Subgroups — D₃×D₁₅₆₃ #34037270

Order 18756.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₁₅₆₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₅₆₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃×C₅₂₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₅₆₃	—	3	1	no	maximal
5	D₃×D₅₂₁	—	3	1	no	maximal
6	C₃²×C₅₂₁	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₅₂₁	—	3	1	no	—
8	D₁₅₆₃	—	3	1	no	—
9	D₁₅₆₃	—	3	1	no	—
10	D₁₅₆₃	—	6	1	no	—
11	D₁₅₆₃	D₃	1	1	yes	characteristic, direct product factor
12	C₃×D₅₂₁	—	3	1	no	—
13	D₃×C₅₂₁	D₃	1	1	yes	characteristic, complemented
14	C₂×D₅₂₁	—	9	1	no	Hall
15	C₃×C₅₂₁	—	2	1	no	—
16	C₃×C₅₂₁	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₅₂₁	C₂×D₃	1	1	yes	characteristic, complemented
18	C₂×C₅₂₁	—	3	1	no	—
19	D₅₂₁	—	3	1	no	—
20	D₅₂₁	—	9	1	no	—
21	C₅₂₁	D₃²	1	1	yes	characteristic, complemented, Sylow
22	D₃²	—	521	1	no	maximal, Hall
23	C₃⋊D₃	—	521	1	no	—
24	C₃×D₃	—	521	1	no	—
25	C₃×D₃	D₅₂₁	1	1	yes	characteristic, complemented
26	C₂×D₃	—	1563	1	no	—
27	C₂×D₃	—	1563	1	no	—
28	C₃²	C₂×D₅₂₁	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	3	1	no	—
30	C₂×C₃	—	1563	1	no	—
31	D₃	—	521	1	no	—
32	D₃	—	1563	1	no	—
33	D₃	—	1563	1	no	—
34	D₃	—	3126	1	no	—
35	D₃	D₁₅₆₃	1	1	yes	characteristic, direct product factor
36	C₂²	—	4689	1	no	Sylow
37	C₃	—	2	1	no	—
38	C₃	D₃×D₅₂₁	1	1	yes	characteristic, complemented
39	C₃	C₂×D₁₅₆₃	1	1	yes	characteristic, complemented
40	C₂	—	3	1	no	—
41	C₂	—	1563	1	no	—
42	C₂	—	4689	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₅₂₁	C₂²
LCS	G ▷ C₃²×C₅₂₁
UCS	C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃⋊D₁₅₆₃	C₂	semidirect
2. C₃×D₁₅₆₃	C₂	semidirect
3. C₃×D₃×C₅₂₁	C₂	semidirect
6. C₃²×C₅₂₁	C₂²	semidirect
11. D₁₅₆₃	D₃	direct (N × H)
13. D₃×C₅₂₁	D₃	semidirect
16. C₃×C₅₂₁	C₂×D₃	semidirect
17. C₃×C₅₂₁	C₂×D₃	semidirect
21. C₅₂₁	D₃²	semidirect
25. C₃×D₃	D₅₂₁	semidirect
28. C₃²	C₂×D₅₂₁	semidirect
35. D₃	D₁₅₆₃	direct (N × H)
38. C₃	D₃×D₅₂₁	semidirect
39. C₃	C₂×D₁₅₆₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃⋊D₁₅₆₃	2
C₃×D₁₅₆₃	2
C₃×D₃×C₅₂₁	2
C₂×D₁₅₆₃	3
D₃×D₅₂₁	3
D₃²	521

Subgroups — D3×D1563 #34037270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₁₅₆₃ #34037270