Subgroups — C₉×#214 #88504

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	C₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#214	C₃	1	1	yes	maximal, characteristic
5	C₉×SD₁₆	—	3	1	no	maximal
6	C₂²×C₃×C₉	—	2	1	no	—
7	C₃×C₄×C₉	C₂²	1	1	yes	characteristic
8	C₉×Dic₃	—	2	1	no	—
9	C₃²×D₄	C₂×C₃	1	1	yes	characteristic
10	C₃×Dic₆	C₂×C₃	1	1	yes	characteristic
11	C₃×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic
12	Q₈×C₉	—	3	1	no	—
13	D₄×C₉	—	2	1	no	—
14	D₄×C₉	D₃	1	1	yes	characteristic
15	C₈×C₉	—	3	1	no	—
16	C₂×C₃×C₉	—	4	1	no	—
17	C₂×C₃×C₉	D₄	1	1	yes	characteristic
18	C₃×SD₁₆	—	3	1	no	—
19	#214	C₉	1	1	yes	characteristic, direct product factor
20	C₂²×C₃²	—	2	1	no	—
21	C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
22	C₃×Dic₃	—	2	1	no	—
23	C₂²×C₉	—	2	2	no	—
24	C₂²×C₉	—	2	1	no	—
25	C₄×C₉	—	2	1	no	—
26	C₄×C₉	—	6	1	no	—
27	C₄×C₉	C₂×D₃	1	1	yes	characteristic
28	C₃×C₉	SD₁₆	1	1	yes	characteristic, complemented, Sylow
29	C₃×Q₈	—	3	1	no	—
30	C₃×D₄	—	2	1	no	—
31	C₃×D₄	C₂×C₉	1	1	yes	characteristic
32	C₃×D₄	C₃×D₃	1	1	yes	characteristic
33	Dic₆	C₂×C₉	1	1	yes	characteristic, complemented
34	C₃×C₈	—	3	1	no	—
35	C₃⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
36	C₂×C₃²	—	4	1	no	—
37	C₂×C₃²	C₃×D₄	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	#67	1	1	yes	characteristic
42	SD₁₆	—	3	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	—	6	1	no	—
48	C₃×C₄	C₂²×C₉	1	1	yes	characteristic
49	C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
50	Dic₃	—	2	1	no	—
51	C₃²	C₃×SD₁₆	1	1	yes	characteristic
52	C₉	—	2	1	no	—
53	C₉	#214	1	1	yes	characteristic, direct product factor
54	Q₈	—	3	1	no	—
55	D₄	D₃×C₉	1	1	yes	characteristic
56	C₈	—	3	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	D₄×C₉	1	1	yes	characteristic
62	C₂×C₃	C₃×#67	1	1	yes	characteristic
63	C₂²	—	2	1	no	—
64	C₄	—	6	1	no	—
65	C₄	C₂×D₃×C₉	1	1	yes	characteristic
66	C₃	—	2	1	no	—
67	C₃	C₉×SD₁₆	1	1	yes	characteristic, complemented
68	C₃	C₃×#214	1	1	yes	characteristic
69	C₂	—	4	1	no	—
70	C₂	C₉×#67	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₉×Dic₆	C₂	semidirect
3. C₉×C₃⋊C₈	C₂	semidirect
19. #214	C₉	direct (N × H)
28. C₃×C₉	SD₁₆	semidirect
33. Dic₆	C₂×C₉	semidirect
35. C₃⋊C₈	C₂×C₉	semidirect
53. C₉	#214	direct (N × H)
67. C₃	C₉×SD₁₆	semidirect

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
C₉×Dic₆	2
C₉×C₃⋊C₈	2
C₃×#214	3
C₉×SD₁₆	3

Subgroups — C9×#214 #88504

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#214 #88504