Finite Group Databasebeta

← C₂×C₄₃×C₁₁²⋊C₃ #44530211

Subgroups — C₂×C₄₃×C₁₁²⋊C₃ #44530211

Order 31218.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×C₁₁²⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₁²×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁²×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×C₄₃	—	3	4	no	—
5	C₂×C₁₁²⋊C₃	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₄₃	—	3	4	no	—
7	C₁₁²⋊C₃	C₂×C₄₃	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃×C₄₃	—	121	1	no	maximal, Hall
9	C₂×C₁₁²	C₃×C₄₃	1	1	yes	characteristic, complemented, Hall
10	C₃×C₄₃	—	121	1	no	Hall
11	C₁₁²	C₂×C₃×C₄₃	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₄₃	C₁₁²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
13	C₄₃	C₂×C₁₁²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂×C₁₁	—	3	4	no	—
15	C₁₁	—	3	4	no	—
16	C₂×C₃	—	121	1	no	Hall
17	C₃	—	121	1	no	Sylow
18	C₂	C₄₃×C₁₁²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₄₃	C₁₁²⋊C₃
commutator, cosocle, hypocenter	C₁₁²	C₂×C₃×C₄₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₁²×C₄₃	C₃
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₂×C₄₃

Complements

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

N	H ≅ G/N	type
1. C₄₃×C₁₁²⋊C₃	C₂	direct (N × H)
2. C₂×C₁₁²×C₄₃	C₃	semidirect
3. C₁₁²×C₄₃	C₂×C₃	semidirect
5. C₂×C₁₁²⋊C₃	C₄₃	direct (N × H)
7. C₁₁²⋊C₃	C₂×C₄₃	direct (N × H)
9. C₂×C₁₁²	C₃×C₄₃	semidirect
11. C₁₁²	C₂×C₃×C₄₃	semidirect
12. C₂×C₄₃	C₁₁²⋊C₃	direct (N × H)
13. C₄₃	C₂×C₁₁²⋊C₃	direct (N × H)
18. C₂	C₄₃×C₁₁²⋊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
C₄₃×C₁₁²⋊C₃	2
C₂×C₁₁²×C₄₃	3
C₂×C₁₁²⋊C₃	43
C₂×C₃×C₄₃	121