Subgroups — D₁₁×C₃₁×D₁₇ #37550856

Order 23188.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×D₁₈₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×D₁₁×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₃₁×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×C₁₇×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃₁×D₁₇	—	11	1	no	maximal, Hall
6	C₂×D₁₁×C₃₁	—	17	1	no	maximal, Hall
7	C₂×C₁₇×C₃₁	—	11	1	no	—
8	C₃₁×D₁₇	—	11	1	no	—
9	C₃₁×D₁₇	D₁₁	1	1	yes	characteristic, direct product factor
10	D₁₁×D₁₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₁₁×C₃₁	—	17	1	no	—
12	D₁₁×C₃₁	—	17	1	no	—
13	D₁₁×C₃₁	D₁₇	1	1	yes	characteristic, direct product factor
14	C₁₇×C₃₁	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
15	D₁₈₇	C₂×C₃₁	1	1	yes	characteristic, complemented
16	C₁₁×D₁₇	C₂×C₃₁	1	1	yes	characteristic, complemented
17	C₁₇×D₁₁	C₂×C₃₁	1	1	yes	characteristic, complemented
18	C₁₁×C₃₁	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
19	C₁₁×C₁₇	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
20	C₂²×C₃₁	—	187	1	no	Hall
21	C₂×D₁₇	—	11	1	no	Hall
22	C₂×C₃₁	—	11	1	no	—
23	C₂×C₃₁	—	17	1	no	—
24	C₂×C₃₁	—	187	1	no	—
25	C₂×D₁₁	—	17	1	no	Hall
26	C₂×C₁₇	—	11	1	no	—
27	D₁₇	—	11	1	no	—
28	D₁₇	D₁₁×C₃₁	1	1	yes	characteristic, direct product factor
29	C₃₁	D₁₁×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₁₁	—	17	1	no	—
31	D₁₁	—	17	1	no	—
32	D₁₁	C₃₁×D₁₇	1	1	yes	characteristic, direct product factor
33	C₁₇	C₂×D₁₁×C₃₁	1	1	yes	characteristic, complemented, Sylow
34	C₁₁	C₂×C₃₁×D₁₇	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	187	1	no	Sylow
36	C₂	—	11	1	no	—
37	C₂	—	17	1	no	—
38	C₂	—	187	1	no	—

	subgroup	G/H
center, hypercenter	C₃₁	D₁₁×D₁₇
commutator, cosocle, hypocenter	C₁₁×C₁₇	C₂²×C₃₁
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₇×C₃₁	C₂²
LCS	G ▷ C₁₁×C₁₇
UCS	C₁ ◁ C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃₁×D₁₈₇	C₂	semidirect
2. C₁₇×D₁₁×C₃₁	C₂	semidirect
3. C₁₁×C₃₁×D₁₇	C₂	semidirect
4. C₁₁×C₁₇×C₃₁	C₂²	semidirect
9. C₃₁×D₁₇	D₁₁	direct (N × H)
10. D₁₁×D₁₇	C₃₁	direct (N × H)
13. D₁₁×C₃₁	D₁₇	direct (N × H)
14. C₁₇×C₃₁	C₂×D₁₁	semidirect
15. D₁₈₇	C₂×C₃₁	semidirect
16. C₁₁×D₁₇	C₂×C₃₁	semidirect
17. C₁₇×D₁₁	C₂×C₃₁	semidirect
18. C₁₁×C₃₁	C₂×D₁₇	semidirect
19. C₁₁×C₁₇	C₂²×C₃₁	semidirect
28. D₁₇	D₁₁×C₃₁	direct (N × H)
29. C₃₁	D₁₁×D₁₇	direct (N × H)
32. D₁₁	C₃₁×D₁₇	direct (N × H)
33. C₁₇	C₂×D₁₁×C₃₁	semidirect
34. C₁₁	C₂×C₃₁×D₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×D₁₈₇	2
C₁₇×D₁₁×C₃₁	2
C₁₁×C₃₁×D₁₇	2
C₂×C₃₁×D₁₇	11
C₂×D₁₁×C₃₁	17
D₁₁×D₁₇	31

Subgroups — D11×C31×D17 #37550856

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×C₃₁×D₁₇ #37550856