Finite Group Databasebeta

← C₂×D₄₇×C₁₇₃ #45654205

Subgroups — C₂×D₄₇×C₁₇₃ #45654205

Order 32524.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄₇×C₁₇₃	C₂	1	2	yes	maximal, direct product factor
3	C₄₇×C₁₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂²×C₁₇₃	—	47	1	no	maximal, Hall
5	C₂×C₁₇₃	—	47	2	no	—
6	C₂×C₁₇₃	D₄₇	1	1	yes	characteristic, direct product factor
7	C₂×D₄₇	C₁₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇₃	C₂×D₄₇	1	1	yes	characteristic, direct product factor, Sylow
9	C₂×C₄₇	C₂×C₁₇₃	1	1	yes	characteristic, complemented
10	D₄₇	C₂×C₁₇₃	1	2	yes	direct product factor
11	C₄₇	C₂²×C₁₇₃	1	1	yes	characteristic, complemented, Sylow
12	C₂²	—	47	1	no	Sylow
13	C₂	—	47	2	no	—
14	C₂	D₄₇×C₁₇₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇₃	D₄₇
commutator, cosocle, hypocenter	C₄₇	C₂²×C₁₇₃
Frattini	C₁	G
Fitting, socle	C₂×C₄₇×C₁₇₃	C₂
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₂×C₁₇₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₇×C₁₇₃	C₂	semidirect
2. D₄₇×C₁₇₃	C₂	direct (N × H)
3. C₄₇×C₁₇₃	C₂²	semidirect
6. C₂×C₁₇₃	D₄₇	direct (N × H)
7. C₂×D₄₇	C₁₇₃	direct (N × H)
8. C₁₇₃	C₂×D₄₇	direct (N × H)
9. C₂×C₄₇	C₂×C₁₇₃	semidirect
10. D₄₇	C₂×C₁₇₃	direct (N × H)
11. C₄₇	C₂²×C₁₇₃	semidirect
14. C₂	D₄₇×C₁₇₃	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×C₄₇×C₁₇₃	2
D₄₇×C₁₇₃	2
C₂²×C₁₇₃	47
C₂×D₄₇	173