Subgroups — #19132798

Order 5504.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	#14582729	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#368	C₂	1	1	yes	maximal, characteristic
4	#13063261	—	2	1	no	—
5	C₄₃⋊C₃₂	C₄	1	2	yes	—
6	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
7	#108×C₄₃	—	2	1	no	—
8	M₁₆×C₄₃	—	4	1	no	—
9	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
10	#10621877	—	4	1	no	—
11	C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₄₃	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
14	C₈×C₄₃	—	8	1	no	—
15	C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
16	C₈×C₄₃	Q₁₆	1	1	yes	characteristic
17	C₄₃⋊C₈	—	8	1	no	—
18	C₂²×C₄₃	Q₃₂	1	1	yes	characteristic
19	C₄×C₄₃	#107	1	1	yes	characteristic
20	C₄×C₄₃	D₁₆	1	1	yes	characteristic
21	#1425	—	43	1	no	maximal, Sylow
22	C₂×C₄₃	—	2	1	no	—
23	C₂×C₄₃	#366	1	1	yes	characteristic
24	C₂×C₃₂	—	43	1	no	—
25	#368	—	43	1	no	—
26	#368	D₄₃	1	1	yes	characteristic
27	C₄₃	#1425	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
29	#108	—	2	1	no	—
30	#108	—	86	1	no	—
31	C₃₂	—	43	2	no	—
32	M₁₆	—	4	1	no	—
33	M₁₆	—	172	1	no	—
34	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
35	C₁₆	Dic₈₆	1	1	yes	characteristic
36	C₁₆	C₄×D₄₃	1	1	yes	characteristic
37	C₂×C₄	#10621882	1	1	yes	characteristic
38	C₈	—	8	1	no	—
39	C₈	—	344	1	no	—
40	C₈	Dic₄₃⋊C₄	1	1	yes	characteristic
41	C₈	#10621885	1	1	yes	characteristic
42	C₂²	#13063271	1	1	yes	characteristic
43	C₄	#13063258	1	1	yes	characteristic
44	C₄	#13063266	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#14582724	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#13063266
commutator	C₁₆×C₄₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₄₃
Fitting	C₄₃×#368	C₂
socle	C₂×C₄₃	#366
hypercenter	#368	D₄₃
hypocenter	C₄₃	#1425
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
27. C₄₃	#1425	semidirect