | — | 36 | 8 | no | — |
| 337 | C2×D32 | — | 36 | 8 | no | — |
| 338 | C2×D32 | — | 36 | 16 | no | — |
| 339 | C2×D32 | — | 72 | 2 | no | — |
| 340 | C2×D32 | — | 72 | 2 | no | — |
| 341 | C32×Q8 | — | 2 | 1 | no | — |
| 342 | C32×Q8 | C2×D32 | 1 | 2 | yes | complemented |
| 343 | C32×D4 | — | 3 | 2 | no | — |
| 344 | C32×D4 | — | 6 | 1 | no | — |
| 345 | #638 | — | 6 | 2 | no | — |
| 346 | C4⋊(C3⋊D3) | — | 3 | 2 | no | — |
| 347 | C4×C3⋊D3 | — | 3 | 2 | no | — |
| 348 | #634 | — | 3 | 2 | no | — |
| 349 | C3×#67 | — | 18 | 2 | no | — |
| 350 | C3×#67 | — | 18 | 2 | no | — |
| 351 | C3×#67 | — | 36 | 1 | no | — |
| 352 | C3×D12 | — | 9 | 2 | no | — |
| 353 | C3×D12 | — | 9 | 2 | no | — |
| 354 | C3×D12 | — | 18 | 1 | no | — |
| 355 | C3×C4×D3 | — | 9 | 2 | no | — |
| 356 | C3×C4×D3 | — | 9 | 2 | no | — |
| 357 | C3×C4×D3 | — | 18 | 1 | no | — |
| 358 | C3×Dic6 | — | 9 | 2 | no | — |
| 359 | C3×Dic6 | — | 9 | 2 | no | — |
| 360 | C3×Dic6 | — | 18 | 1 | no | — |
| 361 | C3×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 362 | C3×SL(2,𝔽3) | — | 3 | 2 | no | — |
| 363 | C3×SL(2,𝔽3) | — | 4 | 1 | no | — |
| 364 | C3×SL(2,𝔽3) | — | 6 | 2 | no | — |
| 365 | C3×SL(2,𝔽3) | — | 6 | 1 | no | — |
| 366 | C3×SL(2,𝔽3) | — | 12 | 1 | no | — |
| 367 | C3×SL(2,𝔽3) | C2×D32 | 1 | 1 | yes | characteristic |
| 368 | #627 | — | 18 | 2 | no | — |
| 369 | #626 | — | 18 | 2 | no | — |
| 370 | #626 | — | 18 | 2 | no | — |
| 371 | #625 | — | 18 | 2 | no | — |
| 372 | #624 | — | 9 | 2 | no | — |
| 373 | D3×Dic3 | — | 9 | 2 | no | — |
| 374 | D3×Dic3 | — | 9 | 2 | no | — |
| 375 | C32×C8 | — | 3 | 2 | no | — |
| 376 | C32×C8 | — | 6 | 1 | no | — |
| 377 | C3⋊(C3⋊C8) | — | 3 | 2 | no | — |
| 378 | C3×C3⋊C8 | — | 9 | 2 | no | — |
| 379 | C3×C3⋊C8 | — | 9 | 2 | no | — |
| 380 | C3×C3⋊C8 | — | 18 | 1 | no | — |
| 381 | C22×SD16 | — | 81 | 1 | no | Sylow |
| 382 | C2×C33 | — | 4 | 2 | no | — |
| 383 | C2×C33 | — | 8 | 1 | no | — |
| 384 | C3⋊(C3⋊D3) | — | 4 | 4 | no | — |
| 385 | C3×C3⋊D3 | — | 4 | 4 | no | — |
| 386 | C3×C3⋊D3 | — | 12 | 4 | no | — |
| 387 | C3×C3⋊D3 | — | 12 | 4 | no | — |
| 388 | C3×C3⋊D3 | — | 24 | 2 | no | — |
| 389 | C32×D3 | — | 4 | 4 | no | — |
| 390 | C32×D3 | — | 8 | 2 | no | — |
| 391 | C32×D3 | — | 12 | 4 | no | — |
| 392 | C32×D3 | — | 12 | 4 | no | — |
| 393 | C32×D3 | — | 24 | 2 | no | — |
| 394 | C2×H(3,𝔽3) | — | 8 | 2 | no | — |
| 395 | C2×H(3,𝔽3) | — | 12 | 1 | no | — |
| 396 | C2×H(3,𝔽3) | — | 16 | 1 | no | — |
| 397 | C2×H(3,𝔽3) | C22×S4 | 1 | 1 | yes | characteristic |
| 398 | #272 | — | 12 | 1 | no | — |
| 399 | #272 | — | 24 | 4 | no | — |
| 400 | #272 | — | 48 | 2 | no | — |
