Subgroups — #21422171

Order 7552.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837223	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#364	C₂	1	1	yes	maximal, characteristic
4	#14273667	—	2	1	no	—
5	C₂×C₅₉⋊C₁₆	C₄	1	1	yes	characteristic
6	C₂×C₅₉⋊C₁₆	C₄	1	1	yes	characteristic
7	M₃₂×C₅₉	—	2	1	no	—
8	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
10	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
11	C₄²×C₅₉	Q₈	1	1	yes	characteristic
12	C₁₆×C₅₉	—	4	1	no	—
13	C₅₉⋊C₁₆	—	2	1	no	—
14	C₅₉⋊C₁₆	—	4	1	no	—
15	C₅₉⋊C₁₆	C₈	1	2	yes	—
16	C₂×C₄×C₅₉	—	2	1	no	—
17	C₂×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₅₉	C₂×C₈	1	1	yes	characteristic
19	C₈×C₅₉	M₁₆	1	1	yes	characteristic
20	C₈×C₅₉	D₈	1	1	yes	characteristic
21	C₈×C₅₉	Q₁₆	1	1	yes	characteristic
22	C₂²×C₅₉	#108	1	1	yes	characteristic
23	C₄×C₅₉	—	2	2	no	—
24	C₄×C₅₉	C₄⋊C₈	1	1	yes	characteristic
25	C₄×C₅₉	#107	1	1	yes	characteristic
26	#1373	—	59	1	no	maximal, Sylow
27	C₂×C₅₉	—	2	1	no	—
28	C₂×C₅₉	#335	1	1	yes	characteristic
29	#364	—	59	1	no	—
30	#364	D₅₉	1	1	yes	characteristic
31	C₄×C₁₆	—	59	1	no	—
32	C₅₉	#1373	1	1	yes	characteristic, complemented, Sylow
33	M₃₂	—	2	1	no	—
34	M₃₂	—	118	1	no	—
35	C₂×C₁₆	—	59	1	no	—
36	C₂×C₁₆	—	59	1	no	—
37	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
38	C₂×C₈	C₄×D₅₉	1	1	yes	characteristic
39	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
40	C₄²	Dic₁₁₈	1	1	yes	characteristic
41	C₁₆	—	4	1	no	—
42	C₁₆	—	59	2	no	—
43	C₁₆	—	118	1	no	—
44	C₁₆	—	236	1	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
47	C₈	C₈×D₅₉	1	1	yes	characteristic
48	C₈	#11745659	1	1	yes	characteristic
49	C₈	#11745669	1	1	yes	characteristic
50	C₈	#11745672	1	1	yes	characteristic
51	C₂²	#14273662	1	1	yes	characteristic
52	C₄	—	2	2	no	—
53	C₄	Dic₅₉⋊C₈	1	1	yes	characteristic
54	C₄	#14273660	1	1	yes	characteristic
55	C₂	—	2	1	no	—
56	C₂	#16837154	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#11745669
commutator	C₈×C₅₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₅₉
Fitting	C₅₉×#364	C₂
socle	C₂×C₅₉	#335
hypercenter	#364	D₅₉
hypocenter	C₅₉	#1373
LCS	G ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
32. C₅₉	#1373	semidirect