Subgroups — #14582946

Order 2752.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10621872	C₂	1	1	yes	maximal, characteristic
2	M₁₆×D₄₃	C₂	1	2	yes	maximal
3	#13063261	C₂	1	1	yes	maximal, characteristic, complemented
4	#13063260	C₂	1	2	yes	maximal, complemented
5	#108×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₄₃	C₂²	1	1	yes	characteristic
7	M₁₆×C₄₃	C₂²	1	2	yes	—
8	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
9	#10621877	C₂²	1	2	yes	—
10	C₂×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
11	#10621872	—	2	2	no	—
12	#10621872	C₄	1	4	yes	—
13	C₈×D₄₃	—	2	2	no	—
14	C₂²×D₄₃	Q₈	1	1	yes	characteristic
15	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
16	C₂×Dic₄₃	Q₈	1	1	yes	characteristic
17	C₄×D₄₃	C₂×C₄	1	2	yes	—
18	C₄×D₄₃	D₄	1	2	yes	—
19	C₈×C₄₃	—	2	2	no	—
20	C₈×C₄₃	C₂×C₄	1	2	yes	—
21	C₄₃⋊C₈	—	2	2	no	—
22	C₄₃⋊C₈	C₂×C₄	1	2	yes	—
23	C₂²×C₄₃	C₂×Q₈	1	1	yes	characteristic
24	C₂×D₄₃	—	4	1	no	—
25	C₂×D₄₃	C₄⋊C₄	1	2	yes	—
26	C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
28	Dic₄₃	C₄⋊C₄	1	2	yes	—
29	C₂×C₄₃	—	2	1	no	—
30	C₂×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
31	D₄₃	—	2	2	no	—
32	#430	—	43	1	no	maximal, Sylow
33	C₄₃	#430	1	1	yes	characteristic, complemented, Sylow
34	C₂×M₁₆	—	43	1	no	—
35	C₂×M₁₆	—	43	2	no	—
36	#108	—	43	2	no	—
37	#108	—	43	1	no	—
38	#108	D₄₃	1	1	yes	characteristic, complemented
39	C₂²×C₄	—	43	1	no	—
40	M₁₆	—	43	4	no	—
41	M₁₆	—	43	2	no	—
42	M₁₆	—	86	2	no	—
43	M₁₆	C₂×D₄₃	1	2	yes	—
44	C₂×C₈	—	43	1	no	—
45	C₂×C₈	—	86	2	no	—
46	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
47	C₂³	—	43	1	no	—
48	C₂×C₄	—	43	1	no	—
49	C₂×C₄	—	43	2	no	—
50	C₂×C₄	—	43	2	no	—
51	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
52	C₈	—	2	2	no	—
53	C₈	—	43	2	no	—
54	C₈	—	86	2	no	—
55	C₈	C₄×D₄₃	1	2	yes	—
56	C₂²	—	43	2	no	—
57	C₂²	—	172	1	no	—
58	C₂²	Q₈×D₄₃	1	1	yes	characteristic
59	C₄	—	43	2	no	—
60	C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
61	C₄	D₄×D₄₃	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	86	2	no	—
64	C₂	C₄⋊C₄×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₄₃
commutator	C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	#108×C₄₃	C₂
socle	C₂×C₄₃	C₂×C₄⋊C₄
prime radical	C₂²×D₄₃	Q₈
cosocle	C₂×C₄×C₄₃	C₂³
hypercenter	#108	D₄₃
hypocenter	C₄₃	#430
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
3. #13063261	C₂	semidirect
4. #13063260	C₂	semidirect
5. #108×C₄₃	C₂	semidirect
33. C₄₃	#430	semidirect
38. #108	D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10621872	2
M₁₆×D₄₃	2
#13063261	2
#13063260	2
#108×C₄₃	2
#430	43