Subgroups — C₁₁×C₃₁×#595 #37550849

Order 23188.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₃₁×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₇×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₃₁×#595	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₄×C₁₁×C₃₁	—	17	1	no	maximal, Hall
5	C₃₁×D₁₇	C₂×C₁₁	1	1	yes	characteristic
6	C₁₁×#595	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₁×C₃₁	—	17	1	no	—
8	C₁₇×C₃₁	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×D₁₇	C₂×C₃₁	1	1	yes	characteristic
10	C₁₁×C₃₁	#595	1	1	yes	characteristic, direct product factor, Hall
11	C₁₁×C₁₇	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
12	C₄×C₃₁	—	17	1	no	Hall
13	#595	C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃₁	—	17	1	no	—
15	C₄×C₁₁	—	17	1	no	Hall
16	D₁₇	C₂×C₁₁×C₃₁	1	1	yes	characteristic
17	C₃₁	C₁₁×#595	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₁₁	—	17	1	no	—
19	C₁₇	C₄×C₁₁×C₃₁	1	1	yes	characteristic, complemented, Sylow
20	C₁₁	C₃₁×#595	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	17	1	no	Sylow
22	C₂	—	17	1	no	—

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

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