Subgroups — C₃×#984 #64254

Order 288.

77 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃×#226	C₂	1	2	yes	maximal, complemented
3	#984	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃×#137	—	3	1	no	maximal
5	C₃×Dic₆	—	4	1	no	maximal
6	C₃×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic
7	C₃×#41	D₃	1	1	yes	characteristic
8	C₂×C₃×Q₈	—	3	1	no	—
9	#41⋊C₃	—	2	1	no	—
10	#41⋊C₃	C₂×C₃	1	1	yes	characteristic
11	#226	C₂×C₃	1	2	yes	complemented
12	C₃×Q₁₆	—	3	2	no	—
13	C₃×SD₁₆	—	3	2	no	—
14	C₃×M₁₆	—	3	1	no	—
15	C₃²×C₄	—	4	1	no	—
16	C₃×Dic₃	—	4	2	no	—
17	#137	—	3	1	no	Sylow
18	C₃×Q₈	—	3	2	no	—
19	C₃×Q₈	—	6	1	no	—
20	C₃×Q₈	C₂×D₃	1	1	yes	characteristic
21	C₃×D₄	—	3	1	no	—
22	C₂×C₃×C₄	—	3	1	no	—
23	C₂×C₃×C₄	—	6	1	no	—
24	Dic₆	—	4	1	no	—
25	SL(2,𝔽₃)	—	2	1	no	—
26	SL(2,𝔽₃)	C₂²×C₃	1	1	yes	characteristic
27	C₃×C₈	—	3	2	no	—
28	C₂×C₃²	—	4	1	no	—
29	#41	C₃×D₃	1	1	yes	characteristic
30	C₂×Q₈	—	3	1	no	—
31	Q₁₆	—	3	2	no	—
32	SD₁₆	—	3	2	no	—
33	M₁₆	—	3	1	no	—
34	C₂²×C₃	—	3	1	no	—
35	C₃×C₄	—	3	1	no	—
36	C₃×C₄	—	4	1	no	—
37	C₃×C₄	—	6	2	no	—
38	C₃×C₄	—	8	1	no	—
39	C₃×C₄	S₄	1	1	yes	characteristic
40	Dic₃	—	4	2	no	—
41	C₃²	—	4	1	no	Sylow
42	Q₈	—	3	2	no	—
43	Q₈	—	6	1	no	—
44	Q₈	C₂×C₃×D₃	1	1	yes	characteristic
45	D₄	—	3	1	no	—
46	C₂×C₄	—	3	1	no	—
47	C₂×C₄	—	6	1	no	—
48	C₈	—	3	2	no	—
49	C₂×C₃	—	4	1	no	—
50	C₂×C₃	—	6	1	no	—
51	C₂×C₃	—	8	1	no	—
52	C₂×C₃	C₂×S₄	1	1	yes	characteristic
53	C₂²	—	3	1	no	—
54	C₄	—	3	1	no	—
55	C₄	—	6	2	no	—
56	C₄	C₃×S₄	1	1	yes	characteristic
57	C₃	—	4	1	no	—
58	C₃	—	8	1	no	—
59	C₃	#984	1	1	yes	characteristic, direct product factor
60	C₂	—	6	1	no	—
61	C₂	C₂×C₃×S₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	C₂×S₄
commutator, cosocle, hypocenter	SL(2,𝔽₃)	C₂²×C₃
Frattini	C₂	C₂×C₃×S₄
Fitting	C₃×#41	D₃
prime radical	C₃×#41⋊C₃	C₂
hypercenter	C₃×C₄	S₄
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
2. C₃×#226	C₂	semidirect
3. #984	C₃	direct (N × H)
11. #226	C₂×C₃	semidirect
59. C₃	#984	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×#41⋊C₃	2
C₃×#226	2
#984	3
C₃×#137	3
C₃×Dic₆	4

Subgroups — C3×#984 #64254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#984 #64254