Subgroups — C₁₇×PSL(2,𝔽₁₁) #26014446

Order 11220.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×A₅	—	11	2	no	maximal, Hall
2	C₁₇×C₁₁⋊C₅	—	12	1	no	maximal, Hall
3	PSL(2,𝔽₁₁)	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×D₃×C₁₇	—	55	1	no	maximal, Hall
5	A₄×C₁₇	—	55	1	no	Hall
6	C₁₁×C₁₇	—	12	1	no	Hall
7	D₅×C₁₇	—	66	1	no	—
8	C₂×C₃×C₁₇	—	55	1	no	—
9	D₃×C₁₇	—	55	2	no	—
10	C₅×C₁₇	—	66	1	no	Hall
11	C₂²×C₁₇	—	55	1	no	Hall
12	A₅	—	11	2	no	Hall
13	C₁₁⋊C₅	—	12	1	no	Hall
14	C₃×C₁₇	—	55	1	no	Hall
15	C₂×C₁₇	—	55	1	no	—
16	C₁₇	PSL(2,𝔽₁₁)	1	1	yes	maximal normal, characteristic, direct product factor, Sylow
17	C₂×D₃	—	55	1	no	Hall
18	A₄	—	55	1	no	Hall
19	C₁₁	—	12	1	no	Sylow
20	D₅	—	66	1	no	—
21	C₂×C₃	—	55	1	no	—
22	D₃	—	55	2	no	—
23	C₅	—	66	1	no	Sylow
24	C₂²	—	55	1	no	Sylow
25	C₃	—	55	1	no	Sylow
26	C₂	—	55	1	no	—

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

N	H ≅ G/N	type
3. PSL(2,𝔽₁₁)	C₁₇	direct (N × H)
16. C₁₇	PSL(2,𝔽₁₁)	direct (N × H)

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