Subgroups — Dic₄₅₃₉ #31827754

Order 18156.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₇×C₈₉	C₂	1	1	yes	maximal, characteristic
2	Dic₁₅₁₃	—	3	1	no	maximal, Hall
3	C₃×C₁₇×C₈₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₇×C₈₉	D₃	1	1	yes	characteristic
5	C₁₇×C₈₉	Dic₃	1	1	yes	characteristic, complemented, Hall
6	Dic₂₆₇	—	17	1	no	maximal, Hall
7	C₂×C₃×C₈₉	D₁₇	1	1	yes	characteristic
8	Dic₈₉	—	51	1	no	Hall
9	C₃×C₈₉	Dic₁₇	1	1	yes	characteristic, complemented, Hall
10	Dic₅₁	—	89	1	no	maximal, Hall
11	C₂×C₈₉	D₅₁	1	1	yes	characteristic
12	C₂×C₃×C₁₇	D₈₉	1	1	yes	characteristic
13	C₈₉	Dic₅₁	1	1	yes	characteristic, complemented, Sylow
14	Dic₁₇	—	267	1	no	Hall
15	C₃×C₁₇	Dic₈₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₇	D₂₆₇	1	1	yes	characteristic
17	C₁₇	Dic₂₆₇	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	1513	1	no	Hall
19	C₂×C₃	D₁₅₁₃	1	1	yes	characteristic
20	C₄	—	4539	1	no	Sylow
21	C₃	Dic₁₅₁₃	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₄₅₃₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₄₅₃₉
commutator, hypocenter	C₃×C₁₇×C₈₉	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₁₇×C₈₉	C₂
LCS	G ▷ C₃×C₁₇×C₈₉
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.