Subgroups — C₂²×C₁₁×C₁₃×C₇⋊C₉ #49114504

Order 36036.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₁₃×C₇⋊C₉	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₇×C₁₁×C₁₃	C₃	1	1	yes	maximal, characteristic
3	C₁₁×C₁₃×C₇⋊C₉	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₇×C₁₁×C₁₃	C₂×C₃	1	3	yes	—
5	C₂²×C₉×C₁₁×C₁₃	—	7	1	no	maximal, Hall
6	C₂²×C₇×C₁₁×C₁₃	C₉	1	1	yes	characteristic, complemented, Hall
7	C₂²×C₁₃×C₇⋊C₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×C₇×C₁₁×C₁₃	C₂²×C₃	1	1	yes	characteristic
9	C₂²×C₁₁×C₇⋊C₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₉×C₁₁×C₁₃	—	7	3	no	—
11	C₂×C₇×C₁₁×C₁₃	C₂×C₉	1	3	yes	complemented
12	C₂²×C₃×C₁₁×C₁₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
13	C₂×C₁₃×C₇⋊C₉	C₂×C₁₁	1	3	yes	direct product factor
14	C₂×C₁₁×C₇⋊C₉	C₂×C₁₃	1	3	yes	direct product factor
15	C₉×C₁₁×C₁₃	—	7	1	no	Hall
16	C₂²×C₃×C₇×C₁₃	C₃×C₁₁	1	1	yes	characteristic
17	C₇×C₁₁×C₁₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
18	C₂²×C₃×C₇×C₁₁	C₃×C₁₃	1	1	yes	characteristic
19	C₂×C₃×C₁₁×C₁₃	C₂×ΓL(1,𝔽₈)	1	3	yes	—
20	C₁₃×C₇⋊C₉	C₂²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
21	C₁₁×C₇⋊C₉	C₂²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
22	C₂²×C₁₁×C₁₃	C₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃×C₇×C₁₃	C₂×C₃×C₁₁	1	3	yes	—
24	C₂²×C₉×C₁₃	—	7	1	no	Hall
25	C₂×C₃×C₇×C₁₁	C₂×C₃×C₁₃	1	3	yes	—
26	C₃×C₁₁×C₁₃	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic
27	C₂²×C₉×C₁₁	—	7	1	no	Hall
28	C₂²×C₇×C₁₃	C₉×C₁₁	1	1	yes	characteristic, complemented, Hall
29	C₂²×C₇×C₁₁	C₉×C₁₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₁₁×C₁₃	C₂×C₇⋊C₉	1	3	yes	direct product factor
31	C₃×C₇×C₁₃	C₂²×C₃×C₁₁	1	1	yes	characteristic
32	C₂²×C₇⋊C₉	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₉×C₁₃	—	7	3	no	—
34	C₃×C₇×C₁₁	C₂²×C₃×C₁₃	1	1	yes	characteristic
35	C₂×C₉×C₁₁	—	7	3	no	—
36	C₂×C₇×C₁₃	C₂×C₉×C₁₁	1	3	yes	complemented
37	C₂²×C₃×C₁₃	C₁₁×ΓL(1,𝔽₈)	1	1	yes	characteristic
38	C₂×C₇×C₁₁	C₂×C₉×C₁₃	1	3	yes	complemented
39	C₁₁×C₁₃	C₂²×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
40	C₂²×C₃×C₁₁	C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
41	C₂×C₇⋊C₉	C₂×C₁₁×C₁₃	1	3	yes	direct product factor
42	C₉×C₁₃	—	7	1	no	Hall
43	C₉×C₁₁	—	7	1	no	Hall
44	C₇×C₁₃	C₂²×C₉×C₁₁	1	1	yes	characteristic, complemented, Hall
45	C₂²×C₃×C₇	C₃×C₁₁×C₁₃	1	1	yes	characteristic
46	C₂×C₃×C₁₃	C₂×C₁₁×ΓL(1,𝔽₈)	1	3	yes	—
47	C₇×C₁₁	C₂²×C₉×C₁₃	1	1	yes	characteristic, complemented, Hall
48	C₂×C₃×C₁₁	C₂×C₁₃×ΓL(1,𝔽₈)	1	3	yes	—
49	C₇⋊C₉	C₂²×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
50	C₂²×C₁₃	C₁₁×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
51	C₂²×C₁₁	C₁₃×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
52	C₂×C₃×C₇	C₂×C₃×C₁₁×C₁₃	1	3	yes	—
