Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
532 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 122 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 | C2×#11718274 | C2 | 1 | 3 | yes | maximal |
| 2 | #13130518 | C2 | 1 | 3 | yes | maximal |
| 3 | D13×#338 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C2×#88237 | C22 | 1 | 3 | yes | — |
| 5 | C22×#6118 | C22 | 1 | 1 | yes | characteristic |
| 6 | C2×M16×D13 | C22 | 1 | 3 | yes | — |
| 7 | #11718274 | — | 2 | 6 | no | — |
| 8 | #11718272 | — | 2 | 6 | no | — |
| 9 | C13×#338 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | #11718152 | C4 | 1 | 3 | yes | complemented |
| 11 | C22×C4×D13 | C23 | 1 | 1 | yes | characteristic |
| 12 | C2×C22⋊#261 | — | 2 | 3 | no | — |
| 13 | C22×#1057 | Q8 | 1 | 2 | yes | — |
| 14 | #88237 | — | 2 | 3 | no | — |
| 15 | #88237 | — | 2 | 3 | no | — |
| 16 | #88237 | — | 2 | 3 | no | — |
| 17 | #88237 | D4 | 1 | 6 | yes | — |
| 18 | C2×C4⋊#261 | — | 2 | 3 | no | — |
| 19 | C2×C4×#261 | — | 2 | 3 | no | — |
| 20 | C2×#6118 | — | 2 | 3 | no | — |
| 21 | C2×#6118 | — | 2 | 3 | no | — |
| 22 | C2×C13×M16 | C2×C4 | 1 | 3 | yes | — |
| 23 | C2×#6099 | C2×C4 | 1 | 3 | yes | — |
| 24 | M16×D13 | — | 2 | 3 | no | — |
| 25 | M16×D13 | — | 2 | 3 | no | — |
| 26 | M16×D13 | — | 2 | 3 | no | — |
| 27 | M16×D13 | — | 2 | 3 | no | — |
| 28 | C2×#6094 | — | 2 | 3 | no | — |
| 29 | C2×C8×D13 | — | 2 | 3 | no | — |
| 30 | #11311 | — | 13 | 1 | no | maximal, Sylow |
| 31 | C23×D13 | #41 | 1 | 1 | yes | characteristic |
| 32 | C22×#261 | — | 4 | 3 | no | — |
| 33 | C22×C4×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 34 | C22×Dic13 | C2×Q8 | 1 | 1 | yes | characteristic |
| 35 | C2×C4×D13 | C2×D4 | 1 | 3 | yes | — |
| 36 | C2×C4×D13 | #41 | 1 | 3 | yes | — |
| 37 | C2×C4×D13 | #41 | 1 | 3 | yes | — |
| 38 | C2×C4×D13 | #41 | 1 | 3 | yes | — |
| 39 | C22⋊#261 | — | 2 | 6 | no | — |
| 40 | C22⋊#261 | — | 4 | 3 | no | — |
| 41 | C2×#1057 | — | 2 | 6 | no | — |
| 42 | C4⋊#261 | — | 2 | 6 | no | — |
| 43 | C4⋊#261 | — | 4 | 3 | no | — |
| 44 | C4×#261 | — | 2 | 6 | no | — |
| 45 | C4×#261 | — | 4 | 3 | no | — |
| 46 | #6118 | — | 4 | 3 | no | — |
| 47 | #6118 | — | 4 | 1 | no | — |
| 48 | C13×M16 | — | 2 | 3 | no | — |
| 49 | C13×M16 | — | 2 | 3 | no | — |
| 50 | C2×C8×C13 | — | 2 | 3 | no | — |
| 51 | #6099 | — | 2 | 3 | no | — |
| 52 | #6099 | — | 2 | 3 | no | — |
| 53 | C2×#1055 | — | 2 | 3 | no | — |
| 54 | #6094 | — | 4 | 3 | no | — |
| 55 | #6094 | — | 4 | 3 | no | — |
| 56 | C8×D13 | — | 4 | 3 | no | — |
| 57 | C8×D13 | — | 4 | 3 | no | — |
| 58 | C2×#344 | — | 13 | 3 | no | — |
