Subgroups — C₂×C₉×D₉ #66369

Order 324.

59 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×D₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₃×C₉	—	3	1	no	maximal
4	C₂×C₃×D₉	C₃	1	1	yes	maximal, characteristic
5	C₉²	C₂²	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₃×C₉	—	2	1	no	—
7	C₂×C₃×C₉	D₃	1	1	yes	characteristic
8	C₂×C₃×C₉	C₂×C₃	1	1	yes	characteristic
9	D₃×C₉	—	3	2	no	—
10	C₃×D₉	C₂×C₃	1	2	yes	—
11	C₂×C₃×D₃	—	3	1	no	—
12	C₂²×C₉	—	9	1	no	—
13	C₂×D₉	C₉	1	1	yes	characteristic, direct product factor
14	C₃×C₉	—	2	1	no	—
15	C₃×C₉	C₂×D₃	1	1	yes	characteristic
16	C₃×C₉	C₂²×C₃	1	1	yes	characteristic
17	C₂×C₃²	C₃×D₃	1	1	yes	characteristic
18	C₃×D₃	—	3	2	no	—
19	C₂×C₉	—	2	3	no	—
20	C₂×C₉	—	2	1	no	—
21	C₂×C₉	—	2	1	no	—
22	C₂×C₉	—	9	2	no	—
23	C₂×C₉	D₉	1	1	yes	characteristic, direct product factor
24	C₂×C₉	C₂×C₉	1	1	yes	characteristic, complemented
25	D₉	C₂×C₉	1	2	yes	direct product factor
26	C₂²×C₃	—	9	1	no	—
27	C₂×D₃	—	3	1	no	—
28	C₃²	C₂×C₃×D₃	1	1	yes	characteristic
29	C₉	—	2	3	no	—
30	C₉	—	2	1	no	—
31	C₉	—	2	1	no	—
32	C₉	C₂×D₉	1	1	yes	characteristic, direct product factor
33	C₉	C₂²×C₉	1	1	yes	characteristic, complemented
34	C₂×C₃	—	2	1	no	—
35	C₂×C₃	—	9	2	no	—
36	C₂×C₃	C₃×D₉	1	1	yes	characteristic
37	C₂×C₃	D₃×C₉	1	1	yes	characteristic
38	D₃	—	3	2	no	—
39	C₂²	—	9	1	no	Sylow
40	C₃	—	2	1	no	—
41	C₃	C₂×C₃×D₉	1	1	yes	characteristic
42	C₃	C₂×D₃×C₉	1	1	yes	characteristic
43	C₂	—	9	2	no	—
44	C₂	C₉×D₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₉	D₉
commutator, hypocenter	C₉	C₂²×C₉
Frattini	C₃²	C₂×C₃×D₃
Fitting	C₂×C₉²	C₂
socle	C₂×C₃²	C₃×D₃
prime radical	C₂×C₃×D₉	C₃
cosocle	C₃×C₉	C₂²×C₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₉

Complements

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

N	H ≅ G/N	type
1. C₂×C₉²	C₂	semidirect
2. C₉×D₉	C₂	direct (N × H)
5. C₉²	C₂²	semidirect
13. C₂×D₉	C₉	direct (N × H)
23. C₂×C₉	D₉	direct (N × H)
24. C₂×C₉	C₂×C₉	semidirect
25. D₉	C₂×C₉	direct (N × H)
32. C₉	C₂×D₉	direct (N × H)
33. C₉	C₂²×C₉	semidirect
44. C₂	C₉×D₉	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×C₉²	2
C₉×D₉	2
C₂×D₃×C₉	3
C₂×C₃×D₉	3

Subgroups — C2×C9×D9 #66369

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×D₉ #66369