Subgroups — C₄×C₉×D₇ #92599

Order 504.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×D₇	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×D₇	C₃	1	1	yes	maximal, characteristic
5	C₂×C₇×C₉	C₂²	1	1	yes	characteristic
6	C₉×D₇	C₄	1	2	yes	direct product factor
7	C₂×C₃×D₇	C₂×C₃	1	1	yes	characteristic
8	C₃×C₄×C₇	C₂×C₃	1	1	yes	characteristic
9	C₃×Dic₇	C₂×C₃	1	1	yes	characteristic
10	C₂×C₄×C₉	—	7	1	no	maximal, Hall
11	C₇×C₉	C₂×C₄	1	1	yes	characteristic, complemented, Hall
12	C₄×D₇	C₉	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₇	C₂²×C₃	1	1	yes	characteristic
14	C₃×D₇	C₃×C₄	1	2	yes	—
15	C₂²×C₉	—	7	1	no	—
16	C₄×C₉	—	7	1	no	—
17	C₄×C₉	D₇	1	1	yes	characteristic, direct product factor
18	C₂×D₇	C₂×C₉	1	1	yes	characteristic
19	C₄×C₇	C₂×C₉	1	1	yes	characteristic, complemented
20	Dic₇	C₂×C₉	1	1	yes	characteristic, complemented
21	C₂×C₃×C₄	—	7	1	no	—
22	C₃×C₇	C₂×C₃×C₄	1	1	yes	characteristic
23	C₂×C₉	—	7	2	no	—
24	C₂×C₉	C₂×D₇	1	1	yes	characteristic
25	C₂×C₇	C₂²×C₉	1	1	yes	characteristic
26	D₇	C₄×C₉	1	2	yes	direct product factor
27	C₂²×C₃	—	7	1	no	—
28	C₃×C₄	—	7	1	no	—
29	C₃×C₄	C₃×D₇	1	1	yes	characteristic
30	C₉	C₄×D₇	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₄	—	7	1	no	Sylow
32	C₇	C₂×C₄×C₉	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃	—	7	2	no	—
34	C₂×C₃	C₂×C₃×D₇	1	1	yes	characteristic
35	C₂²	—	7	1	no	—
36	C₄	—	7	1	no	—
37	C₄	C₉×D₇	1	1	yes	characteristic, direct product factor
38	C₃	C₃×C₄×D₇	1	1	yes	characteristic
39	C₂	—	7	2	no	—
40	C₂	C₂×C₉×D₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₉	D₇
commutator, hypocenter	C₇	C₂×C₄×C₉
Frattini	C₂×C₃	C₂×C₃×D₇
Fitting	C₄×C₇×C₉	C₂
socle, cosocle	C₂×C₃×C₇	C₂²×C₃
prime radical	C₂×C₃×D₇	C₂×C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₄×C₉

Complements

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

N	H ≅ G/N	type
2. C₄×C₇×C₉	C₂	semidirect
3. C₉×Dic₇	C₂	semidirect
6. C₉×D₇	C₄	direct (N × H)
11. C₇×C₉	C₂×C₄	semidirect
12. C₄×D₇	C₉	direct (N × H)
17. C₄×C₉	D₇	direct (N × H)
19. C₄×C₇	C₂×C₉	semidirect
20. Dic₇	C₂×C₉	semidirect
26. D₇	C₄×C₉	direct (N × H)
30. C₉	C₄×D₇	direct (N × H)
32. C₇	C₂×C₄×C₉	semidirect
37. C₄	C₉×D₇	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×C₉×D₇	2
C₄×C₇×C₉	2
C₉×Dic₇	2
C₃×C₄×D₇	3
C₂×C₄×C₉	7

Subgroups — C4×C9×D7 #92599

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₉×D₇ #92599