Subgroups — #3689⋊C₃ #88598

Order 432.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6204	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#215	—	3	1	no	maximal
3	#3689	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×AGL(1,ℤ/9)	—	4	1	no	maximal
5	C₃²×Q₈	D₃	1	1	yes	characteristic
6	C₃×D₁₂	—	3	1	no	—
7	C₃×C₃⋊C₈	—	3	1	no	—
8	Q₈⋊C₉	—	2	1	no	—
9	Q₈⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×3₋¹⁺²	—	4	1	no	—
11	AGL(1,ℤ/9)	—	4	2	no	—
12	C₃×SD₁₆	—	9	1	no	—
13	#215	—	3	1	no	—
14	C₂×C₃×D₃	—	6	1	no	—
15	C₃²×C₄	—	3	1	no	—
16	C₂×D₉	—	4	1	no	—
17	3₋¹⁺²	—	4	1	no	Sylow
18	C₃×Q₈	—	3	1	no	—
19	C₃×Q₈	C₃×D₃	1	1	yes	characteristic
20	C₃×D₄	—	9	1	no	—
21	D₁₂	—	3	1	no	—
22	C₃×C₈	—	9	1	no	—
23	C₃⋊C₈	—	3	1	no	—
24	C₂×C₃²	S₄	1	1	yes	characteristic
25	C₃×D₃	—	12	1	no	—
26	C₂×C₉	—	4	1	no	—
27	C₂×C₉	—	8	1	no	—
28	D₉	—	4	2	no	—
29	SD₁₆	—	9	1	no	Sylow
30	C₂²×C₃	—	18	1	no	—
31	C₂×D₃	—	6	1	no	—
32	C₃×C₄	—	3	1	no	—
33	C₃×C₄	—	3	1	no	—
34	C₃×C₄	—	6	1	no	—
35	C₃²	GL(2,𝔽₃)	1	1	yes	characteristic
36	C₉	—	4	1	no	—
37	C₉	—	8	1	no	—
38	Q₈	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
39	D₄	—	9	1	no	—
40	C₈	—	9	1	no	—
41	C₂×C₃	—	3	1	no	—
42	C₂×C₃	—	36	1	no	—
43	C₂×C₃	C₃×S₄	1	1	yes	characteristic
44	D₃	—	12	1	no	—
45	C₂²	—	18	1	no	—
46	C₄	—	3	1	no	—
47	C₃	—	3	1	no	—
48	C₃	C₃×GL(2,𝔽₃)	1	1	yes	characteristic
49	C₂	—	36	1	no	—
50	C₂	((C₂²⋊C₉)⋊C₂)⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	((C₂²⋊C₉)⋊C₂)⋊C₃
commutator, cosocle, hypocenter	Q₈⋊C₉	C₂×C₃
Frattini, socle	C₂×C₃	C₃×S₄
Fitting	C₃²×Q₈	D₃
LCS	G ▷ Q₈⋊C₉
UCS	C₁ ◁ C₂

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

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