Subgroups — #39905889

Order 25888.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27188246	C₂	1	1	yes	maximal, characteristic
2	#20266436	C₄	1	1	yes	characteristic
3	C₄×C₈₀₉	C₈	1	1	yes	characteristic
4	C₂×C₈₀₉	C₁₆	1	1	yes	characteristic
5	C₈₀₉	C₃₂	1	1	yes	characteristic, complemented, Sylow
6	C₃₂	—	809	1	no	maximal, Sylow
7	C₁₆	—	809	1	no	—
8	C₈	—	809	1	no	—
9	C₄	#20266445	1	1	yes	characteristic
10	C₂	#27188255	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	#20266445
commutator, hypocenter	C₈₀₉	C₃₂
Fitting	C₄×C₈₀₉	C₈
socle, prime radical	C₂×C₈₀₉	C₁₆
cosocle	#27188246	C₂
LCS	G ▷ C₈₀₉
UCS	C₁ ◁ C₄

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

N	H ≅ G/N	type
5. C₈₀₉	C₃₂	semidirect

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

subgroup	index
#27188246	2
C₃₂	809