Subgroups — D₃₂×D₂₅₁ #44552661

Order 32128.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₆×D₂₅₁	C₂	1	2	yes	maximal, complemented
2	D₈₀₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#30631522	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃₂×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
6	D₈×D₂₅₁	—	2	2	no	—
7	D₄₀₁₆	C₂²	1	2	yes	complemented
8	#22548656	—	2	2	no	—
9	C₁₆×D₂₅₁	C₂²	1	1	yes	characteristic
10	C₂₅₁⋊C₃₂	C₂²	1	1	yes	characteristic, complemented
11	D₁₆×C₂₅₁	C₂²	1	2	yes	complemented
12	C₃₂×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
13	D₄×D₂₅₁	—	4	2	no	—
14	D₂₀₀₈	—	2	2	no	—
15	#16860795	—	4	2	no	—
16	C₈×D₂₅₁	D₄	1	1	yes	characteristic
17	C₂₅₁⋊C₁₆	D₄	1	1	yes	characteristic
18	D₈×C₂₅₁	—	2	2	no	—
19	C₁₆×C₂₅₁	C₂³	1	1	yes	characteristic
20	C₂²×D₂₅₁	—	8	2	no	—
21	D₁₀₀₄	—	4	2	no	—
22	C₂²⋊D₂₅₁	—	8	2	no	—
23	C₄×D₂₅₁	D₈	1	1	yes	characteristic
24	C₂₅₁⋊C₈	D₈	1	1	yes	characteristic
25	D₄×C₂₅₁	—	4	2	no	—
26	C₈×C₂₅₁	C₂×D₄	1	1	yes	characteristic
27	C₂²×C₂₅₁	—	8	2	no	—
28	C₂×D₂₅₁	—	8	2	no	—
29	C₂×D₂₅₁	—	16	4	no	—
30	C₂×D₂₅₁	D₁₆	1	1	yes	characteristic
31	C₄×C₂₅₁	C₂×D₈	1	1	yes	characteristic
32	Dic₂₅₁	D₁₆	1	1	yes	characteristic
33	C₂×C₂₅₁	—	16	2	no	—
34	C₂×C₂₅₁	C₂×D₁₆	1	1	yes	characteristic
35	D₂₅₁	—	16	2	no	—
36	D₂₅₁	D₃₂	1	2	yes	direct product factor
37	C₂₅₁	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
38	C₂×D₃₂	—	251	1	no	maximal, Sylow
39	C₂×D₁₆	—	251	2	no	—
40	D₃₂	—	251	2	no	—
41	D₃₂	—	251	1	no	—
42	D₃₂	D₂₅₁	1	1	yes	characteristic, direct product factor
43	C₂×C₃₂	—	251	1	no	—
44	C₂×D₈	—	502	2	no	—
45	D₁₆	—	502	2	no	—
46	D₁₆	—	251	2	no	—
47	D₁₆	C₂×D₂₅₁	1	2	yes	complemented
48	C₂×C₁₆	—	251	1	no	—
49	C₃₂	—	251	1	no	—
50	C₃₂	C₂×D₂₅₁	1	1	yes	characteristic, complemented
51	C₂×D₄	—	1004	2	no	—
52	D₈	—	2	2	no	—
53	D₈	—	1004	2	no	—
54	D₈	—	502	2	no	—
55	C₂×C₈	—	251	1	no	—
56	C₁₆	—	251	1	no	—
57	C₁₆	C₂²×D₂₅₁	1	1	yes	characteristic
58	C₂³	—	2008	2	no	—
59	D₄	—	4	2	no	—
60	D₄	—	2008	2	no	—
61	D₄	—	1004	2	no	—
62	C₂×C₄	—	251	1	no	—
63	C₈	—	251	1	no	—
64	C₈	D₄×D₂₅₁	1	1	yes	characteristic
65	C₂²	—	8	2	no	—
66	C₂²	—	4016	4	no	—
67	C₂²	—	2008	2	no	—
68	C₂²	—	251	1	no	—
69	C₄	—	251	1	no	—
70	C₄	D₈×D₂₅₁	1	1	yes	characteristic
71	C₂	—	16	2	no	—
72	C₂	—	4016	2	no	—
73	C₂	—	251	2	no	—
74	C₂	D₁₆×D₂₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₂₅₁
commutator, cosocle	C₁₆×C₂₅₁	C₂³
Frattini	C₁₆	C₂²×D₂₅₁
Fitting	D₃₂×C₂₅₁	C₂
socle	C₂×C₂₅₁	C₂×D₁₆
hypercenter	D₃₂	D₂₅₁
hypocenter	C₂₅₁	C₂×D₃₂
LCS	G ▷ C₁₆×C₂₅₁ ▷ C₈×C₂₅₁ ▷ C₄×C₂₅₁ ▷ C₂×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₃₂

Complements

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

N	H ≅ G/N	type
1. D₁₆×D₂₅₁	C₂	semidirect
2. D₈₀₃₂	C₂	semidirect
3. #30631522	C₂	semidirect
4. C₃₂×D₂₅₁	C₂	semidirect
5. D₃₂×C₂₅₁	C₂	semidirect
7. D₄₀₁₆	C₂²	semidirect
10. C₂₅₁⋊C₃₂	C₂²	semidirect
11. D₁₆×C₂₅₁	C₂²	semidirect
12. C₃₂×C₂₅₁	C₂²	semidirect
36. D₂₅₁	D₃₂	direct (N × H)
37. C₂₅₁	C₂×D₃₂	semidirect
42. D₃₂	D₂₅₁	direct (N × H)
47. D₁₆	C₂×D₂₅₁	semidirect
50. C₃₂	C₂×D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
D₁₆×D₂₅₁	2
D₈₀₃₂	2
#30631522	2
C₃₂×D₂₅₁	2
D₃₂×C₂₅₁	2
C₂×D₃₂	251

Subgroups — D32×D251 #44552661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₂×D₂₅₁ #44552661