Subgroups — C₃⋊(C₃⋊(C₂₃⋊#261)) #24924558

Order 10764.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₃×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₂₃⋊#261)	—	3	4	no	maximal
3	C₃²×C₁₃×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₂₃×D₁₃	D₃	1	4	yes	—
5	C₂₃⋊#261	—	9	1	no	Hall
6	C₃×C₁₃×C₂₃	Dic₃	1	4	yes	complemented
7	C₃⋊Dic₆₉	—	13	1	no	maximal, Hall
8	C₂₃×D₁₃	C₃⋊D₃	1	1	yes	characteristic
9	C₃⋊(C₃⋊#261)	—	23	1	no	maximal, Hall
10	C₂×C₃²×C₂₃	—	13	1	no	—
11	C₁₃×C₂₃	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
12	Dic₆₉	—	39	4	no	—
13	C₃²×D₁₃	D₂₃	1	1	yes	characteristic
14	C₃²×C₂₃	#261	1	1	yes	characteristic, complemented, Hall
15	C₃⋊#261	—	69	4	no	—
16	C₂×C₃×C₂₃	—	13	4	no	—
17	C₃²×C₁₃	Dic₂₃	1	1	yes	characteristic, complemented, Hall
18	Dic₂₃	—	117	1	no	Hall
19	C₃×D₁₃	D₆₉	1	4	yes	—
20	C₃×C₂₃	C₃⋊#261	1	4	yes	complemented
21	#261	—	207	1	no	Hall
22	C₂×C₂₃	—	13	1	no	—
23	C₃×C₁₃	Dic₆₉	1	4	yes	complemented
24	C₃⋊Dic₃	—	299	1	no	Hall
25	D₁₃	C₃⋊D₆₉	1	1	yes	characteristic
26	C₂₃	C₃⋊(C₃⋊#261)	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃²	—	13	1	no	—
28	C₁₃	C₃⋊Dic₆₉	1	1	yes	characteristic, complemented, Sylow
29	Dic₃	—	897	4	no	—
30	C₃²	C₂₃⋊#261	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	13	4	no	—
32	C₄	—	2691	1	no	Sylow
33	C₃	C₃⋊(C₂₃⋊#261)	1	4	yes	complemented
34	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₃×C₂₃	C₄
prime radical, cosocle	C₃²×C₂₃×D₁₃	C₂
LCS	G ▷ C₃²×C₁₃×C₂₃
UCS	C₁

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