Subgroups — #16817554

Order 3712.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271565	C₂	1	1	yes	maximal, characteristic
2	#14270984	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#364	C₂	1	1	yes	maximal, characteristic
4	#11745232	C₄	1	2	yes	—
5	C₂₉×M₃₂	—	2	1	no	—
6	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
7	#11745166	—	2	1	no	—
8	#11745165	—	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	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
13	C₄⋊Dic₂₉	—	2	2	no	—
14	#90779	—	4	2	no	—
15	C₁₆×C₂₉	—	4	1	no	—
16	#90768	—	4	1	no	—
17	C₂×C₄×C₂₉	—	2	1	no	—
18	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×Dic₂₉	—	4	2	no	—
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	#103	1	1	yes	characteristic
28	C₄×C₂₉	#103	1	1	yes	characteristic
29	Dic₂₉	—	8	2	no	—
30	#499	—	29	1	no	—
31	#364	—	29	1	no	—
32	#364	D₂₉	1	1	yes	characteristic
33	C₂×C₂₉	—	2	1	no	—
34	C₂×C₂₉	#333	1	1	yes	characteristic
35	#125	—	29	2	no	—
36	M₃₂	—	2	1	no	—
37	M₃₂	—	58	1	no	—
38	#107	—	58	1	no	—
39	#106	—	58	1	no	—
40	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
41	C₂₉	#1366	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₈	D₁₁₆	1	1	yes	characteristic
43	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
44	C₄⋊C₄	—	58	2	no	—
45	C₄⋊C₄	—	116	2	no	—
46	C₄²	C₄×D₂₉	1	1	yes	characteristic
47	C₁₆	—	4	1	no	—
48	C₁₆	—	116	1	no	—
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	116	2	no	—
51	C₂×C₄	#90781	1	1	yes	characteristic
52	C₈	#90773	1	1	yes	characteristic
53	C₈	Dic₁₁₆	1	1	yes	characteristic
54	C₈	#90783	1	1	yes	characteristic
55	C₈	#90785	1	1	yes	characteristic
56	C₂²	#11745171	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	232	2	no	—
59	C₄	#11745158	1	1	yes	characteristic
60	C₄	#11745164	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	#14270911	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14270911
commutator	C₄²×C₂₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₉
Fitting	C₂₉×#364	C₂
socle	C₂×C₂₉	#333
prime radical	C₂²×C₂₉	#100
cosocle	C₄×C₈×C₂₉	C₂²
hypercenter	#364	D₂₉
hypocenter	C₂₉	#1366
LCS	G ▷ C₄²×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

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
#14271565	2
#14270984	2
C₂₉×#364	2
#1366	29