Subgroups — C₃×C₃⋊#226 #88969

Order 432.

97 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#226	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×#226	—	3	3	no	maximal
4	C₃×#216	—	3	1	no	maximal
5	C₃×C₃⋊Dic₃	—	4	1	no	maximal
6	C₃²×Q₈	D₃	1	1	yes	characteristic
7	C₃×Dic₆	—	3	1	no	—
8	C₃×SL(2,𝔽₃)	—	2	1	no	—
9	C₃×SL(2,𝔽₃)	—	2	3	no	—
10	C₃×SL(2,𝔽₃)	D₃	1	3	yes	—
11	C₃×SL(2,𝔽₃)	C₂×C₃	1	1	yes	characteristic
12	C₃×C₃⋊C₈	—	3	1	no	—
13	C₂×C₃³	—	4	1	no	—
14	#226	—	3	3	no	—
15	C₃×Q₁₆	—	9	1	no	—
16	#216	—	3	1	no	—
17	C₃²×C₄	—	3	1	no	—
18	C₃⋊Dic₃	—	4	1	no	—
19	C₃×Dic₃	—	6	1	no	—
20	C₃×Dic₃	—	12	3	no	—
21	C₃³	—	4	1	no	Sylow
22	C₃×Q₈	—	2	1	no	—
23	C₃×Q₈	—	9	1	no	—
24	C₃×Q₈	C₃×D₃	1	1	yes	characteristic
25	C₃×Q₈	C₃⋊D₃	1	1	yes	characteristic
26	Dic₆	—	3	1	no	—
27	SL(2,𝔽₃)	—	2	3	no	—
28	SL(2,𝔽₃)	C₃×D₃	1	3	yes	—
29	C₃×C₈	—	9	1	no	—
30	C₃⋊C₈	—	3	1	no	—
31	C₂×C₃²	—	4	1	no	—
32	C₂×C₃²	—	4	3	no	—
33	C₂×C₃²	—	8	3	no	—
34	C₂×C₃²	—	8	1	no	—
35	C₂×C₃²	S₄	1	1	yes	characteristic
36	Q₁₆	—	9	1	no	Sylow
37	C₃×C₄	—	3	1	no	—
38	C₃×C₄	—	3	1	no	—
39	C₃×C₄	—	6	1	no	—
40	C₃×C₄	—	18	1	no	—
41	Dic₃	—	6	1	no	—
42	Dic₃	—	12	3	no	—
43	C₃²	—	4	1	no	—
44	C₃²	—	4	3	no	—
45	C₃²	—	8	3	no	—
46	C₃²	—	8	1	no	—
47	C₃²	#226	1	1	yes	characteristic, complemented
48	Q₈	—	9	1	no	—
49	Q₈	C₃×C₃⋊D₃	1	1	yes	characteristic
50	C₈	—	9	1	no	—
51	C₂×C₃	—	2	1	no	—
52	C₂×C₃	—	4	3	no	—
53	C₂×C₃	—	8	3	no	—
54	C₂×C₃	C₃×S₄	1	1	yes	characteristic
55	C₂×C₃	C₃⋊S₄	1	1	yes	characteristic
56	C₄	—	3	1	no	—
57	C₄	—	18	1	no	—
58	C₃	—	2	1	no	—
59	C₃	—	4	3	no	—
60	C₃	—	8	3	no	—
61	C₃	C₃×#226	1	1	yes	characteristic, complemented
62	C₃	C₃⋊#226	1	1	yes	characteristic, direct product factor
63	C₂	C₃×C₃⋊S₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	C₃⋊S₄
commutator, cosocle, hypocenter	C₃×SL(2,𝔽₃)	C₂×C₃
Frattini	C₂	C₃×C₃⋊S₄
Fitting	C₃²×Q₈	D₃
socle	C₂×C₃²	S₄
prime radical	C₃²×SL(2,𝔽₃)	C₂
LCS	G ▷ C₃×SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. C₃⋊#226	C₃	direct (N × H)
47. C₃²	#226	semidirect
61. C₃	C₃×#226	semidirect
62. C₃	C₃⋊#226	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×SL(2,𝔽₃)	2
C₃⋊#226	3
C₃×#226	3
C₃×#216	3
C₃×C₃⋊Dic₃	4

Subgroups — C3×C3⋊#226 #88969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃⋊#226 #88969