Subgroups — C₂×C₉×H(3,𝔽₃) #92349

Order 486.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
3	C₂×C₃²×C₉	C₃	1	4	yes	maximal, complemented
4	C₂×C₃²⋊C₉	C₃	1	8	yes	maximal, complemented
5	C₃×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
6	C₃²×C₉	C₂×C₃	1	4	yes	complemented
7	C₃²⋊C₉	C₂×C₃	1	8	yes	complemented
8	C₂×C₃³	C₃²	1	4	yes	—
9	C₂×H(3,𝔽₃)	C₉	1	9	yes	direct product factor
10	C₂×C₃×C₉	—	3	12	no	—
11	C₂×C₃×C₉	C₃²	1	8	yes	—
12	C₂×C₃×C₉	C₃²	1	1	yes	characteristic
13	C₃³	C₂×C₃²	1	4	yes	—
14	H(3,𝔽₃)	C₂×C₉	1	9	yes	direct product factor
15	C₃×C₉	—	3	12	no	—
16	C₃×C₉	C₂×C₃²	1	8	yes	—
17	C₃×C₉	C₂×C₃²	1	1	yes	characteristic
18	C₂×C₃²	—	3	4	no	—
19	C₂×C₃²	—	3	8	no	—
20	C₂×C₃²	C₃×C₉	1	12	yes	complemented
21	C₂×C₃²	C₃³	1	1	yes	characteristic
22	C₂×C₉	—	3	8	no	—
23	C₂×C₉	H(3,𝔽₃)	1	3	yes	direct product factor
24	C₃²	—	3	4	no	—
25	C₃²	—	3	8	no	—
26	C₃²	C₂×C₃×C₉	1	12	yes	complemented
27	C₃²	C₂×C₃³	1	1	yes	characteristic
28	C₉	—	3	8	no	—
29	C₉	C₂×H(3,𝔽₃)	1	3	yes	direct product factor
30	C₂×C₃	—	3	12	no	—
31	C₂×C₃	C₃²×C₉	1	1	yes	characteristic
32	C₂×C₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
33	C₂×C₃	#737	1	2	yes	—
34	C₃	—	3	12	no	—
35	C₃	C₂×C₃²×C₉	1	1	yes	characteristic
36	C₃	C₂×C₃×H(3,𝔽₃)	1	1	yes	characteristic
37	C₃	C₂×#737	1	2	yes	—
38	C₂	C₉×H(3,𝔽₃)	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	C₂×C₃×C₉	C₃²
commutator	C₃	C₂×C₃²×C₉
Frattini, cosocle	C₃²	C₂×C₃³
socle	C₂×C₃²	C₃³
prime radical	C₂×C₃×H(3,𝔽₃)	C₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×H(3,𝔽₃)	C₂	direct (N × H)
3. C₂×C₃²×C₉	C₃	semidirect
4. C₂×C₃²⋊C₉	C₃	semidirect
6. C₃²×C₉	C₂×C₃	semidirect
7. C₃²⋊C₉	C₂×C₃	semidirect
9. C₂×H(3,𝔽₃)	C₉	direct (N × H)
14. H(3,𝔽₃)	C₂×C₉	direct (N × H)
20. C₂×C₃²	C₃×C₉	semidirect
23. C₂×C₉	H(3,𝔽₃)	direct (N × H)
26. C₃²	C₂×C₃×C₉	semidirect
29. C₉	C₂×H(3,𝔽₃)	direct (N × H)
38. C₂	C₉×H(3,𝔽₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×H(3,𝔽₃)	2
C₂×C₃×H(3,𝔽₃)	3
C₂×C₃²×C₉	3
C₂×C₃²⋊C₉	3

Subgroups — C2×C9×H(3,𝔽3) #92349

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×H(3,𝔽₃) #92349