Subgroups — C₈×C₉⋊C₈ #10588130

Order 576.

111 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₄×C₉⋊C₈	C₂	1	2	yes	maximal
3	C₈×C₃⋊C₈	—	3	1	no	maximal
4	C₂×C₈×C₉	C₄	1	2	yes	—
5	C₄²×C₉	C₂²	1	1	yes	characteristic
6	C₂×C₉⋊C₈	C₄	1	4	yes	—
7	C₃×C₄×C₈	D₃	1	1	yes	characteristic
8	C₄×C₃⋊C₈	—	3	2	no	—
9	C₂×C₄×C₉	C₂×C₄	1	2	yes	—
10	C₂×C₄×C₉	C₂×C₄	1	1	yes	characteristic
11	C₈×C₉	C₈	1	4	yes	complemented
12	C₉⋊C₈	C₈	1	8	yes	direct product factor
13	C₈²	—	9	1	no	Sylow
14	C₂×C₃×C₈	Dic₃	1	2	yes	—
15	C₃×C₄²	C₂×D₃	1	1	yes	characteristic
16	C₂×C₃⋊C₈	—	3	4	no	—
17	C₂²×C₉	C₄²	1	1	yes	characteristic
18	C₄×C₉	C₂×C₈	1	4	yes	—
19	C₄×C₉	C₂×C₈	1	2	yes	—
20	C₄×C₈	—	9	2	no	—
21	C₄×C₈	D₉	1	1	yes	characteristic
22	C₂×C₃×C₄	C₄×D₃	1	2	yes	—
23	C₂×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
24	C₃×C₈	C₃⋊C₈	1	4	yes	—
25	C₃⋊C₈	—	3	8	no	—
26	C₂×C₉	C₄×C₈	1	1	yes	characteristic
27	C₂×C₉	C₄×C₈	1	2	yes	—
28	C₂×C₈	—	9	4	no	—
29	C₂×C₈	Dic₉	1	2	yes	—
30	C₄²	C₂×D₉	1	1	yes	characteristic
31	C₂²×C₃	C₄×Dic₃	1	1	yes	characteristic
32	C₃×C₄	D₃×C₈	1	4	yes	—
33	C₃×C₄	C₂×C₃⋊C₈	1	2	yes	—
34	C₉	C₈²	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₄	C₄×D₉	1	2	yes	—
36	C₂×C₄	C₂×Dic₉	1	1	yes	characteristic
37	C₈	—	9	8	no	—
38	C₈	C₉⋊C₈	1	4	yes	direct product factor
39	C₂×C₃	C₄×C₃⋊C₈	1	1	yes	characteristic
40	C₂×C₃	C₈×Dic₃	1	2	yes	—
41	C₂²	C₄×Dic₉	1	1	yes	characteristic
42	C₄	C₈×D₉	1	4	yes	—
43	C₄	C₂×C₉⋊C₈	1	2	yes	—
44	C₃	C₈×C₃⋊C₈	1	1	yes	characteristic
45	C₂	C₄×C₉⋊C₈	1	1	yes	characteristic
46	C₂	C₈×Dic₉	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₄×C₈	D₉
commutator, hypocenter	C₉	C₈²
Frattini	C₃×C₄²	C₂×D₃
Fitting	C₄×C₈×C₉	C₂
socle, prime radical	C₂²×C₃	C₄×Dic₃
cosocle	C₄²×C₉	C₂²
LCS	G ▷ C₉
UCS	C₁ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
11. C₈×C₉	C₈	semidirect
12. C₉⋊C₈	C₈	direct (N × H)
34. C₉	C₈²	semidirect
38. C₈	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
C₄×C₈×C₉	2
C₄×C₉⋊C₈	2
C₈×C₃⋊C₈	3

Subgroups — C8×C9⋊C8 #10588130

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₉⋊C₈ #10588130