Subgroups — C₄³×D₉ #11800640

Order 1152.

1908 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×D₉	C₂	1	7	yes	maximal
2	C₄³×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×Dic₉	C₂	1	7	yes	maximal, complemented
4	C₄³×D₃	—	3	1	no	maximal
5	C₂²×C₄×D₉	C₂²	1	7	yes	—
6	C₂×C₄²×C₉	C₂²	1	7	yes	—
7	C₂×C₄×Dic₉	C₂²	1	21	yes	—
8	C₄²×D₉	C₄	1	56	yes	direct product factor
9	C₂×C₄²×D₃	—	3	7	no	—
10	C₃×C₄³	D₃	1	1	yes	characteristic
11	C₄²×Dic₃	—	3	7	no	—
12	C₂³×D₉	C₂³	1	1	yes	characteristic
13	C₂²×C₄×C₉	C₂³	1	7	yes	—
14	C₂²×Dic₉	C₂³	1	7	yes	—
15	C₂×C₄×D₉	C₂×C₄	1	84	yes	—
16	C₄²×C₉	C₂×C₄	1	28	yes	complemented
17	C₄×Dic₉	C₂×C₄	1	84	yes	complemented
18	C₂×C₄³	—	9	1	no	Sylow
19	C₂²×C₄×D₃	—	3	7	no	—
20	C₂×C₃×C₄²	C₂×D₃	1	7	yes	—
21	C₂×C₄×Dic₃	—	3	21	no	—
22	C₄²×D₃	—	3	56	no	—
23	C₂³×C₉	C₂⁴	1	1	yes	characteristic
24	C₂²×D₉	C₂²×C₄	1	14	yes	—
25	C₂×C₄×C₉	C₂²×C₄	1	42	yes	—
26	C₂×Dic₉	C₂²×C₄	1	42	yes	—
27	C₄×D₉	C₄²	1	112	yes	direct product factor
28	C₂²×C₄²	—	9	7	no	—
29	C₄³	—	9	7	no	—
30	C₄³	D₉	1	1	yes	characteristic, direct product factor
31	C₂³×D₃	—	3	1	no	—
32	C₂²×C₃×C₄	C₂²×D₃	1	7	yes	—
33	C₂²×Dic₃	—	3	7	no	—
34	C₂×C₄×D₃	—	3	84	no	—
35	C₃×C₄²	C₄×D₃	1	28	yes	—
36	C₄×Dic₃	—	3	84	no	—
37	C₂²×C₉	C₂³×C₄	1	7	yes	—
38	C₂×D₉	C₂×C₄²	1	28	yes	—
39	C₄×C₉	C₂×C₄²	1	28	yes	complemented
40	Dic₉	C₂×C₄²	1	28	yes	complemented
41	C₂³×C₄	—	9	7	no	—
42	C₂×C₄²	—	9	21	no	—
43	C₂×C₄²	—	9	56	no	—
44	C₂×C₄²	C₂×D₉	1	7	yes	—
45	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
46	C₂²×D₃	—	3	14	no	—
47	C₂×C₃×C₄	C₂×C₄×D₃	1	42	yes	—
48	C₂×Dic₃	—	3	42	no	—
49	C₄×D₃	—	3	112	no	—
50	C₂×C₉	C₂²×C₄²	1	7	yes	—
51	D₉	C₄³	1	8	yes	direct product factor
52	C₂⁴	—	9	1	no	—
53	C₂²×C₄	—	9	7	no	—
54	C₂²×C₄	—	9	84	no	—
55	C₂²×C₄	C₂²×D₉	1	7	yes	—
56	C₄²	—	9	84	no	—
57	C₄²	C₄×D₉	1	28	yes	direct product factor
58	C₂²×C₃	C₂²×C₄×D₃	1	7	yes	—
59	C₂×D₃	—	3	28	no	—
60	C₃×C₄	C₄²×D₃	1	28	yes	—
61	Dic₃	—	3	28	no	—
62	C₉	C₂×C₄³	1	1	yes	characteristic, complemented, Sylow
63	C₂³	—	9	14	no	—
64	C₂³	C₂³×D₉	1	1	yes	characteristic
65	C₂×C₄	—	9	42	no	—
66	C₂×C₄	—	9	112	no	—
67	C₂×C₄	C₂×C₄×D₉	1	42	yes	—
68	C₂×C₃	C₂×C₄²×D₃	1	7	yes	—
69	D₃	—	3	8	no	—
70	C₂²	—	9	28	no	—
71	C₂²	C₂²×C₄×D₉	1	7	yes	—
72	C₄	—	9	28	no	—
73	C₄	C₄²×D₉	1	28	yes	direct product factor
74	C₃	C₄³×D₃	1	1	yes	characteristic
75	C₂	—	9	8	no	—
76	C₂	C₂×C₄²×D₉	1	7	yes	—

	subgroup	G/H
center, hypercenter	C₄³	D₉
commutator, hypocenter	C₉	C₂×C₄³
Frattini, socle	C₂³×C₃	C₂³×D₃
Fitting	C₄³×C₉	C₂
prime radical	C₂³×D₉	C₂³
cosocle	C₂³×C₉	C₂⁴
LCS	G ▷ C₉
UCS	C₁ ◁ C₄³

Complements

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

N	H ≅ G/N	type
2. C₄³×C₉	C₂	semidirect
3. C₄²×Dic₉	C₂	semidirect
8. C₄²×D₉	C₄	direct (N × H)
16. C₄²×C₉	C₂×C₄	semidirect
17. C₄×Dic₉	C₂×C₄	semidirect
27. C₄×D₉	C₄²	direct (N × H)
30. C₄³	D₉	direct (N × H)
39. C₄×C₉	C₂×C₄²	semidirect
40. Dic₉	C₂×C₄²	semidirect
51. D₉	C₄³	direct (N × H)
57. C₄²	C₄×D₉	direct (N × H)
62. C₉	C₂×C₄³	semidirect
73. C₄	C₄²×D₉	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×C₄²×D₉	2
C₄³×C₉	2
C₄²×Dic₉	2
C₄³×D₃	3

Subgroups — C43×D9 #11800640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄³×D₉ #11800640