Subgroups — C₃×GU(2,𝔽₃) #63752

Order 288.

53 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	GU(2,𝔽₃)	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×#104	—	3	1	no	maximal
4	C₃×SL(2,𝔽₃)	C₄	1	1	yes	characteristic, complemented
5	C₃×C₃⋊C₈	—	4	1	no	maximal
6	C₃×#41	D₃	1	1	yes	characteristic
7	#41⋊C₃	—	2	1	no	—
8	#41⋊C₃	C₂×C₃	1	1	yes	characteristic
9	C₃×M₁₆	—	3	1	no	—
10	C₃×C₄²	—	3	1	no	—
11	C₃²×C₄	—	4	1	no	—
12	#104	—	3	1	no	Sylow
13	C₃×Q₈	Dic₃	1	1	yes	characteristic
14	C₃×D₄	—	3	1	no	—
15	C₂×C₃×C₄	—	3	1	no	—
16	C₂×C₃×C₄	—	6	1	no	—
17	SL(2,𝔽₃)	—	2	1	no	—
18	SL(2,𝔽₃)	C₃×C₄	1	1	yes	characteristic, complemented
19	C₃×C₈	—	6	1	no	—
20	C₃⋊C₈	—	4	1	no	—
21	C₂×C₃²	—	4	1	no	—
22	#41	C₃×D₃	1	1	yes	characteristic
23	M₁₆	—	3	1	no	—
24	C₄²	—	3	1	no	—
25	C₂²×C₃	—	3	1	no	—
26	C₃×C₄	—	3	1	no	—
27	C₃×C₄	—	4	1	no	—
28	C₃×C₄	—	6	2	no	—
29	C₃×C₄	—	8	1	no	—
30	C₃×C₄	S₄	1	1	yes	characteristic
31	C₃²	—	4	1	no	Sylow
32	Q₈	C₃×Dic₃	1	1	yes	characteristic
33	D₄	—	3	1	no	—
34	C₂×C₄	—	3	1	no	—
35	C₂×C₄	—	6	1	no	—
36	C₈	—	6	1	no	—
37	C₂×C₃	—	4	1	no	—
38	C₂×C₃	—	6	1	no	—
39	C₂×C₃	—	8	1	no	—
40	C₂×C₃	SL(2,ℤ/4)	1	1	yes	characteristic
41	C₂²	—	3	1	no	—
42	C₄	—	3	1	no	—
43	C₄	—	6	2	no	—
44	C₄	C₃×S₄	1	1	yes	characteristic
45	C₃	—	4	1	no	—
46	C₃	—	8	1	no	—
47	C₃	GU(2,𝔽₃)	1	1	yes	characteristic, direct product factor
48	C₂	—	6	1	no	—
49	C₂	C₃×SL(2,ℤ/4)	1	1	yes	characteristic

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

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