Subgroups — #21424253

Order 7552.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14273659	C₂	1	4	yes	maximal
2	#16837272	C₂	1	2	yes	maximal
3	C₂×C₄×C₈×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊Dic₅₉	—	2	4	no	—
5	C₂×C₄⋊Dic₅₉	C₂²	1	4	yes	—
6	#14273659	—	2	8	no	—
7	C₂²×C₈×C₅₉	C₂²	1	2	yes	—
8	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₅₉	C₄	1	4	yes	complemented
10	C₂²×C₄×C₅₉	D₄	1	2	yes	—
11	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
12	C₂²×Dic₅₉	—	2	4	no	—
13	C₂×C₈×C₅₉	C₂×C₄	1	4	yes	—
14	C₂×C₈×C₅₉	D₄	1	4	yes	—
15	C₂×C₈×C₅₉	Q₈	1	4	yes	—
16	C₄²×C₅₉	C₂×C₄	1	2	yes	—
17	C₄²×C₅₉	Q₈	1	2	yes	—
18	C₄⋊Dic₅₉	—	2	8	no	—
19	C₄⋊Dic₅₉	—	4	8	no	—
20	C₂³×C₅₉	C₂×D₄	1	1	yes	characteristic
21	C₂×C₄×C₅₉	C₄⋊C₄	1	4	yes	—
22	C₂×C₄×C₅₉	SD₁₆	1	8	yes	—
23	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
25	C₂×C₄×C₅₉	C₂×Q₈	1	2	yes	—
26	C₂×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
27	C₂×Dic₅₉	—	4	4	no	—
28	C₂×Dic₅₉	—	4	8	no	—
29	C₈×C₅₉	C₄⋊C₄	1	8	yes	complemented
30	C₂²×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
31	C₂²×C₅₉	#127	1	1	yes	characteristic
32	C₂²×C₅₉	C₄⋊Q₈	1	1	yes	characteristic
33	C₂²×C₅₉	C₂×SD₁₆	1	4	yes	—
34	C₄×C₅₉	#106	1	8	yes	complemented
35	C₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
36	C₄×C₅₉	C₄⋊Q₈	1	2	yes	—
37	Dic₅₉	—	8	4	no	—
38	#1844	—	59	1	no	maximal, Sylow
39	C₂×C₅₉	#384	1	1	yes	characteristic
40	C₂×C₅₉	C₂×#106	1	2	yes	—
41	C₂×C₅₉	#492	1	2	yes	—
42	C₂×C₅₉	#498	1	2	yes	—
43	C₂×#106	—	59	4	no	—
44	C₂×C₄×C₈	D₅₉	1	1	yes	characteristic
45	#384	—	59	2	no	—
46	C₅₉	#1844	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₈	C₂×D₅₉	1	2	yes	—
48	C₂×C₄⋊C₄	—	59	4	no	—
49	C₂×C₄⋊C₄	—	118	4	no	—
50	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
51	#106	—	118	8	no	—
52	C₄×C₈	Dic₅₉	1	4	yes	complemented
53	C₂²×C₄	—	118	4	no	—
54	C₂²×C₄	D₂₃₆	1	2	yes	—
55	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
56	C₂×C₈	Dic₁₁₈	1	4	yes	—
57	C₂×C₈	D₂₃₆	1	4	yes	—
58	C₂×C₈	C₂×Dic₅₉	1	4	yes	—
59	C₄⋊C₄	—	118	8	no	—
60	C₄⋊C₄	—	236	8	no	—
61	C₄²	Dic₁₁₈	1	2	yes	—
62	C₄²	C₂×Dic₅₉	1	2	yes	—
63	C₂³	C₂×D₂₃₆	1	1	yes	characteristic
64	C₂×C₄	—	236	4	no	—
65	C₂×C₄	—	236	8	no	—
66	C₂×C₄	#11745660	1	8	yes	—
67	C₂×C₄	C₄⋊Dic₅₉	1	4	yes	—
68	C₂×C₄	C₂×Dic₁₁₈	1	2	yes	—
69	C₂×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
70	C₂×C₄	C₂×D₂₃₆	1	2	yes	—
71	C₂×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
72	C₈	C₄⋊Dic₅₉	1	8	yes	complemented
73	C₂²	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
74	C₂²	#14273724	1	1	yes	characteristic
75	C₂²	#14273727	1	1	yes	characteristic
76	C₂²	C₂×#11745660	1	4	yes	—
77	C₄	—	472	4	no	—
78	C₄	#14273659	1	8	yes	complemented
79	C₄	C₂×C₄⋊Dic₅₉	1	2	yes	—
80	C₄	#14273727	1	2	yes	—
81	C₂	#16837272	1	1	yes	characteristic
82	C₂	C₂×#14273659	1	2	yes	—
83	C₂	#16837775	1	2	yes	—
84	C₂	#16837800	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₂₃₆
commutator	C₂×C₄×C₅₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₅₉
Fitting	C₂×C₄×C₈×C₅₉	C₂
socle	C₂³×C₅₉	C₂×D₄
hypercenter	C₂×C₄×C₈	D₅₉
hypocenter	C₅₉	#1844
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
9. C₄×C₈×C₅₉	C₄	semidirect
29. C₈×C₅₉	C₄⋊C₄	semidirect
34. C₄×C₅₉	#106	semidirect
46. C₅₉	#1844	semidirect
52. C₄×C₈	Dic₅₉	semidirect
72. C₈	C₄⋊Dic₅₉	semidirect
78. C₄	#14273659	semidirect