Subgroups — D₆₃⋊D₅₃ #27211237

Order 13356.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×D₆₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₄₇₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×D₃₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₁⋊D₅₃	—	3	1	no	maximal
5	C₇×C₉×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₁×C₅₃	—	3	1	no	—
7	C₇×D₁₅₉	—	3	1	no	—
8	C₃×D₃₇₁	D₃	1	1	yes	characteristic
9	D₉×D₅₃	—	7	1	no	maximal, Hall
10	D₇×D₅₃	—	9	1	no	Hall
11	C₃×C₇×C₅₃	C₂×D₃	1	1	yes	characteristic
12	D₄₇₇	D₇	1	1	yes	characteristic, complemented
13	C₉×D₅₃	—	7	1	no	—
14	D₉×C₅₃	—	7	1	no	—
15	D₃₇₁	D₉	1	1	yes	characteristic, complemented
16	C₇×D₅₃	—	9	1	no	—
17	D₇×C₅₃	—	9	1	no	—
18	D₃×D₅₃	—	21	1	no	—
19	C₉×C₅₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	C₇×C₅₃	C₂×D₉	1	1	yes	characteristic, complemented, Hall
21	D₁₅₉	—	3	1	no	—
22	C₃×D₅₃	—	7	1	no	—
23	D₃×C₅₃	—	21	1	no	—
24	D₇×D₉	—	53	1	no	maximal, Hall
25	C₂×D₅₃	—	63	1	no	Hall
26	C₃×C₅₃	D₃×D₇	1	1	yes	characteristic
27	D₆₃	D₅₃	1	1	yes	characteristic, complemented
28	C₉×D₇	—	53	1	no	—
29	C₇×D₉	—	53	1	no	—
30	C₂×C₅₃	—	63	1	no	—
31	D₅₃	—	7	1	no	—
32	D₅₃	—	9	1	no	—
33	D₃×D₇	—	159	1	no	—
34	C₇×C₉	C₂×D₅₃	1	1	yes	characteristic, complemented, Hall
35	C₅₃	D₇×D₉	1	1	yes	characteristic, complemented, Sylow
36	D₂₁	—	3	1	no	—
37	C₃×D₇	—	53	1	no	—
38	D₃×C₇	—	159	1	no	—
39	C₂×D₉	—	371	1	no	Hall
40	C₂×D₇	—	477	1	no	Hall
41	C₃×C₇	D₃×D₅₃	1	1	yes	characteristic
42	C₂×C₉	—	371	1	no	—
43	D₉	—	7	1	no	—
44	D₉	—	53	1	no	—
45	C₂×C₇	—	477	1	no	—
46	D₇	—	9	1	no	—
47	D₇	—	53	1	no	—
48	C₂×D₃	—	1113	1	no	—
49	C₉	D₇×D₅₃	1	1	yes	characteristic, complemented, Sylow
50	C₇	D₉×D₅₃	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	371	1	no	—
52	D₃	—	21	1	no	—
53	D₃	—	159	1	no	—
54	C₂²	—	3339	1	no	Sylow
55	C₃	D₂₁⋊D₅₃	1	1	yes	characteristic
56	C₂	—	63	1	no	—
57	C₂	—	371	1	no	—
58	C₂	—	477	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₇×C₉×C₅₃	C₂²
Frattini	C₃	D₂₁⋊D₅₃
socle	C₃×C₇×C₅₃	C₂×D₃
LCS	G ▷ C₇×C₉×C₅₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅₃×D₆₃	C₂	semidirect
2. C₇×D₄₇₇	C₂	semidirect
3. C₉×D₃₇₁	C₂	semidirect
5. C₇×C₉×C₅₃	C₂²	semidirect
12. D₄₇₇	D₇	semidirect
15. D₃₇₁	D₉	semidirect
19. C₉×C₅₃	C₂×D₇	semidirect
20. C₇×C₅₃	C₂×D₉	semidirect
27. D₆₃	D₅₃	semidirect
34. C₇×C₉	C₂×D₅₃	semidirect
35. C₅₃	D₇×D₉	semidirect
49. C₉	D₇×D₅₃	semidirect
50. C₇	D₉×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×D₆₃	2
C₇×D₄₇₇	2
C₉×D₃₇₁	2
D₂₁⋊D₅₃	3
D₉×D₅₃	7
D₇×D₉	53

Subgroups — D63⋊D53 #27211237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₆₃⋊D₅₃ #27211237