Subgroups — C₇×C₁₁×Dic₁₁₃ #46852425

Order 34804.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₁×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₁×C₁₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×Dic₁₁₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×Dic₁₁₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₁×C₁₁₃	C₂×C₇	1	1	yes	characteristic
6	C₂×C₇×C₁₁₃	C₂×C₁₁	1	1	yes	characteristic
7	C₁₁×C₁₁₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
8	C₇×C₁₁₃	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
9	Dic₁₁₃	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
10	C₄×C₇×C₁₁	—	113	1	no	maximal, Hall
11	C₂×C₁₁₃	C₂×C₇×C₁₁	1	1	yes	characteristic
12	C₂×C₇×C₁₁	D₁₁₃	1	1	yes	characteristic
13	C₁₁₃	C₄×C₇×C₁₁	1	1	yes	characteristic, complemented, Sylow
14	C₇×C₁₁	Dic₁₁₃	1	1	yes	characteristic, direct product factor, Hall
15	C₄×C₁₁	—	113	1	no	Hall
16	C₄×C₇	—	113	1	no	Hall
17	C₂×C₁₁	C₇×D₁₁₃	1	1	yes	characteristic
18	C₂×C₇	C₁₁×D₁₁₃	1	1	yes	characteristic
19	C₁₁	C₇×Dic₁₁₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₇	C₁₁×Dic₁₁₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	113	1	no	Sylow
22	C₂	C₇×C₁₁×D₁₁₃	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.