Subgroups — C₁₂₁⋊(D₄₃⋊C₃) #44530196

Order 31218.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₂₁×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₂₀₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₄₃×C₁₂₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₁₁⋊(D₄₃⋊C₃)	—	11	1	no	maximal
5	C₁₁×C₄₃⋊C₃	D₁₁	1	1	yes	characteristic
6	D₄₇₃	—	11	1	no	—
7	C₃×D₁₂₁	—	43	1	no	maximal, Hall
8	C₁₁×C₄₃	C₃×D₁₁	1	1	yes	characteristic
9	C₃×C₁₂₁	—	43	1	no	Hall
10	D₄₃⋊C₃	—	121	1	no	Hall
11	D₁₂₁	—	43	1	no	Hall
12	C₄₃⋊C₃	D₁₂₁	1	1	yes	characteristic, complemented, Hall
13	C₁₂₁	D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
14	D₄₃	—	121	1	no	Hall
15	C₃×D₁₁	—	473	1	no	—
16	C₄₃	C₃×D₁₂₁	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₁₁	—	43	1	no	—
18	D₁₁	—	473	1	no	—
19	C₁₁	C₁₁⋊(D₄₃⋊C₃)	1	1	yes	characteristic
20	C₂×C₃	—	5203	1	no	Hall
21	C₃	—	43	1	no	Sylow
22	C₂	—	5203	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₄₃×C₁₂₁	C₂×C₃
Frattini	C₁₁	C₁₁⋊(D₄₃⋊C₃)
socle	C₁₁×C₄₃	C₃×D₁₁
LCS	G ▷ C₄₃×C₁₂₁
UCS	C₁

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

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