Subgroups — C₃×#3672 #88501

Order 432.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₁₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#214	—	3	1	no	maximal
5	#3672	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂²×C₃×C₉	—	2	1	no	—
7	C₃×C₄×C₉	C₂²	1	1	yes	characteristic
8	C₃×Dic₉	—	2	1	no	—
9	C₃²×D₄	D₃	1	1	yes	characteristic
10	C₃×Dic₆	—	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
14	Dic₁₈	C₂×C₃	1	1	yes	characteristic, complemented
15	C₉⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
16	C₂×C₃×C₉	—	4	1	no	—
17	C₂×C₃×C₉	D₄	1	1	yes	characteristic
18	C₃×SD₁₆	—	9	1	no	—
19	#214	—	3	1	no	—
20	C₂²×C₃²	—	2	1	no	—
21	C₃²×C₄	C₂×D₃	1	1	yes	characteristic
22	C₃×Dic₃	—	6	1	no	—
23	C₂²×C₉	—	2	2	no	—
24	C₂²×C₉	—	2	1	no	—
25	C₄×C₉	—	2	1	no	—
26	C₄×C₉	C₂²×C₃	1	1	yes	characteristic
27	Dic₉	—	2	1	no	—
28	C₃×C₉	SD₁₆	1	1	yes	characteristic, complemented, Sylow
29	C₃×Q₈	—	9	1	no	—
30	C₃×D₄	—	2	1	no	—
31	C₃×D₄	D₉	1	1	yes	characteristic
32	C₃×D₄	C₃×D₃	1	1	yes	characteristic
33	Dic₆	—	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	C₂×C₉	—	2	1	no	—
39	C₂×C₉	—	4	2	no	—
40	C₂×C₉	—	4	1	no	—
41	C₂×C₉	C₃×D₄	1	1	yes	characteristic
42	SD₁₆	—	9	1	no	Sylow
43	C₂²×C₃	—	2	2	no	—
44	C₂²×C₃	—	2	1	no	—
45	C₂²×C₃	—	2	1	no	—
46	C₃×C₄	—	2	1	no	—
47	C₃×C₄	—	18	1	no	—
48	C₃×C₄	C₂×D₉	1	1	yes	characteristic
49	C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
50	Dic₃	—	6	1	no	—
51	C₃²	#214	1	1	yes	characteristic
52	C₉	—	2	1	no	—
53	C₉	C₃×SD₁₆	1	1	yes	characteristic, complemented
54	Q₈	—	9	1	no	—
55	D₄	C₃×D₉	1	1	yes	characteristic
56	C₈	—	9	1	no	—
57	C₂×C₃	—	2	1	no	—
58	C₂×C₃	—	4	2	no	—
59	C₂×C₃	—	4	1	no	—
60	C₂×C₃	—	4	1	no	—
61	C₂×C₃	#611	1	1	yes	characteristic
62	C₂×C₃	C₃×#67	1	1	yes	characteristic
63	C₂²	—	2	1	no	—
64	C₄	—	18	1	no	—
65	C₄	C₂×C₃×D₉	1	1	yes	characteristic
66	C₃	—	2	1	no	—
67	C₃	#3672	1	1	yes	characteristic, direct product factor
68	C₃	C₃×#214	1	1	yes	characteristic
69	C₂	—	4	1	no	—
70	C₂	C₃×#611	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	#611
commutator, cosocle	C₄×C₉	C₂²×C₃
Frattini	C₃×C₄	C₂×C₃×D₃
Fitting	C₃×D₄×C₉	C₂
socle	C₂×C₃²	#67
prime radical	C₃²×D₄	D₃
hypercenter	C₃×D₄	D₉
hypocenter	C₉	C₃×SD₁₆
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×D₄

Complements

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

N	H ≅ G/N	type
2. C₃×Dic₁₈	C₂	semidirect
3. C₃×C₉⋊C₈	C₂	semidirect
5. #3672	C₃	direct (N × H)
14. Dic₁₈	C₂×C₃	semidirect
15. C₉⋊C₈	C₂×C₃	semidirect
28. C₃×C₉	SD₁₆	semidirect
53. C₉	C₃×SD₁₆	semidirect
67. C₃	#3672	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₄×C₉	2
C₃×Dic₁₈	2
C₃×C₉⋊C₈	2
C₃×#214	3
#3672	3

Subgroups — C3×#3672 #88501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3672 #88501