Subgroups — Dic₂₇₁⋊C₃₂ #46834559

Order 34688.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₇₁⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₆×Dic₂₇₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₂×C₂₇₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₇₁⋊C₁₆	C₄	1	1	yes	characteristic
5	C₈×Dic₂₇₁	C₄	1	1	yes	characteristic
6	C₂₇₁⋊C₃₂	—	2	1	no	—
7	C₂×C₁₆×C₂₇₁	C₂²	1	1	yes	characteristic
8	C₃₂×C₂₇₁	—	2	1	no	—
9	C₂×C₂₇₁⋊C₈	C₈	1	1	yes	characteristic
10	C₄×Dic₂₇₁	C₈	1	1	yes	characteristic
11	C₂₇₁⋊C₁₆	—	2	1	no	—
12	C₂×C₈×C₂₇₁	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₂₇₁	D₄	1	1	yes	characteristic
14	C₁₆×C₂₇₁	Q₈	1	1	yes	characteristic
15	C₂×Dic₂₇₁	C₁₆	1	1	yes	characteristic
16	C₂×Dic₂₇₁	C₁₆	1	1	yes	characteristic
17	C₂₇₁⋊C₈	—	2	1	no	—
18	C₂×C₄×C₂₇₁	C₂×C₈	1	1	yes	characteristic
19	C₈×C₂₇₁	C₄⋊C₄	1	1	yes	characteristic
20	C₈×C₂₇₁	M₁₆	1	1	yes	characteristic
21	C₂²×C₂₇₁	C₂×C₁₆	1	1	yes	characteristic
22	C₄×C₂₇₁	C₄⋊C₈	1	1	yes	characteristic
23	C₄×C₂₇₁	M₃₂	1	1	yes	characteristic
24	Dic₂₇₁	—	2	1	no	—
25	Dic₂₇₁	C₃₂	1	2	yes	complemented
26	C₂×C₂₇₁	C₄⋊C₁₆	1	1	yes	characteristic
27	C₂×C₂₇₁	C₂×C₃₂	1	1	yes	characteristic
28	C₂×C₂₇₁	M₆₄	1	1	yes	characteristic
29	C₂₇₁	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
30	C₄⋊C₃₂	—	271	1	no	maximal, Sylow
31	C₂×C₃₂	—	271	1	no	—
32	C₂×C₃₂	D₂₇₁	1	1	yes	characteristic
33	C₄×C₁₆	—	271	1	no	—
34	C₂×C₁₆	—	271	1	no	—
35	C₂×C₁₆	C₂×D₂₇₁	1	1	yes	characteristic
36	C₄×C₈	—	271	1	no	—
37	C₃₂	—	2	1	no	—
38	C₃₂	—	542	1	no	—
39	C₂×C₈	—	271	1	no	—
40	C₂×C₈	C₄×D₂₇₁	1	1	yes	characteristic
41	C₄²	—	271	1	no	—
42	C₁₆	—	542	1	no	—
43	C₁₆	C₂²⋊D₂₇₁	1	1	yes	characteristic
44	C₁₆	Dic₅₄₂	1	1	yes	characteristic
45	C₂×C₄	—	271	1	no	—
46	C₂×C₄	—	271	1	no	—
47	C₂×C₄	C₈×D₂₇₁	1	1	yes	characteristic
48	C₈	—	542	1	no	—
49	C₈	Dic₂₇₁⋊C₄	1	1	yes	characteristic
50	C₈	#16864637	1	1	yes	characteristic
51	C₂²	C₁₆×D₂₇₁	1	1	yes	characteristic
52	C₄	—	271	2	no	—
53	C₄	—	542	1	no	—
54	C₄	Dic₂₇₁⋊C₈	1	1	yes	characteristic
55	C₄	#22576099	1	1	yes	characteristic
56	C₂	Dic₂₇₁⋊C₁₆	1	1	yes	characteristic
57	C₂	C₃₂×D₂₇₁	1	1	yes	characteristic
58	C₂	#31773730	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×D₂₇₁
commutator	C₂×C₂₇₁	C₂×C₃₂
Fitting	C₂×C₃₂×C₂₇₁	C₂
socle, prime radical	C₂²×C₂₇₁	C₂×C₁₆
cosocle	C₂×C₁₆×C₂₇₁	C₂²
hypercenter	C₂×C₃₂	D₂₇₁
hypocenter	C₂₇₁	C₄⋊C₃₂
LCS	G ▷ C₂×C₂₇₁ ▷ C₂₇₁
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
25. Dic₂₇₁	C₃₂	semidirect
29. C₂₇₁	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×C₂₇₁⋊C₃₂	2
C₁₆×Dic₂₇₁	2
C₂×C₃₂×C₂₇₁	2
C₄⋊C₃₂	271

Subgroups — Dic271⋊C32 #46834559

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₂₇₁⋊C₃₂ #46834559