Subgroups — Dic₁₃₄₄₇ #72289340

Order 53788.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₇×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₇×C₁₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₉₂₁	—	7	1	no	maximal, Hall
4	C₂×C₁₇×C₁₁₃	D₇	1	1	yes	characteristic
5	Dic₇₉₁	—	17	1	no	maximal, Hall
6	C₁₇×C₁₁₃	Dic₇	1	1	yes	characteristic, complemented, Hall
7	C₂×C₇×C₁₁₃	D₁₇	1	1	yes	characteristic
8	C₇×C₁₁₃	Dic₁₇	1	1	yes	characteristic, complemented, Hall
9	Dic₁₁₉	—	113	1	no	maximal, Hall
10	Dic₁₁₃	—	119	1	no	Hall
11	C₂×C₇×C₁₇	D₁₁₃	1	1	yes	characteristic
12	C₂×C₁₁₃	D₁₁₉	1	1	yes	characteristic
13	C₇×C₁₇	Dic₁₁₃	1	1	yes	characteristic, complemented, Hall
14	C₁₁₃	Dic₁₁₉	1	1	yes	characteristic, complemented, Sylow
15	Dic₁₇	—	791	1	no	Hall
16	C₂×C₁₇	D₇₉₁	1	1	yes	characteristic
17	Dic₇	—	1921	1	no	Hall
18	C₁₇	Dic₇₉₁	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₇	D₁₉₂₁	1	1	yes	characteristic
20	C₇	Dic₁₉₂₁	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	13447	1	no	Sylow
22	C₂	D₁₃₄₄₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₃₄₄₇
commutator, hypocenter	C₇×C₁₇×C₁₁₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₇×C₁₇×C₁₁₃	C₂
LCS	G ▷ C₇×C₁₇×C₁₁₃
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.