Subgroups — Dic₃×M₁₆ #5117

Order 192.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#208	C₂	1	1	yes	maximal, characteristic
4	#815	C₂	1	2	yes	maximal, complemented
5	C₈×Dic₃	C₂	1	2	yes	maximal, complemented
6	C₄×M₁₆	—	3	1	no	maximal, Sylow
7	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
8	C₂²×Dic₃	C₄	1	2	yes	—
9	C₃×M₁₆	C₄	1	4	yes	complemented
10	C₂×C₃×C₈	C₂²	1	2	yes	—
11	C₄×Dic₃	C₄	1	2	yes	—
12	C₄×Dic₃	C₂²	1	1	yes	characteristic
13	C₄×Dic₃	C₂²	1	1	yes	characteristic
14	#208	C₄	1	4	yes	complemented
15	C₂×C₃⋊C₈	C₂²	1	2	yes	—
16	C₂×M₁₆	—	3	1	no	—
17	C₂×M₁₆	D₃	1	1	yes	characteristic
18	C₂×C₄²	—	3	1	no	—
19	#97	—	3	2	no	—
20	C₄×C₈	—	3	2	no	—
21	C₂³×C₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
23	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
24	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
25	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
26	C₂×Dic₃	—	2	4	no	—
27	C₂×Dic₃	C₂×C₄	1	2	yes	—
28	C₂×Dic₃	C₂×C₄	1	2	yes	—
29	C₃×C₈	C₂×C₄	1	4	yes	complemented
30	C₃⋊C₈	C₂×C₄	1	4	yes	complemented
31	C₂²×C₄	—	3	2	no	—
32	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
33	M₁₆	—	3	4	no	—
34	M₁₆	Dic₃	1	4	yes	direct product factor
35	C₂×C₈	—	3	2	no	—
36	C₂×C₈	C₂×D₃	1	2	yes	—
37	C₄²	—	3	2	no	—
38	C₄²	—	3	1	no	—
39	C₄²	—	3	1	no	—
40	C₂²×C₃	—	2	2	no	—
41	C₂²×C₃	C₄²	1	2	yes	—
42	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
43	C₃×C₄	C₄²	1	2	yes	—
44	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
45	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
46	Dic₃	—	2	2	no	—
47	Dic₃	M₁₆	1	4	yes	direct product factor
48	C₂³	C₄×D₃	1	1	yes	characteristic
49	C₂×C₄	—	3	2	no	—
50	C₂×C₄	—	3	2	no	—
51	C₂×C₄	—	6	4	no	—
52	C₂×C₄	C₄×D₃	1	1	yes	characteristic
53	C₂×C₄	C₄×D₃	1	2	yes	—
54	C₂×C₄	C₂×Dic₃	1	2	yes	—
55	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
56	C₈	—	3	4	no	—
57	C₈	C₂×Dic₃	1	4	yes	complemented
58	C₂×C₃	—	2	2	no	—
59	C₂×C₃	C₂×C₄²	1	1	yes	characteristic
60	C₂×C₃	C₂×M₁₆	1	2	yes	—
61	C₂²	—	2	2	no	—
62	C₂²	C₄×Dic₃	1	2	yes	—
63	C₂²	C₂×C₄×D₃	1	1	yes	characteristic
64	C₄	—	3	4	no	—
65	C₄	—	6	2	no	—
66	C₄	C₄×Dic₃	1	2	yes	—
67	C₄	C₂×C₄×D₃	1	1	yes	characteristic
68	C₄	C₂²×Dic₃	1	1	yes	characteristic
69	C₃	C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
70	C₂	—	2	2	no	—
71	C₂	D₃×M₁₆	1	2	yes	—
72	C₂	C₂×C₄×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃
commutator	C₂×C₃	C₂×C₄²
Fitting	C₂×C₃×M₁₆	C₂
socle	C₂²×C₃	C₂²×C₄
prime radical	C₂³×C₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂³
hypercenter	C₂×M₁₆	D₃
hypocenter	C₃	C₄×M₁₆
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
4. #815	C₂	semidirect
5. C₈×Dic₃	C₂	semidirect
9. C₃×M₁₆	C₄	semidirect
14. #208	C₄	semidirect
29. C₃×C₈	C₂×C₄	semidirect
30. C₃⋊C₈	C₂×C₄	semidirect
34. M₁₆	Dic₃	direct (N × H)
47. Dic₃	M₁₆	direct (N × H)
57. C₈	C₂×Dic₃	semidirect
69. C₃	C₄×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×M₁₆	2
C₂×C₄×Dic₃	2
C₂×#208	2
#815	2
C₈×Dic₃	2
C₄×M₁₆	3

Subgroups — Dic3×M16 #5117

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃×M₁₆ #5117