Subgroups — #24905643

Order 10624.

74 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	C₂×C₈₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic
3	#366×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₃₂	—	2	1	no	—
5	Dic₆₆₄	—	2	1	no	—
6	Dic₆₆₄	C₄	1	2	yes	complemented
7	C₈₃⋊C₃₂	—	2	1	no	—
8	C₂×C₁₆×C₈₃	C₂²	1	1	yes	characteristic
9	#107×C₈₃	—	2	1	no	—
10	C₂×Dic₁₆₆	—	4	1	no	—
11	Dic₃₃₂	—	2	2	no	—
12	Dic₃₃₂	—	4	1	no	—
13	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
14	C₄⋊C₄×C₈₃	—	4	1	no	—
15	C₁₆×C₈₃	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₈₃	D₄	1	1	yes	characteristic
17	C₂×C₄×C₈₃	—	8	1	no	—
18	C₂×C₄×C₈₃	D₈	1	1	yes	characteristic
19	C₂×Dic₈₃	—	8	1	no	—
20	Dic₁₆₆	—	4	2	no	—
21	Dic₁₆₆	—	8	1	no	—
22	C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₈₃	SD₁₆	1	1	yes	characteristic
24	C₂²×C₈₃	D₁₆	1	1	yes	characteristic
25	C₄×C₈₃	—	16	1	no	—
26	C₄×C₈₃	#102	1	1	yes	characteristic
27	C₄×C₈₃	SD₃₂	1	1	yes	characteristic
28	Dic₈₃	—	8	2	no	—
29	C₂×C₈₃	#357	1	1	yes	characteristic
30	C₂×C₈₃	SD₆₄	1	1	yes	characteristic
31	C₂×C₈₃	Q₆₄	1	1	yes	characteristic
32	#1416	—	83	1	no	maximal, Sylow
33	C₈₃	#1416	1	1	yes	characteristic, complemented, Sylow
34	C₂×Q₃₂	—	83	1	no	—
35	C₂×C₃₂	—	83	1	no	—
36	#366	D₈₃	1	1	yes	characteristic
37	C₂×Q₁₆	—	166	1	no	—
38	Q₃₂	—	83	2	no	—
39	Q₃₂	—	166	1	no	—
40	C₂×C₁₆	C₂×D₈₃	1	1	yes	characteristic
41	#107	—	2	1	no	—
42	C₃₂	—	166	1	no	—
43	C₂×Q₈	—	332	1	no	—
44	Q₁₆	—	332	1	no	—
45	Q₁₆	—	166	2	no	—
46	C₂×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
47	C₄⋊C₄	—	4	1	no	—
48	C₁₆	C₄×D₈₃	1	1	yes	characteristic
49	C₁₆	D₃₃₂	1	1	yes	characteristic
50	Q₈	—	332	2	no	—
51	Q₈	—	664	1	no	—
52	C₂×C₄	—	8	1	no	—
53	C₂×C₄	—	664	1	no	—
54	C₂×C₄	#13050575	1	1	yes	characteristic
55	C₈	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
56	C₈	#13050577	1	1	yes	characteristic
57	C₂²	#14581733	1	1	yes	characteristic
58	C₄	—	16	1	no	—
59	C₄	—	664	2	no	—
60	C₄	#14581712	1	1	yes	characteristic
61	C₄	#14581735	1	1	yes	characteristic
62	C₂	#19127501	1	1	yes	characteristic
63	C₂	#19127539	1	1	yes	characteristic
64	C₂	#19127541	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14581733
commutator	C₁₆×C₈₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₈₃
Fitting	#366×C₈₃	C₂
socle, prime radical	C₂²×C₈₃	D₁₆
cosocle	C₂×C₁₆×C₈₃	C₂²
hypercenter	#366	D₈₃
hypocenter	C₈₃	#1416
LCS	G ▷ C₁₆×C₈₃ ▷ C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
6. Dic₆₆₄	C₄	semidirect
33. C₈₃	#1416	semidirect