Subgroups — #19132658

Order 5504.

76 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	C₈×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₃⋊C₁₆	—	2	1	no	—
5	C₄×C₄₃⋊C₈	C₄	1	1	yes	characteristic
6	C₄×C₄₃⋊C₈	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₄₃	—	2	1	no	—
8	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
10	C₂×C₈×C₄₃	Q₈	1	1	yes	characteristic
11	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄₃⋊C₈	—	2	1	no	—
13	C₂×C₄₃⋊C₈	C₈	1	1	yes	characteristic
14	C₂×C₄₃⋊C₈	C₈	1	1	yes	characteristic
15	C₁₆×C₄₃	—	4	1	no	—
16	C₄₃⋊C₁₆	—	4	1	no	—
17	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
19	C₂×C₄×C₄₃	M₁₆	1	1	yes	characteristic
20	C₈×C₄₃	—	2	1	no	—
21	C₈×C₄₃	SD₁₆	1	1	yes	characteristic
22	C₈×C₄₃	SD₁₆	1	1	yes	characteristic
23	C₄₃⋊C₈	—	2	2	no	—
24	C₄₃⋊C₈	—	2	1	no	—
25	C₄₃⋊C₈	C₁₆	1	2	yes	complemented
26	C₂²×C₄₃	C₄⋊C₈	1	1	yes	characteristic
27	C₄×C₄₃	—	2	1	no	—
28	C₄×C₄₃	#106	1	1	yes	characteristic
29	C₄×C₄₃	#108	1	1	yes	characteristic
30	C₄×C₄₃	C₂×C₁₆	1	1	yes	characteristic
31	C₄×C₄₃	M₃₂	1	1	yes	characteristic
32	#1367	—	43	1	no	maximal, Sylow
33	C₂×C₄₃	#334	1	1	yes	characteristic
34	C₂×C₄₃	C₄⋊C₁₆	1	1	yes	characteristic
35	C₂×C₄₃	#364	1	1	yes	characteristic
36	C₄⋊C₁₆	—	43	1	no	—
37	C₄⋊C₁₆	D₄₃	1	1	yes	characteristic
38	C₈²	—	43	1	no	—
39	C₄₃	#1367	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₁₆	—	2	1	no	—
41	C₂×C₁₆	—	86	1	no	—
42	C₄×C₈	—	43	1	no	—
43	C₄×C₈	—	43	1	no	—
44	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
45	C₂×C₈	—	43	1	no	—
46	C₂×C₈	—	43	1	no	—
47	C₂×C₈	—	86	1	no	—
48	C₂×C₈	Dic₈₆	1	1	yes	characteristic
49	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
50	C₄²	C₄×D₄₃	1	1	yes	characteristic
51	C₁₆	—	4	1	no	—
52	C₁₆	—	172	1	no	—
53	C₂×C₄	C₈×D₄₃	1	1	yes	characteristic
54	C₂×C₄	#10621872	1	1	yes	characteristic
55	C₂×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
56	C₈	—	2	1	no	—
57	C₈	—	43	2	no	—
58	C₈	—	86	2	no	—
59	C₈	—	86	1	no	—
60	C₈	#10621883	1	1	yes	characteristic
61	C₈	#10621884	1	1	yes	characteristic
62	C₂²	Dic₄₃⋊C₈	1	1	yes	characteristic
63	C₄	—	2	1	no	—
64	C₄	#13063256	1	1	yes	characteristic
65	C₄	#13063260	1	1	yes	characteristic
66	C₄	C₁₆×D₄₃	1	1	yes	characteristic
67	C₄	#13063264	1	1	yes	characteristic
68	C₂	#14582649	1	1	yes	characteristic
69	C₂	Dic₄₃⋊C₁₆	1	1	yes	characteristic
70	C₂	#14582719	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₄₃
commutator	C₄×C₄₃	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₄₃
Fitting	C₄₃×C₄⋊C₁₆	C₂
socle	C₂²×C₄₃	C₄⋊C₈
hypercenter	C₄⋊C₁₆	D₄₃
hypocenter	C₄₃	#1367
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
25. C₄₃⋊C₈	C₁₆	semidirect
39. C₄₃	#1367	semidirect