Subgroups — C₂×C₉×D₈ #63534

Order 288.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₉	C₂	1	2	yes	maximal, complemented
2	C₉×D₈	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×D₈	C₃	1	1	yes	maximal, characteristic
5	C₂³×C₉	—	2	2	no	—
6	D₄×C₉	—	2	2	no	—
7	D₄×C₉	C₂²	1	4	yes	complemented
8	C₂×C₄×C₉	C₂²	1	1	yes	characteristic
9	C₈×C₉	C₂²	1	2	yes	complemented
10	C₂×C₃×D₄	C₂×C₃	1	2	yes	—
11	C₃×D₈	C₂×C₃	1	4	yes	—
12	C₂×C₃×C₈	C₂×C₃	1	1	yes	characteristic
13	C₂²×C₉	—	2	4	no	—
14	C₂²×C₉	—	4	4	no	—
15	C₂²×C₉	D₄	1	1	yes	characteristic
16	C₄×C₉	D₄	1	1	yes	characteristic
17	C₄×C₉	C₂³	1	1	yes	characteristic
18	C₂×D₈	C₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₂³×C₃	—	2	2	no	—
20	C₃×D₄	—	2	2	no	—
21	C₃×D₄	C₂²×C₃	1	4	yes	—
22	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
23	C₃×C₈	C₂²×C₃	1	2	yes	—
24	C₂×C₉	—	4	4	no	—
25	C₂×C₉	D₈	1	2	yes	direct product factor
26	C₂×C₉	C₂×D₄	1	1	yes	characteristic
27	C₂×D₄	C₂×C₉	1	2	yes	complemented
28	D₈	C₂×C₉	1	4	yes	direct product factor
29	C₂×C₈	C₂×C₉	1	1	yes	characteristic, complemented
30	C₂²×C₃	—	2	4	no	—
31	C₂²×C₃	—	4	4	no	—
32	C₂²×C₃	C₃×D₄	1	1	yes	characteristic
33	C₃×C₄	C₃×D₄	1	1	yes	characteristic
34	C₃×C₄	C₂³×C₃	1	1	yes	characteristic
35	C₉	C₂×D₈	1	1	yes	characteristic, direct product factor, Sylow
36	C₂³	—	2	2	no	—
37	D₄	—	2	2	no	—
38	D₄	C₂²×C₉	1	4	yes	complemented
39	C₂×C₄	C₂²×C₉	1	1	yes	characteristic
40	C₈	C₂²×C₉	1	2	yes	complemented
41	C₂×C₃	—	4	4	no	—
42	C₂×C₃	C₃×D₈	1	2	yes	—
43	C₂×C₃	C₂×C₃×D₄	1	1	yes	characteristic
44	C₂²	—	2	4	no	—
45	C₂²	—	4	4	no	—
46	C₂²	D₄×C₉	1	1	yes	characteristic
47	C₄	D₄×C₉	1	1	yes	characteristic
48	C₄	C₂³×C₉	1	1	yes	characteristic
49	C₃	C₂×C₃×D₈	1	1	yes	characteristic
50	C₂	—	4	4	no	—
51	C₂	C₉×D₈	1	2	yes	direct product factor
52	C₂	C₂×D₄×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	D₄
commutator	C₄	C₂³×C₉
Frattini, cosocle	C₃×C₄	C₂³×C₃
socle	C₂²×C₃	C₃×D₄
prime radical	C₂×C₃×D₈	C₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×C₉	C₂	semidirect
2. C₉×D₈	C₂	direct (N × H)
3. C₂×C₈×C₉	C₂	semidirect
7. D₄×C₉	C₂²	semidirect
9. C₈×C₉	C₂²	semidirect
18. C₂×D₈	C₉	direct (N × H)
25. C₂×C₉	D₈	direct (N × H)
27. C₂×D₄	C₂×C₉	semidirect
28. D₈	C₂×C₉	direct (N × H)
29. C₂×C₈	C₂×C₉	semidirect
35. C₉	C₂×D₈	direct (N × H)
38. D₄	C₂²×C₉	semidirect
40. C₈	C₂²×C₉	semidirect
51. C₂	C₉×D₈	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×D₄×C₉	2
C₉×D₈	2
C₂×C₈×C₉	2
C₂×C₃×D₈	3

Subgroups — C2×C9×D8 #63534

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×D₈ #63534