Subgroups — C₁₁×Dic₇₂₁ #44540571

Order 31724.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₁×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₁×C₁₀₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×Dic₁₀₃	—	7	1	no	maximal, Hall
4	Dic₇₂₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₁×C₁₀₃	D₇	1	1	yes	characteristic
6	C₂×C₇×C₁₀₃	C₂×C₁₁	1	1	yes	characteristic
7	C₁₁×C₁₀₃	Dic₇	1	1	yes	characteristic, complemented, Hall
8	C₇×C₁₀₃	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
9	Dic₁₀₃	—	7	1	no	Hall
10	C₁₁×Dic₇	—	103	1	no	maximal, Hall
11	C₂×C₁₀₃	C₁₁×D₇	1	1	yes	characteristic
12	C₂×C₇×C₁₁	D₁₀₃	1	1	yes	characteristic
13	C₁₀₃	C₁₁×Dic₇	1	1	yes	characteristic, complemented, Sylow
14	C₇×C₁₁	Dic₁₀₃	1	1	yes	characteristic, complemented, Hall
15	C₄×C₁₁	—	721	1	no	Hall
16	Dic₇	—	103	1	no	Hall
17	C₂×C₁₁	D₇₂₁	1	1	yes	characteristic
18	C₂×C₇	C₁₁×D₁₀₃	1	1	yes	characteristic
19	C₁₁	Dic₇₂₁	1	1	yes	characteristic, direct product factor, Sylow
20	C₇	C₁₁×Dic₁₀₃	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	721	1	no	Sylow
22	C₂	C₁₁×D₇₂₁	1	1	yes	characteristic

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.