Subgroups — C₇×Dic₁₂₆₁ #47977181

Order 35308.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₃×C₉₇	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₃×C₉₇	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₂₆₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×Dic₉₇	—	13	1	no	maximal, Hall
5	C₂×C₁₃×C₉₇	C₂×C₇	1	1	yes	characteristic
6	C₂×C₇×C₉₇	D₁₃	1	1	yes	characteristic
7	C₁₃×C₉₇	C₄×C₇	1	1	yes	characteristic, complemented, Hall
8	C₇×C₉₇	Dic₁₃	1	1	yes	characteristic, complemented, Hall
9	Dic₉₇	—	13	1	no	Hall
10	C₇×Dic₁₃	—	97	1	no	maximal, Hall
11	C₂×C₉₇	C₇×D₁₃	1	1	yes	characteristic
12	C₂×C₇×C₁₃	D₉₇	1	1	yes	characteristic
13	C₉₇	C₇×Dic₁₃	1	1	yes	characteristic, complemented, Sylow
14	C₇×C₁₃	Dic₉₇	1	1	yes	characteristic, complemented, Hall
15	Dic₁₃	—	97	1	no	Hall
16	C₄×C₇	—	1261	1	no	Hall
17	C₂×C₁₃	C₇×D₉₇	1	1	yes	characteristic
18	C₂×C₇	D₁₂₆₁	1	1	yes	characteristic
19	C₁₃	C₇×Dic₉₇	1	1	yes	characteristic, complemented, Sylow
20	C₇	Dic₁₂₆₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	1261	1	no	Sylow
22	C₂	C₇×D₁₂₆₁	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.