Subgroups — #24905660

Order 10624.

58 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	C₁₆×Dic₈₃	C₂	1	1	yes	maximal, characteristic
3	M₆₄×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈₃⋊C₁₆	C₄	1	1	yes	characteristic
5	C₈×Dic₈₃	C₄	1	1	yes	characteristic
6	C₈₃⋊C₃₂	—	2	1	no	—
7	C₂×C₁₆×C₈₃	C₂²	1	1	yes	characteristic
8	C₃₂×C₈₃	—	2	1	no	—
9	C₂×C₈₃⋊C₈	C₈	1	1	yes	characteristic
10	C₄×Dic₈₃	C₈	1	1	yes	characteristic
11	C₈₃⋊C₁₆	—	2	1	no	—
12	C₂×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₈₃	D₄	1	1	yes	characteristic
14	C₁₆×C₈₃	Q₈	1	1	yes	characteristic
15	C₂×C₄×C₈₃	C₂×C₈	1	1	yes	characteristic
16	C₂×Dic₈₃	—	2	1	no	—
17	C₈×C₈₃	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₈₃	M₁₆	1	1	yes	characteristic
19	C₈₃⋊C₈	C₁₆	1	2	yes	—
20	C₂²×C₈₃	M₃₂	1	1	yes	characteristic
21	C₄×C₈₃	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₈₃	C₂×C₁₆	1	1	yes	characteristic
23	Dic₈₃	—	2	2	no	—
24	C₂×C₈₃	—	2	1	no	—
25	C₂×C₈₃	C₄⋊C₁₆	1	1	yes	characteristic
26	#1422	—	83	1	no	maximal, Sylow
27	C₈₃	#1422	1	1	yes	characteristic, complemented, Sylow
28	M₆₄	—	83	1	no	—
29	M₆₄	D₈₃	1	1	yes	characteristic
30	C₄×C₁₆	—	83	1	no	—
31	C₂×C₁₆	—	83	1	no	—
32	C₂×C₁₆	C₂×D₈₃	1	1	yes	characteristic
33	C₄×C₈	—	83	1	no	—
34	C₃₂	—	2	1	no	—
35	C₃₂	—	166	1	no	—
36	C₂×C₈	—	83	1	no	—
37	C₂×C₈	C₄×D₈₃	1	1	yes	characteristic
38	C₄²	—	83	1	no	—
39	C₁₆	—	166	1	no	—
40	C₁₆	Dic₁₆₆	1	1	yes	characteristic
41	C₁₆	C₂²⋊D₈₃	1	1	yes	characteristic
42	C₂×C₄	—	166	1	no	—
43	C₂×C₄	C₈×D₈₃	1	1	yes	characteristic
44	C₈	—	83	2	no	—
45	C₈	Dic₈₃⋊C₄	1	1	yes	characteristic
46	C₈	#13050573	1	1	yes	characteristic
47	C₂²	#14581731	1	1	yes	characteristic
48	C₄	—	166	2	no	—
49	C₄	Dic₈₃⋊C₈	1	1	yes	characteristic
50	C₄	C₁₆×D₈₃	1	1	yes	characteristic
51	C₂	—	2	1	no	—
52	C₂	Dic₈₃⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂²⋊D₈₃
commutator	C₄×C₈₃	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₈₃
Fitting	M₆₄×C₈₃	C₂
socle	C₂×C₈₃	C₄⋊C₁₆
prime radical	C₂²×C₈₃	M₃₂
cosocle	C₂×C₁₆×C₈₃	C₂²
hypercenter	M₆₄	D₈₃
hypocenter	C₈₃	#1422
LCS	G ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
27. C₈₃	#1422	semidirect