Subgroups — C₇×C₁₁×Dic₇₁ #36346113

Order 21868.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₁×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₁×C₇₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×Dic₇₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×Dic₇₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₁×C₇₁	C₂×C₇	1	1	yes	characteristic
6	C₂×C₇×C₇₁	C₂×C₁₁	1	1	yes	characteristic
7	C₁₁×C₇₁	C₄×C₇	1	1	yes	characteristic, complemented, Hall
8	C₇×C₇₁	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₄×C₇×C₁₁	—	71	1	no	maximal, Hall
10	Dic₇₁	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₇×C₁₁	D₇₁	1	1	yes	characteristic
12	C₂×C₇₁	C₂×C₇×C₁₁	1	1	yes	characteristic
13	C₇×C₁₁	Dic₇₁	1	1	yes	characteristic, direct product factor, Hall
14	C₇₁	C₄×C₇×C₁₁	1	1	yes	characteristic, complemented, Sylow
15	C₄×C₁₁	—	71	1	no	Hall
16	C₄×C₇	—	71	1	no	Hall
17	C₂×C₁₁	C₇×D₇₁	1	1	yes	characteristic
18	C₂×C₇	C₁₁×D₇₁	1	1	yes	characteristic
19	C₁₁	C₇×Dic₇₁	1	1	yes	characteristic, direct product factor, Sylow
20	C₇	C₁₁×Dic₇₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	71	1	no	Sylow
22	C₂	C₇×C₁₁×D₇₁	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.