Subgroups — C₃×C₇×C₁₁⋊AGL(1,𝔽₁₃) #49114637

Order 36036.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₁×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇×C₁₁⋊#261	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₁⋊AGL(1,𝔽₁₃)	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₇×C₁₁×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₇×C₁₁×D₁₃⋊C₃	C₂×C₃	1	3	yes	—
6	C₃×C₇×C₁₁×D₁₃	C₂×C₃	1	1	yes	characteristic
7	C₃×C₁₁⋊AGL(1,𝔽₁₃)	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₁₁⋊#261	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×AGL(1,𝔽₁₃)	—	11	1	no	maximal, Hall
10	C₇×C₁₁×C₁₃⋊C₃	C₃×C₄	1	3	yes	complemented
11	C₃×C₇×C₁₁×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented
12	C₃²×C₇×Dic₁₁	—	13	1	no	maximal, Hall
13	C₃×C₁₁×D₁₃⋊C₃	C₂×C₇	1	1	yes	characteristic
14	C₇×C₁₁×D₁₃	C₂×C₃²	1	1	yes	characteristic
15	C₃×C₁₁⋊#261	C₃×C₇	1	1	yes	characteristic, complemented
16	C₁₁⋊AGL(1,𝔽₁₃)	C₃×C₇	1	3	yes	direct product factor
17	C₃×C₇×D₁₃⋊C₃	D₁₁	1	1	yes	characteristic
18	C₂×C₃²×C₇×C₁₁	—	13	1	no	—
19	C₃×C₁₁×C₁₃⋊C₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
20	C₃×C₇×#261	—	11	1	no	—
21	C₇×AGL(1,𝔽₁₃)	—	11	3	no	—
22	C₇×C₁₁×C₁₃	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
23	C₃×C₇×Dic₁₁	—	13	1	no	—
24	C₃×C₇×Dic₁₁	—	13	3	no	—
25	C₃×C₁₁×D₁₃	C₂×C₃×C₇	1	1	yes	characteristic
26	C₁₁×D₁₃⋊C₃	C₂×C₃×C₇	1	3	yes	—
27	C₃×C₇×C₁₃⋊C₃	Dic₁₁	1	1	yes	characteristic, complemented, Hall
28	C₃²×C₇×C₁₁	—	13	1	no	Hall
29	C₁₁⋊#261	C₃²×C₇	1	1	yes	characteristic, complemented, Hall
30	C₃×C₇×D₁₃	C₃×D₁₁	1	1	yes	characteristic
31	C₇×D₁₃⋊C₃	C₃×D₁₁	1	3	yes	—
32	C₃×AGL(1,𝔽₁₃)	—	11	1	no	Hall
33	C₂×C₃×C₇×C₁₁	—	13	3	no	—
34	C₂×C₃×C₇×C₁₁	—	13	1	no	—
35	C₃×C₁₁×C₁₃	C₃×C₄×C₇	1	1	yes	characteristic, complemented
36	C₁₁×C₁₃⋊C₃	C₃×C₄×C₇	1	3	yes	complemented
37	C₃²×Dic₁₁	—	13	1	no	Hall
38	C₇×#261	—	11	1	no	Hall
39	C₇×Dic₁₁	—	13	1	no	Hall
40	C₁₁×D₁₃	C₂×C₃²×C₇	1	1	yes	characteristic
41	C₃×C₇×C₁₃	C₃×Dic₁₁	1	1	yes	characteristic, complemented
42	C₇×C₁₃⋊C₃	C₃×Dic₁₁	1	3	yes	complemented
43	C₃²×C₄×C₇	—	143	1	no	Hall
44	C₃×D₁₃⋊C₃	C₇×D₁₁	1	1	yes	characteristic
45	C₃×C₇×C₁₁	—	13	3	no	—
46	C₃×C₇×C₁₁	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented
47	C₂×C₃²×C₁₁	—	13	1	no	—
48	C₇×D₁₃	C₃²×D₁₁	1	1	yes	characteristic
49	C₃×#261	—	11	1	no	—
50	AGL(1,𝔽₁₃)	—	11	3	no	—
51	C₂×C₇×C₁₁	—	13	1	no	—
52	C₁₁×C₁₃	C₃²×C₄×C₇	1	1	yes	characteristic, complemented, Hall
53	C₃×Dic₁₁	—	13	3	no	—
54	C₃×Dic₁₁	—	13	1	no	—
55	C₂×C₃²×C₇	—	13	1	no	—
56	C₃×C₁₃⋊C₃	C₇×Dic₁₁	1	1	yes	characteristic, complemented, Hall
57	C₃²×C₁₁	—	13	1	no	Hall
58	C₇×C₁₃	C₃²×Dic₁₁	1	1	yes	characteristic, complemented, Hall
59	C₃×C₄×C₇	—	143	3	no	—
60	C₃×C₄×C₇	—	143	1	no	—
61	C₃×D₁₃	C₃×C₇×D₁₁	1	1	yes	characteristic
62	D₁₃⋊C₃	C₃×C₇×D₁₁	1	3	yes	—
63	C₇×C₁₁	C₃×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Hall
64	C₂×C₃×C₁₁	—	13	3	no	—
65	C₂×C₃×C₁₁	—	13	1	no	—
66	C₃²×C₇	—	13	1	no	Hall
67	#261	—	11	1	no	Hall
68	Dic₁₁	—	13	1	no	Hall
69	C₂×C₃×C₇	—	13	3	no	—
70	C₂×C₃×C₇	—	13	1	no	—
71	C₃×C₁₃	C₃×C₇×Dic₁₁	1	1	yes	characteristic, complemented
72	C₁₃⋊C₃	C₃×C₇×Dic₁₁	1	3	yes	complemented
73	C₃²×C₄	—	143	1	no	Hall
74	C₃×C₁₁	—	13	3	no	—
75	C₃×C₁₁	C₇×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented
76	C₄×C₇	—	143	1	no	Hall
77	D₁₃	C₃²×C₇×D₁₁	1	1	yes	characteristic
78	C₂×C₁₁	—	13	1	no	—
79	C₃×C₇	—	13	3	no	—
80	C₃×C₇	C₁₁⋊AGL(1,𝔽₁₃)	1	1	yes	characteristic, direct product factor
81	C₂×C₃²	—	13	1	no	—
82	C₂×C₇	—	13	1	no	—
83	C₁₃	C₃²×C₇×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
84	C₃×C₄	—	143	3	no	—
85	C₃×C₄	—	143	1	no	—
86	C₁₁	C₃×C₇×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
87	C₃²	—	13	1	no	Sylow
88	C₇	C₃×C₁₁⋊AGL(1,𝔽₁₃)	1	1	yes	characteristic, direct product factor, Sylow
89	C₂×C₃	—	13	3	no	—
90	C₂×C₃	—	13	1	no	—
91	C₄	—	143	1	no	Sylow
92	C₃	—	13	3	no	—
93	C₃	C₇×C₁₁⋊AGL(1,𝔽₁₃)	1	1	yes	characteristic, direct product factor
94	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₇	C₁₁⋊AGL(1,𝔽₁₃)
commutator, hypocenter	C₁₁×C₁₃	C₃²×C₄×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁×C₁₃	C₃×C₄
prime radical	C₃×C₇×C₁₁×D₁₃⋊C₃	C₂
cosocle	C₁₁×D₁₃	C₂×C₃²×C₇
LCS	G ▷ C₁₁×C₁₃
UCS	C₁ ◁ C₃×C₇

