Subgroups — C₁₁×C₁₇×#3874 #43242519

Order 28050.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₇×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₅×C₁₁×C₁₇	—	3	1	no	maximal, Hall
3	C₅²×C₁₁×C₁₇	D₃	1	1	yes	characteristic, complemented, Hall
4	C₁₇×#3874	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₁×C₁₇	—	15	1	no	—
6	D₅×C₁₁×C₁₇	—	3	1	no	—
7	C₁₁×#3874	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×C₅²⋊C₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
9	D₃×C₁₁×C₁₇	—	25	1	no	maximal, Hall
10	C₅×C₁₁×C₁₇	—	3	1	no	—
11	C₅×C₁₁×C₁₇	—	3	1	no	—
12	C₅×D₅×C₁₇	—	3	1	no	Hall
13	C₁₁×C₅²⋊C₃	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
14	C₃×C₁₁×C₁₇	—	25	1	no	Hall
15	C₅×D₅×C₁₁	—	3	1	no	Hall
16	C₅²×C₁₇	D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₁×C₁₇	—	15	1	no	Hall
18	C₅²×C₁₁	D₃×C₁₇	1	1	yes	characteristic, complemented, Hall
19	C₁₁×C₁₇	#3874	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₅×C₁₇	—	15	1	no	—
21	D₅×C₁₇	—	3	1	no	—
22	#3874	C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₅×C₁₁	—	15	1	no	—
24	D₅×C₁₁	—	3	1	no	—
25	D₃×C₁₇	—	25	1	no	Hall
26	C₅×C₁₇	—	3	1	no	—
27	C₅×C₁₇	—	3	1	no	—
28	C₅²⋊C₃	C₂×C₁₁×C₁₇	1	1	yes	characteristic, complemented, Hall
29	D₃×C₁₁	—	25	1	no	Hall
30	C₅×C₁₁	—	3	1	no	—
31	C₅×C₁₁	—	3	1	no	—
32	C₃×C₁₇	—	25	1	no	Hall
33	C₅×D₅	—	3	1	no	Hall
34	C₂×C₁₇	—	15	1	no	Hall
35	C₃×C₁₁	—	25	1	no	Hall
36	C₅²	D₃×C₁₁×C₁₇	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₁₁	—	15	1	no	Hall
38	C₁₇	C₁₁×#3874	1	1	yes	characteristic, direct product factor, Sylow
39	C₁₁	C₁₇×#3874	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₅	—	15	1	no	—
41	D₅	—	3	1	no	—
42	D₃	—	25	1	no	Hall
43	C₅	—	3	1	no	—
44	C₅	—	3	1	no	—
45	C₃	—	25	1	no	Sylow
46	C₂	—	15	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₁₇	#3874
commutator, cosocle, hypocenter	C₅²⋊C₃	C₂×C₁₁×C₁₇
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₁₇	D₃
LCS	G ▷ C₅²⋊C₃
UCS	C₁ ◁ C₁₁×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₇×C₅²⋊C₃	C₂	semidirect
3. C₅²×C₁₁×C₁₇	D₃	semidirect
4. C₁₇×#3874	C₁₁	direct (N × H)
7. C₁₁×#3874	C₁₇	direct (N × H)
8. C₁₇×C₅²⋊C₃	C₂×C₁₁	semidirect
13. C₁₁×C₅²⋊C₃	C₂×C₁₇	semidirect
16. C₅²×C₁₇	D₃×C₁₁	semidirect
18. C₅²×C₁₁	D₃×C₁₇	semidirect
19. C₁₁×C₁₇	#3874	direct (N × H)
22. #3874	C₁₁×C₁₇	direct (N × H)
28. C₅²⋊C₃	C₂×C₁₁×C₁₇	semidirect
36. C₅²	D₃×C₁₁×C₁₇	semidirect
38. C₁₇	C₁₁×#3874	direct (N × H)
39. C₁₁	C₁₇×#3874	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×C₁₇×C₅²⋊C₃	2
C₅×D₅×C₁₁×C₁₇	3
C₁₇×#3874	11
C₁₁×#3874	17
D₃×C₁₁×C₁₇	25

Subgroups — C11×C17×#3874 #43242519

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₁₇×#3874 #43242519