Subgroups — C₁₁⋊#10597479 #20269708

Order 6732.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₃⋊D₅₁	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₁×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×D₅₁	—	6	2	no	—
4	C₁₁⋊#595	—	9	1	no	maximal, Hall
5	#10597479	—	11	1	no	maximal, Hall
6	C₃×C₁₁×C₁₇	—	2	2	no	—
7	C₁₁⋊#157	—	17	1	no	maximal, Hall
8	C₁₁×D₁₇	—	9	1	no	—
9	C₃⋊D₅₁	D₁₁	1	1	yes	characteristic
10	C₁₁×C₃⋊D₃	—	17	1	no	—
11	C₁₁×C₁₇	#157	1	1	yes	characteristic, complemented, Hall
12	C₃²×C₁₇	Dic₁₁	1	1	yes	characteristic, complemented, Hall
13	D₅₁	—	6	2	no	—
14	C₃²×C₁₁	#595	1	1	yes	characteristic, complemented, Hall
15	#595	—	99	1	no	Hall
16	D₃×C₁₁	—	102	2	no	—
17	C₃×C₁₇	—	2	2	no	—
18	Dic₁₁	—	153	1	no	Hall
19	#157	—	187	1	no	Hall
20	D₁₇	—	9	1	no	—
21	C₃×C₁₁	—	2	2	no	—
22	C₂×C₁₁	—	153	1	no	—
23	C₃⋊D₃	—	17	1	no	—
24	C₁₇	C₁₁⋊#157	1	1	yes	characteristic, complemented, Sylow
25	C₁₁	#10597479	1	1	yes	characteristic, complemented, Sylow
26	C₃²	C₁₁⋊#595	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	102	2	no	—
28	C₄	—	1683	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	153	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₁×C₁₇	C₄
LCS	G ▷ C₃²×C₁₁×C₁₇
UCS	C₁

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