Subgroups — C₃×D₁₁×#63271 #31825035

Order 18018.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×#63271	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₁×#63271	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₇×C₁₃×D₁₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#63271	C₂×C₃	1	3	yes	complemented
5	C₃×C₇×C₁₁×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃×D₁₁×C₁₃⋊C₃	—	7	1	no	maximal, Hall
7	C₇×C₁₃×D₁₁	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×#63271	—	11	1	no	maximal, Hall
9	C₃×ΓL(1,𝔽₈)×D₁₁	—	13	1	no	maximal, Hall
10	C₃×C₁₁×C₁₃⋊C₃	—	7	1	no	Hall
11	C₇×C₁₁×C₁₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₃×D₁₁	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
13	D₁₁×C₁₃⋊C₃	—	7	3	no	—
14	C₃×#63271	D₁₁	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₁₁×ΓL(1,𝔽₈)	—	13	1	no	Hall
16	C₂×C₃×C₇×C₁₃	—	11	1	no	—
17	C₂×#63271	—	11	3	no	—
18	C₃×C₇×D₁₁	C₁₃⋊C₃	1	1	yes	characteristic, complemented
19	ΓL(1,𝔽₈)×D₁₁	—	13	3	no	—
20	C₃×C₁₁×C₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
21	C₁₁×C₁₃⋊C₃	—	7	3	no	—
22	C₁₃×D₁₁	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
23	C₃×C₇×C₁₃	C₃×D₁₁	1	1	yes	characteristic, complemented
24	#63271	C₃×D₁₁	1	3	yes	direct product factor
25	C₂×C₃×C₁₃⋊C₃	—	77	1	no	Hall
26	C₃×C₇×C₁₁	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
27	C₁₁×ΓL(1,𝔽₈)	—	13	3	no	—
28	C₃²×D₁₁	—	91	1	no	Hall
29	C₂×C₇×C₁₃	—	11	1	no	Hall
30	C₇×D₁₁	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
31	C₁₁×C₁₃	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
32	C₂×C₃×ΓL(1,𝔽₈)	—	143	1	no	Hall
33	C₃×C₁₃⋊C₃	—	7	1	no	Hall
34	C₃²×C₁₁	—	91	1	no	Hall
35	C₇×C₁₃	C₃²×D₁₁	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×C₁₃	—	11	1	no	—
37	C₂×C₁₃⋊C₃	—	77	3	no	—
38	C₇×C₁₁	C₂×C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
39	C₃×D₁₁	—	91	3	no	—
40	C₃×D₁₁	#63271	1	1	yes	characteristic, direct product factor
41	C₃×ΓL(1,𝔽₈)	—	13	1	no	Hall
42	C₂×C₃×C₇	—	11	1	no	—
43	C₂×ΓL(1,𝔽₈)	—	143	3	no	—
44	C₃×C₁₃	ΓL(1,𝔽₈)×D₁₁	1	1	yes	characteristic, complemented
45	C₁₃⋊C₃	—	7	3	no	—
46	C₃×C₁₁	—	91	3	no	—
47	C₃×C₁₁	C₂×#63271	1	1	yes	characteristic, complemented
48	C₂×C₁₃	—	11	1	no	Hall
49	D₁₁	C₃×#63271	1	1	yes	characteristic, direct product factor, Hall
50	C₃×C₇	D₁₁×C₁₃⋊C₃	1	1	yes	characteristic, complemented
51	ΓL(1,𝔽₈)	—	13	3	no	—
52	C₂×C₃²	—	1001	1	no	Hall
53	C₂×C₇	—	11	1	no	Hall
54	C₁₃	C₃×ΓL(1,𝔽₈)×D₁₁	1	1	yes	characteristic, complemented, Sylow
55	C₁₁	C₂×C₃×#63271	1	1	yes	characteristic, complemented, Sylow
56	C₃²	—	91	1	no	Sylow
57	C₇	C₃×D₁₁×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₃	—	11	1	no	—
59	C₂×C₃	—	1001	3	no	—
60	C₃	—	91	3	no	—
61	C₃	D₁₁×#63271	1	1	yes	characteristic, direct product factor
62	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₁₁×#63271
commutator, cosocle, hypocenter	C₇×C₁₁×C₁₃	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁×C₁₃	C₂×C₃
LCS	G ▷ C₇×C₁₁×C₁₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁×#63271	C₂	semidirect
2. D₁₁×#63271	C₃	direct (N × H)
3. C₃×C₇×C₁₃×D₁₁	C₃	semidirect
4. C₁₁×#63271	C₂×C₃	semidirect
5. C₃×C₇×C₁₁×C₁₃	C₂×C₃	semidirect
7. C₇×C₁₃×D₁₁	C₃²	semidirect
11. C₇×C₁₁×C₁₃	C₂×C₃²	semidirect
12. C₃×C₁₃×D₁₁	ΓL(1,𝔽₈)	semidirect
14. C₃×#63271	D₁₁	direct (N × H)
18. C₃×C₇×D₁₁	C₁₃⋊C₃	semidirect
20. C₃×C₁₁×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
22. C₁₃×D₁₁	C₃×ΓL(1,𝔽₈)	semidirect
23. C₃×C₇×C₁₃	C₃×D₁₁	semidirect
24. #63271	C₃×D₁₁	direct (N × H)
26. C₃×C₇×C₁₁	C₂×C₁₃⋊C₃	semidirect
30. C₇×D₁₁	C₃×C₁₃⋊C₃	semidirect
31. C₁₁×C₁₃	C₂×C₃×ΓL(1,𝔽₈)	semidirect
35. C₇×C₁₃	C₃²×D₁₁	semidirect
38. C₇×C₁₁	C₂×C₃×C₁₃⋊C₃	semidirect
40. C₃×D₁₁	#63271	direct (N × H)
44. C₃×C₁₃	ΓL(1,𝔽₈)×D₁₁	semidirect
47. C₃×C₁₁	C₂×#63271	semidirect
49. D₁₁	C₃×#63271	direct (N × H)
50. C₃×C₇	D₁₁×C₁₃⋊C₃	semidirect
54. C₁₃	C₃×ΓL(1,𝔽₈)×D₁₁	semidirect
55. C₁₁	C₂×C₃×#63271	semidirect
57. C₇	C₃×D₁₁×C₁₃⋊C₃	semidirect
61. C₃	D₁₁×#63271	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×C₁₁×#63271	2
D₁₁×#63271	3
C₃×C₇×C₁₃×D₁₁	3
C₃×D₁₁×C₁₃⋊C₃	7
C₂×C₃×#63271	11
C₃×ΓL(1,𝔽₈)×D₁₁	13

Subgroups — C3×D11×#63271 #31825035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₁₁×#63271 #31825035