Subgroups — C₇×C₁₁×Dic₁₀₁ #44527400

Order 31108.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₁×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₁×C₁₀₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×Dic₁₀₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×Dic₁₀₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₁×C₁₀₁	C₂×C₇	1	1	yes	characteristic
6	C₂×C₇×C₁₀₁	C₂×C₁₁	1	1	yes	characteristic
7	C₁₁×C₁₀₁	C₄×C₇	1	1	yes	characteristic, complemented, Hall
8	C₇×C₁₀₁	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
9	Dic₁₀₁	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
10	C₄×C₇×C₁₁	—	101	1	no	maximal, Hall
11	C₂×C₁₀₁	C₂×C₇×C₁₁	1	1	yes	characteristic
12	C₂×C₇×C₁₁	D₁₀₁	1	1	yes	characteristic
13	C₁₀₁	C₄×C₇×C₁₁	1	1	yes	characteristic, complemented, Sylow
14	C₇×C₁₁	Dic₁₀₁	1	1	yes	characteristic, direct product factor, Hall
15	C₄×C₁₁	—	101	1	no	Hall
16	C₄×C₇	—	101	1	no	Hall
17	C₂×C₁₁	C₇×D₁₀₁	1	1	yes	characteristic
18	C₂×C₇	C₁₁×D₁₀₁	1	1	yes	characteristic
19	C₁₁	C₇×Dic₁₀₁	1	1	yes	characteristic, direct product factor, Sylow
20	C₇	C₁₁×Dic₁₀₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	101	1	no	Sylow
22	C₂	C₇×C₁₁×D₁₀₁	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.