Subgroups — C₄₃×D₃₆₃ #44530192

Order 31218.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₃×C₁₂₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₃×D₁₂₁	—	3	1	no	maximal, Hall
3	C₄₃×C₁₂₁	D₃	1	1	yes	characteristic, complemented, Hall
4	C₄₃×D₃₃	—	11	1	no	maximal
5	C₃×C₁₁×C₄₃	D₁₁	1	1	yes	characteristic
6	D₁₁×C₄₃	—	33	1	no	—
7	D₃₆₃	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₁×C₄₃	D₃₃	1	1	yes	characteristic
9	C₃×C₁₂₁	C₂×C₄₃	1	1	yes	characteristic, complemented, Hall
10	D₃×C₄₃	—	121	1	no	Hall
11	D₁₂₁	—	3	1	no	Hall
12	C₃×C₄₃	D₁₂₁	1	1	yes	characteristic, complemented, Hall
13	C₁₂₁	D₃×C₄₃	1	1	yes	characteristic, complemented, Sylow
14	C₂×C₄₃	—	363	1	no	Hall
15	D₃₃	—	11	1	no	—
16	C₄₃	D₃₆₃	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₁₁	D₁₁×C₄₃	1	1	yes	characteristic
18	D₁₁	—	33	1	no	—
19	C₁₁	C₄₃×D₃₃	1	1	yes	characteristic
20	D₃	—	121	1	no	Hall
21	C₃	C₄₃×D₁₂₁	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	363	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₃	D₃₆₃
commutator, cosocle, hypocenter	C₃×C₁₂₁	C₂×C₄₃
Frattini	C₁₁	C₄₃×D₃₃
Fitting	C₃×C₄₃×C₁₂₁	C₂
socle	C₃×C₁₁×C₄₃	D₁₁
LCS	G ▷ C₃×C₁₂₁
UCS	C₁ ◁ C₄₃

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.