Subgroups — #24905652

Order 10624.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃₂₈	C₂	1	1	yes	maximal, characteristic
2	#19127535	C₂	1	1	yes	maximal, characteristic, complemented
3	#368×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₆₆₄	—	2	1	no	—
5	D₁₃₂₈	—	2	1	no	—
6	D₁₃₂₈	C₄	1	2	yes	—
7	C₈₃⋊C₃₂	—	2	1	no	—
8	C₂×C₁₆×C₈₃	C₂²	1	1	yes	characteristic
9	#108×C₈₃	—	2	1	no	—
10	C₂×D₃₃₂	—	4	1	no	—
11	D₆₆₄	—	2	2	no	—
12	D₆₆₄	—	4	1	no	—
13	M₁₆×C₈₃	—	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	C₂²×D₈₃	—	8	1	no	—
18	C₂×C₄×C₈₃	D₈	1	1	yes	characteristic
19	D₃₃₂	—	4	2	no	—
20	D₃₃₂	—	8	1	no	—
21	C₈×C₈₃	—	8	1	no	—
22	C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₈₃	SD₁₆	1	1	yes	characteristic
24	C₂²×C₈₃	SD₃₂	1	1	yes	characteristic
25	C₂×D₈₃	—	8	2	no	—
26	C₂×D₈₃	—	16	2	no	—
27	C₄×C₈₃	#102	1	1	yes	characteristic
28	C₄×C₈₃	D₁₆	1	1	yes	characteristic
29	C₂×C₈₃	—	2	1	no	—
30	C₂×C₈₃	#357	1	1	yes	characteristic
31	D₈₃	—	16	2	no	—
32	#1419	—	83	1	no	maximal, Sylow
33	C₈₃	#1419	1	1	yes	characteristic, complemented, Sylow
34	C₂×D₁₆	—	83	1	no	—
35	M₆₄	—	83	1	no	—
36	#368	D₈₃	1	1	yes	characteristic, complemented
37	C₂×D₈	—	166	1	no	—
38	D₁₆	—	83	2	no	—
39	D₁₆	—	166	1	no	—
40	C₂×C₁₆	C₂×D₈₃	1	1	yes	characteristic
41	#108	—	2	1	no	—
42	C₃₂	—	166	1	no	—
43	C₂×D₄	—	332	1	no	—
44	D₈	—	332	1	no	—
45	D₈	—	166	2	no	—
46	M₁₆	—	4	1	no	—
47	C₂×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
48	C₁₆	C₄×D₈₃	1	1	yes	characteristic
49	C₁₆	D₃₃₂	1	1	yes	characteristic
50	C₂³	—	664	1	no	—
51	D₄	—	332	2	no	—
52	D₄	—	664	1	no	—
53	C₂×C₄	#13050575	1	1	yes	characteristic
54	C₈	—	8	1	no	—
55	C₈	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
56	C₈	#13050577	1	1	yes	characteristic
57	C₂²	—	1328	2	no	—
58	C₂²	—	664	2	no	—
59	C₂²	#14581735	1	1	yes	characteristic
60	C₄	#14581712	1	1	yes	characteristic
61	C₄	#14581733	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	1328	2	no	—
64	C₂	#19127501	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19127501
commutator	C₁₆×C₈₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₈₃
Fitting	#368×C₈₃	C₂
socle	C₂×C₈₃	#357
prime radical	C₂×D₁₃₂₈	C₂
cosocle	C₂×C₁₆×C₈₃	C₂²
hypercenter	#368	D₈₃
hypocenter	C₈₃	#1419
LCS	G ▷ C₁₆×C₈₃ ▷ C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
2. #19127535	C₂	semidirect
3. #368×C₈₃	C₂	semidirect
33. C₈₃	#1419	semidirect
36. #368	D₈₃	semidirect