Finite Group Databasebeta

← D₁₄₉₁₁ #44447299

Subgroups — D₁₄₉₁₁ #44447299

Order 29822.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃₁×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₁₄₇	—	13	1	no	maximal, Hall
3	C₃₁×C₃₇	D₁₃	1	1	yes	characteristic, complemented, Hall
4	D₄₈₁	—	31	1	no	maximal, Hall
5	D₄₀₃	—	37	1	no	maximal, Hall
6	C₁₃×C₃₇	D₃₁	1	1	yes	characteristic, complemented, Hall
7	C₁₃×C₃₁	D₃₇	1	1	yes	characteristic, complemented, Hall
8	D₃₇	—	403	1	no	Hall
9	D₃₁	—	481	1	no	Hall
10	C₃₇	D₄₀₃	1	1	yes	characteristic, complemented, Sylow
11	C₃₁	D₄₈₁	1	1	yes	characteristic, complemented, Sylow
12	D₁₃	—	1147	1	no	Hall
13	C₁₃	D₁₁₄₇	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	14911	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₃₁×C₃₇	C₂
LCS	G ▷ C₁₃×C₃₁×C₃₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃₁×C₃₇	C₂	semidirect
3. C₃₁×C₃₇	D₁₃	semidirect
6. C₁₃×C₃₇	D₃₁	semidirect
7. C₁₃×C₃₁	D₃₇	semidirect
10. C₃₇	D₄₀₃	semidirect
11. C₃₁	D₄₈₁	semidirect
13. C₁₃	D₁₁₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×C₃₁×C₃₇	2
D₁₁₄₇	13
D₄₈₁	31
D₄₀₃	37