Subgroups — C₂×C₉×D₇×C₁₃₇ #46828596

Order 34524.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₇×C₁₃₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₉×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₇×C₁₃₇	C₃	1	1	yes	maximal, characteristic
4	C₇×C₉×C₁₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×D₇×C₁₃₇	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₇×C₁₃₇	C₂×C₃	1	1	yes	characteristic
7	C₂²×C₉×C₁₃₇	—	7	1	no	maximal, Hall
8	C₂×D₇×C₁₃₇	C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₇×C₁₃₇	C₂²×C₃	1	1	yes	characteristic
10	C₂×C₉×C₁₃₇	—	7	2	no	—
11	C₂×C₉×C₁₃₇	D₇	1	1	yes	characteristic, direct product factor
12	C₂×C₇×C₁₃₇	C₂×C₉	1	1	yes	characteristic, complemented
13	D₇×C₁₃₇	C₂×C₉	1	2	yes	direct product factor
14	C₂²×C₃×C₁₃₇	—	7	1	no	—
15	C₉×C₁₃₇	C₂×D₇	1	1	yes	characteristic, direct product factor, Hall
16	C₇×C₁₃₇	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₃₇	—	7	2	no	—
18	C₂×C₃×C₁₃₇	C₃×D₇	1	1	yes	characteristic
19	C₂²×C₁₃₇	—	7	1	no	Hall
20	C₃×C₁₃₇	C₂×C₃×D₇	1	1	yes	characteristic
21	C₂×C₁₃₇	—	7	2	no	—
22	C₂×C₁₃₇	C₉×D₇	1	1	yes	characteristic, direct product factor
23	C₂×C₉×D₇	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₁₃₇	C₂×C₉×D₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₇×C₉	C₂×C₁₃₇	1	1	yes	characteristic, complemented
26	C₉×D₇	C₂×C₁₃₇	1	2	yes	direct product factor
27	C₂×C₃×D₇	C₃×C₁₃₇	1	1	yes	characteristic
28	C₇×C₉	C₂²×C₁₃₇	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₇	C₂×C₃×C₁₃₇	1	1	yes	characteristic
30	C₃×D₇	C₂×C₃×C₁₃₇	1	2	yes	—
31	C₂²×C₉	—	7	1	no	Hall
32	C₂×D₇	C₉×C₁₃₇	1	1	yes	characteristic, direct product factor, Hall
33	C₃×C₇	C₂²×C₃×C₁₃₇	1	1	yes	characteristic
34	C₂×C₉	—	7	2	no	—
35	C₂×C₉	D₇×C₁₃₇	1	1	yes	characteristic, direct product factor
36	C₂×C₇	C₂×C₉×C₁₃₇	1	1	yes	characteristic, complemented
37	D₇	C₂×C₉×C₁₃₇	1	2	yes	direct product factor
38	C₂²×C₃	—	7	1	no	—
39	C₉	C₂×D₇×C₁₃₇	1	1	yes	characteristic, direct product factor, Sylow
40	C₇	C₂²×C₉×C₁₃₇	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	—	7	2	no	—
42	C₂×C₃	C₃×D₇×C₁₃₇	1	1	yes	characteristic
43	C₂²	—	7	1	no	Sylow
44	C₃	C₂×C₃×D₇×C₁₃₇	1	1	yes	characteristic
45	C₂	—	7	2	no	—
46	C₂	C₉×D₇×C₁₃₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₉×C₁₃₇	D₇
commutator, hypocenter	C₇	C₂²×C₉×C₁₃₇
Frattini	C₃	C₂×C₃×D₇×C₁₃₇
Fitting	C₂×C₇×C₉×C₁₃₇	C₂
socle	C₂×C₃×C₇×C₁₃₇	C₂×C₃
prime radical	C₂×C₃×D₇×C₁₃₇	C₃
cosocle	C₃×C₇	C₂²×C₃×C₁₃₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₉×C₁₃₇

Complements

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

N	H ≅ G/N	type
1. C₉×D₇×C₁₃₇	C₂	direct (N × H)
2. C₂×C₇×C₉×C₁₃₇	C₂	semidirect
4. C₇×C₉×C₁₃₇	C₂²	semidirect
8. C₂×D₇×C₁₃₇	C₉	direct (N × H)
11. C₂×C₉×C₁₃₇	D₇	direct (N × H)
12. C₂×C₇×C₁₃₇	C₂×C₉	semidirect
13. D₇×C₁₃₇	C₂×C₉	direct (N × H)
15. C₉×C₁₃₇	C₂×D₇	direct (N × H)
16. C₇×C₁₃₇	C₂²×C₉	semidirect
22. C₂×C₁₃₇	C₉×D₇	direct (N × H)
23. C₂×C₉×D₇	C₁₃₇	direct (N × H)
24. C₁₃₇	C₂×C₉×D₇	direct (N × H)
25. C₂×C₇×C₉	C₂×C₁₃₇	semidirect
26. C₉×D₇	C₂×C₁₃₇	direct (N × H)
28. C₇×C₉	C₂²×C₁₃₇	semidirect
32. C₂×D₇	C₉×C₁₃₇	direct (N × H)
35. C₂×C₉	D₇×C₁₃₇	direct (N × H)
36. C₂×C₇	C₂×C₉×C₁₃₇	semidirect
37. D₇	C₂×C₉×C₁₃₇	direct (N × H)
39. C₉	C₂×D₇×C₁₃₇	direct (N × H)
40. C₇	C₂²×C₉×C₁₃₇	semidirect
46. C₂	C₉×D₇×C₁₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×D₇×C₁₃₇	2
C₂×C₇×C₉×C₁₃₇	2
C₂×C₃×D₇×C₁₃₇	3
C₂²×C₉×C₁₃₇	7
C₂×C₉×D₇	137

Subgroups — C2×C9×D7×C137 #46828596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×D₇×C₁₃₇ #46828596