Subgroups — C₂×D₉×C₆₃₁ #36384263

Order 22716.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₉×C₆₃₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₆₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₆₃₁	—	3	1	no	maximal
4	C₉×C₆₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₆₃₁	D₃	1	1	yes	characteristic
6	D₃×C₆₃₁	—	3	2	no	—
7	C₂²×C₆₃₁	—	9	1	no	Hall
8	C₃×C₆₃₁	C₂×D₃	1	1	yes	characteristic
9	C₂×C₆₃₁	—	9	2	no	—
10	C₂×C₆₃₁	D₉	1	1	yes	characteristic, direct product factor
11	C₆₃₁	C₂×D₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×D₉	C₆₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₉	C₂×C₆₃₁	1	1	yes	characteristic, complemented
14	D₉	C₂×C₆₃₁	1	2	yes	direct product factor
15	C₂×D₃	—	3	1	no	—
16	C₉	C₂²×C₆₃₁	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃	D₃×C₆₃₁	1	1	yes	characteristic
18	D₃	—	3	2	no	—
19	C₂²	—	9	1	no	Sylow
20	C₃	C₂×D₃×C₆₃₁	1	1	yes	characteristic
21	C₂	—	9	2	no	—
22	C₂	D₉×C₆₃₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₆₃₁	D₉
commutator, cosocle, hypocenter	C₉	C₂²×C₆₃₁
Frattini	C₃	C₂×D₃×C₆₃₁
Fitting	C₂×C₉×C₆₃₁	C₂
socle	C₂×C₃×C₆₃₁	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₆₃₁

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.