Subgroups — #16817628

Order 3712.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14270997	C₂	1	2	yes	maximal
2	C₂₉×#346	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₂₉	C₄	1	1	yes	characteristic
4	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
5	C₄×C₈×C₂₉	C₄	1	1	yes	characteristic
6	#11745142	C₄	1	4	yes	complemented
7	C₂×C₈×C₂₉	C₈	1	1	yes	characteristic
8	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₂₉	C₈	1	1	yes	characteristic
10	C₁₆×C₂₉	C₈	1	2	yes	—
11	C₁₆×C₂₉	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₂₉	—	2	1	no	—
13	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
14	C₈×C₂₉	—	2	1	no	—
15	C₈×C₂₉	C₄²	1	1	yes	characteristic
16	C₈×C₂₉	C₂×C₈	1	1	yes	characteristic
17	#1398	—	29	1	no	maximal, Sylow
18	C₂²×C₂₉	M₃₂	1	1	yes	characteristic
19	C₄×C₂₉	—	4	1	no	—
20	C₄×C₂₉	C₄×C₈	1	1	yes	characteristic
21	C₄×C₂₉	M₃₂	1	1	yes	characteristic
22	M₆₄	—	29	2	no	—
23	#346	D₂₉	1	1	yes	characteristic
24	C₂×C₂₉	—	2	1	no	—
25	C₂×C₂₉	#346	1	1	yes	characteristic
26	C₂×C₁₆	Dic₂₉	1	1	yes	characteristic
27	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
28	C₄×C₈	Dic₂₉	1	1	yes	characteristic
29	C₃₂	—	29	4	no	—
30	C₂₉	#1398	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₈	#6597	1	1	yes	characteristic
32	C₂×C₈	C₂×Dic₂₉	1	1	yes	characteristic
33	C₄²	#6597	1	1	yes	characteristic
34	C₁₆	#6597	1	2	yes	—
35	C₁₆	C₄×D₂₉	1	2	yes	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	C₂×#6597	1	1	yes	characteristic
38	C₈	—	2	1	no	—
39	C₈	C₂×#6597	1	1	yes	characteristic
40	C₈	C₄×Dic₂₉	1	1	yes	characteristic
41	C₂²	#11745160	1	1	yes	characteristic
42	C₄	—	4	1	no	—
43	C₄	C₄×#6597	1	1	yes	characteristic
44	C₄	#11745160	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#14270939	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄×Dic₂₉
commutator	C₄×C₂₉	C₄×C₈
Frattini	C₂×C₁₆	C₂×D₂₉
Fitting	C₂₉×#346	C₂
socle	C₂×C₂₉	#346
prime radical	C₂²×C₂₉	M₃₂
cosocle	C₂×C₁₆×C₂₉	C₂²
hypercenter	#346	D₂₉
hypocenter	C₂₉	#1398
LCS	G ▷ C₄×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
6. #11745142	C₄	semidirect
30. C₂₉	#1398	semidirect

Maximal subgroups

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

subgroup	index
#14270997	2
C₂₉×#346	2
#1398	29