Subgroups — C₄⋊#1088 #88629

Order 432.

71 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	—	2	2	no	—
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	D₄	1	1	yes	characteristic
11	#272	Q₈	1	1	yes	characteristic
12	C₃×C₄⋊C₄	—	9	1	no	maximal
13	C₂×C₃×D₃	—	6	1	no	—
14	C₂×C₃×D₃	—	6	1	no	—
15	C₃²×C₄	—	2	1	no	—
16	C₃²×C₄	—	2	1	no	—
17	C₃×Dic₃	—	6	1	no	—
18	C₃×Dic₃	—	6	1	no	—
19	H(3,𝔽₃)	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃×C₄	—	9	1	no	—
21	C₂×C₃×C₄	—	9	2	no	—
22	C₄×D₃	—	6	1	no	—
23	C₄×D₃	—	6	1	no	—
24	C₂×C₃²	—	2	1	no	—
25	C₂×C₃²	—	2	1	no	—
26	C₃×D₃	—	6	1	no	—
27	C₃×D₃	—	6	1	no	—
28	C₃×D₃	—	6	1	no	—
29	C₃×D₃	—	6	1	no	—
30	C₄⋊C₄	—	9	1	no	Sylow
31	C₂²×C₃	—	9	1	no	—
32	C₂×D₃	—	6	1	no	—
33	C₂×D₃	—	6	1	no	—
34	C₃×C₄	—	6	1	no	—
35	C₃×C₄	—	9	1	no	—
36	C₃×C₄	—	12	1	no	—
37	C₃×C₄	—	18	2	no	—
38	C₃×C₄	#157	1	1	yes	characteristic
39	Dic₃	—	6	1	no	—
40	Dic₃	—	6	1	no	—
41	C₃²	—	2	1	no	—
42	C₃²	—	2	1	no	—
43	C₂×C₄	—	9	1	no	—
44	C₂×C₄	—	9	2	no	—
45	C₂×C₃	—	6	1	no	—
46	C₂×C₃	—	9	1	no	—
47	C₂×C₃	—	9	1	no	—
48	C₂×C₃	—	12	1	no	—
49	C₂×C₃	C₂×#157	1	1	yes	characteristic
50	D₃	—	6	1	no	—
51	D₃	—	6	1	no	—
52	D₃	—	6	1	no	—
53	D₃	—	6	1	no	—
54	C₂²	—	9	1	no	—
55	C₄	—	9	1	no	—
56	C₄	—	18	2	no	—
57	C₄	#1088	1	1	yes	characteristic, complemented
58	C₃	—	6	1	no	—
59	C₃	—	12	1	no	—
60	C₃	C₄⋊#157	1	1	yes	characteristic
61	C₂	—	9	1	no	—
62	C₂	—	9	1	no	—
63	C₂	C₂×#1088	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, socle	C₂×C₃	C₂×#157
commutator	C₂×H(3,𝔽₃)	C₂×C₄
Fitting	C₄×H(3,𝔽₃)	C₄
prime radical, cosocle	C₂×#272	C₂²
hypercenter	C₃×C₄	#157
hypocenter	H(3,𝔽₃)	C₄⋊C₄
LCS	G ▷ C₂×H(3,𝔽₃) ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₃ ◁ 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
6. #1084	C₄	semidirect
19. H(3,𝔽₃)	C₄⋊C₄	semidirect
57. C₄	#1088	semidirect

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×C₄⋊C₄	9

Subgroups — C4⋊#1088 #88629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊#1088 #88629