Subgroups — #3746⋊C₃ #88467

Order 432.

71 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#634⋊C₃	C₂	1	2	yes	maximal
2	C₈×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic
3	#3746	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×Dic₁₂	—	3	1	no	maximal
5	C₄×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
6	(C₃⋊Dic₃)⋊C₃	—	2	2	no	—
7	#634	C₂×C₃	1	2	yes	—
8	C₃×Dic₆	—	3	2	no	—
9	C₃²×C₈	—	2	1	no	—
10	C₃²×C₈	D₃	1	1	yes	characteristic
11	C₃²×C₈	C₂×C₃	1	1	yes	characteristic
12	C₂×H(3,𝔽₃)	D₄	1	1	yes	characteristic
13	C₃×Q₁₆	—	9	1	no	—
14	Dic₁₂	—	3	1	no	—
15	Dic₁₂	—	9	1	no	—
16	C₃²×C₄	—	2	1	no	—
17	C₃²×C₄	C₂×D₃	1	1	yes	characteristic
18	C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
19	C₃⋊Dic₃	—	2	2	no	—
20	C₃×Dic₃	—	6	2	no	—
21	H(3,𝔽₃)	Q₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₃×Q₈	—	9	2	no	—
23	Dic₆	—	3	2	no	—
24	Dic₆	—	9	2	no	—
25	C₃×C₈	—	3	1	no	—
26	C₃×C₈	—	6	1	no	—
27	C₃×C₈	—	6	1	no	—
28	C₃×C₈	C₃×D₃	1	1	yes	characteristic
29	C₂×C₃²	—	2	1	no	—
30	C₂×C₃²	D₁₂	1	1	yes	characteristic
31	C₂×C₃²	C₃×D₄	1	1	yes	characteristic
32	Q₁₆	—	9	1	no	Sylow
33	C₃×C₄	—	3	1	no	—
34	C₃×C₄	—	6	1	no	—
35	C₃×C₄	—	6	1	no	—
36	C₃×C₄	—	18	2	no	—
37	C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
38	Dic₃	—	6	2	no	—
39	Dic₃	—	18	2	no	—
40	C₃²	—	2	1	no	—
41	C₃²	Dic₁₂	1	1	yes	characteristic, complemented
42	C₃²	C₃×Q₁₆	1	1	yes	characteristic, complemented
43	Q₈	—	9	2	no	—
44	C₈	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
45	C₂×C₃	—	3	1	no	—
46	C₂×C₃	—	6	1	no	—
47	C₂×C₃	—	6	1	no	—
48	C₂×C₃	C₃×D₁₂	1	1	yes	characteristic
49	C₄	—	18	2	no	—
50	C₄	C₂×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
51	C₃	—	3	1	no	—
52	C₃	—	6	1	no	—
53	C₃	—	6	1	no	—
54	C₃	C₃×Dic₁₂	1	1	yes	characteristic
55	C₂	C₄⋊((C₃⋊D₃)⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₄⋊((C₃⋊D₃)⋊C₃)
commutator, cosocle	C₃²×C₄	C₂²×C₃
Frattini	C₃×C₄	C₂×C₃×D₃
Fitting	C₈×H(3,𝔽₃)	C₂
socle	C₂×C₃	C₃×D₁₂
prime radical	C₂×H(3,𝔽₃)	D₄
hypercenter	C₈	(C₃⋊D₃)⋊C₃
hypocenter	C₃²	C₃×Q₁₆
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
3. #3746	C₃	semidirect
21. H(3,𝔽₃)	Q₁₆	semidirect
41. C₃²	Dic₁₂	semidirect
42. C₃²	C₃×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
#634⋊C₃	2
C₈×H(3,𝔽₃)	2
#3746	3
C₃×Dic₁₂	3

Subgroups — #3746⋊C3 #88467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3746⋊C₃ #88467