Finite Group Databasebeta

← C₂×C₁₁×C₁₇×C₂₉ #24925727

Subgroups — C₂×C₁₁×C₁₇×C₂₉ #24925727

Order 10846.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₇×C₂₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₇×C₂₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₁₁×C₂₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₇×C₂₉	C₂×C₁₁	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₁₁×C₁₇	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₂₉	C₂×C₁₇	1	1	yes	characteristic, direct product factor, Hall
7	C₁₁×C₁₇	C₂×C₂₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₂₉	C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₁₇	C₁₁×C₂₉	1	1	yes	characteristic, direct product factor, Hall
10	C₂₉	C₂×C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
11	C₂×C₁₁	C₁₇×C₂₉	1	1	yes	characteristic, direct product factor, Hall
12	C₁₇	C₂×C₁₁×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₁	C₂×C₁₇×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₁₁×C₁₇×C₂₉	1	1	yes	characteristic, direct product factor, Sylow

	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. C₁₁×C₁₇×C₂₉	C₂	direct (N × H)
2. C₂×C₁₇×C₂₉	C₁₁	direct (N × H)
3. C₂×C₁₁×C₂₉	C₁₇	direct (N × H)
4. C₁₇×C₂₉	C₂×C₁₁	direct (N × H)
5. C₂×C₁₁×C₁₇	C₂₉	direct (N × H)
6. C₁₁×C₂₉	C₂×C₁₇	direct (N × H)
7. C₁₁×C₁₇	C₂×C₂₉	direct (N × H)
8. C₂×C₂₉	C₁₁×C₁₇	direct (N × H)
9. C₂×C₁₇	C₁₁×C₂₉	direct (N × H)
10. C₂₉	C₂×C₁₁×C₁₇	direct (N × H)
11. C₂×C₁₁	C₁₇×C₂₉	direct (N × H)
12. C₁₇	C₂×C₁₁×C₂₉	direct (N × H)
13. C₁₁	C₂×C₁₇×C₂₉	direct (N × H)
14. C₂	C₁₁×C₁₇×C₂₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₁×C₁₇×C₂₉	2
C₂×C₁₇×C₂₉	11
C₂×C₁₁×C₂₉	17
C₂×C₁₁×C₁₇	29