Finite Group Databasebeta

Subgroups — #46798331

Order 33774.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30683267	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₆₂₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃×C₄₃₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	D₄₃₃⋊C₃	—	13	1	no	maximal, Hall
5	C₄₃₃⋊C₃	—	13	1	no	Hall
6	D₄₃₃	—	13	1	no	Hall
7	C₄₃₃	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
8	D₁₃⋊C₃	—	433	1	no	maximal, Hall
9	C₁₃⋊C₃	—	433	1	no	Hall
10	D₁₃	—	433	1	no	Hall
11	C₁₃	D₄₃₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	5629	1	no	Hall
13	C₃	—	5629	1	no	Sylow
14	C₂	—	5629	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₄₃₃	C₂×C₃
LCS	G ▷ C₁₃×C₄₃₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #30683267	C₂	semidirect
2. D₅₆₂₉	C₃	semidirect
3. C₁₃×C₄₃₃	C₂×C₃	semidirect
7. C₄₃₃	D₁₃⋊C₃	semidirect
11. C₁₃	D₄₃₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#30683267	2
D₅₆₂₉	3
D₄₃₃⋊C₃	13
D₁₃⋊C₃	433