Subgroups — C₂×C₁₁×#13093360 #45656751

Order 32604.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#13093360	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁×#10625202	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×C₁₃×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₁×#10625202	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₁×C₁₃×D₁₉	C₂×C₃	1	2	yes	complemented
6	C₂×C₁₁×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×#13093360	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₁×C₁₃×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₁×D₁₉⋊C₃	—	13	1	no	maximal, Hall
10	C₂²×C₁₁×C₁₃⋊C₃	—	19	1	no	maximal, Hall
11	C₂×#10625202	C₂×C₁₁	1	1	yes	characteristic, complemented
12	#13093360	C₂×C₁₁	1	2	yes	direct product factor
13	C₂×C₁₁×C₁₉⋊C₃	—	13	1	no	—
14	C₁₁×D₁₉⋊C₃	—	13	2	no	—
15	C₂×C₁₃×D₁₉	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₁×C₁₃⋊C₃	—	19	2	no	—
17	C₂×C₁₁×C₁₃⋊C₃	—	19	1	no	—
18	C₂×C₁₁×D₁₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
19	#10625202	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
20	C₁₁×C₁₉⋊C₃	—	13	1	no	Hall
21	C₂²×C₁₁×C₁₃	—	19	1	no	Hall
22	C₂×C₁₃×C₁₉	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
23	C₁₃×D₁₉	C₂×C₃×C₁₁	1	2	yes	complemented
24	C₁₁×C₁₃⋊C₃	—	19	1	no	Hall
25	C₂×C₁₁×C₁₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
26	C₁₁×D₁₉	C₂×C₁₃⋊C₃	1	2	yes	complemented
27	C₂×C₁₁×C₁₃	—	19	2	no	—
28	C₂×C₁₁×C₁₃	D₁₉⋊C₃	1	1	yes	characteristic, complemented
29	C₁₃×C₁₉	C₂²×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
30	C₂×D₁₉⋊C₃	—	13	1	no	Hall
31	C₁₁×C₁₉	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
32	C₂²×C₁₃⋊C₃	—	19	1	no	Hall
33	C₁₁×C₁₃	C₂×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
34	C₂²×C₃×C₁₁	—	247	1	no	Hall
35	C₂×C₁₉⋊C₃	—	13	1	no	—
36	D₁₉⋊C₃	—	13	2	no	—
37	C₂×C₁₃⋊C₃	—	19	2	no	—
38	C₂×C₁₃⋊C₃	—	19	1	no	—
39	C₂×D₁₉	C₁₁×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
40	C₂×C₃×C₁₁	—	247	2	no	—
41	C₂×C₃×C₁₁	—	247	1	no	—
42	C₁₉⋊C₃	—	13	1	no	Hall
43	C₂²×C₁₃	—	19	1	no	Hall
44	C₂²×C₁₁	—	19	1	no	Hall
45	C₁₃⋊C₃	—	19	1	no	Hall
46	C₂×C₁₉	C₂×C₁₁×C₁₃⋊C₃	1	1	yes	characteristic, complemented
47	D₁₉	C₂×C₁₁×C₁₃⋊C₃	1	2	yes	complemented
48	C₃×C₁₁	—	247	1	no	Hall
49	C₂×C₁₃	—	19	2	no	—
50	C₂×C₁₃	C₁₁×D₁₉⋊C₃	1	1	yes	characteristic, complemented
51	C₂×C₁₁	—	19	2	no	—
52	C₂×C₁₁	#13093360	1	1	yes	characteristic, direct product factor
53	C₁₉	C₂²×C₁₁×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
54	C₁₃	C₂×C₁₁×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₃	—	247	1	no	Hall
56	C₁₁	C₂×#13093360	1	1	yes	characteristic, direct product factor, Sylow
57	C₂×C₃	—	247	2	no	—
58	C₂×C₃	—	247	1	no	—
59	C₂²	—	19	1	no	Sylow
60	C₃	—	247	1	no	Sylow
61	C₂	—	19	2	no	—
62	C₂	C₁₁×#13093360	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁	#13093360
commutator, cosocle, hypocenter	C₁₃×C₁₉	C₂²×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×#13093360	C₂	direct (N × H)
2. C₂×C₁₁×#10625202	C₂	semidirect
3. C₂×C₁₁×C₁₃×D₁₉	C₃	semidirect
4. C₁₁×#10625202	C₂²	semidirect
5. C₁₁×C₁₃×D₁₉	C₂×C₃	semidirect
6. C₂×C₁₁×C₁₃×C₁₉	C₂×C₃	semidirect
7. C₂×#13093360	C₁₁	direct (N × H)
8. C₁₁×C₁₃×C₁₉	C₂²×C₃	semidirect
11. C₂×#10625202	C₂×C₁₁	semidirect
12. #13093360	C₂×C₁₁	direct (N × H)
15. C₂×C₁₃×D₁₉	C₃×C₁₁	semidirect
18. C₂×C₁₁×D₁₉	C₁₃⋊C₃	semidirect
19. #10625202	C₂²×C₁₁	semidirect
22. C₂×C₁₃×C₁₉	C₂×C₃×C₁₁	semidirect
23. C₁₃×D₁₉	C₂×C₃×C₁₁	semidirect
25. C₂×C₁₁×C₁₉	C₂×C₁₃⋊C₃	semidirect
26. C₁₁×D₁₉	C₂×C₁₃⋊C₃	semidirect
28. C₂×C₁₁×C₁₃	D₁₉⋊C₃	semidirect
29. C₁₃×C₁₉	C₂²×C₃×C₁₁	semidirect
31. C₁₁×C₁₉	C₂²×C₁₃⋊C₃	semidirect
33. C₁₁×C₁₃	C₂×D₁₉⋊C₃	semidirect
39. C₂×D₁₉	C₁₁×C₁₃⋊C₃	semidirect
46. C₂×C₁₉	C₂×C₁₁×C₁₃⋊C₃	semidirect
47. D₁₉	C₂×C₁₁×C₁₃⋊C₃	semidirect
50. C₂×C₁₃	C₁₁×D₁₉⋊C₃	semidirect
52. C₂×C₁₁	#13093360	direct (N × H)
53. C₁₉	C₂²×C₁₁×C₁₃⋊C₃	semidirect
54. C₁₃	C₂×C₁₁×D₁₉⋊C₃	semidirect
56. C₁₁	C₂×#13093360	direct (N × H)
62. C₂	C₁₁×#13093360	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×#13093360	2
C₂×C₁₁×#10625202	2
C₂×C₁₁×C₁₃×D₁₉	3
C₂×#13093360	11
C₂×C₁₁×D₁₉⋊C₃	13
C₂²×C₁₁×C₁₃⋊C₃	19

Subgroups — C2×C11×#13093360 #45656751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#13093360 #45656751