Subgroups — C₉×#104 #63406

Order 288.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#41	C₂	1	1	yes	maximal, characteristic
2	C₉×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#104	C₃	1	1	yes	maximal, characteristic
5	Q₈×C₉	C₄	1	1	yes	characteristic, complemented
6	D₄×C₉	—	2	1	no	—
7	D₄×C₉	C₄	1	1	yes	characteristic, complemented
8	C₂×C₄×C₉	—	2	1	no	—
9	C₂×C₄×C₉	—	2	1	no	—
10	C₂×C₄×C₉	C₂²	1	1	yes	characteristic
11	C₈×C₉	—	2	1	no	—
12	C₃×#41	C₂×C₃	1	1	yes	characteristic
13	C₃×M₁₆	C₂×C₃	1	1	yes	characteristic
14	C₃×C₄²	C₂×C₃	1	1	yes	characteristic
15	C₂²×C₉	—	2	1	no	—
16	C₂²×C₉	D₄	1	1	yes	characteristic
17	C₄×C₉	—	2	2	no	—
18	C₄×C₉	—	2	1	no	—
19	C₄×C₉	C₂×C₄	1	1	yes	characteristic
20	C₄×C₉	D₄	1	1	yes	characteristic
21	#104	C₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₃×Q₈	C₃×C₄	1	1	yes	characteristic
23	C₃×D₄	—	2	1	no	—
24	C₃×D₄	C₃×C₄	1	1	yes	characteristic
25	C₂×C₃×C₄	—	2	1	no	—
26	C₂×C₃×C₄	—	2	1	no	—
27	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
28	C₃×C₈	—	2	1	no	—
29	C₂×C₉	—	2	1	no	—
30	C₂×C₉	—	4	1	no	—
31	C₂×C₉	C₂²⋊C₄	1	1	yes	characteristic
32	#41	C₂×C₉	1	1	yes	characteristic
33	M₁₆	C₂×C₉	1	1	yes	characteristic, complemented
34	C₄²	C₂×C₉	1	1	yes	characteristic, complemented
35	C₂²×C₃	—	2	1	no	—
36	C₂²×C₃	C₃×D₄	1	1	yes	characteristic
37	C₃×C₄	—	2	2	no	—
38	C₃×C₄	—	2	1	no	—
39	C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
40	C₃×C₄	C₃×D₄	1	1	yes	characteristic
41	C₉	#104	1	1	yes	characteristic, direct product factor, Sylow
42	Q₈	C₄×C₉	1	1	yes	characteristic, complemented
43	D₄	—	2	1	no	—
44	D₄	C₄×C₉	1	1	yes	characteristic, complemented
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	—	2	1	no	—
47	C₂×C₄	C₂²×C₉	1	1	yes	characteristic
48	C₈	—	2	1	no	—
49	C₂×C₃	—	2	1	no	—
50	C₂×C₃	—	4	1	no	—
51	C₂×C₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
52	C₂²	—	2	1	no	—
53	C₂²	D₄×C₉	1	1	yes	characteristic
54	C₄	—	2	2	no	—
55	C₄	—	2	1	no	—
56	C₄	C₂×C₄×C₉	1	1	yes	characteristic
57	C₄	D₄×C₉	1	1	yes	characteristic
58	C₃	C₃×#104	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	—	4	1	no	—
61	C₂	C₉×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₉	D₄
commutator	C₄	C₂×C₄×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂²×C₃
socle	C₂×C₃	C₃×C₂²⋊C₄
prime radical	C₃×#41	C₂×C₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₉ ◁ C₂×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×M₁₆	C₂	semidirect
3. C₄²×C₉	C₂	semidirect
5. Q₈×C₉	C₄	semidirect
7. D₄×C₉	C₄	semidirect
21. #104	C₉	direct (N × H)
33. M₁₆	C₂×C₉	semidirect
34. C₄²	C₂×C₉	semidirect
41. C₉	#104	direct (N × H)
42. Q₈	C₄×C₉	semidirect
44. D₄	C₄×C₉	semidirect

Maximal subgroups

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

subgroup	index
C₉×#41	2
C₉×M₁₆	2
C₄²×C₉	2
C₃×#104	3

Subgroups — C9×#104 #63406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#104 #63406