Subgroups — C₄₇×C₃⋊D₁₁₁ #44531087

Order 31302.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₇×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₇×D₁₁₁	—	3	4	no	maximal
3	C₃×C₃₇×C₄₇	D₃	1	4	yes	complemented
4	C₄₇×D₃₇	—	9	1	no	Hall
5	C₃₇×C₄₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
6	C₃⋊D₃×C₄₇	—	37	1	no	maximal, Hall
7	C₃⋊D₁₁₁	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃²×C₄₇	D₃₇	1	1	yes	characteristic, complemented, Hall
9	C₃²×C₃₇	C₂×C₄₇	1	1	yes	characteristic, complemented, Hall
10	D₃×C₄₇	—	111	4	no	—
11	D₁₁₁	—	3	4	no	—
12	C₃×C₄₇	D₁₁₁	1	4	yes	complemented
13	C₃×C₃₇	D₃×C₄₇	1	4	yes	complemented
14	C₂×C₄₇	—	333	1	no	Hall
15	D₃₇	—	9	1	no	Hall
16	C₄₇	C₃⋊D₁₁₁	1	1	yes	characteristic, direct product factor, Sylow
17	C₃₇	C₃⋊D₃×C₄₇	1	1	yes	characteristic, complemented, Sylow
18	C₃⋊D₃	—	37	1	no	Hall
19	C₃²	C₄₇×D₃₇	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	111	4	no	—
21	C₃	C₄₇×D₁₁₁	1	4	yes	complemented
22	C₂	—	333	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₇	C₃⋊D₁₁₁
commutator, cosocle, hypocenter	C₃²×C₃₇	C₂×C₄₇
Frattini	C₁	G
Fitting, socle	C₃²×C₃₇×C₄₇	C₂
LCS	G ▷ C₃²×C₃₇
UCS	C₁ ◁ C₄₇

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.