Subgroups — D₃×D₈₅₉⋊C₃ #44525697

Order 30924.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₈₅₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊(D₈₅₉⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₈₅₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₈₅₉	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×D₈₅₉⋊C₃	—	3	1	no	maximal
6	C₃×C₈₅₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₂₅₇₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×D₈₅₉	C₂×C₃	1	1	yes	characteristic, complemented
9	D₃×C₈₅₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₈₅₉⋊C₃	—	3	1	no	—
11	D₈₅₉⋊C₃	—	2	1	no	—
12	D₈₅₉⋊C₃	—	3	1	no	—
13	D₈₅₉⋊C₃	D₃	1	1	yes	characteristic, direct product factor
14	C₂×D₈₅₉	—	3	1	no	Hall
15	C₃×C₈₅₉	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₈₅₉⋊C₃	—	2	1	no	—
17	C₈₅₉⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
18	C₂×C₈₅₉	—	3	1	no	—
19	D₈₅₉	—	3	1	no	—
20	D₈₅₉	C₃×D₃	1	1	yes	characteristic, complemented
21	C₈₅₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃×D₃	—	859	1	no	maximal, Hall
23	C₂×C₃²	—	859	1	no	—
24	C₃×D₃	—	859	1	no	—
25	C₃×D₃	—	859	1	no	—
26	C₂²×C₃	—	2577	1	no	—
27	C₂×D₃	—	859	1	no	—
28	C₃²	—	859	1	no	Sylow
29	C₂×C₃	—	2577	1	no	—
30	C₂×C₃	—	2577	1	no	—
31	C₂×C₃	—	859	1	no	—
32	C₂×C₃	—	859	1	no	—
33	C₂×C₃	—	1718	1	no	—
34	D₃	—	859	1	no	—
35	D₃	D₈₅₉⋊C₃	1	1	yes	characteristic, direct product factor
36	C₂²	—	2577	1	no	Sylow
37	C₃	—	859	1	no	—
38	C₃	—	1718	1	no	—
39	C₃	C₂×D₈₅₉⋊C₃	1	1	yes	characteristic, complemented
40	C₂	—	3	1	no	—
41	C₂	—	2577	1	no	—
42	C₂	—	859	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₈₅₉	C₂²×C₃
LCS	G ▷ C₃×C₈₅₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₃×C₈₅₉⋊C₃	C₂	semidirect
2. C₃⋊(D₈₅₉⋊C₃)	C₂	semidirect
3. C₃×D₈₅₉⋊C₃	C₂	semidirect
4. D₃×D₈₅₉	C₃	semidirect
6. C₃×C₈₅₉⋊C₃	C₂²	semidirect
7. D₂₅₇₇	C₂×C₃	semidirect
8. C₃×D₈₅₉	C₂×C₃	semidirect
9. D₃×C₈₅₉	C₂×C₃	semidirect
13. D₈₅₉⋊C₃	D₃	direct (N × H)
15. C₃×C₈₅₉	C₂²×C₃	semidirect
17. C₈₅₉⋊C₃	C₂×D₃	semidirect
20. D₈₅₉	C₃×D₃	semidirect
21. C₈₅₉	C₂×C₃×D₃	semidirect
35. D₃	D₈₅₉⋊C₃	direct (N × H)
39. C₃	C₂×D₈₅₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
D₃×C₈₅₉⋊C₃	2
C₃⋊(D₈₅₉⋊C₃)	2
C₃×D₈₅₉⋊C₃	2
D₃×D₈₅₉	3
C₂×D₈₅₉⋊C₃	3
C₂×C₃×D₃	859

Subgroups — D3×D859⋊C3 #44525697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₈₅₉⋊C₃ #44525697