Subgroups — C₇×C₁₇×C₃⋊D₂₁ #28418431

Order 14994.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₇×D₂₁	—	3	4	no	maximal
3	C₃×C₇²×C₁₇	D₃	1	4	yes	complemented
4	C₁₇×C₃⋊D₂₁	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₇×C₁₇×C₃⋊D₃	—	7	1	no	maximal
6	C₇×D₇×C₁₇	—	9	1	no	Hall
7	C₃²×C₇×C₁₇	—	2	3	no	—
8	C₃²×C₇×C₁₇	D₇	1	1	yes	characteristic, complemented
9	C₃²×C₇×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented
10	C₇×C₃⋊D₂₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₇²×C₁₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
12	C₁₇×D₂₁	—	3	4	no	—
13	D₃×C₇×C₁₇	—	21	4	no	—
14	C₃²×C₇²	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
15	C₃×C₇×C₁₇	—	2	12	no	—
16	C₃×C₇×C₁₇	D₃×C₇	1	4	yes	complemented
17	C₃×C₇×C₁₇	D₂₁	1	4	yes	complemented
18	C₁₇×C₃⋊D₃	—	7	1	no	Hall
19	C₇×D₂₁	—	3	4	no	—
20	C₂×C₇×C₁₇	—	63	1	no	—
21	D₇×C₁₇	—	9	1	no	—
22	C₃²×C₁₇	C₇×D₇	1	1	yes	characteristic, complemented, Hall
23	C₃×C₇²	D₃×C₁₇	1	4	yes	complemented
24	C₃⋊D₂₁	C₇×C₁₇	1	1	yes	characteristic, direct product factor
25	C₇×C₃⋊D₃	—	7	1	no	—
26	C₇×C₁₇	—	2	3	no	—
27	C₇×C₁₇	C₇×C₃⋊D₃	1	1	yes	characteristic, complemented
28	C₇×C₁₇	C₃⋊D₂₁	1	1	yes	characteristic, direct product factor
29	D₃×C₁₇	—	21	4	no	—
30	C₇×D₇	—	9	1	no	Hall
31	C₃²×C₇	—	2	3	no	—
32	C₃²×C₇	D₇×C₁₇	1	1	yes	characteristic, complemented
33	C₃²×C₇	C₂×C₇×C₁₇	1	1	yes	characteristic, complemented
34	C₃×C₁₇	C₇×D₂₁	1	4	yes	complemented
35	C₇²	C₁₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
36	D₂₁	—	3	4	no	—
37	D₃×C₇	—	21	4	no	—
38	C₂×C₁₇	—	63	1	no	Hall
39	C₃×C₇	—	2	12	no	—
40	C₃×C₇	D₃×C₇×C₁₇	1	4	yes	complemented
41	C₃×C₇	C₁₇×D₂₁	1	4	yes	complemented
42	C₃⋊D₃	—	7	1	no	Hall
43	C₁₇	C₇×C₃⋊D₂₁	1	1	yes	characteristic, direct product factor, Sylow
44	C₂×C₇	—	63	1	no	—
45	D₇	—	9	1	no	—
46	C₃²	C₇×D₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
47	C₇	—	2	3	no	—
48	C₇	C₇×C₁₇×C₃⋊D₃	1	1	yes	characteristic, complemented
49	C₇	C₁₇×C₃⋊D₂₁	1	1	yes	characteristic, direct product factor
50	D₃	—	21	4	no	—
51	C₃	C₇×C₁₇×D₂₁	1	4	yes	complemented
52	C₂	—	63	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₁₇	C₃⋊D₂₁
commutator, cosocle, hypocenter	C₃²×C₇	C₂×C₇×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₇	C₂
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₇×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇²×C₁₇	C₂	semidirect
3. C₃×C₇²×C₁₇	D₃	semidirect
4. C₁₇×C₃⋊D₂₁	C₇	direct (N × H)
8. C₃²×C₇×C₁₇	D₇	semidirect
9. C₃²×C₇×C₁₇	C₂×C₇	semidirect
10. C₇×C₃⋊D₂₁	C₁₇	direct (N × H)
11. C₇²×C₁₇	C₃⋊D₃	semidirect
14. C₃²×C₇²	C₂×C₁₇	semidirect
16. C₃×C₇×C₁₇	D₃×C₇	semidirect
17. C₃×C₇×C₁₇	D₂₁	semidirect
22. C₃²×C₁₇	C₇×D₇	semidirect
23. C₃×C₇²	D₃×C₁₇	semidirect
24. C₃⋊D₂₁	C₇×C₁₇	direct (N × H)
27. C₇×C₁₇	C₇×C₃⋊D₃	semidirect
28. C₇×C₁₇	C₃⋊D₂₁	direct (N × H)
32. C₃²×C₇	D₇×C₁₇	semidirect
33. C₃²×C₇	C₂×C₇×C₁₇	semidirect
34. C₃×C₁₇	C₇×D₂₁	semidirect
35. C₇²	C₁₇×C₃⋊D₃	semidirect
40. C₃×C₇	D₃×C₇×C₁₇	semidirect
41. C₃×C₇	C₁₇×D₂₁	semidirect
43. C₁₇	C₇×C₃⋊D₂₁	direct (N × H)
46. C₃²	C₇×D₇×C₁₇	semidirect
48. C₇	C₇×C₁₇×C₃⋊D₃	semidirect
49. C₇	C₁₇×C₃⋊D₂₁	direct (N × H)
51. C₃	C₇×C₁₇×D₂₁	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₇²×C₁₇	2
C₇×C₁₇×D₂₁	3
C₁₇×C₃⋊D₂₁	7
C₇×C₁₇×C₃⋊D₃	7
C₇×C₃⋊D₂₁	17

Subgroups — C7×C17×C3⋊D21 #28418431

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₇×C₃⋊D₂₁ #28418431