Subgroups — D₁₆×D₃₁₃ #34094571

Order 20032.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈×D₃₁₃	C₂	1	2	yes	maximal, complemented
2	D₅₀₀₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#23756438	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₃₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₆×C₃₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×D₃₁₃	—	2	2	no	—
7	D₂₅₀₄	C₂²	1	2	yes	complemented
8	#19097546	—	2	2	no	—
9	C₈×D₃₁₃	C₂²	1	1	yes	characteristic
10	#19097536	C₂²	1	1	yes	characteristic, complemented
11	D₈×C₃₁₃	C₂²	1	2	yes	complemented
12	C₁₆×C₃₁₃	C₂²	1	1	yes	characteristic, complemented
13	C₂²×D₃₁₃	—	4	2	no	—
14	D₁₂₅₂	—	2	2	no	—
15	C₂²⋊D₃₁₃	—	4	2	no	—
16	C₄×D₃₁₃	D₄	1	1	yes	characteristic
17	#14578809	D₄	1	1	yes	characteristic
18	D₄×C₃₁₃	—	2	2	no	—
19	C₈×C₃₁₃	C₂³	1	1	yes	characteristic
20	C₂²×C₃₁₃	—	4	2	no	—
21	C₂×D₃₁₃	—	4	2	no	—
22	C₂×D₃₁₃	—	8	4	no	—
23	C₂×D₃₁₃	D₈	1	1	yes	characteristic
24	C₄×C₃₁₃	C₂×D₄	1	1	yes	characteristic
25	Dic₃₁₃	D₈	1	1	yes	characteristic
26	C₂×C₃₁₃	—	8	2	no	—
27	C₂×C₃₁₃	C₂×D₈	1	1	yes	characteristic
28	D₃₁₃	—	8	2	no	—
29	D₃₁₃	D₁₆	1	2	yes	direct product factor
30	C₃₁₃	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
31	C₂×D₁₆	—	313	1	no	maximal, Sylow
32	C₂×D₈	—	313	2	no	—
33	D₁₆	—	313	2	no	—
34	D₁₆	—	313	1	no	—
35	D₁₆	D₃₁₃	1	1	yes	characteristic, direct product factor
36	C₂×C₁₆	—	313	1	no	—
37	C₂×D₄	—	626	2	no	—
38	D₈	—	313	2	no	—
39	D₈	—	626	2	no	—
40	D₈	C₂×D₃₁₃	1	2	yes	complemented
41	C₂×C₈	—	313	1	no	—
42	C₁₆	—	313	1	no	—
43	C₁₆	C₂×D₃₁₃	1	1	yes	characteristic, complemented
44	C₂³	—	1252	2	no	—
45	D₄	—	2	2	no	—
46	D₄	—	626	2	no	—
47	D₄	—	1252	2	no	—
48	C₂×C₄	—	313	1	no	—
49	C₈	—	313	1	no	—
50	C₈	C₂²×D₃₁₃	1	1	yes	characteristic
51	C₂²	—	4	2	no	—
52	C₂²	—	313	1	no	—
53	C₂²	—	2504	4	no	—
54	C₂²	—	1252	2	no	—
55	C₄	—	313	1	no	—
56	C₄	D₄×D₃₁₃	1	1	yes	characteristic
57	C₂	—	8	2	no	—
58	C₂	—	313	2	no	—
59	C₂	—	2504	2	no	—
60	C₂	D₈×D₃₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₃₁₃
commutator, cosocle	C₈×C₃₁₃	C₂³
Frattini	C₈	C₂²×D₃₁₃
Fitting	D₁₆×C₃₁₃	C₂
socle	C₂×C₃₁₃	C₂×D₈
hypercenter	D₁₆	D₃₁₃
hypocenter	C₃₁₃	C₂×D₁₆
LCS	G ▷ C₈×C₃₁₃ ▷ C₄×C₃₁₃ ▷ C₂×C₃₁₃ ▷ C₃₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. D₈×D₃₁₃	C₂	semidirect
2. D₅₀₀₈	C₂	semidirect
3. #23756438	C₂	semidirect
4. C₁₆×D₃₁₃	C₂	semidirect
5. D₁₆×C₃₁₃	C₂	semidirect
7. D₂₅₀₄	C₂²	semidirect
10. #19097536	C₂²	semidirect
11. D₈×C₃₁₃	C₂²	semidirect
12. C₁₆×C₃₁₃	C₂²	semidirect
29. D₃₁₃	D₁₆	direct (N × H)
30. C₃₁₃	C₂×D₁₆	semidirect
35. D₁₆	D₃₁₃	direct (N × H)
40. D₈	C₂×D₃₁₃	semidirect
43. C₁₆	C₂×D₃₁₃	semidirect

Maximal subgroups

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

subgroup	index
D₈×D₃₁₃	2
D₅₀₀₈	2
#23756438	2
C₁₆×D₃₁₃	2
D₁₆×C₃₁₃	2
C₂×D₁₆	313

Subgroups — D16×D313 #34094571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₆×D₃₁₃ #34094571