Subgroups — #41×D₅₂₁ #30659749

Order 16672.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22552365	C₂	1	1	yes	maximal, characteristic, complemented
2	#22552364	C₂	1	3	yes	maximal, complemented
3	#22552363	C₂	1	3	yes	maximal, complemented
4	Q₈×D₅₂₁	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×D₅₂₁	C₂	1	3	yes	maximal, complemented
6	C₂×C₄×D₅₂₁	C₂	1	3	yes	maximal, complemented
7	#41×C₅₂₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₅₂₁	C₂²	1	3	yes	—
9	Dic₁₀₄₂	C₂²	1	3	yes	complemented
10	D₂₀₈₄	C₂²	1	3	yes	complemented
11	C₂²⋊D₅₂₁	C₂²	1	6	yes	complemented
12	C₂×Dic₅₂₁	C₂²	1	3	yes	complemented
13	C₄×D₅₂₁	C₂²	1	1	yes	characteristic
14	C₄×D₅₂₁	C₂²	1	3	yes	—
15	C₄×D₅₂₁	C₂²	1	3	yes	complemented
16	C₄×D₅₂₁	C₂²	1	3	yes	complemented
17	Q₈×C₅₂₁	C₂²	1	1	yes	characteristic, complemented
18	D₄×C₅₂₁	C₂²	1	3	yes	complemented
19	C₂×C₄×C₅₂₁	C₂²	1	3	yes	complemented
20	C₂²×C₅₂₁	C₂³	1	3	yes	—
21	C₂×D₅₂₁	—	2	6	no	—
22	C₂×D₅₂₁	C₂³	1	3	yes	—
23	C₂×D₅₂₁	C₂³	1	1	yes	characteristic
24	C₄×C₅₂₁	C₂³	1	3	yes	—
25	C₄×C₅₂₁	C₂³	1	1	yes	characteristic
26	Dic₅₂₁	C₂³	1	1	yes	characteristic
27	Dic₅₂₁	C₂³	1	3	yes	—
28	C₂×C₅₂₁	—	2	3	no	—
29	C₂×C₅₂₁	C₂⁴	1	1	yes	characteristic
30	D₅₂₁	—	2	3	no	—
31	D₅₂₁	#41	1	2	yes	direct product factor
32	C₅₂₁	C₂×#41	1	1	yes	characteristic, complemented, Sylow
33	C₂×#41	—	521	1	no	maximal, Sylow
34	#41	—	521	1	no	—
35	#41	—	521	3	no	—
36	#41	—	521	3	no	—
37	#41	D₅₂₁	1	1	yes	characteristic, direct product factor
38	C₂×Q₈	—	521	1	no	—
39	C₂×D₄	—	521	3	no	—
40	C₂²×C₄	—	521	3	no	—
41	C₂³	—	521	3	no	—
42	Q₈	—	521	3	no	—
43	Q₈	C₂×D₅₂₁	1	1	yes	characteristic, complemented
44	D₄	—	521	6	no	—
45	D₄	—	521	3	no	—
46	D₄	C₂×D₅₂₁	1	3	yes	complemented
47	C₂×C₄	—	521	3	no	—
48	C₂×C₄	—	521	3	no	—
49	C₂×C₄	—	521	3	no	—
50	C₂×C₄	—	521	1	no	—
51	C₂×C₄	—	521	3	no	—
52	C₂×C₄	C₂×D₅₂₁	1	3	yes	complemented
53	C₂²	—	521	1	no	—
54	C₂²	—	521	3	no	—
55	C₂²	—	1042	6	no	—
56	C₂²	C₂²×D₅₂₁	1	3	yes	—
57	C₄	—	521	1	no	—
58	C₄	—	521	3	no	—
59	C₄	C₂²×D₅₂₁	1	3	yes	—
60	C₄	C₂²×D₅₂₁	1	1	yes	characteristic
61	C₂	—	2	3	no	—
62	C₂	—	521	2	no	—
63	C₂	—	1042	3	no	—
64	C₂	C₂³×D₅₂₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₅₂₁
commutator, socle, cosocle	C₂×C₅₂₁	C₂⁴
Frattini	C₂	C₂³×D₅₂₁
Fitting	#41×C₅₂₁	C₂
hypercenter	#41	D₅₂₁
hypocenter	C₅₂₁	C₂×#41
LCS	G ▷ C₂×C₅₂₁ ▷ C₅₂₁
UCS	C₁ ◁ C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
1. #22552365	C₂	semidirect
2. #22552364	C₂	semidirect
3. #22552363	C₂	semidirect
4. Q₈×D₅₂₁	C₂	semidirect
5. D₄×D₅₂₁	C₂	semidirect
6. C₂×C₄×D₅₂₁	C₂	semidirect
7. #41×C₅₂₁	C₂	semidirect
9. Dic₁₀₄₂	C₂²	semidirect
10. D₂₀₈₄	C₂²	semidirect
11. C₂²⋊D₅₂₁	C₂²	semidirect
12. C₂×Dic₅₂₁	C₂²	semidirect
15. C₄×D₅₂₁	C₂²	semidirect
16. C₄×D₅₂₁	C₂²	semidirect
17. Q₈×C₅₂₁	C₂²	semidirect
18. D₄×C₅₂₁	C₂²	semidirect
19. C₂×C₄×C₅₂₁	C₂²	semidirect
31. D₅₂₁	#41	direct (N × H)
32. C₅₂₁	C₂×#41	semidirect
37. #41	D₅₂₁	direct (N × H)
43. Q₈	C₂×D₅₂₁	semidirect
46. D₄	C₂×D₅₂₁	semidirect
52. C₂×C₄	C₂×D₅₂₁	semidirect

Maximal subgroups

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

subgroup	index
#22552365	2
#22552364	2
#22552363	2
Q₈×D₅₂₁	2
D₄×D₅₂₁	2
C₂×C₄×D₅₂₁	2
#41×C₅₂₁	2
C₂×#41	521

Subgroups — #41×D521 #30659749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #41×D₅₂₁ #30659749