Subgroups — D₃×C₁₃²×C₂₃ #37552247

Order 23322.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₃²×C₂₃	—	3	1	no	maximal, Hall
3	C₁₃²×C₂₃	D₃	1	1	yes	characteristic, direct product factor, Hall
4	D₃×C₁₃×C₂₃	C₁₃	1	14	yes	maximal, direct product factor
5	D₃×C₁₃²	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₁₃×C₂₃	C₂×C₁₃	1	14	yes	complemented
7	C₂×C₁₃×C₂₃	—	3	14	no	—
8	C₃×C₁₃²	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₃²	—	3	1	no	Hall
10	C₁₃×C₂₃	D₃×C₁₃	1	14	yes	direct product factor
11	C₁₃²	D₃×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
12	D₃×C₂₃	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
13	D₃×C₁₃	C₁₃×C₂₃	1	14	yes	direct product factor
14	C₃×C₂₃	C₂×C₁₃²	1	1	yes	characteristic, complemented, Hall
15	C₂×C₂₃	—	3	1	no	Hall
16	C₃×C₁₃	C₂×C₁₃×C₂₃	1	14	yes	complemented
17	C₂×C₁₃	—	3	14	no	—
18	C₂₃	D₃×C₁₃²	1	1	yes	characteristic, direct product factor, Sylow
19	C₁₃	D₃×C₁₃×C₂₃	1	14	yes	direct product factor
20	D₃	C₁₃²×C₂₃	1	1	yes	characteristic, direct product factor, Hall
21	C₃	C₂×C₁₃²×C₂₃	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃²×C₂₃	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₁₃²×C₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₃²×C₂₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₁₃²×C₂₃

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.