Finite Group Databasebeta

← C₁₇²×C₃₁⋊C₃ #41001853

Subgroups — C₁₇²×C₃₁⋊C₃ #41001853

Order 26877.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇²×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×C₃₁⋊C₃	C₁₇	1	18	yes	maximal, direct product factor
3	C₃×C₁₇²	—	31	1	no	maximal, Hall
4	C₁₇×C₃₁	C₃×C₁₇	1	18	yes	complemented
5	C₁₇²	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₃₁⋊C₃	C₁₇²	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₁₇	—	31	18	no	—
8	C₃₁	C₃×C₁₇²	1	1	yes	characteristic, complemented, Sylow
9	C₁₇	C₁₇×C₃₁⋊C₃	1	18	yes	direct product factor
10	C₃	—	31	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇²	C₃₁⋊C₃
commutator, cosocle, hypocenter	C₃₁	C₃×C₁₇²
Frattini	C₁	G
Fitting, socle	C₁₇²×C₃₁	C₃
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₁₇²

Complements

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

N	H ≅ G/N	type
1. C₁₇²×C₃₁	C₃	semidirect
2. C₁₇×C₃₁⋊C₃	C₁₇	direct (N × H)
4. C₁₇×C₃₁	C₃×C₁₇	semidirect
5. C₁₇²	C₃₁⋊C₃	direct (N × H)
6. C₃₁⋊C₃	C₁₇²	direct (N × H)
8. C₃₁	C₃×C₁₇²	semidirect
9. C₁₇	C₁₇×C₃₁⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇²×C₃₁	3
C₁₇×C₃₁⋊C₃	17
C₃×C₁₇²	31