Subgroups — C₄₉×PSL(2,𝔽₁₁) #44568957

Order 32340.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×PSL(2,𝔽₁₁)	C₇	1	1	yes	maximal, characteristic
2	C₄₉×A₅	—	11	2	no	maximal, Hall
3	C₄₉×C₁₁⋊C₅	—	12	1	no	maximal, Hall
4	PSL(2,𝔽₁₁)	C₄₉	1	1	yes	characteristic, direct product factor, Hall
5	C₂×D₃×C₄₉	—	55	1	no	maximal, Hall
6	A₄×C₄₉	—	55	1	no	Hall
7	C₁₁×C₄₉	—	12	1	no	Hall
8	D₅×C₄₉	—	66	1	no	—
9	C₇×A₅	—	11	2	no	—
10	C₇×C₁₁⋊C₅	—	12	1	no	—
11	C₂×C₃×C₄₉	—	55	1	no	—
12	D₃×C₄₉	—	55	2	no	—
13	C₅×C₄₉	—	66	1	no	Hall
14	C₂²×C₄₉	—	55	1	no	Hall
15	C₃×C₄₉	—	55	1	no	Hall
16	C₂×C₄₉	—	55	1	no	—
17	C₂×D₃×C₇	—	55	1	no	—
18	C₇×A₄	—	55	1	no	—
19	C₇×C₁₁	—	12	1	no	—
20	C₇×D₅	—	66	1	no	—
21	A₅	—	11	2	no	Hall
22	C₁₁⋊C₅	—	12	1	no	Hall
23	C₄₉	PSL(2,𝔽₁₁)	1	1	yes	maximal normal, characteristic, direct product factor, Sylow
24	C₂×C₃×C₇	—	55	1	no	—
25	D₃×C₇	—	55	2	no	—
26	C₅×C₇	—	66	1	no	—
27	C₂²×C₇	—	55	1	no	—
28	C₃×C₇	—	55	1	no	—
29	C₂×C₇	—	55	1	no	—
30	C₂×D₃	—	55	1	no	Hall
31	A₄	—	55	1	no	Hall
32	C₁₁	—	12	1	no	Sylow
33	D₅	—	66	1	no	—
34	C₇	C₇×PSL(2,𝔽₁₁)	1	1	yes	characteristic
35	C₂×C₃	—	55	1	no	—
36	D₃	—	55	2	no	—
37	C₅	—	66	1	no	Sylow
38	C₂²	—	55	1	no	Sylow
39	C₃	—	55	1	no	Sylow
40	C₂	—	55	1	no	—

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

N	H ≅ G/N	type
4. PSL(2,𝔽₁₁)	C₄₉	direct (N × H)
23. C₄₉	PSL(2,𝔽₁₁)	direct (N × H)

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