Subgroups — D₆₃×C₁₂₇ #30630656

Order 16002.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₁×C₁₂₇	—	3	1	no	maximal
3	C₃×C₇×C₁₂₇	D₃	1	1	yes	characteristic
4	D₉×C₁₂₇	—	7	1	no	maximal, Hall
5	D₇×C₁₂₇	—	9	1	no	Hall
6	C₉×C₁₂₇	D₇	1	1	yes	characteristic, complemented, Hall
7	C₇×C₁₂₇	D₉	1	1	yes	characteristic, complemented, Hall
8	D₃×C₁₂₇	—	21	1	no	—
9	C₃×C₁₂₇	D₂₁	1	1	yes	characteristic
10	C₂×C₁₂₇	—	63	1	no	Hall
11	C₁₂₇	D₆₃	1	1	yes	characteristic, direct product factor, Sylow
12	D₆₃	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₇×C₉	C₂×C₁₂₇	1	1	yes	characteristic, complemented, Hall
14	D₂₁	—	3	1	no	—
15	C₃×C₇	D₃×C₁₂₇	1	1	yes	characteristic
16	D₉	—	7	1	no	Hall
17	D₇	—	9	1	no	Hall
18	C₉	D₇×C₁₂₇	1	1	yes	characteristic, complemented, Sylow
19	C₇	D₉×C₁₂₇	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	21	1	no	—
21	C₃	D₂₁×C₁₂₇	1	1	yes	characteristic
22	C₂	—	63	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₂₇	D₆₃
commutator, cosocle, hypocenter	C₇×C₉	C₂×C₁₂₇
Frattini	C₃	D₂₁×C₁₂₇
Fitting	C₇×C₉×C₁₂₇	C₂
socle	C₃×C₇×C₁₂₇	D₃
LCS	G ▷ C₇×C₉
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.