Subgroups — Dic₂₁×C₁₃₁ #24926992

Order 11004.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	Dic₇×C₁₃₁	—	3	1	no	maximal, Hall
3	C₃×C₇×C₁₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₃₁	D₃	1	1	yes	characteristic
5	Dic₃×C₁₃₁	—	7	1	no	maximal, Hall
6	C₇×C₁₃₁	Dic₃	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₃₁	D₇	1	1	yes	characteristic
8	C₄×C₁₃₁	—	21	1	no	Hall
9	C₃×C₁₃₁	Dic₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₃₁	D₂₁	1	1	yes	characteristic
11	C₁₃₁	Dic₂₁	1	1	yes	characteristic, direct product factor, Sylow
12	Dic₂₁	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₇	C₂×C₁₃₁	1	1	yes	characteristic
14	Dic₇	—	3	1	no	Hall
15	C₃×C₇	C₄×C₁₃₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇	D₃×C₁₃₁	1	1	yes	characteristic
17	Dic₃	—	7	1	no	Hall
18	C₇	Dic₃×C₁₃₁	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	D₇×C₁₃₁	1	1	yes	characteristic
20	C₄	—	21	1	no	Sylow
21	C₃	Dic₇×C₁₃₁	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₂₁×C₁₃₁	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.