Subgroups — C₄²×C₉⋊C₈ #11783007

Order 1152.

612 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄³×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₉⋊C₈	C₂	1	6	yes	maximal
3	C₄²×C₃⋊C₈	—	3	1	no	maximal
4	C₂×C₄²×C₉	C₄	1	4	yes	—
5	C₂×C₄²×C₉	C₂²	1	3	yes	—
6	C₂²×C₉⋊C₈	C₂²	1	4	yes	—
7	C₄×C₉⋊C₈	C₄	1	24	yes	direct product factor
8	C₃×C₄³	D₃	1	1	yes	characteristic
9	C₂×C₄×C₃⋊C₈	—	3	6	no	—
10	C₂²×C₄×C₉	C₂×C₄	1	6	yes	—
11	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
12	C₄²×C₉	C₈	1	16	yes	complemented
13	C₄²×C₉	C₂×C₄	1	12	yes	—
14	C₂×C₉⋊C₈	C₂×C₄	1	24	yes	—
15	C₄²×C₈	—	9	1	no	Sylow
16	C₂×C₃×C₄²	Dic₃	1	4	yes	—
17	C₂×C₃×C₄²	C₂×D₃	1	3	yes	—
18	C₂²×C₃⋊C₈	—	3	4	no	—
19	C₄×C₃⋊C₈	—	3	24	no	—
20	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₄×C₉	C₄²	1	12	yes	—
22	C₂×C₄×C₉	C₂×C₈	1	24	yes	—
23	C₂×C₄×C₉	C₂²×C₄	1	6	yes	—
24	C₉⋊C₈	C₄²	1	16	yes	direct product factor
25	C₂×C₄×C₈	—	9	6	no	—
26	C₄³	D₉	1	1	yes	characteristic
27	C₂²×C₃×C₄	C₂×Dic₃	1	6	yes	—
28	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
29	C₃×C₄²	C₃⋊C₈	1	16	yes	—
30	C₃×C₄²	C₄×D₃	1	12	yes	—
31	C₂×C₃⋊C₈	—	3	24	no	—
32	C₂²×C₉	C₂×C₄²	1	3	yes	—
33	C₂²×C₉	C₂²×C₈	1	4	yes	—
34	C₄×C₉	C₄×C₈	1	24	yes	complemented
35	C₄×C₉	C₂×C₄²	1	4	yes	—
36	C₂²×C₈	—	9	4	no	—
37	C₂×C₄²	Dic₉	1	4	yes	—
38	C₂×C₄²	C₂×D₉	1	3	yes	—
39	C₄×C₈	—	9	24	no	—
40	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
41	C₂×C₃×C₄	C₂×C₃⋊C₈	1	24	yes	—
42	C₂×C₃×C₄	C₄×Dic₃	1	12	yes	—
43	C₂×C₃×C₄	C₂×C₄×D₃	1	6	yes	—
44	C₃⋊C₈	—	3	16	no	—
45	C₂×C₉	C₄³	1	1	yes	characteristic
46	C₂×C₉	C₂×C₄×C₈	1	6	yes	—
47	C₂²×C₄	C₂×Dic₉	1	6	yes	—
48	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
49	C₂×C₈	—	9	24	no	—
50	C₄²	C₉⋊C₈	1	16	yes	direct product factor
51	C₄²	C₄×D₉	1	12	yes	—
52	C₂²×C₃	C₂²×C₃⋊C₈	1	4	yes	—
53	C₂²×C₃	C₂×C₄×Dic₃	1	3	yes	—
54	C₃×C₄	C₄×C₃⋊C₈	1	24	yes	—
55	C₃×C₄	C₄²×D₃	1	4	yes	—
56	C₉	C₄²×C₈	1	1	yes	characteristic, complemented, Sylow
57	C₂³	C₂²×Dic₉	1	1	yes	characteristic
58	C₂×C₄	C₂×C₉⋊C₈	1	24	yes	—
59	C₂×C₄	C₄×Dic₉	1	12	yes	—
60	C₂×C₄	C₂×C₄×D₉	1	6	yes	—
61	C₈	—	9	16	no	—
62	C₂×C₃	C₂×C₄×C₃⋊C₈	1	6	yes	—
63	C₂×C₃	C₄²×Dic₃	1	1	yes	characteristic
64	C₂²	C₂²×C₉⋊C₈	1	4	yes	—
65	C₂²	C₂×C₄×Dic₉	1	3	yes	—
66	C₄	C₄×C₉⋊C₈	1	24	yes	direct product factor
67	C₄	C₄²×D₉	1	4	yes	—
68	C₃	C₄²×C₃⋊C₈	1	1	yes	characteristic
69	C₂	C₂×C₄×C₉⋊C₈	1	6	yes	—
70	C₂	C₄²×Dic₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄³	D₉
commutator, hypocenter	C₉	C₄²×C₈
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₄³×C₉	C₂
socle, prime radical	C₂³×C₃	C₂²×Dic₃
cosocle	C₂²×C₄×C₉	C₂³
LCS	G ▷ C₉
UCS	C₁ ◁ C₄³

Complements

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

N	H ≅ G/N	type
7. C₄×C₉⋊C₈	C₄	direct (N × H)
12. C₄²×C₉	C₈	semidirect
24. C₉⋊C₈	C₄²	direct (N × H)
34. C₄×C₉	C₄×C₈	semidirect
50. C₄²	C₉⋊C₈	direct (N × H)
56. C₉	C₄²×C₈	semidirect
66. C₄	C₄×C₉⋊C₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄³×C₉	2
C₂×C₄×C₉⋊C₈	2
C₄²×C₃⋊C₈	3

Subgroups — C42×C9⋊C8 #11783007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×C₉⋊C₈ #11783007