Finite Group Databasebeta

← D₁₇×C₃₇₃⋊C₃ #49184792

Subgroups — D₁₇×C₃₇₃⋊C₃ #49184792

Order 38046.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₃₇₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₇×C₃₇₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₇×C₃₇₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃₇₃⋊C₃	—	17	1	no	maximal, Hall
5	C₃₇₃⋊C₃	D₁₇	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₃₇₃	—	17	1	no	Hall
7	C₃₇₃	C₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
8	C₃×D₁₇	—	373	1	no	maximal, Hall
9	C₃×C₁₇	—	373	1	no	Hall
10	D₁₇	C₃₇₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
11	C₁₇	C₂×C₃₇₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	6341	1	no	Hall
13	C₃	—	373	1	no	Sylow
14	C₂	—	17	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₇×C₃₇₃	C₂×C₃
LCS	G ▷ C₁₇×C₃₇₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₃₇₃⋊C₃	C₂	semidirect
2. D₁₇×C₃₇₃	C₃	semidirect
3. C₁₇×C₃₇₃	C₂×C₃	semidirect
5. C₃₇₃⋊C₃	D₁₇	direct (N × H)
7. C₃₇₃	C₃×D₁₇	semidirect
10. D₁₇	C₃₇₃⋊C₃	direct (N × H)
11. C₁₇	C₂×C₃₇₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×C₃₇₃⋊C₃	2
D₁₇×C₃₇₃	3
C₂×C₃₇₃⋊C₃	17
C₃×D₁₇	373