Subgroups — #16813721

Order 3616.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14268659	C₂	1	1	yes	maximal, characteristic
2	#11744753	C₄	1	1	yes	characteristic
3	Dic₁₁₃	C₈	1	1	yes	characteristic
4	C₂×C₁₁₃	C₁₆	1	1	yes	characteristic
5	C₁₁₃	C₃₂	1	1	yes	characteristic, complemented, Sylow
6	C₃₂	—	113	1	no	maximal, Sylow
7	C₁₆	—	113	1	no	—
8	C₈	—	113	1	no	—
9	C₄	—	113	1	no	—
10	C₂	#14268661	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#14268661
commutator, hypocenter	C₁₁₃	C₃₂
Fitting, socle, prime radical	C₂×C₁₁₃	C₁₆
cosocle	#14268659	C₂
LCS	G ▷ C₁₁₃
UCS	C₁ ◁ C₂

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

N	H ≅ G/N	type
5. C₁₁₃	C₃₂	semidirect

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

subgroup	index
#14268659	2
C₃₂	113