Finite Group Databasebeta

← C₂×#19129087 #24924625

Subgroups — C₂×#19129087 #24924625

Order 10768.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19129087	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₄×C₆₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₆₇₃	C₄	1	1	yes	characteristic
4	C₄×C₆₇₃	C₄	1	1	yes	characteristic
5	C₄×C₆₇₃	C₂²	1	1	yes	characteristic
6	C₂×C₆₇₃	C₈	1	2	yes	complemented
7	C₂×C₆₇₃	C₂×C₄	1	1	yes	characteristic
8	C₆₇₃	C₂×C₈	1	1	yes	characteristic, complemented, Sylow
9	C₂×C₈	—	673	1	no	maximal, Sylow
10	C₂×C₄	D₆₇₃	1	1	yes	characteristic
11	C₈	—	673	2	no	—
12	C₂²	Dic₆₇₃	1	1	yes	characteristic
13	C₄	Dic₆₇₃	1	1	yes	characteristic
14	C₄	C₂×D₆₇₃	1	1	yes	characteristic
15	C₂	#19129087	1	2	yes	direct product factor
16	C₂	C₂×Dic₆₇₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	D₆₇₃
commutator, hypocenter	C₆₇₃	C₂×C₈
Frattini	C₄	C₂×D₆₇₃
Fitting	C₂×C₄×C₆₇₃	C₂
socle, prime radical	C₂²×C₆₇₃	C₄
cosocle	C₄×C₆₇₃	C₂²
LCS	G ▷ C₆₇₃
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. #19129087	C₂	direct (N × H)
6. C₂×C₆₇₃	C₈	semidirect
8. C₆₇₃	C₂×C₈	semidirect
15. C₂	#19129087	direct (N × H)