Subgroups — Q₃₂×D₄₁ #14580762

Order 2624.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×D₄₁	C₂	1	2	yes	maximal
2	Dic₃₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#13050110	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₄₁	C₂	1	1	yes	maximal, characteristic
5	Q₃₂×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×D₄₁	—	2	2	no	—
7	Q₁₆×C₄₁	C₂²	1	2	yes	—
8	#10620285	—	2	2	no	—
9	Dic₁₆₄	C₂²	1	2	yes	—
10	C₈×D₄₁	C₂²	1	1	yes	characteristic
11	C₁₆×C₄₁	C₂²	1	1	yes	characteristic
12	#10620268	C₂²	1	1	yes	characteristic
13	Q₈×C₄₁	—	2	2	no	—
14	C₄×D₄₁	—	4	2	no	—
15	C₄×D₄₁	D₄	1	1	yes	characteristic
16	Dic₈₂	—	2	2	no	—
17	Dic₈₂	—	4	2	no	—
18	C₈×C₄₁	C₂³	1	1	yes	characteristic
19	#66491	D₄	1	1	yes	characteristic
20	C₂×D₄₁	D₈	1	1	yes	characteristic
21	C₄×C₄₁	—	4	2	no	—
22	C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
23	Dic₄₁	—	4	2	no	—
24	Dic₄₁	D₈	1	1	yes	characteristic
25	C₂×C₄₁	C₂×D₈	1	1	yes	characteristic
26	D₄₁	Q₃₂	1	2	yes	direct product factor
27	C₂×Q₃₂	—	41	1	no	maximal, Sylow
28	C₄₁	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
29	C₂×Q₁₆	—	41	2	no	—
30	Q₃₂	—	41	2	no	—
31	Q₃₂	—	41	1	no	—
32	Q₃₂	D₄₁	1	1	yes	characteristic, direct product factor
33	C₂×C₁₆	—	41	1	no	—
34	C₂×Q₈	—	82	2	no	—
35	Q₁₆	—	41	2	no	—
36	Q₁₆	—	82	2	no	—
37	Q₁₆	C₂×D₄₁	1	2	yes	—
38	C₂×C₈	—	41	1	no	—
39	C₁₆	—	41	1	no	—
40	C₁₆	C₂×D₄₁	1	1	yes	characteristic
41	Q₈	—	2	2	no	—
42	Q₈	—	82	2	no	—
43	Q₈	—	164	2	no	—
44	C₂×C₄	—	41	1	no	—
45	C₂×C₄	—	164	2	no	—
46	C₈	—	41	1	no	—
47	C₈	C₂²×D₄₁	1	1	yes	characteristic
48	C₂²	—	41	1	no	—
49	C₄	—	4	2	no	—
50	C₄	—	41	1	no	—
51	C₄	—	164	2	no	—
52	C₄	D₄×D₄₁	1	1	yes	characteristic
53	C₂	—	41	2	no	—
54	C₂	D₈×D₄₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₄₁
commutator, cosocle	C₈×C₄₁	C₂³
Frattini	C₈	C₂²×D₄₁
Fitting	Q₃₂×C₄₁	C₂
socle	C₂×C₄₁	C₂×D₈
prime radical	C₂×D₄₁	D₈
hypercenter	Q₃₂	D₄₁
hypocenter	C₄₁	C₂×Q₃₂
LCS	G ▷ C₈×C₄₁ ▷ C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
2. Dic₃₂₈	C₂	semidirect
3. #13050110	C₂	semidirect
5. Q₃₂×C₄₁	C₂	semidirect
26. D₄₁	Q₃₂	direct (N × H)
28. C₄₁	C₂×Q₃₂	semidirect
32. Q₃₂	D₄₁	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₁₆×D₄₁	2
Dic₃₂₈	2
#13050110	2
C₁₆×D₄₁	2
Q₃₂×C₄₁	2
C₂×Q₃₂	41

Subgroups — Q32×D41 #14580762

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₃₂×D₄₁ #14580762