Subgroups — C₃×#3689 #88599

Order 432.

57 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	C₃×#215	—	3	1	no	maximal
3	#3689	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×D₉	—	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×C₃×C₉	—	4	1	no	—
11	C₃×D₉	—	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	C₃×C₉	—	4	1	no	Sylow
18	C₃×Q₈	—	2	1	no	—
19	C₃×Q₈	D₉	1	1	yes	characteristic, complemented
20	C₃×Q₈	C₃×D₃	1	1	yes	characteristic
21	C₃×D₄	—	9	1	no	—
22	D₁₂	—	3	1	no	—
23	C₃×C₈	—	9	1	no	—
24	C₃⋊C₈	—	3	1	no	—
25	C₂×C₃²	S₄	1	1	yes	characteristic
26	C₃×D₃	—	12	1	no	—
27	C₂×C₉	—	4	1	no	—
28	C₂×C₉	—	8	1	no	—
29	D₉	—	4	2	no	—
30	SD₁₆	—	9	1	no	Sylow
31	C₂²×C₃	—	18	1	no	—
32	C₂×D₃	—	6	1	no	—
33	C₃×C₄	—	3	1	no	—
34	C₃×C₄	—	3	1	no	—
35	C₃×C₄	—	6	1	no	—
36	C₃²	GL(2,𝔽₃)	1	1	yes	characteristic
37	C₉	—	4	1	no	—
38	C₉	—	8	1	no	—
39	Q₈	C₃×D₉	1	1	yes	characteristic, complemented
40	D₄	—	9	1	no	—
41	C₈	—	9	1	no	—
42	C₂×C₃	—	2	1	no	—
43	C₂×C₃	—	36	1	no	—
44	C₂×C₃	(C₂²⋊C₉)⋊C₂	1	1	yes	characteristic
45	C₂×C₃	C₃×S₄	1	1	yes	characteristic
46	D₃	—	12	1	no	—
47	C₂²	—	18	1	no	—
48	C₄	—	3	1	no	—
49	C₃	—	2	1	no	—
50	C₃	#3689	1	1	yes	characteristic, direct product factor
51	C₃	C₃×GL(2,𝔽₃)	1	1	yes	characteristic
52	C₂	—	36	1	no	—
53	C₂	C₃×(C₂²⋊C₉)⋊C₂	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃×Q₈⋊C₉	C₂	semidirect
3. #3689	C₃	direct (N × H)
9. Q₈⋊C₉	C₂×C₃	semidirect
19. C₃×Q₈	D₉	semidirect
39. Q₈	C₃×D₉	semidirect
50. C₃	#3689	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×Q₈⋊C₉	2
C₃×#215	3
#3689	3
C₂×C₃×D₉	4

Subgroups — C3×#3689 #88599

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3689 #88599