Subgroups — #14583089

Order 2752.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063306	C₂	1	3	yes	maximal, complemented
2	#13063240	C₂	1	3	yes	maximal, complemented
3	H(5,𝔽₂)×C₄₃	C₂	1	1	yes	maximal, characteristic
4	#41×C₄₃	—	2	3	no	—
5	C₂×D₄×C₄₃	—	2	3	no	—
6	C₂×D₄×C₄₃	C₂²	1	3	yes	—
7	C₂²×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
8	C₂²⋊Dic₄₃	—	2	3	no	—
9	C₂²⋊Dic₄₃	C₂²	1	3	yes	complemented
10	Dic₄₃⋊C₄	—	2	3	no	—
11	C₂³×C₄₃	—	2	1	no	—
12	C₂³×C₄₃	D₄	1	3	yes	—
13	C₂³×C₄₃	C₂³	1	1	yes	characteristic
14	Q₈×C₄₃	—	2	1	no	—
15	D₄×C₄₃	—	2	3	no	—
16	D₄×C₄₃	—	2	6	no	—
17	C₂×C₄×C₄₃	—	2	3	no	—
18	C₂×C₄×C₄₃	D₄	1	3	yes	—
19	C₂×Dic₄₃	—	2	3	no	—
20	C₂×Dic₄₃	—	2	3	no	—
21	C₂²×C₄₃	—	2	3	no	—
22	C₂²×C₄₃	—	4	1	no	—
23	C₂²×C₄₃	—	4	3	no	—
24	C₂²×C₄₃	—	8	1	no	—
25	C₂²×C₄₃	C₂×D₄	1	3	yes	—
26	C₄×C₄₃	—	2	3	no	—
27	Dic₄₃	—	4	3	no	—
28	Dic₄₃	—	4	1	no	—
29	C₂×C₄₃	—	2	3	no	—
30	C₂×C₄₃	—	4	3	no	—
31	C₂×C₄₃	#120	1	1	yes	characteristic
32	#458	—	43	1	no	maximal, Sylow
33	C₄₃	#458	1	1	yes	characteristic, complemented, Sylow
34	H(5,𝔽₂)	D₄₃	1	1	yes	characteristic
35	#123	—	43	3	no	—
36	#99	—	43	3	no	—
37	#41	—	2	3	no	—
38	C₂×D₄	—	2	3	no	—
39	C₂×D₄	C₂×D₄₃	1	3	yes	—
40	C₂²×C₄	—	43	1	no	—
41	C₄⋊C₄	—	86	3	no	—
42	C₂²⋊C₄	—	43	3	no	—
43	C₂²⋊C₄	—	86	3	no	—
44	C₂³	—	2	1	no	—
45	C₂³	C₂²⋊D₄₃	1	3	yes	—
46	C₂³	C₂²×D₄₃	1	1	yes	characteristic
47	Q₈	—	2	1	no	—
48	D₄	—	2	3	no	—
49	D₄	—	2	6	no	—
50	C₂×C₄	—	2	3	no	—
51	C₂×C₄	—	86	3	no	—
52	C₂×C₄	—	86	3	no	—
53	C₂×C₄	C₂²⋊D₄₃	1	3	yes	—
54	C₂²	—	2	3	no	—
55	C₂²	—	4	1	no	—
56	C₂²	—	4	3	no	—
57	C₂²	—	8	1	no	—
58	C₂²	C₂×C₂²⋊D₄₃	1	3	yes	—
59	C₄	—	2	3	no	—
60	C₄	—	172	3	no	—
61	C₄	—	172	1	no	—
62	C₂	—	2	3	no	—
63	C₂	—	4	3	no	—
64	C₂	#13063294	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13063294
commutator, cosocle	C₂³×C₄₃	C₂³
Frattini	C₂³	C₂²×D₄₃
Fitting, prime radical	H(5,𝔽₂)×C₄₃	C₂
socle	C₂×C₄₃	#120
hypercenter	H(5,𝔽₂)	D₄₃
hypocenter	C₄₃	#458
LCS	G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ H(5,𝔽₂)

Complements

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

N	H ≅ G/N	type
1. #13063306	C₂	semidirect
2. #13063240	C₂	semidirect
7. C₂²×Dic₄₃	C₂²	semidirect
9. C₂²⋊Dic₄₃	C₂²	semidirect
33. C₄₃	#458	semidirect

Maximal subgroups

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

subgroup	index
#13063306	2
#13063240	2
H(5,𝔽₂)×C₄₃	2
#458	43