Subgroups — C₈×C₃⋊D₉ #88522

Order 432.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₃⋊D₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×C₃⋊D₃	—	3	1	no	maximal
5	C₈×D₉	—	3	3	no	maximal
6	C₂×C₃⋊D₉	C₄	1	1	yes	characteristic
7	C₃×C₄×C₉	C₂²	1	1	yes	characteristic
8	C₃⋊Dic₉	C₄	1	1	yes	characteristic
9	C₄×C₃⋊D₃	—	3	1	no	—
10	C₃²×C₈	D₃	1	1	yes	characteristic
11	C₃⋊(C₃⋊C₈)	—	3	1	no	—
12	C₄×D₉	—	3	3	no	—
13	C₈×C₉	D₃	1	3	yes	complemented
14	C₉⋊C₈	—	3	3	no	—
15	C₂×C₃×C₉	C₂×C₄	1	1	yes	characteristic
16	C₃⋊D₉	C₈	1	2	yes	direct product factor
17	D₃×C₈	—	9	3	no	—
18	D₃×C₈	—	9	1	no	—
19	C₂×C₃⋊D₃	—	3	1	no	—
20	C₃²×C₄	C₂×D₃	1	1	yes	characteristic
21	C₃⋊Dic₃	—	3	1	no	—
22	C₂×D₉	—	3	3	no	—
23	C₄×C₉	C₂×D₃	1	3	yes	—
24	Dic₉	—	3	3	no	—
25	C₃×C₉	C₂×C₈	1	1	yes	characteristic, complemented, Sylow
26	C₄×D₃	—	9	3	no	—
27	C₄×D₃	—	9	1	no	—
28	C₃×C₈	D₉	1	3	yes	complemented
29	C₃×C₈	C₃⋊D₃	1	1	yes	characteristic
30	C₃⋊C₈	—	9	3	no	—
31	C₃⋊C₈	—	9	1	no	—
32	C₂×C₃²	C₄×D₃	1	1	yes	characteristic
33	C₃⋊D₃	—	3	2	no	—
34	C₂×C₉	C₄×D₃	1	3	yes	—
35	D₉	—	3	6	no	—
36	C₂×C₈	—	27	1	no	Sylow
37	C₂×D₃	—	9	3	no	—
38	C₂×D₃	—	9	1	no	—
39	C₃×C₄	C₂×D₉	1	3	yes	—
40	C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
41	Dic₃	—	9	3	no	—
42	Dic₃	—	9	1	no	—
43	C₃²	D₃×C₈	1	1	yes	characteristic
44	C₉	D₃×C₈	1	3	yes	complemented
45	C₂×C₄	—	27	1	no	—
46	C₈	—	27	1	no	—
47	C₈	C₃⋊D₉	1	1	yes	characteristic, direct product factor
48	C₂×C₃	C₄×D₉	1	3	yes	—
49	C₂×C₃	C₄×C₃⋊D₃	1	1	yes	characteristic
50	D₃	—	9	6	no	—
51	D₃	—	9	2	no	—
52	C₂²	—	27	1	no	—
53	C₄	—	27	1	no	—
54	C₄	C₂×C₃⋊D₉	1	1	yes	characteristic
55	C₃	C₈×D₉	1	3	yes	complemented
56	C₃	C₈×C₃⋊D₃	1	1	yes	characteristic
57	C₂	—	27	2	no	—
58	C₂	C₄×C₃⋊D₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₈	C₃⋊D₉
commutator, hypocenter	C₃×C₉	C₂×C₈
Frattini	C₃×C₄	C₂×C₃⋊D₃
Fitting	C₃×C₈×C₉	C₂
socle	C₂×C₃²	C₄×D₃
prime radical	C₂×C₃⋊D₉	C₄
cosocle	C₃×C₄×C₉	C₂²
LCS	G ▷ C₃×C₉
UCS	C₁ ◁ C₈

Complements

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

N	H ≅ G/N	type
2. C₃×C₈×C₉	C₂	semidirect
3. C₃⋊(C₉⋊C₈)	C₂	semidirect
13. C₈×C₉	D₃	semidirect
16. C₃⋊D₉	C₈	direct (N × H)
25. C₃×C₉	C₂×C₈	semidirect
28. C₃×C₈	D₉	semidirect
44. C₉	D₃×C₈	semidirect
47. C₈	C₃⋊D₉	direct (N × H)
55. C₃	C₈×D₉	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₃⋊D₉	2
C₃×C₈×C₉	2
C₃⋊(C₉⋊C₈)	2
C₈×C₃⋊D₃	3
C₈×D₉	3

Subgroups — C8×C3⋊D9 #88522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₃⋊D₉ #88522