Subgroups — C₉×#41⋊C₃ #88682

Order 432.

65 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#41⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₉×#41	C₃	1	1	yes	maximal, characteristic, complemented
4	#41⋊C₉	C₃	1	2	yes	maximal, complemented
5	C₃×C₄×C₉	—	4	1	no	maximal
6	C₃×SL(2,𝔽₃)	C₂×C₃	1	1	yes	characteristic
7	Q₈×C₉	C₂×C₃	1	1	yes	characteristic
8	D₄×C₉	—	3	1	no	—
9	C₂×C₄×C₉	—	3	1	no	—
10	Q₈⋊C₉	C₂×C₃	1	2	yes	—
11	C₂×C₃×C₉	—	4	1	no	—
12	C₃×#41	C₃²	1	1	yes	characteristic
13	#41⋊C₃	C₉	1	3	yes	direct product factor
14	C₃²×C₄	—	4	1	no	—
15	C₂²×C₉	—	3	1	no	—
16	C₄×C₉	—	3	1	no	—
17	C₄×C₉	—	4	2	no	—
18	C₄×C₉	A₄	1	1	yes	characteristic
19	C₃×C₉	—	4	1	no	Sylow
20	C₃×Q₈	C₂×C₃²	1	1	yes	characteristic
21	C₃×D₄	—	3	1	no	—
22	C₂×C₃×C₄	—	3	1	no	—
23	SL(2,𝔽₃)	C₂×C₉	1	3	yes	complemented
24	C₂×C₃²	—	4	1	no	—
25	C₂×C₉	—	4	2	no	—
26	C₂×C₉	—	6	1	no	—
27	C₂×C₉	C₂×A₄	1	1	yes	characteristic
28	#41	C₃×C₉	1	1	yes	characteristic, complemented, Sylow
29	C₂²×C₃	—	3	1	no	—
30	C₃×C₄	—	3	1	no	—
31	C₃×C₄	—	4	3	no	—
32	C₃×C₄	C₃×A₄	1	1	yes	characteristic
33	C₃²	—	4	1	no	—
34	C₉	—	4	2	no	—
35	C₉	#41⋊C₃	1	1	yes	characteristic, direct product factor
36	Q₈	C₂×C₃×C₉	1	1	yes	characteristic
37	D₄	—	3	1	no	—
38	C₂×C₄	—	3	1	no	—
39	C₂×C₃	—	4	3	no	—
40	C₂×C₃	—	6	1	no	—
41	C₂×C₃	C₂×C₃×A₄	1	1	yes	characteristic
42	C₂²	—	3	1	no	—
43	C₄	—	3	1	no	—
44	C₄	C₉×A₄	1	1	yes	characteristic
45	C₃	—	4	3	no	—
46	C₃	C₃×#41⋊C₃	1	1	yes	characteristic
47	C₂	—	6	1	no	—
48	C₂	C₂×C₉×A₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₉	A₄
commutator, hypocenter	Q₈	C₂×C₃×C₉
Frattini, socle	C₂×C₃	C₂×C₃×A₄
Fitting	C₉×#41	C₃
prime radical	C₃×#41⋊C₃	C₃
cosocle	C₃×Q₈	C₂×C₃²
LCS	G ▷ Q₈
UCS	C₁ ◁ C₄×C₉

Complements

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

N	H ≅ G/N	type
1. C₉×SL(2,𝔽₃)	C₂	semidirect
3. C₉×#41	C₃	semidirect
4. #41⋊C₉	C₃	semidirect
13. #41⋊C₃	C₉	direct (N × H)
23. SL(2,𝔽₃)	C₂×C₉	semidirect
28. #41	C₃×C₉	semidirect
35. C₉	#41⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×SL(2,𝔽₃)	2
C₃×#41⋊C₃	3
C₉×#41	3
#41⋊C₉	3
C₃×C₄×C₉	4

Subgroups — C9×#41⋊C3 #88682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#41⋊C₃ #88682