Subgroups — #21422159

Order 7552.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₅₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
2	C₈×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₅₉×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅₉⋊C₁₆	—	2	1	no	—
5	C₄×C₅₉⋊C₈	C₄	1	1	yes	characteristic
6	C₄×C₅₉⋊C₈	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₅₉	—	2	1	no	—
8	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
10	C₂×C₈×C₅₉	Q₈	1	1	yes	characteristic
11	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₅₉⋊C₈	—	2	1	no	—
13	C₂×C₅₉⋊C₈	C₈	1	1	yes	characteristic
14	C₂×C₅₉⋊C₈	C₈	1	1	yes	characteristic
15	C₁₆×C₅₉	—	4	1	no	—
16	C₅₉⋊C₁₆	—	4	1	no	—
17	C₂×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
19	C₂×C₄×C₅₉	M₁₆	1	1	yes	characteristic
20	C₈×C₅₉	—	2	1	no	—
21	C₈×C₅₉	SD₁₆	1	1	yes	characteristic
22	C₈×C₅₉	SD₁₆	1	1	yes	characteristic
23	C₅₉⋊C₈	—	2	2	no	—
24	C₅₉⋊C₈	—	2	1	no	—
25	C₅₉⋊C₈	C₁₆	1	2	yes	complemented
26	C₂²×C₅₉	C₄⋊C₈	1	1	yes	characteristic
27	C₄×C₅₉	—	2	1	no	—
28	C₄×C₅₉	#106	1	1	yes	characteristic
29	C₄×C₅₉	#108	1	1	yes	characteristic
30	C₄×C₅₉	C₂×C₁₆	1	1	yes	characteristic
31	C₄×C₅₉	M₃₂	1	1	yes	characteristic
32	#1367	—	59	1	no	maximal, Sylow
33	C₂×C₅₉	#334	1	1	yes	characteristic
34	C₂×C₅₉	C₄⋊C₁₆	1	1	yes	characteristic
35	C₂×C₅₉	#364	1	1	yes	characteristic
36	C₄⋊C₁₆	—	59	1	no	—
37	C₄⋊C₁₆	D₅₉	1	1	yes	characteristic
38	C₈²	—	59	1	no	—
39	C₅₉	#1367	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₁₆	—	2	1	no	—
41	C₂×C₁₆	—	118	1	no	—
42	C₄×C₈	—	59	1	no	—
43	C₄×C₈	—	59	1	no	—
44	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
45	C₂×C₈	—	59	1	no	—
46	C₂×C₈	—	59	1	no	—
47	C₂×C₈	—	118	1	no	—
48	C₂×C₈	Dic₁₁₈	1	1	yes	characteristic
49	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
50	C₄²	C₄×D₅₉	1	1	yes	characteristic
51	C₁₆	—	4	1	no	—
52	C₁₆	—	236	1	no	—
53	C₂×C₄	C₈×D₅₉	1	1	yes	characteristic
54	C₂×C₄	#11745659	1	1	yes	characteristic
55	C₂×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
56	C₈	—	2	1	no	—
57	C₈	—	59	2	no	—
58	C₈	—	118	2	no	—
59	C₈	—	118	1	no	—
60	C₈	#11745670	1	1	yes	characteristic
61	C₈	#11745671	1	1	yes	characteristic
62	C₂²	Dic₅₉⋊C₈	1	1	yes	characteristic
63	C₄	—	2	1	no	—
64	C₄	#14273658	1	1	yes	characteristic
65	C₄	#14273662	1	1	yes	characteristic
66	C₄	C₁₆×D₅₉	1	1	yes	characteristic
67	C₄	#14273666	1	1	yes	characteristic
68	C₂	#16837152	1	1	yes	characteristic
69	C₂	Dic₅₉⋊C₁₆	1	1	yes	characteristic
70	C₂	#16837222	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₅₉
commutator	C₄×C₅₉	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₅₉
Fitting	C₅₉×C₄⋊C₁₆	C₂
socle	C₂²×C₅₉	C₄⋊C₈
hypercenter	C₄⋊C₁₆	D₅₉
hypocenter	C₅₉	#1367
LCS	G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
25. C₅₉⋊C₈	C₁₆	semidirect
39. C₅₉	#1367	semidirect