Subgroups — C₇×Dic₉×C₆₇ #30683040

Order 16884.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₉×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₃×C₆₇	—	3	1	no	maximal
3	C₇×C₉×C₆₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇×C₆₇	D₃	1	1	yes	characteristic
5	Dic₉×C₆₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₄×C₇×C₆₇	—	9	1	no	Hall
7	C₃×C₇×C₆₇	Dic₃	1	1	yes	characteristic
8	C₂×C₉×C₆₇	C₂×C₇	1	1	yes	characteristic
9	C₂×C₇×C₆₇	D₉	1	1	yes	characteristic
10	Dic₃×C₆₇	—	3	1	no	—
11	C₉×C₆₇	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₆₇	Dic₉	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₆₇	D₃×C₇	1	1	yes	characteristic
14	C₄×C₆₇	—	9	1	no	Hall
15	C₇×Dic₉	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₃×C₆₇	C₇×Dic₃	1	1	yes	characteristic
17	C₂×C₆₇	C₇×D₉	1	1	yes	characteristic
18	C₂×C₇×C₉	C₂×C₆₇	1	1	yes	characteristic
19	C₇×Dic₃	—	3	1	no	—
20	C₆₇	C₇×Dic₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₇×C₉	C₄×C₆₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇	D₃×C₆₇	1	1	yes	characteristic
23	Dic₉	C₇×C₆₇	1	1	yes	characteristic, direct product factor, Hall
24	C₄×C₇	—	9	1	no	Hall
25	C₃×C₇	Dic₃×C₆₇	1	1	yes	characteristic
26	C₂×C₉	C₂×C₇×C₆₇	1	1	yes	characteristic
27	C₂×C₇	D₉×C₆₇	1	1	yes	characteristic
28	Dic₃	—	3	1	no	—
29	C₉	C₄×C₇×C₆₇	1	1	yes	characteristic, complemented, Sylow
30	C₇	Dic₉×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	D₃×C₇×C₆₇	1	1	yes	characteristic
32	C₄	—	9	1	no	Sylow
33	C₃	C₇×Dic₃×C₆₇	1	1	yes	characteristic
34	C₂	C₇×D₉×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇×C₆₇	D₉
commutator, hypocenter	C₉	C₄×C₇×C₆₇
Frattini	C₂×C₃	D₃×C₇×C₆₇
Fitting	C₂×C₇×C₉×C₆₇	C₂
socle, prime radical	C₂×C₃×C₇×C₆₇	D₃
cosocle	C₂×C₉	C₂×C₇×C₆₇
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₇×C₆₇

Complements

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

N	H ≅ G/N	type
3. C₇×C₉×C₆₇	C₄	semidirect
5. Dic₉×C₆₇	C₇	direct (N × H)
11. C₉×C₆₇	C₄×C₇	semidirect
12. C₇×C₆₇	Dic₉	direct (N × H)
15. C₇×Dic₉	C₆₇	direct (N × H)
20. C₆₇	C₇×Dic₉	direct (N × H)
21. C₇×C₉	C₄×C₆₇	semidirect
23. Dic₉	C₇×C₆₇	direct (N × H)
29. C₉	C₄×C₇×C₆₇	semidirect
30. C₇	Dic₉×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
C₂×C₇×C₉×C₆₇	2
C₇×Dic₃×C₆₇	3
Dic₉×C₆₇	7
C₇×Dic₉	67

Subgroups — C7×Dic9×C67 #30683040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×Dic₉×C₆₇ #30683040