Subgroups — C₃⋊D₂₁×C₁₂₇ #30630736

Order 16002.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₁×C₁₂₇	—	3	4	no	maximal
3	C₃×C₇×C₁₂₇	D₃	1	4	yes	complemented
4	C₃⋊D₃×C₁₂₇	—	7	1	no	maximal, Hall
5	D₇×C₁₂₇	—	9	1	no	Hall
6	C₃²×C₁₂₇	D₇	1	1	yes	characteristic, complemented, Hall
7	C₇×C₁₂₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
8	D₃×C₁₂₇	—	21	4	no	—
9	C₃×C₁₂₇	D₂₁	1	4	yes	complemented
10	C₂×C₁₂₇	—	63	1	no	Hall
11	C₁₂₇	C₃⋊D₂₁	1	1	yes	characteristic, direct product factor, Sylow
12	C₃⋊D₂₁	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃²×C₇	C₂×C₁₂₇	1	1	yes	characteristic, complemented, Hall
14	D₂₁	—	3	4	no	—
15	C₃×C₇	D₃×C₁₂₇	1	4	yes	complemented
16	C₃⋊D₃	—	7	1	no	Hall
17	D₇	—	9	1	no	Hall
18	C₃²	D₇×C₁₂₇	1	1	yes	characteristic, complemented, Sylow
19	C₇	C₃⋊D₃×C₁₂₇	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	21	4	no	—
21	C₃	D₂₁×C₁₂₇	1	4	yes	complemented
22	C₂	—	63	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₂₇	C₃⋊D₂₁
commutator, cosocle, hypocenter	C₃²×C₇	C₂×C₁₂₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₂₇	C₂
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₁₂₇

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.