Subgroups — C₃²×C₁₇×Dic₄₁ #38737101

Order 25092.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₇×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₇×Dic₄₁	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₁₇×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₇×C₄₁	C₂×C₃	1	4	yes	—
5	C₁₇×Dic₄₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₇×C₄₁	C₃×C₄	1	4	yes	complemented
7	C₃²×Dic₄₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₁₇×C₄₁	C₂×C₃²	1	1	yes	characteristic
9	C₂×C₃²×C₄₁	C₂×C₁₇	1	1	yes	characteristic
10	C₁₇×C₄₁	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
11	C₃²×C₄×C₁₇	—	41	1	no	maximal, Hall
12	C₃×Dic₄₁	C₃×C₁₇	1	4	yes	direct product factor
13	C₃²×C₄₁	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃²×C₁₇	D₄₁	1	1	yes	characteristic
15	C₂×C₃×C₄₁	C₂×C₃×C₁₇	1	4	yes	—
16	C₃×C₄×C₁₇	—	41	4	no	—
17	Dic₄₁	C₃²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
18	C₃²×C₁₇	Dic₄₁	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₄₁	C₃×C₄×C₁₇	1	4	yes	complemented
20	C₂×C₃×C₁₇	C₃×D₄₁	1	4	yes	—
21	C₂×C₄₁	C₂×C₃²×C₁₇	1	1	yes	characteristic
22	C₄×C₁₇	—	41	1	no	Hall
23	C₃×C₁₇	C₃×Dic₄₁	1	4	yes	direct product factor
24	C₄₁	C₃²×C₄×C₁₇	1	1	yes	characteristic, complemented, Sylow
25	C₃²×C₄	—	41	1	no	Hall
26	C₂×C₁₇	C₃²×D₄₁	1	1	yes	characteristic
27	C₂×C₃²	C₁₇×D₄₁	1	1	yes	characteristic
28	C₁₇	C₃²×Dic₄₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₃×C₄	—	41	4	no	—
30	C₃²	C₁₇×Dic₄₁	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₃×C₁₇×D₄₁	1	4	yes	—
32	C₄	—	41	1	no	Sylow
33	C₃	C₃×C₁₇×Dic₄₁	1	4	yes	direct product factor
34	C₂	C₃²×C₁₇×D₄₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₁₇	D₄₁
commutator, hypocenter	C₄₁	C₃²×C₄×C₁₇
Frattini	C₂	C₃²×C₁₇×D₄₁
Fitting, socle, prime radical	C₂×C₃²×C₁₇×C₄₁	C₂
cosocle	C₂×C₄₁	C₂×C₃²×C₁₇
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₂×C₃²×C₁₇

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₇×Dic₄₁	C₃	direct (N × H)
3. C₃²×C₁₇×C₄₁	C₄	semidirect
5. C₁₇×Dic₄₁	C₃²	direct (N × H)
6. C₃×C₁₇×C₄₁	C₃×C₄	semidirect
7. C₃²×Dic₄₁	C₁₇	direct (N × H)
10. C₁₇×C₄₁	C₃²×C₄	semidirect
12. C₃×Dic₄₁	C₃×C₁₇	direct (N × H)
13. C₃²×C₄₁	C₄×C₁₇	semidirect
17. Dic₄₁	C₃²×C₁₇	direct (N × H)
18. C₃²×C₁₇	Dic₄₁	direct (N × H)
19. C₃×C₄₁	C₃×C₄×C₁₇	semidirect
23. C₃×C₁₇	C₃×Dic₄₁	direct (N × H)
24. C₄₁	C₃²×C₄×C₁₇	semidirect
28. C₁₇	C₃²×Dic₄₁	direct (N × H)
30. C₃²	C₁₇×Dic₄₁	direct (N × H)
33. C₃	C₃×C₁₇×Dic₄₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₁₇×C₄₁	2
C₃×C₁₇×Dic₄₁	3
C₃²×Dic₄₁	17
C₃²×C₄×C₁₇	41

Subgroups — C32×C17×Dic41 #38737101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₁₇×Dic₄₁ #38737101