Subgroups — #16813672

Order 3616.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14268622	C₂	1	1	yes	maximal, characteristic
2	C₈×C₁₁₃	C₄	1	1	yes	characteristic
3	C₄×C₁₁₃	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	#90673	1	1	yes	characteristic
9	C₄	#11744753	1	1	yes	characteristic
10	C₂	#14268650	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₈	#90673
commutator, hypocenter	C₁₁₃	C₃₂
Fitting	C₈×C₁₁₃	C₄
socle, prime radical	C₂×C₁₁₃	C₁₆
cosocle	#14268622	C₂
LCS	G ▷ C₁₁₃
UCS	C₁ ◁ C₈

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
#14268622	2
C₃₂	113