Subgroups — (C₂²⋊D₇)⋊C₉ #92585

Order 504.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₇⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₇⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₂²⋊D₇	C₃	1	1	yes	maximal, characteristic
5	C₂×C₇⋊C₉	—	2	1	no	—
6	C₂×C₇⋊C₉	C₂²	1	1	yes	characteristic
7	D₇⋊C₉	—	2	1	no	—
8	C₂²×C₃×C₇	C₂×C₃	1	1	yes	characteristic
9	C₂×C₃×D₇	C₂×C₃	1	1	yes	characteristic
10	C₃×Dic₇	C₂×C₃	1	1	yes	characteristic
11	D₄×C₉	—	7	1	no	maximal, Hall
12	C₇⋊C₉	D₄	1	1	yes	characteristic, complemented, Hall
13	C₂²⋊D₇	C₉	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₇	—	2	1	no	—
15	C₂×C₃×C₇	C₂²×C₃	1	1	yes	characteristic
16	C₃×D₇	—	2	1	no	—
17	C₂²×C₉	—	7	1	no	—
18	C₂²×C₉	—	7	1	no	—
19	C₄×C₉	—	7	1	no	—
20	C₂²×C₇	C₂×C₉	1	1	yes	characteristic, complemented
21	C₂×D₇	C₂×C₉	1	1	yes	characteristic, complemented
22	Dic₇	C₂×C₉	1	1	yes	characteristic, complemented
23	C₃×D₄	—	7	1	no	—
24	C₃×C₇	C₃×D₄	1	1	yes	characteristic
25	C₂×C₉	—	7	1	no	—
26	C₂×C₉	—	14	1	no	—
27	C₂×C₉	—	14	1	no	—
28	C₂×C₇	—	2	1	no	—
29	C₂×C₇	C₂²×C₉	1	1	yes	characteristic
30	D₇	—	2	1	no	—
31	C₂²×C₃	—	7	1	no	—
32	C₂²×C₃	AGL(1,𝔽₇)	1	1	yes	characteristic
33	C₃×C₄	—	7	1	no	—
34	C₉	—	7	1	no	Sylow
35	D₄	—	7	1	no	Sylow
36	C₇	D₄×C₉	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃	—	2	1	no	—
38	C₂×C₃	—	14	1	no	—
39	C₂×C₃	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
40	C₂²	—	7	1	no	—
41	C₂²	D₇⋊C₉	1	1	yes	characteristic, complemented
42	C₄	—	7	1	no	—
43	C₃	(C₂²⋊D₇)⋊C₃	1	1	yes	characteristic
44	C₂	—	2	1	no	—
45	C₂	—	14	1	no	—
46	C₂	C₂×D₇⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₃	C₂×AGL(1,𝔽₇)
commutator	C₂×C₇	C₂²×C₉
Fitting	C₂²×C₃×C₇	C₂×C₃
socle, cosocle	C₂×C₃×C₇	C₂²×C₃
prime radical	C₃×C₂²⋊D₇	C₃
hypercenter	C₂²×C₃	AGL(1,𝔽₇)
hypocenter	C₇	D₄×C₉
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇⋊C₉	C₂	semidirect
2. C₂×D₇⋊C₉	C₂	semidirect
3. Dic₇⋊C₉	C₂	semidirect
12. C₇⋊C₉	D₄	semidirect
13. C₂²⋊D₇	C₉	semidirect
20. C₂²×C₇	C₂×C₉	semidirect
21. C₂×D₇	C₂×C₉	semidirect
22. Dic₇	C₂×C₉	semidirect
36. C₇	D₄×C₉	semidirect
41. C₂²	D₇⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₇⋊C₉	2
C₂×D₇⋊C₉	2
Dic₇⋊C₉	2
C₃×C₂²⋊D₇	3
D₄×C₉	7

Subgroups — (C22⋊D7)⋊C9 #92585

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂²⋊D₇)⋊C₉ #92585