Finite Group Databasebeta

Subgroups — #38788845

Order 25818.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27166531	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₄₃₀₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃×C₃₃₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	D₃₃₁⋊C₃	—	13	1	no	maximal, Hall
5	C₃₃₁⋊C₃	—	13	1	no	Hall
6	D₃₃₁	—	13	1	no	Hall
7	C₃₃₁	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
8	D₁₃⋊C₃	—	331	1	no	maximal, Hall
9	C₁₃⋊C₃	—	331	1	no	Hall
10	D₁₃	—	331	1	no	Hall
11	C₁₃	D₃₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	4303	1	no	Hall
13	C₃	—	4303	1	no	Sylow
14	C₂	—	4303	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₃₃₁	C₂×C₃
LCS	G ▷ C₁₃×C₃₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #27166531	C₂	semidirect
2. D₄₃₀₃	C₃	semidirect
3. C₁₃×C₃₃₁	C₂×C₃	semidirect
7. C₃₃₁	D₁₃⋊C₃	semidirect
11. C₁₃	D₃₃₁⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#27166531	2
D₄₃₀₃	3
D₃₃₁⋊C₃	13
D₁₃⋊C₃	331