Subgroups — C₂×C₃³×C₂²⋊C₉ #14519349

Order 1944.

2432 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₂²⋊C₉	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂³×C₃⁴	C₃	1	1	yes	maximal, characteristic
3	C₂×C₃²×C₂²⋊C₉	C₃	1	39	yes	maximal, direct product factor
4	C₂×C₃³×C₉	—	4	1	no	maximal
5	C₂²×C₃⁴	—	3	1	no	—
6	C₂²×C₃⁴	—	3	1	no	—
7	C₂²×C₃⁴	C₂×C₃	1	1	yes	characteristic
8	C₃²×C₂²⋊C₉	C₂×C₃	1	39	yes	direct product factor
9	C₃³×C₉	—	4	1	no	Sylow
10	C₂³×C₃³	C₉	1	27	yes	complemented
11	C₂³×C₃³	C₃²	1	13	yes	—
12	C₂×C₃×C₂²⋊C₉	C₃²	1	117	yes	direct product factor
13	C₂×C₃⁴	—	3	1	no	—
14	C₂×C₃⁴	—	3	1	no	—
15	C₂×C₃⁴	A₄	1	1	yes	characteristic
16	C₂×C₃²×C₉	—	4	39	no	—
17	C₂²×C₃³	—	3	27	no	—
18	C₂²×C₃³	—	3	13	no	—
19	C₂²×C₃³	—	3	27	no	—
20	C₂²×C₃³	—	3	13	no	—
21	C₂²×C₃³	C₂×C₉	1	27	yes	complemented
22	C₂²×C₃³	C₂×C₃²	1	13	yes	—
23	C₃×C₂²⋊C₉	C₂×C₃²	1	117	yes	direct product factor
24	C₃⁴	C₂×A₄	1	1	yes	characteristic
25	C₃²×C₉	—	4	39	no	—
26	C₂³×C₃²	C₃×C₉	1	117	yes	complemented
27	C₂³×C₃²	C₃³	1	13	yes	—
28	C₂×C₂²⋊C₉	C₃³	1	27	yes	direct product factor
29	C₂×C₃³	—	3	27	no	—
30	C₂×C₃³	—	3	27	no	—
31	C₂×C₃³	—	3	13	no	—
32	C₂×C₃³	—	3	13	no	—
33	C₂×C₃³	C₂²⋊C₉	1	27	yes	direct product factor
34	C₂×C₃³	C₃×A₄	1	13	yes	—
35	C₂×C₃×C₉	—	4	117	no	—
36	C₂²×C₃²	—	3	117	no	—
37	C₂²×C₃²	—	3	13	no	—
38	C₂²×C₃²	—	3	117	no	—
39	C₂²×C₃²	—	3	13	no	—
40	C₂²×C₃²	C₂×C₃×C₉	1	117	yes	complemented
41	C₂²×C₃²	C₂×C₃³	1	13	yes	—
42	C₂²⋊C₉	C₂×C₃³	1	27	yes	direct product factor
43	C₃³	C₂×C₂²⋊C₉	1	27	yes	direct product factor
44	C₃³	C₂×C₃×A₄	1	13	yes	—
45	C₃×C₉	—	4	117	no	—
46	C₂³×C₃	C₃²×C₉	1	39	yes	complemented
47	C₂³×C₃	C₃⁴	1	1	yes	characteristic
48	C₂×C₃²	—	3	117	no	—
49	C₂×C₃²	—	3	117	no	—
50	C₂×C₃²	—	3	13	no	—
51	C₂×C₃²	—	3	13	no	—
52	C₂×C₃²	C₃×C₂²⋊C₉	1	117	yes	direct product factor
53	C₂×C₃²	C₃²×A₄	1	13	yes	—
54	C₂×C₉	—	4	27	no	—
55	C₂²×C₃	—	3	39	no	—
56	C₂²×C₃	—	3	1	no	—
57	C₂²×C₃	—	3	39	no	—
58	C₂²×C₃	—	3	1	no	—
59	C₂²×C₃	C₂×C₃²×C₉	1	39	yes	complemented
60	C₂²×C₃	C₂×C₃⁴	1	1	yes	characteristic
61	C₃²	C₂×C₃×C₂²⋊C₉	1	117	yes	direct product factor
62	C₃²	C₂×C₃²×A₄	1	13	yes	—
63	C₉	—	4	27	no	—
64	C₂³	C₃³×C₉	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₃	—	3	1	no	—
66	C₂×C₃	—	3	1	no	—
67	C₂×C₃	—	3	39	no	—
68	C₂×C₃	—	3	39	no	—
69	C₂×C₃	C₃²×C₂²⋊C₉	1	39	yes	direct product factor
70	C₂×C₃	C₃³×A₄	1	1	yes	characteristic
71	C₂²	—	3	1	no	—
72	C₂²	—	3	1	no	—
73	C₂²	C₂×C₃³×C₉	1	1	yes	characteristic, complemented
74	C₃	C₂×C₃²×C₂²⋊C₉	1	39	yes	direct product factor
75	C₃	C₂×C₃³×A₄	1	1	yes	characteristic
76	C₂	—	3	1	no	—
77	C₂	—	3	1	no	—
78	C₂	C₃³×C₂²⋊C₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃⁴	A₄
commutator, hypocenter	C₂²	C₂×C₃³×C₉
Frattini	C₃	C₂×C₃³×A₄
Fitting, socle, prime radical	C₂³×C₃⁴	C₃
cosocle	C₂²×C₃	C₂×C₃⁴
LCS	G ▷ C₂²
UCS	C₁ ◁ C₂×C₃⁴

Complements

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

N	H ≅ G/N	type
1. C₃³×C₂²⋊C₉	C₂	direct (N × H)
3. C₂×C₃²×C₂²⋊C₉	C₃	direct (N × H)
8. C₃²×C₂²⋊C₉	C₂×C₃	direct (N × H)
10. C₂³×C₃³	C₉	semidirect
12. C₂×C₃×C₂²⋊C₉	C₃²	direct (N × H)
21. C₂²×C₃³	C₂×C₉	semidirect
23. C₃×C₂²⋊C₉	C₂×C₃²	direct (N × H)
26. C₂³×C₃²	C₃×C₉	semidirect
28. C₂×C₂²⋊C₉	C₃³	direct (N × H)
33. C₂×C₃³	C₂²⋊C₉	direct (N × H)
40. C₂²×C₃²	C₂×C₃×C₉	semidirect
42. C₂²⋊C₉	C₂×C₃³	direct (N × H)
43. C₃³	C₂×C₂²⋊C₉	direct (N × H)
46. C₂³×C₃	C₃²×C₉	semidirect
52. C₂×C₃²	C₃×C₂²⋊C₉	direct (N × H)
59. C₂²×C₃	C₂×C₃²×C₉	semidirect
61. C₃²	C₂×C₃×C₂²⋊C₉	direct (N × H)
64. C₂³	C₃³×C₉	semidirect
69. C₂×C₃	C₃²×C₂²⋊C₉	direct (N × H)
73. C₂²	C₂×C₃³×C₉	semidirect
74. C₃	C₂×C₃²×C₂²⋊C₉	direct (N × H)
78. C₂	C₃³×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
C₃³×C₂²⋊C₉	2
C₂³×C₃⁴	3
C₂×C₃²×C₂²⋊C₉	3
C₂×C₃³×C₉	4

Subgroups — C2×C33×C22⋊C9 #14519349

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃³×C₂²⋊C₉ #14519349