Subgroups — #49142305

Order 36544.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22603716	C₂	1	1	yes	maximal, characteristic
2	#32912652	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×D₅₇₁	C₂	1	1	yes	maximal, characteristic
4	#32912628	C₂	1	1	yes	maximal, characteristic, complemented
5	#32912627	C₂	1	1	yes	maximal, characteristic, complemented
6	#32912625	C₂	1	1	yes	maximal, characteristic, complemented
7	#106×C₅₇₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₅₇₁	—	2	1	no	—
9	C₂×C₄×D₅₇₁	C₂²	1	1	yes	characteristic
10	#22603716	C₄	1	4	yes	complemented
11	C₂×C₅₇₁⋊C₈	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₅₇₁	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₅₇₁	C₂²	1	1	yes	characteristic
14	Dic₅₇₁⋊C₄	—	2	1	no	—
15	(C₂×D₅₇₁)⋊C₄	—	2	1	no	—
16	C₄×Dic₅₇₁	—	2	1	no	—
17	C₂×C₈×C₅₇₁	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₅₇₁	C₂²	1	1	yes	characteristic
19	C₄⋊C₄×C₅₇₁	C₂²	1	1	yes	characteristic
20	C₂²×D₅₇₁	D₄	1	1	yes	characteristic
21	C₂×Dic₅₇₁	—	2	1	no	—
22	C₂×Dic₅₇₁	—	2	1	no	—
23	C₂×Dic₅₇₁	D₄	1	1	yes	characteristic
24	C₄×D₅₇₁	—	4	2	no	—
25	C₄×D₅₇₁	C₂×C₄	1	2	yes	—
26	C₄×D₅₇₁	Q₈	1	2	yes	—
27	C₅₇₁⋊C₈	C₂×C₄	1	2	yes	complemented
28	C₂×C₄×C₅₇₁	—	2	1	no	—
29	C₂×C₄×C₅₇₁	—	2	1	no	—
30	C₂×C₄×C₅₇₁	C₂³	1	1	yes	characteristic
31	C₈×C₅₇₁	C₂×C₄	1	2	yes	complemented
32	C₂²×C₅₇₁	C₂×D₄	1	1	yes	characteristic
33	C₂×D₅₇₁	—	2	1	no	—
34	C₂×D₅₇₁	—	2	1	no	—
35	C₂×D₅₇₁	C₄⋊C₄	1	2	yes	—
36	C₄×C₅₇₁	—	4	1	no	—
37	C₄×C₅₇₁	—	4	1	no	—
38	C₄×C₅₇₁	C₂²×C₄	1	1	yes	characteristic
39	C₄×C₅₇₁	C₂×Q₈	1	1	yes	characteristic
40	Dic₅₇₁	—	4	1	no	—
41	Dic₅₇₁	—	4	1	no	—
42	Dic₅₇₁	C₄⋊C₄	1	2	yes	—
43	C₂×C₅₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₅₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
45	C₂×C₅₇₁	#137	1	1	yes	characteristic
46	D₅₇₁	—	2	2	no	—
47	C₅₇₁	#428	1	1	yes	characteristic, complemented, Sylow
48	#428	—	571	1	no	maximal, Sylow
49	C₂×M₁₆	—	571	1	no	—
50	#117	—	571	1	no	—
51	C₂×C₄⋊C₄	—	571	1	no	—
52	#107	—	571	1	no	—
53	#107	—	571	1	no	—
54	#106	—	571	1	no	—
55	#106	D₅₇₁	1	1	yes	characteristic, complemented
56	C₂²×C₄	—	571	1	no	—
57	C₂²×C₄	—	1142	1	no	—
58	M₁₆	—	571	4	no	—
59	C₂×C₈	—	571	1	no	—
60	C₂×C₈	C₂×D₅₇₁	1	1	yes	characteristic
61	C₄⋊C₄	—	571	1	no	—
62	C₄⋊C₄	—	571	1	no	—
63	C₄⋊C₄	—	1142	1	no	—
64	C₄⋊C₄	C₂×D₅₇₁	1	1	yes	characteristic
65	C₄⋊C₄	C₂×D₅₇₁	1	1	yes	characteristic
66	C₂²⋊C₄	—	1142	1	no	—
67	C₄²	—	1142	1	no	—
68	C₂³	—	571	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	571	1	no	—
72	C₂×C₄	—	571	2	no	—
73	C₂×C₄	—	571	2	no	—
74	C₂×C₄	—	1142	1	no	—
75	C₂×C₄	—	1142	1	no	—
76	C₂×C₄	—	2284	2	no	—
77	C₂×C₄	C₂²×D₅₇₁	1	1	yes	characteristic
78	C₈	—	571	2	no	—
79	C₈	C₄×D₅₇₁	1	2	yes	complemented
80	C₂²	—	571	2	no	—
81	C₂²	—	1142	1	no	—
82	C₂²	—	1142	1	no	—
83	C₂²	D₄×D₅₇₁	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	571	2	no	—
87	C₄	—	2284	1	no	—
88	C₄	—	2284	1	no	—
89	C₄	C₂×C₄×D₅₇₁	1	1	yes	characteristic
90	C₄	Q₈×D₅₇₁	1	1	yes	characteristic
91	C₂	—	1142	2	no	—
92	C₂	C₄⋊C₄×D₅₇₁	1	1	yes	characteristic
93	C₂	#32912721	1	1	yes	characteristic
94	C₂	#32912723	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₅₇₁
commutator	C₄×C₅₇₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₅₇₁
Fitting	#106×C₅₇₁	C₂
socle	C₂²×C₅₇₁	C₂×D₄
prime radical	C₂²×D₅₇₁	D₄
cosocle	C₂×C₄×C₅₇₁	C₂³
hypercenter	#106	D₅₇₁
hypocenter	C₅₇₁	#428
LCS	G ▷ C₄×C₅₇₁ ▷ C₂×C₅₇₁ ▷ C₅₇₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
4. #32912628	C₂	semidirect
5. #32912627	C₂	semidirect
6. #32912625	C₂	semidirect
7. #106×C₅₇₁	C₂	semidirect
10. #22603716	C₄	semidirect
27. C₅₇₁⋊C₈	C₂×C₄	semidirect
31. C₈×C₅₇₁	C₂×C₄	semidirect
47. C₅₇₁	#428	semidirect
55. #106	D₅₇₁	semidirect
79. C₈	C₄×D₅₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22603716	2
#32912652	2
C₄⋊C₄×D₅₇₁	2
#32912628	2
#32912627	2
#32912625	2
#106×C₅₇₁	2
#428	571