Subgroups — Dic₄₄₃₃ #31801113

Order 17732.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₁₃×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₃×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₄₀₃	—	11	1	no	maximal, Hall
4	Dic₃₄₁	—	13	1	no	maximal, Hall
5	C₂×C₁₃×C₃₁	D₁₁	1	1	yes	characteristic
6	C₂×C₁₁×C₃₁	D₁₃	1	1	yes	characteristic
7	Dic₁₄₃	—	31	1	no	maximal, Hall
8	C₁₃×C₃₁	Dic₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₃₁	Dic₁₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₁×C₁₃	D₃₁	1	1	yes	characteristic
11	C₁₁×C₁₃	Dic₃₁	1	1	yes	characteristic, complemented, Hall
12	Dic₃₁	—	143	1	no	Hall
13	C₂×C₃₁	D₁₄₃	1	1	yes	characteristic
14	Dic₁₃	—	341	1	no	Hall
15	Dic₁₁	—	403	1	no	Hall
16	C₃₁	Dic₁₄₃	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₁₃	D₃₄₁	1	1	yes	characteristic
18	C₂×C₁₁	D₄₀₃	1	1	yes	characteristic
19	C₁₃	Dic₃₄₁	1	1	yes	characteristic, complemented, Sylow
20	C₁₁	Dic₄₀₃	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	4433	1	no	Sylow
22	C₂	D₄₄₃₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₄₄₃₃
commutator, hypocenter	C₁₁×C₁₃×C₃₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₁×C₁₃×C₃₁	C₂
LCS	G ▷ C₁₁×C₁₃×C₃₁
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.