Subgroups — C₂×C₁₁×D₄₇₇ #35230565

Order 20988.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₄₇₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₁₁×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×D₁₅₉	—	3	1	no	maximal
4	C₉×C₁₁×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₁×D₁₅₉	—	3	2	no	—
6	C₂×C₃×C₁₁×C₅₃	D₃	1	1	yes	characteristic
7	C₂×C₁₁×D₅₃	—	9	1	no	Hall
8	C₂×D₄₇₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₁₁×C₅₃	C₂×D₃	1	1	yes	characteristic
10	C₂×C₁₁×C₅₃	D₉	1	1	yes	characteristic, complemented
11	C₁₁×D₅₃	—	9	2	no	—
12	C₂×C₉×C₅₃	C₂×C₁₁	1	1	yes	characteristic, complemented
13	D₄₇₇	C₂×C₁₁	1	2	yes	direct product factor
14	C₂×D₁₅₉	—	3	1	no	—
15	C₁₁×C₅₃	C₂×D₉	1	1	yes	characteristic, complemented, Hall
16	C₉×C₅₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₁×D₉	—	53	1	no	maximal, Hall
18	C₂×C₃×C₅₃	D₃×C₁₁	1	1	yes	characteristic
19	D₁₅₉	—	3	2	no	—
20	C₂×D₅₃	—	9	1	no	Hall
21	C₂×C₉×C₁₁	D₅₃	1	1	yes	characteristic, complemented
22	C₁₁×D₉	—	53	2	no	—
23	C₃×C₅₃	C₂×D₃×C₁₁	1	1	yes	characteristic
24	C₂×D₃×C₁₁	—	159	1	no	—
25	C₂×C₅₃	C₁₁×D₉	1	1	yes	characteristic, complemented
26	D₅₃	—	9	2	no	—
27	C₉×C₁₁	C₂×D₅₃	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₁₁	D₁₅₉	1	1	yes	characteristic
29	D₃×C₁₁	—	159	2	no	—
30	C₅₃	C₂×C₁₁×D₉	1	1	yes	characteristic, complemented, Sylow
31	C₂²×C₁₁	—	477	1	no	Hall
32	C₂×D₉	—	53	1	no	Hall
33	C₃×C₁₁	C₂×D₁₅₉	1	1	yes	characteristic
34	C₂×C₁₁	—	477	2	no	—
35	C₂×C₁₁	D₄₇₇	1	1	yes	characteristic, direct product factor
36	C₂×C₉	C₁₁×D₅₃	1	1	yes	characteristic, complemented
37	D₉	—	53	2	no	—
38	C₂×D₃	—	159	1	no	—
39	C₁₁	C₂×D₄₇₇	1	1	yes	characteristic, direct product factor, Sylow
40	C₉	C₂×C₁₁×D₅₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	C₁₁×D₁₅₉	1	1	yes	characteristic
42	D₃	—	159	2	no	—
43	C₂²	—	477	1	no	Sylow
44	C₃	C₂×C₁₁×D₁₅₉	1	1	yes	characteristic
45	C₂	—	477	2	no	—
46	C₂	C₁₁×D₄₇₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₄₇₇
commutator, cosocle, hypocenter	C₉×C₅₃	C₂²×C₁₁
Frattini	C₃	C₂×C₁₁×D₁₅₉
Fitting	C₂×C₉×C₁₁×C₅₃	C₂
socle	C₂×C₃×C₁₁×C₅₃	D₃
LCS	G ▷ C₉×C₅₃
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₄₇₇	C₂	direct (N × H)
2. C₂×C₉×C₁₁×C₅₃	C₂	semidirect
4. C₉×C₁₁×C₅₃	C₂²	semidirect
8. C₂×D₄₇₇	C₁₁	direct (N × H)
10. C₂×C₁₁×C₅₃	D₉	semidirect
12. C₂×C₉×C₅₃	C₂×C₁₁	semidirect
13. D₄₇₇	C₂×C₁₁	direct (N × H)
15. C₁₁×C₅₃	C₂×D₉	semidirect
16. C₉×C₅₃	C₂²×C₁₁	semidirect
21. C₂×C₉×C₁₁	D₅₃	semidirect
25. C₂×C₅₃	C₁₁×D₉	semidirect
27. C₉×C₁₁	C₂×D₅₃	semidirect
30. C₅₃	C₂×C₁₁×D₉	semidirect
35. C₂×C₁₁	D₄₇₇	direct (N × H)
36. C₂×C₉	C₁₁×D₅₃	semidirect
39. C₁₁	C₂×D₄₇₇	direct (N × H)
40. C₉	C₂×C₁₁×D₅₃	semidirect
46. C₂	C₁₁×D₄₇₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×D₄₇₇	2
C₂×C₉×C₁₁×C₅₃	2
C₂×C₁₁×D₁₅₉	3
C₂×D₄₇₇	11
C₂×C₁₁×D₉	53

Subgroups — C2×C11×D477 #35230565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×D₄₇₇ #35230565