Subgroups — C₉⋊(C₁₁⋊#261) #19104147

Order 5148.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₁×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₁₁⋊#261)	—	3	1	no	maximal
3	C₉×C₁₁×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₁×D₁₃	D₃	1	1	yes	characteristic
5	C₁₁⋊#261	—	9	1	no	Hall
6	C₉⋊#261	—	11	1	no	maximal, Hall
7	C₃×C₁₁×C₁₃	Dic₃	1	1	yes	characteristic
8	Dic₉₉	—	13	1	no	maximal, Hall
9	C₁₁×D₁₃	D₉	1	1	yes	characteristic
10	C₉×D₁₃	D₁₁	1	1	yes	characteristic
11	C₂×C₉×C₁₁	—	13	1	no	—
12	C₃⋊#261	—	33	1	no	—
13	C₁₁×C₁₃	Dic₉	1	1	yes	characteristic, complemented, Hall
14	Dic₃₃	—	39	1	no	—
15	C₉×C₁₃	Dic₁₁	1	1	yes	characteristic, complemented, Hall
16	C₉×C₁₁	#261	1	1	yes	characteristic, complemented, Hall
17	C₃×D₁₃	D₃₃	1	1	yes	characteristic
18	C₂×C₃×C₁₁	—	13	1	no	—
19	#261	—	99	1	no	Hall
20	Dic₁₁	—	117	1	no	Hall
21	C₃×C₁₃	Dic₃₃	1	1	yes	characteristic
22	Dic₉	—	143	1	no	Hall
23	C₃×C₁₁	C₃⋊#261	1	1	yes	characteristic
24	D₁₃	D₉₉	1	1	yes	characteristic
25	C₂×C₁₁	—	13	1	no	—
26	C₂×C₉	—	13	1	no	—
27	C₁₃	Dic₉₉	1	1	yes	characteristic, complemented, Sylow
28	Dic₃	—	429	1	no	—
29	C₁₁	C₉⋊#261	1	1	yes	characteristic, complemented, Sylow
30	C₉	C₁₁⋊#261	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	13	1	no	—
32	C₄	—	1287	1	no	Sylow
33	C₃	C₃⋊(C₁₁⋊#261)	1	1	yes	characteristic
34	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₉×C₁₁×C₁₃	C₄
Frattini	C₃	C₃⋊(C₁₁⋊#261)
socle	C₃×C₁₁×C₁₃	Dic₃
LCS	G ▷ C₉×C₁₁×C₁₃
UCS	C₁

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