Subgroups — Dic₆₇₄₇ #41008752

Order 26988.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₃×C₁₇₃	C₂	1	1	yes	maximal, characteristic
2	Dic₂₂₄₉	—	3	1	no	maximal, Hall
3	C₃×C₁₃×C₁₇₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃×C₁₇₃	D₃	1	1	yes	characteristic
5	C₁₃×C₁₇₃	Dic₃	1	1	yes	characteristic, complemented, Hall
6	Dic₅₁₉	—	13	1	no	maximal, Hall
7	C₂×C₃×C₁₇₃	D₁₃	1	1	yes	characteristic
8	Dic₁₇₃	—	39	1	no	Hall
9	C₃×C₁₇₃	Dic₁₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₇₃	D₃₉	1	1	yes	characteristic
11	C₁₇₃	Dic₃₉	1	1	yes	characteristic, complemented, Sylow
12	Dic₃₉	—	173	1	no	maximal, Hall
13	C₂×C₃×C₁₃	D₁₇₃	1	1	yes	characteristic
14	Dic₁₃	—	519	1	no	Hall
15	C₃×C₁₃	Dic₁₇₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₃	D₅₁₉	1	1	yes	characteristic
17	C₁₃	Dic₅₁₉	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	2249	1	no	Hall
19	C₂×C₃	D₂₂₄₉	1	1	yes	characteristic
20	C₄	—	6747	1	no	Sylow
21	C₃	Dic₂₂₄₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₆₇₄₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₆₇₄₇
commutator, hypocenter	C₃×C₁₃×C₁₇₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₁₃×C₁₇₃	C₂
LCS	G ▷ C₃×C₁₃×C₁₇₃
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.