Subgroups — #16837159

Order 3776.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14273686	C₂	1	2	yes	maximal
2	C₂×M₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₅₉	C₂²	1	1	yes	characteristic
4	M₁₆×C₅₉	—	2	2	no	—
5	C₂×C₈×C₅₉	C₄	1	2	yes	complemented
6	C₂²⋊Dic₅₉	—	2	2	no	—
7	C₄⋊Dic₅₉	—	2	2	no	—
8	C₄×Dic₅₉	C₄	1	4	yes	complemented
9	C₂³×C₅₉	D₄	1	1	yes	characteristic
10	C₂×C₄×C₅₉	C₂×C₄	1	2	yes	—
11	C₂×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₅₉	D₄	1	2	yes	—
13	C₂×C₄×C₅₉	Q₈	1	1	yes	characteristic
14	C₂×Dic₅₉	—	2	4	no	—
15	C₈×C₅₉	—	2	2	no	—
16	C₂²×C₅₉	—	4	1	no	—
17	C₂²×C₅₉	C₂²⋊C₄	1	2	yes	—
18	C₂²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
19	C₄×C₅₉	C₄²	1	1	yes	characteristic
20	C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₅₉	C₄⋊C₄	1	2	yes	—
22	Dic₅₉	—	4	4	no	—
23	C₂×C₅₉	—	2	2	no	—
24	C₂×C₅₉	—	2	1	no	—
25	C₂×C₅₉	#95	1	1	yes	characteristic
26	H(3,ℤ/4)	—	59	1	no	maximal, Sylow
27	C₅₉	H(3,ℤ/4)	1	1	yes	characteristic, complemented, Sylow
28	C₂×M₁₆	D₅₉	1	1	yes	characteristic
29	#117	—	59	2	no	—
30	C₂²×C₄	C₂×D₅₉	1	1	yes	characteristic
31	M₁₆	—	2	2	no	—
32	C₂×C₈	Dic₅₉	1	2	yes	complemented
33	C₄⋊C₄	—	118	2	no	—
34	C₂²⋊C₄	—	118	2	no	—
35	C₄²	—	59	4	no	—
36	C₂³	D₂₃₆	1	1	yes	characteristic
37	C₂×C₄	—	118	4	no	—
38	C₂×C₄	Dic₁₁₈	1	1	yes	characteristic
39	C₂×C₄	C₄×D₅₉	1	2	yes	—
40	C₂×C₄	C₂×Dic₅₉	1	1	yes	characteristic
41	C₂×C₄	C₂²⋊D₅₉	1	2	yes	—
42	C₈	—	2	2	no	—
43	C₂²	—	4	1	no	—
44	C₂²	C₄⋊Dic₅₉	1	1	yes	characteristic
45	C₂²	(C₂×D₅₉)⋊C₄	1	2	yes	—
46	C₄	—	236	4	no	—
47	C₄	C₄×Dic₅₉	1	1	yes	characteristic
48	C₄	Dic₅₉⋊C₄	1	2	yes	—
49	C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
50	C₂	—	2	2	no	—
51	C₂	—	2	1	no	—
52	C₂	C₅₉⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×Dic₅₉
commutator	C₄×C₅₉	C₄²
Frattini	C₂²×C₄	C₂×D₅₉
Fitting	C₂×M₁₆×C₅₉	C₂
socle	C₂×C₅₉	#95
prime radical	C₂³×C₅₉	D₄
cosocle	C₂²×C₄×C₅₉	C₂²
hypercenter	C₂×M₁₆	D₅₉
hypocenter	C₅₉	H(3,ℤ/4)
LCS	G ▷ C₄×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
5. C₂×C₈×C₅₉	C₄	semidirect
8. C₄×Dic₅₉	C₄	semidirect
27. C₅₉	H(3,ℤ/4)	semidirect
32. C₂×C₈	Dic₅₉	semidirect

Maximal subgroups

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

subgroup	index
#14273686	2
C₂×M₁₆×C₅₉	2
H(3,ℤ/4)	59