Subgroups — #21425495

Order 7552.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837450	C₂	1	3	yes	maximal, complemented
2	C₂×#14273643	C₂	1	3	yes	maximal
3	C₅₉×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₂₃₆	C₂²	1	1	yes	characteristic
5	C₂×#11745664	C₂²	1	3	yes	—
6	#14273662	—	2	6	no	—
7	#14273643	—	2	6	no	—
8	C₂×M₁₆×C₅₉	C₂²	1	3	yes	—
9	C₂³×D₅₉	Q₈	1	2	yes	—
10	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
11	C₂×D₂₃₆	—	2	3	no	—
12	C₂×D₂₃₆	—	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	C₂²×D₅₉	—	2	6	no	—
21	C₂²×D₅₉	—	8	2	no	—
22	C₂×C₄×C₅₉	C₂×D₄	1	3	yes	—
23	C₂×C₄×C₅₉	#41	1	3	yes	—
24	D₂₃₆	—	4	3	no	—
25	D₂₃₆	—	4	1	no	—
26	C₈×C₅₉	—	4	3	no	—
27	C₅₉⋊C₈	—	2	6	no	—
28	C₂²×C₅₉	—	4	1	no	—
29	C₂²×C₅₉	C₂²⋊Q₈	1	3	yes	—
30	C₂×D₅₉	—	4	2	no	—
31	C₂×D₅₉	—	8	6	no	—
32	C₄×C₅₉	#121	1	3	yes	—
33	C₄×C₅₉	#126	1	1	yes	characteristic
34	#2069	—	59	1	no	maximal, Sylow
35	C₂×C₅₉	—	2	3	no	—
36	C₂×C₅₉	#396	1	1	yes	characteristic
37	D₅₉	—	8	2	no	—
38	#430	—	59	3	no	—
39	C₂×#100	—	59	3	no	—
40	#338	D₅₉	1	1	yes	characteristic, complemented
41	C₅₉	#2069	1	1	yes	characteristic, complemented, Sylow
42	C₂²×D₄	—	59	1	no	—
43	C₂×M₁₆	—	59	3	no	—
44	C₂×M₁₆	C₂×D₅₉	1	3	yes	—
45	#108	—	118	6	no	—
46	#100	—	118	6	no	—
47	C₂⁴	—	59	2	no	—
48	C₂×D₄	—	118	3	no	—
49	C₂×D₄	—	118	3	no	—
50	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
51	M₁₆	—	2	3	no	—
52	M₁₆	—	2	3	no	—
53	M₁₆	—	59	6	no	—
54	M₁₆	—	118	3	no	—
55	C₂×C₈	—	2	3	no	—
56	C₂×C₈	—	118	3	no	—
57	C₂³	—	118	6	no	—
58	C₂³	—	472	2	no	—
59	C₂³	Q₈×D₅₉	1	1	yes	characteristic
60	D₄	—	236	3	no	—
61	D₄	—	236	1	no	—
62	C₂×C₄	#11745685	1	3	yes	—
63	C₂×C₄	D₄×D₅₉	1	3	yes	—
64	C₈	—	4	3	no	—
65	C₈	—	118	6	no	—
66	C₂²	—	4	1	no	—
67	C₂²	—	472	6	no	—
68	C₂²	—	236	2	no	—
69	C₂²	#14273705	1	3	yes	—
70	C₄	#14273700	1	3	yes	—
71	C₄	#14273721	1	1	yes	characteristic
72	C₂	—	2	3	no	—
73	C₂	—	472	2	no	—
74	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	#2069
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
1. #16837450	C₂	semidirect
3. C₅₉×#338	C₂	semidirect
40. #338	D₅₉	semidirect
41. C₅₉	#2069	semidirect