Finite Group Databasebeta

← C₂×D₅₃₆₃ #36339804

Subgroups — C₂×D₅₃₆₃ #36339804

Order 21452.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅₃₆₃	C₂	1	2	yes	maximal, direct product factor
3	C₃₁×C₁₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₇₃	—	31	1	no	maximal, Hall
5	C₂×C₁₇₃	D₃₁	1	1	yes	characteristic, complemented
6	D₁₇₃	—	31	2	no	—
7	C₁₇₃	C₂×D₃₁	1	1	yes	characteristic, complemented, Sylow
8	C₂×D₃₁	—	173	1	no	maximal, Hall
9	C₂×C₃₁	D₁₇₃	1	1	yes	characteristic, complemented
10	D₃₁	—	173	2	no	—
11	C₃₁	C₂×D₁₇₃	1	1	yes	characteristic, complemented, Sylow
12	C₂²	—	5363	1	no	Sylow
13	C₂	—	5363	2	no	—
14	C₂	D₅₃₆₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₅₃₆₃
commutator, cosocle, hypocenter	C₃₁×C₁₇₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃₁×C₁₇₃	C₂
LCS	G ▷ C₃₁×C₁₇₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×C₁₇₃	C₂	semidirect
2. D₅₃₆₃	C₂	direct (N × H)
3. C₃₁×C₁₇₃	C₂²	semidirect
5. C₂×C₁₇₃	D₃₁	semidirect
7. C₁₇₃	C₂×D₃₁	semidirect
9. C₂×C₃₁	D₁₇₃	semidirect
11. C₃₁	C₂×D₁₇₃	semidirect
14. C₂	D₅₃₆₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×C₁₇₃	2
D₅₃₆₃	2
C₂×D₁₇₃	31
C₂×D₃₁	173