Subgroups — #3673⋊C₃ #88508

Order 432.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄⋊AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic, complemented
3	3₋¹⁺²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#213	—	3	1	no	maximal
5	#3673	C₃	1	1	yes	maximal, characteristic, complemented
6	C₂²×3₋¹⁺²	—	2	1	no	—
7	C₂×AGL(1,ℤ/9)	—	2	1	no	—
8	C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
9	C₃²×D₄	D₃	1	1	yes	characteristic
10	C₃×D₁₂	—	3	1	no	—
11	C₃×C₃⋊C₈	—	3	1	no	—
12	D₄×C₉	—	2	1	no	—
13	D₄×C₉	C₂×C₃	1	1	yes	characteristic, complemented
14	D₃₆	C₂×C₃	1	1	yes	characteristic, complemented
15	C₉⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
16	C₂×3₋¹⁺²	—	4	1	no	—
17	C₂×3₋¹⁺²	D₄	1	1	yes	characteristic
18	AGL(1,ℤ/9)	—	4	1	no	—
19	C₃×D₈	—	9	1	no	—
20	#213	—	3	1	no	—
21	C₂²×C₃²	—	2	1	no	—
22	C₂×C₃×D₃	—	6	1	no	—
23	C₃²×C₄	C₂×D₃	1	1	yes	characteristic
24	C₂²×C₉	—	2	2	no	—
25	C₂²×C₉	—	2	1	no	—
26	C₂×D₉	—	2	1	no	—
27	C₄×C₉	—	2	1	no	—
28	C₄×C₉	C₂²×C₃	1	1	yes	characteristic
29	3₋¹⁺²	D₈	1	1	yes	characteristic, complemented, Sylow
30	C₃×D₄	—	3	1	no	—
31	C₃×D₄	—	9	1	no	—
32	C₃×D₄	C₃×D₃	1	1	yes	characteristic
33	D₁₂	—	3	1	no	—
34	C₃×C₈	—	9	1	no	—
35	C₃⋊C₈	—	3	1	no	—
36	C₂×C₃²	—	4	1	no	—
37	C₂×C₃²	#67	1	1	yes	characteristic
38	C₃×D₃	—	12	1	no	—
39	C₂×C₉	—	2	1	no	—
40	C₂×C₉	—	4	2	no	—
41	C₂×C₉	—	4	1	no	—
42	C₂×C₉	C₃×D₄	1	1	yes	characteristic
43	D₉	—	4	1	no	—
44	D₈	—	9	1	no	Sylow
45	C₂²×C₃	—	2	1	no	—
46	C₂²×C₃	—	6	1	no	—
47	C₂²×C₃	—	18	1	no	—
48	C₂×D₃	—	6	1	no	—
49	C₃×C₄	—	3	1	no	—
50	C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
51	C₃²	#213	1	1	yes	characteristic
52	C₉	—	2	1	no	—
53	C₉	C₃×D₈	1	1	yes	characteristic, complemented
54	D₄	—	9	1	no	—
55	D₄	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
56	C₈	—	9	1	no	—
57	C₂×C₃	—	3	1	no	—
58	C₂×C₃	—	4	1	no	—
59	C₂×C₃	—	12	1	no	—
60	C₂×C₃	—	36	1	no	—
61	C₂×C₃	C₃×#67	1	1	yes	characteristic
62	D₃	—	12	1	no	—
63	C₂²	—	2	1	no	—
64	C₂²	—	18	1	no	—
65	C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
66	C₃	—	3	1	no	—
67	C₃	C₃×#213	1	1	yes	characteristic
68	C₂	—	4	1	no	—
69	C₂	—	36	1	no	—
70	C₂	#611⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#611⋊C₃
commutator, cosocle	C₄×C₉	C₂²×C₃
Frattini	C₃×C₄	C₂×C₃×D₃
Fitting	D₄×3₋¹⁺²	C₂
socle	C₂×C₃	C₃×#67
hypercenter	D₄	AGL(1,ℤ/9)
hypocenter	C₉	C₃×D₈
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. D₄×3₋¹⁺²	C₂	semidirect
2. C₄⋊AGL(1,ℤ/9)	C₂	semidirect
3. 3₋¹⁺²⋊C₈	C₂	semidirect
5. #3673	C₃	semidirect
13. D₄×C₉	C₂×C₃	semidirect
14. D₃₆	C₂×C₃	semidirect
15. C₉⋊C₈	C₂×C₃	semidirect
29. 3₋¹⁺²	D₈	semidirect
53. C₉	C₃×D₈	semidirect
55. D₄	AGL(1,ℤ/9)	semidirect

Maximal subgroups

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

subgroup	index
D₄×3₋¹⁺²	2
C₄⋊AGL(1,ℤ/9)	2
3₋¹⁺²⋊C₈	2
C₃×#213	3
#3673	3

Subgroups — #3673⋊C3 #88508

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3673⋊C₃ #88508