Subgroups — D₁₁₇⋊D₅₃ #37613622

Order 24804.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×D₁₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×D₄₇₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×D₆₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₉⋊D₅₃	—	3	1	no	maximal
5	C₉×C₁₃×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₅₃×D₃₉	—	3	1	no	—
7	C₁₃×D₁₅₉	—	3	1	no	—
8	C₃×D₆₈₉	D₃	1	1	yes	characteristic
9	D₁₃×D₅₃	—	9	1	no	Hall
10	C₃×C₁₃×C₅₃	C₂×D₃	1	1	yes	characteristic
11	D₉×D₅₃	—	13	1	no	maximal, Hall
12	D₆₈₉	D₉	1	1	yes	characteristic, complemented
13	C₁₃×D₅₃	—	9	1	no	—
14	D₁₃×C₅₃	—	9	1	no	—
15	D₄₇₇	D₁₃	1	1	yes	characteristic, complemented
16	C₉×D₅₃	—	13	1	no	—
17	D₉×C₅₃	—	13	1	no	—
18	C₁₃×C₅₃	C₂×D₉	1	1	yes	characteristic, complemented, Hall
19	D₃×D₅₃	—	39	1	no	—
20	C₉×C₅₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
21	D₉×D₁₃	—	53	1	no	maximal, Hall
22	D₁₅₉	—	3	1	no	—
23	C₃×D₅₃	—	13	1	no	—
24	D₃×C₅₃	—	39	1	no	—
25	D₁₁₇	D₅₃	1	1	yes	characteristic, complemented
26	C₉×D₁₃	—	53	1	no	—
27	C₁₃×D₉	—	53	1	no	—
28	C₂×D₅₃	—	117	1	no	Hall
29	C₃×C₅₃	D₃×D₁₃	1	1	yes	characteristic
30	D₃×D₁₃	—	159	1	no	—
31	C₉×C₁₃	C₂×D₅₃	1	1	yes	characteristic, complemented, Hall
32	C₂×C₅₃	—	117	1	no	—
33	D₅₃	—	9	1	no	—
34	D₅₃	—	13	1	no	—
35	D₃₉	—	3	1	no	—
36	C₃×D₁₃	—	53	1	no	—
37	D₃×C₁₃	—	159	1	no	—
38	C₅₃	D₉×D₁₃	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₁₃	—	477	1	no	Hall
40	C₃×C₁₃	D₃×D₅₃	1	1	yes	characteristic
41	C₂×D₉	—	689	1	no	Hall
42	C₂×C₁₃	—	477	1	no	—
43	D₁₃	—	9	1	no	—
44	D₁₃	—	53	1	no	—
45	C₂×C₉	—	689	1	no	—
46	D₉	—	13	1	no	—
47	D₉	—	53	1	no	—
48	C₁₃	D₉×D₅₃	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₃	—	2067	1	no	—
50	C₉	D₁₃×D₅₃	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	689	1	no	—
52	D₃	—	39	1	no	—
53	D₃	—	159	1	no	—
54	C₂²	—	6201	1	no	Sylow
55	C₃	D₃₉⋊D₅₃	1	1	yes	characteristic
56	C₂	—	117	1	no	—
57	C₂	—	689	1	no	—
58	C₂	—	477	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₃×C₅₃	C₂²
Frattini	C₃	D₃₉⋊D₅₃
socle	C₃×C₁₃×C₅₃	C₂×D₃
LCS	G ▷ C₉×C₁₃×C₅₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅₃×D₁₁₇	C₂	semidirect
2. C₁₃×D₄₇₇	C₂	semidirect
3. C₉×D₆₈₉	C₂	semidirect
5. C₉×C₁₃×C₅₃	C₂²	semidirect
12. D₆₈₉	D₉	semidirect
15. D₄₇₇	D₁₃	semidirect
18. C₁₃×C₅₃	C₂×D₉	semidirect
20. C₉×C₅₃	C₂×D₁₃	semidirect
25. D₁₁₇	D₅₃	semidirect
31. C₉×C₁₃	C₂×D₅₃	semidirect
38. C₅₃	D₉×D₁₃	semidirect
48. C₁₃	D₉×D₅₃	semidirect
50. C₉	D₁₃×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×D₁₁₇	2
C₁₃×D₄₇₇	2
C₉×D₆₈₉	2
D₃₉⋊D₅₃	3
D₉×D₅₃	13
D₉×D₁₃	53

Subgroups — D117⋊D53 #37613622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁₇⋊D₅₃ #37613622