Subgroups — Dic₂₇₁₇ #24925875

Order 10868.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₃×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₂₄₇	—	11	1	no	maximal, Hall
4	Dic₂₀₉	—	13	1	no	maximal, Hall
5	Dic₁₄₃	—	19	1	no	maximal, Hall
6	C₂×C₁₃×C₁₉	D₁₁	1	1	yes	characteristic
7	C₂×C₁₁×C₁₉	D₁₃	1	1	yes	characteristic
8	C₂×C₁₁×C₁₃	D₁₉	1	1	yes	characteristic
9	C₁₃×C₁₉	Dic₁₁	1	1	yes	characteristic, complemented, Hall
10	C₁₁×C₁₉	Dic₁₃	1	1	yes	characteristic, complemented, Hall
11	C₁₁×C₁₃	Dic₁₉	1	1	yes	characteristic, complemented, Hall
12	Dic₁₉	—	143	1	no	Hall
13	Dic₁₃	—	209	1	no	Hall
14	Dic₁₁	—	247	1	no	Hall
15	C₂×C₁₉	D₁₄₃	1	1	yes	characteristic
16	C₂×C₁₃	D₂₀₉	1	1	yes	characteristic
17	C₂×C₁₁	D₂₄₇	1	1	yes	characteristic
18	C₁₉	Dic₁₄₃	1	1	yes	characteristic, complemented, Sylow
19	C₁₃	Dic₂₀₉	1	1	yes	characteristic, complemented, Sylow
20	C₁₁	Dic₂₄₇	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	2717	1	no	Sylow
22	C₂	D₂₇₁₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₂₇₁₇
commutator, hypocenter	C₁₁×C₁₃×C₁₉	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₁×C₁₃×C₁₉	C₂
LCS	G ▷ C₁₁×C₁₃×C₁₉
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.