Subgroups — C₉×Dic₃⋊C₄ #88485

Order 432.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₃×Dic₃⋊C₄	C₃	1	1	yes	maximal, characteristic
5	C₉×C₄⋊C₄	—	3	1	no	maximal
6	C₂²×C₃×C₉	C₂²	1	1	yes	characteristic
7	C₃×C₄×C₉	—	2	1	no	—
8	C₉×Dic₃	—	2	1	no	—
9	C₉×Dic₃	C₄	1	2	yes	complemented
10	C₂×C₃²×C₄	C₂×C₃	1	1	yes	characteristic
11	C₂×C₃×Dic₃	C₂×C₃	1	1	yes	characteristic
12	C₂×C₃×Dic₃	C₂×C₃	1	1	yes	characteristic
13	C₂×C₄×C₉	—	2	1	no	—
14	C₂×C₄×C₉	—	3	1	no	—
15	C₂×C₄×C₉	—	3	1	no	—
16	C₂×C₄×C₉	D₃	1	1	yes	characteristic
17	C₂×C₃×C₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₃×C₉	D₄	1	1	yes	characteristic
19	C₂×C₃×C₉	Q₈	1	1	yes	characteristic
20	C₃×C₄⋊C₄	—	3	1	no	—
21	Dic₃⋊C₄	C₉	1	1	yes	characteristic, direct product factor
22	C₂²×C₃²	C₂²×C₃	1	1	yes	characteristic
23	C₃²×C₄	—	2	1	no	—
24	C₃×Dic₃	—	2	1	no	—
25	C₃×Dic₃	C₃×C₄	1	2	yes	—
26	C₂²×C₉	—	2	1	no	—
27	C₂²×C₉	C₂×D₃	1	1	yes	characteristic
28	C₄×C₉	—	2	2	no	—
29	C₄×C₉	—	2	1	no	—
30	C₄×C₉	—	3	2	no	—
31	C₄×C₉	—	6	1	no	—
32	C₃×C₉	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃×C₄	—	2	1	no	—
34	C₂×C₃×C₄	—	3	1	no	—
35	C₂×C₃×C₄	—	3	1	no	—
36	C₂×C₃×C₄	C₂×C₉	1	1	yes	characteristic
37	C₂×C₃×C₄	C₃×D₃	1	1	yes	characteristic
38	C₂×Dic₃	C₂×C₉	1	1	yes	characteristic
39	C₂×Dic₃	C₂×C₉	1	1	yes	characteristic
40	C₂×C₃²	C₂×C₃×C₄	1	1	yes	characteristic
41	C₂×C₃²	C₃×D₄	1	1	yes	characteristic
42	C₂×C₃²	C₃×Q₈	1	1	yes	characteristic
43	C₂×C₉	—	2	1	no	—
44	C₂×C₉	—	2	1	no	—
45	C₂×C₉	—	2	1	no	—
46	C₂×C₉	Dic₆	1	1	yes	characteristic
47	C₂×C₉	C₄×D₃	1	1	yes	characteristic
48	C₂×C₉	#67	1	1	yes	characteristic
49	C₄⋊C₄	—	3	1	no	Sylow
50	C₂²×C₃	—	2	1	no	—
51	C₂²×C₃	C₂²×C₉	1	1	yes	characteristic
52	C₂²×C₃	C₂×C₃×D₃	1	1	yes	characteristic
53	C₃×C₄	—	2	2	no	—
54	C₃×C₄	—	2	1	no	—
55	C₃×C₄	—	2	1	no	—
56	C₃×C₄	—	3	2	no	—
57	C₃×C₄	—	6	1	no	—
58	Dic₃	—	2	1	no	—
59	Dic₃	C₄×C₉	1	2	yes	complemented
60	C₃²	C₃×C₄⋊C₄	1	1	yes	characteristic
61	C₉	—	2	1	no	—
62	C₉	Dic₃⋊C₄	1	1	yes	characteristic, direct product factor
63	C₂×C₄	—	3	1	no	—
64	C₂×C₄	—	3	1	no	—
65	C₂×C₄	D₃×C₉	1	1	yes	characteristic
66	C₂×C₃	—	2	1	no	—
67	C₂×C₃	—	2	1	no	—
68	C₂×C₃	—	2	1	no	—
69	C₂×C₃	C₂×C₄×C₉	1	1	yes	characteristic
70	C₂×C₃	D₄×C₉	1	1	yes	characteristic
71	C₂×C₃	Q₈×C₉	1	1	yes	characteristic
72	C₂×C₃	C₃×Dic₆	1	1	yes	characteristic
73	C₂×C₃	C₃×C₄×D₃	1	1	yes	characteristic
74	C₂×C₃	C₃×#67	1	1	yes	characteristic
75	C₂²	C₂×D₃×C₉	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	3	2	no	—
78	C₄	—	6	1	no	—
79	C₃	—	2	1	no	—
80	C₃	C₉×C₄⋊C₄	1	1	yes	characteristic, complemented
81	C₃	C₃×Dic₃⋊C₄	1	1	yes	characteristic
82	C₂	C₉×Dic₆	1	1	yes	characteristic
83	C₂	C₄×D₃×C₉	1	1	yes	characteristic
84	C₂	C₉×#67	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
9. C₉×Dic₃	C₄	semidirect
21. Dic₃⋊C₄	C₉	direct (N × H)
32. C₃×C₉	C₄⋊C₄	semidirect
59. Dic₃	C₄×C₉	semidirect
62. C₉	Dic₃⋊C₄	direct (N × H)
80. C₃	C₉×C₄⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×C₉	2
C₂×C₉×Dic₃	2
C₃×Dic₃⋊C₄	3
C₉×C₄⋊C₄	3

Subgroups — C9×Dic3⋊C4 #88485

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×Dic₃⋊C₄ #88485