Finite Group Databasebeta

← C₂²×C₇²×C₆₇ #27190076

Subgroups — C₂²×C₇²×C₆₇ #27190076

Order 13132.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇²×C₆₇	C₂	1	3	yes	maximal, direct product factor
2	C₇²×C₆₇	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₇×C₆₇	C₇	1	8	yes	maximal, direct product factor
4	C₂×C₇×C₆₇	C₂×C₇	1	24	yes	direct product factor
5	C₇×C₆₇	C₂²×C₇	1	8	yes	direct product factor
6	C₂²×C₆₇	C₇²	1	1	yes	characteristic, direct product factor, Hall
7	C₂²×C₇²	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₆₇	C₂×C₇²	1	3	yes	direct product factor
9	C₂×C₇²	C₂×C₆₇	1	3	yes	direct product factor
10	C₆₇	C₂²×C₇²	1	1	yes	characteristic, direct product factor, Sylow
11	C₇²	C₂²×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₂²×C₇	C₇×C₆₇	1	8	yes	direct product factor
13	C₂×C₇	C₂×C₇×C₆₇	1	24	yes	direct product factor
14	C₇	C₂²×C₇×C₆₇	1	8	yes	direct product factor
15	C₂²	C₇²×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₂	C₂×C₇²×C₆₇	1	3	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. C₂×C₇²×C₆₇	C₂	direct (N × H)
2. C₇²×C₆₇	C₂²	direct (N × H)
3. C₂²×C₇×C₆₇	C₇	direct (N × H)
4. C₂×C₇×C₆₇	C₂×C₇	direct (N × H)
5. C₇×C₆₇	C₂²×C₇	direct (N × H)
6. C₂²×C₆₇	C₇²	direct (N × H)
7. C₂²×C₇²	C₆₇	direct (N × H)
8. C₂×C₆₇	C₂×C₇²	direct (N × H)
9. C₂×C₇²	C₂×C₆₇	direct (N × H)
10. C₆₇	C₂²×C₇²	direct (N × H)
11. C₇²	C₂²×C₆₇	direct (N × H)
12. C₂²×C₇	C₇×C₆₇	direct (N × H)
13. C₂×C₇	C₂×C₇×C₆₇	direct (N × H)
14. C₇	C₂²×C₇×C₆₇	direct (N × H)
15. C₂²	C₇²×C₆₇	direct (N × H)
16. C₂	C₂×C₇²×C₆₇	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×C₇²×C₆₇	2
C₂²×C₇×C₆₇	7
C₂²×C₇²	67