Subgroups — C₄×C₇×D₉ #92604

Order 504.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×D₉	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₃×C₇	—	3	1	no	maximal
5	C₂×C₇×C₉	C₂²	1	1	yes	characteristic
6	C₇×D₉	C₄	1	2	yes	direct product factor
7	C₂×D₃×C₇	—	3	1	no	—
8	C₃×C₄×C₇	D₃	1	1	yes	characteristic
9	C₇×Dic₃	—	3	1	no	—
10	C₄×D₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₇×C₉	C₂×C₄	1	1	yes	characteristic, complemented, Hall
12	C₂×C₄×C₇	—	9	1	no	Hall
13	C₂×C₃×C₇	C₂×D₃	1	1	yes	characteristic
14	D₃×C₇	—	3	2	no	—
15	C₂×D₉	C₂×C₇	1	1	yes	characteristic
16	C₄×C₉	C₂×C₇	1	1	yes	characteristic, complemented
17	Dic₉	C₂×C₇	1	1	yes	characteristic, complemented
18	C₂²×C₇	—	9	1	no	—
19	C₄×C₇	—	9	1	no	—
20	C₄×C₇	D₉	1	1	yes	characteristic, direct product factor
21	C₄×D₃	—	3	1	no	—
22	C₃×C₇	C₄×D₃	1	1	yes	characteristic
23	C₂×C₉	C₂²×C₇	1	1	yes	characteristic
24	D₉	C₄×C₇	1	2	yes	direct product factor
25	C₂×C₇	—	9	2	no	—
26	C₂×C₇	C₂×D₉	1	1	yes	characteristic
27	C₂×D₃	—	3	1	no	—
28	C₃×C₄	D₃×C₇	1	1	yes	characteristic
29	Dic₃	—	3	1	no	—
30	C₉	C₂×C₄×C₇	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₄	—	9	1	no	Sylow
32	C₇	C₄×D₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₃	C₂×D₃×C₇	1	1	yes	characteristic
34	D₃	—	3	2	no	—
35	C₂²	—	9	1	no	—
36	C₄	—	9	1	no	—
37	C₄	C₇×D₉	1	1	yes	characteristic, direct product factor
38	C₃	C₄×D₃×C₇	1	1	yes	characteristic
39	C₂	—	9	2	no	—
40	C₂	C₂×C₇×D₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₇	D₉
commutator, hypocenter	C₉	C₂×C₄×C₇
Frattini	C₂×C₃	C₂×D₃×C₇
Fitting	C₄×C₇×C₉	C₂
socle	C₂×C₃×C₇	C₂×D₃
prime radical	C₂×C₇×D₉	C₂
cosocle	C₂×C₉	C₂²×C₇
LCS	G ▷ C₉
UCS	C₁ ◁ C₄×C₇

Complements

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

N	H ≅ G/N	type
2. C₄×C₇×C₉	C₂	semidirect
3. C₇×Dic₉	C₂	semidirect
6. C₇×D₉	C₄	direct (N × H)
10. C₄×D₉	C₇	direct (N × H)
11. C₇×C₉	C₂×C₄	semidirect
16. C₄×C₉	C₂×C₇	semidirect
17. Dic₉	C₂×C₇	semidirect
20. C₄×C₇	D₉	direct (N × H)
24. D₉	C₄×C₇	direct (N × H)
30. C₉	C₂×C₄×C₇	semidirect
32. C₇	C₄×D₉	direct (N × H)
37. C₄	C₇×D₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×D₉	2
C₄×C₇×C₉	2
C₇×Dic₉	2
C₄×D₃×C₇	3
C₄×D₉	7

Subgroups — C4×C7×D9 #92604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇×D₉ #92604