Subgroups — #36378920

Order 22592.

14 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26015091	C₂	1	1	yes	maximal, characteristic
2	#19150749	C₄	1	1	yes	characteristic
3	#15667732	C₈	1	1	yes	characteristic
4	Dic₃₅₃	C₁₆	1	1	yes	characteristic
5	C₂×C₃₅₃	C₃₂	1	1	yes	characteristic
6	C₃₅₃	C₆₄	1	1	yes	characteristic, complemented, Sylow
7	C₆₄	—	353	1	no	maximal, Sylow
8	C₃₂	—	353	1	no	—
9	C₁₆	—	353	1	no	—
10	C₈	—	353	1	no	—
11	C₄	—	353	1	no	—
12	C₂	#26015093	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#26015093
commutator, hypocenter	C₃₅₃	C₆₄
Fitting, socle, prime radical	C₂×C₃₅₃	C₃₂
cosocle	#26015091	C₂
LCS	G ▷ C₃₅₃
UCS	C₁ ◁ C₂

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

N	H ≅ G/N	type
6. C₃₅₃	C₆₄	semidirect

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

subgroup	index
#26015091	2
C₆₄	353