Subgroups — C₄₃⋊#1309 #19132508

Order 5504.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14582923	C₂	1	2	yes	maximal
2	C₄₃×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×#10621877	C₄	1	4	yes	—
4	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
5	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
6	C₂×M₁₆×C₄₃	C₄	1	2	yes	—
7	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
8	C₄⋊C₈×C₄₃	—	2	2	no	—
9	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
10	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
11	M₁₆×C₄₃	—	4	2	no	—
12	C₂×C₈×C₄₃	—	2	2	no	—
13	C₄²×C₄₃	D₄	1	1	yes	characteristic
14	C₄²×C₄₃	D₄	1	2	yes	—
15	C₄²×C₄₃	Q₈	1	1	yes	characteristic
16	#10621877	—	4	4	no	—
17	C₂×C₄₃⋊C₈	—	2	4	no	—
18	C₂³×C₄₃	C₄²	1	1	yes	characteristic
19	C₂×C₄×C₄₃	—	2	2	no	—
20	C₂×C₄×C₄₃	—	2	1	no	—
21	C₂×C₄×C₄₃	—	2	2	no	—
22	C₂×C₄×C₄₃	—	2	1	no	—
23	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
24	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
26	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
27	C₈×C₄₃	—	4	2	no	—
28	C₄₃⋊C₈	—	4	4	no	—
29	C₂²×C₄₃	—	2	2	no	—
30	C₂²×C₄₃	—	2	1	no	—
31	C₂²×C₄₃	#95	1	1	yes	characteristic
32	C₄×C₄₃	—	2	2	no	—
33	C₄×C₄₃	—	2	1	no	—
34	C₄×C₄₃	#100	1	2	yes	—
35	C₄×C₄₃	#100	1	1	yes	characteristic
36	C₄×C₄₃	#101	1	2	yes	—
37	C₄×C₄₃	#101	1	1	yes	characteristic
38	#1309	—	43	1	no	maximal, Sylow
39	C₂×C₄₃	—	4	1	no	—
40	C₂×C₄₃	#343	1	2	yes	—
41	C₂×C₄₃	#343	1	1	yes	characteristic
42	#423	—	43	2	no	—
43	#423	D₄₃	1	1	yes	characteristic
44	C₄₃	#1309	1	1	yes	characteristic, complemented, Sylow
45	C₂×M₁₆	—	43	4	no	—
46	C₂×M₁₆	Dic₄₃	1	2	yes	—
47	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
48	C₄⋊C₈	—	2	2	no	—
49	C₄⋊C₈	—	86	2	no	—
50	C₄⋊C₈	—	86	2	no	—
51	C₂²×C₄	C₄×D₄₃	1	2	yes	—
52	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
53	M₁₆	—	4	2	no	—
54	M₁₆	—	172	4	no	—
55	C₂×C₈	—	2	2	no	—
56	C₂×C₈	—	86	4	no	—
57	C₄²	Dic₈₆	1	1	yes	characteristic
58	C₄²	D₁₇₂	1	1	yes	characteristic
59	C₄²	C₂²⋊D₄₃	1	2	yes	—
60	C₂³	C₄×Dic₄₃	1	1	yes	characteristic
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	2	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	Dic₄₃⋊C₄	1	2	yes	—
66	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
67	C₂×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
68	C₂×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
69	C₈	—	4	2	no	—
70	C₈	—	172	4	no	—
71	C₂²	—	2	2	no	—
72	C₂²	—	2	1	no	—
73	C₂²	C₄₃⋊#95	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	2	1	no	—
76	C₄	#13063241	1	2	yes	—
77	C₄	#13063242	1	1	yes	characteristic
78	C₄	#13063243	1	2	yes	—
79	C₄	#13063244	1	1	yes	characteristic
80	C₂	—	4	1	no	—
81	C₂	#14582667	1	2	yes	—
82	C₂	#14582668	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄₃⋊#95
commutator	C₂³×C₄₃	C₄²
Frattini	C₂×C₄²	C₂×D₄₃
Fitting	C₄₃×#423	C₂
socle	C₂²×C₄₃	#95
hypercenter	#423	D₄₃
hypocenter	C₄₃	#1309
LCS	G ▷ C₂³×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
44. C₄₃	#1309	semidirect

Subgroups — C43⋊#1309 #19132508

Conjugacy classes of subgroups

Complements

Subgroups — C₄₃⋊#1309 #19132508