Subgroups — Dic₁₇₆₇ #20296608

Order 7068.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₉×C₃₁	C₂	1	1	yes	maximal, characteristic
2	Dic₅₈₉	—	3	1	no	maximal, Hall
3	C₃×C₁₉×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₉×C₃₁	D₃	1	1	yes	characteristic
5	C₁₉×C₃₁	Dic₃	1	1	yes	characteristic, complemented, Hall
6	Dic₉₃	—	19	1	no	maximal, Hall
7	Dic₅₇	—	31	1	no	maximal, Hall
8	C₂×C₃×C₃₁	D₁₉	1	1	yes	characteristic
9	Dic₃₁	—	57	1	no	Hall
10	C₂×C₃×C₁₉	D₃₁	1	1	yes	characteristic
11	C₃×C₃₁	Dic₁₉	1	1	yes	characteristic, complemented, Hall
12	Dic₁₉	—	93	1	no	Hall
13	C₂×C₃₁	D₅₇	1	1	yes	characteristic
14	C₃×C₁₉	Dic₃₁	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₉	D₉₃	1	1	yes	characteristic
16	C₃₁	Dic₅₇	1	1	yes	characteristic, complemented, Sylow
17	C₁₉	Dic₉₃	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	589	1	no	Hall
19	C₂×C₃	D₅₈₉	1	1	yes	characteristic
20	C₄	—	1767	1	no	Sylow
21	C₃	Dic₅₈₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₁₇₆₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₇₆₇
commutator, hypocenter	C₃×C₁₉×C₃₁	C₄
Fitting, socle	C₂×C₃×C₁₉×C₃₁	C₂
LCS	G ▷ C₃×C₁₉×C₃₁
UCS	C₁ ◁ C₂

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