Subgroups — C₄×#1088 #88628

Order 432.

77 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#1088	C₂	1	2	yes	maximal
2	C₄×#272	C₂	1	1	yes	maximal, characteristic
3	C₂×#272	C₂²	1	1	yes	characteristic
4	#1088	C₄	1	4	yes	direct product factor
5	C₄×H(3,𝔽₃)	C₄	1	1	yes	characteristic, complemented
6	#1084	C₄	1	1	yes	characteristic, complemented
7	C₃×C₄×D₃	—	6	1	no	—
8	C₃×C₄×D₃	—	6	1	no	—
9	C₂×H(3,𝔽₃)	C₂×C₄	1	1	yes	characteristic
10	#272	C₂×C₄	1	2	yes	—
11	C₃×C₄²	—	9	1	no	maximal
12	C₂×C₃×D₃	—	6	1	no	—
13	C₂×C₃×D₃	—	6	1	no	—
14	C₃²×C₄	—	2	1	no	—
15	C₃²×C₄	—	2	1	no	—
16	C₃×Dic₃	—	6	1	no	—
17	C₃×Dic₃	—	6	1	no	—
18	H(3,𝔽₃)	C₄²	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃×C₄	—	9	2	no	—
20	C₂×C₃×C₄	—	9	1	no	—
21	C₄×D₃	—	6	1	no	—
22	C₄×D₃	—	6	1	no	—
23	C₂×C₃²	—	2	1	no	—
24	C₂×C₃²	—	2	1	no	—
25	C₃×D₃	—	6	2	no	—
26	C₃×D₃	—	6	2	no	—
27	C₄²	—	9	1	no	Sylow
28	C₂²×C₃	—	9	1	no	—
29	C₂×D₃	—	6	1	no	—
30	C₂×D₃	—	6	1	no	—
31	C₃×C₄	—	6	1	no	—
32	C₃×C₄	—	9	4	no	—
33	C₃×C₄	—	9	1	no	—
34	C₃×C₄	—	12	1	no	—
35	C₃×C₄	#157	1	1	yes	characteristic
36	Dic₃	—	6	1	no	—
37	Dic₃	—	6	1	no	—
38	C₃²	—	2	1	no	—
39	C₃²	—	2	1	no	—
40	C₂×C₄	—	9	2	no	—
41	C₂×C₄	—	9	1	no	—
42	C₂×C₃	—	6	1	no	—
43	C₂×C₃	—	9	2	no	—
44	C₂×C₃	—	12	1	no	—
45	C₂×C₃	C₂×#157	1	1	yes	characteristic
46	D₃	—	6	2	no	—
47	D₃	—	6	2	no	—
48	C₂²	—	9	1	no	—
49	C₄	—	9	4	no	—
50	C₄	—	9	1	no	—
51	C₄	#1088	1	1	yes	characteristic, direct product factor
52	C₃	—	6	1	no	—
53	C₃	—	12	1	no	—
54	C₃	C₄×#157	1	1	yes	characteristic
55	C₂	—	9	2	no	—
56	C₂	C₂×#1088	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄	#157
commutator, hypocenter	H(3,𝔽₃)	C₄²
Frattini, socle	C₂×C₃	C₂×#157
Fitting	C₄×H(3,𝔽₃)	C₄
prime radical, cosocle	C₂×#272	C₂²
LCS	G ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
4. #1088	C₄	direct (N × H)
5. C₄×H(3,𝔽₃)	C₄	semidirect
6. #1084	C₄	semidirect
18. H(3,𝔽₃)	C₄²	semidirect
51. C₄	#1088	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#1088	2
C₄×#272	2
C₃×C₄²	9

Subgroups — C4×#1088 #88628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#1088 #88628