Subgroups — C₃×C₁₇×PSL(2,𝔽₁₁) #46778218

Order 33660.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×PSL(2,𝔽₁₁)	C₃	1	1	yes	maximal, characteristic, direct product factor
2	C₃×C₁₇×A₅	—	11	2	no	maximal, Hall
3	C₃×C₁₇×C₁₁⋊C₅	—	12	1	no	maximal
4	C₃×PSL(2,𝔽₁₁)	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₇×A₅	—	11	2	no	—
6	C₁₇×C₁₁⋊C₅	—	12	1	no	Hall
7	PSL(2,𝔽₁₁)	C₃×C₁₇	1	1	yes	characteristic, direct product factor
8	C₂×C₃×D₃×C₁₇	—	55	1	no	maximal, Hall
9	C₃×A₄×C₁₇	—	55	1	no	Hall
10	C₃×C₁₁×C₁₇	—	12	1	no	—
11	C₃×D₅×C₁₇	—	66	1	no	—
12	C₂×C₃²×C₁₇	—	55	1	no	—
13	C₃×D₃×C₁₇	—	55	2	no	—
14	C₃×C₅×C₁₇	—	66	1	no	—
15	C₂²×C₃×C₁₇	—	55	1	no	—
16	C₂×D₃×C₁₇	—	55	1	no	—
17	A₄×C₁₇	—	55	1	no	—
18	A₄×C₁₇	—	55	2	no	—
19	C₁₁×C₁₇	—	12	1	no	Hall
20	C₃×A₅	—	11	2	no	Hall
21	D₅×C₁₇	—	66	1	no	—
22	C₃×C₁₁⋊C₅	—	12	1	no	—
23	C₃²×C₁₇	—	55	1	no	Hall
24	C₂×C₃×C₁₇	—	55	1	no	—
25	C₂×C₃×C₁₇	—	55	1	no	—
26	C₂×C₃×C₁₇	—	110	1	no	—
27	D₃×C₁₇	—	55	2	no	—
28	C₅×C₁₇	—	66	1	no	Hall
29	C₂²×C₁₇	—	55	1	no	Hall
30	A₅	—	11	2	no	—
31	C₁₁⋊C₅	—	12	1	no	Hall
32	C₃×C₁₇	—	55	1	no	—
33	C₃×C₁₇	—	110	1	no	—
34	C₃×C₁₇	PSL(2,𝔽₁₁)	1	1	yes	maximal normal, characteristic, direct product factor
35	C₂×C₃×D₃	—	55	1	no	Hall
36	C₃×A₄	—	55	1	no	Hall
37	C₂×C₁₇	—	55	1	no	—
38	C₃×C₁₁	—	12	1	no	—
39	C₃×D₅	—	66	1	no	—
40	C₂×C₃²	—	55	1	no	—
41	C₃×D₃	—	55	2	no	—
42	C₁₇	C₃×PSL(2,𝔽₁₁)	1	1	yes	characteristic, direct product factor, Sylow
43	C₃×C₅	—	66	1	no	—
44	C₂²×C₃	—	55	1	no	—
45	C₂×D₃	—	55	1	no	—
46	A₄	—	55	1	no	—
47	A₄	—	55	2	no	—
48	C₁₁	—	12	1	no	Sylow
49	D₅	—	66	1	no	—
50	C₃²	—	55	1	no	Sylow
51	C₂×C₃	—	55	1	no	—
52	C₂×C₃	—	55	1	no	—
53	C₂×C₃	—	110	1	no	—
54	D₃	—	55	2	no	—
55	C₅	—	66	1	no	Sylow
56	C₂²	—	55	1	no	Sylow
57	C₃	—	55	1	no	—
58	C₃	—	110	1	no	—
59	C₃	C₁₇×PSL(2,𝔽₁₁)	1	1	yes	characteristic, direct product factor
60	C₂	—	55	1	no	—

	subgroup	G/H
center, Fitting, hypercenter	C₃×C₁₇	PSL(2,𝔽₁₁)
commutator, hypocenter	PSL(2,𝔽₁₁)	C₃×C₁₇
Frattini	C₁	G
LCS	G ▷ PSL(2,𝔽₁₁)
UCS	C₁ ◁ C₃×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×PSL(2,𝔽₁₁)	C₃	direct (N × H)
4. C₃×PSL(2,𝔽₁₁)	C₁₇	direct (N × H)
7. PSL(2,𝔽₁₁)	C₃×C₁₇	direct (N × H)
34. C₃×C₁₇	PSL(2,𝔽₁₁)	direct (N × H)
42. C₁₇	C₃×PSL(2,𝔽₁₁)	direct (N × H)
59. C₃	C₁₇×PSL(2,𝔽₁₁)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×PSL(2,𝔽₁₁)	3
C₃×C₁₇×A₅	11
C₃×C₁₇×C₁₁⋊C₅	12
C₃×PSL(2,𝔽₁₁)	17
C₂×C₃×D₃×C₁₇	55

Subgroups — C3×C17×PSL(2,𝔽11) #46778218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₇×PSL(2,𝔽₁₁) #46778218