Subgroups — #27159434

Order 12448.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20261941	C₂	1	1	yes	maximal, characteristic
2	C₈×C₃₈₉	C₄	1	1	yes	characteristic
3	C₄×C₃₈₉	C₈	1	1	yes	characteristic
4	C₂×C₃₈₉	C₁₆	1	1	yes	characteristic
5	C₃₈₉	C₃₂	1	1	yes	characteristic, complemented, Sylow
6	C₃₂	—	389	1	no	maximal, Sylow
7	C₁₆	—	389	1	no	—
8	C₈	#13095555	1	1	yes	characteristic
9	C₄	#15691012	1	1	yes	characteristic
10	C₂	#20261969	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₈	#13095555
commutator, hypocenter	C₃₈₉	C₃₂
Fitting	C₈×C₃₈₉	C₄
socle, prime radical	C₂×C₃₈₉	C₁₆
cosocle	#20261941	C₂
LCS	G ▷ C₃₈₉
UCS	C₁ ◁ C₈

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

N	H ≅ G/N	type
5. C₃₈₉	C₃₂	semidirect

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

subgroup	index
#20261941	2
C₃₂	389