| 401 | #272 | C2×GL(2,𝔽3) | 1 | 2 | yes | complemented |
| 402 | (C3⋊D3)⋊C3 | — | 8 | 4 | no | — |
| 403 | (C3⋊D3)⋊C3 | — | 12 | 2 | no | — |
| 404 | (C3⋊D3)⋊C3 | — | 24 | 4 | no | — |
| 405 | (C3⋊D3)⋊C3 | C2×GL(2,𝔽3) | 1 | 4 | yes | complemented |
| 406 | C23×D3 | — | 54 | 1 | no | — |
| 407 | C23×D3 | — | 54 | 2 | no | — |
| 408 | C23×D3 | — | 108 | 1 | no | — |
| 409 | C2×C3×Q8 | — | 9 | 2 | no | — |
| 410 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 411 | C2×C3×D4 | — | 27 | 1 | no | — |
| 412 | C2×C3×D4 | — | 27 | 2 | no | — |
| 413 | C2×#67 | — | 54 | 1 | no | — |
| 414 | C2×#67 | — | 54 | 2 | no | — |
| 415 | D3×Q8 | — | 3 | 2 | no | — |
| 416 | D3×Q8 | — | 3 | 2 | no | — |
| 417 | D3×Q8 | — | 6 | 1 | no | — |
| 418 | D3×Q8 | — | 9 | 2 | no | — |
| 419 | D3×Q8 | — | 27 | 2 | no | — |
| 420 | D3×Q8 | — | 27 | 2 | no | — |
| 421 | D3×Q8 | — | 27 | 2 | no | — |
| 422 | D3×D4 | — | 9 | 2 | no | — |
| 423 | D3×D4 | — | 9 | 2 | no | — |
| 424 | D3×D4 | — | 18 | 1 | no | — |
| 425 | D3×D4 | — | 27 | 2 | no | — |
| 426 | D3×D4 | — | 27 | 2 | no | — |
| 427 | D3×D4 | — | 27 | 2 | no | — |
| 428 | D3×D4 | — | 27 | 2 | no | — |
| 429 | D3×D4 | — | 54 | 2 | no | — |
| 430 | D3×D4 | — | 54 | 2 | no | — |
| 431 | D3×D4 | — | 54 | 2 | no | — |
| 432 | C2×D12 | — | 27 | 1 | no | — |
| 433 | C2×D12 | — | 27 | 2 | no | — |
| 434 | C2×C4×D3 | — | 27 | 1 | no | — |
| 435 | C2×C4×D3 | — | 27 | 2 | no | — |
| 436 | C2×Dic6 | — | 27 | 1 | no | — |
| 437 | C2×Dic6 | — | 27 | 2 | no | — |
| 438 | C2×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 439 | C2×SL(2,𝔽3) | — | 9 | 2 | no | — |
| 440 | C2×SL(2,𝔽3) | — | 18 | 1 | no | — |
| 441 | C2×SL(2,𝔽3) | — | 18 | 2 | no | — |
| 442 | GL(2,𝔽3) | — | 9 | 1 | no | — |
| 443 | GL(2,𝔽3) | — | 9 | 2 | no | — |
| 444 | GL(2,𝔽3) | — | 18 | 2 | no | — |
| 445 | GL(2,𝔽3) | — | 18 | 2 | no | — |
| 446 | GL(2,𝔽3) | — | 36 | 1 | no | — |
| 447 | GL(2,𝔽3) | — | 54 | 2 | no | — |
| 448 | GL(2,𝔽3) | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, direct product factor |
| 449 | C3×SD16 | — | 3 | 1 | no | — |
| 450 | C3×SD16 | — | 9 | 2 | no | — |
| 451 | C3×SD16 | — | 18 | 1 | no | — |
| 452 | C3×SD16 | — | 27 | 1 | no | — |
| 453 | C3×SD16 | — | 27 | 2 | no | — |
| 454 | C3×SD16 | — | 27 | 1 | no | — |
| 455 | C3×SD16 | — | 27 | 2 | no | — |
| 456 | C3×SD16 | — | 27 | 2 | no | — |
| 457 | C3×SD16 | — | 27 | 1 | no | — |
| 458 | C2×C3×C8 | — | 27 | 1 | no | — |
| 459 | C2×C3×C8 | — | 27 | 2 | no | — |
| 460 | #215 | — | 9 | 2 | no | — |
| 461 | #215 | — | 9 | 2 | no | — |
| 462 | #215 | — | 18 | 1 | no | — |
| 463 | #215 | — | 27 | 2 | no | — |
