Subgroups — #24905657

Order 10624.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₆₆₄	C₂	1	1	yes	maximal, characteristic
2	#19127531	C₂	1	1	yes	maximal, characteristic
3	M₆₄×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₃₂	—	2	1	no	—
5	Dic₆₆₄	—	2	1	no	—
6	Dic₆₆₄	C₄	1	2	yes	—
7	#14581728	—	2	1	no	—
8	C₂×C₁₆×C₈₃	C₂²	1	1	yes	characteristic
9	C₃₂×C₈₃	—	2	1	no	—
10	C₂×Dic₁₆₆	—	4	1	no	—
11	Dic₃₃₂	—	2	2	no	—
12	Dic₃₃₂	—	4	1	no	—
13	#13050574	—	4	1	no	—
14	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
15	C₁₆×C₈₃	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₈₃	D₄	1	1	yes	characteristic
17	C₂×C₄×C₈₃	D₈	1	1	yes	characteristic
18	C₂×Dic₈₃	—	8	1	no	—
19	Dic₁₆₆	—	4	2	no	—
20	Dic₁₆₆	—	8	1	no	—
21	C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₈₃	SD₁₆	1	1	yes	characteristic
23	C₈₃⋊C₈	—	8	1	no	—
24	C₂²×C₈₃	SD₃₂	1	1	yes	characteristic
25	C₄×C₈₃	#102	1	1	yes	characteristic
26	C₄×C₈₃	D₁₆	1	1	yes	characteristic
27	Dic₈₃	—	8	2	no	—
28	C₂×C₈₃	—	2	1	no	—
29	C₂×C₈₃	#357	1	1	yes	characteristic
30	#1420	—	83	1	no	maximal, Sylow
31	C₈₃	#1420	1	1	yes	characteristic, complemented, Sylow
32	C₂×Q₃₂	—	83	1	no	—
33	M₆₄	D₈₃	1	1	yes	characteristic
34	#368	—	83	1	no	—
35	C₂×Q₁₆	—	166	1	no	—
36	Q₃₂	—	83	2	no	—
37	Q₃₂	—	166	1	no	—
38	C₂×C₁₆	C₂×D₈₃	1	1	yes	characteristic
39	#108	—	166	1	no	—
40	C₃₂	—	2	1	no	—
41	C₂×Q₈	—	332	1	no	—
42	Q₁₆	—	332	1	no	—
43	Q₁₆	—	166	2	no	—
44	M₁₆	—	332	1	no	—
45	C₂×C₈	D₃₃₂	1	1	yes	characteristic
46	C₁₆	C₄×D₈₃	1	1	yes	characteristic
47	C₁₆	C₂²⋊D₈₃	1	1	yes	characteristic
48	Q₈	—	332	2	no	—
49	Q₈	—	664	1	no	—
50	C₂×C₄	—	664	1	no	—
51	C₂×C₄	D₆₆₄	1	1	yes	characteristic
52	C₈	—	664	1	no	—
53	C₈	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
54	C₈	#13050579	1	1	yes	characteristic
55	C₂²	#14581737	1	1	yes	characteristic
56	C₄	—	664	2	no	—
57	C₄	#14581714	1	1	yes	characteristic
58	C₄	D₁₃₂₈	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	#19127503	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19127503
commutator	C₁₆×C₈₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₈₃
Fitting	M₆₄×C₈₃	C₂
socle	C₂×C₈₃	#357
prime radical	C₂²×C₈₃	SD₃₂
cosocle	C₂×C₁₆×C₈₃	C₂²
hypercenter	M₆₄	D₈₃
hypocenter	C₈₃	#1420
LCS	G ▷ C₁₆×C₈₃ ▷ C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
31. C₈₃	#1420	semidirect