Finite Group Databasebeta

Subgroups — #42123003

Order 27716.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×C₁₃⋊D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃²×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
3	#14523823	—	13	14	no	maximal
4	D₁₃×C₄₁	—	13	14	no	—
5	#10621728	—	41	1	no	maximal, Hall
6	C₁₃×C₄₁	#261	1	14	yes	complemented
7	C₁₃⋊D₁₃	D₄₁	1	1	yes	characteristic
8	C₁₃²	Dic₄₁	1	1	yes	characteristic, complemented, Sylow
9	Dic₄₁	—	169	1	no	Hall
10	C₂×C₄₁	—	169	1	no	—
11	#261	—	533	14	no	—
12	C₄₁	#10621728	1	1	yes	characteristic, complemented, Sylow
13	D₁₃	—	13	14	no	—
14	C₁₃	#14523823	1	14	yes	complemented
15	C₄	—	6929	1	no	Sylow
16	C₂	—	169	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃²×C₄₁	C₄
prime radical, cosocle	C₄₁×C₁₃⋊D₁₃	C₂
LCS	G ▷ C₁₃²×C₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₁₃²×C₄₁	C₄	semidirect
6. C₁₃×C₄₁	#261	semidirect
8. C₁₃²	Dic₄₁	semidirect
12. C₄₁	#10621728	semidirect
14. C₁₃	#14523823	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×C₁₃⋊D₁₃	2
#14523823	13
#10621728	41