Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
592 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 89 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 | #14575016 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | #14564462 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C19×#1309 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11927094 | C22 | 1 | 3 | yes | — |
| 5 | #11926835 | — | 2 | 6 | no | — |
| 6 | #11926797 | — | 2 | 6 | no | — |
| 7 | #11926740 | — | 2 | 6 | no | — |
| 8 | C2×#10597282 | — | 2 | 6 | no | — |
| 9 | C42×Dic19 | C22 | 1 | 1 | yes | characteristic |
| 10 | C19×#423 | C22 | 1 | 3 | yes | — |
| 11 | C2×#64541 | — | 2 | 3 | no | — |
| 12 | C2×M16×C19 | D4 | 1 | 6 | yes | — |
| 13 | C2×C42×C19 | C23 | 1 | 1 | yes | characteristic |
| 14 | #10597376 | — | 2 | 6 | no | — |
| 15 | C2×C4×Dic19 | — | 2 | 3 | no | — |
| 16 | C2×D152 | — | 2 | 6 | no | — |
| 17 | #10597321 | — | 2 | 3 | no | — |
| 18 | #10597320 | D4 | 1 | 3 | yes | — |
| 19 | C4×D76 | — | 2 | 6 | no | — |
| 20 | #10597315 | D4 | 1 | 3 | yes | — |
| 21 | C19×C4⋊C8 | — | 2 | 6 | no | — |
| 22 | #10597282 | — | 4 | 12 | no | — |
| 23 | #10597278 | — | 2 | 12 | no | — |
| 24 | #10597274 | — | 2 | 6 | no | — |
| 25 | C22×C4×C19 | C2×D4 | 1 | 3 | yes | — |
| 26 | C2×C22⋊D19 | — | 4 | 3 | no | — |
| 27 | C22×Dic19 | — | 4 | 1 | no | — |
| 28 | #64541 | — | 4 | 6 | no | — |
| 29 | #64541 | — | 4 | 6 | no | — |
| 30 | C2×D76 | — | 2 | 6 | no | — |
| 31 | C2×D76 | — | 2 | 3 | no | — |
| 32 | C2×C4×D19 | — | 4 | 3 | no | — |
| 33 | C2×Dic38 | — | 2 | 3 | no | — |
| 34 | M16×C19 | — | 4 | 6 | no | — |
| 35 | C2×C8×C19 | — | 2 | 6 | no | — |
| 36 | C42×C19 | C2×D4 | 1 | 3 | yes | — |
| 37 | C42×C19 | #41 | 1 | 1 | yes | characteristic |
| 38 | (C2×D19)⋊C4 | — | 4 | 6 | no | — |
| 39 | C4⋊Dic19 | — | 2 | 6 | no | — |
| 40 | C4×Dic19 | — | 2 | 6 | no | — |
| 41 | C4×Dic19 | — | 4 | 3 | no | — |
| 42 | D152 | — | 8 | 6 | no | — |
| 43 | #10300 | — | 19 | 1 | no | maximal, Sylow |
| 44 | C23×C19 | #127 | 1 | 1 | yes | characteristic |
| 45 | C22×D19 | — | 4 | 3 | no | — |
| 46 | C2×C4×C19 | — | 2 | 3 | no | — |
| 47 | C2×C4×C19 | — | 2 | 3 | no | — |
| 48 | C2×C4×C19 | #120 | 1 | 3 | yes | — |
| 49 | C2×C4×C19 | #121 | 1 | 3 | yes | — |
| 50 | C22⋊D19 | — | 8 | 6 | no | — |
| 51 | C2×Dic19 | — | 4 | 6 | no | — |
| 52 | C2×Dic19 | — | 4 | 3 | no | — |
| 53 | D76 | — | 4 | 6 | no | — |
| 54 | D76 | — | 4 | 6 | no | — |
| 55 | D76 | — | 4 | 6 | no | — |
| 56 | C4×D19 | — | 8 | 3 | no | — |
| 57 | C4×D19 | — | 8 | 3 | no | — |
| 58 | Dic38 | — | 4 | 6 | no | — |
| 59 | C8×C19 | — | 4 | 6 | no | — |
| 60 | #3253 | — | 19 | 3 | no | — |
| 61 | #1962 | — | 19 | 3 | no | — |
| 62 | #1309 | D19 | 1 | 1 | yes | characteristic, complemented |
| 63 | C22×C19 | — | 2 | 3 | no | — |
| 64 | C22×C19 | #392 | 1 | 1 | yes | characteristic |
| 65 | C2×D19 | — | 8 | 3 | no | — |
| 66 | C2×D19 | — | 8 | 6 | no | — |
| 67 | C4×C19 | — | 2 | 3 | no | — |
| 68 | C4×C19 | #453 | 1 | 3 | yes | — |
| 69 | C4×C19 | #454 | 1 | 3 | yes | — |
| 70 | Dic19 | — | 4 | 4 | no | — |