| 59 | #1733 | — | 13 | 3 | no | — |
| 60 | C2×#338 | — | 13 | 1 | no | — |
| 61 | C23×C13 | C4×Q8 | 1 | 1 | yes | characteristic |
| 62 | C22×D13 | — | 8 | 1 | no | — |
| 63 | C22×D13 | #123 | 1 | 3 | yes | — |
| 64 | C22×D13 | #126 | 1 | 3 | yes | — |
| 65 | C2×#261 | — | 4 | 6 | no | — |
| 66 | C2×#261 | — | 8 | 6 | no | — |
| 67 | C2×C4×C13 | #117 | 1 | 3 | yes | — |
| 68 | C2×C4×C13 | C4×D4 | 1 | 3 | yes | — |
| 69 | C2×Dic13 | C22⋊Q8 | 1 | 3 | yes | — |
| 70 | C2×Dic13 | #125 | 1 | 3 | yes | — |
| 71 | C4×D13 | #121 | 1 | 3 | yes | — |
| 72 | C4×D13 | #123 | 1 | 3 | yes | — |
| 73 | C4×D13 | #124 | 1 | 3 | yes | — |
| 74 | C4×D13 | #126 | 1 | 1 | yes | characteristic |
| 75 | C4×D13 | #126 | 1 | 3 | yes | — |
| 76 | C4×D13 | #126 | 1 | 3 | yes | — |
| 77 | #1057 | — | 4 | 2 | no | — |
| 78 | C8×C13 | — | 4 | 3 | no | — |
| 79 | #1055 | — | 4 | 3 | no | — |
| 80 | C22×M16 | — | 13 | 1 | no | — |
| 81 | C22×M16 | — | 13 | 3 | no | — |
| 82 | C2×#117 | — | 13 | 3 | no | — |
| 83 | #344 | — | 26 | 6 | no | — |
| 84 | #339 | — | 26 | 6 | no | — |
| 85 | #338 | — | 13 | 3 | no | — |
| 86 | #338 | #261 | 1 | 1 | yes | characteristic, complemented |
| 87 | C22×C13 | — | 4 | 1 | no | — |
| 88 | C22×C13 | #387 | 1 | 3 | yes | — |
| 89 | C2×D13 | — | 4 | 3 | no | — |
| 90 | C2×D13 | — | 4 | 3 | no | — |
| 91 | C2×D13 | #397 | 1 | 3 | yes | — |
| 92 | C2×D13 | #401 | 1 | 1 | yes | characteristic |
| 93 | #261 | — | 8 | 6 | no | — |
| 94 | C4×C13 | #383 | 1 | 1 | yes | characteristic |
| 95 | C4×C13 | #388 | 1 | 3 | yes | — |
| 96 | Dic13 | #396 | 1 | 1 | yes | characteristic |
| 97 | Dic13 | #400 | 1 | 3 | yes | — |
| 98 | C23×C4 | — | 13 | 1 | no | — |
| 99 | C2×M16 | — | 13 | 3 | no | — |
| 100 | C2×M16 | — | 26 | 3 | no | — |
| 101 | C2×M16 | — | 26 | 3 | no | — |
| 102 | C2×M16 | — | 26 | 3 | no | — |
| 103 | C2×M16 | — | 26 | 3 | no | — |
| 104 | C2×M16 | — | 26 | 3 | no | — |
| 105 | C2×M16 | — | 26 | 3 | no | — |
| 106 | C2×M16 | — | 26 | 3 | no | — |
| 107 | C2×M16 | C2×#261 | 1 | 3 | yes | — |
| 108 | C22×C8 | — | 13 | 2 | no | — |
| 109 | C22×C8 | — | 26 | 3 | no | — |
| 110 | #117 | — | 13 | 6 | no | — |
| 111 | #117 | — | 26 | 3 | no | — |
| 112 | #117 | — | 26 | 3 | no | — |
| 113 | #117 | — | 26 | 3 | no | — |
| 114 | C2×C4⋊C4 | — | 26 | 3 | no | — |
| 115 | C2×C22⋊C4 | — | 26 | 3 | no | — |
| 116 | C2×C42 | — | 26 | 3 | no | — |
| 117 | C2×C13 | — | 2 | 3 | no | — |
| 118 | C2×C13 | #1443 | 1 | 1 | yes | characteristic |
| 119 | D13 | — | 2 | 3 | no | — |
| 120 | D13 | — | 2 | 1 | no | — |
| 121 | C24 | — | 13 | 1 | no | — |
| 122 | C22×C4 | — | 13 | 1 | no | — |
