Subgroups — #19132668

Order 5504.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#14582652	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#335	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₃⋊C₁₆	C₄	1	1	yes	characteristic
5	C₂×C₄₃⋊C₁₆	C₄	1	1	yes	characteristic
6	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
7	C₄⋊C₈×C₄₃	—	2	1	no	—
8	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₄₃	—	4	1	no	—
10	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
11	C₂×C₈×C₄₃	Q₈	1	1	yes	characteristic
12	C₄²×C₄₃	D₄	1	1	yes	characteristic
13	C₂×C₄₃⋊C₈	—	4	1	no	—
14	C₄₃⋊C₁₆	—	2	1	no	—
15	C₄₃⋊C₁₆	C₈	1	2	yes	complemented
16	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
17	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
18	C₂×C₄×C₄₃	Q₁₆	1	1	yes	characteristic
19	C₈×C₄₃	—	2	1	no	—
20	C₈×C₄₃	—	8	1	no	—
21	C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
22	C₈×C₄₃	M₁₆	1	1	yes	characteristic
23	C₄₃⋊C₈	—	8	1	no	—
24	C₂²×C₄₃	#107	1	1	yes	characteristic
25	C₄×C₄₃	—	2	1	no	—
26	C₄×C₄₃	C₄⋊C₈	1	1	yes	characteristic
27	C₄×C₄₃	#108	1	1	yes	characteristic
28	C₄×C₄₃	SD₃₂	1	1	yes	characteristic
29	C₄×C₄₃	SD₃₂	1	1	yes	characteristic
30	#1372	—	43	1	no	maximal, Sylow
31	C₂×C₄₃	#335	1	1	yes	characteristic
32	C₂×C₄₃	#367	1	1	yes	characteristic
33	C₂×C₄₃	#368	1	1	yes	characteristic
34	C₄×C₁₆	—	43	1	no	—
35	#335	—	43	1	no	—
36	#335	D₄₃	1	1	yes	characteristic
37	C₄₃	#1372	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₁₆	—	43	1	no	—
39	C₂×C₁₆	—	43	1	no	—
40	C₄⋊C₈	—	2	1	no	—
41	C₄⋊C₈	—	86	1	no	—
42	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
43	C₂×C₈	—	4	1	no	—
44	C₂×C₈	—	172	1	no	—
45	C₂×C₈	Dic₈₆	1	1	yes	characteristic
46	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
47	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
48	C₁₆	—	43	2	no	—
49	C₁₆	—	86	1	no	—
50	C₂×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
51	C₂×C₄	#10621882	1	1	yes	characteristic
52	C₂×C₄	#10621885	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	—	8	1	no	—
55	C₈	—	344	1	no	—
56	C₈	C₈×D₄₃	1	1	yes	characteristic
57	C₈	#10621872	1	1	yes	characteristic
58	C₂²	#13063258	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	Dic₄₃⋊C₈	1	1	yes	characteristic
61	C₄	#13063260	1	1	yes	characteristic
62	C₄	#13063268	1	1	yes	characteristic
63	C₄	#13063269	1	1	yes	characteristic
64	C₂	#14582651	1	1	yes	characteristic
65	C₂	#14582726	1	1	yes	characteristic
66	C₂	#14582728	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10621882
commutator	C₈×C₄₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₄₃
Fitting	C₄₃×#335	C₂
socle	C₂²×C₄₃	#107
hypercenter	#335	D₄₃
hypocenter	C₄₃	#1372
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
15. C₄₃⋊C₁₆	C₈	semidirect
37. C₄₃	#1372	semidirect