Subgroups — #568⋊C₃ #5454

Order 192.

73 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#131⋊C₃	C₂	1	2	yes	maximal, complemented
3	#568	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
4	#41⋊C₃	C₄	1	1	yes	characteristic
5	#41⋊C₃	C₂²	1	1	yes	characteristic
6	C₂×SL(2,𝔽₃)	C₄	1	1	yes	characteristic
7	C₃×M₁₆	—	4	1	no	maximal
8	C₂×#41	C₂×C₃	1	1	yes	characteristic
9	#131	—	3	2	no	—
10	#131	C₂×C₃	1	2	yes	complemented
11	C₂×M₁₆	—	3	1	no	—
12	C₂×M₁₆	—	3	1	no	—
13	C₂×C₃×C₄	—	4	1	no	—
14	SL(2,𝔽₃)	C₂×C₄	1	1	yes	characteristic
15	C₃×C₈	—	4	2	no	—
16	#41	—	3	1	no	—
17	#41	—	3	1	no	—
18	#41	C₃×C₄	1	1	yes	characteristic
19	#41	C₂²×C₃	1	1	yes	characteristic
20	C₂×Q₈	C₃×C₄	1	1	yes	characteristic
21	C₂×D₄	—	3	1	no	—
22	C₂²×C₄	—	3	1	no	—
23	M₁₆	—	3	1	no	—
24	M₁₆	—	3	2	no	—
25	M₁₆	—	3	2	no	—
26	M₁₆	A₄	1	1	yes	characteristic
27	C₂×C₈	—	3	2	no	—
28	C₂×C₈	—	3	2	no	—
29	C₂²×C₃	—	4	1	no	—
30	C₃×C₄	—	4	1	no	—
31	C₃×C₄	—	4	1	no	—
32	C₂³	—	3	1	no	—
33	Q₈	—	3	1	no	—
34	Q₈	C₂×C₃×C₄	1	1	yes	characteristic
35	D₄	—	3	1	no	—
36	D₄	—	3	1	no	—
37	D₄	—	3	2	no	—
38	C₂×C₄	—	3	1	no	—
39	C₂×C₄	—	3	1	no	—
40	C₂×C₄	—	3	1	no	—
41	C₂×C₄	—	3	1	no	—
42	C₂×C₄	—	3	1	no	—
43	C₂×C₄	C₂×A₄	1	1	yes	characteristic
44	C₈	—	3	2	no	—
45	C₈	C₂×A₄	1	2	yes	—
46	C₂×C₃	—	4	1	no	—
47	C₂×C₃	—	8	1	no	—
48	C₂²	—	3	1	no	—
49	C₂²	—	3	1	no	—
50	C₂²	—	12	1	no	—
51	C₂²	C₄×A₄	1	1	yes	characteristic
52	C₄	—	3	1	no	—
53	C₄	—	3	1	no	—
54	C₄	C₄×A₄	1	1	yes	characteristic
55	C₄	C₂²×A₄	1	1	yes	characteristic
56	C₃	—	4	1	no	Sylow
57	C₂	—	2	1	no	—
58	C₂	—	6	1	no	—
59	C₂	—	6	1	no	—
60	C₂	C₂×C₄×A₄	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×A₄
commutator, hypocenter	Q₈	C₂×C₃×C₄
Fitting	#568	C₃
socle	C₂	C₂×C₄×A₄
prime radical	C₂×#41⋊C₃	C₂
cosocle	#41	C₂²×C₃
hypercenter	M₁₆	A₄
LCS	G ▷ Q₈
UCS	C₁ ◁ C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
2. #131⋊C₃	C₂	semidirect
3. #568	C₃	semidirect
10. #131	C₂×C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41⋊C₃	2
#131⋊C₃	2
#568	3
C₃×M₁₆	4

Subgroups — #568⋊C3 #5454

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #568⋊C₃ #5454