Subgroups — #24905539

Order 10624.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19127522	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₈₃	C₂	1	1	yes	maximal, characteristic
3	#14581732	—	2	2	no	—
4	C₂×C₁₆×C₈₃	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₈₃	C₄	1	1	yes	characteristic
6	C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
7	C₈₃⋊C₁₆	—	4	2	no	—
8	C₂×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
10	C₄²×C₈₃	Q₈	1	1	yes	characteristic
11	C₁₆×C₈₃	—	2	1	no	—
12	C₁₆×C₈₃	C₈	1	2	yes	—
13	C₂×C₄×C₈₃	—	2	1	no	—
14	C₂×C₄×C₈₃	C₄⋊C₄	1	1	yes	characteristic
15	C₈×C₈₃	C₂×C₈	1	1	yes	characteristic
16	C₈×C₈₃	M₁₆	1	1	yes	characteristic
17	C₈×C₈₃	D₈	1	1	yes	characteristic
18	C₈×C₈₃	Q₁₆	1	1	yes	characteristic
19	C₂²×C₈₃	#108	1	1	yes	characteristic
20	C₄×C₈₃	—	2	2	no	—
21	C₄×C₈₃	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₈₃	#107	1	1	yes	characteristic
23	C₂×C₈₃	—	2	1	no	—
24	C₂×C₈₃	#335	1	1	yes	characteristic
25	#1373	—	83	1	no	maximal, Sylow
26	C₈₃	#1373	1	1	yes	characteristic, complemented, Sylow
27	#364	—	83	2	no	—
28	C₄×C₁₆	D₈₃	1	1	yes	characteristic
29	M₃₂	—	166	2	no	—
30	C₂×C₁₆	Dic₈₃	1	1	yes	characteristic
31	C₂×C₁₆	Dic₈₃	1	1	yes	characteristic
32	C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
33	C₂×C₈	D₃₃₂	1	1	yes	characteristic
34	C₂×C₈	C₂×Dic₈₃	1	1	yes	characteristic
35	C₄²	Dic₁₆₆	1	1	yes	characteristic
36	C₁₆	—	2	1	no	—
37	C₁₆	—	332	2	no	—
38	C₁₆	C₈₃⋊C₈	1	2	yes	—
39	C₂×C₄	—	2	1	no	—
40	C₂×C₄	C₄⋊Dic₈₃	1	1	yes	characteristic
41	C₈	C₂×C₈₃⋊C₈	1	1	yes	characteristic
42	C₈	#13050574	1	1	yes	characteristic
43	C₈	D₆₆₄	1	1	yes	characteristic
44	C₈	Dic₃₃₂	1	1	yes	characteristic
45	C₂²	#14581728	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	C₄⋊(C₈₃⋊C₈)	1	1	yes	characteristic
48	C₄	#14581726	1	1	yes	characteristic
49	C₂	—	2	1	no	—
50	C₂	#19127454	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₆₆₄
commutator	C₈×C₈₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₈₃
Fitting	C₄×C₁₆×C₈₃	C₂
socle	C₂×C₈₃	#335
prime radical	C₂²×C₈₃	#108
cosocle	C₄×C₈×C₈₃	C₂²
hypercenter	C₄×C₁₆	D₈₃
hypocenter	C₈₃	#1373
LCS	G ▷ C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
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
26. C₈₃	#1373	semidirect