Subgroups — C₂²×#1113 #89122

Order 432.

642 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₃⋊D₃	C₂	1	3	yes	maximal, complemented
2	C₂×#1113	C₂	1	12	yes	maximal, direct product factor
3	C₂²×D₃²	—	3	3	no	maximal
4	C₂²×C₃³	C₂²	1	1	yes	characteristic, complemented
5	C₂×C₃×C₃⋊D₃	C₂²	1	18	yes	complemented
6	#1113	C₂²	1	16	yes	direct product factor
7	C₂²×C₃⋊D₃	D₃	1	3	yes	complemented
8	C₂²×C₃×D₃	—	3	6	no	—
9	C₂²×C₃×D₃	—	6	3	no	—
10	C₂×D₃²	—	3	36	no	—
11	C₂×C₃³	C₂³	1	3	yes	complemented
12	C₃×C₃⋊D₃	C₂³	1	12	yes	complemented
13	C₂³×D₃	—	9	3	no	—
14	C₂²×C₃²	—	2	3	no	—
15	C₂²×C₃²	—	4	1	no	—
16	C₂²×C₃²	C₂×D₃	1	3	yes	complemented
17	C₂×C₃⋊D₃	C₂×D₃	1	18	yes	complemented
18	C₂×C₃×D₃	—	3	36	no	—
19	C₂×C₃×D₃	—	6	18	no	—
20	D₃²	—	3	48	no	—
21	C₃³	C₂⁴	1	1	yes	characteristic, complemented, Sylow
22	C₂³×C₃	—	9	3	no	—
23	C₂²×D₃	—	3	6	no	—
24	C₂²×D₃	—	6	3	no	—
25	C₂²×D₃	—	9	36	no	—
26	C₂×C₃²	—	2	9	no	—
27	C₂×C₃²	—	4	3	no	—
28	C₂×C₃²	C₂²×D₃	1	9	yes	complemented
29	C₃⋊D₃	C₂²×D₃	1	12	yes	complemented
30	C₃×D₃	—	3	24	no	—
31	C₃×D₃	—	6	12	no	—
32	C₂⁴	—	27	1	no	Sylow
33	C₂²×C₃	—	2	3	no	—
34	C₂²×C₃	—	4	1	no	—
35	C₂²×C₃	—	9	18	no	—
36	C₂²×C₃	D₃²	1	3	yes	complemented
37	C₂×D₃	—	3	36	no	—
38	C₂×D₃	—	6	18	no	—
39	C₂×D₃	—	9	48	no	—
40	C₃²	—	2	3	no	—
41	C₃²	—	4	1	no	—
42	C₃²	C₂³×D₃	1	3	yes	complemented
43	C₂³	—	9	3	no	—
44	C₂³	—	27	12	no	—
45	C₂×C₃	—	2	9	no	—
46	C₂×C₃	—	4	3	no	—
47	C₂×C₃	—	9	12	no	—
48	C₂×C₃	C₂×D₃²	1	9	yes	complemented
49	D₃	—	3	24	no	—
50	D₃	—	6	12	no	—
51	C₂²	—	9	18	no	—
52	C₂²	—	27	16	no	—
53	C₂²	#1113	1	1	yes	characteristic, direct product factor
54	C₃	—	2	3	no	—
55	C₃	—	4	1	no	—
56	C₃	C₂²×D₃²	1	3	yes	complemented
57	C₂	—	9	12	no	—
58	C₂	C₂×#1113	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	#1113
commutator, cosocle, hypocenter	C₃³	C₂⁴
Frattini	C₁	G
Fitting, socle	C₂²×C₃³	C₂²
LCS	G ▷ C₃³
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₃⋊D₃	C₂	semidirect
2. C₂×#1113	C₂	direct (N × H)
4. C₂²×C₃³	C₂²	semidirect
5. C₂×C₃×C₃⋊D₃	C₂²	semidirect
6. #1113	C₂²	direct (N × H)
7. C₂²×C₃⋊D₃	D₃	semidirect
11. C₂×C₃³	C₂³	semidirect
12. C₃×C₃⋊D₃	C₂³	semidirect
16. C₂²×C₃²	C₂×D₃	semidirect
17. C₂×C₃⋊D₃	C₂×D₃	semidirect
21. C₃³	C₂⁴	semidirect
28. C₂×C₃²	C₂²×D₃	semidirect
29. C₃⋊D₃	C₂²×D₃	semidirect
36. C₂²×C₃	D₃²	semidirect
42. C₃²	C₂³×D₃	semidirect
48. C₂×C₃	C₂×D₃²	semidirect
53. C₂²	#1113	direct (N × H)
56. C₃	C₂²×D₃²	semidirect
58. C₂	C₂×#1113	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₃⋊D₃	2
C₂×#1113	2
C₂²×D₃²	3

Subgroups — C22×#1113 #89122

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#1113 #89122