Finite Group Databasebeta

Subgroups — #38787196

Order 25664.

14 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27165787	C₂	1	1	yes	maximal, characteristic
2	#20264341	C₄	1	1	yes	characteristic
3	C₈×C₄₀₁	C₈	1	1	yes	characteristic
4	C₄×C₄₀₁	C₁₆	1	1	yes	characteristic
5	C₂×C₄₀₁	C₃₂	1	1	yes	characteristic
6	C₄₀₁	C₆₄	1	1	yes	characteristic, complemented, Sylow
7	C₆₄	—	401	1	no	maximal, Sylow
8	C₃₂	—	401	1	no	—
9	C₁₆	—	401	1	no	—
10	C₈	#15692008	1	1	yes	characteristic
11	C₄	#20264378	1	1	yes	characteristic
12	C₂	#27165827	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₈	#15692008
commutator, hypocenter	C₄₀₁	C₆₄
Fitting	C₈×C₄₀₁	C₈
socle, prime radical	C₂×C₄₀₁	C₃₂
cosocle	#27165787	C₂
LCS	G ▷ C₄₀₁
UCS	C₁ ◁ C₈

Complements

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

N	H ≅ G/N	type
6. C₄₀₁	C₆₄	semidirect

Maximal subgroups

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

subgroup	index
#27165787	2
C₆₄	401