Subgroups — #19132777

Order 5504.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₃₄₄	C₂	1	1	yes	maximal, characteristic
2	#14582725	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₇₂	—	2	1	no	—
5	Dic₃₄₄	—	2	1	no	—
6	Dic₃₄₄	C₄	1	2	yes	complemented
7	#13063259	—	2	1	no	—
8	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
9	C₃₂×C₄₃	—	2	1	no	—
10	C₂×Dic₈₆	—	4	1	no	—
11	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
12	C₄⋊Dic₄₃	—	4	1	no	—
13	Dic₁₇₂	—	2	2	no	—
14	Dic₁₇₂	—	4	1	no	—
15	C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₄₃	D₄	1	1	yes	characteristic
17	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
18	C₂×Dic₄₃	—	8	1	no	—
19	C₂×Dic₄₃	—	8	1	no	—
20	Dic₈₆	—	4	2	no	—
21	Dic₈₆	—	8	1	no	—
22	C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₄₃	SD₁₆	1	1	yes	characteristic
24	C₂²×C₄₃	D₁₆	1	1	yes	characteristic
25	C₄×C₄₃	#102	1	1	yes	characteristic
26	C₄×C₄₃	SD₃₂	1	1	yes	characteristic
27	Dic₄₃	—	8	2	no	—
28	Dic₄₃	—	16	1	no	—
29	#1416	—	43	1	no	maximal, Sylow
30	C₂×C₄₃	#357	1	1	yes	characteristic
31	C₂×C₄₃	SD₆₄	1	1	yes	characteristic
32	C₂×C₄₃	Q₆₄	1	1	yes	characteristic
33	C₂×Q₃₂	—	43	1	no	—
34	C₂×C₃₂	D₄₃	1	1	yes	characteristic
35	#366	—	43	1	no	—
36	C₄₃	#1416	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₁₆	—	86	1	no	—
38	Q₃₂	—	43	2	no	—
39	Q₃₂	—	86	1	no	—
40	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
41	#107	—	86	1	no	—
42	C₃₂	—	2	1	no	—
43	C₂×Q₈	—	172	1	no	—
44	Q₁₆	—	86	2	no	—
45	Q₁₆	—	172	1	no	—
46	C₂×C₈	D₁₇₂	1	1	yes	characteristic
47	C₄⋊C₄	—	172	1	no	—
48	C₁₆	C₄×D₄₃	1	1	yes	characteristic
49	C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
50	Q₈	—	344	1	no	—
51	Q₈	—	172	2	no	—
52	C₂×C₄	—	344	1	no	—
53	C₂×C₄	—	344	1	no	—
54	C₂×C₄	D₃₄₄	1	1	yes	characteristic
55	C₈	#10621873	1	1	yes	characteristic
56	C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
57	C₂²	D₆₈₈	1	1	yes	characteristic
58	C₄	—	344	2	no	—
59	C₄	—	688	1	no	—
60	C₄	#13063247	1	1	yes	characteristic
61	C₄	#13063270	1	1	yes	characteristic
62	C₂	#14582701	1	1	yes	characteristic
63	C₂	#14582738	1	1	yes	characteristic
64	C₂	Dic₆₈₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₆₈₈
commutator	C₁₆×C₄₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₄₃
Fitting	C₂×C₃₂×C₄₃	C₂
socle	C₂²×C₄₃	D₁₆
hypercenter	C₂×C₃₂	D₄₃
hypocenter	C₄₃	#1416
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
6. Dic₃₄₄	C₄	semidirect
36. C₄₃	#1416	semidirect