Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
224 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 41 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 | #11927274 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11926729 | C2 | 1 | 2 | yes | maximal |
| 3 | #11926726 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11926342 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C19×#356 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10597433 | C22 | 1 | 1 | yes | characteristic |
| 7 | C19×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 8 | #10597390 | — | 2 | 1 | no | — |
| 9 | #10597390 | C22 | 1 | 2 | yes | — |
| 10 | #10597388 | — | 2 | 1 | no | — |
| 11 | #10597355 | — | 2 | 2 | no | — |
| 12 | #10597334 | — | 2 | 2 | no | — |
| 13 | #10597333 | — | 2 | 2 | no | — |
| 14 | C4×Dic38 | — | 2 | 1 | no | — |
| 15 | C19×#101 | C22 | 1 | 2 | yes | — |
| 16 | #10597293 | C22 | 1 | 1 | yes | characteristic |
| 17 | #10597282 | — | 2 | 2 | no | — |
| 18 | #10597262 | — | 2 | 1 | no | — |
| 19 | C2×Q8×C19 | D4 | 1 | 1 | yes | characteristic |
| 20 | C2×Q8×C19 | C23 | 1 | 1 | yes | characteristic |
| 21 | #64545 | — | 4 | 1 | no | — |
| 22 | Q8×D19 | — | 4 | 1 | no | — |
| 23 | #64541 | — | 2 | 1 | no | — |
| 24 | #64541 | — | 2 | 2 | no | — |
| 25 | C2×Dic38 | — | 2 | 1 | no | — |
| 26 | C2×Dic38 | — | 2 | 1 | no | — |
| 27 | C2×Dic38 | D4 | 1 | 2 | yes | — |
| 28 | M16×C19 | — | 2 | 2 | no | — |
| 29 | C4⋊C4×C19 | — | 2 | 2 | no | — |
| 30 | C42×C19 | D4 | 1 | 1 | yes | characteristic |
| 31 | #64528 | — | 4 | 1 | no | — |
| 32 | #64527 | — | 4 | 1 | no | — |
| 33 | C4⋊Dic19 | — | 2 | 1 | no | — |
| 34 | Dic19⋊C4 | — | 2 | 2 | no | — |
| 35 | Dic19⋊C4 | — | 2 | 2 | no | — |
| 36 | Dic19⋊C4 | — | 2 | 2 | no | — |
| 37 | C4×Dic19 | — | 2 | 1 | no | — |
| 38 | C4×Dic19 | — | 2 | 2 | no | — |
| 39 | C4×Dic19 | D4 | 1 | 2 | yes | — |
| 40 | #64520 | — | 2 | 1 | no | — |
| 41 | Dic76 | — | 4 | 2 | no | — |
| 42 | #64516 | — | 4 | 2 | no | — |
| 43 | Q8×C19 | — | 4 | 1 | no | — |
| 44 | Q8×C19 | — | 4 | 1 | no | — |
| 45 | C2×C4×C19 | — | 2 | 1 | no | — |
| 46 | C2×C4×C19 | — | 2 | 1 | no | — |
| 47 | C2×C4×C19 | C2×D4 | 1 | 1 | yes | characteristic |
| 48 | C2×C4×C19 | C2×D4 | 1 | 2 | yes | — |
| 49 | C22⋊D19 | — | 4 | 1 | no | — |
| 50 | C2×Dic19 | — | 2 | 2 | no | — |
| 51 | C2×Dic19 | — | 2 | 2 | no | — |
| 52 | D76 | — | 2 | 2 | no | — |
| 53 | D76 | — | 2 | 1 | no | — |
| 54 | C4×D19 | — | 4 | 1 | no | — |
| 55 | C4×D19 | — | 4 | 2 | no | — |
| 56 | Dic38 | — | 2 | 4 | no | — |
| 57 | Dic38 | — | 2 | 2 | no | — |
| 58 | Dic38 | — | 2 | 1 | no | — |
| 59 | Dic38 | — | 4 | 2 | no | — |
| 60 | Dic38 | — | 8 | 1 | no | — |
| 61 | C8×C19 | — | 4 | 2 | no | — |
| 62 | C19⋊C8 | — | 4 | 1 | no | — |
| 63 | #2205 | — | 19 | 1 | no | maximal, Sylow |
| 64 | C22×C19 | #120 | 1 | 1 | yes | characteristic |
| 65 | C2×D19 | — | 4 | 1 | no | — |
| 66 | C4×C19 | — | 2 | 2 | no | — |
| 67 | C4×C19 | — | 2 | 1 | no | — |
| 68 | C4×C19 | — | 2 | 2 | no | — |
| 69 | C4×C19 | — | 4 | 1 | no | — |
| 70 | Dic19 | — | 2 | 4 | no | — |
| 71 | Dic19 | — | 4 | 1 | no | — |
| 72 | Dic19 | — | 4 | 2 | no | — |
| 73 | Q82 | — | 19 | 1 | no | — |
| 74 | #456 | — | 19 | 1 | no | — |
| 75 | #456 | — | 19 | 2 | no | — |