| 123 | C22×C4 | — | 13 | 3 | no | — |
| 124 | C22×C4 | — | 13 | 3 | no | — |
| 125 | C22×C4 | — | 13 | 3 | no | — |
| 126 | C22×C4 | — | 13 | 3 | no | — |
| 127 | C22×C4 | — | 52 | 3 | no | — |
| 128 | C22×C4 | C22×#261 | 1 | 1 | yes | characteristic |
| 129 | M16 | — | 2 | 3 | no | — |
| 130 | M16 | — | 2 | 3 | no | — |
| 131 | M16 | — | 26 | 3 | no | — |
| 132 | M16 | — | 26 | 3 | no | — |
| 133 | M16 | — | 52 | 3 | no | — |
| 134 | M16 | — | 52 | 3 | no | — |
| 135 | M16 | — | 52 | 1 | no | — |
| 136 | M16 | — | 52 | 3 | no | — |
| 137 | C2×C8 | — | 2 | 3 | no | — |
| 138 | C2×C8 | — | 26 | 6 | no | — |
| 139 | C2×C8 | — | 26 | 3 | no | — |
| 140 | C2×C8 | — | 52 | 3 | no | — |
| 141 | C2×C8 | — | 52 | 3 | no | — |
| 142 | C4⋊C4 | — | 26 | 6 | no | — |
| 143 | C4⋊C4 | — | 52 | 3 | no | — |
| 144 | C22⋊C4 | — | 26 | 6 | no | — |
| 145 | C22⋊C4 | — | 52 | 3 | no | — |
| 146 | C42 | — | 26 | 6 | no | — |
| 147 | C42 | — | 52 | 3 | no | — |
| 148 | C13 | #11311 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 149 | C23 | — | 13 | 3 | no | — |
| 150 | C23 | — | 13 | 3 | no | — |
| 151 | C23 | — | 104 | 1 | no | — |
| 152 | C23 | Q8×#261 | 1 | 1 | yes | characteristic |
| 153 | C2×C4 | — | 13 | 3 | no | — |
| 154 | C2×C4 | — | 13 | 3 | no | — |
| 155 | C2×C4 | — | 13 | 3 | no | — |
| 156 | C2×C4 | — | 13 | 1 | no | — |
| 157 | C2×C4 | — | 13 | 3 | no | — |
| 158 | C2×C4 | — | 13 | 3 | no | — |
| 159 | C2×C4 | — | 13 | 3 | no | — |
| 160 | C2×C4 | — | 13 | 3 | no | — |
| 161 | C2×C4 | — | 52 | 6 | no | — |
| 162 | C2×C4 | — | 104 | 6 | no | — |
| 163 | C2×C4 | #88237 | 1 | 3 | yes | — |
| 164 | C2×C4 | D4×#261 | 1 | 3 | yes | — |
| 165 | C8 | — | 4 | 3 | no | — |
| 166 | C8 | — | 52 | 2 | no | — |
| 167 | C8 | — | 52 | 3 | no | — |
| 168 | C22 | — | 4 | 1 | no | — |
| 169 | C22 | — | 13 | 3 | no | — |
| 170 | C22 | — | 13 | 1 | no | — |
| 171 | C22 | — | 52 | 3 | no | — |
| 172 | C22 | — | 52 | 3 | no | — |
| 173 | C22 | #11719082 | 1 | 3 | yes | — |
| 174 | C4 | — | 13 | 1 | no | — |
| 175 | C4 | — | 13 | 3 | no | — |
| 176 | C4 | — | 104 | 6 | no | — |
| 177 | C4 | #11719061 | 1 | 1 | yes | characteristic |
| 178 | C4 | #11719071 | 1 | 3 | yes | — |
| 179 | C2 | — | 2 | 3 | no | — |
| 180 | C2 | — | 26 | 3 | no | — |
| 181 | C2 | — | 26 | 1 | no | — |
| 182 | C2 | #13130023 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C13×#338 | C4 | semidirect |
| 10. #11718152 | C4 | semidirect |
| 86. #338 | #261 | semidirect |
| 148. C13 | #11311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11718274 | 2 |
| #13130518 | 2 |
| D13×#338 | 2 |
| #11311 | 13 |