Subgroups — C₂³×C₉×Dic₃ #11722644

Order 864.

842 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₉×Dic₃	C₂	1	14	yes	maximal, direct product factor
3	C₂³×C₃×Dic₃	C₃	1	1	yes	maximal, characteristic
4	C₂³×C₄×C₉	—	3	1	no	maximal
5	C₂³×C₃×C₉	C₄	1	8	yes	complemented
6	C₂³×C₃×C₉	C₂²	1	7	yes	—
7	C₂×C₉×Dic₃	C₂²	1	28	yes	direct product factor
8	C₂⁴×C₃²	C₂×C₃	1	1	yes	characteristic
9	C₂²×C₃×Dic₃	C₂×C₃	1	14	yes	—
10	C₂⁴×C₉	—	2	1	no	—
11	C₂⁴×C₉	D₃	1	1	yes	characteristic
12	C₂²×C₄×C₉	—	3	14	no	—
13	C₂²×C₃×C₉	C₂×C₄	1	28	yes	complemented
14	C₂²×C₃×C₉	C₂³	1	7	yes	—
15	C₉×Dic₃	C₂³	1	8	yes	direct product factor
16	C₂³×C₃×C₄	—	3	1	no	—
17	C₂³×Dic₃	C₉	1	1	yes	characteristic, direct product factor
18	C₂³×C₃²	C₃×C₄	1	8	yes	—
19	C₂³×C₃²	C₂²×C₃	1	7	yes	—
20	C₂×C₃×Dic₃	C₂²×C₃	1	28	yes	—
21	C₂³×C₉	—	2	8	no	—
22	C₂³×C₉	—	2	7	no	—
23	C₂³×C₉	Dic₃	1	8	yes	direct product factor
24	C₂³×C₉	C₂×D₃	1	7	yes	—
25	C₂×C₄×C₉	—	3	28	no	—
26	C₂×C₃×C₉	C₂²×C₄	1	14	yes	complemented
27	C₂×C₃×C₉	C₂⁴	1	1	yes	characteristic
28	C₂⁴×C₃	—	2	1	no	—
29	C₂⁴×C₃	C₂×C₉	1	1	yes	characteristic
30	C₂⁴×C₃	C₃×D₃	1	1	yes	characteristic
31	C₂²×C₃×C₄	—	3	14	no	—
32	C₂²×Dic₃	C₂×C₉	1	14	yes	direct product factor
33	C₂²×C₃²	C₂×C₃×C₄	1	28	yes	—
34	C₂²×C₃²	C₂³×C₃	1	7	yes	—
35	C₃×Dic₃	C₂³×C₃	1	8	yes	—
36	C₂²×C₉	—	2	28	no	—
37	C₂²×C₉	—	2	7	no	—
38	C₂²×C₉	C₂×Dic₃	1	28	yes	direct product factor
39	C₂²×C₉	C₂²×D₃	1	7	yes	—
40	C₄×C₉	—	3	8	no	—
41	C₂³×C₄	—	3	1	no	Sylow
42	C₃×C₉	C₂³×C₄	1	1	yes	characteristic, complemented, Sylow
43	C₂³×C₃	—	2	8	no	—
44	C₂³×C₃	—	2	7	no	—
45	C₂³×C₃	C₄×C₉	1	8	yes	complemented
46	C₂³×C₃	C₂²×C₉	1	7	yes	—
47	C₂³×C₃	C₃×Dic₃	1	8	yes	—
48	C₂³×C₃	C₂×C₃×D₃	1	7	yes	—
49	C₂×C₃×C₄	—	3	28	no	—
50	C₂×Dic₃	C₂²×C₉	1	28	yes	direct product factor
51	C₂×C₃²	C₂²×C₃×C₄	1	14	yes	—
52	C₂×C₃²	C₂⁴×C₃	1	1	yes	characteristic
53	C₂×C₉	—	2	1	no	—
54	C₂×C₉	—	2	14	no	—
55	C₂×C₉	C₂²×Dic₃	1	14	yes	direct product factor
56	C₂×C₉	C₂³×D₃	1	1	yes	characteristic
57	C₂⁴	D₃×C₉	1	1	yes	characteristic
58	C₂²×C₄	—	3	14	no	—
59	C₂²×C₃	—	2	28	no	—
60	C₂²×C₃	—	2	7	no	—
61	C₂²×C₃	C₂×C₄×C₉	1	28	yes	complemented
62	C₂²×C₃	C₂³×C₉	1	7	yes	—
63	C₂²×C₃	C₂×C₃×Dic₃	1	28	yes	—
64	C₂²×C₃	C₂²×C₃×D₃	1	7	yes	—
65	C₃×C₄	—	3	8	no	—
66	Dic₃	C₂³×C₉	1	8	yes	direct product factor
67	C₃²	C₂³×C₃×C₄	1	1	yes	characteristic
68	C₉	—	2	1	no	—
69	C₉	C₂³×Dic₃	1	1	yes	characteristic, direct product factor
70	C₂³	C₉×Dic₃	1	8	yes	direct product factor
71	C₂³	C₂×D₃×C₉	1	7	yes	—
72	C₂×C₄	—	3	28	no	—
73	C₂×C₃	—	2	1	no	—
74	C₂×C₃	—	2	14	no	—
75	C₂×C₃	C₂²×C₄×C₉	1	14	yes	complemented
76	C₂×C₃	C₂⁴×C₉	1	1	yes	characteristic
77	C₂×C₃	C₂²×C₃×Dic₃	1	14	yes	—
78	C₂×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
79	C₂²	C₂×C₉×Dic₃	1	28	yes	direct product factor
80	C₂²	C₂²×D₃×C₉	1	7	yes	—
81	C₄	—	3	8	no	—
82	C₃	—	2	1	no	—
83	C₃	C₂³×C₄×C₉	1	1	yes	characteristic, complemented
84	C₃	C₂³×C₃×Dic₃	1	1	yes	characteristic
85	C₂	C₂²×C₉×Dic₃	1	14	yes	direct product factor
86	C₂	C₂³×D₃×C₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁴×C₉	D₃
commutator, hypocenter	C₃	C₂³×C₄×C₉
Frattini	C₂×C₃	C₂³×C₃×D₃
Fitting	C₂⁴×C₃×C₉	C₂
socle, prime radical	C₂⁴×C₃²	C₂×C₃
cosocle	C₂×C₃²	C₂⁴×C₃
LCS	G ▷ C₃
UCS	C₁ ◁ C₂⁴×C₉

