Subgroups — D₂₉×D₃₂ #16821788

Order 3712.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₆×D₂₉	C₂	1	2	yes	maximal, complemented
2	D₉₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#14270998	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×D₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	D₈×D₂₉	—	2	2	no	—
7	C₂₉×D₁₆	C₂²	1	2	yes	complemented
8	#11745174	—	2	2	no	—
9	D₄₆₄	C₂²	1	2	yes	complemented
10	C₁₆×D₂₉	C₂²	1	1	yes	characteristic
11	C₂₉×C₃₂	C₂²	1	1	yes	characteristic, complemented
12	#11745142	C₂²	1	1	yes	characteristic, complemented
13	D₄×D₂₉	—	4	2	no	—
14	D₈×C₂₉	—	2	2	no	—
15	#90782	—	4	2	no	—
16	D₂₃₂	—	2	2	no	—
17	C₈×D₂₉	D₄	1	1	yes	characteristic
18	C₁₆×C₂₉	C₂³	1	1	yes	characteristic
19	#90768	D₄	1	1	yes	characteristic
20	C₂²×D₂₉	—	8	2	no	—
21	D₄×C₂₉	—	4	2	no	—
22	C₂²⋊D₂₉	—	8	2	no	—
23	D₁₁₆	—	4	2	no	—
24	C₄×D₂₉	D₈	1	1	yes	characteristic
25	C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
26	#6597	D₈	1	1	yes	characteristic
27	C₂×D₃₂	—	29	1	no	maximal, Sylow
28	C₂²×C₂₉	—	8	2	no	—
29	C₂×D₂₉	—	8	2	no	—
30	C₂×D₂₉	—	16	4	no	—
31	C₂×D₂₉	D₁₆	1	1	yes	characteristic
32	C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
33	Dic₂₉	D₁₆	1	1	yes	characteristic
34	C₂×D₁₆	—	29	2	no	—
35	D₃₂	—	29	2	no	—
36	D₃₂	—	29	1	no	—
37	D₃₂	D₂₉	1	1	yes	characteristic, direct product factor
38	C₂×C₃₂	—	29	1	no	—
39	C₂×C₂₉	—	16	2	no	—
40	C₂×C₂₉	C₂×D₁₆	1	1	yes	characteristic
41	D₂₉	—	16	2	no	—
42	D₂₉	D₃₂	1	2	yes	direct product factor
43	C₂×D₈	—	58	2	no	—
44	D₁₆	—	29	2	no	—
45	D₁₆	—	58	2	no	—
46	D₁₆	C₂×D₂₉	1	2	yes	complemented
47	C₂×C₁₆	—	29	1	no	—
48	C₃₂	—	29	1	no	—
49	C₃₂	C₂×D₂₉	1	1	yes	characteristic, complemented
50	C₂₉	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
51	C₂×D₄	—	116	2	no	—
52	D₈	—	2	2	no	—
53	D₈	—	58	2	no	—
54	D₈	—	116	2	no	—
55	C₂×C₈	—	29	1	no	—
56	C₁₆	—	29	1	no	—
57	C₁₆	C₂²×D₂₉	1	1	yes	characteristic
58	C₂³	—	232	2	no	—
59	D₄	—	4	2	no	—
60	D₄	—	116	2	no	—
61	D₄	—	232	2	no	—
62	C₂×C₄	—	29	1	no	—
63	C₈	—	29	1	no	—
64	C₈	D₄×D₂₉	1	1	yes	characteristic
65	C₂²	—	8	2	no	—
66	C₂²	—	29	1	no	—
67	C₂²	—	464	4	no	—
68	C₂²	—	232	2	no	—
69	C₄	—	29	1	no	—
70	C₄	D₈×D₂₉	1	1	yes	characteristic
71	C₂	—	16	2	no	—
72	C₂	—	29	2	no	—
73	C₂	—	464	2	no	—
74	C₂	D₁₆×D₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₂₉
commutator, cosocle	C₁₆×C₂₉	C₂³
Frattini	C₁₆	C₂²×D₂₉
Fitting	C₂₉×D₃₂	C₂
socle	C₂×C₂₉	C₂×D₁₆
hypercenter	D₃₂	D₂₉
hypocenter	C₂₉	C₂×D₃₂
LCS	G ▷ C₁₆×C₂₉ ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₃₂

Complements

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

N	H ≅ G/N	type
1. D₁₆×D₂₉	C₂	semidirect
2. D₉₂₈	C₂	semidirect
3. #14270998	C₂	semidirect
4. C₃₂×D₂₉	C₂	semidirect
5. C₂₉×D₃₂	C₂	semidirect
7. C₂₉×D₁₆	C₂²	semidirect
9. D₄₆₄	C₂²	semidirect
11. C₂₉×C₃₂	C₂²	semidirect
12. #11745142	C₂²	semidirect
37. D₃₂	D₂₉	direct (N × H)
42. D₂₉	D₃₂	direct (N × H)
46. D₁₆	C₂×D₂₉	semidirect
49. C₃₂	C₂×D₂₉	semidirect
50. C₂₉	C₂×D₃₂	semidirect

Maximal subgroups

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

subgroup	index
D₁₆×D₂₉	2
D₉₂₈	2
#14270998	2
C₃₂×D₂₉	2
C₂₉×D₃₂	2
C₂×D₃₂	29

Subgroups — D29×D32 #16821788

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₉×D₃₂ #16821788