Subgroups — C₃×C₃⋊(C₂₃⋊#261) #24924550

Order 10764.

56 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)	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₂₃⋊#261	—	3	1	no	maximal
4	C₃²×C₁₃×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₂₃×D₁₃	—	2	1	no	—
6	C₃×C₂₃×D₁₃	D₃	1	1	yes	characteristic
7	C₃×C₂₃×D₁₃	C₂×C₃	1	1	yes	characteristic
8	C₂₃⋊#261	—	3	1	no	Hall
9	C₃×C₁₃×C₂₃	—	2	1	no	—
10	C₃×C₁₃×C₂₃	Dic₃	1	1	yes	characteristic, complemented
11	C₃×C₁₃×C₂₃	C₃×C₄	1	1	yes	characteristic, complemented
12	C₃×Dic₆₉	—	13	1	no	maximal, Hall
13	C₂₃×D₁₃	C₃×D₃	1	1	yes	characteristic
14	C₃×C₃⋊#261	—	23	1	no	maximal, Hall
15	C₂×C₃²×C₂₃	—	13	1	no	—
16	C₁₃×C₂₃	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
17	Dic₆₉	—	13	1	no	—
18	C₃×Dic₂₃	—	39	1	no	—
19	C₃²×D₁₃	D₂₃	1	1	yes	characteristic
20	C₃²×C₂₃	#261	1	1	yes	characteristic, complemented, Hall
21	C₃⋊#261	—	23	1	no	—
22	C₃×#261	—	69	1	no	—
23	C₂×C₃×C₂₃	—	13	1	no	—
24	C₂×C₃×C₂₃	—	13	1	no	—
25	C₂×C₃×C₂₃	—	26	1	no	—
26	C₃²×C₁₃	Dic₂₃	1	1	yes	characteristic, complemented, Hall
27	Dic₂₃	—	39	1	no	Hall
28	C₃×D₁₃	—	2	1	no	—
29	C₃×D₁₃	C₃×D₂₃	1	1	yes	characteristic
30	C₃×D₁₃	D₆₉	1	1	yes	characteristic
31	C₃×C₂₃	—	2	1	no	—
32	C₃×C₂₃	C₃×#261	1	1	yes	characteristic, complemented
33	C₃×C₂₃	C₃⋊#261	1	1	yes	characteristic, complemented
34	#261	—	69	1	no	Hall
35	C₂×C₂₃	—	13	1	no	—
36	C₃×C₁₃	—	2	1	no	—
37	C₃×C₁₃	C₃×Dic₂₃	1	1	yes	characteristic, complemented
38	C₃×C₁₃	Dic₆₉	1	1	yes	characteristic, complemented
39	C₃×Dic₃	—	299	1	no	Hall
40	D₁₃	C₃×D₆₉	1	1	yes	characteristic
41	C₂₃	C₃×C₃⋊#261	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃²	—	13	1	no	—
43	C₁₃	C₃×Dic₆₉	1	1	yes	characteristic, complemented, Sylow
44	C₃×C₄	—	897	1	no	—
45	Dic₃	—	299	1	no	—
46	C₃²	C₂₃⋊#261	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	—	13	1	no	—
48	C₂×C₃	—	13	1	no	—
49	C₂×C₃	—	26	1	no	—
50	C₄	—	897	1	no	Sylow
51	C₃	—	2	1	no	—
52	C₃	C₃×C₂₃⋊#261	1	1	yes	characteristic, complemented
53	C₃	C₃⋊(C₂₃⋊#261)	1	1	yes	characteristic, direct product factor
54	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₃⋊(C₂₃⋊#261)
commutator, hypocenter	C₃×C₁₃×C₂₃	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₂₃	C₄
prime radical	C₃²×C₂₃×D₁₃	C₂
cosocle	C₃×C₂₃×D₁₃	C₂×C₃
LCS	G ▷ C₃×C₁₃×C₂₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₂₃⋊#261)	C₃	direct (N × H)
4. C₃²×C₁₃×C₂₃	C₄	semidirect
10. C₃×C₁₃×C₂₃	Dic₃	semidirect
11. C₃×C₁₃×C₂₃	C₃×C₄	semidirect
16. C₁₃×C₂₃	C₃×Dic₃	semidirect
20. C₃²×C₂₃	#261	semidirect
26. C₃²×C₁₃	Dic₂₃	semidirect
32. C₃×C₂₃	C₃×#261	semidirect
33. C₃×C₂₃	C₃⋊#261	semidirect
37. C₃×C₁₃	C₃×Dic₂₃	semidirect
38. C₃×C₁₃	Dic₆₉	semidirect
41. C₂₃	C₃×C₃⋊#261	semidirect
43. C₁₃	C₃×Dic₆₉	semidirect
46. C₃²	C₂₃⋊#261	semidirect
52. C₃	C₃×C₂₃⋊#261	semidirect
53. C₃	C₃⋊(C₂₃⋊#261)	direct (N × H)

Subgroups — C3×C3⋊(C23⋊#261) #24924550

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₃⋊(C₂₃⋊#261) #24924550