Subgroups — C₁₁⋊(C₅₉⋊#157) #37552521

Order 23364.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₃⋊D₃×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₁×C₅₉	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₁₁×C₅₉	—	6	2	no	—
4	Dic₆₄₉	—	9	1	no	maximal, Hall
5	C₅₉⋊#157	—	11	1	no	maximal, Hall
6	C₃×C₁₁×C₅₉	—	2	2	no	—
7	C₂×C₁₁×C₅₉	—	9	1	no	—
8	C₃⋊D₃×C₅₉	D₁₁	1	1	yes	characteristic
9	C₁₁×C₅₉	#157	1	1	yes	characteristic, complemented, Hall
10	C₃²×C₅₉	Dic₁₁	1	1	yes	characteristic, complemented, Hall
11	C₁₁⋊#157	—	59	1	no	maximal, Hall
12	D₃×C₅₉	—	6	2	no	—
13	Dic₅₉	—	99	1	no	Hall
14	C₁₁×C₃⋊D₃	D₅₉	1	1	yes	characteristic
15	C₃×C₅₉	—	2	2	no	—
16	C₂×C₅₉	—	9	1	no	—
17	C₃²×C₁₁	Dic₅₉	1	1	yes	characteristic, complemented, Hall
18	D₃×C₁₁	—	6	2	no	—
19	C₅₉	C₁₁⋊#157	1	1	yes	characteristic, complemented, Sylow
20	Dic₁₁	—	531	1	no	Hall
21	#157	—	649	1	no	Hall
22	C₃×C₁₁	—	2	2	no	—
23	C₂×C₁₁	—	9	1	no	—
24	C₃⋊D₃	D₆₄₉	1	1	yes	characteristic
25	C₁₁	C₅₉⋊#157	1	1	yes	characteristic, complemented, Sylow
26	C₃²	Dic₆₄₉	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	6	2	no	—
28	C₄	—	5841	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₁×C₅₉	C₄
prime radical, cosocle	C₁₁×C₃⋊D₃×C₅₉	C₂
LCS	G ▷ C₃²×C₁₁×C₅₉
UCS	C₁

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.