| 464 | #215 | — | 27 | 2 | no | — |
| 465 | #215 | — | 27 | 2 | no | — |
| 466 | #215 | — | 27 | 2 | no | — |
| 467 | #214 | — | 9 | 2 | no | — |
| 468 | #214 | — | 9 | 2 | no | — |
| 469 | #214 | — | 18 | 1 | no | — |
| 470 | #214 | — | 27 | 2 | no | — |
| 471 | #214 | — | 27 | 2 | no | — |
| 472 | #214 | — | 27 | 2 | no | — |
| 473 | #214 | — | 27 | 2 | no | — |
| 474 | C2×C3⋊C8 | — | 27 | 1 | no | — |
| 475 | C2×C3⋊C8 | — | 27 | 2 | no | — |
| 476 | #204 | — | 9 | 2 | no | — |
| 477 | #204 | — | 9 | 2 | no | — |
| 478 | #204 | — | 18 | 1 | no | — |
| 479 | #204 | — | 27 | 2 | no | — |
| 480 | #204 | — | 27 | 2 | no | — |
| 481 | #204 | — | 27 | 2 | no | — |
| 482 | #204 | — | 27 | 2 | no | — |
| 483 | D3×C8 | — | 9 | 2 | no | — |
| 484 | D3×C8 | — | 9 | 2 | no | — |
| 485 | D3×C8 | — | 18 | 1 | no | — |
| 486 | D3×C8 | — | 27 | 2 | no | — |
| 487 | D3×C8 | — | 27 | 2 | no | — |
| 488 | D3×C8 | — | 27 | 2 | no | — |
| 489 | D3×C8 | — | 27 | 2 | no | — |
| 490 | C22×C32 | — | 6 | 2 | no | — |
| 491 | C22×C32 | — | 12 | 1 | no | — |
| 492 | C22×C32 | — | 36 | 1 | no | — |
| 493 | C22×C32 | — | 36 | 2 | no | — |
| 494 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 495 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 496 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 497 | C2×C3⋊D3 | — | 12 | 4 | no | — |
| 498 | C2×C3⋊D3 | — | 24 | 2 | no | — |
| 499 | C2×C3⋊D3 | — | 24 | 1 | no | — |
| 500 | C2×C3⋊D3 | — | 36 | 2 | no | — |
| 501 | C2×C3⋊D3 | — | 36 | 4 | no | — |
| 502 | C2×C3⋊D3 | — | 36 | 8 | no | — |
| 503 | C2×C3⋊D3 | — | 72 | 2 | no | — |
| 504 | C2×C3⋊D3 | D3×S4 | 1 | 2 | yes | — |
| 505 | C2×C3×D3 | — | 3 | 2 | no | — |
| 506 | C2×C3×D3 | — | 3 | 2 | no | — |
| 507 | C2×C3×D3 | — | 4 | 1 | no | — |
| 508 | C2×C3×D3 | — | 6 | 1 | no | — |
| 509 | C2×C3×D3 | — | 12 | 2 | no | — |
| 510 | C2×C3×D3 | — | 12 | 2 | no | — |
| 511 | C2×C3×D3 | — | 12 | 2 | no | — |
| 512 | C2×C3×D3 | — | 18 | 2 | no | — |
| 513 | C2×C3×D3 | — | 18 | 2 | no | — |
| 514 | C2×C3×D3 | — | 24 | 2 | no | — |
| 515 | C2×C3×D3 | — | 24 | 2 | no | — |
| 516 | C2×C3×D3 | — | 24 | 1 | no | — |
| 517 | C2×C3×D3 | — | 24 | 1 | no | — |
| 518 | C2×C3×D3 | — | 36 | 2 | no | — |
| 519 | C2×C3×D3 | — | 36 | 4 | no | — |
| 520 | C2×C3×D3 | — | 36 | 8 | no | — |
| 521 | C2×C3×D3 | — | 36 | 1 | no | — |
| 522 | C2×C3×D3 | — | 36 | 2 | no | — |
| 523 | C2×C3×D3 | — | 36 | 1 | no | — |
| 524 | C2×C3×D3 | — | 36 | 4 | no | — |
| 525 | C2×C3×D3 | — | 36 | 4 | no | — |
| 526 | C2×C3×D3 | — | 36 | 4 | no | — |
| 527 | C2×C3×D3 | — | 36 | 8 | no | — |
| 528 | C2×C3×D3 | — | 48 | 1 | no | — |
