Subgroups — #19132736

Order 5504.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583315	C₂	1	1	yes	maximal, characteristic
2	#14582733	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#13063331	C₄	1	1	yes	characteristic
5	#13063265	C₄	1	1	yes	characteristic
6	#13063264	—	2	1	no	—
7	C₁₆×D₄₃	—	2	1	no	—
8	C₄₃⋊C₃₂	—	2	1	no	—
9	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
10	C₃₂×C₄₃	—	2	1	no	—
11	#10621898	C₈	1	1	yes	characteristic
12	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
13	#10621877	C₈	1	1	yes	characteristic
14	#10621872	—	2	1	no	—
15	C₈×D₄₃	—	2	1	no	—
16	C₁₆×C₄₃	D₄	1	1	yes	characteristic
17	C₁₆×C₄₃	D₄	1	1	yes	characteristic
18	C₄₃⋊C₁₆	—	2	1	no	—
19	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
20	C₂²⋊D₄₃	—	2	1	no	—
21	D₁₇₂	C₁₆	1	1	yes	characteristic
22	C₄×D₄₃	—	2	1	no	—
23	Dic₈₆	C₁₆	1	1	yes	characteristic
24	C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₄₃	M₁₆	1	1	yes	characteristic
26	C₄₃⋊C₈	—	2	1	no	—
27	C₂²×C₄₃	M₃₂	1	1	yes	characteristic
28	C₂×D₄₃	—	2	1	no	—
29	C₄×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
30	C₄×C₄₃	C₂×C₁₆	1	1	yes	characteristic
31	Dic₄₃	—	2	1	no	—
32	#1401	—	43	1	no	maximal, Sylow
33	C₂×C₄₃	—	2	1	no	—
34	C₂×C₄₃	C₂²⋊C₁₆	1	1	yes	characteristic
35	D₄₃	—	4	1	no	—
36	#504	—	43	1	no	—
37	M₆₄	—	43	1	no	—
38	C₂×C₃₂	D₄₃	1	1	yes	characteristic, complemented
39	C₄₃	#1401	1	1	yes	characteristic, complemented, Sylow
40	#131	—	43	1	no	—
41	M₃₂	—	43	1	no	—
42	M₃₂	—	86	1	no	—
43	C₂×C₁₆	—	86	1	no	—
44	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
45	C₃₂	—	2	1	no	—
46	C₃₂	—	86	1	no	—
47	#41	—	43	1	no	—
48	M₁₆	—	43	1	no	—
49	M₁₆	—	86	1	no	—
50	C₂×C₈	—	86	1	no	—
51	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
52	C₁₆	—	86	1	no	—
53	C₁₆	D₁₇₂	1	1	yes	characteristic
54	C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
55	Q₈	—	43	1	no	—
56	D₄	—	43	1	no	—
57	D₄	—	86	1	no	—
58	C₂×C₄	—	86	1	no	—
59	C₂×C₄	C₈×D₄₃	1	1	yes	characteristic
60	C₈	—	86	1	no	—
61	C₈	#10621872	1	1	yes	characteristic
62	C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
63	C₂²	—	86	1	no	—
64	C₂²	#13063264	1	1	yes	characteristic
65	C₄	—	86	1	no	—
66	C₄	(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
67	C₄	C₁₆×D₄₃	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	172	1	no	—
70	C₂	(C₂×D₄₃)⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	D₁₇₂
commutator	C₄×C₄₃	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₄₃
Fitting	C₂×C₃₂×C₄₃	C₂
socle	C₂×C₄₃	C₂²⋊C₁₆
hypercenter	C₂×C₃₂	D₄₃
hypocenter	C₄₃	#1401
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #14582733	C₂	semidirect
3. C₂×C₃₂×C₄₃	C₂	semidirect
38. C₂×C₃₂	D₄₃	semidirect
39. C₄₃	#1401	semidirect