Subgroups — Q₃₂×D₂₅₁ #30632113

Order 16064.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×D₂₅₁	C₂	1	2	yes	maximal
2	Dic₂₀₀₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#22548661	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₂₅₁	C₂	1	1	yes	maximal, characteristic
5	Q₃₂×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×D₂₅₁	—	2	2	no	—
7	Dic₁₀₀₄	C₂²	1	2	yes	—
8	#16860800	—	2	2	no	—
9	C₈×D₂₅₁	C₂²	1	1	yes	characteristic
10	C₂₅₁⋊C₁₆	C₂²	1	1	yes	characteristic
11	Q₁₆×C₂₅₁	C₂²	1	2	yes	—
12	C₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
13	Dic₅₀₂	—	2	2	no	—
14	Dic₅₀₂	—	4	2	no	—
15	C₄×D₂₅₁	—	4	2	no	—
16	C₄×D₂₅₁	D₄	1	1	yes	characteristic
17	C₂₅₁⋊C₈	D₄	1	1	yes	characteristic
18	Q₈×C₂₅₁	—	2	2	no	—
19	C₈×C₂₅₁	C₂³	1	1	yes	characteristic
20	C₂×D₂₅₁	D₈	1	1	yes	characteristic
21	C₄×C₂₅₁	—	4	2	no	—
22	C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
23	Dic₂₅₁	—	4	2	no	—
24	Dic₂₅₁	D₈	1	1	yes	characteristic
25	C₂×C₂₅₁	C₂×D₈	1	1	yes	characteristic
26	D₂₅₁	Q₃₂	1	2	yes	direct product factor
27	C₂₅₁	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
28	C₂×Q₃₂	—	251	1	no	maximal, Sylow
29	C₂×Q₁₆	—	251	2	no	—
30	Q₃₂	—	251	2	no	—
31	Q₃₂	—	251	1	no	—
32	Q₃₂	D₂₅₁	1	1	yes	characteristic, direct product factor
33	C₂×C₁₆	—	251	1	no	—
34	C₂×Q₈	—	502	2	no	—
35	Q₁₆	—	502	2	no	—
36	Q₁₆	—	251	2	no	—
37	Q₁₆	C₂×D₂₅₁	1	2	yes	—
38	C₂×C₈	—	251	1	no	—
39	C₁₆	—	251	1	no	—
40	C₁₆	C₂×D₂₅₁	1	1	yes	characteristic
41	Q₈	—	2	2	no	—
42	Q₈	—	1004	2	no	—
43	Q₈	—	502	2	no	—
44	C₂×C₄	—	1004	2	no	—
45	C₂×C₄	—	251	1	no	—
46	C₈	—	251	1	no	—
47	C₈	C₂²×D₂₅₁	1	1	yes	characteristic
48	C₂²	—	251	1	no	—
49	C₄	—	4	2	no	—
50	C₄	—	1004	2	no	—
51	C₄	—	251	1	no	—
52	C₄	D₄×D₂₅₁	1	1	yes	characteristic
53	C₂	—	251	2	no	—
54	C₂	D₈×D₂₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₂₅₁
commutator, cosocle	C₈×C₂₅₁	C₂³
Frattini	C₈	C₂²×D₂₅₁
Fitting	Q₃₂×C₂₅₁	C₂
socle	C₂×C₂₅₁	C₂×D₈
prime radical	C₂×D₂₅₁	D₈
hypercenter	Q₃₂	D₂₅₁
hypocenter	C₂₅₁	C₂×Q₃₂
LCS	G ▷ C₈×C₂₅₁ ▷ C₄×C₂₅₁ ▷ C₂×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
2. Dic₂₀₀₈	C₂	semidirect
3. #22548661	C₂	semidirect
5. Q₃₂×C₂₅₁	C₂	semidirect
26. D₂₅₁	Q₃₂	direct (N × H)
27. C₂₅₁	C₂×Q₃₂	semidirect
32. Q₃₂	D₂₅₁	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×D₂₅₁	2
Dic₂₀₀₈	2
#22548661	2
C₁₆×D₂₅₁	2
Q₃₂×C₂₅₁	2
C₂×Q₃₂	251

Subgroups — Q32×D251 #30632113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₃₂×D₂₅₁ #30632113