Subgroups — C₂×C₄×C₇×C₉ #92613

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	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₉	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₄×C₇	C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₇	C₃×C₄	1	2	yes	—
12	C₂×C₃×C₇	C₂²×C₃	1	1	yes	characteristic
13	C₂²×C₉	C₂×C₇	1	1	yes	characteristic
14	C₄×C₉	C₂×C₇	1	2	yes	direct product factor
15	C₂²×C₇	C₂×C₉	1	1	yes	characteristic
16	C₄×C₇	C₂×C₉	1	2	yes	direct product factor
17	C₂×C₃×C₄	C₃×C₇	1	1	yes	characteristic
18	C₃×C₇	C₂×C₃×C₄	1	1	yes	characteristic
19	C₂×C₉	C₄×C₇	1	2	yes	direct product factor
20	C₂×C₉	C₂²×C₇	1	1	yes	characteristic
21	C₂×C₇	C₄×C₉	1	2	yes	direct product factor
22	C₂×C₇	C₂²×C₉	1	1	yes	characteristic
23	C₂²×C₃	C₂×C₃×C₇	1	1	yes	characteristic
24	C₃×C₄	C₂×C₃×C₇	1	2	yes	—
25	C₉	C₂×C₄×C₇	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₄	C₇×C₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	C₂×C₄×C₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	C₃×C₄×C₇	1	2	yes	—
29	C₂×C₃	C₂²×C₃×C₇	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×C₃×C₄×C₇	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	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂²×C₃×C₇
socle, prime radical	C₂²×C₃×C₇	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

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)
8. C₂×C₄×C₉	C₇	direct (N × H)
9. C₇×C₉	C₂×C₄	direct (N × H)
10. C₂×C₄×C₇	C₉	direct (N × H)
14. C₄×C₉	C₂×C₇	direct (N × H)
16. C₄×C₇	C₂×C₉	direct (N × H)
19. C₂×C₉	C₄×C₇	direct (N × H)
21. C₂×C₇	C₄×C₉	direct (N × H)
25. C₉	C₂×C₄×C₇	direct (N × H)
26. C₂×C₄	C₇×C₉	direct (N × H)
27. C₇	C₂×C₄×C₉	direct (N × H)
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 #92613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₇×C₉ #92613