| 71 | Dic19 | — | 8 | 3 | no | — |
| 72 | #532 | — | 19 | 3 | no | — |
| 73 | #476 | — | 38 | 6 | no | — |
| 74 | #469 | — | 38 | 6 | no | — |
| 75 | #459 | — | 38 | 6 | no | — |
| 76 | #423 | C2×D19 | 1 | 3 | yes | — |
| 77 | C2×#104 | — | 38 | 6 | no | — |
| 78 | C43 | — | 19 | 1 | no | — |
| 79 | C2×C19 | — | 4 | 1 | no | — |
| 80 | C2×C19 | #2006 | 1 | 3 | yes | — |
| 81 | D19 | — | 16 | 3 | no | — |
| 82 | C2×#41 | — | 38 | 3 | no | — |
| 83 | C2×D8 | — | 38 | 6 | no | — |
| 84 | C2×M16 | D76 | 1 | 6 | yes | — |
| 85 | C4⋊Q8 | — | 19 | 3 | no | — |
| 86 | #127 | — | 19 | 3 | no | — |
| 87 | #124 | — | 38 | 3 | no | — |
| 88 | #121 | — | 38 | 6 | no | — |
| 89 | C4×D4 | — | 38 | 6 | no | — |
| 90 | C2×C42 | — | 38 | 3 | no | — |
| 91 | C2×C42 | C22×D19 | 1 | 1 | yes | characteristic |
| 92 | #106 | — | 38 | 6 | no | — |
| 93 | C4⋊C8 | — | 2 | 6 | no | — |
| 94 | #104 | — | 76 | 12 | no | — |
| 95 | #102 | — | 38 | 12 | no | — |
| 96 | C19 | #10300 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 97 | #41 | — | 76 | 6 | no | — |
| 98 | #41 | — | 76 | 6 | no | — |
| 99 | C2×Q8 | — | 38 | 3 | no | — |
| 100 | C2×D4 | — | 38 | 6 | no | — |
| 101 | C2×D4 | — | 38 | 3 | no | — |
| 102 | C2×D4 | — | 76 | 3 | no | — |
| 103 | C22×C4 | — | 76 | 1 | no | — |
| 104 | C22×C4 | — | 76 | 3 | no | — |
| 105 | C22×C4 | C2×D76 | 1 | 3 | yes | — |
| 106 | D8 | — | 152 | 6 | no | — |
| 107 | M16 | — | 4 | 6 | no | — |
| 108 | C2×C8 | — | 2 | 6 | no | — |
| 109 | C4⋊C4 | — | 38 | 6 | no | — |
| 110 | C22⋊C4 | — | 76 | 6 | no | — |
| 111 | C42 | — | 38 | 6 | no | — |
| 112 | C42 | — | 76 | 3 | no | — |
| 113 | C42 | D4×D19 | 1 | 3 | yes | — |
| 114 | C42 | #64545 | 1 | 1 | yes | characteristic |
| 115 | C23 | — | 76 | 3 | no | — |
| 116 | C23 | #10597320 | 1 | 1 | yes | characteristic |
| 117 | Q8 | — | 76 | 6 | no | — |
| 118 | D4 | — | 76 | 6 | no | — |
| 119 | D4 | — | 76 | 6 | no | — |
| 120 | D4 | — | 76 | 6 | no | — |
| 121 | D4 | — | 152 | 6 | no | — |
| 122 | C2×C4 | — | 2 | 3 | no | — |
| 123 | C2×C4 | — | 2 | 3 | no | — |
| 124 | C2×C4 | — | 76 | 6 | no | — |
| 125 | C2×C4 | — | 76 | 3 | no | — |
| 126 | C2×C4 | — | 152 | 3 | no | — |
| 127 | C2×C4 | — | 152 | 3 | no | — |
| 128 | C2×C4 | #10597328 | 1 | 3 | yes | — |
| 129 | C2×C4 | #10597341 | 1 | 3 | yes | — |
| 130 | C8 | — | 4 | 6 | no | — |
| 131 | C22 | — | 2 | 3 | no | — |
| 132 | C22 | — | 152 | 3 | no | — |
| 133 | C22 | — | 152 | 6 | no | — |
| 134 | C22 | #11926454 | 1 | 1 | yes | characteristic |
| 135 | C4 | — | 2 | 3 | no | — |
| 136 | C4 | — | 76 | 4 | no | — |
| 137 | C4 | — | 152 | 3 | no | — |
| 138 | C4 | #11926714 | 1 | 3 | yes | — |
| 139 | C4 | #11926719 | 1 | 3 | yes | — |
| 140 | C2 | — | 4 | 1 | no | — |
| 141 | C2 | — | 304 | 3 | no | — |
| 142 | C2 | #14564679 | 1 | 3 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14575016 | C2 | semidirect |
| 2. #14564462 | C2 | semidirect |
| 3. C19×#1309 | C2 | semidirect |
| 62. #1309 | D19 | semidirect |
| 96. C19 | #10300 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14575016 | 2 |
| #14564462 | 2 |
| C19×#1309 | 2 |
| #10300 | 19 |