Finite Group Databasebeta

← C₄₁×(C₁₁⋊D₁₁)⋊C₃ #44446705

Subgroups — C₄₁×(C₁₁⋊D₁₁)⋊C₃ #44446705

Order 29766.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×C₁₁²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₁×C₁₁⋊D₁₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁²×C₄₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	D₁₁×C₄₁	—	33	4	no	—
5	(C₁₁⋊D₁₁)⋊C₃	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₄₁	—	3	4	no	—
7	C₁₁²⋊C₃	C₂×C₄₁	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×C₄₁	—	121	1	no	maximal, Hall
9	C₁₁⋊D₁₁	C₃×C₄₁	1	1	yes	characteristic, complemented, Hall
10	C₃×C₄₁	—	121	1	no	Hall
11	C₁₁²	C₂×C₃×C₄₁	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₄₁	—	121	1	no	Hall
13	C₄₁	(C₁₁⋊D₁₁)⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
14	D₁₁	—	33	4	no	—
15	C₁₁	—	3	4	no	—
16	C₂×C₃	—	121	1	no	Hall
17	C₃	—	121	1	no	Sylow
18	C₂	—	121	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₁	(C₁₁⋊D₁₁)⋊C₃
commutator, cosocle, hypocenter	C₁₁²	C₂×C₃×C₄₁
Frattini	C₁	G
Fitting, socle	C₁₁²×C₄₁	C₂×C₃
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₄₁

Complements

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

N	H ≅ G/N	type
1. C₄₁×C₁₁²⋊C₃	C₂	semidirect
2. C₄₁×C₁₁⋊D₁₁	C₃	semidirect
3. C₁₁²×C₄₁	C₂×C₃	semidirect
5. (C₁₁⋊D₁₁)⋊C₃	C₄₁	direct (N × H)
7. C₁₁²⋊C₃	C₂×C₄₁	semidirect
9. C₁₁⋊D₁₁	C₃×C₄₁	semidirect
11. C₁₁²	C₂×C₃×C₄₁	semidirect
13. C₄₁	(C₁₁⋊D₁₁)⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×C₁₁²⋊C₃	2
C₄₁×C₁₁⋊D₁₁	3
(C₁₁⋊D₁₁)⋊C₃	41
C₂×C₃×C₄₁	121