Subgroups — C₉×#131 #63533

Order 288.

93 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	3	yes	maximal, complemented
3	C₂×C₈×C₉	C₂	1	3	yes	maximal, complemented
4	C₃×#131	C₃	1	1	yes	maximal, characteristic
5	Q₈×C₉	C₄	1	1	yes	characteristic
6	D₄×C₉	C₄	1	3	yes	—
7	C₂×C₄×C₉	C₂²	1	3	yes	—
8	C₈×C₉	C₂²	1	3	yes	—
9	C₈×C₉	C₂²	1	1	yes	characteristic
10	C₃×#41	C₂×C₃	1	1	yes	characteristic
11	C₃×M₁₆	C₂×C₃	1	3	yes	—
12	C₂×C₃×C₈	C₂×C₃	1	3	yes	—
13	C₂²×C₉	C₂×C₄	1	3	yes	—
14	C₄×C₉	C₂×C₄	1	3	yes	—
15	C₄×C₉	C₂³	1	1	yes	characteristic
16	#131	C₉	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×Q₈	C₃×C₄	1	1	yes	characteristic
18	C₃×D₄	C₃×C₄	1	3	yes	—
19	C₂×C₃×C₄	C₂²×C₃	1	3	yes	—
20	C₃×C₈	C₂²×C₃	1	3	yes	—
21	C₃×C₈	C₂²×C₃	1	1	yes	characteristic
22	C₂×C₉	—	2	3	no	—
23	C₂×C₉	C₂²×C₄	1	1	yes	characteristic
24	#41	C₂×C₉	1	1	yes	characteristic
25	M₁₆	C₂×C₉	1	3	yes	complemented
26	C₂×C₈	C₂×C₉	1	3	yes	complemented
27	C₂²×C₃	C₂×C₃×C₄	1	3	yes	—
28	C₃×C₄	C₂×C₃×C₄	1	3	yes	—
29	C₃×C₄	C₂³×C₃	1	1	yes	characteristic
30	C₉	#131	1	1	yes	characteristic, direct product factor, Sylow
31	Q₈	C₄×C₉	1	1	yes	characteristic
32	D₄	C₄×C₉	1	3	yes	—
33	C₂×C₄	C₂²×C₉	1	3	yes	—
34	C₈	C₂²×C₉	1	1	yes	characteristic
35	C₈	C₂²×C₉	1	3	yes	—
36	C₂×C₃	—	2	3	no	—
37	C₂×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
38	C₂²	C₂×C₄×C₉	1	3	yes	—
39	C₄	C₂×C₄×C₉	1	3	yes	—
40	C₄	C₂³×C₉	1	1	yes	characteristic
41	C₃	C₃×#131	1	1	yes	characteristic
42	C₂	—	2	3	no	—
43	C₂	C₂²×C₄×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₉	C₂²
commutator	C₂	C₂²×C₄×C₉
Frattini, cosocle	C₃×C₄	C₂³×C₃
socle	C₂×C₃	C₂²×C₃×C₄
prime radical	C₃×#41	C₂×C₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×M₁₆	C₂	semidirect
3. C₂×C₈×C₉	C₂	semidirect
16. #131	C₉	direct (N × H)
25. M₁₆	C₂×C₉	semidirect
26. C₂×C₈	C₂×C₉	semidirect
30. C₉	#131	direct (N × H)

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
C₂×C₈×C₉	2
C₃×#131	3

Subgroups — C9×#131 #63533

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#131 #63533