Subgroups — #344×C₅₀₃ #44565757

Order 32192.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×C₅₀₃	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×C₅₀₃	C₂	1	1	yes	maximal, characteristic
3	#117×C₅₀₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₅₀₃	C₂²	1	1	yes	characteristic
5	M₁₆×C₅₀₃	—	2	1	no	—
6	M₁₆×C₅₀₃	—	2	1	no	—
7	M₁₆×C₅₀₃	—	2	1	no	—
8	M₁₆×C₅₀₃	C₄	1	2	yes	complemented
9	C₂×C₈×C₅₀₃	—	2	1	no	—
10	C₂×C₈×C₅₀₃	C₄	1	2	yes	complemented
11	C₄⋊C₄×C₅₀₃	—	2	1	no	—
12	C₂²⋊C₄×C₅₀₃	C₄	1	2	yes	—
13	C₄²×C₅₀₃	—	2	1	no	—
14	C₂³×C₅₀₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₅₀₃	—	2	2	no	—
16	C₂×C₄×C₅₀₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₅₀₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₅₀₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₅₀₃	D₄	1	1	yes	characteristic
20	C₂×C₄×C₅₀₃	D₄	1	1	yes	characteristic
21	C₂×C₄×C₅₀₃	Q₈	1	1	yes	characteristic
22	C₈×C₅₀₃	—	2	2	no	—
23	C₈×C₅₀₃	—	2	2	no	—
24	C₂²×C₅₀₃	—	4	1	no	—
25	C₂²×C₅₀₃	C₄²	1	1	yes	characteristic
26	C₂²×C₅₀₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×C₅₀₃	C₄⋊C₄	1	1	yes	characteristic
28	C₄×C₅₀₃	—	4	2	no	—
29	C₄×C₅₀₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₄×C₅₀₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₄×C₅₀₃	C₄⋊C₄	1	1	yes	characteristic
32	C₄×C₅₀₃	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₅₀₃	—	2	1	no	—
34	C₂×C₅₀₃	—	2	1	no	—
35	C₂×C₅₀₃	—	2	1	no	—
36	C₂×C₅₀₃	#95	1	1	yes	characteristic
37	C₅₀₃	#344	1	1	yes	characteristic, direct product factor, Sylow
38	#344	C₅₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂×M₁₆	C₂×C₅₀₃	1	1	yes	characteristic
40	C₂×M₁₆	C₂×C₅₀₃	1	1	yes	characteristic
41	#117	C₂×C₅₀₃	1	1	yes	characteristic
42	C₂²×C₄	C₂²×C₅₀₃	1	1	yes	characteristic
43	M₁₆	—	2	1	no	—
44	M₁₆	—	2	1	no	—
45	M₁₆	—	2	1	no	—
46	M₁₆	C₄×C₅₀₃	1	2	yes	complemented
47	C₂×C₈	—	2	1	no	—
48	C₂×C₈	C₄×C₅₀₃	1	2	yes	complemented
49	C₄⋊C₄	—	2	1	no	—
50	C₂²⋊C₄	C₄×C₅₀₃	1	2	yes	—
51	C₄²	—	2	1	no	—
52	C₂³	C₂×C₄×C₅₀₃	1	1	yes	characteristic
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	C₂×C₄×C₅₀₃	1	1	yes	characteristic
55	C₂×C₄	C₂×C₄×C₅₀₃	1	1	yes	characteristic
56	C₂×C₄	D₄×C₅₀₃	1	1	yes	characteristic
57	C₂×C₄	D₄×C₅₀₃	1	1	yes	characteristic
58	C₂×C₄	D₄×C₅₀₃	1	1	yes	characteristic
59	C₂×C₄	Q₈×C₅₀₃	1	1	yes	characteristic
60	C₈	—	2	2	no	—
61	C₈	—	2	2	no	—
62	C₂²	—	4	1	no	—
63	C₂²	C₄²×C₅₀₃	1	1	yes	characteristic
64	C₂²	C₂²⋊C₄×C₅₀₃	1	1	yes	characteristic
65	C₂²	C₄⋊C₄×C₅₀₃	1	1	yes	characteristic
66	C₄	—	4	2	no	—
67	C₄	C₂²⋊C₄×C₅₀₃	1	1	yes	characteristic
68	C₄	C₂²⋊C₄×C₅₀₃	1	1	yes	characteristic
69	C₄	C₄⋊C₄×C₅₀₃	1	1	yes	characteristic
70	C₄	C₄⋊C₄×C₅₀₃	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	—	2	1	no	—
73	C₂	—	2	1	no	—
74	C₂	#95×C₅₀₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅₀₃	C₂²⋊C₄
commutator	C₂²	C₄²×C₅₀₃
Frattini, cosocle	C₂²×C₄	C₂²×C₅₀₃
socle	C₂×C₅₀₃	#95
prime radical	C₂³×C₅₀₃	C₂×C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅₀₃ ◁ C₂²×C₄×C₅₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
8. M₁₆×C₅₀₃	C₄	semidirect
10. C₂×C₈×C₅₀₃	C₄	semidirect
37. C₅₀₃	#344	direct (N × H)
38. #344	C₅₀₃	direct (N × H)
46. M₁₆	C₄×C₅₀₃	semidirect
48. C₂×C₈	C₄×C₅₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×C₅₀₃	2
#117×C₅₀₃	2
#344	503

Subgroups — #344×C503 #44565757

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #344×C₅₀₃ #44565757