Subgroups — C₄×C₉×C₃⋊C₈ #11720364

Order 864.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×C₃⋊C₈	C₂	1	2	yes	maximal
3	C₃×C₄×C₃⋊C₈	C₃	1	1	yes	maximal, characteristic
4	C₄×C₈×C₉	—	3	1	no	maximal
5	C₂×C₃×C₄×C₉	C₄	1	2	yes	—
6	C₂×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
7	C₉×C₃⋊C₈	C₄	1	4	yes	direct product factor
8	C₃²×C₄²	C₂×C₃	1	1	yes	characteristic
9	C₂×C₃×C₃⋊C₈	C₂×C₃	1	2	yes	—
10	C₂×C₈×C₉	—	3	2	no	—
11	C₄²×C₉	—	2	1	no	—
12	C₄²×C₉	D₃	1	1	yes	characteristic
13	C₂²×C₃×C₉	C₂×C₄	1	1	yes	characteristic
14	C₃×C₄×C₉	C₈	1	4	yes	complemented
15	C₃×C₄×C₉	C₂×C₄	1	2	yes	—
16	C₃×C₄×C₈	—	3	1	no	—
17	C₄×C₃⋊C₈	C₉	1	1	yes	characteristic, direct product factor
18	C₂×C₃²×C₄	C₃×C₄	1	2	yes	—
19	C₂×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
20	C₃×C₃⋊C₈	C₃×C₄	1	4	yes	—
21	C₂×C₄×C₉	—	2	2	no	—
22	C₂×C₄×C₉	—	2	1	no	—
23	C₂×C₄×C₉	Dic₃	1	2	yes	—
24	C₂×C₄×C₉	C₂×D₃	1	1	yes	characteristic
25	C₈×C₉	—	3	4	no	—
26	C₂×C₃×C₉	C₄²	1	1	yes	characteristic
27	C₂×C₃×C₉	C₂×C₈	1	2	yes	—
28	C₂×C₃×C₈	—	3	2	no	—
29	C₃×C₄²	—	2	1	no	—
30	C₃×C₄²	C₂×C₉	1	1	yes	characteristic
31	C₃×C₄²	C₃×D₃	1	1	yes	characteristic
32	C₂×C₃⋊C₈	C₂×C₉	1	2	yes	—
33	C₂²×C₃²	C₂×C₃×C₄	1	1	yes	characteristic
34	C₃²×C₄	C₃×C₈	1	4	yes	—
35	C₃²×C₄	C₂×C₃×C₄	1	2	yes	—
36	C₂²×C₉	—	2	1	no	—
37	C₂²×C₉	C₂×Dic₃	1	1	yes	characteristic
38	C₄×C₉	—	2	4	no	—
39	C₄×C₉	—	2	2	no	—
40	C₄×C₉	C₃⋊C₈	1	4	yes	direct product factor
41	C₄×C₉	C₄×D₃	1	2	yes	—
42	C₄×C₈	—	3	1	no	Sylow
43	C₃×C₉	C₄×C₈	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₃×C₄	—	2	2	no	—
45	C₂×C₃×C₄	—	2	1	no	—
46	C₂×C₃×C₄	C₄×C₉	1	2	yes	—
47	C₂×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
48	C₂×C₃×C₄	C₃×Dic₃	1	2	yes	—
49	C₂×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
50	C₃×C₈	—	3	4	no	—
51	C₃⋊C₈	C₄×C₉	1	4	yes	direct product factor
52	C₂×C₃²	C₃×C₄²	1	1	yes	characteristic
53	C₂×C₃²	C₂×C₃×C₈	1	2	yes	—
54	C₂×C₉	—	2	2	no	—
55	C₂×C₉	—	2	1	no	—
56	C₂×C₉	C₂×C₃⋊C₈	1	2	yes	—
57	C₂×C₉	C₄×Dic₃	1	1	yes	characteristic
58	C₂×C₈	—	3	2	no	—
59	C₄²	D₃×C₉	1	1	yes	characteristic
60	C₂²×C₃	—	2	1	no	—
61	C₂²×C₃	C₂×C₄×C₉	1	1	yes	characteristic
62	C₂²×C₃	C₂×C₃×Dic₃	1	1	yes	characteristic
63	C₃×C₄	—	2	4	no	—
64	C₃×C₄	—	2	2	no	—
65	C₃×C₄	C₈×C₉	1	4	yes	complemented
66	C₃×C₄	C₂×C₄×C₉	1	2	yes	—
67	C₃×C₄	C₃×C₃⋊C₈	1	4	yes	—
68	C₃×C₄	C₃×C₄×D₃	1	2	yes	—
69	C₃²	C₃×C₄×C₈	1	1	yes	characteristic
70	C₉	—	2	1	no	—
71	C₉	C₄×C₃⋊C₈	1	1	yes	characteristic, direct product factor
72	C₂×C₄	C₉×Dic₃	1	2	yes	—
73	C₂×C₄	C₂×D₃×C₉	1	1	yes	characteristic
74	C₈	—	3	4	no	—
75	C₂×C₃	—	2	2	no	—
76	C₂×C₃	—	2	1	no	—
77	C₂×C₃	C₄²×C₉	1	1	yes	characteristic
78	C₂×C₃	C₂×C₈×C₉	1	2	yes	—
79	C₂×C₃	C₂×C₃×C₃⋊C₈	1	2	yes	—
80	C₂×C₃	C₃×C₄×Dic₃	1	1	yes	characteristic
81	C₂²	C₂×C₉×Dic₃	1	1	yes	characteristic
82	C₄	C₉×C₃⋊C₈	1	4	yes	direct product factor
83	C₄	C₄×D₃×C₉	1	2	yes	—
84	C₃	—	2	1	no	—
85	C₃	C₄×C₈×C₉	1	1	yes	characteristic, complemented
86	C₃	C₃×C₄×C₃⋊C₈	1	1	yes	characteristic
87	C₂	C₂×C₉×C₃⋊C₈	1	2	yes	—
88	C₂	C₄×C₉×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄²×C₉	D₃
commutator, hypocenter	C₃	C₄×C₈×C₉
Frattini	C₂×C₃×C₄	C₂×C₃×D₃
Fitting	C₃×C₄²×C₉	C₂
socle, prime radical	C₂²×C₃²	C₂×C₃×C₄
cosocle	C₂×C₃²×C₄	C₂²×C₃
LCS	G ▷ C₃
UCS	C₁ ◁ C₄²×C₉

Complements

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

N	H ≅ G/N	type
7. C₉×C₃⋊C₈	C₄	direct (N × H)
14. C₃×C₄×C₉	C₈	semidirect
17. C₄×C₃⋊C₈	C₉	direct (N × H)
40. C₄×C₉	C₃⋊C₈	direct (N × H)
43. C₃×C₉	C₄×C₈	semidirect
51. C₃⋊C₈	C₄×C₉	direct (N × H)
65. C₃×C₄	C₈×C₉	semidirect
71. C₉	C₄×C₃⋊C₈	direct (N × H)
82. C₄	C₉×C₃⋊C₈	direct (N × H)
85. C₃	C₄×C₈×C₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄²×C₉	2
C₂×C₉×C₃⋊C₈	2
C₃×C₄×C₃⋊C₈	3
C₄×C₈×C₉	3

Subgroups — C4×C9×C3⋊C8 #11720364

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₉×C₃⋊C₈ #11720364