Subgroups — C₁₁⋊#90865 #19104239

Order 5148.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₁×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₁₁×C₁₃	—	6	2	no	—
4	Dic₁₄₃	—	9	1	no	maximal, Hall
5	#90865	—	11	1	no	maximal, Hall
6	C₃×C₁₁×C₁₃	—	2	2	no	—
7	C₁₁⋊#157	—	13	1	no	maximal, Hall
8	C₂×C₁₁×C₁₃	—	9	1	no	—
9	C₁₃×C₃⋊D₃	D₁₁	1	1	yes	characteristic
10	C₁₁×C₃⋊D₃	D₁₃	1	1	yes	characteristic
11	C₁₁×C₁₃	#157	1	1	yes	characteristic, complemented, Hall
12	C₃²×C₁₃	Dic₁₁	1	1	yes	characteristic, complemented, Hall
13	C₃²×C₁₁	Dic₁₃	1	1	yes	characteristic, complemented, Hall
14	D₃×C₁₃	—	6	2	no	—
15	D₃×C₁₁	—	6	2	no	—
16	Dic₁₃	—	99	1	no	Hall
17	Dic₁₁	—	117	1	no	Hall
18	C₃×C₁₃	—	2	2	no	—
19	#157	—	143	1	no	Hall
20	C₃×C₁₁	—	2	2	no	—
21	C₂×C₁₃	—	9	1	no	—
22	C₂×C₁₁	—	9	1	no	—
23	C₃⋊D₃	D₁₄₃	1	1	yes	characteristic
24	C₁₃	C₁₁⋊#157	1	1	yes	characteristic, complemented, Sylow
25	C₁₁	#90865	1	1	yes	characteristic, complemented, Sylow
26	C₃²	Dic₁₄₃	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	6	2	no	—
28	C₄	—	1287	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×C₁₃	C₄
LCS	G ▷ C₃²×C₁₁×C₁₃
UCS	C₁

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