Subgroups — #97×D₅₀₃ #44566228

Order 32192.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₅₀₃	C₂	1	2	yes	maximal
2	C₄²×D₅₀₃	C₂	1	1	yes	maximal, characteristic
3	#30632775	C₂	1	1	yes	maximal, characteristic, complemented
4	#30632774	C₂	1	2	yes	maximal, complemented
5	#97×C₅₀₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₅₀₃	C₄	1	2	yes	—
7	C₂×C₄×D₅₀₃	C₂²	1	1	yes	characteristic
8	C₂×C₅₀₃⋊C₈	C₂²	1	2	yes	—
9	C₈×D₅₀₃	C₄	1	8	yes	complemented
10	C₄×Dic₅₀₃	C₄	1	2	yes	—
11	C₄×Dic₅₀₃	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₅₀₃	C₂²	1	2	yes	—
13	C₄²×C₅₀₃	C₂²	1	1	yes	characteristic
14	C₂²×D₅₀₃	C₂×C₄	1	1	yes	characteristic
15	C₂×Dic₅₀₃	C₂×C₄	1	2	yes	—
16	C₂×Dic₅₀₃	C₂×C₄	1	1	yes	characteristic
17	C₄×D₅₀₃	—	2	4	no	—
18	C₄×D₅₀₃	C₂×C₄	1	4	yes	—
19	C₅₀₃⋊C₈	C₂×C₄	1	4	yes	complemented
20	C₂×C₄×C₅₀₃	C₂×C₄	1	2	yes	—
21	C₂×C₄×C₅₀₃	C₂³	1	1	yes	characteristic
22	C₈×C₅₀₃	C₂×C₄	1	4	yes	complemented
23	C₂²×C₅₀₃	C₂²×C₄	1	1	yes	characteristic
24	C₂×D₅₀₃	C₄²	1	2	yes	—
25	C₂×D₅₀₃	M₁₆	1	4	yes	—
26	C₄×C₅₀₃	—	2	2	no	—
27	C₄×C₅₀₃	C₂²×C₄	1	2	yes	—
28	Dic₅₀₃	—	2	2	no	—
29	Dic₅₀₃	C₄²	1	2	yes	—
30	C₂×C₅₀₃	C₂×C₄²	1	1	yes	characteristic
31	C₂×C₅₀₃	C₂×M₁₆	1	2	yes	—
32	D₅₀₃	#97	1	4	yes	direct product factor
33	C₅₀₃	C₂×#97	1	1	yes	characteristic, complemented, Sylow
34	C₂×#97	—	503	1	no	maximal, Sylow
35	C₂²×C₈	—	503	2	no	—
36	C₂×C₄²	—	503	1	no	—
37	#97	—	503	2	no	—
38	#97	—	503	1	no	—
39	#97	D₅₀₃	1	1	yes	characteristic, direct product factor
40	C₂²×C₄	—	503	2	no	—
41	C₂²×C₄	—	503	1	no	—
42	C₂×C₈	—	503	2	no	—
43	C₂×C₈	—	503	8	no	—
44	C₂×C₈	C₂×D₅₀₃	1	2	yes	—
45	C₄²	—	503	2	no	—
46	C₄²	—	503	1	no	—
47	C₄²	C₂×D₅₀₃	1	1	yes	characteristic
48	C₂³	—	503	1	no	—
49	C₂×C₄	—	1006	4	no	—
50	C₂×C₄	—	503	2	no	—
51	C₂×C₄	—	503	1	no	—
52	C₂×C₄	—	503	4	no	—
53	C₂×C₄	C₄×D₅₀₃	1	2	yes	—
54	C₂×C₄	C₂²×D₅₀₃	1	1	yes	characteristic
55	C₈	—	503	4	no	—
56	C₈	C₄×D₅₀₃	1	4	yes	complemented
57	C₂²	—	503	2	no	—
58	C₂²	—	503	4	no	—
59	C₂²	C₂×C₄×D₅₀₃	1	1	yes	characteristic
60	C₄	—	2	2	no	—
61	C₄	—	1006	2	no	—
62	C₄	—	503	2	no	—
63	C₄	C₂×C₄×D₅₀₃	1	2	yes	—
64	C₂	—	503	4	no	—
65	C₂	C₄²×D₅₀₃	1	1	yes	characteristic
66	C₂	M₁₆×D₅₀₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₅₀₃
commutator	C₂×C₅₀₃	C₂×C₄²
Fitting	#97×C₅₀₃	C₂
socle	C₂²×C₅₀₃	C₂²×C₄
prime radical	C₂²×D₅₀₃	C₂×C₄
cosocle	C₂×C₄×C₅₀₃	C₂³
hypercenter	#97	D₅₀₃
hypocenter	C₅₀₃	C₂×#97
LCS	G ▷ C₂×C₅₀₃ ▷ C₅₀₃
UCS	C₁ ◁ C₂×C₄ ◁ #97

Complements

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

N	H ≅ G/N	type
3. #30632775	C₂	semidirect
4. #30632774	C₂	semidirect
5. #97×C₅₀₃	C₂	semidirect
9. C₈×D₅₀₃	C₄	semidirect
19. C₅₀₃⋊C₈	C₂×C₄	semidirect
22. C₈×C₅₀₃	C₂×C₄	semidirect
32. D₅₀₃	#97	direct (N × H)
33. C₅₀₃	C₂×#97	semidirect
39. #97	D₅₀₃	direct (N × H)
56. C₈	C₄×D₅₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₅₀₃	2
C₄²×D₅₀₃	2
#30632775	2
#30632774	2
#97×C₅₀₃	2
C₂×#97	503

Subgroups — #97×D503 #44566228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #97×D₅₀₃ #44566228