Subgroups — #21424239

Order 7552.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837157	C₂	1	6	yes	maximal
2	C₄³×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅₉⋊C₈	C₂²	1	4	yes	—
4	C₂×C₄²×C₅₉	C₄	1	3	yes	—
5	C₂×C₄²×C₅₉	C₄	1	1	yes	characteristic
6	C₂×C₄²×C₅₉	C₂²	1	3	yes	—
7	C₂²×C₄×C₅₉	C₂×C₄	1	3	yes	—
8	C₂²×C₄×C₅₉	C₂×C₄	1	3	yes	—
9	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
10	C₄²×C₅₉	—	2	6	no	—
11	C₄²×C₅₉	—	2	6	no	—
12	C₄²×C₅₉	C₈	1	4	yes	complemented
13	C₂×C₅₉⋊C₈	—	2	12	no	—
14	C₂³×C₅₉	C₂²×C₄	1	1	yes	characteristic
15	C₂×C₄×C₅₉	—	2	3	no	—
16	C₂×C₄×C₅₉	—	2	3	no	—
17	C₂×C₄×C₅₉	—	2	3	no	—
18	C₂×C₄×C₅₉	—	2	3	no	—
19	C₂×C₄×C₅₉	C₂×C₈	1	6	yes	—
20	C₂×C₄×C₅₉	M₁₆	1	6	yes	—
21	C₂×C₄×C₅₉	#41	1	6	yes	—
22	C₅₉⋊C₈	—	4	4	no	—
23	C₂²×C₅₉	#117	1	3	yes	—
24	C₂²×C₅₉	C₂²×C₈	1	1	yes	characteristic
25	C₂²×C₅₉	C₂×M₁₆	1	3	yes	—
26	C₄×C₅₉	—	2	6	no	—
27	C₄×C₅₉	—	2	6	no	—
28	C₄×C₅₉	#126	1	4	yes	—
29	#1839	—	59	1	no	maximal, Sylow
30	C₂×C₅₉	#383	1	1	yes	characteristic
31	C₂×C₅₉	#431	1	3	yes	—
32	C₂×C₅₉	#432	1	3	yes	—
33	C₄³	D₅₉	1	1	yes	characteristic
34	#336	—	59	6	no	—
35	C₅₉	#1839	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₈	—	59	4	no	—
37	C₂×C₄²	Dic₅₉	1	3	yes	—
38	C₂×C₄²	Dic₅₉	1	1	yes	characteristic
39	C₂×C₄²	C₂×D₅₉	1	3	yes	—
40	C₂²×C₄	C₂×Dic₅₉	1	3	yes	—
41	C₂²×C₄	C₂×Dic₅₉	1	3	yes	—
42	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
43	C₂×C₈	—	118	12	no	—
44	C₄²	—	2	6	no	—
45	C₄²	—	2	6	no	—
46	C₄²	C₅₉⋊C₈	1	4	yes	complemented
47	C₂³	C₂²×Dic₅₉	1	1	yes	characteristic
48	C₂×C₄	—	2	3	no	—
49	C₂×C₄	—	2	3	no	—
50	C₂×C₄	—	2	3	no	—
51	C₂×C₄	—	2	3	no	—
52	C₂×C₄	C₂×C₅₉⋊C₈	1	6	yes	—
53	C₂×C₄	#11745664	1	6	yes	—
54	C₂×C₄	#11745685	1	6	yes	—
55	C₈	—	236	4	no	—
56	C₂²	#14273686	1	3	yes	—
57	C₂²	C₂²×C₅₉⋊C₈	1	1	yes	characteristic
58	C₂²	C₂×#11745664	1	3	yes	—
59	C₄	—	2	6	no	—
60	C₄	—	2	6	no	—
61	C₄	#14273721	1	4	yes	—
62	C₂	#16837270	1	1	yes	characteristic
63	C₂	#16837455	1	3	yes	—
64	C₂	#16837459	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₅₉
commutator	C₂²×C₅₉	C₂²×C₈
Fitting	C₄³×C₅₉	C₂
socle	C₂³×C₅₉	C₂²×C₄
hypercenter	C₄³	D₅₉
hypocenter	C₅₉	#1839
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³

Complements

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

N	H ≅ G/N	type
12. C₄²×C₅₉	C₈	semidirect
35. C₅₉	#1839	semidirect
46. C₄²	C₅₉⋊C₈	semidirect