Subgroups — Dic₈₇₈₉ #47975868

Order 35156.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₁₇×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₇×C₄₇	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₇₉₉	—	11	1	no	maximal, Hall
4	Dic₅₁₇	—	17	1	no	maximal, Hall
5	C₂×C₁₇×C₄₇	D₁₁	1	1	yes	characteristic
6	C₂×C₁₁×C₄₇	D₁₇	1	1	yes	characteristic
7	C₁₇×C₄₇	Dic₁₁	1	1	yes	characteristic, complemented, Hall
8	Dic₁₈₇	—	47	1	no	maximal, Hall
9	C₁₁×C₄₇	Dic₁₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₁×C₁₇	D₄₇	1	1	yes	characteristic
11	Dic₄₇	—	187	1	no	Hall
12	C₁₁×C₁₇	Dic₄₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₄₇	D₁₈₇	1	1	yes	characteristic
14	Dic₁₇	—	517	1	no	Hall
15	C₄₇	Dic₁₈₇	1	1	yes	characteristic, complemented, Sylow
16	Dic₁₁	—	799	1	no	Hall
17	C₂×C₁₇	D₅₁₇	1	1	yes	characteristic
18	C₂×C₁₁	D₇₉₉	1	1	yes	characteristic
19	C₁₇	Dic₅₁₇	1	1	yes	characteristic, complemented, Sylow
20	C₁₁	Dic₇₉₉	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	8789	1	no	Sylow
22	C₂	D₈₇₈₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₈₇₈₉
commutator, hypocenter	C₁₁×C₁₇×C₄₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₁×C₁₇×C₄₇	C₂
LCS	G ▷ C₁₁×C₁₇×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.