Subgroups — #19132636

Order 5504.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14582720	C₂	1	2	yes	maximal, complemented
2	C₄₃×#492	C₂	1	1	yes	maximal, characteristic
3	#13063265	—	2	2	no	—
4	C₂×SD₁₆×C₄₃	—	2	2	no	—
5	C₄⋊Q₈×C₄₃	C₄	1	1	yes	characteristic
6	#127×C₄₃	C₄	1	1	yes	characteristic
7	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
8	C₂×Q₈×C₄₃	—	2	1	no	—
9	C₂×D₄×C₄₃	—	2	1	no	—
10	C₂×D₄×C₄₃	—	4	1	no	—
11	SD₁₆×C₄₃	—	4	2	no	—
12	SD₁₆×C₄₃	—	4	2	no	—
13	C₂×C₈×C₄₃	D₄	1	2	yes	—
14	C₄⋊C₄×C₄₃	—	4	1	no	—
15	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₄₃⋊C₁₆	—	4	2	no	—
17	C₂³×C₄₃	—	4	1	no	—
18	Q₈×C₄₃	—	4	2	no	—
19	D₄×C₄₃	—	4	2	no	—
20	D₄×C₄₃	—	8	2	no	—
21	C₂×C₄×C₄₃	—	2	1	no	—
22	C₂×C₄×C₄₃	—	4	1	no	—
23	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
24	C₈×C₄₃	D₈	1	2	yes	—
25	C₈×C₄₃	SD₁₆	1	2	yes	—
26	C₂²×C₄₃	—	8	2	no	—
27	C₂²×C₄₃	—	8	1	no	—
28	C₂²×C₄₃	#100	1	1	yes	characteristic
29	C₄×C₄₃	—	2	2	no	—
30	C₄×C₄₃	—	8	1	no	—
31	C₄×C₄₃	#102	1	2	yes	—
32	#1359	—	43	1	no	maximal, Sylow
33	C₂×C₄₃	—	2	1	no	—
34	C₂×C₄₃	—	16	1	no	—
35	C₂×C₄₃	#331	1	1	yes	characteristic
36	#492	D₄₃	1	1	yes	characteristic
37	#364	—	43	2	no	—
38	C₄₃	#1359	1	1	yes	characteristic, complemented, Sylow
39	C₂×SD₁₆	—	2	2	no	—
40	C₄⋊Q₈	Dic₄₃	1	1	yes	characteristic
41	#127	Dic₄₃	1	1	yes	characteristic
42	M₃₂	—	86	2	no	—
43	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
44	C₂×Q₈	—	2	1	no	—
45	C₂×D₄	—	2	1	no	—
46	C₂×D₄	—	4	1	no	—
47	SD₁₆	—	4	2	no	—
48	SD₁₆	—	4	2	no	—
49	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
50	C₄⋊C₄	—	4	1	no	—
51	C₄²	C₂×Dic₄₃	1	1	yes	characteristic
52	C₁₆	—	172	2	no	—
53	C₂³	—	4	1	no	—
54	Q₈	—	4	2	no	—
55	D₄	—	4	2	no	—
56	D₄	—	8	2	no	—
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	4	1	no	—
59	C₂×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
60	C₈	#10621882	1	2	yes	—
61	C₈	#10621883	1	2	yes	—
62	C₂²	—	8	2	no	—
63	C₂²	—	8	1	no	—
64	C₂²	#13063242	1	1	yes	characteristic
65	C₄	—	2	2	no	—
66	C₄	—	8	1	no	—
67	C₄	#13063246	1	2	yes	—
68	C₂	—	2	1	no	—
69	C₂	—	16	1	no	—
70	C₂	#14582643	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14582643
commutator	C₄²×C₄₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₄₃
Fitting	C₄₃×#492	C₂
socle	C₂×C₄₃	#331
hypercenter	#492	D₄₃
hypocenter	C₄₃	#1359
LCS	G ▷ C₄²×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #492

Complements

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

N	H ≅ G/N	type
1. #14582720	C₂	semidirect
38. C₄₃	#1359	semidirect