| 529 | C2×C3×D3 | — | 72 | 2 | no | — |
| 530 | C2×C3×D3 | — | 72 | 2 | no | — |
| 531 | C2×C3×D3 | — | 72 | 2 | no | — |
| 532 | C2×C3×D3 | — | 144 | 1 | no | — |
| 533 | D32 | — | 3 | 8 | no | — |
| 534 | D32 | — | 12 | 8 | no | — |
| 535 | D32 | — | 12 | 8 | no | — |
| 536 | D32 | — | 24 | 4 | no | — |
| 537 | D32 | — | 36 | 8 | no | — |
| 538 | D32 | — | 36 | 4 | no | — |
| 539 | D32 | — | 36 | 4 | no | — |
| 540 | D32 | — | 36 | 8 | no | — |
| 541 | D32 | — | 36 | 8 | no | — |
| 542 | D32 | — | 36 | 8 | no | — |
| 543 | D32 | — | 36 | 4 | no | — |
| 544 | D32 | — | 72 | 8 | no | — |
| 545 | D32 | — | 72 | 8 | no | — |
| 546 | C32×C4 | — | 3 | 2 | no | — |
| 547 | C32×C4 | — | 6 | 1 | no | — |
| 548 | C3⋊Dic3 | — | 3 | 2 | no | — |
| 549 | C3×Dic3 | — | 9 | 2 | no | — |
| 550 | C3×Dic3 | — | 9 | 2 | no | — |
| 551 | C3×Dic3 | — | 18 | 1 | no | — |
| 552 | C22×Q8 | — | 27 | 1 | no | — |
| 553 | C22×D4 | — | 81 | 1 | no | — |
| 554 | C2×SD16 | — | 27 | 1 | no | — |
| 555 | C2×SD16 | — | 27 | 2 | no | — |
| 556 | C2×SD16 | — | 81 | 1 | no | — |
| 557 | C2×SD16 | — | 81 | 2 | no | — |
| 558 | C2×SD16 | — | 81 | 2 | no | — |
| 559 | C2×SD16 | — | 81 | 1 | no | — |
| 560 | C2×SD16 | — | 81 | 2 | no | — |
| 561 | C2×SD16 | — | 81 | 1 | no | — |
| 562 | C22×C8 | — | 81 | 1 | no | — |
| 563 | C33 | — | 4 | 2 | no | — |
| 564 | C33 | — | 8 | 1 | no | — |
| 565 | H(3,𝔽3) | — | 8 | 2 | no | — |
| 566 | H(3,𝔽3) | — | 16 | 1 | no | — |
| 567 | H(3,𝔽3) | C22×GL(2,𝔽3) | 1 | 1 | yes | characteristic, complemented |
| 568 | C23×C3 | — | 54 | 1 | no | — |
| 569 | C23×C3 | — | 54 | 2 | no | — |
| 570 | C23×C3 | — | 108 | 1 | no | — |
| 571 | C22×D3 | — | 9 | 1 | no | — |
| 572 | C22×D3 | — | 9 | 2 | no | — |
| 573 | C22×D3 | — | 18 | 2 | no | — |
| 574 | C22×D3 | — | 18 | 2 | no | — |
| 575 | C22×D3 | — | 36 | 1 | no | — |
| 576 | C22×D3 | — | 36 | 2 | no | — |
| 577 | C22×D3 | — | 36 | 1 | no | — |
| 578 | C22×D3 | — | 54 | 2 | no | — |
| 579 | C22×D3 | — | 54 | 2 | no | — |
| 580 | C22×D3 | — | 54 | 2 | no | — |
| 581 | C22×D3 | — | 54 | 2 | no | — |
| 582 | C22×D3 | — | 54 | 1 | no | — |
| 583 | C22×D3 | — | 54 | 2 | no | — |
| 584 | C22×D3 | — | 108 | 4 | no | — |
| 585 | C22×D3 | — | 108 | 8 | no | — |
| 586 | C22×D3 | — | 108 | 8 | no | — |
| 587 | C22×D3 | — | 108 | 2 | no | — |
| 588 | C22×D3 | — | 108 | 1 | no | — |
| 589 | C22×D3 | — | 216 | 1 | no | — |
| 590 | C22×D3 | — | 216 | 2 | no | — |
| 591 | C3×Q8 | — | 3 | 2 | no | — |
| 592 | C3×Q8 | — | 6 | 1 | no | — |
| 593 | C3×Q8 | — | 27 | 1 | no | — |
| 594 | C3×Q8 | — | 27 | 2 | no | — |
| 595 | C3×Q8 | D33 | 1 | 1 | yes | characteristic |