| 76 | #356 | — | 19 | 2 | no | — |
| 77 | #356 | D19 | 1 | 1 | yes | characteristic, complemented |
| 78 | C2×C19 | — | 2 | 1 | no | — |
| 79 | C2×C19 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 80 | D19 | — | 8 | 1 | no | — |
| 81 | 2−1+4 | — | 19 | 1 | no | — |
| 82 | #137 | — | 38 | 2 | no | — |
| 83 | #137 | — | 38 | 1 | no | — |
| 84 | C4⋊Q8 | — | 19 | 2 | no | — |
| 85 | C4⋊Q8 | — | 38 | 2 | no | — |
| 86 | C4⋊Q8 | — | 38 | 1 | no | — |
| 87 | C4⋊Q8 | C2×D19 | 1 | 1 | yes | characteristic |
| 88 | C4×Q8 | — | 38 | 2 | no | — |
| 89 | C4×Q8 | — | 38 | 1 | no | — |
| 90 | #104 | — | 38 | 2 | no | — |
| 91 | #104 | — | 38 | 1 | no | — |
| 92 | #101 | — | 19 | 1 | no | — |
| 93 | #101 | C2×D19 | 1 | 2 | yes | — |
| 94 | C19 | #2205 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 95 | #41 | — | 38 | 1 | no | — |
| 96 | #41 | — | 38 | 2 | no | — |
| 97 | #41 | — | 76 | 1 | no | — |
| 98 | C2×Q8 | — | 19 | 2 | no | — |
| 99 | C2×Q8 | — | 38 | 1 | no | — |
| 100 | C2×Q8 | — | 38 | 1 | no | — |
| 101 | C2×Q8 | — | 76 | 1 | no | — |
| 102 | C2×Q8 | D76 | 1 | 1 | yes | characteristic |
| 103 | C2×Q8 | C22×D19 | 1 | 1 | yes | characteristic |
| 104 | Q16 | — | 76 | 2 | no | — |
| 105 | Q16 | — | 76 | 1 | no | — |
| 106 | SD16 | — | 76 | 2 | no | — |
| 107 | SD16 | — | 76 | 1 | no | — |
| 108 | M16 | — | 2 | 2 | no | — |
| 109 | M16 | — | 38 | 1 | no | — |
| 110 | C4⋊C4 | — | 2 | 2 | no | — |
| 111 | C4⋊C4 | — | 38 | 2 | no | — |
| 112 | C4⋊C4 | — | 38 | 1 | no | — |
| 113 | C4⋊C4 | — | 38 | 2 | no | — |
| 114 | C4⋊C4 | — | 38 | 2 | no | — |
| 115 | C42 | — | 19 | 2 | no | — |
| 116 | C42 | — | 38 | 2 | no | — |
| 117 | C42 | — | 38 | 1 | no | — |
| 118 | C42 | D76 | 1 | 1 | yes | characteristic |
| 119 | Q8 | — | 4 | 1 | no | — |
| 120 | Q8 | — | 4 | 1 | no | — |
| 121 | Q8 | — | 38 | 4 | no | — |
| 122 | Q8 | — | 38 | 2 | no | — |
| 123 | Q8 | — | 38 | 1 | no | — |
| 124 | Q8 | — | 76 | 2 | no | — |
| 125 | Q8 | — | 152 | 1 | no | — |
| 126 | D4 | — | 38 | 2 | no | — |
| 127 | D4 | — | 38 | 1 | no | — |
| 128 | D4 | — | 76 | 1 | no | — |
| 129 | C2×C4 | — | 2 | 1 | no | — |
| 130 | C2×C4 | — | 2 | 1 | no | — |
| 131 | C2×C4 | — | 38 | 2 | no | — |
| 132 | C2×C4 | — | 38 | 2 | no | — |
| 133 | C2×C4 | — | 76 | 2 | no | — |
| 134 | C2×C4 | — | 76 | 1 | no | — |
| 135 | C2×C4 | C2×D76 | 1 | 1 | yes | characteristic |
| 136 | C2×C4 | D4×D19 | 1 | 2 | yes | — |
| 137 | C8 | — | 4 | 2 | no | — |
| 138 | C8 | — | 76 | 1 | no | — |
| 139 | C22 | — | 76 | 1 | no | — |
| 140 | C22 | #10597328 | 1 | 1 | yes | characteristic |
| 141 | C4 | — | 2 | 2 | no | — |
| 142 | C4 | — | 2 | 2 | no | — |
| 143 | C4 | — | 2 | 1 | no | — |
| 144 | C4 | — | 4 | 1 | no | — |
| 145 | C4 | — | 38 | 4 | no | — |
| 146 | C4 | — | 76 | 2 | no | — |
| 147 | C4 | — | 76 | 1 | no | — |
| 148 | C2 | — | 2 | 1 | no | — |
| 149 | C2 | — | 152 | 1 | no | — |
| 150 | C2 | #11926732 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11927274 | C2 | semidirect |
| 4. #11926342 | C2 | semidirect |
| 5. C19×#356 | C2 | semidirect |
| 77. #356 | D19 | semidirect |
| 94. C19 | #2205 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927274 | 2 |
| #11926729 | 2 |
| #11926726 | 2 |
| #11926342 | 2 |
| C19×#356 | 2 |
| #2205 | 19 |