Subgroups — #16834606

Order 3712.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745144	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₆×D₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₂₉	C₄	1	1	yes	characteristic
4	C₂×C₁₆×C₂₉	C₄	1	1	yes	characteristic
5	C₂×#90768	C₂²	1	1	yes	characteristic
6	C₁₆×D₂₉	—	2	2	no	—
7	#11745144	—	2	2	no	—
8	C₂×C₄×D₂₉	C₈	1	1	yes	characteristic
9	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
10	C₂×#6597	C₈	1	1	yes	characteristic
11	C₈×D₂₉	—	2	1	no	—
12	C₈×D₂₉	—	2	1	no	—
13	C₁₆×C₂₉	—	2	1	no	—
14	#90768	D₄	1	2	yes	—
15	C₂²×D₂₉	C₁₆	1	1	yes	characteristic
16	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
17	C₂×Dic₂₉	C₁₆	1	1	yes	characteristic
18	C₄×D₂₉	—	2	1	no	—
19	C₄×D₂₉	—	2	1	no	—
20	C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₈×C₂₉	M₁₆	1	1	yes	characteristic
22	#6597	—	2	1	no	—
23	C₂²⋊C₃₂	—	29	1	no	maximal, Sylow
24	C₂²×C₂₉	C₂×C₁₆	1	1	yes	characteristic
25	C₂×D₂₉	—	2	1	no	—
26	C₂×D₂₉	—	2	1	no	—
27	C₂×D₂₉	C₃₂	1	2	yes	complemented
28	C₄×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
29	C₄×C₂₉	M₃₂	1	1	yes	characteristic
30	Dic₂₉	—	2	1	no	—
31	C₂²×C₁₆	—	29	1	no	—
32	C₂×C₃₂	—	29	2	no	—
33	C₂×C₂₉	C₂²⋊C₁₆	1	1	yes	characteristic
34	C₂×C₂₉	C₂×C₃₂	1	1	yes	characteristic
35	C₂×C₂₉	M₆₄	1	1	yes	characteristic
36	D₂₉	—	2	2	no	—
37	C₂²×C₈	—	29	1	no	—
38	C₂×C₁₆	—	29	1	no	—
39	C₂×C₁₆	—	58	2	no	—
40	C₂×C₁₆	#1181	1	1	yes	characteristic
41	C₃₂	—	58	2	no	—
42	C₂₉	C₂²⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₄	—	29	1	no	—
44	C₂×C₈	—	29	1	no	—
45	C₂×C₈	—	58	1	no	—
46	C₂×C₈	—	58	1	no	—
47	C₂×C₈	C₂×#1181	1	1	yes	characteristic
48	C₁₆	—	2	1	no	—
49	C₁₆	—	29	2	no	—
50	C₂³	—	29	1	no	—
51	C₂×C₄	—	29	1	no	—
52	C₂×C₄	—	58	1	no	—
53	C₂×C₄	—	58	1	no	—
54	C₂×C₄	D₂₉⋊C₈	1	1	yes	characteristic
55	C₈	—	58	1	no	—
56	C₈	#90796	1	1	yes	characteristic
57	C₈	C₂²⋊#1181	1	1	yes	characteristic
58	C₂²	—	29	2	no	—
59	C₂²	—	58	1	no	—
60	C₂²	—	58	1	no	—
61	C₂²	D₂₉⋊C₁₆	1	1	yes	characteristic
62	C₄	—	58	1	no	—
63	C₄	#11745206	1	1	yes	characteristic
64	C₄	#11745219	1	1	yes	characteristic
65	C₂	—	58	2	no	—
66	C₂	#14272058	1	1	yes	characteristic
67	C₂	D₂₉⋊C₃₂	1	1	yes	characteristic
68	C₂	#14272096	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×#11745144	C₂	semidirect
27. C₂×D₂₉	C₃₂	semidirect
42. C₂₉	C₂²⋊C₃₂	semidirect

Maximal subgroups

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

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