Subgroups — C₃⋊#3689 #88609

Order 432.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#3755	—	3	1	no	maximal
3	#3689	—	3	3	no	maximal
4	C₂×C₃⋊D₉	—	4	1	no	maximal
5	C₃²×Q₈	D₃	1	1	yes	characteristic
6	C₄⋊(C₃⋊D₃)	—	3	1	no	—
7	C₃⋊(C₃⋊C₈)	—	3	1	no	—
8	Q₈⋊C₉	D₃	1	3	yes	complemented
9	C₂×C₃×C₉	—	4	1	no	—
10	C₃⋊D₉	—	4	2	no	—
11	#215	—	9	3	no	—
12	#215	—	9	1	no	—
13	C₂×C₃⋊D₃	—	6	1	no	—
14	C₃²×C₄	—	3	1	no	—
15	C₂×D₉	—	12	3	no	—
16	C₃×C₉	—	4	1	no	Sylow
17	C₃×Q₈	D₉	1	3	yes	complemented
18	C₃×Q₈	C₃⋊D₃	1	1	yes	characteristic
19	D₁₂	—	9	3	no	—
20	D₁₂	—	9	1	no	—
21	C₃⋊C₈	—	9	3	no	—
22	C₃⋊C₈	—	9	1	no	—
23	C₂×C₃²	S₄	1	1	yes	characteristic
24	C₃⋊D₃	—	12	1	no	—
25	C₂×C₉	—	4	3	no	—
26	D₉	—	12	6	no	—
27	SD₁₆	—	27	1	no	Sylow
28	C₂×D₃	—	18	3	no	—
29	C₂×D₃	—	18	1	no	—
30	C₃×C₄	—	3	3	no	—
31	C₃×C₄	—	3	1	no	—
32	C₃²	GL(2,𝔽₃)	1	1	yes	characteristic
33	C₉	—	4	3	no	—
34	Q₈	C₃⋊D₉	1	1	yes	characteristic, complemented
35	D₄	—	27	1	no	—
36	C₈	—	27	1	no	—
37	C₂×C₃	(C₂²⋊C₉)⋊C₂	1	3	yes	—
38	C₂×C₃	C₃⋊S₄	1	1	yes	characteristic
39	D₃	—	36	3	no	—
40	D₃	—	36	1	no	—
41	C₂²	—	54	1	no	—
42	C₄	—	3	1	no	—
43	C₃	#3689	1	3	yes	complemented
44	C₃	C₃⋊GL(2,𝔽₃)	1	1	yes	characteristic
45	C₂	—	108	1	no	—
46	C₂	C₃⋊((C₂²⋊C₉)⋊C₂)	1	1	yes	characteristic

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