Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
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 | #14583629 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #14583084 | C2 | 1 | 2 | yes | maximal |
| 3 | #14583081 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #14582697 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C43×#356 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13063373 | C22 | 1 | 1 | yes | characteristic |
| 7 | #13063358 | — | 2 | 2 | no | — |
| 8 | #13063356 | — | 2 | 1 | no | — |
| 9 | #13063324 | — | 2 | 2 | no | — |
| 10 | #13063323 | — | 2 | 1 | no | — |
| 11 | #13063323 | C22 | 1 | 2 | yes | — |
| 12 | C4×Dic86 | — | 2 | 1 | no | — |
| 13 | #13063290 | — | 2 | 2 | no | — |
| 14 | #13063253 | — | 2 | 1 | no | — |
| 15 | #13063251 | — | 2 | 2 | no | — |
| 16 | #13063244 | C22 | 1 | 1 | yes | characteristic |
| 17 | C4⋊Q8×C43 | C22 | 1 | 1 | yes | characteristic |
| 18 | #101×C43 | C22 | 1 | 2 | yes | — |
| 19 | C2×Q8×C43 | D4 | 1 | 1 | yes | characteristic |
| 20 | C2×Q8×C43 | C23 | 1 | 1 | yes | characteristic |
| 21 | #10621902 | — | 4 | 1 | no | — |
| 22 | Q8×D43 | — | 4 | 1 | no | — |
| 23 | #10621898 | — | 2 | 2 | no | — |
| 24 | #10621898 | — | 2 | 1 | no | — |
| 25 | C2×Dic86 | — | 2 | 1 | no | — |
| 26 | C2×Dic86 | — | 2 | 1 | no | — |
| 27 | C2×Dic86 | D4 | 1 | 2 | yes | — |
| 28 | M16×C43 | — | 2 | 2 | no | — |
| 29 | C4⋊C4×C43 | — | 2 | 2 | no | — |
| 30 | C42×C43 | D4 | 1 | 1 | yes | characteristic |
| 31 | #10621885 | — | 4 | 1 | no | — |
| 32 | #10621884 | — | 4 | 1 | no | — |
| 33 | C4⋊Dic43 | — | 2 | 1 | no | — |
| 34 | Dic43⋊C4 | — | 2 | 2 | no | — |
| 35 | Dic43⋊C4 | — | 2 | 2 | no | — |
| 36 | Dic43⋊C4 | — | 2 | 2 | no | — |
| 37 | C4×Dic43 | — | 2 | 1 | no | — |
| 38 | C4×Dic43 | — | 2 | 2 | no | — |
| 39 | C4×Dic43 | D4 | 1 | 2 | yes | — |
| 40 | #10621877 | — | 2 | 1 | no | — |
| 41 | Dic172 | — | 4 | 2 | no | — |
| 42 | #10621873 | — | 4 | 2 | no | — |
| 43 | Q8×C43 | — | 4 | 1 | no | — |
| 44 | Q8×C43 | — | 4 | 1 | no | — |
| 45 | C2×C4×C43 | — | 2 | 1 | no | — |
| 46 | C2×C4×C43 | — | 2 | 1 | no | — |
| 47 | C2×C4×C43 | C2×D4 | 1 | 1 | yes | characteristic |
| 48 | C2×C4×C43 | C2×D4 | 1 | 2 | yes | — |
| 49 | C22⋊D43 | — | 4 | 1 | no | — |
| 50 | C2×Dic43 | — | 2 | 2 | no | — |
| 51 | C2×Dic43 | — | 2 | 2 | no | — |
| 52 | D172 | — | 2 | 2 | no | — |
| 53 | D172 | — | 2 | 1 | no | — |
| 54 | C4×D43 | — | 4 | 1 | no | — |
| 55 | C4×D43 | — | 4 | 2 | no | — |
| 56 | Dic86 | — | 2 | 4 | no | — |
| 57 | Dic86 | — | 2 | 2 | no | — |
| 58 | Dic86 | — | 2 | 1 | no | — |
| 59 | Dic86 | — | 4 | 2 | no | — |
| 60 | Dic86 | — | 8 | 1 | no | — |
| 61 | C8×C43 | — | 4 | 2 | no | — |
| 62 | C43⋊C8 | — | 4 | 1 | no | — |
| 63 | C22×C43 | #120 | 1 | 1 | yes | characteristic |
| 64 | C2×D43 | — | 4 | 1 | no | — |
| 65 | C4×C43 | — | 2 | 2 | no | — |
| 66 | C4×C43 | — | 2 | 1 | no | — |
| 67 | C4×C43 | — | 2 | 2 | no | — |
| 68 | C4×C43 | — | 4 | 1 | no | — |
| 69 | Dic43 | — | 2 | 4 | no | — |
| 70 | Dic43 | — | 4 | 1 | no | — |
| 71 | Dic43 | — | 4 | 2 | no | — |
| 72 | #2205 | — | 43 | 1 | no | maximal, Sylow |
