Subgroups — #4175⋊C₃ #92282

Order 486.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6909	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊((C₃⋊D₃)⋊C₃)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×(C₃⋊D₃)⋊C₃	—	3	1	no	maximal
4	#4175	C₃	1	3	yes	maximal, complemented
5	C₃×3₋¹⁺²	—	2	1	no	—
6	C₃×H(3,𝔽₃)	D₃	1	1	yes	characteristic, complemented
7	C₃×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic, complemented
8	AΣL(1,𝔽₂₇)	—	2	3	no	—
9	AΣL(1,𝔽₂₇)	C₂×C₃	1	3	yes	complemented
10	C₃⋊(C₃⋊D₃)	C₃²	1	1	yes	characteristic, complemented
11	C₃×C₃⋊D₃	—	3	1	no	—
12	C₃²×D₃	—	9	1	no	—
13	(C₃⋊D₃)⋊C₃	—	3	3	no	—
14	(C₃⋊D₃)⋊C₃	—	9	1	no	—
15	C₃³	—	2	1	no	—
16	C₃³	—	3	1	no	—
17	C₃³	C₃×D₃	1	1	yes	characteristic
18	C₃³	C₂×C₃²	1	1	yes	characteristic, complemented
19	3₋¹⁺²	—	2	3	no	—
20	3₋¹⁺²	—	6	1	no	—
21	3₋¹⁺²	—	6	1	no	—
22	H(3,𝔽₃)	—	3	1	no	—
23	H(3,𝔽₃)	—	6	1	no	—
24	H(3,𝔽₃)	—	6	1	no	—
25	H(3,𝔽₃)	C₃×D₃	1	3	yes	—
26	C₃×C₉	—	6	1	no	—
27	C₂×C₃²	—	27	1	no	—
28	C₃⋊D₃	—	3	1	no	—
29	C₃⋊D₃	—	9	1	no	—
30	C₃⋊D₃	—	27	1	no	—
31	C₃×D₃	—	9	3	no	—
32	C₃×D₃	—	9	1	no	—
33	C₃×D₃	—	27	1	no	—
34	C₃²	—	2	1	no	—
35	C₃²	—	3	3	no	—
36	C₃²	—	3	1	no	—
37	C₃²	—	6	1	no	—
38	C₃²	—	9	1	no	—
39	C₃²	—	9	1	no	—
40	C₃²	—	9	1	no	—
41	C₃²	—	18	1	no	—
42	C₃²	—	18	1	no	—
43	C₃²	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
44	C₃²	C₃²×D₃	1	1	yes	characteristic
45	C₉	—	6	3	no	—
46	C₂×C₃	—	27	1	no	—
47	C₂×C₃	—	27	3	no	—
48	D₃	—	9	1	no	—
49	D₃	—	27	1	no	—
50	D₃	—	81	1	no	—
51	C₃	—	3	1	no	—
52	C₃	—	3	1	no	—
53	C₃	—	6	1	no	—
54	C₃	—	9	1	no	—
55	C₃	—	9	3	no	—
56	C₃	—	18	1	no	—
57	C₃	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
58	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃³	C₂×C₃²
Frattini	C₃²	C₃²×D₃
Fitting	#6909	C₂
socle	C₃	C₃×(C₃⋊D₃)⋊C₃
LCS	G ▷ C₃³
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #6909	C₂	semidirect
2. C₃⋊((C₃⋊D₃)⋊C₃)	C₃	semidirect
4. #4175	C₃	semidirect
6. C₃×H(3,𝔽₃)	D₃	semidirect
7. C₃×H(3,𝔽₃)	C₂×C₃	semidirect
9. AΣL(1,𝔽₂₇)	C₂×C₃	semidirect
10. C₃⋊(C₃⋊D₃)	C₃²	semidirect
18. C₃³	C₂×C₃²	semidirect

Maximal subgroups

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

subgroup	index
#6909	2
C₃⋊((C₃⋊D₃)⋊C₃)	3
C₃×(C₃⋊D₃)⋊C₃	3
#4175	3

Subgroups — #4175⋊C3 #92282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #4175⋊C₃ #92282