Subgroups — C₃×Dic₁₃₉₇ #30660913

Order 16764.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₁×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	Dic₁₃₉₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₁×C₁₂₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×C₁₂₇	C₂×C₃	1	1	yes	characteristic
5	C₃×Dic₁₂₇	—	11	1	no	maximal, Hall
6	C₁₁×C₁₂₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₂₇	D₁₁	1	1	yes	characteristic
8	Dic₁₂₇	—	11	1	no	Hall
9	C₃×C₁₂₇	Dic₁₁	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₂₇	C₃×D₁₁	1	1	yes	characteristic
11	C₃×Dic₁₁	—	127	1	no	maximal, Hall
12	C₁₂₇	C₃×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₃×C₁₁	D₁₂₇	1	1	yes	characteristic
14	Dic₁₁	—	127	1	no	Hall
15	C₃×C₁₁	Dic₁₂₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₁	C₃×D₁₂₇	1	1	yes	characteristic
17	C₃×C₄	—	1397	1	no	Hall
18	C₁₁	C₃×Dic₁₂₇	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	D₁₃₉₇	1	1	yes	characteristic
20	C₄	—	1397	1	no	Sylow
21	C₃	Dic₁₃₉₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×D₁₃₉₇	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.