Subgroups — #19132661

Order 5504.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14582650	C₂	1	2	yes	maximal
2	C₄₃×#346	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
4	C₂×C₁₆×C₄₃	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₄₃	C₄	1	1	yes	characteristic
6	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
8	C₂×C₈×C₄₃	Q₈	1	1	yes	characteristic
9	C₄²×C₄₃	D₄	1	1	yes	characteristic
10	C₂×C₄₃⋊C₈	—	4	2	no	—
11	C₁₆×C₄₃	—	2	1	no	—
12	C₁₆×C₄₃	C₈	1	2	yes	complemented
13	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₄×C₄₃	SD₁₆	1	2	yes	—
15	C₈×C₄₃	—	2	1	no	—
16	C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
17	C₈×C₄₃	M₁₆	1	1	yes	characteristic
18	C₄₃⋊C₈	—	8	2	no	—
19	C₂²×C₄₃	#106	1	1	yes	characteristic
20	C₄×C₄₃	—	2	2	no	—
21	C₄×C₄₃	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₄₃	#108	1	1	yes	characteristic
23	#1368	—	43	1	no	maximal, Sylow
24	C₂×C₄₃	#334	1	1	yes	characteristic
25	C₂×C₄₃	#365	1	2	yes	—
26	#346	D₄₃	1	1	yes	characteristic
27	#334	—	43	2	no	—
28	C₄₃	#1368	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₁₆	Dic₄₃	1	1	yes	characteristic
30	C₂×C₁₆	Dic₄₃	1	1	yes	characteristic
31	C₄⋊C₈	—	86	2	no	—
32	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
33	C₂×C₈	—	172	2	no	—
34	C₂×C₈	Dic₈₆	1	1	yes	characteristic
35	C₂×C₈	C₂×Dic₄₃	1	1	yes	characteristic
36	C₄²	D₁₇₂	1	1	yes	characteristic
37	C₁₆	—	2	1	no	—
38	C₁₆	C₄₃⋊C₈	1	2	yes	complemented
39	C₂×C₄	#10621873	1	2	yes	—
40	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
41	C₈	—	2	1	no	—
42	C₈	—	344	2	no	—
43	C₈	C₂×C₄₃⋊C₈	1	1	yes	characteristic
44	C₈	#10621877	1	1	yes	characteristic
45	C₂²	#13063257	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	C₄⋊(C₄₃⋊C₈)	1	1	yes	characteristic
48	C₄	#13063261	1	1	yes	characteristic
49	C₂	#14582650	1	1	yes	characteristic
50	C₂	#14582722	1	2	yes	—

	subgroup	G/H
center	C₂²	#13063257
commutator	C₈×C₄₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₄₃
Fitting	C₄₃×#346	C₂
socle	C₂²×C₄₃	#106
hypercenter	#346	D₄₃
hypocenter	C₄₃	#1368
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
12. C₁₆×C₄₃	C₈	semidirect
28. C₄₃	#1368	semidirect
38. C₁₆	C₄₃⋊C₈	semidirect