Subgroups — #16837185

Order 3776.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14273733	C₂	1	1	yes	maximal, characteristic
2	#14273667	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745685	C₄	1	1	yes	characteristic
5	C₂×C₈×C₅₉	C₂²	1	1	yes	characteristic
6	#11745664	C₄	1	1	yes	characteristic
7	#11745659	—	2	1	no	—
8	C₈×D₅₉	—	2	1	no	—
9	C₁₆×C₅₉	—	2	1	no	—
10	C₅₉⋊C₁₆	—	2	1	no	—
11	C₂×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
12	C₂²⋊D₅₉	—	2	1	no	—
13	D₂₃₆	C₈	1	1	yes	characteristic
14	C₄×D₅₉	—	2	1	no	—
15	Dic₁₁₈	C₈	1	1	yes	characteristic
16	C₈×C₅₉	D₄	1	1	yes	characteristic
17	C₈×C₅₉	D₄	1	1	yes	characteristic
18	C₅₉⋊C₈	—	2	1	no	—
19	C₂²×C₅₉	M₁₆	1	1	yes	characteristic
20	C₂×D₅₉	—	2	1	no	—
21	C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
23	Dic₅₉	—	2	1	no	—
24	C₂×C₅₉	—	2	1	no	—
25	C₂×C₅₉	C₂²⋊C₈	1	1	yes	characteristic
26	D₅₉	—	4	1	no	—
27	#350	—	59	1	no	maximal, Sylow
28	C₅₉	#350	1	1	yes	characteristic, complemented, Sylow
29	#131	—	59	1	no	—
30	M₃₂	—	59	1	no	—
31	C₂×C₁₆	D₅₉	1	1	yes	characteristic, complemented
32	#41	—	59	1	no	—
33	M₁₆	—	59	1	no	—
34	M₁₆	—	118	1	no	—
35	C₂×C₈	—	118	1	no	—
36	C₂×C₈	C₂×D₅₉	1	1	yes	characteristic
37	C₁₆	—	2	1	no	—
38	C₁₆	—	118	1	no	—
39	Q₈	—	59	1	no	—
40	D₄	—	59	1	no	—
41	D₄	—	118	1	no	—
42	C₂×C₄	—	118	1	no	—
43	C₂×C₄	C₄×D₅₉	1	1	yes	characteristic
44	C₈	—	118	1	no	—
45	C₈	D₂₃₆	1	1	yes	characteristic
46	C₈	C₂²⋊D₅₉	1	1	yes	characteristic
47	C₂²	—	118	1	no	—
48	C₂²	#11745659	1	1	yes	characteristic
49	C₄	—	118	1	no	—
50	C₄	C₈×D₅₉	1	1	yes	characteristic
51	C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	236	1	no	—
54	C₂	(C₂×D₅₉)⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₂₃₆
commutator	C₄×C₅₉	C₂×C₈
Frattini	C₂×C₈	C₂×D₅₉
Fitting	C₂×C₁₆×C₅₉	C₂
socle	C₂×C₅₉	C₂²⋊C₈
prime radical	#11745685	C₄
cosocle	C₂×C₈×C₅₉	C₂²
hypercenter	C₂×C₁₆	D₅₉
hypocenter	C₅₉	#350
LCS	G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. #14273667	C₂	semidirect
3. C₂×C₁₆×C₅₉	C₂	semidirect
28. C₅₉	#350	semidirect
31. C₂×C₁₆	D₅₉	semidirect

Maximal subgroups

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

subgroup	index
#14273733	2
#14273667	2
C₂×C₁₆×C₅₉	2
#350	59