53	C₃×C₁₃	C₂²×C₁₁×ΓL(1,𝔽₈)	1	1	yes	characteristic
54	C₂²×C₉	—	7	1	no	Hall
55	C₃×C₁₁	C₂²×C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
56	C₂²×C₇	C₉×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Hall
57	C₂×C₁₃	C₂×C₁₁×C₇⋊C₉	1	3	yes	direct product factor
58	C₂×C₁₁	C₂×C₁₃×C₇⋊C₉	1	3	yes	direct product factor
59	C₃×C₇	C₂²×C₃×C₁₁×C₁₃	1	1	yes	characteristic
60	C₂×C₉	—	7	3	no	—
61	C₂×C₇	C₂×C₉×C₁₁×C₁₃	1	3	yes	complemented
62	C₁₃	C₂²×C₁₁×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
63	C₂²×C₃	C₁₁×C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
64	C₁₁	C₂²×C₁₃×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
65	C₉	—	7	1	no	Sylow
66	C₇	C₂²×C₉×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₃	C₂×C₁₁×C₁₃×ΓL(1,𝔽₈)	1	3	yes	—
68	C₂²	C₁₁×C₁₃×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
69	C₃	C₂²×C₁₁×C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
70	C₂	C₂×C₁₁×C₁₃×C₇⋊C₉	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃×C₁₁×C₁₃	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₂²×C₉×C₁₁×C₁₃
Frattini	C₃	C₂²×C₁₁×C₁₃×ΓL(1,𝔽₈)
Fitting, socle, prime radical	C₂²×C₃×C₇×C₁₁×C₁₃	C₃
cosocle	C₃×C₇	C₂²×C₃×C₁₁×C₁₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₂²×C₃×C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×C₁₃×C₇⋊C₉	C₂	direct (N × H)
3. C₁₁×C₁₃×C₇⋊C₉	C₂²	direct (N × H)
6. C₂²×C₇×C₁₁×C₁₃	C₉	semidirect
7. C₂²×C₁₃×C₇⋊C₉	C₁₁	direct (N × H)
9. C₂²×C₁₁×C₇⋊C₉	C₁₃	direct (N × H)
11. C₂×C₇×C₁₁×C₁₃	C₂×C₉	semidirect
13. C₂×C₁₃×C₇⋊C₉	C₂×C₁₁	direct (N × H)
14. C₂×C₁₁×C₇⋊C₉	C₂×C₁₃	direct (N × H)
17. C₇×C₁₁×C₁₃	C₂²×C₉	semidirect
20. C₁₃×C₇⋊C₉	C₂²×C₁₁	direct (N × H)
21. C₁₁×C₇⋊C₉	C₂²×C₁₃	direct (N × H)
22. C₂²×C₁₁×C₁₃	C₇⋊C₉	direct (N × H)
28. C₂²×C₇×C₁₃	C₉×C₁₁	semidirect
29. C₂²×C₇×C₁₁	C₉×C₁₃	semidirect
30. C₂×C₁₁×C₁₃	C₂×C₇⋊C₉	direct (N × H)
32. C₂²×C₇⋊C₉	C₁₁×C₁₃	direct (N × H)
36. C₂×C₇×C₁₃	C₂×C₉×C₁₁	semidirect
38. C₂×C₇×C₁₁	C₂×C₉×C₁₃	semidirect
39. C₁₁×C₁₃	C₂²×C₇⋊C₉	direct (N × H)
41. C₂×C₇⋊C₉	C₂×C₁₁×C₁₃	direct (N × H)
44. C₇×C₁₃	C₂²×C₉×C₁₁	semidirect
47. C₇×C₁₁	C₂²×C₉×C₁₃	semidirect
49. C₇⋊C₉	C₂²×C₁₁×C₁₃	direct (N × H)
50. C₂²×C₁₃	C₁₁×C₇⋊C₉	direct (N × H)
51. C₂²×C₁₁	C₁₃×C₇⋊C₉	direct (N × H)
56. C₂²×C₇	C₉×C₁₁×C₁₃	semidirect
57. C₂×C₁₃	C₂×C₁₁×C₇⋊C₉	direct (N × H)
58. C₂×C₁₁	C₂×C₁₃×C₇⋊C₉	direct (N × H)
61. C₂×C₇	C₂×C₉×C₁₁×C₁₃	semidirect
62. C₁₃	C₂²×C₁₁×C₇⋊C₉	direct (N × H)
64. C₁₁	C₂²×C₁₃×C₇⋊C₉	direct (N × H)
66. C₇	C₂²×C₉×C₁₁×C₁₃	semidirect
68. C₂²	C₁₁×C₁₃×C₇⋊C₉	direct (N × H)
70. C₂	C₂×C₁₁×C₁₃×C₇⋊C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁×C₁₃×C₇⋊C₉	2
C₂²×C₃×C₇×C₁₁×C₁₃	3
C₂²×C₉×C₁₁×C₁₃	7
C₂²×C₁₃×C₇⋊C₉	11
C₂²×C₁₁×C₇⋊C₉	13

Subgroups — C22×C11×C13×C7⋊C9 #49114504

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁×C₁₃×C₇⋊C₉ #49114504