Subgroups — D₅₂₁⋊#101 #45688417

Order 33344.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₂₁⋊M₁₆	C₂	1	2	yes	maximal
2	#30659769	C₂	1	4	yes	maximal, complemented
3	C₂×Q₈×D₅₂₁	C₂	1	1	yes	maximal, characteristic
4	#22552374	—	2	2	no	—
5	#22552373	C₂²	1	4	yes	—
6	#22552372	—	2	2	no	—
7	C₂×Dic₁₀₄₂	C₄	1	1	yes	characteristic
8	C₂×Dic₁₀₄₂	C₂²	1	2	yes	—
9	Q₈×D₅₂₁	—	2	2	no	—
10	Q₈×D₅₂₁	—	2	2	no	—
11	C₂×C₄×D₅₂₁	C₄	1	2	yes	—
12	C₂×C₄×D₅₂₁	C₂²	1	1	yes	characteristic
13	C₂×Q₈×C₅₂₁	C₄	1	1	yes	characteristic
14	#16861967	—	2	4	no	—
15	C₂²×D₅₂₁	C₂×C₄	1	1	yes	characteristic
16	Dic₁₀₄₂	—	2	2	no	—
17	Dic₁₀₄₂	—	2	4	no	—
18	C₂×Dic₅₂₁	C₂×C₄	1	2	yes	—
19	C₂×Dic₅₂₁	C₂³	1	1	yes	characteristic
20	C₄×D₅₂₁	—	2	2	no	—
21	C₄×D₅₂₁	—	2	2	no	—
22	C₄×D₅₂₁	D₄	1	2	yes	—
23	C₄×D₅₂₁	D₄	1	2	yes	—
24	Q₈×C₅₂₁	—	2	2	no	—
25	C₂×C₄×C₅₂₁	C₂×C₄	1	2	yes	—
26	C₂×C₄×C₅₂₁	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₅₂₁	C₂²×C₄	1	1	yes	characteristic
28	C₂×D₅₂₁	—	2	2	no	—
29	C₂×D₅₂₁	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×D₅₂₁	C₂²⋊C₄	1	1	yes	characteristic
31	C₄×C₅₂₁	—	2	2	no	—
32	C₄×C₅₂₁	C₂²⋊C₄	1	2	yes	—
33	Dic₅₂₁	—	2	2	no	—
34	Dic₅₂₁	C₂×D₄	1	2	yes	—
35	C₂×C₅₂₁	—	2	1	no	—
36	C₂×C₅₂₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
37	D₅₂₁	—	2	1	no	—
38	D₅₂₁	#101	1	2	yes	complemented
39	C₅₂₁	C₂×#101	1	1	yes	characteristic, complemented, Sylow
40	C₂×#101	—	521	1	no	maximal, Sylow
41	C₂²×Q₈	—	521	1	no	—
42	C₂×M₁₆	—	521	2	no	—
43	#101	—	521	4	no	—
44	C₂×Q₈	—	521	2	no	—
45	C₂×Q₈	—	521	1	no	—
46	C₂×Q₈	—	1042	2	no	—
47	C₂×Q₈	—	1042	2	no	—
48	C₂×Q₈	#14523438	1	1	yes	characteristic
49	C₂²×C₄	—	521	1	no	—
50	C₂²×C₄	—	521	2	no	—
51	M₁₆	—	521	4	no	—
52	M₁₆	—	1042	2	no	—
53	C₂×C₈	—	1042	2	no	—
54	C₂³	—	521	1	no	—
55	Q₈	—	2	2	no	—
56	Q₈	—	1042	4	no	—
57	Q₈	—	1042	2	no	—
58	C₂×C₄	—	521	1	no	—
59	C₂×C₄	—	521	2	no	—
60	C₂×C₄	—	521	2	no	—
61	C₂×C₄	—	521	2	no	—
62	C₂×C₄	—	1042	2	no	—
63	C₂×C₄	—	1042	2	no	—
64	C₂×C₄	C₂×#14523438	1	2	yes	—
65	C₂×C₄	C₂×#14523438	1	1	yes	characteristic
66	C₈	—	1042	4	no	—
67	C₂²	—	521	1	no	—
68	C₂²	—	521	1	no	—
69	C₂²	—	1042	2	no	—
70	C₂²	C₂²×#14523438	1	1	yes	characteristic
71	C₄	—	2	2	no	—
72	C₄	—	521	2	no	—
73	C₄	—	1042	2	no	—
74	C₄	C₂²⋊#14523438	1	2	yes	—
75	C₂	—	2	1	no	—
76	C₂	—	521	2	no	—
77	C₂	—	1042	1	no	—
78	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×Q₈×C₅₂₁	C₄
socle	C₂×C₅₂₁	C₂×C₂²⋊C₄
prime radical	C₂²×D₅₂₁	C₂×C₄
cosocle	C₂×Dic₅₂₁	C₂³
hypercenter	C₂×Q₈	#14523438
hypocenter	C₅₂₁	C₂×#101
LCS	G ▷ C₂²×C₅₂₁ ▷ C₂×C₅₂₁ ▷ C₅₂₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #30659769	C₂	semidirect
38. D₅₂₁	#101	semidirect
39. C₅₂₁	C₂×#101	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
#30659769	2
C₂×Q₈×D₅₂₁	2
C₂×#101	521

Subgroups — D521⋊#101 #45688417

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₂₁⋊#101 #45688417