Subgroups — #14583016

Order 2752.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063332	C₂	1	2	yes	maximal, complemented
2	#13063261	C₂	1	1	yes	maximal, characteristic, complemented
3	#13063252	C₂	1	2	yes	maximal, complemented
4	C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#135×C₄₃	C₂	1	1	yes	maximal, characteristic
6	#41×C₄₃	C₂²	1	2	yes	—
7	Q₁₆×C₄₃	C₄	1	1	yes	characteristic, complemented
8	SD₁₆×C₄₃	C₄	1	2	yes	complemented
9	D₈×C₄₃	C₄	1	1	yes	characteristic, complemented
10	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₄×Dic₄₃	C₂²	1	1	yes	characteristic
12	#10621877	—	2	2	no	—
13	#10621877	C₂²	1	2	yes	—
14	C₂×C₄₃⋊C₈	—	2	2	no	—
15	C₂×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
16	Q₈×C₄₃	C₂×C₄	1	2	yes	—
17	D₄×C₄₃	—	2	2	no	—
18	D₄×C₄₃	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₄₃	—	2	2	no	—
20	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
21	C₂×Dic₄₃	—	2	1	no	—
22	C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
23	C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
24	C₄₃⋊C₈	—	2	2	no	—
25	C₄₃⋊C₈	D₄	1	1	yes	characteristic
26	C₄₃⋊C₈	D₄	1	1	yes	characteristic
27	C₂²×C₄₃	—	2	2	no	—
28	C₂²×C₄₃	#41	1	1	yes	characteristic
29	C₄×C₄₃	—	2	2	no	—
30	C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
32	Dic₄₃	—	2	2	no	—
33	C₂×C₄₃	—	2	1	no	—
34	C₂×C₄₃	—	4	2	no	—
35	C₂×C₄₃	C₄×D₄	1	1	yes	characteristic
36	#443	—	43	1	no	maximal, Sylow
37	C₄₃	#443	1	1	yes	characteristic, complemented, Sylow
38	#135	D₄₃	1	1	yes	characteristic
39	#131	—	43	2	no	—
40	#108	—	43	1	no	—
41	#104	—	43	2	no	—
42	C₄×C₈	—	43	1	no	—
43	#41	C₂×D₄₃	1	2	yes	—
44	Q₁₆	Dic₄₃	1	1	yes	characteristic, complemented
45	SD₁₆	Dic₄₃	1	2	yes	complemented
46	D₈	Dic₄₃	1	1	yes	characteristic, complemented
47	M₁₆	—	43	2	no	—
48	M₁₆	—	86	2	no	—
49	C₂×C₈	—	43	1	no	—
50	C₂×C₈	—	86	2	no	—
51	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
52	C₄²	—	43	1	no	—
53	Q₈	C₂×Dic₄₃	1	2	yes	—
54	D₄	—	2	2	no	—
55	D₄	C₂×Dic₄₃	1	2	yes	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	86	1	no	—
58	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
59	C₈	—	43	1	no	—
60	C₈	—	43	1	no	—
61	C₈	—	86	2	no	—
62	C₈	C₂×Dic₄₃	1	1	yes	characteristic
63	C₈	C₂×Dic₄₃	1	1	yes	characteristic
64	C₂²	—	2	2	no	—
65	C₂²	#10621900	1	1	yes	characteristic
66	C₄	—	2	2	no	—
67	C₄	—	86	2	no	—
68	C₄	D₄×D₄₃	1	1	yes	characteristic
69	C₄	C₂²×Dic₄₃	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	4	2	no	—
72	C₂	D₄×Dic₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₄₃
commutator	C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₃
Fitting, prime radical	#135×C₄₃	C₂
socle	C₂×C₄₃	C₄×D₄
cosocle	C₂×C₄×C₄₃	C₂³
hypercenter	#135	D₄₃
hypocenter	C₄₃	#443
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #135

Complements

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

N	H ≅ G/N	type
1. #13063332	C₂	semidirect
2. #13063261	C₂	semidirect
3. #13063252	C₂	semidirect
4. C₈×Dic₄₃	C₂	semidirect
7. Q₁₆×C₄₃	C₄	semidirect
8. SD₁₆×C₄₃	C₄	semidirect
9. D₈×C₄₃	C₄	semidirect
37. C₄₃	#443	semidirect
44. Q₁₆	Dic₄₃	semidirect
45. SD₁₆	Dic₄₃	semidirect
46. D₈	Dic₄₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#13063332	2
#13063261	2
#13063252	2
C₈×Dic₄₃	2
#135×C₄₃	2
#443	43