Finite Group Databasebeta

← C₂²×C₇×C₉ #6976

Subgroups — C₂²×C₇×C₉ #6976

Order 252.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₉	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₇	C₃	1	1	yes	maximal, characteristic
3	C₇×C₉	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₇	C₂×C₃	1	3	yes	—
5	C₂²×C₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₇	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₇	C₂²×C₃	1	1	yes	characteristic
8	C₂×C₉	C₂×C₇	1	3	yes	direct product factor
9	C₂×C₇	C₂×C₉	1	3	yes	direct product factor
10	C₂²×C₃	C₃×C₇	1	1	yes	characteristic
11	C₉	C₂²×C₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₇	C₂²×C₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₃	C₂×C₃×C₇	1	3	yes	—
14	C₂²	C₇×C₉	1	1	yes	characteristic, direct product factor, Sylow
15	C₃	C₂²×C₃×C₇	1	1	yes	characteristic
16	C₂	C₂×C₇×C₉	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂²×C₃×C₇
socle, prime radical	C₂²×C₃×C₇	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×C₉	C₂	direct (N × H)
3. C₇×C₉	C₂²	direct (N × H)
5. C₂²×C₉	C₇	direct (N × H)
6. C₂²×C₇	C₉	direct (N × H)
8. C₂×C₉	C₂×C₇	direct (N × H)
9. C₂×C₇	C₂×C₉	direct (N × H)
11. C₉	C₂²×C₇	direct (N × H)
12. C₇	C₂²×C₉	direct (N × H)
14. C₂²	C₇×C₉	direct (N × H)
16. C₂	C₂×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
C₂×C₇×C₉	2
C₂²×C₃×C₇	3
C₂²×C₉	7