Subgroups — #19132730

Order 5504.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14582733	C₂	1	1	yes	maximal, characteristic
2	#14582674	C₂	1	1	yes	maximal, characteristic
3	C₄₃×M₆₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₃⋊C₁₆	C₄	1	1	yes	characteristic
5	C₈×Dic₄₃	C₄	1	1	yes	characteristic
6	C₄₃⋊C₃₂	C₄	1	2	yes	complemented
7	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
8	C₃₂×C₄₃	C₄	1	2	yes	complemented
9	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
10	C₄×Dic₄₃	C₈	1	1	yes	characteristic
11	C₂×C₄₃⋊C₈	C₈	1	1	yes	characteristic
12	C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
14	C₄₃⋊C₁₆	C₈	1	2	yes	—
15	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
16	C₂×Dic₄₃	—	2	1	no	—
17	C₈×C₄₃	C₄²	1	1	yes	characteristic
18	C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
19	C₄₃⋊C₈	—	2	1	no	—
20	C₂²×C₄₃	M₃₂	1	1	yes	characteristic
21	C₄×C₄₃	C₄×C₈	1	1	yes	characteristic
22	C₄×C₄₃	M₃₂	1	1	yes	characteristic
23	Dic₄₃	—	4	1	no	—
24	#1398	—	43	1	no	maximal, Sylow
25	C₂×C₄₃	—	2	1	no	—
26	C₂×C₄₃	#346	1	1	yes	characteristic
27	M₆₄	—	43	1	no	—
28	M₆₄	D₄₃	1	1	yes	characteristic
29	#346	—	43	1	no	—
30	C₄₃	#1398	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₁₆	—	43	1	no	—
32	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
33	C₄×C₈	—	43	1	no	—
34	C₃₂	—	43	2	no	—
35	C₃₂	Dic₄₃	1	2	yes	complemented
36	C₂×C₈	—	43	1	no	—
37	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
38	C₄²	—	43	1	no	—
39	C₁₆	—	43	2	no	—
40	C₁₆	C₄×D₄₃	1	1	yes	characteristic
41	C₁₆	C₂×Dic₄₃	1	1	yes	characteristic
42	C₂×C₄	—	86	1	no	—
43	C₂×C₄	C₈×D₄₃	1	1	yes	characteristic
44	C₈	—	86	1	no	—
45	C₈	C₈×D₄₃	1	1	yes	characteristic
46	C₈	C₄×Dic₄₃	1	1	yes	characteristic
47	C₂²	#13063264	1	1	yes	characteristic
48	C₄	—	172	1	no	—
49	C₄	C₈×Dic₄₃	1	1	yes	characteristic
50	C₄	#13063264	1	1	yes	characteristic
51	C₂	—	2	1	no	—
52	C₂	#14582674	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄×Dic₄₃
commutator	C₄×C₄₃	C₄×C₈
Frattini	C₂×C₁₆	C₂×D₄₃
Fitting	C₄₃×M₆₄	C₂
socle	C₂×C₄₃	#346
hypercenter	M₆₄	D₄₃
hypocenter	C₄₃	#1398
LCS	G ▷ C₄×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₈ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
6. C₄₃⋊C₃₂	C₄	semidirect
8. C₃₂×C₄₃	C₄	semidirect
30. C₄₃	#1398	semidirect
35. C₃₂	Dic₄₃	semidirect