Subgroups — C₂×C₄×C₇⋊C₉ #92593

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
2	C₄×C₇⋊C₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₄×C₇	C₃	1	1	yes	maximal, characteristic
4	C₂×C₇⋊C₉	C₄	1	2	yes	direct product factor
5	C₂×C₇⋊C₉	C₂²	1	1	yes	characteristic
6	C₂²×C₃×C₇	C₂×C₃	1	1	yes	characteristic
7	C₃×C₄×C₇	C₂×C₃	1	2	yes	—
8	C₂×C₄×C₉	—	7	1	no	maximal, Hall
9	C₇⋊C₉	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₄×C₇	C₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₇	C₃×C₄	1	2	yes	—
12	C₂×C₃×C₇	C₂²×C₃	1	1	yes	characteristic
13	C₂²×C₉	—	7	1	no	—
14	C₄×C₉	—	7	2	no	—
15	C₂²×C₇	C₂×C₉	1	1	yes	characteristic
16	C₄×C₇	C₂×C₉	1	2	yes	complemented
17	C₂×C₃×C₄	ΓL(1,𝔽₈)	1	1	yes	characteristic
18	C₃×C₇	C₂×C₃×C₄	1	1	yes	characteristic
19	C₂×C₉	—	7	2	no	—
20	C₂×C₉	—	7	1	no	—
21	C₂×C₇	C₄×C₉	1	2	yes	complemented
22	C₂×C₇	C₂²×C₉	1	1	yes	characteristic
23	C₂²×C₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
24	C₃×C₄	C₂×ΓL(1,𝔽₈)	1	2	yes	—
25	C₉	—	7	1	no	Sylow
26	C₂×C₄	C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	C₂×C₄×C₉	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	C₄×ΓL(1,𝔽₈)	1	2	yes	—
29	C₂×C₃	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic
30	C₂²	C₂×C₇⋊C₉	1	1	yes	characteristic
31	C₄	C₂×C₇⋊C₉	1	2	yes	direct product factor
32	C₃	C₂×C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic
33	C₂	C₄×C₇⋊C₉	1	2	yes	direct product factor
34	C₂	C₂²×C₇⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₄	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₂×C₄×C₉
Frattini	C₂×C₃	C₂²×ΓL(1,𝔽₈)
Fitting	C₂×C₃×C₄×C₇	C₃
socle, prime radical	C₂²×C₃×C₇	C₂×C₃
cosocle	C₂×C₃×C₇	C₂²×C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₄

Complements

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

N	H ≅ G/N	type
2. C₄×C₇⋊C₉	C₂	direct (N × H)
4. C₂×C₇⋊C₉	C₄	direct (N × H)
9. C₇⋊C₉	C₂×C₄	direct (N × H)
10. C₂×C₄×C₇	C₉	semidirect
16. C₄×C₇	C₂×C₉	semidirect
21. C₂×C₇	C₄×C₉	semidirect
26. C₂×C₄	C₇⋊C₉	direct (N × H)
27. C₇	C₂×C₄×C₉	semidirect
31. C₄	C₂×C₇⋊C₉	direct (N × H)
33. C₂	C₄×C₇⋊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
C₂²×C₇⋊C₉	2
C₄×C₇⋊C₉	2
C₂×C₃×C₄×C₇	3
C₂×C₄×C₉	7

Subgroups — C2×C4×C7⋊C9 #92593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₇⋊C₉ #92593