Subgroups — C₃⋊D₅₂₇₁ #44539451

Order 31626.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₂₇₁	—	3	4	no	maximal
3	C₃×C₇×C₂₅₁	D₃	1	4	yes	complemented
4	C₃⋊D₇₅₃	—	7	1	no	maximal, Hall
5	D₁₇₅₇	—	9	1	no	Hall
6	C₃²×C₂₅₁	D₇	1	1	yes	characteristic, complemented, Hall
7	C₇×C₂₅₁	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
8	D₇₅₃	—	21	4	no	—
9	C₃×C₂₅₁	D₂₁	1	4	yes	complemented
10	D₂₅₁	—	63	1	no	Hall
11	C₂₅₁	C₃⋊D₂₁	1	1	yes	characteristic, complemented, Sylow
12	C₃⋊D₂₁	—	251	1	no	maximal, Hall
13	C₃²×C₇	D₂₅₁	1	1	yes	characteristic, complemented, Hall
14	D₂₁	—	753	4	no	—
15	C₃×C₇	D₇₅₃	1	4	yes	complemented
16	C₃⋊D₃	—	1757	1	no	Hall
17	D₇	—	2259	1	no	Hall
18	C₃²	D₁₇₅₇	1	1	yes	characteristic, complemented, Sylow
19	C₇	C₃⋊D₇₅₃	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	5271	4	no	—
21	C₃	D₅₂₇₁	1	4	yes	complemented
22	C₂	—	15813	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₇×C₂₅₁	C₂
LCS	G ▷ C₃²×C₇×C₂₅₁
UCS	C₁

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.