Subgroups — #21422172

Order 7552.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837223	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic
3	#14273667	—	2	2	no	—
4	C₂×C₁₆×C₅₉	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₅₉	C₄	1	1	yes	characteristic
6	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
8	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
9	C₄²×C₅₉	Q₈	1	1	yes	characteristic
10	C₁₆×C₅₉	—	2	1	no	—
11	C₁₆×C₅₉	C₈	1	2	yes	—
12	C₅₉⋊C₁₆	—	4	2	no	—
13	C₂×C₄×C₅₉	—	2	1	no	—
14	C₂×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
15	C₈×C₅₉	C₂×C₈	1	1	yes	characteristic
16	C₈×C₅₉	M₁₆	1	1	yes	characteristic
17	C₈×C₅₉	D₈	1	1	yes	characteristic
18	C₈×C₅₉	Q₁₆	1	1	yes	characteristic
19	C₂²×C₅₉	#108	1	1	yes	characteristic
20	C₄×C₅₉	—	2	2	no	—
21	C₄×C₅₉	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₅₉	#107	1	1	yes	characteristic
23	#1373	—	59	1	no	maximal, Sylow
24	C₂×C₅₉	—	2	1	no	—
25	C₂×C₅₉	#335	1	1	yes	characteristic
26	#364	—	59	2	no	—
27	C₄×C₁₆	D₅₉	1	1	yes	characteristic
28	C₅₉	#1373	1	1	yes	characteristic, complemented, Sylow
29	M₃₂	—	118	2	no	—
30	C₂×C₁₆	Dic₅₉	1	1	yes	characteristic
31	C₂×C₁₆	Dic₅₉	1	1	yes	characteristic
32	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
33	C₂×C₈	D₂₃₆	1	1	yes	characteristic
34	C₂×C₈	C₂×Dic₅₉	1	1	yes	characteristic
35	C₄²	Dic₁₁₈	1	1	yes	characteristic
36	C₁₆	—	2	1	no	—
37	C₁₆	—	236	2	no	—
38	C₁₆	C₅₉⋊C₈	1	2	yes	—
39	C₂×C₄	—	2	1	no	—
40	C₂×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
41	C₈	D₄₇₂	1	1	yes	characteristic
42	C₈	Dic₂₃₆	1	1	yes	characteristic
43	C₈	C₂×C₅₉⋊C₈	1	1	yes	characteristic
44	C₈	#11745664	1	1	yes	characteristic
45	C₂²	#14273663	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	C₄⋊(C₅₉⋊C₈)	1	1	yes	characteristic
48	C₄	#14273661	1	1	yes	characteristic
49	C₂	—	2	1	no	—
50	C₂	#16837155	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₄₇₂
commutator	C₈×C₅₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₅₉
Fitting	C₄×C₁₆×C₅₉	C₂
socle	C₂×C₅₉	#335
hypercenter	C₄×C₁₆	D₅₉
hypocenter	C₅₉	#1373
LCS	G ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

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