Subgroups — C₁₁×#15688303 #45656704

Order 32604.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#13093365	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₉×#261	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁×#10625203	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁×C₁₉×D₁₃	C₂×C₃	1	1	yes	characteristic
5	#15688303	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₁₃×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₄×C₁₁×C₁₉⋊C₃	—	13	1	no	maximal, Hall
8	C₁₁×AGL(1,𝔽₁₃)	—	19	1	no	maximal, Hall
9	#13093365	C₂×C₁₁	1	1	yes	characteristic
10	C₂×C₁₁×C₁₉⋊C₃	—	13	1	no	—
11	C₁₉×#261	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₁₁×D₁₃⋊C₃	—	19	1	no	—
13	C₄×C₁₁×C₁₉	—	13	1	no	Hall
14	#10625203	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₁₁×C₁₉⋊C₃	—	13	1	no	Hall
16	C₁₁×#261	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₁₉×D₁₃	C₂×C₃×C₁₁	1	1	yes	characteristic
18	C₁₁×C₁₃⋊C₃	—	19	1	no	Hall
19	C₂×C₁₁×C₁₉	—	13	1	no	—
20	C₁₁×D₁₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic
21	C₁₃×C₁₉	C₃×C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
22	C₄×C₁₉⋊C₃	—	13	1	no	Hall
23	C₁₁×C₁₉	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Hall
24	AGL(1,𝔽₁₃)	—	19	1	no	Hall
25	C₁₁×C₁₃	C₄×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
26	C₃×C₄×C₁₁	—	247	1	no	Hall
27	C₂×C₁₉⋊C₃	—	13	1	no	—
28	D₁₃⋊C₃	—	19	1	no	—
29	C₄×C₁₉	—	13	1	no	Hall
30	C₂×C₃×C₁₁	—	247	1	no	—
31	C₁₉⋊C₃	—	13	1	no	Hall
32	#261	C₁₁×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
33	C₄×C₁₁	—	13	1	no	Hall
34	C₁₃⋊C₃	—	19	1	no	Hall
35	C₂×C₁₉	—	13	1	no	—
36	C₃×C₁₁	—	247	1	no	Hall
37	D₁₃	C₂×C₁₁×C₁₉⋊C₃	1	1	yes	characteristic
38	C₂×C₁₁	—	13	1	no	—
39	C₁₉	C₁₁×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
40	C₁₃	C₄×C₁₁×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
41	C₃×C₄	—	247	1	no	Hall
42	C₁₁	#15688303	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	—	247	1	no	—
44	C₄	—	13	1	no	Sylow
45	C₃	—	247	1	no	Sylow
46	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	#15688303
commutator, hypocenter	C₁₃×C₁₉	C₃×C₄×C₁₁
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₃×C₁₉	C₃×C₄
prime radical	C₁₁×#13093365	C₂
cosocle	C₁₉×D₁₃	C₂×C₃×C₁₁
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
2. C₁₁×C₁₉×#261	C₃	semidirect
3. C₁₁×#10625203	C₄	semidirect
5. #15688303	C₁₁	direct (N × H)
6. C₁₁×C₁₃×C₁₉	C₃×C₄	semidirect
11. C₁₉×#261	C₃×C₁₁	semidirect
14. #10625203	C₄×C₁₁	semidirect
16. C₁₁×#261	C₁₉⋊C₃	semidirect
21. C₁₃×C₁₉	C₃×C₄×C₁₁	semidirect
23. C₁₁×C₁₉	AGL(1,𝔽₁₃)	semidirect
25. C₁₁×C₁₃	C₄×C₁₉⋊C₃	semidirect
32. #261	C₁₁×C₁₉⋊C₃	semidirect
39. C₁₉	C₁₁×AGL(1,𝔽₁₃)	semidirect
40. C₁₃	C₄×C₁₁×C₁₉⋊C₃	semidirect
42. C₁₁	#15688303	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₁×#13093365	2
C₁₁×C₁₉×#261	3
#15688303	11
C₄×C₁₁×C₁₉⋊C₃	13
C₁₁×AGL(1,𝔽₁₃)	19

Subgroups — C11×#15688303 #45656704

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#15688303 #45656704