Subgroups — SD₁₆×D₆₆₁ #35232545

Order 21152.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₆₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×D₆₆₁	C₂	1	1	yes	maximal, characteristic
3	#24902361	C₂	1	1	yes	maximal, characteristic, complemented
4	#24902360	C₂	1	1	yes	maximal, characteristic, complemented
5	#24902359	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×D₆₆₁	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₁₆×C₆₆₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₆₆₁	—	2	1	no	—
9	Dic₁₃₂₂	—	2	1	no	—
10	Dic₁₃₂₂	C₂²	1	1	yes	characteristic, complemented
11	D₂₆₄₄	C₂²	1	1	yes	characteristic
12	C₂²⋊D₆₆₁	—	2	1	no	—
13	C₄×D₆₆₁	—	2	1	no	—
14	C₄×D₆₆₁	C₂²	1	1	yes	characteristic
15	#19126971	C₂²	1	1	yes	characteristic, complemented
16	Q₈×C₆₆₁	C₂²	1	1	yes	characteristic, complemented
17	D₄×C₆₆₁	C₂²	1	1	yes	characteristic
18	C₈×C₆₆₁	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₆₆₁	—	2	1	no	—
20	C₂×D₆₆₁	—	2	1	no	—
21	C₂×D₆₆₁	—	4	2	no	—
22	C₂×D₆₆₁	D₄	1	1	yes	characteristic
23	C₄×C₆₆₁	—	2	1	no	—
24	C₄×C₆₆₁	C₂³	1	1	yes	characteristic
25	Dic₆₆₁	—	2	1	no	—
26	Dic₆₆₁	D₄	1	1	yes	characteristic
27	C₂×C₆₆₁	—	4	1	no	—
28	C₂×C₆₆₁	C₂×D₄	1	1	yes	characteristic
29	D₆₆₁	—	4	1	no	—
30	D₆₆₁	SD₁₆	1	2	yes	direct product factor
31	C₆₆₁	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
32	C₂×SD₁₆	—	661	1	no	maximal, Sylow
33	C₂×Q₈	—	661	1	no	—
34	C₂×D₄	—	661	1	no	—
35	SD₁₆	—	661	1	no	—
36	SD₁₆	—	661	1	no	—
37	SD₁₆	—	661	1	no	—
38	SD₁₆	D₆₆₁	1	1	yes	characteristic, direct product factor
39	C₂×C₈	—	661	1	no	—
40	C₂³	—	1322	1	no	—
41	Q₈	—	1322	1	no	—
42	Q₈	—	661	1	no	—
43	Q₈	C₂×D₆₆₁	1	1	yes	characteristic, complemented
44	D₄	—	1322	1	no	—
45	D₄	—	661	1	no	—
46	D₄	C₂×D₆₆₁	1	1	yes	characteristic
47	C₂×C₄	—	1322	1	no	—
48	C₂×C₄	—	661	1	no	—
49	C₈	—	661	1	no	—
50	C₈	C₂×D₆₆₁	1	1	yes	characteristic, complemented
51	C₂²	—	2	1	no	—
52	C₂²	—	1322	1	no	—
53	C₂²	—	2644	2	no	—
54	C₂²	—	661	1	no	—
55	C₄	—	2	1	no	—
56	C₄	—	1322	1	no	—
57	C₄	—	661	1	no	—
58	C₄	C₂²×D₆₆₁	1	1	yes	characteristic
59	C₂	—	4	1	no	—
60	C₂	—	2644	1	no	—
61	C₂	—	661	2	no	—
62	C₂	D₄×D₆₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₆₆₁
commutator, cosocle	C₄×C₆₆₁	C₂³
Frattini	C₄	C₂²×D₆₆₁
Fitting	SD₁₆×C₆₆₁	C₂
socle	C₂×C₆₆₁	C₂×D₄
prime radical	D₄×D₆₆₁	C₂
hypercenter	SD₁₆	D₆₆₁
hypocenter	C₆₆₁	C₂×SD₁₆
LCS	G ▷ C₄×C₆₆₁ ▷ C₂×C₆₆₁ ▷ C₆₆₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

Complements

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

N	H ≅ G/N	type
1. Q₈×D₆₆₁	C₂	semidirect
3. #24902361	C₂	semidirect
4. #24902360	C₂	semidirect
5. #24902359	C₂	semidirect
6. C₈×D₆₆₁	C₂	semidirect
7. SD₁₆×C₆₆₁	C₂	semidirect
10. Dic₁₃₂₂	C₂²	semidirect
15. #19126971	C₂²	semidirect
16. Q₈×C₆₆₁	C₂²	semidirect
18. C₈×C₆₆₁	C₂²	semidirect
30. D₆₆₁	SD₁₆	direct (N × H)
31. C₆₆₁	C₂×SD₁₆	semidirect
38. SD₁₆	D₆₆₁	direct (N × H)
43. Q₈	C₂×D₆₆₁	semidirect
50. C₈	C₂×D₆₆₁	semidirect

Maximal subgroups

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

subgroup	index
Q₈×D₆₆₁	2
D₄×D₆₆₁	2
#24902361	2
#24902360	2
#24902359	2
C₈×D₆₆₁	2
SD₁₆×C₆₆₁	2
C₂×SD₁₆	661

Subgroups — SD16×D661 #35232545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₁₆×D₆₆₁ #35232545