Subgroups — #19132773

Order 5504.

82 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, complemented
2	#14582725	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
4	#13063259	—	2	1	no	—
5	C₄₃⋊C₃₂	—	2	1	no	—
6	C₂×D₈×C₄₃	—	2	1	no	—
7	D₁₆×C₄₃	—	2	1	no	—
8	D₁₆×C₄₃	C₄	1	2	yes	complemented
9	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×D₄×C₄₃	—	4	1	no	—
11	D₈×C₄₃	—	2	2	no	—
12	D₈×C₄₃	—	4	1	no	—
13	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
14	C₄⋊Dic₄₃	—	4	1	no	—
15	C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₄₃	D₄	1	1	yes	characteristic
17	C₂³×C₄₃	—	8	1	no	—
18	D₄×C₄₃	—	4	2	no	—
19	D₄×C₄₃	—	8	1	no	—
20	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
21	C₂×Dic₄₃	—	8	1	no	—
22	C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₄₃	SD₁₆	1	1	yes	characteristic
24	C₂²×C₄₃	—	8	2	no	—
25	C₂²×C₄₃	—	16	1	no	—
26	C₂²×C₄₃	—	16	1	no	—
27	C₂²×C₄₃	D₁₆	1	1	yes	characteristic
28	C₄×C₄₃	#102	1	1	yes	characteristic
29	C₄×C₄₃	SD₃₂	1	1	yes	characteristic
30	Dic₄₃	—	16	1	no	—
31	#1415	—	43	1	no	maximal, Sylow
32	C₂×C₄₃	—	16	2	no	—
33	C₂×C₄₃	#357	1	1	yes	characteristic
34	C₂×C₄₃	D₃₂	1	1	yes	characteristic
35	C₂×C₄₃	SD₆₄	1	1	yes	characteristic
36	C₂×D₁₆	D₄₃	1	1	yes	characteristic
37	C₂×C₃₂	—	43	1	no	—
38	#366	—	43	1	no	—
39	C₄₃	#1415	1	1	yes	characteristic, complemented, Sylow
40	C₂×D₈	—	2	1	no	—
41	D₁₆	—	2	1	no	—
42	D₁₆	Dic₄₃	1	2	yes	complemented
43	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
44	#107	—	86	1	no	—
45	C₃₂	—	86	1	no	—
46	C₂×D₄	—	4	1	no	—
47	D₈	—	2	2	no	—
48	D₈	—	4	1	no	—
49	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
50	C₄⋊C₄	—	172	1	no	—
51	C₁₆	C₂×Dic₄₃	1	1	yes	characteristic
52	C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
53	C₂³	—	8	1	no	—
54	D₄	—	4	2	no	—
55	D₄	—	8	1	no	—
56	C₂×C₄	—	344	1	no	—
57	C₂×C₄	#10621882	1	1	yes	characteristic
58	C₈	#10621883	1	1	yes	characteristic
59	C₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
60	C₂²	—	8	2	no	—
61	C₂²	—	16	1	no	—
62	C₂²	—	16	1	no	—
63	C₂²	#13063266	1	1	yes	characteristic
64	C₄	—	688	1	no	—
65	C₄	#13063246	1	1	yes	characteristic
66	C₄	#13063269	1	1	yes	characteristic
67	C₂	—	16	2	no	—
68	C₂	#14582700	1	1	yes	characteristic
69	C₂	#14582734	1	1	yes	characteristic
70	C₂	#14582737	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13063266
commutator	C₁₆×C₄₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₄₃
Fitting	C₂×D₁₆×C₄₃	C₂
socle	C₂²×C₄₃	D₁₆
hypercenter	C₂×D₁₆	D₄₃
hypocenter	C₄₃	#1415
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×D₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃⋊C₃₂	C₂	semidirect
2. #14582725	C₂	semidirect
8. D₁₆×C₄₃	C₄	semidirect
39. C₄₃	#1415	semidirect
42. D₁₆	Dic₄₃	semidirect