Subgroups — #334×C₅₀₃ #44565747

Order 32192.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊C₈×C₅₀₃	C₂	1	2	yes	maximal
2	C₄×C₈×C₅₀₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₅₀₃	—	2	2	no	—
4	C₂×C₈×C₅₀₃	C₄	1	1	yes	characteristic
5	C₂×C₈×C₅₀₃	C₄	1	1	yes	characteristic
6	C₄²×C₅₀₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₅₀₃	C₂×C₄	1	1	yes	characteristic
8	C₂×C₄×C₅₀₃	D₄	1	1	yes	characteristic
9	C₂×C₄×C₅₀₃	Q₈	1	1	yes	characteristic
10	C₈×C₅₀₃	—	2	1	no	—
11	C₈×C₅₀₃	—	4	2	no	—
12	C₈×C₅₀₃	C₈	1	2	yes	complemented
13	C₂²×C₅₀₃	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₅₀₃	—	2	1	no	—
15	C₄×C₅₀₃	C₂×C₈	1	1	yes	characteristic
16	C₄×C₅₀₃	M₁₆	1	1	yes	characteristic
17	C₄×C₅₀₃	SD₁₆	1	2	yes	—
18	C₂×C₅₀₃	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₅₀₃	#106	1	1	yes	characteristic
20	C₂×C₅₀₃	#108	1	1	yes	characteristic
21	C₅₀₃	#334	1	1	yes	characteristic, direct product factor, Sylow
22	#334	C₅₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₄⋊C₈	C₂×C₅₀₃	1	2	yes	—
24	C₄×C₈	C₂×C₅₀₃	1	1	yes	characteristic
25	C₂×C₈	—	2	2	no	—
26	C₂×C₈	C₄×C₅₀₃	1	1	yes	characteristic
27	C₂×C₈	C₄×C₅₀₃	1	1	yes	characteristic
28	C₄²	C₂²×C₅₀₃	1	1	yes	characteristic
29	C₂×C₄	C₂×C₄×C₅₀₃	1	1	yes	characteristic
30	C₂×C₄	D₄×C₅₀₃	1	1	yes	characteristic
31	C₂×C₄	Q₈×C₅₀₃	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	—	4	2	no	—
34	C₈	C₈×C₅₀₃	1	2	yes	complemented
35	C₂²	C₄⋊C₄×C₅₀₃	1	1	yes	characteristic
36	C₄	—	2	1	no	—
37	C₄	C₂×C₈×C₅₀₃	1	1	yes	characteristic
38	C₄	M₁₆×C₅₀₃	1	1	yes	characteristic
39	C₄	SD₁₆×C₅₀₃	1	2	yes	—
40	C₂	C₄⋊C₈×C₅₀₃	1	1	yes	characteristic
41	C₂	#106×C₅₀₃	1	1	yes	characteristic
42	C₂	#108×C₅₀₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅₀₃	D₄
commutator	C₄	C₂×C₈×C₅₀₃
Frattini, cosocle	C₄²	C₂²×C₅₀₃
socle, prime radical	C₂²×C₅₀₃	C₄⋊C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₀₃ ◁ C₄²×C₅₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
12. C₈×C₅₀₃	C₈	semidirect
21. C₅₀₃	#334	direct (N × H)
22. #334	C₅₀₃	direct (N × H)
34. C₈	C₈×C₅₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊C₈×C₅₀₃	2
C₄×C₈×C₅₀₃	2
#334	503

Subgroups — #334×C503 #44565747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #334×C₅₀₃ #44565747