Subgroups — #19132800

Order 5504.

52 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	#14582729	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#367	C₂	1	1	yes	maximal, characteristic
4	#13063261	—	2	1	no	—
5	C₄₃⋊C₃₂	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
7	#107×C₄₃	—	2	1	no	—
8	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
9	C₄⋊C₄×C₄₃	—	4	1	no	—
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	—	8	1	no	—
14	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
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	SD₃₂	1	1	yes	characteristic
19	C₄×C₄₃	—	16	1	no	—
20	C₄×C₄₃	#107	1	1	yes	characteristic
21	C₄×C₄₃	SD₃₂	1	1	yes	characteristic
22	#1426	—	43	1	no	maximal, Sylow
23	C₂×C₄₃	—	2	1	no	—
24	C₂×C₄₃	#367	1	1	yes	characteristic
25	M₆₄	—	43	1	no	—
26	#368	—	43	1	no	—
27	#367	D₄₃	1	1	yes	characteristic
28	C₄₃	#1426	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
30	#108	—	86	1	no	—
31	#107	—	2	1	no	—
32	C₃₂	—	43	2	no	—
33	M₁₆	—	172	1	no	—
34	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
35	C₄⋊C₄	—	4	1	no	—
36	C₁₆	Dic₈₆	1	1	yes	characteristic
37	C₁₆	C₄×D₄₃	1	1	yes	characteristic
38	C₂×C₄	—	8	1	no	—
39	C₂×C₄	#10621882	1	1	yes	characteristic
40	C₈	—	344	1	no	—
41	C₈	Dic₄₃⋊C₄	1	1	yes	characteristic
42	C₈	#10621885	1	1	yes	characteristic
43	C₂²	#13063269	1	1	yes	characteristic
44	C₄	—	16	1	no	—
45	C₄	#13063258	1	1	yes	characteristic
46	C₄	#13063268	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#14582726	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14582726
commutator	C₁₆×C₄₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₄₃
Fitting	C₄₃×#367	C₂
socle	C₂×C₄₃	#367
hypercenter	#367	D₄₃
hypocenter	C₄₃	#1426
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #367

Complements

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

N	H ≅ G/N	type
5. C₄₃⋊C₃₂	C₄	semidirect
28. C₄₃	#1426	semidirect