Subgroups — SD₁₆×D₅₂₁ #30659720

Order 16672.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₅₂₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×D₅₂₁	C₂	1	1	yes	maximal, characteristic
3	#22552353	C₂	1	1	yes	maximal, characteristic, complemented
4	#22552352	C₂	1	1	yes	maximal, characteristic, complemented
5	#22552351	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×D₅₂₁	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₁₆×C₅₂₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₅₂₁	—	2	1	no	—
9	Dic₁₀₄₂	—	2	1	no	—
10	Dic₁₀₄₂	C₂²	1	1	yes	characteristic, complemented
11	D₂₀₈₄	C₂²	1	1	yes	characteristic
12	C₂²⋊D₅₂₁	—	2	1	no	—
13	C₄×D₅₂₁	—	2	1	no	—
14	C₄×D₅₂₁	C₂²	1	1	yes	characteristic
15	#16861960	C₂²	1	1	yes	characteristic, complemented
16	Q₈×C₅₂₁	C₂²	1	1	yes	characteristic, complemented
17	D₄×C₅₂₁	C₂²	1	1	yes	characteristic
18	C₈×C₅₂₁	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₅₂₁	—	2	1	no	—
20	C₂×D₅₂₁	—	2	1	no	—
21	C₂×D₅₂₁	—	4	2	no	—
22	C₂×D₅₂₁	D₄	1	1	yes	characteristic
23	C₄×C₅₂₁	—	2	1	no	—
24	C₄×C₅₂₁	C₂³	1	1	yes	characteristic
25	Dic₅₂₁	—	2	1	no	—
26	Dic₅₂₁	D₄	1	1	yes	characteristic
27	C₂×C₅₂₁	—	4	1	no	—
28	C₂×C₅₂₁	C₂×D₄	1	1	yes	characteristic
29	D₅₂₁	—	4	1	no	—
30	D₅₂₁	SD₁₆	1	2	yes	direct product factor
31	C₅₂₁	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
32	C₂×SD₁₆	—	521	1	no	maximal, Sylow
33	C₂×Q₈	—	521	1	no	—
34	C₂×D₄	—	521	1	no	—
35	SD₁₆	—	521	1	no	—
36	SD₁₆	—	521	1	no	—
37	SD₁₆	—	521	1	no	—
38	SD₁₆	D₅₂₁	1	1	yes	characteristic, direct product factor
39	C₂×C₈	—	521	1	no	—
40	C₂³	—	1042	1	no	—
41	Q₈	—	521	1	no	—
42	Q₈	—	1042	1	no	—
43	Q₈	C₂×D₅₂₁	1	1	yes	characteristic, complemented
44	D₄	—	521	1	no	—
45	D₄	—	1042	1	no	—
46	D₄	C₂×D₅₂₁	1	1	yes	characteristic
47	C₂×C₄	—	521	1	no	—
48	C₂×C₄	—	1042	1	no	—
49	C₈	—	521	1	no	—
50	C₈	C₂×D₅₂₁	1	1	yes	characteristic, complemented
51	C₂²	—	2	1	no	—
52	C₂²	—	521	1	no	—
53	C₂²	—	1042	1	no	—
54	C₂²	—	2084	2	no	—
55	C₄	—	2	1	no	—
56	C₄	—	521	1	no	—
57	C₄	—	1042	1	no	—
58	C₄	C₂²×D₅₂₁	1	1	yes	characteristic
59	C₂	—	4	1	no	—
60	C₂	—	521	2	no	—
61	C₂	—	2084	1	no	—
62	C₂	D₄×D₅₂₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₅₂₁
commutator, cosocle	C₄×C₅₂₁	C₂³
Frattini	C₄	C₂²×D₅₂₁
Fitting	SD₁₆×C₅₂₁	C₂
socle	C₂×C₅₂₁	C₂×D₄
prime radical	D₄×D₅₂₁	C₂
hypercenter	SD₁₆	D₅₂₁
hypocenter	C₅₂₁	C₂×SD₁₆
LCS	G ▷ C₄×C₅₂₁ ▷ C₂×C₅₂₁ ▷ C₅₂₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

Complements

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

N	H ≅ G/N	type
1. Q₈×D₅₂₁	C₂	semidirect
3. #22552353	C₂	semidirect
4. #22552352	C₂	semidirect
5. #22552351	C₂	semidirect
6. C₈×D₅₂₁	C₂	semidirect
7. SD₁₆×C₅₂₁	C₂	semidirect
10. Dic₁₀₄₂	C₂²	semidirect
15. #16861960	C₂²	semidirect
16. Q₈×C₅₂₁	C₂²	semidirect
18. C₈×C₅₂₁	C₂²	semidirect
30. D₅₂₁	SD₁₆	direct (N × H)
31. C₅₂₁	C₂×SD₁₆	semidirect
38. SD₁₆	D₅₂₁	direct (N × H)
43. Q₈	C₂×D₅₂₁	semidirect
50. C₈	C₂×D₅₂₁	semidirect

Maximal subgroups

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

subgroup	index
Q₈×D₅₂₁	2
D₄×D₅₂₁	2
#22552353	2
#22552352	2
#22552351	2
C₈×D₅₂₁	2
SD₁₆×C₅₂₁	2
C₂×SD₁₆	521

Subgroups — SD16×D521 #30659720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₁₆×D₅₂₁ #30659720