Subgroups — C₂×C₃×C₁₁²×D₁₇ #37590659

Order 24684.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁²×D₁₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₁²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁²×D₁₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₁²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₁²×D₁₇	C₂×C₃	1	2	yes	direct product factor
6	C₂×C₁₁²×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₃×C₁₁×D₁₇	C₁₁	1	12	yes	maximal, direct product factor
8	C₁₁²×C₁₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂²×C₃×C₁₁²	—	17	1	no	maximal, Hall
10	C₂×C₃×C₁₁×C₁₇	C₂×C₁₁	1	12	yes	complemented
11	C₃×C₁₁×D₁₇	C₂×C₁₁	1	24	yes	direct product factor
12	C₂×C₁₁×D₁₇	C₃×C₁₁	1	12	yes	direct product factor
13	C₂×C₃×C₁₁²	—	17	2	no	—
14	C₂×C₃×C₁₁²	D₁₇	1	1	yes	characteristic, direct product factor
15	C₃×C₁₁×C₁₇	C₂²×C₁₁	1	12	yes	complemented
16	C₂²×C₁₁²	—	17	1	no	Hall
17	C₂×C₁₁×C₁₇	C₂×C₃×C₁₁	1	12	yes	complemented
18	C₁₁×D₁₇	C₂×C₃×C₁₁	1	24	yes	direct product factor
19	C₃×C₁₁²	C₂×D₁₇	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₁₁²	—	17	2	no	—
21	C₂×C₁₁²	C₃×D₁₇	1	1	yes	characteristic, direct product factor
22	C₂×C₃×D₁₇	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
23	C₁₁×C₁₇	C₂²×C₃×C₁₁	1	12	yes	complemented
24	C₂²×C₃×C₁₁	—	17	12	no	—
25	C₁₁²	C₂×C₃×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₃×C₁₇	C₂×C₁₁²	1	1	yes	characteristic, complemented
27	C₃×D₁₇	C₂×C₁₁²	1	2	yes	direct product factor
28	C₂×D₁₇	C₃×C₁₁²	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₃×C₁₁	—	17	24	no	—
30	C₂×C₃×C₁₁	C₁₁×D₁₇	1	12	yes	direct product factor
31	C₃×C₁₇	C₂²×C₁₁²	1	1	yes	characteristic, complemented, Hall
32	C₂²×C₁₁	—	17	12	no	—
33	C₂×C₁₇	C₂×C₃×C₁₁²	1	1	yes	characteristic, complemented
34	D₁₇	C₂×C₃×C₁₁²	1	2	yes	direct product factor
35	C₃×C₁₁	C₂×C₁₁×D₁₇	1	12	yes	direct product factor
36	C₂×C₁₁	—	17	24	no	—
37	C₂×C₁₁	C₃×C₁₁×D₁₇	1	12	yes	direct product factor
38	C₁₇	C₂²×C₃×C₁₁²	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₃	—	17	1	no	Hall
40	C₁₁	C₂×C₃×C₁₁×D₁₇	1	12	yes	direct product factor
41	C₂×C₃	—	17	2	no	—
42	C₂×C₃	C₁₁²×D₁₇	1	1	yes	characteristic, direct product factor
43	C₂²	—	17	1	no	Sylow
44	C₃	C₂×C₁₁²×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	17	2	no	—
46	C₂	C₃×C₁₁²×D₁₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₁²	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂²×C₃×C₁₁²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₁²×C₁₇	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₃×C₁₁²

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁²×D₁₇	C₂	direct (N × H)
2. C₂×C₃×C₁₁²×C₁₇	C₂	semidirect
3. C₂×C₁₁²×D₁₇	C₃	direct (N × H)
4. C₃×C₁₁²×C₁₇	C₂²	semidirect
5. C₁₁²×D₁₇	C₂×C₃	direct (N × H)
6. C₂×C₁₁²×C₁₇	C₂×C₃	semidirect
7. C₂×C₃×C₁₁×D₁₇	C₁₁	direct (N × H)
8. C₁₁²×C₁₇	C₂²×C₃	semidirect
10. C₂×C₃×C₁₁×C₁₇	C₂×C₁₁	semidirect
11. C₃×C₁₁×D₁₇	C₂×C₁₁	direct (N × H)
12. C₂×C₁₁×D₁₇	C₃×C₁₁	direct (N × H)
14. C₂×C₃×C₁₁²	D₁₇	direct (N × H)
15. C₃×C₁₁×C₁₇	C₂²×C₁₁	semidirect
17. C₂×C₁₁×C₁₇	C₂×C₃×C₁₁	semidirect
18. C₁₁×D₁₇	C₂×C₃×C₁₁	direct (N × H)
19. C₃×C₁₁²	C₂×D₁₇	direct (N × H)
21. C₂×C₁₁²	C₃×D₁₇	direct (N × H)
22. C₂×C₃×D₁₇	C₁₁²	direct (N × H)
23. C₁₁×C₁₇	C₂²×C₃×C₁₁	semidirect
25. C₁₁²	C₂×C₃×D₁₇	direct (N × H)
26. C₂×C₃×C₁₇	C₂×C₁₁²	semidirect
27. C₃×D₁₇	C₂×C₁₁²	direct (N × H)
28. C₂×D₁₇	C₃×C₁₁²	direct (N × H)
30. C₂×C₃×C₁₁	C₁₁×D₁₇	direct (N × H)
31. C₃×C₁₇	C₂²×C₁₁²	semidirect
33. C₂×C₁₇	C₂×C₃×C₁₁²	semidirect
34. D₁₇	C₂×C₃×C₁₁²	direct (N × H)
35. C₃×C₁₁	C₂×C₁₁×D₁₇	direct (N × H)
37. C₂×C₁₁	C₃×C₁₁×D₁₇	direct (N × H)
38. C₁₇	C₂²×C₃×C₁₁²	semidirect
40. C₁₁	C₂×C₃×C₁₁×D₁₇	direct (N × H)
42. C₂×C₃	C₁₁²×D₁₇	direct (N × H)
44. C₃	C₂×C₁₁²×D₁₇	direct (N × H)
46. C₂	C₃×C₁₁²×D₁₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₁²×D₁₇	2
C₂×C₃×C₁₁²×C₁₇	2
C₂×C₁₁²×D₁₇	3
C₂×C₃×C₁₁×D₁₇	11
C₂²×C₃×C₁₁²	17

Subgroups — C2×C3×C112×D17 #37590659

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₁²×D₁₇ #37590659