Complements

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

N	H ≅ G/N	type
2. C₂²×C₉×Dic₃	C₂	direct (N × H)
5. C₂³×C₃×C₉	C₄	semidirect
7. C₂×C₉×Dic₃	C₂²	direct (N × H)
13. C₂²×C₃×C₉	C₂×C₄	semidirect
15. C₉×Dic₃	C₂³	direct (N × H)
17. C₂³×Dic₃	C₉	direct (N × H)
23. C₂³×C₉	Dic₃	direct (N × H)
26. C₂×C₃×C₉	C₂²×C₄	semidirect
32. C₂²×Dic₃	C₂×C₉	direct (N × H)
38. C₂²×C₉	C₂×Dic₃	direct (N × H)
42. C₃×C₉	C₂³×C₄	semidirect
45. C₂³×C₃	C₄×C₉	semidirect
50. C₂×Dic₃	C₂²×C₉	direct (N × H)
55. C₂×C₉	C₂²×Dic₃	direct (N × H)
61. C₂²×C₃	C₂×C₄×C₉	semidirect
66. Dic₃	C₂³×C₉	direct (N × H)
69. C₉	C₂³×Dic₃	direct (N × H)
70. C₂³	C₉×Dic₃	direct (N × H)
75. C₂×C₃	C₂²×C₄×C₉	semidirect
79. C₂²	C₂×C₉×Dic₃	direct (N × H)
83. C₃	C₂³×C₄×C₉	semidirect
85. C₂	C₂²×C₉×Dic₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃×C₉	2
C₂²×C₉×Dic₃	2
C₂³×C₃×Dic₃	3
C₂³×C₄×C₉	3

Subgroups — C23×C9×Dic3 #11722644

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₉×Dic₃ #11722644