Subgroups — #16817553

Order 3712.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14270984	C₂	1	1	yes	maximal, characteristic
2	#14270984	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#499	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#125	C₄	1	2	yes	—
5	C₂₉×#107	—	2	1	no	—
6	C₂₉×#106	—	2	1	no	—
7	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
8	#11745160	—	2	1	no	—
9	#11745160	—	2	1	no	—
10	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
11	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
12	C₄⋊C₄×C₂₉	—	2	2	no	—
13	C₄⋊C₄×C₂₉	—	4	2	no	—
14	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
15	#90768	—	4	1	no	—
16	#90768	—	4	1	no	—
17	C₂×C₄×C₂₉	—	2	1	no	—
18	C₂×C₄×C₂₉	—	4	2	no	—
19	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
20	C₈×C₂₉	SD₁₆	1	1	yes	characteristic
21	C₈×C₂₉	SD₁₆	1	1	yes	characteristic
22	C₈×C₂₉	Q₁₆	1	1	yes	characteristic
23	C₈×C₂₉	Q₁₆	1	1	yes	characteristic
24	#1366	—	29	1	no	maximal, Sylow
25	C₂²×C₂₉	#100	1	1	yes	characteristic
26	C₄×C₂₉	—	4	1	no	—
27	C₄×C₂₉	—	8	2	no	—
28	C₄×C₂₉	#103	1	1	yes	characteristic
29	C₄×C₂₉	#103	1	1	yes	characteristic
30	#499	D₂₉	1	1	yes	characteristic
31	#364	—	29	1	no	—
32	#364	—	29	1	no	—
33	C₂×C₂₉	—	2	1	no	—
34	C₂×C₂₉	#333	1	1	yes	characteristic
35	#125	Dic₂₉	1	2	yes	—
36	M₃₂	—	58	1	no	—
37	M₃₂	—	58	1	no	—
38	#107	—	2	1	no	—
39	#106	—	2	1	no	—
40	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
41	C₂₉	#1366	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
43	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
44	C₄⋊C₄	—	2	2	no	—
45	C₄⋊C₄	—	4	2	no	—
46	C₄²	C₂×Dic₂₉	1	1	yes	characteristic
47	C₁₆	—	116	1	no	—
48	C₁₆	—	116	1	no	—
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	4	2	no	—
51	C₂×C₄	C₂²⋊Dic₂₉	1	1	yes	characteristic
52	C₈	#90784	1	1	yes	characteristic
53	C₈	#90784	1	1	yes	characteristic
54	C₈	#90785	1	1	yes	characteristic
55	C₈	#90785	1	1	yes	characteristic
56	C₂²	#11745181	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	8	2	no	—
59	C₄	#11745183	1	1	yes	characteristic
60	C₄	#11745183	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	#14270912	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14270912
commutator	C₄²×C₂₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₉
Fitting	C₂₉×#499	C₂
socle	C₂×C₂₉	#333
prime radical	C₂²×C₂₉	#100
cosocle	C₄×C₈×C₂₉	C₂²
hypercenter	#499	D₂₉
hypocenter	C₂₉	#1366
LCS	G ▷ C₄²×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #499

Complements

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

N	H ≅ G/N	type
41. C₂₉	#1366	semidirect

Maximal subgroups

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

subgroup	index
#14270984	2
C₂₉×#499	2
#1366	29