Subgroups — #44566003

Order 32192.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅₀₃⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅₀₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×C₅₀₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅₀₃⋊C₈	C₄	1	2	yes	—
5	C₂×C₅₀₃⋊C₈	C₄	1	2	yes	—
6	C₂×C₈×C₅₀₃	C₄	1	2	yes	—
7	C₄²×C₅₀₃	C₂²	1	1	yes	characteristic
8	C₅₀₃⋊C₈	—	2	2	no	—
9	C₅₀₃⋊C₈	C₈	1	4	yes	complemented
10	C₂×C₄×C₅₀₃	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₅₀₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₅₀₃	C₂×C₄	1	1	yes	characteristic
13	C₈×C₅₀₃	—	2	2	no	—
14	C₂²×C₅₀₃	C₄²	1	1	yes	characteristic
15	C₄×C₅₀₃	C₂×C₈	1	2	yes	—
16	C₄×C₅₀₃	M₁₆	1	2	yes	—
17	C₄×C₅₀₃	M₁₆	1	2	yes	—
18	C₂×C₅₀₃	C₄×C₈	1	1	yes	characteristic
19	C₂×C₅₀₃	#97	1	1	yes	characteristic
20	C₂×C₅₀₃	#97	1	1	yes	characteristic
21	C₅₀₃	#322	1	1	yes	characteristic, complemented, Sylow
22	#322	—	503	1	no	maximal, Sylow
23	C₄×C₈	—	503	1	no	—
24	C₄×C₈	—	503	1	no	—
25	C₄×C₈	D₅₀₃	1	1	yes	characteristic
26	C₂×C₈	—	503	2	no	—
27	C₂×C₈	—	503	2	no	—
28	C₂×C₈	Dic₅₀₃	1	2	yes	—
29	C₄²	C₂×D₅₀₃	1	1	yes	characteristic
30	C₂×C₄	C₄×D₅₀₃	1	1	yes	characteristic
31	C₂×C₄	C₄×D₅₀₃	1	1	yes	characteristic
32	C₂×C₄	C₂×Dic₅₀₃	1	1	yes	characteristic
33	C₈	—	2	2	no	—
34	C₈	—	1006	2	no	—
35	C₈	—	503	4	no	—
36	C₂²	C₄×Dic₅₀₃	1	1	yes	characteristic
37	C₄	C₈×D₅₀₃	1	2	yes	—
38	C₄	#22548866	1	2	yes	—
39	C₄	#22548867	1	2	yes	—
40	C₂	C₈×Dic₅₀₃	1	1	yes	characteristic
41	C₂	#30632774	1	1	yes	characteristic
42	C₂	#30632775	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂×D₅₀₃
commutator	C₂×C₅₀₃	C₄×C₈
Fitting	C₄×C₈×C₅₀₃	C₂
socle, prime radical	C₂²×C₅₀₃	C₄²
cosocle	C₄²×C₅₀₃	C₂²
hypercenter	C₄×C₈	D₅₀₃
hypocenter	C₅₀₃	#322
LCS	G ▷ C₂×C₅₀₃ ▷ C₅₀₃
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
9. C₅₀₃⋊C₈	C₈	semidirect
21. C₅₀₃	#322	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅₀₃⋊C₈	2
C₄×C₈×C₅₀₃	2
#322	503