Finite Group Databasebeta

← C₂³×C₇×C₂₂₃ #72190832

Subgroups — C₂³×C₇×C₂₂₃ #72190832

Order 12488.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×C₂₂₃	C₂	1	7	yes	maximal, direct product factor
2	C₂×C₇×C₂₂₃	C₂²	1	7	yes	direct product factor
3	C₂³×C₂₂₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₂₂₃	C₂³	1	1	yes	characteristic, direct product factor, Hall
5	C₂²×C₂₂₃	C₂×C₇	1	7	yes	direct product factor
6	C₂×C₂₂₃	C₂²×C₇	1	7	yes	direct product factor
7	C₂₂₃	C₂³×C₇	1	1	yes	characteristic, direct product factor, Sylow
8	C₂³×C₇	C₂₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₇	C₂×C₂₂₃	1	7	yes	direct product factor
10	C₂×C₇	C₂²×C₂₂₃	1	7	yes	direct product factor
11	C₂³	C₇×C₂₂₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₇	C₂³×C₂₂₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₂²	C₂×C₇×C₂₂₃	1	7	yes	direct product factor
14	C₂	C₂²×C₇×C₂₂₃	1	7	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇×C₂₂₃	C₂	direct (N × H)
2. C₂×C₇×C₂₂₃	C₂²	direct (N × H)
3. C₂³×C₂₂₃	C₇	direct (N × H)
4. C₇×C₂₂₃	C₂³	direct (N × H)
5. C₂²×C₂₂₃	C₂×C₇	direct (N × H)
6. C₂×C₂₂₃	C₂²×C₇	direct (N × H)
7. C₂₂₃	C₂³×C₇	direct (N × H)
8. C₂³×C₇	C₂₂₃	direct (N × H)
9. C₂²×C₇	C₂×C₂₂₃	direct (N × H)
10. C₂×C₇	C₂²×C₂₂₃	direct (N × H)
11. C₂³	C₇×C₂₂₃	direct (N × H)
12. C₇	C₂³×C₂₂₃	direct (N × H)
13. C₂²	C₂×C₇×C₂₂₃	direct (N × H)
14. C₂	C₂²×C₇×C₂₂₃	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×C₂₂₃	2
C₂³×C₂₂₃	7
C₂³×C₇	223