Subgroups — C₂×C₃×D₇×C₂₈₉ #37566182

Order 24276.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₇×C₂₈₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₇×C₂₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₇×C₂₈₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₇×C₂₈₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₇×C₂₈₉	C₂×C₃	1	2	yes	direct product factor
6	C₂×C₇×C₂₈₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂²×C₃×C₂₈₉	—	7	1	no	maximal, Hall
8	C₇×C₂₈₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₂₈₉	—	7	2	no	—
10	C₂×C₃×C₂₈₉	D₇	1	1	yes	characteristic, direct product factor
11	C₂×C₃×D₇×C₁₇	C₁₇	1	1	yes	maximal, characteristic
12	C₂²×C₂₈₉	—	7	1	no	Hall
13	C₃×C₂₈₉	C₂×D₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₇×C₁₇	C₂×C₁₇	1	1	yes	characteristic
15	C₃×D₇×C₁₇	C₂×C₁₇	1	2	yes	—
16	C₂×C₂₈₉	—	7	2	no	—
17	C₂×C₂₈₉	C₃×D₇	1	1	yes	characteristic, direct product factor
18	C₂×D₇×C₁₇	C₃×C₁₇	1	1	yes	characteristic
19	C₃×C₇×C₁₇	C₂²×C₁₇	1	1	yes	characteristic
20	C₂₈₉	C₂×C₃×D₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×C₇×C₁₇	C₂×C₃×C₁₇	1	1	yes	characteristic
22	D₇×C₁₇	C₂×C₃×C₁₇	1	2	yes	—
23	C₂²×C₃×C₁₇	—	7	1	no	—
24	C₇×C₁₇	C₂²×C₃×C₁₇	1	1	yes	characteristic
25	C₂×C₃×C₁₇	—	7	2	no	—
26	C₂×C₃×C₁₇	D₇×C₁₇	1	1	yes	characteristic
27	C₂×C₃×D₇	C₂₈₉	1	1	yes	characteristic, direct product factor, Hall
28	C₂²×C₁₇	—	7	1	no	—
29	C₃×C₁₇	C₂×D₇×C₁₇	1	1	yes	characteristic
30	C₂×C₃×C₇	C₂×C₂₈₉	1	1	yes	characteristic, complemented
31	C₃×D₇	C₂×C₂₈₉	1	2	yes	direct product factor
32	C₂×C₁₇	—	7	2	no	—
33	C₂×C₁₇	C₃×D₇×C₁₇	1	1	yes	characteristic
34	C₂×D₇	C₃×C₂₈₉	1	1	yes	characteristic, direct product factor, Hall
35	C₃×C₇	C₂²×C₂₈₉	1	1	yes	characteristic, complemented, Hall
36	C₁₇	C₂×C₃×D₇×C₁₇	1	1	yes	characteristic
37	C₂×C₇	C₂×C₃×C₂₈₉	1	1	yes	characteristic, complemented
38	D₇	C₂×C₃×C₂₈₉	1	2	yes	direct product factor
39	C₂²×C₃	—	7	1	no	Hall
40	C₇	C₂²×C₃×C₂₈₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	—	7	2	no	—
42	C₂×C₃	D₇×C₂₈₉	1	1	yes	characteristic, direct product factor
43	C₂²	—	7	1	no	Sylow
44	C₃	C₂×D₇×C₂₈₉	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	7	2	no	—
46	C₂	C₃×D₇×C₂₈₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₈₉	D₇
commutator, hypocenter	C₇	C₂²×C₃×C₂₈₉
Frattini	C₁₇	C₂×C₃×D₇×C₁₇
Fitting	C₂×C₃×C₇×C₂₈₉	C₂
socle	C₂×C₃×C₇×C₁₇	C₂×C₁₇
prime radical	C₂×C₃×D₇×C₁₇	C₁₇
cosocle	C₇×C₁₇	C₂²×C₃×C₁₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₂₈₉

Complements

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

N	H ≅ G/N	type
1. C₃×D₇×C₂₈₉	C₂	direct (N × H)
2. C₂×C₃×C₇×C₂₈₉	C₂	semidirect
3. C₂×D₇×C₂₈₉	C₃	direct (N × H)
4. C₃×C₇×C₂₈₉	C₂²	semidirect
5. D₇×C₂₈₉	C₂×C₃	direct (N × H)
6. C₂×C₇×C₂₈₉	C₂×C₃	semidirect
8. C₇×C₂₈₉	C₂²×C₃	semidirect
10. C₂×C₃×C₂₈₉	D₇	direct (N × H)
13. C₃×C₂₈₉	C₂×D₇	direct (N × H)
17. C₂×C₂₈₉	C₃×D₇	direct (N × H)
20. C₂₈₉	C₂×C₃×D₇	direct (N × H)
27. C₂×C₃×D₇	C₂₈₉	direct (N × H)
30. C₂×C₃×C₇	C₂×C₂₈₉	semidirect
31. C₃×D₇	C₂×C₂₈₉	direct (N × H)
34. C₂×D₇	C₃×C₂₈₉	direct (N × H)
35. C₃×C₇	C₂²×C₂₈₉	semidirect
37. C₂×C₇	C₂×C₃×C₂₈₉	semidirect
38. D₇	C₂×C₃×C₂₈₉	direct (N × H)
40. C₇	C₂²×C₃×C₂₈₉	semidirect
42. C₂×C₃	D₇×C₂₈₉	direct (N × H)
44. C₃	C₂×D₇×C₂₈₉	direct (N × H)
46. C₂	C₃×D₇×C₂₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₇×C₂₈₉	2
C₂×C₃×C₇×C₂₈₉	2
C₂×D₇×C₂₈₉	3
C₂²×C₃×C₂₈₉	7
C₂×C₃×D₇×C₁₇	17

Subgroups — C2×C3×D7×C289 #37566182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₇×C₂₈₉ #37566182