Subgroups — C₃×Dic₉⋊C₄ #88482

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×C₃×Dic₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×Dic₉	C₂	1	1	yes	maximal, characteristic
4	C₃×Dic₃⋊C₄	—	3	1	no	maximal
5	Dic₉⋊C₄	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂²×C₃×C₉	C₂²	1	1	yes	characteristic
7	C₃×C₄×C₉	—	2	1	no	—
8	C₃×Dic₉	—	2	1	no	—
9	C₃×Dic₉	C₄	1	2	yes	complemented
10	C₂×C₃²×C₄	D₃	1	1	yes	characteristic
11	C₂×C₃×Dic₃	—	3	1	no	—
12	C₂×C₃×Dic₃	—	3	1	no	—
13	C₂×C₄×C₉	—	2	1	no	—
14	C₂×C₄×C₉	C₂×C₃	1	1	yes	characteristic
15	C₂×Dic₉	C₂×C₃	1	1	yes	characteristic
16	C₂×Dic₉	C₂×C₃	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	—	9	1	no	—
21	Dic₃⋊C₄	—	3	1	no	—
22	C₂²×C₃²	C₂×D₃	1	1	yes	characteristic
23	C₃²×C₄	—	2	1	no	—
24	C₃×Dic₃	—	3	2	no	—
25	C₃×Dic₃	—	6	1	no	—
26	C₂²×C₉	—	2	1	no	—
27	C₂²×C₉	C₂²×C₃	1	1	yes	characteristic
28	C₄×C₉	—	2	2	no	—
29	C₄×C₉	—	2	1	no	—
30	Dic₉	—	2	1	no	—
31	Dic₉	C₃×C₄	1	2	yes	complemented
32	C₃×C₉	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃×C₄	—	2	1	no	—
34	C₂×C₃×C₄	—	9	1	no	—
35	C₂×C₃×C₄	—	9	1	no	—
36	C₂×C₃×C₄	D₉	1	1	yes	characteristic
37	C₂×C₃×C₄	C₃×D₃	1	1	yes	characteristic
38	C₂×Dic₃	—	3	1	no	—
39	C₂×Dic₃	—	3	1	no	—
40	C₂×C₃²	Dic₆	1	1	yes	characteristic
41	C₂×C₃²	C₄×D₃	1	1	yes	characteristic
42	C₂×C₃²	#67	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	C₂×C₃×C₄	1	1	yes	characteristic
47	C₂×C₉	C₃×D₄	1	1	yes	characteristic
48	C₂×C₉	C₃×Q₈	1	1	yes	characteristic
49	C₄⋊C₄	—	9	1	no	Sylow
50	C₂²×C₃	—	2	1	no	—
51	C₂²×C₃	C₂×D₉	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	—	9	2	no	—
57	C₃×C₄	—	18	1	no	—
58	Dic₃	—	3	2	no	—
59	Dic₃	—	6	1	no	—
60	C₃²	Dic₃⋊C₄	1	1	yes	characteristic
61	C₉	—	2	1	no	—
62	C₉	C₃×C₄⋊C₄	1	1	yes	characteristic, complemented
63	C₂×C₄	—	9	1	no	—
64	C₂×C₄	—	9	1	no	—
65	C₂×C₄	C₃×D₉	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	Dic₁₈	1	1	yes	characteristic
70	C₂×C₃	C₄×D₉	1	1	yes	characteristic
71	C₂×C₃	#611	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×C₃×D₉	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	9	2	no	—
78	C₄	—	18	1	no	—
79	C₃	—	2	1	no	—
80	C₃	Dic₉⋊C₄	1	1	yes	characteristic, direct product factor
81	C₃	C₃×Dic₃⋊C₄	1	1	yes	characteristic
82	C₂	C₃×Dic₁₈	1	1	yes	characteristic
83	C₂	C₃×C₄×D₉	1	1	yes	characteristic
84	C₂	C₃×#611	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
5. Dic₉⋊C₄	C₃	direct (N × H)
9. C₃×Dic₉	C₄	semidirect
31. Dic₉	C₃×C₄	semidirect
32. C₃×C₉	C₄⋊C₄	semidirect
62. C₉	C₃×C₄⋊C₄	semidirect
80. C₃	Dic₉⋊C₄	direct (N × H)

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×C₃×Dic₉	2
C₃×Dic₃⋊C₄	3
Dic₉⋊C₄	3

Subgroups — C3×Dic9⋊C4 #88482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Dic₉⋊C₄ #88482