Subgroups — C₄×#1094 #88685

Order 432.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#1094	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃²×C₄	C₃	1	1	yes	maximal, characteristic
3	C₄×C₂²⋊C₉	C₃	1	3	yes	maximal, complemented
4	#1094	C₄	1	1	yes	characteristic, direct product factor
5	C₄×3₋¹⁺²	—	4	1	no	maximal
6	C₂³×C₃²	C₂×C₃	1	1	yes	characteristic
7	C₂×C₃²×C₄	—	3	1	no	—
8	C₂×C₃²×C₄	—	3	1	no	—
9	C₂×C₂²⋊C₉	C₂×C₃	1	3	yes	—
10	C₂×3₋¹⁺²	—	4	1	no	—
11	C₂²×C₃×C₄	—	3	1	no	—
12	C₂²×C₃×C₄	C₃²	1	1	yes	characteristic
13	C₂²×C₃²	—	3	1	no	—
14	C₂²×C₃²	—	3	1	no	—
15	C₂²×C₃²	C₃×C₄	1	1	yes	characteristic
16	C₃²×C₄	—	3	1	no	—
17	C₃²×C₄	A₄	1	1	yes	characteristic
18	C₂²⋊C₉	C₃×C₄	1	3	yes	complemented
19	C₄×C₉	—	4	3	no	—
20	3₋¹⁺²	—	4	1	no	Sylow
21	C₂³×C₃	—	3	1	no	—
22	C₂³×C₃	C₂×C₃²	1	1	yes	characteristic
23	C₂×C₃×C₄	—	3	3	no	—
24	C₂×C₃×C₄	—	3	3	no	—
25	C₂×C₃×C₄	—	3	1	no	—
26	C₂×C₃×C₄	—	3	1	no	—
27	C₂×C₃²	—	3	1	no	—
28	C₂×C₃²	—	3	1	no	—
29	C₂×C₃²	C₂×A₄	1	1	yes	characteristic
30	C₂×C₉	—	4	3	no	—
31	C₂²×C₄	3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
32	C₂²×C₃	—	3	1	no	—
33	C₂²×C₃	—	3	3	no	—
34	C₂²×C₃	—	3	3	no	—
35	C₂²×C₃	—	3	1	no	—
36	C₂²×C₃	—	3	1	no	—
37	C₂²×C₃	C₃²×C₄	1	1	yes	characteristic
38	C₃×C₄	—	3	3	no	—
39	C₃×C₄	—	3	1	no	—
40	C₃×C₄	—	3	1	no	—
41	C₃×C₄	C₃×A₄	1	1	yes	characteristic
42	C₃²	C₄×A₄	1	1	yes	characteristic
43	C₉	—	4	3	no	—
44	C₂³	C₂×3₋¹⁺²	1	1	yes	characteristic
45	C₂×C₄	—	3	1	no	—
46	C₂×C₄	—	3	1	no	—
47	C₂×C₃	—	3	3	no	—
48	C₂×C₃	—	3	3	no	—
49	C₂×C₃	—	3	1	no	—
50	C₂×C₃	—	3	1	no	—
51	C₂×C₃	—	3	1	no	—
52	C₂×C₃	C₂×C₃×A₄	1	1	yes	characteristic
53	C₂²	—	3	1	no	—
54	C₂²	—	3	1	no	—
55	C₂²	C₄×3₋¹⁺²	1	1	yes	characteristic, complemented
56	C₄	—	3	1	no	—
57	C₄	#1094	1	1	yes	characteristic, direct product factor
58	C₃	—	3	1	no	—
59	C₃	C₃×C₄×A₄	1	1	yes	characteristic
60	C₂	—	3	1	no	—
61	C₂	—	3	1	no	—
62	C₂	C₂×#1094	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₃×A₄
commutator	C₂²×C₃	C₃²×C₄
Frattini	C₂×C₃	C₂×C₃×A₄
Fitting	C₂²×C₃²×C₄	C₃
socle, cosocle	C₂³×C₃	C₂×C₃²
prime radical	C₂³×C₃²	C₂×C₃
hypercenter	C₃²×C₄	A₄
hypocenter	C₂²	C₄×3₋¹⁺²
LCS	G ▷ C₂²×C₃ ▷ C₂²
UCS	C₁ ◁ C₃×C₄ ◁ C₃²×C₄

Complements

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

N	H ≅ G/N	type
3. C₄×C₂²⋊C₉	C₃	semidirect
4. #1094	C₄	direct (N × H)
18. C₂²⋊C₉	C₃×C₄	semidirect
31. C₂²×C₄	3₋¹⁺²	semidirect
55. C₂²	C₄×3₋¹⁺²	semidirect
57. C₄	#1094	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×#1094	2
C₂²×C₃²×C₄	3
C₄×C₂²⋊C₉	3
C₄×3₋¹⁺²	4

Subgroups — C4×#1094 #88685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#1094 #88685