Subgroups — C₂²×C₄×D₉ #63705

Order 288.

354 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₉	C₂	1	12	yes	maximal, direct product factor
5	C₂²×C₄×D₃	—	3	1	no	maximal
6	C₂³×C₉	C₂²	1	1	yes	characteristic
7	C₂²×D₉	C₄	1	8	yes	direct product factor
8	C₂²×D₉	C₂²	1	6	yes	—
9	C₂×C₄×C₉	C₂²	1	6	yes	complemented
10	C₂×Dic₉	C₂²	1	6	yes	complemented
11	C₄×D₉	C₂²	1	16	yes	direct product factor
12	C₂³×D₃	—	3	1	no	—
13	C₂²×C₃×C₄	D₃	1	1	yes	characteristic
14	C₂²×Dic₃	—	3	1	no	—
15	C₂×C₄×D₃	—	3	12	no	—
16	C₂²×C₉	C₂×C₄	1	4	yes	complemented
17	C₂²×C₉	C₂³	1	3	yes	—
18	C₂×D₉	C₂×C₄	1	24	yes	direct product factor
19	C₂×D₉	C₂³	1	4	yes	—
20	C₄×C₉	C₂³	1	4	yes	complemented
21	Dic₉	C₂³	1	4	yes	complemented
22	C₂³×C₄	—	9	1	no	Sylow
23	C₂³×C₃	C₂×D₃	1	1	yes	characteristic
24	C₂²×D₃	—	3	8	no	—
25	C₂²×D₃	—	3	6	no	—
26	C₂×C₃×C₄	C₂×D₃	1	6	yes	—
27	C₂×Dic₃	—	3	6	no	—
28	C₄×D₃	—	3	16	no	—
29	C₂×C₉	C₂²×C₄	1	6	yes	complemented
30	C₂×C₉	C₂⁴	1	1	yes	characteristic
31	D₉	C₂²×C₄	1	8	yes	direct product factor
32	C₂⁴	—	9	1	no	—
33	C₂²×C₄	—	9	1	no	—
34	C₂²×C₄	—	9	12	no	—
35	C₂²×C₄	D₉	1	1	yes	characteristic, direct product factor
36	C₂²×C₃	C₄×D₃	1	4	yes	—
37	C₂²×C₃	C₂²×D₃	1	3	yes	—
38	C₂×D₃	—	3	24	no	—
39	C₂×D₃	—	3	4	no	—
40	C₃×C₄	C₂²×D₃	1	4	yes	—
41	Dic₃	—	3	4	no	—
42	C₉	C₂³×C₄	1	1	yes	characteristic, complemented, Sylow
43	C₂³	—	9	8	no	—
44	C₂³	—	9	6	no	—
45	C₂³	C₂×D₉	1	1	yes	characteristic
46	C₂×C₄	—	9	6	no	—
47	C₂×C₄	—	9	16	no	—
48	C₂×C₄	C₂×D₉	1	6	yes	direct product factor
49	C₂×C₃	C₂×C₄×D₃	1	6	yes	—
50	C₂×C₃	C₂³×D₃	1	1	yes	characteristic
51	D₃	—	3	8	no	—
52	C₂²	—	9	24	no	—
53	C₂²	—	9	4	no	—
54	C₂²	C₄×D₉	1	4	yes	direct product factor
55	C₂²	C₂²×D₉	1	3	yes	—
56	C₄	—	9	4	no	—
57	C₄	C₂²×D₉	1	4	yes	direct product factor
58	C₃	C₂²×C₄×D₃	1	1	yes	characteristic
59	C₂	—	9	8	no	—
60	C₂	C₂×C₄×D₉	1	6	yes	direct product factor
61	C₂	C₂³×D₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₄	D₉
commutator, hypocenter	C₉	C₂³×C₄
Frattini	C₂×C₃	C₂³×D₃
Fitting	C₂²×C₄×C₉	C₂
socle	C₂³×C₃	C₂×D₃
prime radical	C₂³×D₉	C₂
cosocle	C₂×C₉	C₂⁴
LCS	G ▷ C₉
UCS	C₁ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₉	C₂	semidirect
3. C₂²×Dic₉	C₂	semidirect
4. C₂×C₄×D₉	C₂	direct (N × H)
7. C₂²×D₉	C₄	direct (N × H)
9. C₂×C₄×C₉	C₂²	semidirect
10. C₂×Dic₉	C₂²	semidirect
11. C₄×D₉	C₂²	direct (N × H)
16. C₂²×C₉	C₂×C₄	semidirect
18. C₂×D₉	C₂×C₄	direct (N × H)
20. C₄×C₉	C₂³	semidirect
21. Dic₉	C₂³	semidirect
29. C₂×C₉	C₂²×C₄	semidirect
31. D₉	C₂²×C₄	direct (N × H)
35. C₂²×C₄	D₉	direct (N × H)
42. C₉	C₂³×C₄	semidirect
48. C₂×C₄	C₂×D₉	direct (N × H)
54. C₂²	C₄×D₉	direct (N × H)
57. C₄	C₂²×D₉	direct (N × H)
60. C₂	C₂×C₄×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
C₂³×D₉	2
C₂²×C₄×C₉	2
C₂²×Dic₉	2
C₂×C₄×D₉	2
C₂²×C₄×D₃	3

Subgroups — C22×C4×D9 #63705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×D₉ #63705