Subgroups — C₉⋊(C₂₃⋊#261) #24924489

Order 10764.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₃×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₂₃⋊#261)	—	3	1	no	maximal
3	C₉×C₁₃×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₂₃×D₁₃	D₃	1	1	yes	characteristic
5	C₂₃⋊#261	—	9	1	no	Hall
6	C₃×C₁₃×C₂₃	Dic₃	1	1	yes	characteristic
7	Dic₂₀₇	—	13	1	no	maximal, Hall
8	C₂₃×D₁₃	D₉	1	1	yes	characteristic
9	C₉⋊#261	—	23	1	no	maximal, Hall
10	C₂×C₉×C₂₃	—	13	1	no	—
11	C₁₃×C₂₃	Dic₉	1	1	yes	characteristic, complemented, Hall
12	Dic₆₉	—	39	1	no	—
13	C₉×D₁₃	D₂₃	1	1	yes	characteristic
14	C₉×C₂₃	#261	1	1	yes	characteristic, complemented, Hall
15	C₃⋊#261	—	69	1	no	—
16	C₂×C₃×C₂₃	—	13	1	no	—
17	C₉×C₁₃	Dic₂₃	1	1	yes	characteristic, complemented, Hall
18	Dic₂₃	—	117	1	no	Hall
19	C₃×D₁₃	D₆₉	1	1	yes	characteristic
20	C₃×C₂₃	C₃⋊#261	1	1	yes	characteristic
21	#261	—	207	1	no	Hall
22	C₂×C₂₃	—	13	1	no	—
23	C₃×C₁₃	Dic₆₉	1	1	yes	characteristic
24	Dic₉	—	299	1	no	Hall
25	D₁₃	D₂₀₇	1	1	yes	characteristic
26	C₂₃	C₉⋊#261	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₉	—	13	1	no	—
28	C₁₃	Dic₂₀₇	1	1	yes	characteristic, complemented, Sylow
29	Dic₃	—	897	1	no	—
30	C₉	C₂₃⋊#261	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	13	1	no	—
32	C₄	—	2691	1	no	Sylow
33	C₃	C₃⋊(C₂₃⋊#261)	1	1	yes	characteristic
34	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₉×C₁₃×C₂₃	C₄
Frattini	C₃	C₃⋊(C₂₃⋊#261)
socle	C₃×C₁₃×C₂₃	Dic₃
prime radical	C₃×C₂₃×D₁₃	D₃
cosocle	C₉×C₂₃×D₁₃	C₂
LCS	G ▷ C₉×C₁₃×C₂₃
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.