Subgroups — C₃×#822 #63608

Order 288.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×#208	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₃×#108	—	3	1	no	maximal
5	#822	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
7	C₃²×C₈	—	2	1	no	—
8	C₃×C₃⋊C₈	—	2	1	no	—
9	C₃×C₃⋊C₈	C₄	1	2	yes	—
10	C₃×M₁₆	—	2	1	no	—
11	C₃×M₁₆	—	3	1	no	—
12	C₃×M₁₆	D₃	1	1	yes	characteristic
13	C₃×M₁₆	C₂×C₃	1	1	yes	characteristic
14	C₂×C₃×C₈	—	3	1	no	—
15	#208	C₂×C₃	1	1	yes	characteristic
16	C₂×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic
17	C₂²×C₃²	Q₈	1	1	yes	characteristic
18	C₃²×C₄	C₂×C₄	1	1	yes	characteristic
19	C₃²×C₄	D₄	1	1	yes	characteristic
20	#108	—	3	1	no	Sylow
21	C₂×C₃×C₄	—	2	1	no	—
22	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
23	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
24	C₃×C₈	—	2	2	no	—
25	C₃×C₈	—	2	1	no	—
26	C₃×C₈	—	2	1	no	—
27	C₃×C₈	—	3	2	no	—
28	C₃×C₈	—	6	1	no	—
29	C₃⋊C₈	—	2	1	no	—
30	C₃⋊C₈	C₃×C₄	1	2	yes	—
31	C₂×C₃²	—	2	1	no	—
32	C₂×C₃²	C₄⋊C₄	1	1	yes	characteristic
33	M₁₆	—	3	1	no	—
34	M₁₆	C₃×D₃	1	1	yes	characteristic
35	C₂×C₈	—	3	1	no	—
36	C₂²×C₃	—	2	1	no	—
37	C₂²×C₃	Dic₆	1	1	yes	characteristic
38	C₂²×C₃	C₃×Q₈	1	1	yes	characteristic
39	C₃×C₄	—	2	1	no	—
40	C₃×C₄	—	2	1	no	—
41	C₃×C₄	C₄×D₃	1	1	yes	characteristic
42	C₃×C₄	#67	1	1	yes	characteristic
43	C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
44	C₃×C₄	C₃×D₄	1	1	yes	characteristic
45	C₃²	#108	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₄	C₂×C₃×D₃	1	1	yes	characteristic
47	C₈	—	2	1	no	—
48	C₈	—	3	2	no	—
49	C₈	—	6	1	no	—
50	C₂×C₃	—	2	1	no	—
51	C₂×C₃	—	2	1	no	—
52	C₂×C₃	—	2	1	no	—
53	C₂×C₃	—	4	1	no	—
54	C₂×C₃	Dic₃⋊C₄	1	1	yes	characteristic
55	C₂×C₃	C₃×C₄⋊C₄	1	1	yes	characteristic
56	C₂²	C₃×Dic₆	1	1	yes	characteristic
57	C₄	C₃×C₄×D₃	1	1	yes	characteristic
58	C₄	C₃×#67	1	1	yes	characteristic
59	C₃	—	2	1	no	—
60	C₃	#822	1	1	yes	characteristic, direct product factor
61	C₃	C₃×#108	1	1	yes	characteristic, complemented
62	C₂	—	2	1	no	—
63	C₂	C₃×Dic₃⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	#67
commutator	C₃×C₄	C₂×C₃×C₄
Frattini	C₂×C₄	C₂×C₃×D₃
Fitting	C₃²×M₁₆	C₂
socle	C₂×C₃²	C₄⋊C₄
prime radical	C₂²×C₃²	Q₈
cosocle	C₂×C₃×C₄	C₂²×C₃
hypercenter	C₃×M₁₆	D₃
hypocenter	C₃	C₃×#108
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₄ ◁ C₃×M₁₆

Complements

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

N	H ≅ G/N	type
5. #822	C₃	direct (N × H)
45. C₃²	#108	semidirect
60. C₃	#822	direct (N × H)
61. 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
C₃²×M₁₆	2
C₃×#208	2
C₂×C₃×C₃⋊C₈	2
C₃×#108	3
#822	3

Subgroups — C3×#822 #63608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#822 #63608