Subgroups — C₁₁×C₃⋊(C₃⋊#6923) #37563550

Order 24156.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₁×D₆₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₃⋊#6923	—	3	4	no	maximal
3	C₃²×C₁₁×C₆₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₁×D₆₁	D₃	1	4	yes	—
5	C₁₁×#6923	—	9	1	no	Hall
6	C₃⋊(C₃⋊#6923)	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₁₁×C₆₁	Dic₃	1	4	yes	complemented
8	C₁₁×D₆₁	C₃⋊D₃	1	1	yes	characteristic
9	C₃²×D₆₁	C₂×C₁₁	1	1	yes	characteristic
10	C₃⋊#6923	—	3	4	no	—
11	C₁₁×C₆₁	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
12	C₃²×C₆₁	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₁₁×C₃⋊Dic₃	—	61	1	no	maximal, Hall
14	C₃×D₆₁	D₃×C₁₁	1	4	yes	—
15	#6923	—	9	1	no	Hall
16	C₂×C₃²×C₁₁	—	61	1	no	—
17	C₃×C₆₁	C₁₁×Dic₃	1	4	yes	complemented
18	C₁₁×Dic₃	—	183	4	no	—
19	D₆₁	C₁₁×C₃⋊D₃	1	1	yes	characteristic
20	C₃²×C₁₁	#6923	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₁₁	—	61	4	no	—
22	C₆₁	C₁₁×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
23	C₄×C₁₁	—	549	1	no	Hall
24	C₃⋊Dic₃	—	61	1	no	Hall
25	C₃×C₁₁	C₃⋊#6923	1	4	yes	complemented
26	C₂×C₁₁	—	61	1	no	—
27	C₂×C₃²	—	61	1	no	—
28	Dic₃	—	183	4	no	—
29	C₁₁	C₃⋊(C₃⋊#6923)	1	1	yes	characteristic, direct product factor, Sylow
30	C₃²	C₁₁×#6923	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	61	4	no	—
32	C₄	—	549	1	no	Sylow
33	C₃	C₁₁×C₃⋊#6923	1	4	yes	complemented
34	C₂	—	61	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.