Subgroups — Dic₂₇₅₁ #24926993

Order 11004.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	Dic₉₁₇	—	3	1	no	maximal, Hall
3	C₃×C₇×C₁₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₃₁	D₃	1	1	yes	characteristic
5	Dic₃₉₃	—	7	1	no	maximal, Hall
6	C₇×C₁₃₁	Dic₃	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₃₁	D₇	1	1	yes	characteristic
8	Dic₁₃₁	—	21	1	no	Hall
9	C₃×C₁₃₁	Dic₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₃₁	D₂₁	1	1	yes	characteristic
11	C₁₃₁	Dic₂₁	1	1	yes	characteristic, complemented, Sylow
12	Dic₂₁	—	131	1	no	maximal, Hall
13	C₂×C₃×C₇	D₁₃₁	1	1	yes	characteristic
14	Dic₇	—	393	1	no	Hall
15	C₃×C₇	Dic₁₃₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇	D₃₉₃	1	1	yes	characteristic
17	Dic₃	—	917	1	no	Hall
18	C₇	Dic₃₉₃	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	D₉₁₇	1	1	yes	characteristic
20	C₄	—	2751	1	no	Sylow
21	C₃	Dic₉₁₇	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₂₇₅₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₂₇₅₁
commutator, hypocenter	C₃×C₇×C₁₃₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₇×C₁₃₁	C₂
LCS	G ▷ C₃×C₇×C₁₃₁
UCS	C₁ ◁ C₂

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.