Finite Group Databasebeta

Subgroups — #39910329

Order 26176.

14 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27189767	C₂	1	1	yes	maximal, characteristic
2	#20266963	C₄	1	1	yes	characteristic
3	C₈×C₄₀₉	C₈	1	1	yes	characteristic
4	C₄×C₄₀₉	C₁₆	1	1	yes	characteristic
5	C₂×C₄₀₉	C₃₂	1	1	yes	characteristic
6	C₄₀₉	C₆₄	1	1	yes	characteristic, complemented, Sylow
7	C₆₄	—	409	1	no	maximal, Sylow
8	C₃₂	—	409	1	no	—
9	C₁₆	—	409	1	no	—
10	C₈	#15692552	1	1	yes	characteristic
11	C₄	#20267000	1	1	yes	characteristic
12	C₂	#27189807	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₈	#15692552
commutator, hypocenter	C₄₀₉	C₆₄
Fitting	C₈×C₄₀₉	C₈
socle, prime radical	C₂×C₄₀₉	C₃₂
cosocle	#27189767	C₂
LCS	G ▷ C₄₀₉
UCS	C₁ ◁ C₈

Complements

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

N	H ≅ G/N	type
6. C₄₀₉	C₆₄	semidirect

Maximal subgroups

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

subgroup	index
#27189767	2
C₆₄	409