Subgroups — C₇×C₃⋊D₃₅₇ #28418430

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×D₃₅₇	—	3	4	no	maximal
3	C₃×C₇²×C₁₇	D₃	1	4	yes	complemented
4	C₃⋊D₃₅₇	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₇×C₃⋊D₅₁	—	7	1	no	maximal
6	C₇×D₁₁₉	—	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	—	17	1	no	maximal, Hall
11	C₇²×C₁₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
12	D₃₅₇	—	3	4	no	—
13	C₇×D₅₁	—	21	4	no	—
14	C₃²×C₇²	D₁₇	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	C₃⋊D₅₁	—	7	1	no	Hall
19	C₇×D₂₁	—	51	4	no	—
20	D₁₁₉	—	9	1	no	—
21	C₇×D₁₇	—	63	1	no	—
22	C₃²×C₁₇	C₇×D₇	1	1	yes	characteristic, complemented, Hall
23	C₃×C₇²	D₅₁	1	4	yes	complemented
24	C₃⋊D₂₁	—	17	1	no	—
25	C₇×C₃⋊D₃	—	119	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, complemented
29	D₅₁	—	21	4	no	—
30	C₇×D₇	—	153	1	no	Hall
31	C₃²×C₇	—	2	3	no	—
32	C₃²×C₇	C₇×D₁₇	1	1	yes	characteristic, complemented
33	C₃²×C₇	D₁₁₉	1	1	yes	characteristic, complemented
34	C₃×C₁₇	C₇×D₂₁	1	4	yes	complemented
35	C₇²	C₃⋊D₅₁	1	1	yes	characteristic, complemented, Sylow
36	D₂₁	—	51	4	no	—
37	D₃×C₇	—	357	4	no	—
38	D₁₇	—	63	1	no	Hall
39	C₃×C₇	—	2	12	no	—
40	C₃×C₇	C₇×D₅₁	1	4	yes	complemented
41	C₃×C₇	D₃₅₇	1	4	yes	complemented
42	C₃⋊D₃	—	119	1	no	Hall
43	C₁₇	C₇×C₃⋊D₂₁	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₇	—	1071	1	no	—
45	D₇	—	153	1	no	—
46	C₃²	C₇×D₁₁₉	1	1	yes	characteristic, complemented, Sylow
47	C₇	—	2	3	no	—
48	C₇	C₇×C₃⋊D₅₁	1	1	yes	characteristic, complemented
49	C₇	C₃⋊D₃₅₇	1	1	yes	characteristic, direct product factor
50	D₃	—	357	4	no	—
51	C₃	C₇×D₃₅₇	1	4	yes	complemented
52	C₂	—	1071	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	C₃⋊D₃₅₇
commutator, cosocle, hypocenter	C₃²×C₇×C₁₇	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₇	C₂
LCS	G ▷ C₃²×C₇×C₁₇
UCS	C₁ ◁ C₇

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. C₃⋊D₃₅₇	C₇	direct (N × H)
8. C₃²×C₇×C₁₇	D₇	semidirect
9. C₃²×C₇×C₁₇	C₂×C₇	semidirect
11. C₇²×C₁₇	C₃⋊D₃	semidirect
14. C₃²×C₇²	D₁₇	semidirect
16. C₃×C₇×C₁₇	D₃×C₇	semidirect
17. C₃×C₇×C₁₇	D₂₁	semidirect
22. C₃²×C₁₇	C₇×D₇	semidirect
23. C₃×C₇²	D₅₁	semidirect
27. C₇×C₁₇	C₇×C₃⋊D₃	semidirect
28. C₇×C₁₇	C₃⋊D₂₁	semidirect
32. C₃²×C₇	C₇×D₁₇	semidirect
33. C₃²×C₇	D₁₁₉	semidirect
34. C₃×C₁₇	C₇×D₂₁	semidirect
35. C₇²	C₃⋊D₅₁	semidirect
40. C₃×C₇	C₇×D₅₁	semidirect
41. C₃×C₇	D₃₅₇	semidirect
43. C₁₇	C₇×C₃⋊D₂₁	semidirect
46. C₃²	C₇×D₁₁₉	semidirect
48. C₇	C₇×C₃⋊D₅₁	semidirect
49. C₇	C₃⋊D₃₅₇	direct (N × H)
51. C₃	C₇×D₃₅₇	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×D₃₅₇	3
C₃⋊D₃₅₇	7
C₇×C₃⋊D₅₁	7
C₇×C₃⋊D₂₁	17

Subgroups — C7×C3⋊D357 #28418430

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₃⋊D₃₅₇ #28418430