Subgroups — D₃×#95 #4663

Order 192.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₃	C₂	1	3	yes	maximal
2	C₃×#95	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊#95	C₂	1	3	yes	maximal, complemented
4	C₂×#95	—	3	1	no	maximal, Sylow
5	C₂³×D₃	C₂²	1	1	yes	characteristic
6	C₂²×C₃×C₄	C₂²	1	3	yes	—
7	C₂²×Dic₃	C₂²	1	3	yes	—
8	C₂×C₄×D₃	—	2	12	no	—
9	C₂×C₄×D₃	C₄	1	12	yes	complemented
10	C₂³×C₄	—	3	3	no	—
11	#95	—	3	3	no	—
12	#95	D₃	1	1	yes	characteristic, direct product factor
13	C₂³×C₃	C₂³	1	1	yes	characteristic
14	C₂²×D₃	C₂×C₄	1	6	yes	—
15	C₂²×D₃	D₄	1	6	yes	—
16	C₂²×D₃	Q₈	1	2	yes	—
17	C₂×C₃×C₄	—	2	6	no	—
18	C₂×C₃×C₄	C₂×C₄	1	6	yes	complemented
19	C₂×Dic₃	—	2	6	no	—
20	C₂×Dic₃	C₂×C₄	1	6	yes	complemented
21	C₄×D₃	—	2	24	no	—
22	C₂⁴	—	3	1	no	—
23	C₂²×C₄	—	3	3	no	—
24	C₂²×C₄	—	3	12	no	—
25	C₂²×C₄	—	6	12	no	—
26	C₂²×C₄	C₂×D₃	1	3	yes	—
27	C₂²×C₃	C₂²×C₄	1	3	yes	—
28	C₂²×C₃	C₂×D₄	1	3	yes	—
29	C₂²×C₃	C₂×Q₈	1	1	yes	characteristic
30	C₂×D₃	C₄²	1	4	yes	—
31	C₂×D₃	C₂²⋊C₄	1	12	yes	—
32	C₂×D₃	C₄⋊C₄	1	12	yes	—
33	C₃×C₄	—	2	6	no	—
34	Dic₃	—	2	6	no	—
35	C₂³	—	3	6	no	—
36	C₂³	—	3	6	no	—
37	C₂³	—	3	2	no	—
38	C₂³	C₂²×D₃	1	1	yes	characteristic
39	C₂×C₄	—	2	6	no	—
40	C₂×C₄	—	3	6	no	—
41	C₂×C₄	—	6	24	no	—
42	C₂×C₄	—	6	6	no	—
43	C₂×C₄	C₄×D₃	1	6	yes	complemented
44	C₂×C₃	C₂×C₄²	1	1	yes	characteristic
45	C₂×C₃	C₂×C₂²⋊C₄	1	3	yes	—
46	C₂×C₃	C₂×C₄⋊C₄	1	3	yes	—
47	D₃	#95	1	8	yes	direct product factor
48	C₂²	—	3	4	no	—
49	C₂²	—	3	12	no	—
50	C₂²	—	3	12	no	—
51	C₂²	C₂×C₄×D₃	1	3	yes	—
52	C₂²	D₃×D₄	1	3	yes	—
53	C₂²	D₃×Q₈	1	1	yes	characteristic
54	C₄	—	2	6	no	—
55	C₄	—	6	6	no	—
56	C₃	C₂×#95	1	1	yes	characteristic, complemented, Sylow
57	C₂	—	3	8	no	—
58	C₂	C₄²×D₃	1	1	yes	characteristic
59	C₂	D₃×C₂²⋊C₄	1	3	yes	—
60	C₂	D₃×C₄⋊C₄	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₃
commutator	C₂×C₃	C₂×C₄²
Fitting	C₃×#95	C₂
socle, cosocle	C₂³×C₃	C₂³
prime radical	C₂³×D₃	C₂²
hypercenter	#95	D₃
hypocenter	C₃	C₂×#95
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
2. C₃×#95	C₂	semidirect
3. C₃⋊#95	C₂	semidirect
9. C₂×C₄×D₃	C₄	semidirect
12. #95	D₃	direct (N × H)
18. C₂×C₃×C₄	C₂×C₄	semidirect
20. C₂×Dic₃	C₂×C₄	semidirect
43. C₂×C₄	C₄×D₃	semidirect
47. D₃	#95	direct (N × H)
56. C₃	C₂×#95	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₃	2
C₃×#95	2
C₃⋊#95	2
C₂×#95	3

Subgroups — D3×#95 #4663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#95 #4663