Subgroups — Dic₉₂₆₉ #49150504

Order 37076.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₂₃×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₂₃×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₇₁₃	—	13	1	no	maximal, Hall
4	Dic₄₀₃	—	23	1	no	maximal, Hall
5	C₂×C₂₃×C₃₁	D₁₃	1	1	yes	characteristic
6	Dic₂₉₉	—	31	1	no	maximal, Hall
7	C₂×C₁₃×C₃₁	D₂₃	1	1	yes	characteristic
8	C₂₃×C₃₁	Dic₁₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₃×C₂₃	D₃₁	1	1	yes	characteristic
10	C₁₃×C₃₁	Dic₂₃	1	1	yes	characteristic, complemented, Hall
11	C₁₃×C₂₃	Dic₃₁	1	1	yes	characteristic, complemented, Hall
12	Dic₃₁	—	299	1	no	Hall
13	Dic₂₃	—	403	1	no	Hall
14	C₂×C₃₁	D₂₉₉	1	1	yes	characteristic
15	Dic₁₃	—	713	1	no	Hall
16	C₂×C₂₃	D₄₀₃	1	1	yes	characteristic
17	C₃₁	Dic₂₉₉	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₁₃	D₇₁₃	1	1	yes	characteristic
19	C₂₃	Dic₄₀₃	1	1	yes	characteristic, complemented, Sylow
20	C₁₃	Dic₇₁₃	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	9269	1	no	Sylow
22	C₂	D₉₂₆₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₉₂₆₉
commutator, hypocenter	C₁₃×C₂₃×C₃₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₃×C₂₃×C₃₁	C₂
LCS	G ▷ C₁₃×C₂₃×C₃₁
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.