| 596 | C3×D4 | — | 3 | 1 | no | — |
| 597 | C3×D4 | — | 9 | 2 | no | — |
| 598 | C3×D4 | — | 18 | 1 | no | — |
| 599 | C3×D4 | — | 27 | 1 | no | — |
| 600 | C3×D4 | — | 27 | 2 | no | — |
| 601 | C3×D4 | — | 54 | 1 | no | — |
| 602 | C3×D4 | — | 54 | 2 | no | — |
| 603 | C2×C3×C4 | — | 27 | 1 | no | — |
| 604 | C2×C3×C4 | — | 27 | 2 | no | — |
| 605 | #67 | — | 18 | 2 | no | — |
| 606 | #67 | — | 18 | 2 | no | — |
| 607 | #67 | — | 36 | 1 | no | — |
| 608 | #67 | — | 54 | 2 | no | — |
| 609 | #67 | — | 54 | 2 | no | — |
| 610 | #67 | — | 54 | 2 | no | — |
| 611 | #67 | — | 54 | 2 | no | — |
| 612 | C2×Dic3 | — | 27 | 1 | no | — |
| 613 | C2×Dic3 | — | 27 | 2 | no | — |
| 614 | D12 | — | 9 | 2 | no | — |
| 615 | D12 | — | 9 | 2 | no | — |
| 616 | D12 | — | 18 | 1 | no | — |
| 617 | D12 | — | 27 | 2 | no | — |
| 618 | D12 | — | 54 | 1 | no | — |
| 619 | D12 | — | 54 | 2 | no | — |
| 620 | C4×D3 | — | 9 | 2 | no | — |
| 621 | C4×D3 | — | 9 | 2 | no | — |
| 622 | C4×D3 | — | 18 | 1 | no | — |
| 623 | C4×D3 | — | 27 | 2 | no | — |
| 624 | C4×D3 | — | 27 | 2 | no | — |
| 625 | C4×D3 | — | 27 | 2 | no | — |
| 626 | C4×D3 | — | 27 | 2 | no | — |
| 627 | Dic6 | — | 9 | 2 | no | — |
| 628 | Dic6 | — | 9 | 2 | no | — |
| 629 | Dic6 | — | 18 | 1 | no | — |
| 630 | Dic6 | — | 27 | 2 | no | — |
| 631 | Dic6 | — | 54 | 1 | no | — |
| 632 | Dic6 | — | 54 | 2 | no | — |
| 633 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 634 | SL(2,𝔽3) | — | 6 | 2 | no | — |
| 635 | SL(2,𝔽3) | — | 12 | 1 | no | — |
| 636 | SL(2,𝔽3) | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 637 | C3×C8 | — | 3 | 1 | no | — |
| 638 | C3×C8 | — | 9 | 2 | no | — |
| 639 | C3×C8 | — | 18 | 1 | no | — |
| 640 | C3×C8 | — | 27 | 1 | no | — |
| 641 | C3×C8 | — | 27 | 2 | no | — |
| 642 | C3⋊C8 | — | 9 | 2 | no | — |
| 643 | C3⋊C8 | — | 9 | 2 | no | — |
| 644 | C3⋊C8 | — | 18 | 1 | no | — |
| 645 | C3⋊C8 | — | 27 | 2 | no | — |
| 646 | C2×C32 | — | 2 | 1 | no | — |
| 647 | C2×C32 | — | 4 | 1 | no | — |
| 648 | C2×C32 | — | 8 | 2 | no | — |
| 649 | C2×C32 | — | 12 | 2 | no | — |
| 650 | C2×C32 | — | 12 | 2 | no | — |
| 651 | C2×C32 | — | 16 | 1 | no | — |
| 652 | C2×C32 | — | 24 | 2 | no | — |
| 653 | C2×C32 | — | 24 | 1 | no | — |
| 654 | C2×C32 | — | 24 | 1 | no | — |
| 655 | C2×C32 | — | 36 | 2 | no | — |
| 656 | C2×C32 | — | 36 | 4 | no | — |
| 657 | C2×C32 | — | 48 | 1 | no | — |
| 658 | C2×C32 | C2×D3×S4 | 1 | 2 | yes | — |
| 659 | C3⋊D3 | — | 12 | 4 | no | — |
| 660 | C3⋊D3 | — | 12 | 4 | no | — |
| 661 | C3⋊D3 | — | 12 | 2 | no | — |
| 662 | C3⋊D3 | — | 24 | 2 | no | — |
| 663 | C3⋊D3 | — | 24 | 4 | no | — |
