Subgroups — C₁₆×Dic₃₁ #14520822

Order 1984.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
5	C₄×Dic₃₁	C₄	1	1	yes	characteristic
6	C₂×C₃₁⋊C₈	C₄	1	1	yes	characteristic
7	C₁₆×C₃₁	C₄	1	2	yes	complemented
8	C₃₁⋊C₁₆	C₄	1	2	yes	complemented
9	C₂×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
10	C₂×Dic₃₁	C₈	1	2	yes	—
11	C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
12	C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
13	C₃₁⋊C₈	C₈	1	2	yes	—
14	C₂²×C₃₁	C₂×C₈	1	1	yes	characteristic
15	C₄×C₃₁	C₄²	1	1	yes	characteristic
16	C₄×C₃₁	C₂×C₈	1	1	yes	characteristic
17	Dic₃₁	C₁₆	1	4	yes	direct product factor
18	C₄×C₁₆	—	31	1	no	maximal, Sylow
19	C₂×C₃₁	C₄×C₈	1	1	yes	characteristic
20	C₂×C₃₁	C₂×C₁₆	1	2	yes	—
21	C₂×C₁₆	—	31	1	no	—
22	C₂×C₁₆	D₃₁	1	1	yes	characteristic
23	C₄×C₈	—	31	1	no	—
24	C₃₁	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₈	—	31	1	no	—
26	C₂×C₈	C₂×D₃₁	1	1	yes	characteristic
27	C₄²	—	31	1	no	—
28	C₁₆	—	31	2	no	—
29	C₁₆	Dic₃₁	1	2	yes	direct product factor
30	C₂×C₄	—	31	2	no	—
31	C₂×C₄	C₄×D₃₁	1	1	yes	characteristic
32	C₈	—	31	2	no	—
33	C₈	C₄×D₃₁	1	1	yes	characteristic
34	C₈	C₂×Dic₃₁	1	1	yes	characteristic
35	C₂²	C₈×D₃₁	1	1	yes	characteristic
36	C₄	—	31	4	no	—
37	C₄	C₈×D₃₁	1	1	yes	characteristic
38	C₄	C₄×Dic₃₁	1	1	yes	characteristic
39	C₂	C₁₆×D₃₁	1	2	yes	—
40	C₂	C₈×Dic₃₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₆	D₃₁
commutator, hypocenter	C₃₁	C₄×C₁₆
Frattini	C₂×C₈	C₂×D₃₁
Fitting	C₂×C₁₆×C₃₁	C₂
socle, prime radical	C₂²×C₃₁	C₂×C₈
cosocle	C₂×C₈×C₃₁	C₂²
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
7. C₁₆×C₃₁	C₄	semidirect
8. C₃₁⋊C₁₆	C₄	semidirect
17. Dic₃₁	C₁₆	direct (N × H)
24. C₃₁	C₄×C₁₆	semidirect
29. C₁₆	Dic₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₆×C₃₁	2
C₈×Dic₃₁	2
C₂×C₃₁⋊C₁₆	2
C₄×C₁₆	31

Subgroups — C16×Dic31 #14520822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₆×Dic₃₁ #14520822