Subgroups — D₁₁×C₁₀₃⋊C₉ #35205170

Order 20394.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₀₃⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₁×C₁₀₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₁×C₁₀₃	C₂×C₃	1	1	yes	characteristic
4	D₁₁×C₁₀₃	C₉	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₀₃⋊C₉	—	11	1	no	maximal, Hall
6	C₁₁×C₁₀₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
7	C₁₀₃⋊C₉	D₁₁	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃×C₁₀₃	—	11	1	no	—
9	C₃×C₁₀₃	C₃×D₁₁	1	1	yes	characteristic
10	C₂×C₁₀₃	—	11	1	no	Hall
11	C₉×D₁₁	—	103	1	no	maximal, Hall
12	C₁₀₃	C₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
13	C₉×C₁₁	—	103	1	no	Hall
14	C₃×D₁₁	C₁₀₃⋊C₃	1	1	yes	characteristic
15	C₃×C₁₁	C₂×C₁₀₃⋊C₃	1	1	yes	characteristic
16	D₁₁	C₁₀₃⋊C₉	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₉	—	1133	1	no	Hall
18	C₁₁	C₂×C₁₀₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
19	C₉	—	103	1	no	Sylow
20	C₂×C₃	—	11	1	no	—
21	C₃	D₁₁×C₁₀₃⋊C₃	1	1	yes	characteristic
22	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₁₁×C₁₀₃⋊C₃
commutator, hypocenter	C₁₁×C₁₀₃	C₂×C₉
Fitting, socle, cosocle	C₃×C₁₁×C₁₀₃	C₂×C₃
prime radical	C₃×D₁₁×C₁₀₃	C₃
LCS	G ▷ C₁₁×C₁₀₃
UCS	C₁ ◁ C₃

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.