Subgroups — D₃×D₃₂ #69375

Order 384.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×D₁₆	C₂	1	2	yes	maximal, complemented
2	C₃×D₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#4519	C₂	1	2	yes	maximal, complemented
4	D₉₆	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₃₂	—	3	1	no	maximal, Sylow
7	D₃×D₈	—	2	2	no	—
8	C₃×D₁₆	C₂²	1	2	yes	complemented
9	#826	—	2	2	no	—
10	D₄₈	C₂²	1	2	yes	complemented
11	D₃×C₁₆	C₂²	1	1	yes	characteristic
12	C₃×C₃₂	C₂²	1	1	yes	characteristic, complemented
13	C₃⋊C₃₂	C₂²	1	1	yes	characteristic, complemented
14	C₂×D₁₆	—	3	2	no	—
15	D₃₂	—	3	2	no	—
16	D₃₂	—	3	1	no	—
17	D₃₂	D₃	1	1	yes	characteristic, direct product factor
18	C₂×C₃₂	—	3	1	no	—
19	D₃×D₄	—	4	2	no	—
20	C₃×D₈	—	2	2	no	—
21	#213	—	4	2	no	—
22	D₂₄	—	2	2	no	—
23	D₃×C₈	D₄	1	1	yes	characteristic
24	C₃×C₁₆	C₂³	1	1	yes	characteristic
25	C₃⋊C₁₆	D₄	1	1	yes	characteristic
26	C₂×D₈	—	6	2	no	—
27	D₁₆	—	3	2	no	—
28	D₁₆	—	6	2	no	—
29	D₁₆	C₂×D₃	1	2	yes	complemented
30	C₂×C₁₆	—	3	1	no	—
31	C₃₂	—	3	1	no	—
32	C₃₂	C₂×D₃	1	1	yes	characteristic, complemented
33	C₂²×D₃	—	8	2	no	—
34	C₃×D₄	—	4	2	no	—
35	#67	—	8	2	no	—
36	D₁₂	—	4	2	no	—
37	C₄×D₃	D₈	1	1	yes	characteristic
38	C₃×C₈	C₂×D₄	1	1	yes	characteristic
39	C₃⋊C₈	D₈	1	1	yes	characteristic
40	C₂×D₄	—	12	2	no	—
41	D₈	—	2	2	no	—
42	D₈	—	6	2	no	—
43	D₈	—	12	2	no	—
44	C₂×C₈	—	3	1	no	—
45	C₁₆	—	3	1	no	—
46	C₁₆	C₂²×D₃	1	1	yes	characteristic
47	C₂²×C₃	—	8	2	no	—
48	C₂×D₃	—	8	2	no	—
49	C₂×D₃	—	16	4	no	—
50	C₂×D₃	D₁₆	1	1	yes	characteristic
51	C₃×C₄	C₂×D₈	1	1	yes	characteristic
52	Dic₃	D₁₆	1	1	yes	characteristic
53	C₂³	—	24	2	no	—
54	D₄	—	4	2	no	—
55	D₄	—	12	2	no	—
56	D₄	—	24	2	no	—
57	C₂×C₄	—	3	1	no	—
58	C₈	—	3	1	no	—
59	C₈	D₃×D₄	1	1	yes	characteristic
60	C₂×C₃	—	16	2	no	—
61	C₂×C₃	C₂×D₁₆	1	1	yes	characteristic
62	D₃	—	16	2	no	—
63	D₃	D₃₂	1	2	yes	direct product factor
64	C₂²	—	3	1	no	—
65	C₂²	—	8	2	no	—
66	C₂²	—	24	2	no	—
67	C₂²	—	48	4	no	—
68	C₄	—	3	1	no	—
69	C₄	D₃×D₈	1	1	yes	characteristic
70	C₃	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
71	C₂	—	3	2	no	—
72	C₂	—	16	2	no	—
73	C₂	—	48	2	no	—
74	C₂	D₃×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₃×D₁₆
commutator, cosocle	C₃×C₁₆	C₂³
Frattini	C₁₆	C₂²×D₃
Fitting	C₃×D₃₂	C₂
socle	C₂×C₃	C₂×D₁₆
hypercenter	D₃₂	D₃
hypocenter	C₃	C₂×D₃₂
LCS	G ▷ C₃×C₁₆ ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₃₂

Complements

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

N	H ≅ G/N	type
1. D₃×D₁₆	C₂	semidirect
2. C₃×D₃₂	C₂	semidirect
3. #4519	C₂	semidirect
4. D₉₆	C₂	semidirect
5. D₃×C₃₂	C₂	semidirect
8. C₃×D₁₆	C₂²	semidirect
10. D₄₈	C₂²	semidirect
12. C₃×C₃₂	C₂²	semidirect
13. C₃⋊C₃₂	C₂²	semidirect
17. D₃₂	D₃	direct (N × H)
29. D₁₆	C₂×D₃	semidirect
32. C₃₂	C₂×D₃	semidirect
63. D₃	D₃₂	direct (N × H)
70. C₃	C₂×D₃₂	semidirect

Maximal subgroups

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

subgroup	index
D₃×D₁₆	2
C₃×D₃₂	2
#4519	2
D₉₆	2
D₃×C₃₂	2
C₂×D₃₂	3

Subgroups — D3×D32 #69375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₃₂ #69375