Subgroups — Q₃₂×D₂₈₁ #31823889

Order 17984.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×D₂₈₁	C₂	1	2	yes	maximal
2	Dic₂₂₄₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#22582825	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₂₈₁	C₂	1	1	yes	maximal, characteristic
5	Q₃₂×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×D₂₈₁	—	2	2	no	—
7	Dic₁₁₂₄	C₂²	1	2	yes	—
8	#17985128	—	2	2	no	—
9	C₈×D₂₈₁	C₂²	1	1	yes	characteristic
10	#17985113	C₂²	1	1	yes	characteristic
11	Q₁₆×C₂₈₁	C₂²	1	2	yes	—
12	C₁₆×C₂₈₁	C₂²	1	1	yes	characteristic
13	Dic₅₆₂	—	2	2	no	—
14	Dic₅₆₂	—	4	2	no	—
15	C₄×D₂₈₁	—	4	2	no	—
16	C₄×D₂₈₁	D₄	1	1	yes	characteristic
17	#14555886	D₄	1	1	yes	characteristic
18	Q₈×C₂₈₁	—	2	2	no	—
19	C₈×C₂₈₁	C₂³	1	1	yes	characteristic
20	C₂×D₂₈₁	D₈	1	1	yes	characteristic
21	C₄×C₂₈₁	—	4	2	no	—
22	C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
23	Dic₂₈₁	—	4	2	no	—
24	Dic₂₈₁	D₈	1	1	yes	characteristic
25	C₂×C₂₈₁	C₂×D₈	1	1	yes	characteristic
26	D₂₈₁	Q₃₂	1	2	yes	direct product factor
27	C₂₈₁	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
28	C₂×Q₃₂	—	281	1	no	maximal, Sylow
29	C₂×Q₁₆	—	281	2	no	—
30	Q₃₂	—	281	2	no	—
31	Q₃₂	—	281	1	no	—
32	Q₃₂	D₂₈₁	1	1	yes	characteristic, direct product factor
33	C₂×C₁₆	—	281	1	no	—
34	C₂×Q₈	—	562	2	no	—
35	Q₁₆	—	281	2	no	—
36	Q₁₆	—	562	2	no	—
37	Q₁₆	C₂×D₂₈₁	1	2	yes	—
38	C₂×C₈	—	281	1	no	—
39	C₁₆	—	281	1	no	—
40	C₁₆	C₂×D₂₈₁	1	1	yes	characteristic
41	Q₈	—	2	2	no	—
42	Q₈	—	562	2	no	—
43	Q₈	—	1124	2	no	—
44	C₂×C₄	—	281	1	no	—
45	C₂×C₄	—	1124	2	no	—
46	C₈	—	281	1	no	—
47	C₈	C₂²×D₂₈₁	1	1	yes	characteristic
48	C₂²	—	281	1	no	—
49	C₄	—	4	2	no	—
50	C₄	—	281	1	no	—
51	C₄	—	1124	2	no	—
52	C₄	D₄×D₂₈₁	1	1	yes	characteristic
53	C₂	—	281	2	no	—
54	C₂	D₈×D₂₈₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₂₈₁
commutator, cosocle	C₈×C₂₈₁	C₂³
Frattini	C₈	C₂²×D₂₈₁
Fitting	Q₃₂×C₂₈₁	C₂
socle	C₂×C₂₈₁	C₂×D₈
prime radical	C₂×D₂₈₁	D₈
hypercenter	Q₃₂	D₂₈₁
hypocenter	C₂₈₁	C₂×Q₃₂
LCS	G ▷ C₈×C₂₈₁ ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
2. Dic₂₂₄₈	C₂	semidirect
3. #22582825	C₂	semidirect
5. Q₃₂×C₂₈₁	C₂	semidirect
26. D₂₈₁	Q₃₂	direct (N × H)
27. C₂₈₁	C₂×Q₃₂	semidirect
32. Q₃₂	D₂₈₁	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×D₂₈₁	2
Dic₂₂₄₈	2
#22582825	2
C₁₆×D₂₈₁	2
Q₃₂×C₂₈₁	2
C₂×Q₃₂	281

Subgroups — Q32×D281 #31823889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₃₂×D₂₈₁ #31823889