Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
656 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 94 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 | #21462005 | C2 | 1 | 3 | yes | maximal |
| 2 | #21461359 | C2 | 1 | 3 | yes | maximal |
| 3 | #21460313 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #16840767 | C22 | 1 | 3 | yes | — |
| 5 | C42×#6923 | C22 | 1 | 1 | yes | characteristic |
| 6 | #16840632 | — | 2 | 6 | no | — |
| 7 | #16840621 | — | 2 | 6 | no | — |
| 8 | C61⋊#564 | C4 | 1 | 3 | yes | complemented |
| 9 | #16840489 | — | 2 | 6 | no | — |
| 10 | #16840371 | — | 2 | 6 | no | — |
| 11 | #16840318 | C22 | 1 | 3 | yes | — |
| 12 | C61×#564 | C4 | 1 | 1 | yes | characteristic, complemented |
| 13 | C2×#11758213 | — | 2 | 3 | no | — |
| 14 | C2×C4×#6923 | — | 2 | 3 | no | — |
| 15 | #14519844 | — | 2 | 6 | no | — |
| 16 | #14519776 | — | 2 | 6 | no | — |
| 17 | #14519776 | D4 | 1 | 6 | yes | — |
| 18 | #14519772 | — | 2 | 6 | no | — |
| 19 | #14519771 | — | 2 | 2 | no | — |
| 20 | #14519769 | C2×C4 | 1 | 3 | yes | — |
| 21 | #14519768 | — | 2 | 6 | no | — |
| 22 | #14519767 | — | 2 | 6 | no | — |
| 23 | #14519767 | — | 2 | 6 | no | — |
| 24 | #14519767 | — | 2 | 6 | no | — |
| 25 | #14519755 | — | 2 | 6 | no | — |
| 26 | C4×Dic122 | — | 2 | 6 | no | — |
| 27 | #14519742 | — | 2 | 6 | no | — |
| 28 | #14519742 | — | 2 | 6 | no | — |
| 29 | #14519735 | D4 | 1 | 6 | yes | — |
| 30 | C42×D61 | C23 | 1 | 1 | yes | characteristic |
| 31 | #125×C61 | — | 2 | 6 | no | — |
| 32 | #125×C61 | C2×C4 | 1 | 3 | yes | — |
| 33 | C22×#6923 | — | 4 | 1 | no | — |
| 34 | C2×C4×D61 | C2×D4 | 1 | 3 | yes | — |
| 35 | C2×Dic122 | — | 2 | 6 | no | — |
| 36 | C2×#92420 | — | 4 | 3 | no | — |
| 37 | C4×#6923 | — | 2 | 6 | no | — |
| 38 | C4×#6923 | — | 4 | 3 | no | — |
| 39 | #11758213 | — | 4 | 6 | no | — |
| 40 | C4⋊C4×C61 | — | 2 | 6 | no | — |
| 41 | C4⋊C4×C61 | — | 2 | 6 | no | — |
| 42 | C4⋊C4×C61 | C22⋊C4 | 1 | 6 | yes | — |
| 43 | C42×C61 | — | 2 | 2 | no | — |
| 44 | C42×C61 | C22×C4 | 1 | 1 | yes | characteristic |
| 45 | #11758198 | — | 2 | 6 | no | — |
| 46 | C4⋊Dic61 | — | 2 | 6 | no | — |
| 47 | C4⋊Dic61 | C22⋊C4 | 1 | 6 | yes | — |
| 48 | #11758196 | — | 2 | 6 | no | — |
| 49 | #11758196 | — | 2 | 6 | no | — |
| 50 | #11758196 | — | 2 | 6 | no | — |
| 51 | #11758196 | — | 2 | 6 | no | — |
| 52 | C4×Dic61 | — | 2 | 6 | no | — |
| 53 | C4×Dic61 | — | 2 | 6 | no | — |
| 54 | C4×Dic61 | C2×D4 | 1 | 3 | yes | — |
| 55 | C22×D61 | #120 | 1 | 1 | yes | characteristic |
| 56 | C2×#6923 | — | 4 | 6 | no | — |
| 57 | C2×C4×C61 | — | 2 | 6 | no | — |
| 58 | C2×C4×C61 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 59 | C2×Dic61 | — | 2 | 6 | no | — |
| 60 | C2×Dic61 | #120 | 1 | 3 | yes | — |
| 61 | C4×D61 | — | 2 | 3 | no | — |
| 62 | C4×D61 | — | 2 | 3 | no | — |
| 63 | Dic122 | — | 4 | 6 | no | — |
| 64 | Dic122 | — | 4 | 6 | no | — |
| 65 | #92420 | — | 8 | 3 | no | — |
| 66 | #8533 | — | 61 | 1 | no | maximal, Sylow |
| 67 | C22×C61 | #379 | 1 | 1 | yes | characteristic |
| 68 | C2×D61 | — | 2 | 3 | no | — |
| 69 | #6923 | — | 4 | 4 | no | — |
| 70 | C4×C61 | — | 2 | 3 | no | — |
| 71 | C4×C61 | — | 4 | 6 | no | — |
| 72 | Dic61 | — | 4 | 6 | no | — |
| 73 | Dic61 | #454 | 1 | 3 | yes | — |
| 74 | Dic61 | #456 | 1 | 3 | yes | — |
