Subgroups — Dic₇₈₈₁ #44538607

Order 31524.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₃₇×C₇₁	C₂	1	1	yes	maximal, characteristic
2	Dic₂₆₂₇	—	3	1	no	maximal, Hall
3	C₃×C₃₇×C₇₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃₇×C₇₁	D₃	1	1	yes	characteristic
5	C₃₇×C₇₁	Dic₃	1	1	yes	characteristic, complemented, Hall
6	Dic₂₁₃	—	37	1	no	maximal, Hall
7	Dic₁₁₁	—	71	1	no	maximal, Hall
8	C₂×C₃×C₇₁	D₃₇	1	1	yes	characteristic
9	Dic₇₁	—	111	1	no	Hall
10	C₂×C₃×C₃₇	D₇₁	1	1	yes	characteristic
11	C₃×C₇₁	Dic₃₇	1	1	yes	characteristic, complemented, Hall
12	Dic₃₇	—	213	1	no	Hall
13	C₂×C₇₁	D₁₁₁	1	1	yes	characteristic
14	C₃×C₃₇	Dic₇₁	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃₇	D₂₁₃	1	1	yes	characteristic
16	C₇₁	Dic₁₁₁	1	1	yes	characteristic, complemented, Sylow
17	C₃₇	Dic₂₁₃	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	2627	1	no	Hall
19	C₂×C₃	D₂₆₂₇	1	1	yes	characteristic
20	C₄	—	7881	1	no	Sylow
21	C₃	Dic₂₆₂₇	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₇₈₈₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇₈₈₁
commutator, hypocenter	C₃×C₃₇×C₇₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₃₇×C₇₁	C₂
LCS	G ▷ C₃×C₃₇×C₇₁
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.