Subgroups — C₁₁×(C₁₂₇⋊C₃)⋊C₄ #30660918

Order 16764.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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