Subgroups — #3676⋊C₃ #88520

Order 432.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic
2	C₂×3₋¹⁺²⋊C₄	C₂	1	2	yes	maximal, complemented
3	C₃×#217	—	3	1	no	maximal
4	#3676	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂²×3₋¹⁺²	—	2	2	no	—
6	C₂²×3₋¹⁺²	C₄	1	2	yes	complemented
7	C₂²×3₋¹⁺²	C₂²	1	1	yes	characteristic
8	3₋¹⁺²⋊C₄	—	2	2	no	—
9	C₂³×C₃²	D₃	1	1	yes	characteristic
10	C₂×C₃×Dic₃	—	3	2	no	—
11	C₂³×C₉	—	2	1	no	—
12	C₂³×C₉	C₂×C₃	1	1	yes	characteristic
13	C₂×Dic₉	C₂×C₃	1	2	yes	complemented
14	C₂×3₋¹⁺²	—	2	2	no	—
15	C₂×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
16	C₂×3₋¹⁺²	D₄	1	2	yes	—
17	C₃×C₂²⋊C₄	—	9	1	no	—
18	#217	—	3	1	no	—
19	C₂²×C₃²	—	2	2	no	—
20	C₂²×C₃²	Dic₃	1	2	yes	—
21	C₂²×C₃²	C₂×D₃	1	1	yes	characteristic
22	C₃×Dic₃	—	6	2	no	—
23	C₂²×C₉	—	2	4	no	—
24	C₂²×C₉	—	2	2	no	—
25	C₂²×C₉	—	2	2	no	—
26	C₂²×C₉	—	2	1	no	—
27	C₂²×C₉	C₃×C₄	1	2	yes	complemented
28	C₂²×C₉	C₂²×C₃	1	1	yes	characteristic
29	Dic₉	—	2	2	no	—
30	3₋¹⁺²	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
31	C₂³×C₃	—	3	1	no	—
32	C₂³×C₃	C₃×D₃	1	1	yes	characteristic
33	C₂×C₃×C₄	—	9	2	no	—
34	C₂×Dic₃	—	3	2	no	—
35	C₂×C₃²	—	2	2	no	—
36	C₂×C₃²	C₂×Dic₃	1	1	yes	characteristic
37	C₂×C₃²	#67	1	2	yes	—
38	C₂×C₉	—	2	4	no	—
39	C₂×C₉	—	2	2	no	—
40	C₂×C₉	—	2	1	no	—
41	C₂×C₉	—	2	2	no	—
42	C₂×C₉	C₂×C₃×C₄	1	1	yes	characteristic
43	C₂×C₉	C₃×D₄	1	2	yes	—
44	C₂²⋊C₄	—	9	1	no	Sylow
45	C₂²×C₃	—	2	2	no	—
46	C₂²×C₃	—	3	2	no	—
47	C₂²×C₃	—	3	1	no	—
48	C₂²×C₃	—	6	2	no	—
49	C₂²×C₃	C₃×Dic₃	1	2	yes	—
50	C₂²×C₃	C₂×C₃×D₃	1	1	yes	characteristic
51	C₃×C₄	—	18	2	no	—
52	Dic₃	—	6	2	no	—
53	C₃²	#217	1	1	yes	characteristic
54	C₉	—	2	1	no	—
55	C₉	C₃×C₂²⋊C₄	1	1	yes	characteristic, complemented
56	C₂³	AGL(1,ℤ/9)	1	1	yes	characteristic
57	C₂×C₄	—	9	2	no	—
58	C₂×C₃	—	2	2	no	—
59	C₂×C₃	—	3	1	no	—
60	C₂×C₃	—	3	2	no	—
61	C₂×C₃	—	6	2	no	—
62	C₂×C₃	C₂×C₃×Dic₃	1	1	yes	characteristic
63	C₂×C₃	C₃×#67	1	2	yes	—
64	C₂²	—	2	2	no	—
65	C₂²	3₋¹⁺²⋊C₄	1	2	yes	complemented
66	C₂²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
67	C₄	—	18	2	no	—
68	C₃	—	3	1	no	—
69	C₃	C₃×#217	1	1	yes	characteristic
70	C₂	—	2	2	no	—
71	C₂	C₂×3₋¹⁺²⋊C₄	1	1	yes	characteristic
72	C₂	#611⋊C₃	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×AGL(1,ℤ/9)
commutator	C₂×C₉	C₂×C₃×C₄
Frattini, socle	C₂²×C₃	C₂×C₃×D₃
Fitting	C₂³×3₋¹⁺²	C₂
prime radical	C₂³×C₃²	D₃
cosocle	C₂²×C₉	C₂²×C₃
hypercenter	C₂³	AGL(1,ℤ/9)
hypocenter	C₉	C₃×C₂²⋊C₄
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂³

Complements

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

N	H ≅ G/N	type
2. C₂×3₋¹⁺²⋊C₄	C₂	semidirect
4. #3676	C₃	semidirect
6. C₂²×3₋¹⁺²	C₄	semidirect
13. C₂×Dic₉	C₂×C₃	semidirect
27. C₂²×C₉	C₃×C₄	semidirect
30. 3₋¹⁺²	C₂²⋊C₄	semidirect
55. C₉	C₃×C₂²⋊C₄	semidirect
65. C₂²	3₋¹⁺²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂³×3₋¹⁺²	2
C₂×3₋¹⁺²⋊C₄	2
C₃×#217	3
#3676	3

Subgroups — #3676⋊C3 #88520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3676⋊C₃ #88520