Subgroups — Q₃₂×D₅₂₁ #45687858

Order 33344.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×D₅₂₁	C₂	1	2	yes	maximal
2	Dic₄₁₆₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#30659654	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₅₂₁	C₂	1	1	yes	maximal, characteristic
5	Q₃₂×C₅₂₁	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×D₅₂₁	—	2	2	no	—
7	Dic₂₀₈₄	C₂²	1	2	yes	—
8	#22552354	—	2	2	no	—
9	C₈×D₅₂₁	C₂²	1	1	yes	characteristic
10	#22552339	C₂²	1	1	yes	characteristic
11	Q₁₆×C₅₂₁	C₂²	1	2	yes	—
12	C₁₆×C₅₂₁	C₂²	1	1	yes	characteristic
13	Dic₁₀₄₂	—	2	2	no	—
14	Dic₁₀₄₂	—	4	2	no	—
15	C₄×D₅₂₁	—	4	2	no	—
16	C₄×D₅₂₁	D₄	1	1	yes	characteristic
17	#16861960	D₄	1	1	yes	characteristic
18	Q₈×C₅₂₁	—	2	2	no	—
19	C₈×C₅₂₁	C₂³	1	1	yes	characteristic
20	C₂×D₅₂₁	D₈	1	1	yes	characteristic
21	C₄×C₅₂₁	—	4	2	no	—
22	C₄×C₅₂₁	C₂×D₄	1	1	yes	characteristic
23	Dic₅₂₁	—	4	2	no	—
24	Dic₅₂₁	D₈	1	1	yes	characteristic
25	C₂×C₅₂₁	C₂×D₈	1	1	yes	characteristic
26	D₅₂₁	Q₃₂	1	2	yes	direct product factor
27	C₅₂₁	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
28	C₂×Q₃₂	—	521	1	no	maximal, Sylow
29	C₂×Q₁₆	—	521	2	no	—
30	Q₃₂	—	521	2	no	—
31	Q₃₂	—	521	1	no	—
32	Q₃₂	D₅₂₁	1	1	yes	characteristic, direct product factor
33	C₂×C₁₆	—	521	1	no	—
34	C₂×Q₈	—	1042	2	no	—
35	Q₁₆	—	521	2	no	—
36	Q₁₆	—	1042	2	no	—
37	Q₁₆	C₂×D₅₂₁	1	2	yes	—
38	C₂×C₈	—	521	1	no	—
39	C₁₆	—	521	1	no	—
40	C₁₆	C₂×D₅₂₁	1	1	yes	characteristic
41	Q₈	—	2	2	no	—
42	Q₈	—	1042	2	no	—
43	Q₈	—	2084	2	no	—
44	C₂×C₄	—	521	1	no	—
45	C₂×C₄	—	2084	2	no	—
46	C₈	—	521	1	no	—
47	C₈	C₂²×D₅₂₁	1	1	yes	characteristic
48	C₂²	—	521	1	no	—
49	C₄	—	4	2	no	—
50	C₄	—	521	1	no	—
51	C₄	—	2084	2	no	—
52	C₄	D₄×D₅₂₁	1	1	yes	characteristic
53	C₂	—	521	2	no	—
54	C₂	D₈×D₅₂₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₅₂₁
commutator, cosocle	C₈×C₅₂₁	C₂³
Frattini	C₈	C₂²×D₅₂₁
Fitting	Q₃₂×C₅₂₁	C₂
socle	C₂×C₅₂₁	C₂×D₈
prime radical	C₂×D₅₂₁	D₈
hypercenter	Q₃₂	D₅₂₁
hypocenter	C₅₂₁	C₂×Q₃₂
LCS	G ▷ C₈×C₅₂₁ ▷ C₄×C₅₂₁ ▷ C₂×C₅₂₁ ▷ C₅₂₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
2. Dic₄₁₆₈	C₂	semidirect
3. #30659654	C₂	semidirect
5. Q₃₂×C₅₂₁	C₂	semidirect
26. D₅₂₁	Q₃₂	direct (N × H)
27. C₅₂₁	C₂×Q₃₂	semidirect
32. Q₃₂	D₅₂₁	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×D₅₂₁	2
Dic₄₁₆₈	2
#30659654	2
C₁₆×D₅₂₁	2
Q₃₂×C₅₂₁	2
C₂×Q₃₂	521

Subgroups — Q32×D521 #45687858

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₃₂×D₅₂₁ #45687858