Subgroups — C₃×D₂₁×C₁₇₃ #36345477

Order 21798.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₁×C₁₇₃	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×D₇×C₁₇₃	—	3	1	no	maximal
4	C₃×C₇×C₁₇₃	—	2	1	no	—
5	C₃×C₇×C₁₇₃	D₃	1	1	yes	characteristic, complemented
6	C₃×C₇×C₁₇₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×D₃×C₁₇₃	—	7	1	no	maximal, Hall
8	D₇×C₁₇₃	—	3	1	no	Hall
9	C₃²×C₁₇₃	D₇	1	1	yes	characteristic, complemented, Hall
10	C₇×C₁₇₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₁₇₃	—	21	1	no	—
12	D₃×C₁₇₃	—	7	1	no	—
13	C₃×C₁₇₃	—	2	1	no	—
14	C₃×C₁₇₃	C₃×D₇	1	1	yes	characteristic, complemented
15	C₃×C₁₇₃	D₂₁	1	1	yes	characteristic, direct product factor
16	C₂×C₁₇₃	—	21	1	no	Hall
17	C₁₇₃	C₃×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×D₂₁	C₁₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₃²×C₇	C₂×C₁₇₃	1	1	yes	characteristic, complemented, Hall
20	D₂₁	C₃×C₁₇₃	1	1	yes	characteristic, direct product factor
21	C₃×D₇	—	3	1	no	—
22	C₃×C₇	—	2	1	no	—
23	C₃×C₇	D₃×C₁₇₃	1	1	yes	characteristic, complemented
24	C₃×C₇	C₂×C₃×C₁₇₃	1	1	yes	characteristic, complemented
25	C₃×D₃	—	7	1	no	Hall
26	D₇	—	3	1	no	Hall
27	C₃²	D₇×C₁₇₃	1	1	yes	characteristic, complemented, Sylow
28	C₇	C₃×D₃×C₁₇₃	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	21	1	no	—
30	D₃	—	7	1	no	—
31	C₃	—	2	1	no	—
32	C₃	C₃×D₇×C₁₇₃	1	1	yes	characteristic, complemented
33	C₃	D₂₁×C₁₇₃	1	1	yes	characteristic, direct product factor
34	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₇₃	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂×C₃×C₁₇₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₇₃	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₃×C₁₇₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₇₃	C₂	semidirect
2. D₂₁×C₁₇₃	C₃	direct (N × H)
5. C₃×C₇×C₁₇₃	D₃	semidirect
6. C₃×C₇×C₁₇₃	C₂×C₃	semidirect
9. C₃²×C₁₇₃	D₇	semidirect
10. C₇×C₁₇₃	C₃×D₃	semidirect
14. C₃×C₁₇₃	C₃×D₇	semidirect
15. C₃×C₁₇₃	D₂₁	direct (N × H)
17. C₁₇₃	C₃×D₂₁	direct (N × H)
18. C₃×D₂₁	C₁₇₃	direct (N × H)
19. C₃²×C₇	C₂×C₁₇₃	semidirect
20. D₂₁	C₃×C₁₇₃	direct (N × H)
23. C₃×C₇	D₃×C₁₇₃	semidirect
24. C₃×C₇	C₂×C₃×C₁₇₃	semidirect
27. C₃²	D₇×C₁₇₃	semidirect
28. C₇	C₃×D₃×C₁₇₃	semidirect
32. C₃	C₃×D₇×C₁₇₃	semidirect
33. C₃	D₂₁×C₁₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₇×C₁₇₃	2
D₂₁×C₁₇₃	3
C₃×D₇×C₁₇₃	3
C₃×D₃×C₁₇₃	7
C₃×D₂₁	173

Subgroups — C3×D21×C173 #36345477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₂₁×C₁₇₃ #36345477