Subgroups — #21425498

Order 7552.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837450	C₂	1	3	yes	maximal
2	C₂×#14273645	C₂	1	3	yes	maximal
3	C₅₉×#338	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₁₁₈	C₂²	1	1	yes	characteristic
5	C₂×#11745664	C₂²	1	3	yes	—
6	#14273662	—	2	6	no	—
7	#14273645	—	2	6	no	—
8	C₂×M₁₆×C₅₉	C₂²	1	3	yes	—
9	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
10	C₂²×Dic₅₉	Q₈	1	2	yes	—
11	C₂×Dic₁₁₈	—	2	3	no	—
12	C₂×Dic₁₁₈	—	2	3	no	—
13	M₁₆×C₅₉	—	2	3	no	—
14	M₁₆×C₅₉	—	2	3	no	—
15	C₂×C₈×C₅₉	—	2	3	no	—
16	#11745664	—	2	3	no	—
17	#11745664	D₄	1	6	yes	—
18	C₂×C₅₉⋊C₈	—	2	3	no	—
19	C₂³×C₅₉	C₂×Q₈	1	1	yes	characteristic
20	C₂×C₄×C₅₉	C₂×D₄	1	3	yes	—
21	C₂×C₄×C₅₉	#41	1	3	yes	—
22	C₂×Dic₅₉	—	2	6	no	—
23	Dic₁₁₈	—	4	3	no	—
24	Dic₁₁₈	—	4	1	no	—
25	C₈×C₅₉	—	4	3	no	—
26	C₅₉⋊C₈	—	2	6	no	—
27	C₂²×C₅₉	—	4	1	no	—
28	C₂²×C₅₉	C₂²⋊Q₈	1	3	yes	—
29	C₄×C₅₉	#121	1	3	yes	—
30	C₄×C₅₉	#126	1	1	yes	characteristic
31	Dic₅₉	—	4	2	no	—
32	#2070	—	59	1	no	maximal, Sylow
33	C₂×C₅₉	—	2	3	no	—
34	C₂×C₅₉	#396	1	1	yes	characteristic
35	#430	—	59	3	no	—
36	C₂×#101	—	59	3	no	—
37	#338	D₅₉	1	1	yes	characteristic
38	C₅₉	#2070	1	1	yes	characteristic, complemented, Sylow
39	C₂²×Q₈	—	59	1	no	—
40	C₂×M₁₆	—	59	3	no	—
41	C₂×M₁₆	C₂×D₅₉	1	3	yes	—
42	#108	—	118	6	no	—
43	#101	—	118	6	no	—
44	C₂×Q₈	—	118	3	no	—
45	C₂×Q₈	—	118	3	no	—
46	C₂²×C₄	—	59	2	no	—
47	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
48	M₁₆	—	2	3	no	—
49	M₁₆	—	2	3	no	—
50	M₁₆	—	59	6	no	—
51	M₁₆	—	118	3	no	—
52	C₂×C₈	—	2	3	no	—
53	C₂×C₈	—	118	3	no	—
54	C₂³	Q₈×D₅₉	1	1	yes	characteristic
55	Q₈	—	236	3	no	—
56	Q₈	—	236	1	no	—
57	C₂×C₄	—	118	6	no	—
58	C₂×C₄	#11745685	1	3	yes	—
59	C₂×C₄	D₄×D₅₉	1	3	yes	—
60	C₈	—	4	3	no	—
61	C₈	—	118	6	no	—
62	C₂²	—	4	1	no	—
63	C₂²	#14273705	1	3	yes	—
64	C₄	—	236	2	no	—
65	C₄	#14273700	1	3	yes	—
66	C₄	#14273721	1	1	yes	characteristic
67	C₂	—	2	3	no	—
68	C₂	#16837326	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16837326
commutator	C₂²×C₄×C₅₉	C₂³
Frattini	C₂²×C₄	C₂²×D₅₉
Fitting	C₅₉×#338	C₂
socle	C₂×C₅₉	#396
hypercenter	#338	D₅₉
hypocenter	C₅₉	#2070
LCS	G ▷ C₂²×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
38. C₅₉	#2070	semidirect