Subgroups — #88428

Order 432.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6226	C₂	1	1	yes	maximal, characteristic
2	C₉×Dic₆	C₂	1	1	yes	maximal, characteristic
3	C₃×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#3719	—	3	1	no	maximal
5	#3674	—	3	1	no	maximal
6	C₃×C₄×C₉	C₂²	1	1	yes	characteristic
7	C₃⋊Dic₉	—	2	1	no	—
8	C₉×Dic₃	—	2	1	no	—
9	#634	—	3	1	no	—
10	C₃×Dic₆	D₃	1	1	yes	characteristic
11	C₃×C₃⋊C₈	—	3	1	no	—
12	Q₈×C₉	—	3	1	no	—
13	Dic₁₈	—	3	1	no	—
14	Dic₁₈	—	6	1	no	—
15	C₉⋊C₈	D₃	1	1	yes	characteristic
16	C₂×C₃×C₉	D₄	1	1	yes	characteristic
17	#216	—	9	1	no	—
18	Dic₁₂	—	9	1	no	—
19	C₃²×C₄	C₂×D₃	1	1	yes	characteristic
20	C₃⋊Dic₃	—	6	1	no	—
21	C₃×Dic₃	—	2	1	no	—
22	C₄×C₉	—	2	1	no	—
23	C₄×C₉	—	6	1	no	—
24	C₄×C₉	C₂×D₃	1	1	yes	characteristic
25	Dic₉	—	6	2	no	—
26	Dic₉	—	6	1	no	—
27	C₃×C₉	Q₁₆	1	1	yes	characteristic, complemented, Sylow
28	C₃×Q₈	—	3	1	no	—
29	Dic₆	—	9	1	no	—
30	Dic₆	—	9	1	no	—
31	Dic₆	—	18	1	no	—
32	Dic₆	D₉	1	1	yes	characteristic
33	C₃×C₈	—	9	1	no	—
34	C₃⋊C₈	—	3	1	no	—
35	C₂×C₃²	#67	1	1	yes	characteristic
36	C₂×C₉	—	2	1	no	—
37	C₂×C₉	D₁₂	1	1	yes	characteristic
38	Q₁₆	—	27	1	no	Sylow
39	C₃×C₄	—	2	1	no	—
40	C₃×C₄	—	6	1	no	—
41	C₃×C₄	C₂×D₉	1	1	yes	characteristic
42	C₃×C₄	D₃²	1	1	yes	characteristic
43	Dic₃	—	2	1	no	—
44	Dic₃	—	18	2	no	—
45	Dic₃	—	18	1	no	—
46	Dic₃	—	18	1	no	—
47	C₃²	#216	1	1	yes	characteristic
48	C₉	—	2	1	no	—
49	C₉	Dic₁₂	1	1	yes	characteristic, complemented
50	Q₈	—	3	1	no	—
51	Q₈	—	27	1	no	—
52	C₈	—	9	1	no	—
53	C₂×C₃	—	2	1	no	—
54	C₂×C₃	#611	1	1	yes	characteristic
55	C₂×C₃	#626	1	1	yes	characteristic
56	C₄	—	6	1	no	—
57	C₄	—	54	1	no	—
58	C₄	D₃×D₉	1	1	yes	characteristic
59	C₃	—	2	1	no	—
60	C₃	#3674	1	1	yes	characteristic, complemented
61	C₃	#3719	1	1	yes	characteristic
62	C₂	#6195	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#6195
commutator, Fitting, cosocle	C₃×C₄×C₉	C₂²
Frattini	C₃×C₄	D₃²
socle, prime radical	C₂×C₃²	#67
hypercenter	C₄	D₃×D₉
hypocenter	C₃×C₉	Q₁₆
LCS	G ▷ C₃×C₄×C₉ ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
27. C₃×C₉	Q₁₆	semidirect
49. C₉	Dic₁₂	semidirect
60. C₃	#3674	semidirect

Maximal subgroups

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

subgroup	index
#6226	2
C₉×Dic₆	2
C₃×C₉⋊C₈	2
#3719	3
#3674	3