Subgroups — C₃×#3774 #88929

Order 432.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#625	C₂	1	2	yes	maximal, complemented
2	C₃×#622	C₂	1	1	yes	maximal, characteristic, complemented
3	#3774	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃²×D₃	—	2	2	no	—
5	C₃×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
6	C₃×#67	—	6	2	no	—
7	#625	C₂×C₃	1	2	yes	complemented
8	#622	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×C₃³	D₄	1	1	yes	characteristic
10	C₃²×D₃	—	4	2	no	—
11	C₃×D₈	—	9	1	no	maximal
12	C₂²×C₃²	—	6	2	no	—
13	C₂×C₃×D₃	—	2	2	no	—
14	C₂×C₃×D₃	—	2	2	no	—
15	C₂×C₃×D₃	—	4	2	no	—
16	C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
17	C₃×Dic₃	—	6	2	no	—
18	C₃³	D₈	1	1	yes	characteristic, complemented, Sylow
19	C₃×D₄	—	9	2	no	—
20	#67	—	6	2	no	—
21	C₃×C₈	—	9	1	no	—
22	C₂×C₃²	—	2	2	no	—
23	C₂×C₃²	—	4	2	no	—
24	C₂×C₃²	—	12	2	no	—
25	C₂×C₃²	C₃×D₄	1	1	yes	characteristic
26	C₃×D₃	—	4	2	no	—
27	C₃×D₃	—	4	4	no	—
28	C₃×D₃	—	4	2	no	—
29	D₈	—	9	1	no	Sylow
30	C₂²×C₃	—	6	2	no	—
31	C₂²×C₃	—	6	2	no	—
32	C₂²×C₃	—	12	2	no	—
33	C₂×D₃	—	2	2	no	—
34	C₃×C₄	—	9	1	no	—
35	Dic₃	—	6	2	no	—
36	C₃²	—	2	2	no	—
37	C₃²	—	4	2	no	—
38	C₃²	C₃×D₈	1	1	yes	characteristic, complemented
39	D₄	—	9	2	no	—
40	C₈	—	9	1	no	—
41	C₂×C₃	—	2	2	no	—
42	C₂×C₃	—	4	2	no	—
43	C₂×C₃	—	12	2	no	—
44	C₂×C₃	—	12	4	no	—
45	C₂×C₃	—	12	2	no	—
46	C₂×C₃	GO⁺(4,𝔽₂)	1	1	yes	characteristic
47	D₃	—	4	2	no	—
48	C₂²	—	6	2	no	—
49	C₄	—	9	1	no	—
50	C₃	—	2	2	no	—
51	C₃	—	4	2	no	—
52	C₃	#3774	1	1	yes	characteristic, direct product factor
53	C₂	—	12	2	no	—
54	C₂	C₃×GO⁺(4,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	GO⁺(4,𝔽₂)
commutator, cosocle	C₃⋊Dic₃	C₂²×C₃
Frattini	C₂	C₃×GO⁺(4,𝔽₂)
Fitting, socle	C₂×C₃³	D₄
hypocenter	C₃²	C₃×D₈
LCS	G ▷ C₃⋊Dic₃ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×#625	C₂	semidirect
2. C₃×#622	C₂	semidirect
3. #3774	C₃	direct (N × H)
7. #625	C₂×C₃	semidirect
8. #622	C₂×C₃	semidirect
18. C₃³	D₈	semidirect
38. C₃²	C₃×D₈	semidirect
52. C₃	#3774	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#625	2
C₃×#622	2
#3774	3
C₃×D₈	9

Subgroups — C3×#3774 #88929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3774 #88929