Subgroups — Dic₁₃₁₀₁ #72288694

Order 52404.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₁×C₃₉₇	C₂	1	1	yes	maximal, characteristic
2	Dic₄₃₆₇	—	3	1	no	maximal, Hall
3	C₃×C₁₁×C₃₉₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×C₃₉₇	D₃	1	1	yes	characteristic
5	Dic₁₁₉₁	—	11	1	no	maximal, Hall
6	C₁₁×C₃₉₇	Dic₃	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₃₉₇	D₁₁	1	1	yes	characteristic
8	Dic₃₉₇	—	33	1	no	Hall
9	C₃×C₃₉₇	Dic₁₁	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃₉₇	D₃₃	1	1	yes	characteristic
11	C₃₉₇	Dic₃₃	1	1	yes	characteristic, complemented, Sylow
12	Dic₃₃	—	397	1	no	maximal, Hall
13	C₂×C₃×C₁₁	D₃₉₇	1	1	yes	characteristic
14	Dic₁₁	—	1191	1	no	Hall
15	C₃×C₁₁	Dic₃₉₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₁	D₁₁₉₁	1	1	yes	characteristic
17	Dic₃	—	4367	1	no	Hall
18	C₁₁	Dic₁₁₉₁	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	D₄₃₆₇	1	1	yes	characteristic
20	C₄	—	13101	1	no	Sylow
21	C₃	Dic₄₃₆₇	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₁₃₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₃₁₀₁
commutator, hypocenter	C₃×C₁₁×C₃₉₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₁₁×C₃₉₇	C₂
LCS	G ▷ C₃×C₁₁×C₃₉₇
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.