Subgroups — Dic₂₅₁⋊C₃₂ #44548560

Order 32128.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₅₁⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₆×Dic₂₅₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₂×C₂₅₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₅₁⋊C₁₆	C₄	1	1	yes	characteristic
5	C₈×Dic₂₅₁	C₄	1	1	yes	characteristic
6	C₂₅₁⋊C₃₂	—	2	1	no	—
7	C₂×C₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
8	C₃₂×C₂₅₁	—	2	1	no	—
9	C₂×C₂₅₁⋊C₈	C₈	1	1	yes	characteristic
10	C₄×Dic₂₅₁	C₈	1	1	yes	characteristic
11	C₂₅₁⋊C₁₆	—	2	1	no	—
12	C₂×C₈×C₂₅₁	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₂₅₁	D₄	1	1	yes	characteristic
14	C₁₆×C₂₅₁	Q₈	1	1	yes	characteristic
15	C₂×Dic₂₅₁	C₁₆	1	1	yes	characteristic
16	C₂×Dic₂₅₁	C₁₆	1	1	yes	characteristic
17	C₂₅₁⋊C₈	—	2	1	no	—
18	C₂×C₄×C₂₅₁	C₂×C₈	1	1	yes	characteristic
19	C₈×C₂₅₁	C₄⋊C₄	1	1	yes	characteristic
20	C₈×C₂₅₁	M₁₆	1	1	yes	characteristic
21	C₂²×C₂₅₁	C₂×C₁₆	1	1	yes	characteristic
22	C₄×C₂₅₁	C₄⋊C₈	1	1	yes	characteristic
23	C₄×C₂₅₁	M₃₂	1	1	yes	characteristic
24	Dic₂₅₁	—	2	1	no	—
25	Dic₂₅₁	C₃₂	1	2	yes	complemented
26	C₂×C₂₅₁	C₄⋊C₁₆	1	1	yes	characteristic
27	C₂×C₂₅₁	C₂×C₃₂	1	1	yes	characteristic
28	C₂×C₂₅₁	M₆₄	1	1	yes	characteristic
29	C₂₅₁	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
30	C₄⋊C₃₂	—	251	1	no	maximal, Sylow
31	C₂×C₃₂	—	251	1	no	—
32	C₂×C₃₂	D₂₅₁	1	1	yes	characteristic
33	C₄×C₁₆	—	251	1	no	—
34	C₂×C₁₆	—	251	1	no	—
35	C₂×C₁₆	C₂×D₂₅₁	1	1	yes	characteristic
36	C₄×C₈	—	251	1	no	—
37	C₃₂	—	2	1	no	—
38	C₃₂	—	502	1	no	—
39	C₂×C₈	—	251	1	no	—
40	C₂×C₈	C₄×D₂₅₁	1	1	yes	characteristic
41	C₄²	—	251	1	no	—
42	C₁₆	—	502	1	no	—
43	C₁₆	C₂²⋊D₂₅₁	1	1	yes	characteristic
44	C₁₆	Dic₅₀₂	1	1	yes	characteristic
45	C₂×C₄	—	251	1	no	—
46	C₂×C₄	—	251	1	no	—
47	C₂×C₄	C₈×D₂₅₁	1	1	yes	characteristic
48	C₈	—	502	1	no	—
49	C₈	Dic₂₅₁⋊C₄	1	1	yes	characteristic
50	C₈	#16860793	1	1	yes	characteristic
51	C₂²	C₁₆×D₂₅₁	1	1	yes	characteristic
52	C₄	—	502	1	no	—
53	C₄	—	251	2	no	—
54	C₄	Dic₂₅₁⋊C₈	1	1	yes	characteristic
55	C₄	#22548654	1	1	yes	characteristic
56	C₂	Dic₂₅₁⋊C₁₆	1	1	yes	characteristic
57	C₂	C₃₂×D₂₅₁	1	1	yes	characteristic
58	C₂	#30631520	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×D₂₅₁
commutator	C₂×C₂₅₁	C₂×C₃₂
Fitting	C₂×C₃₂×C₂₅₁	C₂
socle, prime radical	C₂²×C₂₅₁	C₂×C₁₆
cosocle	C₂×C₁₆×C₂₅₁	C₂²
hypercenter	C₂×C₃₂	D₂₅₁
hypocenter	C₂₅₁	C₄⋊C₃₂
LCS	G ▷ C₂×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
25. Dic₂₅₁	C₃₂	semidirect
29. C₂₅₁	C₄⋊C₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₅₁⋊C₃₂	2
C₁₆×Dic₂₅₁	2
C₂×C₃₂×C₂₅₁	2
C₄⋊C₃₂	251

Subgroups — Dic251⋊C32 #44548560

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₂₅₁⋊C₃₂ #44548560