Subgroups — C₃₁×C₃⋊D₁₈₃ #46801435

Order 34038.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₁×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₁×D₁₈₃	—	3	4	no	maximal
3	C₃×C₃₁×C₆₁	D₃	1	4	yes	complemented
4	C₃₁×D₆₁	—	9	1	no	Hall
5	C₃₁×C₆₁	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
6	C₃⋊D₁₈₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃⋊D₃×C₃₁	—	61	1	no	maximal, Hall
8	C₃²×C₆₁	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
9	D₁₈₃	—	3	4	no	—
10	C₃²×C₃₁	D₆₁	1	1	yes	characteristic, complemented, Hall
11	D₃×C₃₁	—	183	4	no	—
12	C₃×C₆₁	D₃×C₃₁	1	4	yes	complemented
13	D₆₁	—	9	1	no	Hall
14	C₃×C₃₁	D₁₈₃	1	4	yes	complemented
15	C₂×C₃₁	—	549	1	no	Hall
16	C₆₁	C₃⋊D₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
17	C₃₁	C₃⋊D₁₈₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₃⋊D₃	—	61	1	no	Hall
19	C₃²	C₃₁×D₆₁	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	183	4	no	—
21	C₃	C₃₁×D₁₈₃	1	4	yes	complemented
22	C₂	—	549	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₁	C₃⋊D₁₈₃
commutator, cosocle, hypocenter	C₃²×C₆₁	C₂×C₃₁
Frattini	C₁	G
Fitting, socle	C₃²×C₃₁×C₆₁	C₂
LCS	G ▷ C₃²×C₆₁
UCS	C₁ ◁ 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.