Complements

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

N	H ≅ G/N	type
2. C₃×C₇×C₁₁⋊#261	C₃	semidirect
3. C₇×C₁₁⋊AGL(1,𝔽₁₃)	C₃	direct (N × H)
4. C₃×C₇×C₁₁×C₁₃⋊C₃	C₄	semidirect
7. C₃×C₁₁⋊AGL(1,𝔽₁₃)	C₇	direct (N × H)
8. C₇×C₁₁⋊#261	C₃²	semidirect
10. C₇×C₁₁×C₁₃⋊C₃	C₃×C₄	semidirect
11. C₃×C₇×C₁₁×C₁₃	C₃×C₄	semidirect
15. C₃×C₁₁⋊#261	C₃×C₇	semidirect
16. C₁₁⋊AGL(1,𝔽₁₃)	C₃×C₇	direct (N × H)
19. C₃×C₁₁×C₁₃⋊C₃	C₄×C₇	semidirect
22. C₇×C₁₁×C₁₃	C₃²×C₄	semidirect
27. C₃×C₇×C₁₃⋊C₃	Dic₁₁	semidirect
29. C₁₁⋊#261	C₃²×C₇	semidirect
35. C₃×C₁₁×C₁₃	C₃×C₄×C₇	semidirect
36. C₁₁×C₁₃⋊C₃	C₃×C₄×C₇	semidirect
41. C₃×C₇×C₁₃	C₃×Dic₁₁	semidirect
42. C₇×C₁₃⋊C₃	C₃×Dic₁₁	semidirect
46. C₃×C₇×C₁₁	AGL(1,𝔽₁₃)	semidirect
52. C₁₁×C₁₃	C₃²×C₄×C₇	semidirect
56. C₃×C₁₃⋊C₃	C₇×Dic₁₁	semidirect
58. C₇×C₁₃	C₃²×Dic₁₁	semidirect
63. C₇×C₁₁	C₃×AGL(1,𝔽₁₃)	semidirect
71. C₃×C₁₃	C₃×C₇×Dic₁₁	semidirect
72. C₁₃⋊C₃	C₃×C₇×Dic₁₁	semidirect
75. C₃×C₁₁	C₇×AGL(1,𝔽₁₃)	semidirect
80. C₃×C₇	C₁₁⋊AGL(1,𝔽₁₃)	direct (N × H)
83. C₁₃	C₃²×C₇×Dic₁₁	semidirect
86. C₁₁	C₃×C₇×AGL(1,𝔽₁₃)	semidirect
88. C₇	C₃×C₁₁⋊AGL(1,𝔽₁₃)	direct (N × H)
93. C₃	C₇×C₁₁⋊AGL(1,𝔽₁₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₁×D₁₃⋊C₃	2
C₃×C₇×C₁₁⋊#261	3
C₇×C₁₁⋊AGL(1,𝔽₁₃)	3
C₃×C₁₁⋊AGL(1,𝔽₁₃)	7
C₃×C₇×AGL(1,𝔽₁₃)	11
C₃²×C₇×Dic₁₁	13

Subgroups — C3×C7×C11⋊AGL(1,𝔽13) #49114637

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×C₁₁⋊AGL(1,𝔽₁₃) #49114637