Subgroups — #577⋊C₃ #5459

Order 192.

73 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	2₋¹⁺⁴⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#994	C₂	1	1	yes	maximal, characteristic, complemented
3	#131⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#577	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
5	#41⋊C₃	—	2	1	no	—
6	#41⋊C₃	C₂²	1	1	yes	characteristic
7	C₂×SL(2,𝔽₃)	—	2	1	no	—
8	C₃×SD₁₆	—	4	1	no	maximal
9	2₋¹⁺⁴	C₂×C₃	1	1	yes	characteristic
10	H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic, complemented
11	#137	—	3	1	no	—
12	AGL(1,ℤ/8)	—	3	1	no	—
13	#135	—	3	1	no	—
14	C₂×SD₁₆	—	3	1	no	—
15	#131	C₂×C₃	1	1	yes	characteristic, complemented
16	C₃×Q₈	—	4	1	no	—
17	C₃×D₄	—	4	1	no	—
18	SL(2,𝔽₃)	D₄	1	1	yes	characteristic
19	C₃×C₈	—	4	1	no	—
20	#41	—	2	1	no	—
21	#41	—	3	1	no	—
22	#41	—	3	1	no	—
23	#41	—	6	1	no	—
24	#41	C₂²×C₃	1	1	yes	characteristic
25	C₂×Q₈	—	2	1	no	—
26	C₂×Q₈	—	3	1	no	—
27	C₂×D₄	—	3	1	no	—
28	C₂×D₄	—	6	1	no	—
29	Q₁₆	—	3	1	no	—
30	SD₁₆	—	3	2	no	—
31	SD₁₆	—	3	1	no	—
32	SD₁₆	A₄	1	1	yes	characteristic
33	D₈	—	3	1	no	—
34	M₁₆	—	3	1	no	—
35	C₂×C₈	—	3	1	no	—
36	C₂²×C₃	—	8	1	no	—
37	C₃×C₄	—	4	1	no	—
38	C₃×C₄	—	8	1	no	—
39	C₂³	—	6	1	no	—
40	Q₈	—	3	1	no	—
41	Q₈	—	6	1	no	—
42	Q₈	C₃×D₄	1	1	yes	characteristic
43	Q₈	C₂×A₄	1	1	yes	characteristic
44	D₄	—	3	1	no	—
45	D₄	—	3	1	no	—
46	D₄	—	6	1	no	—
47	D₄	—	6	1	no	—
48	D₄	—	6	1	no	—
49	D₄	C₂×A₄	1	1	yes	characteristic
50	C₂×C₄	—	3	1	no	—
51	C₂×C₄	—	6	1	no	—
52	C₂×C₄	—	6	1	no	—
53	C₂×C₄	—	6	1	no	—
54	C₈	—	3	1	no	—
55	C₈	C₂×A₄	1	1	yes	characteristic
56	C₂×C₃	—	4	1	no	—
57	C₂×C₃	—	16	1	no	—
58	C₂²	—	2	1	no	—
59	C₂²	—	3	1	no	—
60	C₂²	—	6	1	no	—
61	C₂²	—	24	1	no	—
62	C₄	—	2	1	no	—
63	C₄	—	3	1	no	—
64	C₄	—	6	1	no	—
65	C₄	C₂²×A₄	1	1	yes	characteristic
66	C₃	—	4	1	no	Sylow
67	C₂	—	4	1	no	—
68	C₂	—	6	1	no	—
69	C₂	—	12	1	no	—
70	C₂	D₄×A₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	D₄×A₄
commutator, cosocle	#41	C₂²×C₃
Frattini	C₄	C₂²×A₄
Fitting	#577	C₃
hypercenter	SD₁₆	A₄
hypocenter	Q₈	C₃×D₄
LCS	G ▷ #41 ▷ Q₈
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

Complements

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

N	H ≅ G/N	type
1. 2₋¹⁺⁴⋊C₃	C₂	semidirect
2. #994	C₂	semidirect
3. #131⋊C₃	C₂	semidirect
4. #577	C₃	semidirect
10. H(5,𝔽₂)	C₂×C₃	semidirect
15. #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
2₋¹⁺⁴⋊C₃	2
#994	2
#131⋊C₃	2
#577	3
C₃×SD₁₆	4

Subgroups — #577⋊C3 #5459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #577⋊C₃ #5459