Subgroups — C₂×C₇×D₉×C₆₇ #30683092

Order 16884.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₉×C₆₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₉×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₇×C₆₇	—	3	1	no	maximal
4	C₇×C₉×C₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃×C₇×C₆₇	—	3	2	no	—
6	C₂×C₃×C₇×C₆₇	D₃	1	1	yes	characteristic
7	C₂×D₉×C₆₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₇×C₆₇	—	9	1	no	Hall
9	C₃×C₇×C₆₇	C₂×D₃	1	1	yes	characteristic
10	C₂×C₉×C₆₇	C₂×C₇	1	1	yes	characteristic, complemented
11	D₉×C₆₇	C₂×C₇	1	2	yes	direct product factor
12	C₂×C₇×C₆₇	—	9	2	no	—
13	C₂×C₇×C₆₇	D₉	1	1	yes	characteristic, direct product factor
14	C₂×D₃×C₆₇	—	3	1	no	—
15	C₉×C₆₇	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
16	C₇×C₆₇	C₂×D₉	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₆₇	D₃×C₇	1	1	yes	characteristic
18	D₃×C₆₇	—	3	2	no	—
19	C₂²×C₆₇	—	9	1	no	Hall
20	C₂×C₇×D₉	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₃×C₆₇	C₂×D₃×C₇	1	1	yes	characteristic
22	C₂×C₆₇	—	9	2	no	—
23	C₂×C₆₇	C₇×D₉	1	1	yes	characteristic, direct product factor
24	C₂×C₇×C₉	C₂×C₆₇	1	1	yes	characteristic, complemented
25	C₇×D₉	C₂×C₆₇	1	2	yes	direct product factor
26	C₂×D₃×C₇	—	3	1	no	—
27	C₆₇	C₂×C₇×D₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₇×C₉	C₂²×C₆₇	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₇	D₃×C₆₇	1	1	yes	characteristic
30	D₃×C₇	—	3	2	no	—
31	C₂×D₉	C₇×C₆₇	1	1	yes	characteristic, direct product factor, Hall
32	C₂²×C₇	—	9	1	no	Hall
33	C₃×C₇	C₂×D₃×C₆₇	1	1	yes	characteristic
34	C₂×C₉	C₂×C₇×C₆₇	1	1	yes	characteristic, complemented
35	D₉	C₂×C₇×C₆₇	1	2	yes	direct product factor
36	C₂×C₇	—	9	2	no	—
37	C₂×C₇	D₉×C₆₇	1	1	yes	characteristic, direct product factor
38	C₂×D₃	—	3	1	no	—
39	C₉	C₂²×C₇×C₆₇	1	1	yes	characteristic, complemented, Sylow
40	C₇	C₂×D₉×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₃	D₃×C₇×C₆₇	1	1	yes	characteristic
42	D₃	—	3	2	no	—
43	C₂²	—	9	1	no	Sylow
44	C₃	C₂×D₃×C₇×C₆₇	1	1	yes	characteristic
45	C₂	—	9	2	no	—
46	C₂	C₇×D₉×C₆₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇×C₆₇	D₉
commutator, cosocle, hypocenter	C₉	C₂²×C₇×C₆₇
Frattini	C₃	C₂×D₃×C₇×C₆₇
Fitting	C₂×C₇×C₉×C₆₇	C₂
socle	C₂×C₃×C₇×C₆₇	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₇×C₆₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₉×C₆₇	C₂	direct (N × H)
2. C₂×C₇×C₉×C₆₇	C₂	semidirect
4. C₇×C₉×C₆₇	C₂²	semidirect
7. C₂×D₉×C₆₇	C₇	direct (N × H)
10. C₂×C₉×C₆₇	C₂×C₇	semidirect
11. D₉×C₆₇	C₂×C₇	direct (N × H)
13. C₂×C₇×C₆₇	D₉	direct (N × H)
15. C₉×C₆₇	C₂²×C₇	semidirect
16. C₇×C₆₇	C₂×D₉	direct (N × H)
20. C₂×C₇×D₉	C₆₇	direct (N × H)
23. C₂×C₆₇	C₇×D₉	direct (N × H)
24. C₂×C₇×C₉	C₂×C₆₇	semidirect
25. C₇×D₉	C₂×C₆₇	direct (N × H)
27. C₆₇	C₂×C₇×D₉	direct (N × H)
28. C₇×C₉	C₂²×C₆₇	semidirect
31. C₂×D₉	C₇×C₆₇	direct (N × H)
34. C₂×C₉	C₂×C₇×C₆₇	semidirect
35. D₉	C₂×C₇×C₆₇	direct (N × H)
37. C₂×C₇	D₉×C₆₇	direct (N × H)
39. C₉	C₂²×C₇×C₆₇	semidirect
40. C₇	C₂×D₉×C₆₇	direct (N × H)
46. C₂	C₇×D₉×C₆₇	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×D₉×C₆₇	2
C₂×C₇×C₉×C₆₇	2
C₂×D₃×C₇×C₆₇	3
C₂×D₉×C₆₇	7
C₂×C₇×D₉	67

Subgroups — C2×C7×D9×C67 #30683092

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₉×C₆₇ #30683092