Finite Group Databasebeta

← C₇×C₁₇×D₉₇ #37528136

Subgroups — C₇×C₁₇×D₉₇ #37528136

Order 23086.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₇×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×D₉₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₇×C₉₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
4	C₇×D₉₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₉₇	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
6	C₂×C₇×C₁₇	—	97	1	no	maximal, Hall
7	D₉₇	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
8	C₇×C₁₇	D₉₇	1	1	yes	characteristic, direct product factor, Hall
9	C₉₇	C₂×C₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₁₇	—	97	1	no	Hall
11	C₁₇	C₇×D₉₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₇	—	97	1	no	Hall
13	C₇	C₁₇×D₉₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	97	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₁₇	D₉₇
commutator, cosocle, hypocenter	C₉₇	C₂×C₇×C₁₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₇×C₉₇	C₂
LCS	G ▷ C₉₇
UCS	C₁ ◁ C₇×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₇×C₉₇	C₂	semidirect
2. C₁₇×D₉₇	C₇	direct (N × H)
3. C₁₇×C₉₇	C₂×C₇	semidirect
4. C₇×D₉₇	C₁₇	direct (N × H)
5. C₇×C₉₇	C₂×C₁₇	semidirect
7. D₉₇	C₇×C₁₇	direct (N × H)
8. C₇×C₁₇	D₉₇	direct (N × H)
9. C₉₇	C₂×C₇×C₁₇	semidirect
11. C₁₇	C₇×D₉₇	direct (N × H)
13. C₇	C₁₇×D₉₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₁₇×C₉₇	2
C₁₇×D₉₇	7
C₇×D₉₇	17
C₂×C₇×C₁₇	97