Subgroups — C₃²×D₇×C₃₁ #16840913

Order 3906.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₇×C₃₁	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₇×C₃₁	C₂×C₃	1	4	yes	complemented
4	C₂×C₃²×C₃₁	—	7	1	no	maximal, Hall
5	D₇×C₃₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₃₁	D₇	1	1	yes	characteristic, direct product factor, Hall
7	C₇×C₃₁	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×C₃₁	—	7	4	no	—
9	C₃²×D₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₃₁	C₃×D₇	1	4	yes	direct product factor
11	C₃²×C₇	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃₁	—	7	1	no	Hall
13	C₃×D₇	C₃×C₃₁	1	4	yes	direct product factor
14	C₃₁	C₃²×D₇	1	1	yes	characteristic, direct product factor, Sylow
15	C₃×C₇	C₂×C₃×C₃₁	1	4	yes	complemented
16	C₂×C₃²	—	7	1	no	Hall
17	D₇	C₃²×C₃₁	1	1	yes	characteristic, direct product factor, Hall
18	C₃²	D₇×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₇	C₂×C₃²×C₃₁	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃	—	7	4	no	—
21	C₃	C₃×D₇×C₃₁	1	4	yes	direct product factor
22	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₃₁	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₃²×C₃₁
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₃₁	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃²×C₃₁

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.