Subgroups — #49142249

Order 36544.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22603734	C₂	1	1	yes	maximal, characteristic
2	M₁₆×D₅₇₁	C₂	1	2	yes	maximal, complemented
3	#32912613	C₂	1	1	yes	maximal, characteristic, complemented
4	#32912610	C₂	1	2	yes	maximal, complemented
5	#101×C₅₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#22603734	—	2	2	no	—
7	#22603734	—	2	2	no	—
8	C₂×D₂₂₈₄	C₄	1	2	yes	—
9	C₂×D₂₂₈₄	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₅₇₁	C₄	1	2	yes	—
11	C₂×C₄×D₅₇₁	C₂²	1	1	yes	characteristic
12	#22603717	C₂²	1	2	yes	—
13	#22603716	—	2	2	no	—
14	C₈×D₅₇₁	—	2	2	no	—
15	C₂×Q₈×C₅₇₁	C₂²	1	1	yes	characteristic
16	M₁₆×C₅₇₁	C₂²	1	2	yes	—
17	C₂²×D₅₇₁	C₂×C₄	1	2	yes	—
18	C₂²×D₅₇₁	C₂×C₄	1	1	yes	characteristic
19	D₂₂₈₄	—	2	4	no	—
20	D₂₂₈₄	—	2	2	no	—
21	C₂×Dic₅₇₁	C₂×C₄	1	1	yes	characteristic
22	C₄×D₅₇₁	—	2	2	no	—
23	C₄×D₅₇₁	—	2	2	no	—
24	C₄×D₅₇₁	D₄	1	2	yes	—
25	C₄×D₅₇₁	D₄	1	2	yes	—
26	C₅₇₁⋊C₈	—	2	2	no	—
27	Q₈×C₅₇₁	—	2	2	no	—
28	C₂×C₄×C₅₇₁	C₂×C₄	1	2	yes	—
29	C₂×C₄×C₅₇₁	C₂³	1	1	yes	characteristic
30	C₈×C₅₇₁	—	2	2	no	—
31	C₂²×C₅₇₁	C₂²×C₄	1	1	yes	characteristic
32	C₂×D₅₇₁	—	2	2	no	—
33	C₂×D₅₇₁	—	4	1	no	—
34	C₂×D₅₇₁	—	4	2	no	—
35	C₂×D₅₇₁	C₂²⋊C₄	1	2	yes	—
36	C₄×C₅₇₁	—	2	2	no	—
37	C₄×C₅₇₁	C₂×D₄	1	2	yes	—
38	Dic₅₇₁	C₂²⋊C₄	1	1	yes	characteristic
39	Dic₅₇₁	C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₅₇₁	—	2	1	no	—
41	C₂×C₅₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
42	D₅₇₁	—	2	2	no	—
43	D₅₇₁	—	4	2	no	—
44	C₅₇₁	#413	1	1	yes	characteristic, complemented, Sylow
45	#413	—	571	1	no	maximal, Sylow
46	C₂×#41	—	571	1	no	—
47	C₂×M₁₆	—	571	2	no	—
48	#101	—	571	1	no	—
49	#101	D₅₇₁	1	1	yes	characteristic, complemented
50	#100	—	571	2	no	—
51	#41	—	1142	2	no	—
52	#41	—	1142	2	no	—
53	C₂×Q₈	C₂×D₅₇₁	1	1	yes	characteristic
54	C₂×D₄	—	571	2	no	—
55	C₂×D₄	—	571	1	no	—
56	C₂²×C₄	—	571	1	no	—
57	C₂²×C₄	—	571	2	no	—
58	M₁₆	—	571	2	no	—
59	M₁₆	—	1142	2	no	—
60	M₁₆	C₂×D₅₇₁	1	2	yes	—
61	C₂×C₈	—	1142	2	no	—
62	C₂³	—	571	1	no	—
63	C₂³	—	571	2	no	—
64	Q₈	—	2	2	no	—
65	D₄	—	1142	4	no	—
66	D₄	—	1142	2	no	—
67	C₂×C₄	—	571	1	no	—
68	C₂×C₄	—	571	2	no	—
69	C₂×C₄	—	571	2	no	—
70	C₂×C₄	—	1142	2	no	—
71	C₂×C₄	—	1142	2	no	—
72	C₂×C₄	C₄×D₅₇₁	1	2	yes	—
73	C₂×C₄	C₂²×D₅₇₁	1	1	yes	characteristic
74	C₈	—	2	2	no	—
75	C₈	—	1142	2	no	—
76	C₂²	—	571	2	no	—
77	C₂²	—	1142	2	no	—
78	C₂²	—	2284	1	no	—
79	C₂²	—	2284	2	no	—
80	C₂²	C₂×C₄×D₅₇₁	1	1	yes	characteristic
81	C₄	—	2	2	no	—
82	C₄	—	571	1	no	—
83	C₄	—	571	1	no	—
84	C₄	D₄×D₅₇₁	1	2	yes	—
85	C₂	—	2	1	no	—
86	C₂	—	1142	2	no	—
87	C₂	—	2284	2	no	—
88	C₂	C₂²⋊C₄×D₅₇₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊C₄×D₅₇₁
commutator	C₂²×C₅₇₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₅₇₁
Fitting	#101×C₅₇₁	C₂
socle	C₂×C₅₇₁	C₂×C₂²⋊C₄
prime radical	C₂×#22603734	C₂
cosocle	C₂×C₄×C₅₇₁	C₂³
hypercenter	#101	D₅₇₁
hypocenter	C₅₇₁	#413
LCS	G ▷ C₂²×C₅₇₁ ▷ C₂×C₅₇₁ ▷ C₅₇₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #101

Complements

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

N	H ≅ G/N	type
2. M₁₆×D₅₇₁	C₂	semidirect
3. #32912613	C₂	semidirect
4. #32912610	C₂	semidirect
5. #101×C₅₇₁	C₂	semidirect
44. C₅₇₁	#413	semidirect
49. #101	D₅₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22603734	2
M₁₆×D₅₇₁	2
#32912613	2
#32912610	2
#101×C₅₇₁	2
#413	571