Subgroups — C₄⋊#1084 #88541

Order 432.

143 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic
2	C₂×#1084	C₂	1	2	yes	maximal
3	C₃×C₄⋊Dic₃	—	3	4	no	maximal
4	C₂²×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
5	C₄×H(3,𝔽₃)	C₄	1	2	yes	complemented
6	#1084	—	2	2	no	—
7	C₂×C₃²×C₄	D₃	1	4	yes	—
8	C₂×C₃×Dic₃	—	3	8	no	—
9	C₂×H(3,𝔽₃)	C₂×C₄	1	1	yes	characteristic
10	C₂×H(3,𝔽₃)	D₄	1	1	yes	characteristic
11	C₂×H(3,𝔽₃)	Q₈	1	1	yes	characteristic
12	C₃×C₄⋊C₄	—	9	1	no	—
13	C₄⋊Dic₃	—	3	4	no	—
14	C₂²×C₃²	C₂×D₃	1	4	yes	—
15	C₃²×C₄	Dic₃	1	8	yes	complemented
16	C₃×Dic₃	—	6	8	no	—
17	H(3,𝔽₃)	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃×C₄	—	3	4	no	—
19	C₂×C₃×C₄	—	9	2	no	—
20	C₂×C₃×C₄	C₃⋊D₃	1	1	yes	characteristic
21	C₂×Dic₃	—	3	8	no	—
22	C₂×C₃²	Dic₆	1	4	yes	—
23	C₂×C₃²	D₁₂	1	4	yes	—
24	C₂×C₃²	C₂×Dic₃	1	4	yes	—
25	C₄⋊C₄	—	9	1	no	Sylow
26	C₂²×C₃	—	3	4	no	—
27	C₂²×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
28	C₃×C₄	—	3	8	no	—
29	C₃×C₄	—	18	2	no	—
30	C₃×C₄	C₃⋊Dic₃	1	2	yes	—
31	Dic₃	—	6	8	no	—
32	C₃²	C₄⋊Dic₃	1	4	yes	complemented
33	C₂×C₄	—	9	2	no	—
34	C₂×C₄	#272	1	1	yes	characteristic
35	C₂×C₃	—	3	4	no	—
36	C₂×C₃	—	3	4	no	—
37	C₂×C₃	—	3	4	no	—
38	C₂×C₃	#634	1	1	yes	characteristic
39	C₂×C₃	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
40	C₂×C₃	C₂×C₃⋊Dic₃	1	1	yes	characteristic
41	C₂²	C₂×#272	1	1	yes	characteristic
42	C₄	—	18	2	no	—
43	C₄	#1084	1	2	yes	complemented
44	C₃	—	3	4	no	—
45	C₃	C₄⋊(C₃⋊Dic₃)	1	1	yes	characteristic
46	C₂	#6229	1	1	yes	characteristic
47	C₂	C₄⋊#272	1	1	yes	characteristic
48	C₂	C₂×#1084	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
5. C₄×H(3,𝔽₃)	C₄	semidirect
15. C₃²×C₄	Dic₃	semidirect
17. H(3,𝔽₃)	C₄⋊C₄	semidirect
32. C₃²	C₄⋊Dic₃	semidirect
43. C₄	#1084	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×H(3,𝔽₃)	2
C₂×#1084	2
C₃×C₄⋊Dic₃	3

Subgroups — C4⋊#1084 #88541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊#1084 #88541