Subgroups — C₁₂₇×Dic₃₃ #30660916

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	Dic₁₁×C₁₂₇	—	3	1	no	maximal, Hall
3	C₃×C₁₁×C₁₂₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×C₁₂₇	D₃	1	1	yes	characteristic
5	Dic₃×C₁₂₇	—	11	1	no	maximal, Hall
6	C₁₁×C₁₂₇	Dic₃	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₂₇	D₁₁	1	1	yes	characteristic
8	C₄×C₁₂₇	—	33	1	no	Hall
9	C₃×C₁₂₇	Dic₁₁	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₂₇	D₃₃	1	1	yes	characteristic
11	Dic₃₃	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₂₇	Dic₃₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₃×C₁₁	C₂×C₁₂₇	1	1	yes	characteristic
14	Dic₁₁	—	3	1	no	Hall
15	C₃×C₁₁	C₄×C₁₂₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₁	D₃×C₁₂₇	1	1	yes	characteristic
17	Dic₃	—	11	1	no	Hall
18	C₁₁	Dic₃×C₁₂₇	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	D₁₁×C₁₂₇	1	1	yes	characteristic
20	C₄	—	33	1	no	Sylow
21	C₃	Dic₁₁×C₁₂₇	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₃₃×C₁₂₇	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.