| 664 | C3⋊D3 | — | 36 | 4 | no | — |
| 665 | C3⋊D3 | — | 72 | 4 | no | — |
| 666 | C3⋊D3 | D3×GL(2,𝔽3) | 1 | 4 | yes | complemented |
| 667 | C3×D3 | — | 3 | 4 | no | — |
| 668 | C3×D3 | — | 3 | 4 | no | — |
| 669 | C3×D3 | — | 4 | 2 | no | — |
| 670 | C3×D3 | — | 6 | 2 | no | — |
| 671 | C3×D3 | — | 12 | 4 | no | — |
| 672 | C3×D3 | — | 12 | 4 | no | — |
| 673 | C3×D3 | — | 12 | 4 | no | — |
| 674 | C3×D3 | — | 24 | 4 | no | — |
| 675 | C3×D3 | — | 24 | 4 | no | — |
| 676 | C3×D3 | — | 24 | 2 | no | — |
| 677 | C3×D3 | — | 24 | 2 | no | — |
| 678 | C3×D3 | — | 36 | 4 | no | — |
| 679 | C3×D3 | — | 36 | 2 | no | — |
| 680 | C3×D3 | — | 36 | 4 | no | — |
| 681 | C3×D3 | — | 36 | 2 | no | — |
| 682 | C3×D3 | — | 36 | 2 | no | — |
| 683 | C3×D3 | — | 48 | 2 | no | — |
| 684 | C3×D3 | — | 72 | 1 | no | — |
| 685 | C3×D3 | — | 72 | 4 | no | — |
| 686 | C3×D3 | — | 72 | 4 | no | — |
| 687 | C3×D3 | — | 144 | 2 | no | — |
| 688 | C24 | — | 162 | 1 | no | — |
| 689 | C2×Q8 | — | 9 | 1 | no | — |
| 690 | C2×Q8 | — | 9 | 2 | no | — |
| 691 | C2×Q8 | — | 81 | 1 | no | — |
| 692 | C2×Q8 | — | 81 | 2 | no | — |
| 693 | C2×D4 | — | 27 | 1 | no | — |
| 694 | C2×D4 | — | 27 | 2 | no | — |
| 695 | C2×D4 | — | 81 | 1 | no | — |
| 696 | C2×D4 | — | 81 | 2 | no | — |
| 697 | C2×D4 | — | 162 | 2 | no | — |
| 698 | C2×D4 | — | 162 | 1 | no | — |
| 699 | C22×C4 | — | 81 | 1 | no | — |
| 700 | SD16 | — | 3 | 1 | no | — |
| 701 | SD16 | — | 27 | 1 | no | — |
| 702 | SD16 | — | 27 | 2 | no | — |
| 703 | SD16 | — | 27 | 1 | no | — |
| 704 | SD16 | — | 27 | 2 | no | — |
| 705 | SD16 | — | 27 | 1 | no | — |
| 706 | SD16 | — | 27 | 2 | no | — |
| 707 | SD16 | — | 81 | 2 | no | — |
| 708 | SD16 | — | 81 | 2 | no | — |
| 709 | SD16 | — | 81 | 2 | no | — |
| 710 | C2×C8 | — | 27 | 1 | no | — |
| 711 | C2×C8 | — | 27 | 2 | no | — |
| 712 | C2×C8 | — | 81 | 2 | no | — |
| 713 | C2×C8 | — | 81 | 1 | no | — |
| 714 | C22×C3 | — | 6 | 1 | no | — |
| 715 | C22×C3 | — | 9 | 2 | no | — |
| 716 | C22×C3 | — | 9 | 1 | no | — |
| 717 | C22×C3 | — | 18 | 2 | no | — |
| 718 | C22×C3 | — | 36 | 1 | no | — |
| 719 | C22×C3 | — | 36 | 1 | no | — |
| 720 | C22×C3 | — | 36 | 2 | no | — |
| 721 | C22×C3 | — | 54 | 2 | no | — |
| 722 | C22×C3 | — | 54 | 1 | no | — |
| 723 | C22×C3 | — | 72 | 1 | no | — |
| 724 | C22×C3 | — | 72 | 2 | no | — |
| 725 | C22×C3 | — | 108 | 4 | no | — |
| 726 | C22×C3 | — | 108 | 2 | no | — |
| 727 | C22×C3 | — | 108 | 4 | no | — |
| 728 | C2×D3 | — | 3 | 2 | no | — |
| 729 | C2×D3 | — | 3 | 2 | no | — |
| 730 | C2×D3 | — | 4 | 1 | no | — |
| 731 | C2×D3 | — | 6 | 1 | no | — |
| 732 | C2×D3 | — | 9 | 2 | no | — |