| 75 | #3556 | — | 61 | 1 | no | — |
| 76 | #1994 | — | 61 | 3 | no | — |
| 77 | #1561 | — | 61 | 3 | no | — |
| 78 | C2×C61 | #1793 | 1 | 3 | yes | — |
| 79 | D61 | — | 4 | 1 | no | — |
| 80 | #564 | — | 61 | 3 | no | — |
| 81 | #564 | #6923 | 1 | 1 | yes | characteristic, complemented |
| 82 | #557 | — | 122 | 6 | no | — |
| 83 | #541 | — | 122 | 6 | no | — |
| 84 | #533 | — | 61 | 3 | no | — |
| 85 | #423 | — | 61 | 3 | no | — |
| 86 | C43 | — | 61 | 1 | no | — |
| 87 | #339 | — | 122 | 6 | no | — |
| 88 | #332 | — | 122 | 6 | no | — |
| 89 | C61 | #8533 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 90 | C2×M16 | — | 122 | 3 | no | — |
| 91 | C4⋊Q8 | — | 61 | 6 | no | — |
| 92 | C4⋊Q8 | — | 122 | 6 | no | — |
| 93 | #126 | — | 122 | 2 | no | — |
| 94 | #126 | — | 122 | 6 | no | — |
| 95 | #125 | — | 2 | 6 | no | — |
| 96 | #125 | — | 61 | 3 | no | — |
| 97 | #125 | — | 122 | 6 | no | — |
| 98 | #125 | — | 122 | 6 | no | — |
| 99 | #125 | — | 122 | 6 | no | — |
| 100 | #125 | — | 122 | 6 | no | — |
| 101 | #125 | C2×#6923 | 1 | 3 | yes | — |
| 102 | C22⋊Q8 | — | 122 | 6 | no | — |
| 103 | C4×Q8 | — | 122 | 6 | no | — |
| 104 | C4×Q8 | — | 122 | 6 | no | — |
| 105 | C4×Q8 | — | 122 | 6 | no | — |
| 106 | #117 | — | 61 | 6 | no | — |
| 107 | C2×C42 | — | 61 | 1 | no | — |
| 108 | C2×C42 | — | 122 | 3 | no | — |
| 109 | C4⋊C8 | — | 122 | 6 | no | — |
| 110 | C2×Q8 | — | 122 | 6 | no | — |
| 111 | C22×C4 | — | 61 | 3 | no | — |
| 112 | C22×C4 | — | 244 | 1 | no | — |
| 113 | M16 | — | 244 | 6 | no | — |
| 114 | C2×C8 | — | 244 | 3 | no | — |
| 115 | C4⋊C4 | — | 2 | 6 | no | — |
| 116 | C4⋊C4 | — | 2 | 6 | no | — |
| 117 | C4⋊C4 | — | 61 | 6 | no | — |
| 118 | C4⋊C4 | — | 122 | 6 | no | — |
| 119 | C4⋊C4 | — | 122 | 6 | no | — |
| 120 | C4⋊C4 | — | 122 | 6 | no | — |
| 121 | C4⋊C4 | — | 122 | 6 | no | — |
| 122 | C4⋊C4 | — | 122 | 6 | no | — |
| 123 | C4⋊C4 | C22⋊#6923 | 1 | 6 | yes | — |
| 124 | C22⋊C4 | — | 122 | 6 | no | — |
| 125 | C42 | — | 2 | 2 | no | — |
| 126 | C42 | — | 61 | 3 | no | — |
| 127 | C42 | — | 122 | 6 | no | — |
| 128 | C42 | — | 122 | 6 | no | — |
| 129 | C42 | — | 122 | 6 | no | — |
| 130 | C42 | — | 244 | 3 | no | — |
| 131 | C42 | C22×#6923 | 1 | 1 | yes | characteristic |
| 132 | C23 | — | 61 | 1 | no | — |
| 133 | Q8 | — | 244 | 6 | no | — |
| 134 | Q8 | — | 244 | 6 | no | — |
| 135 | C2×C4 | — | 2 | 6 | no | — |
| 136 | C2×C4 | — | 61 | 3 | no | — |
| 137 | C2×C4 | — | 122 | 3 | no | — |
| 138 | C2×C4 | — | 122 | 3 | no | — |
| 139 | C2×C4 | — | 122 | 6 | no | — |
| 140 | C2×C4 | — | 244 | 6 | no | — |
| 141 | C2×C4 | C2×C22⋊#6923 | 1 | 3 | yes | — |
| 142 | C8 | — | 488 | 3 | no | — |
| 143 | C22 | — | 122 | 3 | no | — |
| 144 | C22 | #16840703 | 1 | 1 | yes | characteristic |
| 145 | C4 | — | 2 | 3 | no | — |
| 146 | C4 | — | 4 | 6 | no | — |
| 147 | C4 | — | 61 | 3 | no | — |
| 148 | C4 | — | 61 | 3 | no | — |
| 149 | C4 | — | 244 | 4 | no | — |
| 150 | C4 | — | 244 | 6 | no | — |
| 151 | C2 | — | 244 | 1 | no | — |
| 152 | C2 | #21461666 | 1 | 3 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C61⋊#564 | C4 | semidirect |
| 12. C61×#564 | C4 | semidirect |
| 81. #564 | #6923 | semidirect |
| 89. C61 | #8533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462005 | 2 |
| #21461359 | 2 |
| #21460313 | 2 |
| #8533 | 61 |