Subgroups — Dic₈₀₀₇ #44545083

Order 32028.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₇×C₁₅₇	C₂	1	1	yes	maximal, characteristic
2	Dic₂₆₆₉	—	3	1	no	maximal, Hall
3	C₃×C₁₇×C₁₅₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₇×C₁₅₇	D₃	1	1	yes	characteristic
5	C₁₇×C₁₅₇	Dic₃	1	1	yes	characteristic, complemented, Hall
6	Dic₄₇₁	—	17	1	no	maximal, Hall
7	C₂×C₃×C₁₅₇	D₁₇	1	1	yes	characteristic
8	Dic₁₅₇	—	51	1	no	Hall
9	C₃×C₁₅₇	Dic₁₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₅₇	D₅₁	1	1	yes	characteristic
11	Dic₅₁	—	157	1	no	maximal, Hall
12	C₁₅₇	Dic₅₁	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₃×C₁₇	D₁₅₇	1	1	yes	characteristic
14	Dic₁₇	—	471	1	no	Hall
15	C₃×C₁₇	Dic₁₅₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₇	D₄₇₁	1	1	yes	characteristic
17	C₁₇	Dic₄₇₁	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	2669	1	no	Hall
19	C₂×C₃	D₂₆₆₉	1	1	yes	characteristic
20	C₄	—	8007	1	no	Sylow
21	C₃	Dic₂₆₆₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₈₀₀₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₈₀₀₇
commutator, hypocenter	C₃×C₁₇×C₁₅₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₁₇×C₁₅₇	C₂
LCS	G ▷ C₃×C₁₇×C₁₅₇
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.