Subgroups — #21423852

Order 7552.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837360	C₂	1	3	yes	maximal
2	#16837159	C₂	1	3	yes	maximal
3	C₅₉×#338	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
5	#14273686	C₂²	1	3	yes	—
6	#14273637	C₄	1	6	yes	complemented
7	C₈×Dic₅₉	C₄	1	6	yes	complemented
8	C₂×M₁₆×C₅₉	C₂²	1	3	yes	—
9	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
10	M₁₆×C₅₉	—	2	6	no	—
11	C₂×C₈×C₅₉	C₂×C₄	1	6	yes	—
12	C₂²⋊Dic₅₉	—	2	3	no	—
13	C₄⋊Dic₅₉	—	2	3	no	—
14	C₄×Dic₅₉	C₂×C₄	1	6	yes	—
15	C₂×C₅₉⋊C₈	C₂×C₄	1	3	yes	—
16	C₂×C₅₉⋊C₈	C₂×C₄	1	3	yes	—
17	C₂³×C₅₉	#41	1	1	yes	characteristic
18	C₂×C₄×C₅₉	C₂²×C₄	1	3	yes	—
19	C₂×C₄×C₅₉	#41	1	3	yes	—
20	C₂×Dic₅₉	—	2	6	no	—
21	C₈×C₅₉	—	2	6	no	—
22	C₅₉⋊C₈	C₄²	1	1	yes	characteristic
23	C₅₉⋊C₈	C₄²	1	3	yes	—
24	C₂²×C₅₉	—	4	1	no	—
25	C₂²×C₅₉	#117	1	3	yes	—
26	C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
27	C₄×C₅₉	#117	1	3	yes	—
28	Dic₅₉	—	4	6	no	—
29	#1747	—	59	1	no	maximal, Sylow
30	C₂×C₅₉	—	2	3	no	—
31	C₂×C₅₉	#376	1	1	yes	characteristic
32	#405	—	59	3	no	—
33	#338	D₅₉	1	1	yes	characteristic
34	H(3,ℤ/4)	—	59	3	no	—
35	C₅₉	#1747	1	1	yes	characteristic, complemented, Sylow
36	C₂×M₁₆	C₂×D₅₉	1	3	yes	—
37	C₂²×C₈	—	59	1	no	—
38	#117	—	59	3	no	—
39	#97	—	59	6	no	—
40	C₄×C₈	—	59	6	no	—
41	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
42	M₁₆	—	2	6	no	—
43	C₂×C₈	—	59	3	no	—
44	C₂×C₈	—	59	3	no	—
45	C₂×C₈	C₄×D₅₉	1	6	yes	—
46	C₄⋊C₄	—	118	3	no	—
47	C₂²⋊C₄	—	118	3	no	—
48	C₄²	—	59	6	no	—
49	C₂³	#11745689	1	1	yes	characteristic
50	C₂×C₄	—	118	6	no	—
51	C₂×C₄	C₂×C₄×D₅₉	1	3	yes	—
52	C₂×C₄	#11745687	1	3	yes	—
53	C₈	—	2	6	no	—
54	C₈	—	59	1	no	—
55	C₈	—	59	3	no	—
56	C₂²	—	4	1	no	—
57	C₂²	#14273685	1	3	yes	—
58	C₄	—	236	6	no	—
59	C₄	C₄²×D₅₉	1	1	yes	characteristic
60	C₄	#14273683	1	3	yes	—
61	C₂	—	2	3	no	—
62	C₂	#16837247	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄²×D₅₉
commutator	C₄×C₅₉	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₅₉
Fitting	C₅₉×#338	C₂
socle	C₂×C₅₉	#376
hypercenter	#338	D₅₉
hypocenter	C₅₉	#1747
LCS	G ▷ C₄×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
6. #14273637	C₄	semidirect
7. C₈×Dic₅₉	C₄	semidirect
35. C₅₉	#1747	semidirect