Subgroups — D₅₂₁⋊#100 #45688415

Order 33344.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₂₁⋊M₁₆	C₂	1	2	yes	maximal, complemented
2	#30659768	C₂	1	4	yes	maximal, complemented
3	C₂×D₄×D₅₂₁	C₂	1	1	yes	maximal, characteristic
4	#22552374	—	2	2	no	—
5	#22552373	C₂²	1	4	yes	complemented
6	#22552372	—	2	2	no	—
7	C₂³×D₅₂₁	C₄	1	2	yes	—
8	C₂×D₂₀₈₄	C₄	1	1	yes	characteristic
9	C₂×C₂²⋊D₅₂₁	C₂²	1	2	yes	—
10	D₄×D₅₂₁	—	2	2	no	—
11	D₄×D₅₂₁	—	2	2	no	—
12	C₂×C₄×D₅₂₁	C₂²	1	1	yes	characteristic
13	C₂×D₄×C₅₂₁	C₄	1	1	yes	characteristic
14	#16861967	—	2	4	no	—
15	C₂²×D₅₂₁	—	2	2	no	—
16	C₂²×D₅₂₁	—	2	2	no	—
17	C₂²×D₅₂₁	—	4	4	no	—
18	C₂²×D₅₂₁	C₂×C₄	1	1	yes	characteristic
19	C₂²×D₅₂₁	C₂×C₄	1	2	yes	—
20	D₂₀₈₄	—	2	2	no	—
21	C₂²⋊D₅₂₁	—	2	4	no	—
22	C₂×Dic₅₂₁	C₂³	1	1	yes	characteristic
23	C₄×D₅₂₁	D₄	1	2	yes	—
24	C₄×D₅₂₁	D₄	1	2	yes	—
25	C₂³×C₅₂₁	C₂×C₄	1	2	yes	—
26	D₄×C₅₂₁	—	2	2	no	—
27	C₂×C₄×C₅₂₁	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₅₂₁	—	2	2	no	—
29	C₂²×C₅₂₁	—	4	2	no	—
30	C₂²×C₅₂₁	C₂²×C₄	1	1	yes	characteristic
31	C₂×D₅₂₁	—	2	2	no	—
32	C₂×D₅₂₁	—	2	2	no	—
33	C₂×D₅₂₁	—	4	4	no	—
34	C₂×D₅₂₁	—	4	4	no	—
35	C₂×D₅₂₁	—	4	2	no	—
36	C₂×D₅₂₁	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×D₅₂₁	C₂²⋊C₄	1	1	yes	characteristic
38	C₄×C₅₂₁	C₂²⋊C₄	1	2	yes	—
39	Dic₅₂₁	C₂×D₄	1	2	yes	—
40	C₂×C₅₂₁	—	2	1	no	—
41	C₂×C₅₂₁	—	4	2	no	—
42	C₂×C₅₂₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
43	D₅₂₁	—	2	1	no	—
44	D₅₂₁	—	4	2	no	—
45	D₅₂₁	#100	1	2	yes	complemented
46	C₅₂₁	C₂×#100	1	1	yes	characteristic, complemented, Sylow
47	C₂×#100	—	521	1	no	maximal, Sylow
48	C₂²×D₄	—	521	1	no	—
49	C₂×M₁₆	—	521	2	no	—
50	#100	—	521	4	no	—
51	C₂⁴	—	521	2	no	—
52	C₂×D₄	—	521	2	no	—
53	C₂×D₄	—	521	1	no	—
54	C₂×D₄	—	1042	2	no	—
55	C₂×D₄	—	1042	2	no	—
56	C₂×D₄	#14523438	1	1	yes	characteristic
57	C₂²×C₄	—	521	1	no	—
58	M₁₆	—	521	4	no	—
59	M₁₆	—	1042	2	no	—
60	C₂×C₈	—	1042	2	no	—
61	C₂³	—	521	1	no	—
62	C₂³	—	521	2	no	—
63	C₂³	—	1042	2	no	—
64	C₂³	—	1042	2	no	—
65	C₂³	—	2084	4	no	—
66	C₂³	C₂×#14523438	1	2	yes	—
67	D₄	—	2	2	no	—
68	D₄	—	1042	4	no	—
69	D₄	—	1042	2	no	—
70	C₂×C₄	—	521	1	no	—
71	C₂×C₄	—	521	2	no	—
72	C₂×C₄	—	521	2	no	—
73	C₂×C₄	C₂×#14523438	1	1	yes	characteristic
74	C₈	—	1042	4	no	—
75	C₂²	—	2	2	no	—
76	C₂²	—	4	2	no	—
77	C₂²	—	521	1	no	—
78	C₂²	—	521	1	no	—
79	C₂²	—	1042	2	no	—
80	C₂²	—	1042	2	no	—
81	C₂²	—	2084	2	no	—
82	C₂²	—	2084	4	no	—
83	C₂²	—	2084	4	no	—
84	C₂²	C₂²×#14523438	1	1	yes	characteristic
85	C₄	—	521	2	no	—
86	C₄	C₂²⋊#14523438	1	2	yes	—
87	C₂	—	2	1	no	—
88	C₂	—	4	2	no	—
89	C₂	—	521	2	no	—
90	C₂	—	1042	1	no	—
91	C₂	—	2084	2	no	—
92	C₂	C₂×C₂²⋊#14523438	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊#14523438
commutator	C₂²×C₅₂₁	C₂²×C₄
Frattini	C₂²	C₂²×#14523438
Fitting	C₂×D₄×C₅₂₁	C₄
socle	C₂×C₅₂₁	C₂×C₂²⋊C₄
prime radical	C₂×D₄×D₅₂₁	C₂
cosocle	C₂×Dic₅₂₁	C₂³
hypercenter	C₂×D₄	#14523438
hypocenter	C₅₂₁	C₂×#100
LCS	G ▷ C₂²×C₅₂₁ ▷ C₂×C₅₂₁ ▷ C₅₂₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. D₅₂₁⋊M₁₆	C₂	semidirect
2. #30659768	C₂	semidirect
5. #22552373	C₂²	semidirect
45. D₅₂₁	#100	semidirect
46. C₅₂₁	C₂×#100	semidirect

Maximal subgroups

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

subgroup	index
D₅₂₁⋊M₁₆	2
#30659768	2
C₂×D₄×D₅₂₁	2
C₂×#100	521

Subgroups — D521⋊#100 #45688415

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₂₁⋊#100 #45688415