Subgroups — C₇×C₁₇×D₁₁₇ #42123798

Order 27846.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×C₁₃×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₇×D₃₉	—	3	1	no	maximal
3	C₃×C₇×C₁₃×C₁₇	D₃	1	1	yes	characteristic
4	C₁₇×D₁₁₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₁₇×D₁₃	—	9	1	no	Hall
6	C₇×C₁₇×D₉	—	13	1	no	maximal, Hall
7	C₉×C₁₃×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
8	C₇×D₁₁₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₁₃×C₁₇	D₉	1	1	yes	characteristic, complemented, Hall
10	C₁₇×D₃₉	—	3	1	no	—
11	C₇×C₉×C₁₇	D₁₃	1	1	yes	characteristic, complemented, Hall
12	C₇×C₉×C₁₃	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
13	D₃×C₇×C₁₇	—	39	1	no	—
14	C₃×C₁₃×C₁₇	D₃×C₇	1	1	yes	characteristic
15	C₇×D₃₉	—	3	1	no	—
16	C₁₇×D₁₃	—	9	1	no	Hall
17	C₃×C₇×C₁₇	D₃₉	1	1	yes	characteristic
18	C₁₇×D₉	—	13	1	no	Hall
19	C₃×C₇×C₁₃	D₃×C₁₇	1	1	yes	characteristic
20	C₂×C₇×C₁₇	—	117	1	no	Hall
21	D₁₁₇	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
22	C₁₃×C₁₇	C₇×D₉	1	1	yes	characteristic, complemented, Hall
23	C₇×D₁₃	—	9	1	no	Hall
24	C₉×C₁₇	C₇×D₁₃	1	1	yes	characteristic, complemented, Hall
25	C₇×D₉	—	13	1	no	Hall
26	C₇×C₁₇	D₁₁₇	1	1	yes	characteristic, direct product factor, Hall
27	C₉×C₁₃	C₂×C₇×C₁₇	1	1	yes	characteristic, complemented, Hall
28	D₃×C₁₇	—	39	1	no	—
29	C₇×C₁₃	C₁₇×D₉	1	1	yes	characteristic, complemented, Hall
30	D₃₉	—	3	1	no	—
31	C₇×C₉	C₁₇×D₁₃	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₇	C₇×D₃₉	1	1	yes	characteristic
33	D₃×C₇	—	39	1	no	—
34	C₃×C₁₃	D₃×C₇×C₁₇	1	1	yes	characteristic
35	C₂×C₁₇	—	117	1	no	Hall
36	D₁₃	—	9	1	no	Hall
37	C₃×C₇	C₁₇×D₃₉	1	1	yes	characteristic
38	D₉	—	13	1	no	Hall
39	C₁₇	C₇×D₁₁₇	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₇	—	117	1	no	Hall
41	C₁₃	C₇×C₁₇×D₉	1	1	yes	characteristic, complemented, Sylow
42	C₉	C₇×C₁₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
43	C₇	C₁₇×D₁₁₇	1	1	yes	characteristic, direct product factor, Sylow
44	D₃	—	39	1	no	—
45	C₃	C₇×C₁₇×D₃₉	1	1	yes	characteristic
46	C₂	—	117	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₁₇	D₁₁₇
commutator, cosocle, hypocenter	C₉×C₁₃	C₂×C₇×C₁₇
Frattini	C₃	C₇×C₁₇×D₃₉
Fitting	C₇×C₉×C₁₃×C₁₇	C₂
socle	C₃×C₇×C₁₃×C₁₇	D₃
LCS	G ▷ C₉×C₁₃
UCS	C₁ ◁ C₇×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₉×C₁₃×C₁₇	C₂	semidirect
4. C₁₇×D₁₁₇	C₇	direct (N × H)
7. C₉×C₁₃×C₁₇	C₂×C₇	semidirect
8. C₇×D₁₁₇	C₁₇	direct (N × H)
9. C₇×C₁₃×C₁₇	D₉	semidirect
11. C₇×C₉×C₁₇	D₁₃	semidirect
12. C₇×C₉×C₁₃	C₂×C₁₇	semidirect
21. D₁₁₇	C₇×C₁₇	direct (N × H)
22. C₁₃×C₁₇	C₇×D₉	semidirect
24. C₉×C₁₇	C₇×D₁₃	semidirect
26. C₇×C₁₇	D₁₁₇	direct (N × H)
27. C₉×C₁₃	C₂×C₇×C₁₇	semidirect
29. C₇×C₁₃	C₁₇×D₉	semidirect
31. C₇×C₉	C₁₇×D₁₃	semidirect
39. C₁₇	C₇×D₁₁₇	direct (N × H)
41. C₁₃	C₇×C₁₇×D₉	semidirect
42. C₉	C₇×C₁₇×D₁₃	semidirect
43. C₇	C₁₇×D₁₁₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₉×C₁₃×C₁₇	2
C₇×C₁₇×D₃₉	3
C₁₇×D₁₁₇	7
C₇×C₁₇×D₉	13
C₇×D₁₁₇	17

Subgroups — C7×C17×D117 #42123798

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₇×D₁₁₇ #42123798