Subgroups — #24905385

Order 10624.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19127477	C₂	1	1	yes	maximal, characteristic
2	#19127422	C₂	1	1	yes	maximal, characteristic
3	#346×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈₃⋊C₁₆	C₄	1	2	yes	—
5	C₄×C₈₃⋊C₈	C₄	1	2	yes	—
6	C₂×C₁₆×C₈₃	C₄	1	2	yes	—
7	C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
8	C₂×C₈₃⋊C₈	—	2	2	no	—
9	C₈₃⋊C₁₆	C₈	1	4	yes	complemented
10	C₂×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
11	C₂×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
12	C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₈₃	—	2	2	no	—
14	C₂×C₄×C₈₃	C₄²	1	1	yes	characteristic
15	C₂×C₄×C₈₃	M₁₆	1	2	yes	—
16	C₈×C₈₃	C₂×C₈	1	2	yes	—
17	C₈×C₈₃	M₁₆	1	2	yes	—
18	C₈₃⋊C₈	—	4	2	no	—
19	C₂²×C₈₃	#97	1	1	yes	characteristic
20	C₄×C₈₃	—	2	2	no	—
21	C₄×C₈₃	C₄×C₈	1	1	yes	characteristic
22	C₄×C₈₃	#97	1	1	yes	characteristic
23	C₂×C₈₃	#322	1	1	yes	characteristic
24	C₂×C₈₃	#347	1	2	yes	—
25	#1313	—	83	1	no	maximal, Sylow
26	C₈₃	#1313	1	1	yes	characteristic, complemented, Sylow
27	#346	—	83	1	no	—
28	#346	D₈₃	1	1	yes	characteristic
29	#322	—	83	1	no	—
30	C₂×C₁₆	—	83	2	no	—
31	C₂×C₁₆	Dic₈₃	1	2	yes	—
32	C₄×C₈	—	83	2	no	—
33	C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
34	C₂×C₈	—	166	2	no	—
35	C₂×C₈	C₄×D₈₃	1	1	yes	characteristic
36	C₂×C₈	C₂×Dic₈₃	1	1	yes	characteristic
37	C₄²	C₄×D₈₃	1	1	yes	characteristic
38	C₁₆	—	2	2	no	—
39	C₁₆	—	83	4	no	—
40	C₂×C₄	C₄×Dic₈₃	1	1	yes	characteristic
41	C₂×C₄	#13050573	1	2	yes	—
42	C₈	—	332	2	no	—
43	C₈	C₈×D₈₃	1	2	yes	—
44	C₈	#13050574	1	2	yes	—
45	C₂²	#14581702	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	C₈×Dic₈₃	1	1	yes	characteristic
48	C₄	#14581703	1	1	yes	characteristic
49	C₂	#19127423	1	1	yes	characteristic
50	C₂	#19127478	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄×Dic₈₃
commutator	C₄×C₈₃	C₄×C₈
Frattini	C₄×C₈	C₂×D₈₃
Fitting	#346×C₈₃	C₂
socle, prime radical	C₂²×C₈₃	#97
cosocle	C₄×C₈×C₈₃	C₂²
hypercenter	#346	D₈₃
hypocenter	C₈₃	#1313
LCS	G ▷ C₄×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ #346

Complements

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

N	H ≅ G/N	type
9. C₈₃⋊C₁₆	C₈	semidirect
26. C₈₃	#1313	semidirect