Subgroups — D₃×M₃₂ #4906

Order 192.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#812	C₂	1	1	yes	maximal, characteristic, complemented
4	#798	C₂	1	2	yes	maximal, complemented
5	D₃×C₁₆	C₂	1	2	yes	maximal, complemented
6	C₂×M₃₂	—	3	1	no	maximal, Sylow
7	C₂×C₄×D₃	C₄	1	1	yes	characteristic
8	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
9	C₂×C₃⋊C₈	C₄	1	1	yes	characteristic
10	D₃×C₈	C₄	1	1	yes	characteristic
11	D₃×C₈	C₄	1	1	yes	characteristic
12	D₃×C₈	C₂²	1	1	yes	characteristic
13	D₃×C₈	C₂²	1	1	yes	characteristic
14	C₃×C₁₆	C₂²	1	2	yes	complemented
15	C₃⋊C₁₆	C₂²	1	2	yes	complemented
16	C₂²×C₈	—	3	1	no	—
17	M₃₂	—	3	1	no	—
18	M₃₂	—	3	2	no	—
19	M₃₂	D₃	1	1	yes	characteristic, direct product factor
20	C₂×C₁₆	—	3	2	no	—
21	C₂²×D₃	C₈	1	1	yes	characteristic
22	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
23	C₂×Dic₃	C₈	1	1	yes	characteristic
24	C₄×D₃	C₈	1	1	yes	characteristic
25	C₄×D₃	C₈	1	1	yes	characteristic
26	C₄×D₃	C₂×C₄	1	1	yes	characteristic
27	C₄×D₃	C₂×C₄	1	1	yes	characteristic
28	C₃×C₈	C₂×C₄	1	1	yes	characteristic
29	C₃×C₈	C₂³	1	1	yes	characteristic
30	C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
31	C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₄	—	3	1	no	—
33	C₂×C₈	—	3	1	no	—
34	C₂×C₈	—	3	1	no	—
35	C₂×C₈	—	3	1	no	—
36	C₂×C₈	—	3	1	no	—
37	C₂×C₈	—	3	1	no	—
38	C₂×C₈	C₂×D₃	1	1	yes	characteristic
39	C₁₆	—	3	2	no	—
40	C₁₆	C₂×D₃	1	2	yes	complemented
41	C₂²×C₃	C₂×C₈	1	1	yes	characteristic
42	C₂×D₃	—	2	2	no	—
43	C₂×D₃	C₂×C₈	1	1	yes	characteristic
44	C₂×D₃	C₂×C₈	1	1	yes	characteristic
45	C₃×C₄	C₂×C₈	1	1	yes	characteristic
46	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
47	Dic₃	C₂×C₈	1	1	yes	characteristic
48	Dic₃	C₂×C₈	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	C₄×D₃	1	1	yes	characteristic
56	C₈	—	3	1	no	—
57	C₈	—	3	1	no	—
58	C₈	C₄×D₃	1	1	yes	characteristic
59	C₈	C₂²×D₃	1	1	yes	characteristic
60	C₂×C₃	—	2	1	no	—
61	C₂×C₃	C₂²×C₈	1	1	yes	characteristic
62	D₃	—	2	1	no	—
63	D₃	M₃₂	1	2	yes	direct product factor
64	C₂²	—	3	1	no	—
65	C₂²	—	3	1	no	—
66	C₂²	—	6	2	no	—
67	C₂²	D₃×C₈	1	1	yes	characteristic
68	C₄	—	3	1	no	—
69	C₄	—	3	1	no	—
70	C₄	D₃×C₈	1	1	yes	characteristic
71	C₄	C₂×C₄×D₃	1	1	yes	characteristic
72	C₃	C₂×M₃₂	1	1	yes	characteristic, complemented, Sylow
73	C₂	—	2	1	no	—
74	C₂	—	3	2	no	—
75	C₂	—	6	1	no	—
76	C₂	C₂×D₃×C₈	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×D₃
commutator, socle	C₂×C₃	C₂²×C₈
Fitting	C₃×M₃₂	C₂
prime radical	C₂²×D₃	C₈
cosocle	C₃×C₈	C₂³
hypercenter	M₃₂	D₃
hypocenter	C₃	C₂×M₃₂
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. C₃×M₃₂	C₂	semidirect
3. #812	C₂	semidirect
4. #798	C₂	semidirect
5. D₃×C₁₆	C₂	semidirect
14. C₃×C₁₆	C₂²	semidirect
15. C₃⋊C₁₆	C₂²	semidirect
19. M₃₂	D₃	direct (N × H)
40. C₁₆	C₂×D₃	semidirect
63. D₃	M₃₂	direct (N × H)
72. C₃	C₂×M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×C₈	2
C₃×M₃₂	2
#812	2
#798	2
D₃×C₁₆	2
C₂×M₃₂	3

Subgroups — D3×M32 #4906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×M₃₂ #4906