Finite Group Databasebeta

← C₁₇×D₁₇×C₄₁ #37557113

Subgroups — C₁₇×D₁₇×C₄₁ #37557113

Order 23698.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇²×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₇×C₄₁	—	17	1	no	maximal
3	D₁₇×C₄₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor
4	C₁₇×C₄₁	—	2	8	no	—
5	C₁₇×C₄₁	D₁₇	1	1	yes	characteristic, direct product factor
6	C₁₇×C₄₁	C₂×C₁₇	1	1	yes	characteristic, complemented
7	C₁₇×D₁₇	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇²	C₂×C₄₁	1	1	yes	characteristic, complemented, Sylow
9	C₂×C₄₁	—	17	1	no	Hall
10	C₄₁	C₁₇×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
11	C₂×C₁₇	—	17	1	no	—
12	D₁₇	C₁₇×C₄₁	1	1	yes	characteristic, direct product factor
13	C₁₇	—	2	8	no	—
14	C₁₇	D₁₇×C₄₁	1	1	yes	characteristic, direct product factor
15	C₁₇	C₂×C₁₇×C₄₁	1	1	yes	characteristic, complemented
16	C₂	—	17	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇×C₄₁	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₁₇×C₄₁
Frattini	C₁	G
Fitting, socle	C₁₇²×C₄₁	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₁₇×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₁₇²×C₄₁	C₂	semidirect
3. D₁₇×C₄₁	C₁₇	direct (N × H)
5. C₁₇×C₄₁	D₁₇	direct (N × H)
6. C₁₇×C₄₁	C₂×C₁₇	semidirect
7. C₁₇×D₁₇	C₄₁	direct (N × H)
8. C₁₇²	C₂×C₄₁	semidirect
10. C₄₁	C₁₇×D₁₇	direct (N × H)
12. D₁₇	C₁₇×C₄₁	direct (N × H)
14. C₁₇	D₁₇×C₄₁	direct (N × H)
15. C₁₇	C₂×C₁₇×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₇²×C₄₁	2
C₂×C₁₇×C₄₁	17
D₁₇×C₄₁	17
C₁₇×D₁₇	41