Subgroups — #49142049

Order 36544.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#32912700	C₂	1	1	yes	maximal, characteristic
2	#32912634	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₆×C₅₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#22603733	C₄	1	1	yes	characteristic
5	#22603717	C₄	1	1	yes	characteristic
6	#22603716	—	2	1	no	—
7	C₈×D₅₇₁	—	2	1	no	—
8	C₅₇₁⋊C₁₆	—	2	1	no	—
9	C₂×C₈×C₅₇₁	C₂²	1	1	yes	characteristic
10	C₁₆×C₅₇₁	—	2	1	no	—
11	Dic₁₁₄₂	C₈	1	1	yes	characteristic
12	D₂₂₈₄	C₈	1	1	yes	characteristic
13	C₂²⋊D₅₇₁	—	2	1	no	—
14	C₄×D₅₇₁	—	2	1	no	—
15	C₅₇₁⋊C₈	—	2	1	no	—
16	C₂×C₄×C₅₇₁	C₂×C₄	1	1	yes	characteristic
17	C₈×C₅₇₁	D₄	1	1	yes	characteristic
18	C₈×C₅₇₁	D₄	1	1	yes	characteristic
19	C₂²×C₅₇₁	M₁₆	1	1	yes	characteristic
20	C₂×D₅₇₁	—	2	1	no	—
21	C₄×C₅₇₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₅₇₁	C₂×C₈	1	1	yes	characteristic
23	Dic₅₇₁	—	2	1	no	—
24	C₂×C₅₇₁	—	2	1	no	—
25	C₂×C₅₇₁	C₂²⋊C₈	1	1	yes	characteristic
26	D₅₇₁	—	4	1	no	—
27	C₅₇₁	#350	1	1	yes	characteristic, complemented, Sylow
28	#350	—	571	1	no	maximal, Sylow
29	#131	—	571	1	no	—
30	M₃₂	—	571	1	no	—
31	C₂×C₁₆	D₅₇₁	1	1	yes	characteristic, complemented
32	#41	—	571	1	no	—
33	M₁₆	—	571	1	no	—
34	M₁₆	—	1142	1	no	—
35	C₂×C₈	—	1142	1	no	—
36	C₂×C₈	C₂×D₅₇₁	1	1	yes	characteristic
37	C₁₆	—	2	1	no	—
38	C₁₆	—	1142	1	no	—
39	Q₈	—	571	1	no	—
40	D₄	—	571	1	no	—
41	D₄	—	1142	1	no	—
42	C₂×C₄	—	1142	1	no	—
43	C₂×C₄	C₄×D₅₇₁	1	1	yes	characteristic
44	C₈	—	1142	1	no	—
45	C₈	C₂²⋊D₅₇₁	1	1	yes	characteristic
46	C₈	D₂₂₈₄	1	1	yes	characteristic
47	C₂²	—	1142	1	no	—
48	C₂²	#22603716	1	1	yes	characteristic
49	C₄	—	1142	1	no	—
50	C₄	(C₂×D₅₇₁)⋊C₄	1	1	yes	characteristic
51	C₄	C₈×D₅₇₁	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	2284	1	no	—
54	C₂	(C₂×D₅₇₁)⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₂₂₈₄
commutator	C₄×C₅₇₁	C₂×C₈
Frattini	C₂×C₈	C₂×D₅₇₁
Fitting	C₂×C₁₆×C₅₇₁	C₂
socle	C₂×C₅₇₁	C₂²⋊C₈
prime radical	#22603733	C₄
cosocle	C₂×C₈×C₅₇₁	C₂²
hypercenter	C₂×C₁₆	D₅₇₁
hypocenter	C₅₇₁	#350
LCS	G ▷ C₄×C₅₇₁ ▷ C₂×C₅₇₁ ▷ C₅₇₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. #32912634	C₂	semidirect
3. C₂×C₁₆×C₅₇₁	C₂	semidirect
27. C₅₇₁	#350	semidirect
31. C₂×C₁₆	D₅₇₁	semidirect

Maximal subgroups

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

subgroup	index
#32912700	2
#32912634	2
C₂×C₁₆×C₅₇₁	2
#350	571