Subgroups — SD₃₂×D₄₁ #14580758

Order 2624.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×D₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₈×D₄₁	C₂	1	1	yes	maximal, characteristic
3	#13050109	C₂	1	1	yes	maximal, characteristic, complemented
4	#13050108	C₂	1	1	yes	maximal, characteristic, complemented
5	#13050107	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₆×D₄₁	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₃₂×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×D₄₁	—	2	1	no	—
9	D₄×D₄₁	—	2	1	no	—
10	Q₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
11	D₈×C₄₁	C₂²	1	1	yes	characteristic
12	#10620285	—	2	1	no	—
13	#10620282	—	2	1	no	—
14	Dic₁₆₄	C₂²	1	1	yes	characteristic, complemented
15	D₃₂₈	C₂²	1	1	yes	characteristic
16	C₈×D₄₁	C₂²	1	1	yes	characteristic
17	C₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
18	#10620268	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₄₁	—	4	1	no	—
20	Q₈×C₄₁	—	2	1	no	—
21	D₄×C₄₁	—	2	1	no	—
22	C₂²⋊D₄₁	—	4	1	no	—
23	D₁₆₄	—	2	1	no	—
24	C₄×D₄₁	—	4	1	no	—
25	C₄×D₄₁	D₄	1	1	yes	characteristic
26	Dic₈₂	—	2	1	no	—
27	Dic₈₂	—	4	1	no	—
28	C₈×C₄₁	C₂³	1	1	yes	characteristic
29	#66491	D₄	1	1	yes	characteristic
30	C₂²×C₄₁	—	4	1	no	—
31	C₂×D₄₁	—	4	1	no	—
32	C₂×D₄₁	—	8	2	no	—
33	C₂×D₄₁	D₈	1	1	yes	characteristic
34	C₄×C₄₁	—	4	1	no	—
35	C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
36	Dic₄₁	—	4	1	no	—
37	Dic₄₁	D₈	1	1	yes	characteristic
38	C₂×C₄₁	—	8	1	no	—
39	C₂×C₄₁	C₂×D₈	1	1	yes	characteristic
40	D₄₁	—	8	1	no	—
41	D₄₁	SD₃₂	1	2	yes	direct product factor
42	C₂×SD₃₂	—	41	1	no	maximal, Sylow
43	C₄₁	C₂×SD₃₂	1	1	yes	characteristic, complemented, Sylow
44	C₂×Q₁₆	—	41	1	no	—
45	C₂×D₈	—	41	1	no	—
46	SD₃₂	—	41	1	no	—
47	SD₃₂	—	41	1	no	—
48	SD₃₂	—	41	1	no	—
49	SD₃₂	D₄₁	1	1	yes	characteristic, direct product factor
50	C₂×C₁₆	—	41	1	no	—
51	C₂×Q₈	—	82	1	no	—
52	C₂×D₄	—	82	1	no	—
53	Q₁₆	—	41	1	no	—
54	Q₁₆	—	82	1	no	—
55	Q₁₆	C₂×D₄₁	1	1	yes	characteristic, complemented
56	D₈	—	41	1	no	—
57	D₈	—	82	1	no	—
58	D₈	C₂×D₄₁	1	1	yes	characteristic
59	C₂×C₈	—	41	1	no	—
60	C₁₆	—	41	1	no	—
61	C₁₆	C₂×D₄₁	1	1	yes	characteristic, complemented
62	C₂³	—	164	1	no	—
63	Q₈	—	2	1	no	—
64	Q₈	—	82	1	no	—
65	Q₈	—	164	1	no	—
66	D₄	—	2	1	no	—
67	D₄	—	82	1	no	—
68	D₄	—	164	1	no	—
69	C₂×C₄	—	41	1	no	—
70	C₂×C₄	—	164	1	no	—
71	C₈	—	41	1	no	—
72	C₈	C₂²×D₄₁	1	1	yes	characteristic
73	C₂²	—	4	1	no	—
74	C₂²	—	41	1	no	—
75	C₂²	—	328	2	no	—
76	C₂²	—	164	1	no	—
77	C₄	—	4	1	no	—
78	C₄	—	41	1	no	—
79	C₄	—	164	1	no	—
80	C₄	D₄×D₄₁	1	1	yes	characteristic
81	C₂	—	8	1	no	—
82	C₂	—	41	2	no	—
83	C₂	—	328	1	no	—
84	C₂	D₈×D₄₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₄₁
commutator, cosocle	C₈×C₄₁	C₂³
Frattini	C₈	C₂²×D₄₁
Fitting	SD₃₂×C₄₁	C₂
socle	C₂×C₄₁	C₂×D₈
prime radical	D₈×D₄₁	C₂
hypercenter	SD₃₂	D₄₁
hypocenter	C₄₁	C₂×SD₃₂
LCS	G ▷ C₈×C₄₁ ▷ C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ SD₃₂

Complements

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

N	H ≅ G/N	type
1. Q₁₆×D₄₁	C₂	semidirect
3. #13050109	C₂	semidirect
4. #13050108	C₂	semidirect
5. #13050107	C₂	semidirect
6. C₁₆×D₄₁	C₂	semidirect
7. SD₃₂×C₄₁	C₂	semidirect
10. Q₁₆×C₄₁	C₂²	semidirect
14. Dic₁₆₄	C₂²	semidirect
17. C₁₆×C₄₁	C₂²	semidirect
18. #10620268	C₂²	semidirect
41. D₄₁	SD₃₂	direct (N × H)
43. C₄₁	C₂×SD₃₂	semidirect
49. SD₃₂	D₄₁	direct (N × H)
55. Q₁₆	C₂×D₄₁	semidirect
61. C₁₆	C₂×D₄₁	semidirect

Maximal subgroups

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

subgroup	index
Q₁₆×D₄₁	2
D₈×D₄₁	2
#13050109	2
#13050108	2
#13050107	2
C₁₆×D₄₁	2
SD₃₂×C₄₁	2
C₂×SD₃₂	41

Subgroups — SD32×D41 #14580758

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₃₂×D₄₁ #14580758