Subgroups — C₃×#16838463 #26039607

Order 11466.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃⋊#3862	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₉₁	C₃	1	1	yes	maximal, characteristic, complemented
3	#16838463	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
5	C₁₃⋊#3862	C₂×C₃	1	3	yes	complemented
6	C₃×#10587723	—	7	1	no	maximal
7	C₃×#10587716	—	7	1	no	maximal
8	C₇×D₉₁	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×#64422	—	13	1	no	maximal, Hall
10	C₃×#63271	—	7	1	no	—
11	C₃×#63270	—	7	1	no	—
12	C₇²×C₁₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
13	C₃×D₉₁	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
14	C₃×C₇×D₁₃	—	7	1	no	—
15	#10587723	—	7	3	no	—
16	#10587716	—	7	3	no	—
17	C₃×#3862	—	13	1	no	Hall
18	C₃×C₇×D₇	—	13	1	no	—
19	#64422	—	13	3	no	—
20	C₃×C₇×C₁₃	—	6	1	no	—
21	C₃×C₇×C₁₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
22	C₃×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
23	#63271	—	7	3	no	—
24	#63270	—	7	3	no	—
25	C₃×D₁₃⋊C₃	—	49	1	no	Hall
26	D₉₁	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
27	C₇×D₁₃	—	7	1	no	—
28	C₃×C₇²	D₁₃⋊C₃	1	1	yes	characteristic, complemented
29	#3862	—	13	3	no	—
30	C₂×C₃×ΓL(1,𝔽₈)	—	91	1	no	—
31	C₃×AGL(1,𝔽₇)	—	91	1	no	—
32	C₃×C₁₃⋊C₃	—	49	1	no	Hall
33	C₇×D₇	—	13	1	no	Hall
34	C₇×C₁₃	—	6	1	no	—
35	C₇×C₁₃	C₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
36	C₇×C₁₃	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
37	C₃×D₁₃	—	7	1	no	—
38	D₁₃⋊C₃	—	49	3	no	—
39	C₃×ΓL(1,𝔽₈)	—	91	1	no	—
40	C₃×ΓL(1,𝔽₈)	—	91	1	no	—
41	C₇²	C₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃×C₇	—	91	1	no	—
43	C₃×D₇	—	13	1	no	—
44	C₂×ΓL(1,𝔽₈)	—	91	3	no	—
45	AGL(1,𝔽₇)	—	91	3	no	—
46	C₃×C₁₃	#64422	1	1	yes	characteristic, complemented
47	C₁₃⋊C₃	—	49	3	no	—
48	D₁₃	—	7	1	no	Hall
49	C₃×C₇	—	6	1	no	—
50	C₃×C₇	#10587716	1	1	yes	characteristic, complemented
51	C₃×C₇	#10587723	1	1	yes	characteristic, complemented
52	ΓL(1,𝔽₈)	—	91	3	no	—
53	ΓL(1,𝔽₈)	—	91	3	no	—
54	C₂×C₃²	—	637	1	no	Hall
55	C₂×C₇	—	91	1	no	—
56	D₇	—	13	1	no	—
57	C₁₃	C₃×#64422	1	1	yes	characteristic, complemented, Sylow
58	C₃²	—	637	1	no	Sylow
59	C₇	—	6	1	no	—
60	C₇	C₃×#10587716	1	1	yes	characteristic, complemented
61	C₇	C₃×#10587723	1	1	yes	characteristic, complemented
62	C₂×C₃	—	91	1	no	—
63	C₂×C₃	—	637	3	no	—
64	C₃	—	637	3	no	—
65	C₃	#16838463	1	1	yes	characteristic, direct product factor
66	C₂	—	91	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#16838463
commutator, cosocle, hypocenter	C₇²×C₁₃	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃⋊#3862	C₂	semidirect
2. C₃×C₇×D₉₁	C₃	semidirect
3. #16838463	C₃	direct (N × H)
4. C₃×C₇²×C₁₃	C₂×C₃	semidirect
5. C₁₃⋊#3862	C₂×C₃	semidirect
8. C₇×D₉₁	C₃²	semidirect
12. C₇²×C₁₃	C₂×C₃²	semidirect
13. C₃×D₉₁	ΓL(1,𝔽₈)	semidirect
21. C₃×C₇×C₁₃	AGL(1,𝔽₇)	semidirect
22. C₃×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
26. D₉₁	C₃×ΓL(1,𝔽₈)	semidirect
28. C₃×C₇²	D₁₃⋊C₃	semidirect
35. C₇×C₁₃	C₃×AGL(1,𝔽₇)	semidirect
36. C₇×C₁₃	C₂×C₃×ΓL(1,𝔽₈)	semidirect
41. C₇²	C₃×D₁₃⋊C₃	semidirect
46. C₃×C₁₃	#64422	semidirect
50. C₃×C₇	#10587716	semidirect
51. C₃×C₇	#10587723	semidirect
57. C₁₃	C₃×#64422	semidirect
60. C₇	C₃×#10587716	semidirect
61. C₇	C₃×#10587723	semidirect
65. C₃	#16838463	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×C₁₃⋊#3862	2
C₃×C₇×D₉₁	3
#16838463	3
C₃×#10587723	7
C₃×#10587716	7
C₃×#64422	13

Subgroups — C3×#16838463 #26039607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#16838463 #26039607