| 733 | C2×D3 | — | 9 | 4 | no | — |
| 734 | C2×D3 | — | 9 | 8 | no | — |
| 735 | C2×D3 | — | 18 | 2 | no | — |
| 736 | C2×D3 | — | 18 | 2 | no | — |
| 737 | C2×D3 | — | 36 | 1 | no | — |
| 738 | C2×D3 | — | 36 | 2 | no | — |
| 739 | C2×D3 | — | 36 | 1 | no | — |
| 740 | C2×D3 | — | 36 | 4 | no | — |
| 741 | C2×D3 | — | 36 | 4 | no | — |
| 742 | C2×D3 | — | 36 | 4 | no | — |
| 743 | C2×D3 | — | 36 | 8 | no | — |
| 744 | C2×D3 | — | 54 | 2 | no | — |
| 745 | C2×D3 | — | 72 | 2 | no | — |
| 746 | C2×D3 | — | 72 | 2 | no | — |
| 747 | C2×D3 | — | 72 | 2 | no | — |
| 748 | C2×D3 | — | 108 | 4 | no | — |
| 749 | C2×D3 | — | 108 | 4 | no | — |
| 750 | C2×D3 | — | 108 | 4 | no | — |
| 751 | C2×D3 | — | 108 | 2 | no | — |
| 752 | C2×D3 | — | 108 | 8 | no | — |
| 753 | C2×D3 | — | 108 | 4 | no | — |
| 754 | C2×D3 | — | 108 | 4 | no | — |
| 755 | C2×D3 | — | 108 | 4 | no | — |
| 756 | C2×D3 | — | 144 | 1 | no | — |
| 757 | C2×D3 | — | 216 | 2 | no | — |
| 758 | C2×D3 | — | 216 | 4 | no | — |
| 759 | C2×D3 | — | 216 | 8 | no | — |
| 760 | C3×C4 | — | 3 | 1 | no | — |
| 761 | C3×C4 | — | 9 | 2 | no | — |
| 762 | C3×C4 | — | 18 | 1 | no | — |
| 763 | C3×C4 | — | 27 | 2 | no | — |
| 764 | C3×C4 | — | 27 | 1 | no | — |
| 765 | Dic3 | — | 9 | 2 | no | — |
| 766 | Dic3 | — | 9 | 2 | no | — |
| 767 | Dic3 | — | 18 | 1 | no | — |
| 768 | Dic3 | — | 27 | 2 | no | — |
| 769 | C32 | — | 2 | 1 | no | — |
| 770 | C32 | — | 4 | 1 | no | — |
| 771 | C32 | — | 8 | 2 | no | — |
| 772 | C32 | — | 12 | 2 | no | — |
| 773 | C32 | — | 16 | 1 | no | — |
| 774 | C32 | — | 24 | 2 | no | — |
| 775 | C32 | — | 24 | 1 | no | — |
| 776 | C32 | — | 48 | 1 | no | — |
| 777 | C32 | C2×D3×GL(2,𝔽3) | 1 | 2 | yes | complemented |
| 778 | C23 | — | 27 | 1 | no | — |
| 779 | C23 | — | 54 | 1 | no | — |
| 780 | C23 | — | 54 | 2 | no | — |
| 781 | C23 | — | 324 | 4 | no | — |
| 782 | C23 | — | 162 | 1 | no | — |
| 783 | C23 | — | 162 | 2 | no | — |
| 784 | Q8 | — | 27 | 1 | no | — |
| 785 | Q8 | — | 27 | 2 | no | — |
| 786 | Q8 | — | 162 | 1 | no | — |
| 787 | Q8 | D3×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 788 | D4 | — | 3 | 1 | no | — |
| 789 | D4 | — | 27 | 1 | no | — |
| 790 | D4 | — | 27 | 2 | no | — |
| 791 | D4 | — | 54 | 1 | no | — |
| 792 | D4 | — | 54 | 2 | no | — |
| 793 | D4 | — | 162 | 1 | no | — |
| 794 | D4 | — | 162 | 2 | no | — |
| 795 | C2×C4 | — | 27 | 1 | no | — |
| 796 | C2×C4 | — | 27 | 2 | no | — |
| 797 | C2×C4 | — | 81 | 2 | no | — |
| 798 | C2×C4 | — | 81 | 1 | no | — |
| 799 | C8 | — | 3 | 1 | no | — |
| 800 | C8 | — | 27 | 1 | no | — |
| 801 | C8 | — | 27 | 2 | no | — |
