Subgroups — C₃×C₃⋊(#41⋊C₃) #88975

Order 432.

105 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#239	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×#41⋊C₃	—	3	1	no	maximal
4	C₃⋊(#41⋊C₃)	C₃	1	3	yes	maximal, direct product factor
5	C₃²×Dic₃	—	4	1	no	maximal
6	C₃²×Q₈	C₂×C₃	1	1	yes	characteristic
7	C₃×D₁₂	—	3	1	no	—
8	C₃×C₄×D₃	—	3	1	no	—
9	C₃×SL(2,𝔽₃)	—	2	1	no	—
10	C₃×SL(2,𝔽₃)	—	2	3	no	—
11	C₃×SL(2,𝔽₃)	D₃	1	1	yes	characteristic, complemented
12	C₃×SL(2,𝔽₃)	C₂×C₃	1	3	yes	complemented
13	C₂×C₃³	—	4	1	no	—
14	C₃×#41	—	3	1	no	—
15	#239	C₃²	1	1	yes	characteristic, complemented
16	#41⋊C₃	—	3	3	no	—
17	C₂×C₃×D₃	—	3	1	no	—
18	C₃²×C₄	—	3	1	no	—
19	C₃²×C₄	—	12	1	no	—
20	C₃×Dic₃	—	4	3	no	—
21	C₃×Dic₃	A₄	1	1	yes	characteristic
22	C₃³	—	4	1	no	Sylow
23	C₃×Q₈	—	2	1	no	—
24	C₃×Q₈	C₃×D₃	1	1	yes	characteristic
25	C₃×Q₈	C₂×C₃²	1	1	yes	characteristic
26	C₃×D₄	—	9	1	no	—
27	C₂×C₃×C₄	—	9	1	no	—
28	D₁₂	—	3	1	no	—
29	C₄×D₃	—	3	1	no	—
30	SL(2,𝔽₃)	—	2	3	no	—
31	SL(2,𝔽₃)	C₃×D₃	1	3	yes	complemented
32	C₂×C₃²	—	4	1	no	—
33	C₂×C₃²	—	4	3	no	—
34	C₂×C₃²	—	8	3	no	—
35	C₂×C₃²	—	8	1	no	—
36	C₂×C₃²	C₂×A₄	1	1	yes	characteristic
37	C₃×D₃	—	6	1	no	—
38	#41	—	3	1	no	Sylow
39	C₂²×C₃	—	9	1	no	—
40	C₂×D₃	—	3	1	no	—
41	C₃×C₄	—	3	1	no	—
42	C₃×C₄	—	3	1	no	—
43	C₃×C₄	—	3	1	no	—
44	C₃×C₄	—	6	1	no	—
45	C₃×C₄	—	12	3	no	—
46	Dic₃	C₃×A₄	1	1	yes	characteristic
47	C₃²	—	4	1	no	—
48	C₃²	—	4	3	no	—
49	C₃²	—	8	3	no	—
50	C₃²	—	8	1	no	—
51	C₃²	#41⋊C₃	1	1	yes	characteristic, complemented
52	Q₈	C₃²×D₃	1	1	yes	characteristic
53	D₄	—	9	1	no	—
54	C₂×C₄	—	9	1	no	—
55	C₂×C₃	—	2	1	no	—
56	C₂×C₃	—	4	3	no	—
57	C₂×C₃	—	8	3	no	—
58	C₂×C₃	—	18	1	no	—
59	C₂×C₃	D₃×A₄	1	1	yes	characteristic
60	C₂×C₃	C₂×C₃×A₄	1	1	yes	characteristic
61	D₃	—	6	1	no	—
62	C₂²	—	9	1	no	—
63	C₄	—	3	1	no	—
64	C₄	—	3	1	no	—
65	C₃	—	2	1	no	—
66	C₃	—	4	3	no	—
67	C₃	—	8	3	no	—
68	C₃	C₃⋊(#41⋊C₃)	1	1	yes	characteristic, direct product factor
69	C₃	C₃×#41⋊C₃	1	1	yes	characteristic, complemented
70	C₂	—	18	1	no	—
71	C₂	C₃×D₃×A₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	D₃×A₄
commutator, cosocle, hypocenter	C₃×Q₈	C₂×C₃²
Frattini	C₂	C₃×D₃×A₄
Fitting	C₃²×Q₈	C₂×C₃
socle	C₂×C₃²	C₂×A₄
LCS	G ▷ C₃×Q₈
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×SL(2,𝔽₃)	C₂	semidirect
2. C₃×#239	C₃	semidirect
4. C₃⋊(#41⋊C₃)	C₃	direct (N × H)
11. C₃×SL(2,𝔽₃)	D₃	semidirect
12. C₃×SL(2,𝔽₃)	C₂×C₃	semidirect
15. #239	C₃²	semidirect
31. SL(2,𝔽₃)	C₃×D₃	semidirect
51. C₃²	#41⋊C₃	semidirect
68. C₃	C₃⋊(#41⋊C₃)	direct (N × H)
69. C₃	C₃×#41⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃²×SL(2,𝔽₃)	2
C₃×#239	3
C₃×#41⋊C₃	3
C₃⋊(#41⋊C₃)	3
C₃²×Dic₃	4

Subgroups — C3×C3⋊(#41⋊C3) #88975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃⋊(#41⋊C₃) #88975