Subgroups — #30632895

Order 16096.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22548883	C₂	1	1	yes	maximal, characteristic
2	#22548873	C₂	1	2	yes	maximal, complemented
3	#22548870	C₂	1	2	yes	maximal, complemented
4	#22548867	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈×C₅₀₃	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₁₀₀₆	C₂²	1	1	yes	characteristic
7	D₂₀₁₂	C₂²	1	1	yes	characteristic
8	C₂²⋊D₅₀₃	—	2	1	no	—
9	C₄×D₅₀₃	—	2	1	no	—
10	C₅₀₃⋊C₈	C₂²	1	2	yes	—
11	Q₈×C₅₀₃	—	2	1	no	—
12	Q₈×C₅₀₃	C₂²	1	2	yes	—
13	C₂×C₄×C₅₀₃	—	2	1	no	—
14	C₂×C₄×C₅₀₃	C₂²	1	1	yes	characteristic
15	C₂²×C₅₀₃	D₄	1	1	yes	characteristic
16	C₂×D₅₀₃	—	2	1	no	—
17	C₄×C₅₀₃	—	2	2	no	—
18	C₄×C₅₀₃	D₄	1	1	yes	characteristic
19	C₄×C₅₀₃	C₂³	1	1	yes	characteristic
20	Dic₅₀₃	—	2	1	no	—
21	C₂×C₅₀₃	—	2	1	no	—
22	C₂×C₅₀₃	C₂×D₄	1	1	yes	characteristic
23	D₅₀₃	—	4	1	no	—
24	C₅₀₃	#137	1	1	yes	characteristic, complemented, Sylow
25	#137	—	503	1	no	maximal, Sylow
26	#41	—	503	1	no	—
27	C₂×Q₈	D₅₀₃	1	1	yes	characteristic, complemented
28	Q₁₆	—	503	2	no	—
29	SD₁₆	—	503	2	no	—
30	M₁₆	—	503	1	no	—
31	Q₈	—	2	1	no	—
32	Q₈	—	503	1	no	—
33	Q₈	C₂×D₅₀₃	1	2	yes	—
34	D₄	—	1006	1	no	—
35	D₄	—	503	1	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	1006	1	no	—
38	C₂×C₄	C₂×D₅₀₃	1	1	yes	characteristic
39	C₈	—	503	2	no	—
40	C₂²	—	1006	1	no	—
41	C₂²	C₂²⋊D₅₀₃	1	1	yes	characteristic
42	C₄	—	2	2	no	—
43	C₄	—	1006	1	no	—
44	C₄	C₂²⋊D₅₀₃	1	1	yes	characteristic
45	C₄	C₂²×D₅₀₃	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	2012	1	no	—
48	C₂	C₂×C₂²⋊D₅₀₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊D₅₀₃
commutator, cosocle	C₄×C₅₀₃	C₂³
Frattini	C₄	C₂²×D₅₀₃
Fitting	C₂×Q₈×C₅₀₃	C₂
socle	C₂×C₅₀₃	C₂×D₄
prime radical	#22548883	C₂
hypercenter	C₂×Q₈	D₅₀₃
hypocenter	C₅₀₃	#137
LCS	G ▷ C₄×C₅₀₃ ▷ C₂×C₅₀₃ ▷ C₅₀₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #22548873	C₂	semidirect
3. #22548870	C₂	semidirect
4. #22548867	C₂	semidirect
5. C₂×Q₈×C₅₀₃	C₂	semidirect
24. C₅₀₃	#137	semidirect
27. C₂×Q₈	D₅₀₃	semidirect

Maximal subgroups

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

subgroup	index
#22548883	2
#22548873	2
#22548870	2
#22548867	2
C₂×Q₈×C₅₀₃	2
#137	503