Subgroups — Dic₁₄₁₄₇ #72290621

Order 56588.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₄₃×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₇×C₄₃×C₄₇	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₂₀₂₁	—	7	1	no	maximal, Hall
4	C₂×C₄₃×C₄₇	D₇	1	1	yes	characteristic
5	C₄₃×C₄₇	Dic₇	1	1	yes	characteristic, complemented, Hall
6	Dic₃₂₉	—	43	1	no	maximal, Hall
7	Dic₃₀₁	—	47	1	no	maximal, Hall
8	C₂×C₇×C₄₇	D₄₃	1	1	yes	characteristic
9	C₂×C₇×C₄₃	D₄₇	1	1	yes	characteristic
10	C₇×C₄₇	Dic₄₃	1	1	yes	characteristic, complemented, Hall
11	C₇×C₄₃	Dic₄₇	1	1	yes	characteristic, complemented, Hall
12	Dic₄₇	—	301	1	no	Hall
13	Dic₄₃	—	329	1	no	Hall
14	C₂×C₄₇	D₃₀₁	1	1	yes	characteristic
15	C₂×C₄₃	D₃₂₉	1	1	yes	characteristic
16	C₄₇	Dic₃₀₁	1	1	yes	characteristic, complemented, Sylow
17	C₄₃	Dic₃₂₉	1	1	yes	characteristic, complemented, Sylow
18	Dic₇	—	2021	1	no	Hall
19	C₂×C₇	D₂₀₂₁	1	1	yes	characteristic
20	C₇	Dic₂₀₂₁	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	14147	1	no	Sylow
22	C₂	D₁₄₁₄₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₄₁₄₇
commutator, hypocenter	C₇×C₄₃×C₄₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₇×C₄₃×C₄₇	C₂
LCS	G ▷ C₇×C₄₃×C₄₇
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.