Subgroups — C₁₇×C₁₁⋊#3874 #43242521

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×C₁₇×D₅₅	—	3	1	no	maximal, Hall
3	C₅²×C₁₁×C₁₇	D₃	1	1	yes	characteristic, complemented, Hall
4	C₁₇×#3874	—	11	1	no	maximal, Hall
5	C₁₇×D₅₅	—	3	1	no	—
6	C₅×C₁₇×D₁₁	—	15	1	no	—
7	C₁₁⋊#3874	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×C₅²⋊C₃	D₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₇×D₃₃	—	25	1	no	maximal, Hall
10	C₅×C₁₁×C₁₇	—	3	1	no	—
11	C₅×C₁₁×C₁₇	—	3	1	no	—
12	C₅×D₅×C₁₇	—	33	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×D₅₅	—	3	1	no	Hall
16	C₅²×C₁₇	D₃₃	1	1	yes	characteristic, complemented, Hall
17	C₁₇×D₁₁	—	15	1	no	Hall
18	C₅²×C₁₁	D₃×C₁₇	1	1	yes	characteristic, complemented, Hall
19	C₁₁×C₁₇	#3874	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×C₁₇	—	165	1	no	—
21	D₅×C₁₇	—	33	1	no	—
22	#3874	—	11	1	no	Hall
23	D₅₅	—	3	1	no	—
24	C₅×D₁₁	—	15	1	no	—
25	D₃×C₁₇	—	275	1	no	Hall
26	C₅×C₁₇	—	3	1	no	—
27	C₅×C₁₇	—	3	1	no	—
28	C₅²⋊C₃	C₁₇×D₁₁	1	1	yes	characteristic, complemented, Hall
29	D₃₃	—	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	—	33	1	no	Hall
34	C₂×C₁₇	—	165	1	no	Hall
35	C₃×C₁₁	—	25	1	no	Hall
36	C₅²	C₁₇×D₃₃	1	1	yes	characteristic, complemented, Sylow
37	D₁₁	—	15	1	no	Hall
38	C₁₇	C₁₁⋊#3874	1	1	yes	characteristic, direct product factor, Sylow
39	C₁₁	C₁₇×#3874	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₅	—	165	1	no	—
41	D₅	—	33	1	no	—
42	D₃	—	275	1	no	Hall
43	C₅	—	3	1	no	—
44	C₅	—	3	1	no	—
45	C₃	—	25	1	no	Sylow
46	C₂	—	165	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇	C₁₁⋊#3874
commutator, cosocle, hypocenter	C₁₁×C₅²⋊C₃	C₂×C₁₇
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₁₇	D₃
LCS	G ▷ C₁₁×C₅²⋊C₃
UCS	C₁ ◁ 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
7. C₁₁⋊#3874	C₁₇	direct (N × H)
8. C₁₇×C₅²⋊C₃	D₁₁	semidirect
13. C₁₁×C₅²⋊C₃	C₂×C₁₇	semidirect
16. C₅²×C₁₇	D₃₃	semidirect
18. C₅²×C₁₁	D₃×C₁₇	semidirect
19. C₁₁×C₁₇	#3874	semidirect
28. C₅²⋊C₃	C₁₇×D₁₁	semidirect
36. C₅²	C₁₇×D₃₃	semidirect
38. C₁₇	C₁₁⋊#3874	direct (N × H)
39. C₁₁	C₁₇×#3874	semidirect

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×C₁₇×D₅₅	3
C₁₇×#3874	11
C₁₁⋊#3874	17
C₁₇×D₃₃	25

Subgroups — C17×C11⋊#3874 #43242521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×C₁₁⋊#3874 #43242521