Subgroups — Dic₇₀₇₇ #43246717

Order 28308.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₃₃₇	C₂	1	1	yes	maximal, characteristic
2	Dic₂₃₅₉	—	3	1	no	maximal, Hall
3	C₃×C₇×C₃₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₃₃₇	D₃	1	1	yes	characteristic
5	Dic₁₀₁₁	—	7	1	no	maximal, Hall
6	C₇×C₃₃₇	Dic₃	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₃₃₇	D₇	1	1	yes	characteristic
8	Dic₃₃₇	—	21	1	no	Hall
9	C₃×C₃₃₇	Dic₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃₃₇	D₂₁	1	1	yes	characteristic
11	C₃₃₇	Dic₂₁	1	1	yes	characteristic, complemented, Sylow
12	Dic₂₁	—	337	1	no	maximal, Hall
13	C₂×C₃×C₇	D₃₃₇	1	1	yes	characteristic
14	Dic₇	—	1011	1	no	Hall
15	C₃×C₇	Dic₃₃₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇	D₁₀₁₁	1	1	yes	characteristic
17	Dic₃	—	2359	1	no	Hall
18	C₇	Dic₁₀₁₁	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	D₂₃₅₉	1	1	yes	characteristic
20	C₄	—	7077	1	no	Sylow
21	C₃	Dic₂₃₅₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₇₀₇₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇₀₇₇
commutator, hypocenter	C₃×C₇×C₃₃₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₇×C₃₃₇	C₂
LCS	G ▷ C₃×C₇×C₃₃₇
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.