| 802 | C2×C3 | — | 3 | 2 | no | — |
| 803 | C2×C3 | — | 4 | 1 | no | — |
| 804 | C2×C3 | — | 6 | 1 | no | — |
| 805 | C2×C3 | — | 8 | 1 | no | — |
| 806 | C2×C3 | — | 9 | 4 | no | — |
| 807 | C2×C3 | — | 9 | 2 | no | — |
| 808 | C2×C3 | — | 12 | 1 | no | — |
| 809 | C2×C3 | — | 24 | 2 | no | — |
| 810 | C2×C3 | — | 36 | 2 | no | — |
| 811 | C2×C3 | — | 36 | 4 | no | — |
| 812 | C2×C3 | — | 36 | 2 | no | — |
| 813 | C2×C3 | — | 48 | 1 | no | — |
| 814 | C2×C3 | — | 72 | 2 | no | — |
| 815 | C2×C3 | — | 72 | 4 | no | — |
| 816 | C2×C3 | — | 72 | 1 | no | — |
| 817 | C2×C3 | — | 108 | 2 | no | — |
| 818 | C2×C3 | — | 108 | 1 | no | — |
| 819 | C2×C3 | D32×S4 | 1 | 1 | yes | characteristic |
| 820 | D3 | — | 3 | 4 | no | — |
| 821 | D3 | — | 3 | 4 | no | — |
| 822 | D3 | — | 4 | 2 | no | — |
| 823 | D3 | — | 6 | 2 | no | — |
| 824 | D3 | — | 9 | 4 | no | — |
| 825 | D3 | — | 36 | 2 | no | — |
| 826 | D3 | — | 36 | 2 | no | — |
| 827 | D3 | — | 36 | 4 | no | — |
| 828 | D3 | — | 36 | 2 | no | — |
| 829 | D3 | — | 72 | 1 | no | — |
| 830 | D3 | — | 72 | 4 | no | — |
| 831 | D3 | — | 72 | 4 | no | — |
| 832 | D3 | — | 108 | 2 | no | — |
| 833 | D3 | — | 144 | 2 | no | — |
| 834 | D3 | — | 216 | 4 | no | — |
| 835 | C22 | — | 6 | 1 | no | — |
| 836 | C22 | — | 9 | 1 | no | — |
| 837 | C22 | — | 9 | 2 | no | — |
| 838 | C22 | — | 27 | 4 | no | — |
| 839 | C22 | — | 54 | 1 | no | — |
| 840 | C22 | — | 54 | 2 | no | — |
| 841 | C22 | — | 324 | 2 | no | — |
| 842 | C22 | — | 324 | 4 | no | — |
| 843 | C22 | — | 108 | 2 | no | — |
| 844 | C22 | — | 108 | 4 | no | — |
| 845 | C4 | — | 3 | 1 | no | — |
| 846 | C4 | — | 27 | 1 | no | — |
| 847 | C4 | — | 27 | 2 | no | — |
| 848 | C3 | — | 3 | 2 | no | — |
| 849 | C3 | — | 4 | 1 | no | — |
| 850 | C3 | — | 6 | 1 | no | — |
| 851 | C3 | — | 8 | 1 | no | — |
| 852 | C3 | — | 24 | 2 | no | — |
| 853 | C3 | — | 48 | 1 | no | — |
| 854 | C3 | D32×GL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 855 | C2 | — | 9 | 2 | no | — |
| 856 | C2 | — | 9 | 4 | no | — |
| 857 | C2 | — | 12 | 1 | no | — |
| 858 | C2 | — | 108 | 1 | no | — |
| 859 | C2 | — | 108 | 2 | no | — |
| 860 | C2 | S4×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | S4×((C3⋊D3)⋊C3)⋊C2 |
| commutator, cosocle, hypocenter | SL(2,𝔽3)×H(3,𝔽3) | C23 |
| Frattini, socle | C2×C3 | D32×S4 |
| Fitting | Q8×H(3,𝔽3) | C22×D3 |
| LCS | G ▷ SL(2,𝔽3)×H(3,𝔽3) | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72244580 | 2 |
| GL(2,𝔽3)×#272 | 2 |
| GL(2,𝔽3)×(C3⋊D3)⋊C3 | 2 |
| SL(2,𝔽3)×((C3⋊D3)⋊C3)⋊C2 | 2 |
| #72220376 | 2 |
| D32×GL(2,𝔽3) | 3 |
| SD16×((C3⋊D3)⋊C3)⋊C2 | 3 |
| C2×D3×((C3⋊D3)⋊C3)⋊C2 | 4 |