Subgroups — Dic₂₆₇₉ #24924266

Order 10716.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₉×C₄₇	C₂	1	1	yes	maximal, characteristic
2	Dic₈₉₃	—	3	1	no	maximal, Hall
3	C₃×C₁₉×C₄₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₉×C₄₇	D₃	1	1	yes	characteristic
5	C₁₉×C₄₇	Dic₃	1	1	yes	characteristic, complemented, Hall
6	Dic₁₄₁	—	19	1	no	maximal, Hall
7	C₂×C₃×C₄₇	D₁₉	1	1	yes	characteristic
8	Dic₅₇	—	47	1	no	maximal, Hall
9	Dic₄₇	—	57	1	no	Hall
10	C₃×C₄₇	Dic₁₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₁₉	D₄₇	1	1	yes	characteristic
12	C₂×C₄₇	D₅₇	1	1	yes	characteristic
13	Dic₁₉	—	141	1	no	Hall
14	C₃×C₁₉	Dic₄₇	1	1	yes	characteristic, complemented, Hall
15	C₄₇	Dic₅₇	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₁₉	D₁₄₁	1	1	yes	characteristic
17	C₁₉	Dic₁₄₁	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	893	1	no	Hall
19	C₂×C₃	D₈₉₃	1	1	yes	characteristic
20	C₄	—	2679	1	no	Sylow
21	C₃	Dic₈₉₃	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₂₆₇₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₂₆₇₉
commutator, hypocenter	C₃×C₁₉×C₄₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₁₉×C₄₇	C₂
LCS	G ▷ C₃×C₁₉×C₄₇
UCS	C₁ ◁ C₂

Splittings G = N ⋊ H with N normal; H ≅ G/N.