Subgroups — #19132547

Order 5504.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14582927	C₂	1	1	yes	maximal, characteristic
2	#14582681	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#349	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄₃⋊C₈	C₄	1	1	yes	characteristic
5	#13063284	C₄	1	1	yes	characteristic
6	#13063265	—	2	1	no	—
7	Dic₄₃⋊C₈	—	2	1	no	—
8	Dic₄₃⋊C₈	—	2	1	no	—
9	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
10	M₃₂×C₄₃	—	2	1	no	—
11	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
12	M₁₆×C₄₃	—	4	1	no	—
13	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
14	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
15	C₂²⋊Dic₄₃	C₈	1	2	yes	—
16	C₄⋊Dic₄₃	—	2	1	no	—
17	C₄×Dic₄₃	—	2	1	no	—
18	C₂×C₄₃⋊C₈	—	2	1	no	—
19	C₂×C₄₃⋊C₈	—	4	1	no	—
20	C₁₆×C₄₃	—	4	1	no	—
21	C₄₃⋊C₁₆	—	4	1	no	—
22	C₂³×C₄₃	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₄₃	—	2	1	no	—
24	C₂×C₄×C₄₃	—	2	1	no	—
25	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₄₃	M₁₆	1	1	yes	characteristic
27	C₂×Dic₄₃	—	2	2	no	—
28	C₈×C₄₃	—	2	1	no	—
29	C₈×C₄₃	—	2	1	no	—
30	C₄₃⋊C₈	—	4	1	no	—
31	C₂²×C₄₃	—	2	1	no	—
32	C₂²×C₄₃	—	4	1	no	—
33	C₂²×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
34	C₄×C₄₃	—	2	1	no	—
35	C₄×C₄₃	#99	1	1	yes	characteristic
36	C₄×C₄₃	#101	1	1	yes	characteristic
37	Dic₄₃	—	4	2	no	—
38	#1328	—	43	1	no	maximal, Sylow
39	C₂×C₄₃	—	2	1	no	—
40	C₂×C₄₃	—	4	1	no	—
41	C₂×C₄₃	#324	1	1	yes	characteristic
42	#424	—	43	1	no	—
43	#349	—	43	1	no	—
44	#349	D₄₃	1	1	yes	characteristic
45	C₄₃	#1328	1	1	yes	characteristic, complemented, Sylow
46	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
47	C₂²×C₈	—	43	1	no	—
48	#117	—	43	1	no	—
49	M₃₂	—	2	1	no	—
50	M₃₂	—	86	1	no	—
51	C₄⋊C₈	—	86	1	no	—
52	C₄⋊C₈	—	86	1	no	—
53	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
54	M₁₆	—	4	1	no	—
55	C₂×C₈	—	86	1	no	—
56	C₂×C₈	—	172	1	no	—
57	C₂×C₈	D₁₇₂	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
59	C₄⋊C₄	—	86	1	no	—
60	C₂²⋊C₄	—	43	2	no	—
61	C₄²	—	86	1	no	—
62	C₁₆	—	4	1	no	—
63	C₁₆	—	172	1	no	—
64	C₂³	C₈×D₄₃	1	1	yes	characteristic
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	86	2	no	—
68	C₂×C₄	#10621872	1	1	yes	characteristic
69	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
70	C₈	—	2	1	no	—
71	C₈	—	2	1	no	—
72	C₈	—	172	1	no	—
73	C₂²	—	2	1	no	—
74	C₂²	—	4	1	no	—
75	C₂²	(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	172	2	no	—
78	C₄	#13063239	1	1	yes	characteristic
79	C₄	#13063243	1	1	yes	characteristic
80	C₂	—	2	1	no	—
81	C₂	—	4	1	no	—
82	C₂	#14582624	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#13063239
commutator	C₂³×C₄₃	C₂×C₈
Frattini	C₂×M₁₆	C₂×D₄₃
Fitting	C₄₃×#349	C₂
socle	C₂×C₄₃	#324
hypercenter	#349	D₄₃
hypocenter	C₄₃	#1328
LCS	G ▷ C₂³×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

Complements

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

N	H ≅ G/N	type
45. C₄₃	#1328	semidirect