Subgroups — C₄×D₇⋊C₉ #92582

Order 504.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₇⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₇⋊C₉	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	D₇⋊C₉	C₄	1	1	yes	characteristic, direct product factor
7	D₇⋊C₉	C₄	1	1	yes	characteristic, direct product factor
8	C₂×C₃×D₇	C₂×C₃	1	1	yes	characteristic
9	C₃×C₄×C₇	C₂×C₃	1	1	yes	characteristic
10	C₃×Dic₇	C₂×C₃	1	1	yes	characteristic
11	C₂×C₄×C₉	—	7	1	no	maximal, Hall
12	C₇⋊C₉	C₂×C₄	1	1	yes	characteristic, complemented, Hall
13	C₄×D₇	C₉	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₇	C₂²×C₃	1	1	yes	characteristic
15	C₃×D₇	C₃×C₄	1	1	yes	characteristic
16	C₃×D₇	C₃×C₄	1	1	yes	characteristic
17	C₂²×C₉	—	7	1	no	—
18	C₄×C₉	—	7	1	no	—
19	C₄×C₉	—	7	1	no	—
20	C₂×D₇	C₂×C₉	1	1	yes	characteristic
21	C₄×C₇	C₂×C₉	1	1	yes	characteristic, complemented
22	Dic₇	C₂×C₉	1	1	yes	characteristic, complemented
23	C₂×C₃×C₄	—	21	1	no	—
24	C₃×C₇	C₂×C₃×C₄	1	1	yes	characteristic
25	C₂×C₉	—	7	1	no	—
26	C₂×C₉	—	7	1	no	—
27	C₂×C₉	—	7	1	no	—
28	C₂×C₇	C₂²×C₉	1	1	yes	characteristic
29	D₇	C₄×C₉	1	1	yes	characteristic, complemented
30	D₇	C₄×C₉	1	1	yes	characteristic, complemented
31	C₂²×C₃	—	21	1	no	—
32	C₃×C₄	—	21	1	no	—
33	C₃×C₄	AGL(1,𝔽₇)	1	1	yes	characteristic
34	C₉	—	7	1	no	Sylow
35	C₂×C₄	—	21	1	no	Sylow
36	C₇	C₂×C₄×C₉	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃	—	7	1	no	—
38	C₂×C₃	—	21	1	no	—
39	C₂×C₃	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
40	C₂²	—	21	1	no	—
41	C₄	—	21	1	no	—
42	C₄	D₇⋊C₉	1	1	yes	characteristic, direct product factor
43	C₃	C₄×AGL(1,𝔽₇)	1	1	yes	characteristic
44	C₂	—	7	1	no	—
45	C₂	—	21	1	no	—
46	C₂	C₂×D₇⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₂×C₄×C₉
Frattini	C₂×C₃	C₂×AGL(1,𝔽₇)
Fitting	C₃×C₄×C₇	C₂×C₃
socle, cosocle	C₂×C₃×C₇	C₂²×C₃
prime radical	C₂×C₃×D₇	C₂×C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
2. C₄×C₇⋊C₉	C₂	semidirect
3. Dic₇⋊C₉	C₂	semidirect
6. D₇⋊C₉	C₄	direct (N × H)
7. D₇⋊C₉	C₄	direct (N × H)
12. C₇⋊C₉	C₂×C₄	semidirect
13. C₄×D₇	C₉	semidirect
21. C₄×C₇	C₂×C₉	semidirect
22. Dic₇	C₂×C₉	semidirect
29. D₇	C₄×C₉	semidirect
30. D₇	C₄×C₉	semidirect
36. C₇	C₂×C₄×C₉	semidirect
42. C₄	D₇⋊C₉	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×D₇⋊C₉	2
C₄×C₇⋊C₉	2
Dic₇⋊C₉	2
C₃×C₄×D₇	3
C₂×C₄×C₉	7

Subgroups — C4×D7⋊C9 #92582

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₇⋊C₉ #92582