| 73 | C2×C43 | — | 2 | 1 | no | — |
| 74 | C2×C43 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 75 | D43 | — | 8 | 1 | no | — |
| 76 | Q82 | — | 43 | 1 | no | — |
| 77 | #456 | — | 43 | 1 | no | — |
| 78 | #456 | — | 43 | 2 | no | — |
| 79 | #356 | — | 43 | 2 | no | — |
| 80 | #356 | D43 | 1 | 1 | yes | characteristic, complemented |
| 81 | C43 | #2205 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 82 | 2−1+4 | — | 43 | 1 | no | — |
| 83 | #137 | — | 86 | 2 | no | — |
| 84 | #137 | — | 86 | 1 | no | — |
| 85 | C4⋊Q8 | — | 43 | 2 | no | — |
| 86 | C4⋊Q8 | — | 86 | 2 | no | — |
| 87 | C4⋊Q8 | — | 86 | 1 | no | — |
| 88 | C4⋊Q8 | C2×D43 | 1 | 1 | yes | characteristic |
| 89 | C4×Q8 | — | 86 | 2 | no | — |
| 90 | C4×Q8 | — | 86 | 1 | no | — |
| 91 | #104 | — | 86 | 2 | no | — |
| 92 | #104 | — | 86 | 1 | no | — |
| 93 | #101 | — | 43 | 1 | no | — |
| 94 | #101 | C2×D43 | 1 | 2 | yes | — |
| 95 | #41 | — | 86 | 1 | no | — |
| 96 | #41 | — | 86 | 2 | no | — |
| 97 | #41 | — | 172 | 1 | no | — |
| 98 | C2×Q8 | — | 43 | 2 | no | — |
| 99 | C2×Q8 | — | 86 | 1 | no | — |
| 100 | C2×Q8 | — | 86 | 1 | no | — |
| 101 | C2×Q8 | — | 172 | 1 | no | — |
| 102 | C2×Q8 | D172 | 1 | 1 | yes | characteristic |
| 103 | C2×Q8 | C22×D43 | 1 | 1 | yes | characteristic |
| 104 | Q16 | — | 172 | 2 | no | — |
| 105 | Q16 | — | 172 | 1 | no | — |
| 106 | SD16 | — | 172 | 2 | no | — |
| 107 | SD16 | — | 172 | 1 | no | — |
| 108 | M16 | — | 2 | 2 | no | — |
| 109 | M16 | — | 86 | 1 | no | — |
| 110 | C4⋊C4 | — | 2 | 2 | no | — |
| 111 | C4⋊C4 | — | 86 | 2 | no | — |
| 112 | C4⋊C4 | — | 86 | 1 | no | — |
| 113 | C4⋊C4 | — | 86 | 2 | no | — |
| 114 | C4⋊C4 | — | 86 | 2 | no | — |
| 115 | C42 | — | 43 | 2 | no | — |
| 116 | C42 | — | 86 | 2 | no | — |
| 117 | C42 | — | 86 | 1 | no | — |
| 118 | C42 | D172 | 1 | 1 | yes | characteristic |
| 119 | Q8 | — | 4 | 1 | no | — |
| 120 | Q8 | — | 4 | 1 | no | — |
| 121 | Q8 | — | 86 | 4 | no | — |
| 122 | Q8 | — | 86 | 2 | no | — |
| 123 | Q8 | — | 86 | 1 | no | — |
| 124 | Q8 | — | 344 | 1 | no | — |
| 125 | Q8 | — | 172 | 2 | no | — |
| 126 | D4 | — | 86 | 2 | no | — |
| 127 | D4 | — | 86 | 1 | no | — |
| 128 | D4 | — | 172 | 1 | no | — |
| 129 | C2×C4 | — | 2 | 1 | no | — |
| 130 | C2×C4 | — | 2 | 1 | no | — |
| 131 | C2×C4 | — | 86 | 2 | no | — |
| 132 | C2×C4 | — | 86 | 2 | no | — |
| 133 | C2×C4 | — | 172 | 2 | no | — |
| 134 | C2×C4 | — | 172 | 1 | no | — |
| 135 | C2×C4 | C2×D172 | 1 | 1 | yes | characteristic |
| 136 | C2×C4 | D4×D43 | 1 | 2 | yes | — |
| 137 | C8 | — | 4 | 2 | no | — |
| 138 | C8 | — | 172 | 1 | no | — |
| 139 | C22 | — | 172 | 1 | no | — |
| 140 | C22 | #13063295 | 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 | — | 86 | 4 | no | — |
| 146 | C4 | — | 172 | 2 | no | — |
| 147 | C4 | — | 172 | 1 | no | — |
| 148 | C2 | — | 2 | 1 | no | — |
| 149 | C2 | — | 344 | 1 | no | — |
| 150 | C2 | #14583087 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583629 | C2 | semidirect |
| 4. #14582697 | C2 | semidirect |
| 5. C43×#356 | C2 | semidirect |
| 80. #356 | D43 | semidirect |
| 81. C43 | #2205 | semidirect |