Subgroups — C₁₁⋊(#11725132⋊C₃) #44415744

Order 29172.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₇×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁⋊#11725132	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁×C₁₇×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁×C₁₇×D₁₃	C₂×C₃	1	1	yes	characteristic
5	#11725132⋊C₃	—	11	1	no	maximal, Hall
6	C₁₁×C₁₃×C₁₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₃×Dic₁₈₇	—	13	1	no	maximal, Hall
8	C₁₁⋊AGL(1,𝔽₁₃)	—	17	1	no	maximal, Hall
9	C₁₇×D₁₃⋊C₃	D₁₁	1	1	yes	characteristic
10	C₂×C₃×C₁₁×C₁₇	—	13	1	no	—
11	#11725132	—	11	1	no	Hall
12	C₁₁×D₁₃⋊C₃	D₁₇	1	1	yes	characteristic
13	Dic₁₈₇	—	13	1	no	Hall
14	C₁₇×C₁₃⋊C₃	Dic₁₁	1	1	yes	characteristic, complemented, Hall
15	C₁₁⋊#261	—	17	1	no	Hall
16	C₃×C₁₁×C₁₇	—	52	1	no	Hall
17	C₁₇×D₁₃	C₃×D₁₁	1	1	yes	characteristic
18	C₁₁×C₁₃⋊C₃	Dic₁₇	1	1	yes	characteristic, complemented, Hall
19	C₂×C₁₁×C₁₇	—	13	1	no	—
20	C₁₁×D₁₃	C₃×D₁₇	1	1	yes	characteristic
21	C₁₃×C₁₇	C₃×Dic₁₁	1	1	yes	characteristic, complemented, Hall
22	C₃×Dic₁₇	—	143	1	no	Hall
23	C₁₁×C₁₇	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Hall
24	AGL(1,𝔽₁₃)	—	187	1	no	Hall
25	C₁₁×C₁₃	C₃×Dic₁₇	1	1	yes	characteristic, complemented, Hall
26	C₃×Dic₁₁	—	221	1	no	Hall
27	C₂×C₃×C₁₇	—	13	1	no	—
28	D₁₃⋊C₃	D₁₈₇	1	1	yes	characteristic
29	Dic₁₇	—	143	1	no	Hall
30	C₂×C₃×C₁₁	—	13	1	no	—
31	#261	—	187	1	no	Hall
32	C₃×C₁₇	—	52	1	no	Hall
33	Dic₁₁	—	221	1	no	Hall
34	C₁₃⋊C₃	Dic₁₈₇	1	1	yes	characteristic, complemented, Hall
35	C₂×C₁₇	—	13	1	no	—
36	C₃×C₁₁	—	52	1	no	Hall
37	D₁₃	C₃×D₁₈₇	1	1	yes	characteristic
38	C₂×C₁₁	—	13	1	no	—
39	C₁₇	C₁₁⋊AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
40	C₁₃	C₃×Dic₁₈₇	1	1	yes	characteristic, complemented, Sylow
41	C₃×C₄	—	2431	1	no	Hall
42	C₁₁	#11725132⋊C₃	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	13	1	no	—
44	C₄	—	2431	1	no	Sylow
45	C₃	—	52	1	no	Sylow
46	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₁×C₁₃×C₁₇	C₃×C₄
prime radical	C₁₁×C₁₇×D₁₃⋊C₃	C₂
cosocle	C₁₁×C₁₇×D₁₃	C₂×C₃
LCS	G ▷ C₁₁×C₁₃×C₁₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₁₁⋊#11725132	C₃	semidirect
3. C₁₁×C₁₇×C₁₃⋊C₃	C₄	semidirect
6. C₁₁×C₁₃×C₁₇	C₃×C₄	semidirect
14. C₁₇×C₁₃⋊C₃	Dic₁₁	semidirect
18. C₁₁×C₁₃⋊C₃	Dic₁₇	semidirect
21. C₁₃×C₁₇	C₃×Dic₁₁	semidirect
23. C₁₁×C₁₇	AGL(1,𝔽₁₃)	semidirect
25. C₁₁×C₁₃	C₃×Dic₁₇	semidirect
34. C₁₃⋊C₃	Dic₁₈₇	semidirect
39. C₁₇	C₁₁⋊AGL(1,𝔽₁₃)	semidirect
40. C₁₃	C₃×Dic₁₈₇	semidirect
42. C₁₁	#11725132⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₁₇×D₁₃⋊C₃	2
C₁₁⋊#11725132	3
#11725132⋊C₃	11
C₃×Dic₁₈₇	13
C₁₁⋊AGL(1,𝔽₁₃)	17

Subgroups — C11⋊(#11725132⋊C3) #44415744

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁⋊(#11725132⋊C₃) #44415744