Subgroups — C₂²×C₃×C₂²⋊C₉ #88901

Order 432.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂²⋊C₉	C₂	1	3	yes	maximal, direct product factor
2	C₂⁴×C₃²	C₃	1	1	yes	maximal, characteristic
3	C₂²×C₂²⋊C₉	C₃	1	3	yes	maximal, direct product factor
4	C₂²×C₃×C₉	—	4	1	no	maximal
5	C₃×C₂²⋊C₉	C₂²	1	1	yes	characteristic, direct product factor
6	C₂³×C₃²	—	3	3	no	—
7	C₂³×C₃²	—	3	1	no	—
8	C₂³×C₃²	C₂×C₃	1	3	yes	—
9	C₂×C₂²⋊C₉	C₂×C₃	1	9	yes	direct product factor
10	C₂×C₃×C₉	—	4	3	no	—
11	C₂⁴×C₃	C₉	1	3	yes	complemented
12	C₂⁴×C₃	C₃²	1	1	yes	characteristic
13	C₂²×C₃²	—	3	3	no	—
14	C₂²×C₃²	—	3	2	no	—
15	C₂²×C₃²	—	3	3	no	—
16	C₂²×C₃²	—	3	3	no	—
17	C₂²×C₃²	A₄	1	1	yes	characteristic
18	C₂²×C₃²	C₂²×C₃	1	1	yes	characteristic
19	C₂²×C₉	—	4	3	no	—
20	C₂²⋊C₉	C₂²×C₃	1	3	yes	direct product factor
21	C₃×C₉	—	4	1	no	Sylow
22	C₂³×C₃	—	3	9	no	—
23	C₂³×C₃	—	3	3	no	—
24	C₂³×C₃	—	3	3	no	—
25	C₂³×C₃	—	3	1	no	—
26	C₂³×C₃	C₂×C₉	1	9	yes	complemented
27	C₂³×C₃	C₂×C₃²	1	3	yes	—
28	C₂×C₃²	—	3	3	no	—
29	C₂×C₃²	—	3	1	no	—
30	C₂×C₃²	C₂×A₄	1	3	yes	—
31	C₂×C₉	—	4	9	no	—
32	C₂⁴	C₃×C₉	1	1	yes	characteristic, complemented, Sylow
33	C₂²×C₃	—	3	9	no	—
34	C₂²×C₃	—	3	3	no	—
35	C₂²×C₃	—	3	2	no	—
36	C₂²×C₃	—	3	6	no	—
37	C₂²×C₃	—	3	9	no	—
38	C₂²×C₃	—	3	9	no	—
39	C₂²×C₃	—	3	3	no	—
40	C₂²×C₃	—	3	3	no	—
41	C₂²×C₃	C₂²⋊C₉	1	3	yes	direct product factor
42	C₂²×C₃	C₂²×C₉	1	3	yes	complemented
43	C₂²×C₃	C₃×A₄	1	1	yes	characteristic
44	C₂²×C₃	C₂²×C₃²	1	1	yes	characteristic
45	C₃²	C₂²×A₄	1	1	yes	characteristic
46	C₉	—	4	3	no	—
47	C₂³	—	3	3	no	—
48	C₂³	—	3	1	no	—
49	C₂³	C₂×C₃×C₉	1	3	yes	complemented
50	C₂×C₃	—	3	1	no	—
51	C₂×C₃	—	3	3	no	—
52	C₂×C₃	—	3	3	no	—
53	C₂×C₃	—	3	9	no	—
54	C₂×C₃	C₂×C₂²⋊C₉	1	9	yes	direct product factor
55	C₂×C₃	C₂×C₃×A₄	1	3	yes	—
56	C₂²	—	3	3	no	—
57	C₂²	—	3	2	no	—
58	C₂²	—	3	3	no	—
59	C₂²	—	3	3	no	—
60	C₂²	C₃×C₂²⋊C₉	1	1	yes	characteristic, direct product factor
61	C₂²	C₂²×C₃×C₉	1	1	yes	characteristic, complemented
62	C₃	C₂²×C₂²⋊C₉	1	3	yes	direct product factor
63	C₃	C₂²×C₃×A₄	1	1	yes	characteristic
64	C₂	—	3	1	no	—
65	C₂	—	3	3	no	—
66	C₂	C₂×C₃×C₂²⋊C₉	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃²	A₄
commutator, hypocenter	C₂²	C₂²×C₃×C₉
Frattini	C₃	C₂²×C₃×A₄
Fitting, socle, prime radical	C₂⁴×C₃²	C₃
cosocle	C₂²×C₃	C₂²×C₃²
LCS	G ▷ C₂²
UCS	C₁ ◁ C₂²×C₃²

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₂²⋊C₉	C₂	direct (N × H)
3. C₂²×C₂²⋊C₉	C₃	direct (N × H)
5. C₃×C₂²⋊C₉	C₂²	direct (N × H)
9. C₂×C₂²⋊C₉	C₂×C₃	direct (N × H)
11. C₂⁴×C₃	C₉	semidirect
20. C₂²⋊C₉	C₂²×C₃	direct (N × H)
26. C₂³×C₃	C₂×C₉	semidirect
32. C₂⁴	C₃×C₉	semidirect
41. C₂²×C₃	C₂²⋊C₉	direct (N × H)
42. C₂²×C₃	C₂²×C₉	semidirect
49. C₂³	C₂×C₃×C₉	semidirect
54. C₂×C₃	C₂×C₂²⋊C₉	direct (N × H)
60. C₂²	C₃×C₂²⋊C₉	direct (N × H)
61. C₂²	C₂²×C₃×C₉	semidirect
62. C₃	C₂²×C₂²⋊C₉	direct (N × H)
66. C₂	C₂×C₃×C₂²⋊C₉	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×C₃×C₂²⋊C₉	2
C₂⁴×C₃²	3
C₂²×C₂²⋊C₉	3
C₂²×C₃×C₉	4

Subgroups — C22×C3×C22⋊C9 #88901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₂²⋊C₉ #88901