Subgroups — C₉×C₃⋊C₃₂ #11720098

Order 864.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃⋊C₃₂	C₃	1	1	yes	maximal, characteristic
3	C₉×C₃₂	—	3	1	no	maximal
4	C₃×C₈×C₉	C₄	1	1	yes	characteristic
5	C₃²×C₁₆	C₂×C₃	1	1	yes	characteristic
6	C₉×C₁₆	—	2	1	no	—
7	C₉×C₁₆	D₃	1	1	yes	characteristic
8	C₃×C₄×C₉	C₈	1	1	yes	characteristic
9	C₃×C₃₂	—	3	1	no	—
10	C₃⋊C₃₂	C₉	1	1	yes	characteristic, direct product factor
11	C₃²×C₈	C₃×C₄	1	1	yes	characteristic
12	C₈×C₉	—	2	1	no	—
13	C₈×C₉	Dic₃	1	1	yes	characteristic
14	C₂×C₃×C₉	C₁₆	1	1	yes	characteristic
15	C₃×C₁₆	—	2	1	no	—
16	C₃×C₁₆	C₂×C₉	1	1	yes	characteristic
17	C₃×C₁₆	C₃×D₃	1	1	yes	characteristic
18	C₃²×C₄	C₃×C₈	1	1	yes	characteristic
19	C₄×C₉	—	2	1	no	—
20	C₄×C₉	C₃⋊C₈	1	1	yes	characteristic
21	C₃₂	—	3	1	no	Sylow
22	C₃×C₉	C₃₂	1	1	yes	characteristic, complemented, Sylow
23	C₃×C₈	—	2	1	no	—
24	C₃×C₈	C₄×C₉	1	1	yes	characteristic
25	C₃×C₈	C₃×Dic₃	1	1	yes	characteristic
26	C₂×C₃²	C₃×C₁₆	1	1	yes	characteristic
27	C₂×C₉	—	2	1	no	—
28	C₂×C₉	C₃⋊C₁₆	1	1	yes	characteristic
29	C₁₆	D₃×C₉	1	1	yes	characteristic
30	C₃×C₄	—	2	1	no	—
31	C₃×C₄	C₈×C₉	1	1	yes	characteristic
32	C₃×C₄	C₃×C₃⋊C₈	1	1	yes	characteristic
33	C₃²	C₃×C₃₂	1	1	yes	characteristic
34	C₉	—	2	1	no	—
35	C₉	C₃⋊C₃₂	1	1	yes	characteristic, direct product factor
36	C₈	C₉×Dic₃	1	1	yes	characteristic
37	C₂×C₃	—	2	1	no	—
38	C₂×C₃	C₉×C₁₆	1	1	yes	characteristic
39	C₂×C₃	C₃×C₃⋊C₁₆	1	1	yes	characteristic
40	C₄	C₉×C₃⋊C₈	1	1	yes	characteristic
41	C₃	—	2	1	no	—
42	C₃	C₉×C₃₂	1	1	yes	characteristic, complemented
43	C₃	C₃×C₃⋊C₃₂	1	1	yes	characteristic
44	C₂	C₉×C₃⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₉×C₁₆	D₃
commutator, hypocenter	C₃	C₉×C₃₂
Frattini	C₃×C₁₆	C₃×D₃
Fitting	C₃×C₉×C₁₆	C₂
socle, prime radical	C₂×C₃²	C₃×C₁₆
cosocle	C₃²×C₁₆	C₂×C₃
LCS	G ▷ C₃
UCS	C₁ ◁ C₉×C₁₆

Complements

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

N	H ≅ G/N	type
10. C₃⋊C₃₂	C₉	direct (N × H)
22. C₃×C₉	C₃₂	semidirect
35. C₉	C₃⋊C₃₂	direct (N × H)
42. C₃	C₉×C₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×C₁₆	2
C₃×C₃⋊C₃₂	3
C₉×C₃₂	3

Subgroups — C9×C3⋊C32 #11720098

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₃⋊C₃₂ #11720098