Subgroups — #272⋊C₉ #92179

Order 486.

67 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	H(3,𝔽₃)⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×#272	C₃	1	1	yes	maximal, characteristic
3	C₃×D₃×C₉	—	3	1	no	maximal
4	C₃×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
5	C₃²×C₉	D₃	1	1	yes	characteristic, complemented
6	C₃²⋊C₉	—	2	1	no	—
7	C₃²×D₃	—	3	1	no	—
8	C₃²×D₃	—	9	1	no	—
9	C₂×C₃×C₉	—	9	1	no	—
10	#272	C₉	1	1	yes	characteristic, complemented
11	D₃×C₉	—	3	3	no	—
12	C₃³	—	3	1	no	—
13	C₃³	C₃×D₃	1	1	yes	characteristic
14	H(3,𝔽₃)	—	2	1	no	—
15	H(3,𝔽₃)	—	6	1	no	—
16	H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic, complemented
17	C₃×C₉	—	3	1	no	—
18	C₃×C₉	—	3	3	no	—
19	C₃×C₉	—	6	1	no	—
20	C₂×C₃²	—	9	1	no	—
21	C₃×D₃	—	3	1	no	—
22	C₃×D₃	—	3	1	no	—
23	C₃×D₃	—	3	1	no	—
24	C₃×D₃	—	3	1	no	—
25	C₃×D₃	—	9	1	no	—
26	C₃×D₃	—	9	1	no	—
27	C₃×D₃	—	9	1	no	—
28	C₃×D₃	—	9	1	no	—
29	C₂×C₉	—	9	3	no	—
30	C₃²	—	2	1	no	—
31	C₃²	—	3	1	no	—
32	C₃²	—	3	1	no	—
33	C₃²	—	3	1	no	—
34	C₃²	—	3	1	no	—
35	C₃²	—	6	1	no	—
36	C₃²	—	9	1	no	—
37	C₃²	—	9	1	no	—
38	C₃²	—	9	1	no	—
39	C₃²	D₃×C₉	1	1	yes	characteristic
40	C₃²	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
41	C₉	—	3	3	no	—
42	C₉	—	18	1	no	—
43	C₂×C₃	—	9	1	no	—
44	C₂×C₃	—	9	1	no	—
45	C₂×C₃	—	9	1	no	—
46	C₂×C₃	—	9	1	no	—
47	D₃	—	3	1	no	—
48	D₃	—	9	1	no	—
49	C₃	—	3	1	no	—
50	C₃	—	6	1	no	—
51	C₃	—	9	1	no	—
52	C₃	—	18	1	no	—
53	C₃	(C₃⋊D₃)⋊C₉	1	1	yes	characteristic
54	C₃	#4174	1	1	yes	characteristic
55	C₃	#4176	1	1	yes	characteristic
56	C₃	#4178	1	1	yes	characteristic
57	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, socle, hypercenter	C₃²	(C₃⋊D₃)⋊C₃
commutator, hypocenter	H(3,𝔽₃)	C₂×C₉
Frattini	C₃³	C₃×D₃
Fitting	H(3,𝔽₃)⋊C₉	C₂
prime radical	C₃×#272	C₃
cosocle	C₃×H(3,𝔽₃)	C₂×C₃
LCS	G ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₃²

Complements

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

N	H ≅ G/N	type
1. H(3,𝔽₃)⋊C₉	C₂	semidirect
5. C₃²×C₉	D₃	semidirect
10. #272	C₉	semidirect
16. H(3,𝔽₃)	C₂×C₉	semidirect

Maximal subgroups

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

subgroup	index
H(3,𝔽₃)⋊C₉	2
C₃×#272	3
C₃×D₃×C₉	3

Subgroups — #272⋊C9 #92179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #272⋊C₉ #92179