Subgroups — #19132650

Order 5504.

86 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×#500	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₃⋊C₁₆	—	2	1	no	—
5	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
6	C₄⋊Q₈×C₄₃	—	2	1	no	—
7	#107×C₄₃	—	2	1	no	—
8	#107×C₄₃	C₄	1	2	yes	—
9	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×Q₈×C₄₃	—	4	1	no	—
11	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
13	C₄⋊C₄×C₄₃	—	2	2	no	—
14	C₄⋊C₄×C₄₃	—	4	1	no	—
15	C₄²×C₄₃	D₄	1	1	yes	characteristic
16	C₂×C₄₃⋊C₈	—	4	1	no	—
17	C₄₃⋊C₁₆	—	4	1	no	—
18	Q₈×C₄₃	—	8	1	no	—
19	Q₈×C₄₃	—	8	1	no	—
20	C₂×C₄×C₄₃	—	4	2	no	—
21	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
23	C₂×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
24	C₈×C₄₃	—	2	1	no	—
25	C₈×C₄₃	SD₁₆	1	1	yes	characteristic
26	C₈×C₄₃	Q₁₆	1	1	yes	characteristic
27	C₄₃⋊C₈	—	8	1	no	—
28	C₂²×C₄₃	#102	1	1	yes	characteristic
29	C₄×C₄₃	—	2	1	no	—
30	C₄×C₄₃	—	8	2	no	—
31	C₄×C₄₃	#101	1	1	yes	characteristic
32	C₄×C₄₃	#103	1	1	yes	characteristic
33	C₄×C₄₃	D₁₆	1	1	yes	characteristic
34	C₄×C₄₃	SD₃₂	1	1	yes	characteristic
35	#1364	—	43	1	no	maximal, Sylow
36	C₂×C₄₃	#332	1	1	yes	characteristic
37	C₂×C₄₃	#357	1	1	yes	characteristic
38	C₂×C₄₃	#362	1	1	yes	characteristic
39	#500	D₄₃	1	1	yes	characteristic
40	C₄⋊C₁₆	—	43	1	no	—
41	#335	—	43	1	no	—
42	C₄₃	#1364	1	1	yes	characteristic, complemented, Sylow
43	C₄⋊Q₈	—	2	1	no	—
44	C₂×C₁₆	—	86	1	no	—
45	#107	—	2	1	no	—
46	#107	Dic₄₃	1	2	yes	—
47	C₄⋊C₈	—	86	1	no	—
48	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
49	C₂×Q₈	—	4	1	no	—
50	C₂×C₈	—	172	1	no	—
51	C₂×C₈	C₂×Dic₄₃	1	1	yes	characteristic
52	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
53	C₄⋊C₄	—	2	2	no	—
54	C₄⋊C₄	—	4	1	no	—
55	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
56	C₁₆	—	172	1	no	—
57	Q₈	—	8	1	no	—
58	Q₈	—	8	1	no	—
59	C₂×C₄	—	4	2	no	—
60	C₂×C₄	#10621882	1	1	yes	characteristic
61	C₂×C₄	#10621883	1	1	yes	characteristic
62	C₂×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	344	1	no	—
65	C₈	#10621884	1	1	yes	characteristic
66	C₈	#10621885	1	1	yes	characteristic
67	C₂²	#13063246	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	8	2	no	—
70	C₄	#13063244	1	1	yes	characteristic
71	C₄	#13063249	1	1	yes	characteristic
72	C₄	#13063266	1	1	yes	characteristic
73	C₄	#13063269	1	1	yes	characteristic
74	C₂	#14582645	1	1	yes	characteristic
75	C₂	#14582700	1	1	yes	characteristic
76	C₂	#14582715	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13063246
commutator	C₂×C₈×C₄₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₄₃
Fitting	C₄₃×#500	C₂
socle	C₂²×C₄₃	#102
hypercenter	#500	D₄₃
hypocenter	C₄₃	#1364
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #500

Complements

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

N	H ≅ G/N	type
42. C₄₃	#1364	semidirect