Subgroups — D₃×D₁₆ #4910

Order 192.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×D₈	C₂	1	2	yes	maximal, complemented
2	C₃×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#826	C₂	1	2	yes	maximal, complemented
4	D₄₈	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₆	—	3	1	no	maximal, Sylow
7	D₃×D₄	—	2	2	no	—
8	C₃×D₈	C₂²	1	2	yes	complemented
9	#213	—	2	2	no	—
10	D₂₄	C₂²	1	2	yes	complemented
11	D₃×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
13	C₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
14	C₂×D₈	—	3	2	no	—
15	D₁₆	—	3	2	no	—
16	D₁₆	—	3	1	no	—
17	D₁₆	D₃	1	1	yes	characteristic, direct product factor
18	C₂×C₁₆	—	3	1	no	—
19	C₂²×D₃	—	4	2	no	—
20	C₃×D₄	—	2	2	no	—
21	#67	—	4	2	no	—
22	D₁₂	—	2	2	no	—
23	C₄×D₃	D₄	1	1	yes	characteristic
24	C₃×C₈	C₂³	1	1	yes	characteristic
25	C₃⋊C₈	D₄	1	1	yes	characteristic
26	C₂×D₄	—	6	2	no	—
27	D₈	—	3	2	no	—
28	D₈	—	6	2	no	—
29	D₈	C₂×D₃	1	2	yes	complemented
30	C₂×C₈	—	3	1	no	—
31	C₁₆	—	3	1	no	—
32	C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
33	C₂²×C₃	—	4	2	no	—
34	C₂×D₃	—	4	2	no	—
35	C₂×D₃	—	8	4	no	—
36	C₂×D₃	D₈	1	1	yes	characteristic
37	C₃×C₄	C₂×D₄	1	1	yes	characteristic
38	Dic₃	D₈	1	1	yes	characteristic
39	C₂³	—	12	2	no	—
40	D₄	—	2	2	no	—
41	D₄	—	6	2	no	—
42	D₄	—	12	2	no	—
43	C₂×C₄	—	3	1	no	—
44	C₈	—	3	1	no	—
45	C₈	C₂²×D₃	1	1	yes	characteristic
46	C₂×C₃	—	8	2	no	—
47	C₂×C₃	C₂×D₈	1	1	yes	characteristic
48	D₃	—	8	2	no	—
49	D₃	D₁₆	1	2	yes	direct product factor
50	C₂²	—	3	1	no	—
51	C₂²	—	4	2	no	—
52	C₂²	—	12	2	no	—
53	C₂²	—	24	4	no	—
54	C₄	—	3	1	no	—
55	C₄	D₃×D₄	1	1	yes	characteristic
56	C₃	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
57	C₂	—	3	2	no	—
58	C₂	—	8	2	no	—
59	C₂	—	24	2	no	—
60	C₂	D₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₃×D₈
commutator, cosocle	C₃×C₈	C₂³
Frattini	C₈	C₂²×D₃
Fitting	C₃×D₁₆	C₂
socle	C₂×C₃	C₂×D₈
hypercenter	D₁₆	D₃
hypocenter	C₃	C₂×D₁₆
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. D₃×D₈	C₂	semidirect
2. C₃×D₁₆	C₂	semidirect
3. #826	C₂	semidirect
4. D₄₈	C₂	semidirect
5. D₃×C₁₆	C₂	semidirect
8. C₃×D₈	C₂²	semidirect
10. D₂₄	C₂²	semidirect
12. C₃×C₁₆	C₂²	semidirect
13. C₃⋊C₁₆	C₂²	semidirect
17. D₁₆	D₃	direct (N × H)
29. D₈	C₂×D₃	semidirect
32. C₁₆	C₂×D₃	semidirect
49. D₃	D₁₆	direct (N × H)
56. C₃	C₂×D₁₆	semidirect

Maximal subgroups

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

subgroup	index
D₃×D₈	2
C₃×D₁₆	2
#826	2
D₄₈	2
D₃×C₁₆	2
C₂×D₁₆	3

Subgroups — D3×D16 #4910

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₁₆ #4910