Subgroups — C₃×C₄×C₂²⋊C₉ #88684

Order 432.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂²⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃²×C₄	C₃	1	1	yes	maximal, characteristic
3	C₄×C₂²⋊C₉	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₂²⋊C₉	C₄	1	1	yes	characteristic, direct product factor
5	C₃×C₄×C₉	—	4	1	no	maximal
6	C₂³×C₃²	C₂×C₃	1	1	yes	characteristic
7	C₂×C₃²×C₄	—	3	1	no	—
8	C₂×C₃²×C₄	—	3	1	no	—
9	C₂×C₂²⋊C₉	C₂×C₃	1	3	yes	—
10	C₂×C₃×C₉	—	4	1	no	—
11	C₂²×C₃×C₄	C₉	1	3	yes	complemented
12	C₂²×C₃×C₄	C₃²	1	1	yes	characteristic
13	C₂²×C₃²	—	3	1	no	—
14	C₂²×C₃²	—	3	1	no	—
15	C₂²×C₃²	C₃×C₄	1	1	yes	characteristic
16	C₃²×C₄	—	3	1	no	—
17	C₃²×C₄	A₄	1	1	yes	characteristic
18	C₂²⋊C₉	C₃×C₄	1	3	yes	direct product factor
19	C₄×C₉	—	4	3	no	—
20	C₃×C₉	—	4	1	no	Sylow
21	C₂³×C₃	C₂×C₉	1	3	yes	—
22	C₂³×C₃	C₂×C₃²	1	1	yes	characteristic
23	C₂×C₃×C₄	—	3	3	no	—
24	C₂×C₃×C₄	—	3	1	no	—
25	C₂×C₃×C₄	—	3	3	no	—
26	C₂×C₃×C₄	—	3	1	no	—
27	C₂×C₃²	—	3	1	no	—
28	C₂×C₃²	—	3	1	no	—
29	C₂×C₃²	C₂×A₄	1	1	yes	characteristic
30	C₂×C₉	—	4	3	no	—
31	C₂²×C₄	C₃×C₉	1	1	yes	characteristic, complemented, Sylow
32	C₂²×C₃	—	3	3	no	—
33	C₂²×C₃	—	3	1	no	—
34	C₂²×C₃	—	3	3	no	—
35	C₂²×C₃	—	3	1	no	—
36	C₂²×C₃	C₄×C₉	1	3	yes	complemented
37	C₂²×C₃	C₃²×C₄	1	1	yes	characteristic
38	C₃×C₄	—	3	3	no	—
39	C₃×C₄	—	3	1	no	—
40	C₃×C₄	C₂²⋊C₉	1	3	yes	direct product factor
41	C₃×C₄	C₃×A₄	1	1	yes	characteristic
42	C₃²	C₄×A₄	1	1	yes	characteristic
43	C₉	—	4	3	no	—
44	C₂³	C₂×C₃×C₉	1	1	yes	characteristic
45	C₂×C₄	—	3	1	no	—
46	C₂×C₄	—	3	1	no	—
47	C₂×C₃	—	3	3	no	—
48	C₂×C₃	—	3	3	no	—
49	C₂×C₃	—	3	1	no	—
50	C₂×C₃	—	3	1	no	—
51	C₂×C₃	C₂×C₂²⋊C₉	1	3	yes	—
52	C₂×C₃	C₂×C₃×A₄	1	1	yes	characteristic
53	C₂²	—	3	1	no	—
54	C₂²	—	3	1	no	—
55	C₂²	C₃×C₄×C₉	1	1	yes	characteristic, complemented
56	C₄	—	3	1	no	—
57	C₄	C₃×C₂²⋊C₉	1	1	yes	characteristic, direct product factor
58	C₃	C₄×C₂²⋊C₉	1	3	yes	direct product factor
59	C₃	C₃×C₄×A₄	1	1	yes	characteristic
60	C₂	—	3	1	no	—
61	C₂	—	3	1	no	—
62	C₂	C₂×C₃×C₂²⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃²×C₄	A₄
commutator, hypocenter	C₂²	C₃×C₄×C₉
Frattini	C₂×C₃	C₂×C₃×A₄
Fitting	C₂²×C₃²×C₄	C₃
socle, prime radical	C₂³×C₃²	C₂×C₃
cosocle	C₂³×C₃	C₂×C₃²
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃²×C₄

Complements

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

N	H ≅ G/N	type
3. C₄×C₂²⋊C₉	C₃	direct (N × H)
4. C₃×C₂²⋊C₉	C₄	direct (N × H)
11. C₂²×C₃×C₄	C₉	semidirect
18. C₂²⋊C₉	C₃×C₄	direct (N × H)
31. C₂²×C₄	C₃×C₉	semidirect
36. C₂²×C₃	C₄×C₉	semidirect
40. C₃×C₄	C₂²⋊C₉	direct (N × H)
55. C₂²	C₃×C₄×C₉	semidirect
57. C₄	C₃×C₂²⋊C₉	direct (N × H)
58. C₃	C₄×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
C₂²×C₃²×C₄	3
C₄×C₂²⋊C₉	3
C₃×C₄×C₉	4

Subgroups — C3×C4×C22⋊C9 #88684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₂²⋊C₉ #88684