Subgroups — C₁₂₇×C₃⋊D₃₉ #44446146

Order 29718.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₉×C₁₂₇	—	3	4	no	maximal
3	C₃×C₁₃×C₁₂₇	D₃	1	4	yes	complemented
4	D₁₃×C₁₂₇	—	9	1	no	Hall
5	C₃⋊D₃×C₁₂₇	—	13	1	no	maximal, Hall
6	C₁₃×C₁₂₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
7	C₃²×C₁₂₇	D₁₃	1	1	yes	characteristic, complemented, Hall
8	D₃×C₁₂₇	—	39	4	no	—
9	C₃×C₁₂₇	D₃₉	1	4	yes	complemented
10	C₂×C₁₂₇	—	117	1	no	Hall
11	C₃⋊D₃₉	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₂₇	C₃⋊D₃₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₃²×C₁₃	C₂×C₁₂₇	1	1	yes	characteristic, complemented, Hall
14	D₃₉	—	3	4	no	—
15	C₃×C₁₃	D₃×C₁₂₇	1	4	yes	complemented
16	D₁₃	—	9	1	no	Hall
17	C₃⋊D₃	—	13	1	no	Hall
18	C₁₃	C₃⋊D₃×C₁₂₇	1	1	yes	characteristic, complemented, Sylow
19	C₃²	D₁₃×C₁₂₇	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	39	4	no	—
21	C₃	D₃₉×C₁₂₇	1	4	yes	complemented
22	C₂	—	117	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₂₇	C₃⋊D₃₉
commutator, cosocle, hypocenter	C₃²×C₁₃	C₂×C₁₂₇
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₁₂₇	C₂
LCS	G ▷ C₃²×C₁₃
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.