Subgroups — C₁₁⋊#14556844 #38788156

Order 25740.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₃×C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₁₁×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁⋊#90865	—	5	1	no	maximal, Hall
4	C₁₁×C₁₃×D₁₅	—	6	2	no	—
5	C₁₁⋊#63120	—	9	1	no	maximal, Hall
6	C₁₁×C₁₃×C₃⋊D₃	—	5	1	no	—
7	#14556844	—	11	1	no	maximal, Hall
8	C₃×C₅×C₁₁×C₁₃	—	2	2	no	—
9	C₁₁⋊#4380	—	13	1	no	maximal, Hall
10	D₅×C₁₁×C₁₃	—	9	1	no	—
11	C₃²×C₁₁×C₁₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₁₃×C₃⋊D₁₅	D₁₁	1	1	yes	characteristic
13	C₁₁×C₃⋊D₁₅	D₁₃	1	1	yes	characteristic
14	D₃×C₁₁×C₁₃	—	30	2	no	—
15	C₅×C₁₁×C₁₃	#157	1	1	yes	characteristic, complemented, Hall
16	C₃²×C₅×C₁₃	Dic₁₁	1	1	yes	characteristic, complemented, Hall
17	Dic₁₄₃	—	45	1	no	Hall
18	C₃²×C₅×C₁₁	Dic₁₃	1	1	yes	characteristic, complemented, Hall
19	#90865	—	55	1	no	Hall
20	C₃×C₁₁×C₁₃	—	2	2	no	—
21	C₁₁⋊#157	—	65	1	no	Hall
22	C₁₃×D₁₅	—	6	2	no	—
23	C₁₁×D₁₅	—	6	2	no	—
24	C₂×C₁₁×C₁₃	—	45	1	no	—
25	#63120	—	99	1	no	Hall
26	C₁₃×C₃⋊D₃	—	5	1	no	—
27	C₁₁⋊AGL(1,𝔽₅)	—	117	1	no	Hall
28	C₁₁×C₃⋊D₃	—	5	1	no	—
29	C₃×C₅×C₁₃	—	2	2	no	—
30	#4380	—	143	1	no	Hall
31	C₃×C₅×C₁₁	—	2	2	no	—
32	C₁₁×C₁₃	#4380	1	1	yes	characteristic, complemented, Hall
33	D₅×C₁₃	—	9	1	no	—
34	C₃²×C₁₃	C₁₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
35	D₅×C₁₁	—	9	1	no	—
36	C₃²×C₁₁	#63120	1	1	yes	characteristic, complemented, Hall
37	C₃⋊D₁₅	D₁₄₃	1	1	yes	characteristic
38	D₃×C₁₃	—	30	2	no	—
39	D₃×C₁₁	—	30	2	no	—
40	C₅×C₁₃	C₁₁⋊#157	1	1	yes	characteristic, complemented, Hall
41	C₅×C₁₁	#90865	1	1	yes	characteristic, complemented, Hall
42	Dic₁₃	—	495	1	no	Hall
43	C₃²×C₅	Dic₁₄₃	1	1	yes	characteristic, complemented, Hall
44	Dic₁₁	—	585	1	no	Hall
45	C₃×C₁₃	—	2	2	no	—
46	#157	—	715	1	no	Hall
47	C₃×C₁₁	—	2	2	no	—
48	D₁₅	—	6	2	no	—
49	C₂×C₁₃	—	45	1	no	—
50	C₂×C₁₁	—	45	1	no	—
51	AGL(1,𝔽₅)	—	1287	1	no	Hall
52	C₃⋊D₃	—	5	1	no	—
53	C₃×C₅	—	2	2	no	—
54	C₁₃	C₁₁⋊#4380	1	1	yes	characteristic, complemented, Sylow
55	C₁₁	#14556844	1	1	yes	characteristic, complemented, Sylow
56	D₅	—	9	1	no	—
57	C₃²	C₁₁⋊#63120	1	1	yes	characteristic, complemented, Sylow
58	D₃	—	30	2	no	—
59	C₅	C₁₁⋊#90865	1	1	yes	characteristic, complemented, Sylow
60	C₄	—	6435	1	no	Sylow
61	C₃	—	2	2	no	—
62	C₂	—	45	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅×C₁₁×C₁₃	C₄
prime radical, cosocle	C₁₁×C₁₃×C₃⋊D₁₅	C₂
LCS	G ▷ C₃²×C₅×C₁₁×C₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅×C₁₁×C₁₃	C₄	semidirect
11. C₃²×C₁₁×C₁₃	AGL(1,𝔽₅)	semidirect
15. C₅×C₁₁×C₁₃	#157	semidirect
16. C₃²×C₅×C₁₃	Dic₁₁	semidirect
18. C₃²×C₅×C₁₁	Dic₁₃	semidirect
32. C₁₁×C₁₃	#4380	semidirect
34. C₃²×C₁₃	C₁₁⋊AGL(1,𝔽₅)	semidirect
36. C₃²×C₁₁	#63120	semidirect
40. C₅×C₁₃	C₁₁⋊#157	semidirect
41. C₅×C₁₁	#90865	semidirect
43. C₃²×C₅	Dic₁₄₃	semidirect
54. C₁₃	C₁₁⋊#4380	semidirect
55. C₁₁	#14556844	semidirect
57. C₃²	C₁₁⋊#63120	semidirect
59. C₅	C₁₁⋊#90865	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₁₃×C₃⋊D₁₅	2
C₁₁⋊#90865	5
C₁₁⋊#63120	9
#14556844	11
C₁₁⋊#4380	13

Subgroups — C11⋊#14556844 #38788156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁⋊#14556844 #38788156