Subgroups — C₃×#819 #63605

Order 288.

71 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₈	C₂	1	1	yes	maximal, characteristic
2	C₃×#208	C₂	1	2	yes	maximal
3	C₃×#108	—	3	1	no	maximal
4	#819	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
6	C₃²×C₈	C₄	1	2	yes	—
7	C₃×C₃⋊C₈	—	2	2	no	—
8	C₃×M₁₆	—	3	2	no	—
9	C₂×C₃×C₈	—	2	1	no	—
10	C₂×C₃×C₈	D₃	1	1	yes	characteristic
11	C₂×C₃×C₈	C₂×C₃	1	1	yes	characteristic
12	#208	C₂×C₃	1	2	yes	—
13	C₂²×C₃²	Q₈	1	1	yes	characteristic
14	C₃²×C₄	C₂×C₄	1	1	yes	characteristic
15	C₃²×C₄	D₄	1	1	yes	characteristic
16	#108	—	3	1	no	Sylow
17	C₂×C₃×C₄	—	2	1	no	—
18	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
19	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
20	C₃×C₈	—	2	2	no	—
21	C₃×C₈	—	6	2	no	—
22	C₃×C₈	Dic₃	1	2	yes	—
23	C₃×C₈	C₃×C₄	1	2	yes	—
24	C₃⋊C₈	—	2	2	no	—
25	C₂×C₃²	—	2	1	no	—
26	C₂×C₃²	C₄⋊C₄	1	1	yes	characteristic
27	M₁₆	—	3	2	no	—
28	C₂×C₈	C₃×D₃	1	1	yes	characteristic
29	C₂²×C₃	—	2	1	no	—
30	C₂²×C₃	Dic₆	1	1	yes	characteristic
31	C₂²×C₃	C₃×Q₈	1	1	yes	characteristic
32	C₃×C₄	—	2	1	no	—
33	C₃×C₄	—	2	1	no	—
34	C₃×C₄	D₁₂	1	1	yes	characteristic
35	C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
36	C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
37	C₃×C₄	C₃×D₄	1	1	yes	characteristic
38	C₃²	#108	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₄	C₂×C₃×D₃	1	1	yes	characteristic
40	C₈	—	6	2	no	—
41	C₈	C₃×Dic₃	1	2	yes	—
42	C₂×C₃	—	2	2	no	—
43	C₂×C₃	—	2	1	no	—
44	C₂×C₃	—	2	1	no	—
45	C₂×C₃	—	2	1	no	—
46	C₂×C₃	C₄⋊Dic₃	1	1	yes	characteristic
47	C₂×C₃	C₃×C₄⋊C₄	1	1	yes	characteristic
48	C₂²	C₃×Dic₆	1	1	yes	characteristic
49	C₄	C₃×D₁₂	1	1	yes	characteristic
50	C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
51	C₃	—	2	1	no	—
52	C₃	#819	1	1	yes	characteristic, direct product factor
53	C₃	C₃×#108	1	1	yes	characteristic, complemented
54	C₂	—	2	1	no	—
55	C₂	C₃×C₄⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	D₁₂
commutator	C₃×C₄	C₂×C₃×C₄
Frattini	C₂×C₄	C₂×C₃×D₃
Fitting	C₂×C₃²×C₈	C₂
socle	C₂×C₃²	C₄⋊C₄
prime radical	C₂²×C₃²	Q₈
cosocle	C₂×C₃×C₄	C₂²×C₃
hypercenter	C₂×C₃×C₈	D₃
hypocenter	C₃	C₃×#108
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈

Complements

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

N	H ≅ G/N	type
4. #819	C₃	direct (N × H)
38. C₃²	#108	semidirect
52. C₃	#819	direct (N × H)
53. C₃	C₃×#108	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₈	2
C₃×#208	2
C₃×#108	3
#819	3

Subgroups — C3×#819 #63605

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#819 #63605