Subgroups — C₂×D₂₉⋊C₃₂ #16835911

Order 3712.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₉⋊C₃₂	C₂	1	4	yes	maximal, direct product factor
2	C₂×#11745144	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₆×D₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×D₂₉	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₂₉	C₄	1	1	yes	characteristic
6	C₂×#90768	C₂²	1	1	yes	characteristic
7	C₁₆×D₂₉	C₄	1	2	yes	—
8	C₁₆×D₂₉	C₂²	1	2	yes	—
9	#11745144	C₂²	1	4	yes	complemented
10	C₂×C₄×D₂₉	C₈	1	1	yes	characteristic
11	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
12	C₂×#6597	C₈	1	1	yes	characteristic
13	C₈×D₂₉	C₈	1	2	yes	—
14	C₈×D₂₉	C₂×C₄	1	2	yes	—
15	C₁₆×C₂₉	C₂×C₄	1	2	yes	—
16	#90768	C₂×C₄	1	1	yes	characteristic
17	#90768	C₂³	1	1	yes	characteristic
18	C₂²×D₂₉	C₁₆	1	1	yes	characteristic
19	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
20	C₂×Dic₂₉	C₁₆	1	1	yes	characteristic
21	C₄×D₂₉	C₁₆	1	2	yes	—
22	C₄×D₂₉	C₂×C₈	1	2	yes	—
23	C₈×C₂₉	C₂×C₈	1	1	yes	characteristic
24	C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
25	#6597	C₂×C₈	1	2	yes	—
26	C₂²×C₃₂	—	29	1	no	maximal, Sylow
27	C₂²×C₂₉	C₂×C₁₆	1	1	yes	characteristic
28	C₂×D₂₉	C₃₂	1	4	yes	complemented
29	C₂×D₂₉	C₂×C₁₆	1	2	yes	—
30	C₄×C₂₉	C₂×C₁₆	1	1	yes	characteristic
31	C₄×C₂₉	C₂²×C₈	1	1	yes	characteristic
32	Dic₂₉	C₂×C₁₆	1	2	yes	—
33	C₂²×C₁₆	—	29	1	no	—
34	C₂×C₃₂	—	29	2	no	—
35	C₂×C₃₂	—	29	4	no	—
36	C₂×C₂₉	C₂×C₃₂	1	2	yes	complemented
37	C₂×C₂₉	C₂²×C₁₆	1	1	yes	characteristic
38	D₂₉	C₂×C₃₂	1	4	yes	complemented
39	C₂²×C₈	—	29	1	no	—
40	C₂×C₁₆	—	29	1	no	—
41	C₂×C₁₆	—	29	2	no	—
42	C₂×C₁₆	—	29	2	no	—
43	C₂×C₁₆	#1181	1	1	yes	characteristic
44	C₃₂	—	29	4	no	—
45	C₂₉	C₂²×C₃₂	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₄	—	29	1	no	—
47	C₂×C₈	—	29	1	no	—
48	C₂×C₈	—	29	2	no	—
49	C₂×C₈	—	29	2	no	—
50	C₂×C₈	C₂×#1181	1	1	yes	characteristic
51	C₁₆	—	29	1	no	—
52	C₁₆	—	29	1	no	—
53	C₁₆	C₂×#1181	1	2	yes	—
54	C₂³	—	29	1	no	—
55	C₂×C₄	—	29	1	no	—
56	C₂×C₄	—	29	2	no	—
57	C₂×C₄	—	29	2	no	—
58	C₂×C₄	D₂₉⋊C₈	1	1	yes	characteristic
59	C₈	—	29	2	no	—
60	C₈	D₂₉⋊C₈	1	1	yes	characteristic
61	C₈	C₂²×#1181	1	1	yes	characteristic
62	C₂²	—	29	4	no	—
63	C₂²	—	29	2	no	—
64	C₂²	D₂₉⋊C₁₆	1	1	yes	characteristic
65	C₄	—	29	2	no	—
66	C₄	D₂₉⋊C₁₆	1	1	yes	characteristic
67	C₄	C₂×D₂₉⋊C₈	1	1	yes	characteristic
68	C₂	—	29	4	no	—
69	C₂	D₂₉⋊C₃₂	1	2	yes	direct product factor
70	C₂	C₂×D₂₉⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₆	#1181
commutator, hypocenter	C₂₉	C₂²×C₃₂
Frattini	C₈	C₂²×#1181
Fitting	C₂×C₁₆×C₂₉	C₄
socle	C₂²×C₂₉	C₂×C₁₆
prime radical	C₂²×D₂₉	C₁₆
cosocle	#90768	C₂³
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. D₂₉⋊C₃₂	C₂	direct (N × H)
2. C₂×#11745144	C₂	semidirect
9. #11745144	C₂²	semidirect
28. C₂×D₂₉	C₃₂	semidirect
36. C₂×C₂₉	C₂×C₃₂	semidirect
38. D₂₉	C₂×C₃₂	semidirect
45. C₂₉	C₂²×C₃₂	semidirect
69. C₂	D₂₉⋊C₃₂	direct (N × H)

Maximal subgroups

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

subgroup	index
D₂₉⋊C₃₂	2
C₂×#11745144	2
C₂×C₁₆×D₂₉	2
C₂²×C₃₂	29

Subgroups — C2×D29⋊C32 #16835911

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₂₉⋊C₃₂ #16835911