Subgroups — #24905656

Order 10624.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19127535	C₂	1	1	yes	maximal, characteristic
2	#19127531	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₃₂×C₈₃	C₂	1	1	yes	maximal, characteristic
4	#14581728	—	2	1	no	—
5	C₈₃⋊C₃₂	—	2	1	no	—
6	C₂×Q₁₆×C₈₃	—	2	1	no	—
7	Q₃₂×C₈₃	—	2	1	no	—
8	Q₃₂×C₈₃	C₄	1	2	yes	—
9	C₂×C₁₆×C₈₃	C₂²	1	1	yes	characteristic
10	#13050574	—	4	1	no	—
11	C₂×Q₈×C₈₃	—	4	1	no	—
12	Q₁₆×C₈₃	—	2	2	no	—
13	Q₁₆×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	Q₈×C₈₃	—	4	2	no	—
18	Q₈×C₈₃	—	8	1	no	—
19	C₂×C₄×C₈₃	—	8	1	no	—
20	C₂×C₄×C₈₃	D₈	1	1	yes	characteristic
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	—	8	2	no	—
26	C₄×C₈₃	#102	1	1	yes	characteristic
27	C₄×C₈₃	D₁₆	1	1	yes	characteristic
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	D₈₃	1	1	yes	characteristic
33	M₆₄	—	83	1	no	—
34	#368	—	83	1	no	—
35	C₂×Q₁₆	—	2	1	no	—
36	Q₃₂	—	2	1	no	—
37	Q₃₂	Dic₈₃	1	2	yes	—
38	C₂×C₁₆	C₂×D₈₃	1	1	yes	characteristic
39	#108	—	166	1	no	—
40	C₃₂	—	166	1	no	—
41	C₂×Q₈	—	4	1	no	—
42	Q₁₆	—	2	2	no	—
43	Q₁₆	—	4	1	no	—
44	M₁₆	—	332	1	no	—
45	C₂×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
46	C₁₆	C₂×Dic₈₃	1	1	yes	characteristic
47	C₁₆	C₂²⋊D₈₃	1	1	yes	characteristic
48	Q₈	—	4	2	no	—
49	Q₈	—	8	1	no	—
50	C₂×C₄	—	8	1	no	—
51	C₂×C₄	#13050575	1	1	yes	characteristic
52	C₈	—	664	1	no	—
53	C₈	C₂²⋊Dic₈₃	1	1	yes	characteristic
54	C₈	#13050578	1	1	yes	characteristic
55	C₂²	#14581736	1	1	yes	characteristic
56	C₄	—	8	2	no	—
57	C₄	#14581713	1	1	yes	characteristic
58	C₄	#14581733	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	#19127502	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19127502
commutator	C₁₆×C₈₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₈₃
Fitting	C₂×Q₃₂×C₈₃	C₂
socle	C₂×C₈₃	#357
prime radical	C₂²×C₈₃	SD₃₂
cosocle	C₂×C₁₆×C₈₃	C₂²
hypercenter	C₂×Q₃₂	D₈₃
hypocenter	C₈₃	#1420
LCS	G ▷ C₁₆×C₈₃ ▷ C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×Q₃₂

Complements

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

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