Subgroups — D₃×#108 #4892

Order 192.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×M₁₆	C₂	1	2	yes	maximal
2	C₂×D₃×C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
4	#822	C₂	1	2	yes	maximal, complemented
5	#819	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#108	—	3	1	no	maximal, Sylow
7	C₂×C₄×D₃	C₂²	1	1	yes	characteristic
8	C₃×M₁₆	C₂²	1	2	yes	—
9	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
10	#208	C₂²	1	2	yes	—
11	C₂×C₃⋊C₈	C₂²	1	1	yes	characteristic
12	ΓL(1,𝔽₂₅)	—	2	2	no	—
13	D₃×C₈	—	2	2	no	—
14	D₃×C₈	C₄	1	2	yes	—
15	D₃×C₈	C₄	1	2	yes	—
16	C₂×M₁₆	—	3	2	no	—
17	C₂²×C₈	—	3	1	no	—
18	#108	—	3	2	no	—
19	#108	—	3	1	no	—
20	#108	D₃	1	1	yes	characteristic, direct product factor
21	C₂²×D₃	Q₈	1	1	yes	characteristic
22	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
23	C₂×Dic₃	Q₈	1	1	yes	characteristic
24	C₄×D₃	C₂×C₄	1	1	yes	characteristic
25	C₄×D₃	C₂×C₄	1	1	yes	characteristic
26	C₄×D₃	D₄	1	1	yes	characteristic
27	C₄×D₃	D₄	1	1	yes	characteristic
28	C₃×C₈	—	2	2	no	—
29	C₃×C₈	C₂×C₄	1	2	yes	—
30	C₃⋊C₈	—	2	2	no	—
31	C₃⋊C₈	C₂×C₄	1	2	yes	—
32	C₂²×C₄	—	3	1	no	—
33	M₁₆	—	3	2	no	—
34	M₁₆	—	6	2	no	—
35	M₁₆	C₂×D₃	1	2	yes	—
36	C₂×C₈	—	3	1	no	—
37	C₂×C₈	—	3	2	no	—
38	C₂×C₈	—	3	2	no	—
39	C₂×C₈	—	6	2	no	—
40	C₂×C₈	C₂×D₃	1	1	yes	characteristic
41	C₂²×C₃	C₂×Q₈	1	1	yes	characteristic
42	C₂×D₃	—	2	2	no	—
43	C₂×D₃	C₄⋊C₄	1	1	yes	characteristic
44	C₂×D₃	C₄⋊C₄	1	1	yes	characteristic
45	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
46	C₃×C₄	C₂×D₄	1	1	yes	characteristic
47	Dic₃	C₄⋊C₄	1	1	yes	characteristic
48	Dic₃	C₄⋊C₄	1	1	yes	characteristic
49	C₂³	—	3	1	no	—
50	C₂×C₄	—	3	1	no	—
51	C₂×C₄	—	3	1	no	—
52	C₂×C₄	—	3	1	no	—
53	C₂×C₄	—	3	1	no	—
54	C₂×C₄	—	3	1	no	—
55	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
56	C₈	—	2	2	no	—
57	C₈	—	3	2	no	—
58	C₈	—	6	2	no	—
59	C₈	C₄×D₃	1	2	yes	—
60	C₂×C₃	—	2	1	no	—
61	C₂×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
62	D₃	—	2	1	no	—
63	D₃	#108	1	2	yes	direct product factor
64	C₂²	—	3	1	no	—
65	C₂²	—	3	1	no	—
66	C₂²	—	6	2	no	—
67	C₂²	D₃×Q₈	1	1	yes	characteristic
68	C₄	—	3	1	no	—
69	C₄	—	3	1	no	—
70	C₄	C₂×C₄×D₃	1	1	yes	characteristic
71	C₄	D₃×D₄	1	1	yes	characteristic
72	C₃	C₂×#108	1	1	yes	characteristic, complemented, Sylow
73	C₂	—	2	1	no	—
74	C₂	—	3	2	no	—
75	C₂	—	6	1	no	—
76	C₂	D₃×C₄⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₃×D₄
commutator	C₃×C₄	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₃×#108	C₂
socle	C₂×C₃	C₂×C₄⋊C₄
prime radical	C₂²×D₃	Q₈
cosocle	C₂×C₃×C₄	C₂³
hypercenter	#108	D₃
hypocenter	C₃	C₂×#108
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
3. C₃×#108	C₂	semidirect
4. #822	C₂	semidirect
5. #819	C₂	semidirect
20. #108	D₃	direct (N × H)
63. D₃	#108	direct (N × H)
72. C₃	C₂×#108	semidirect

Maximal subgroups

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

subgroup	index
D₃×M₁₆	2
C₂×D₃×C₈	2
C₃×#108	2
#822	2
#819	2
C₂×#108	3

Subgroups — D3×#108 #4892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#108 #4892