Subgroups — C₂×C₃×C₄×C₉ #6236

Order 216.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃²×C₄	C₃	1	1	yes	maximal, characteristic
4	C₂×C₄×C₉	C₃	1	3	yes	maximal, direct product factor
5	C₂×C₃×C₉	C₄	1	2	yes	direct product factor
6	C₂×C₃×C₉	C₂²	1	1	yes	characteristic
7	C₂²×C₃²	C₂×C₃	1	1	yes	characteristic
8	C₃²×C₄	C₂×C₃	1	2	yes	—
9	C₂²×C₉	C₂×C₃	1	3	yes	—
10	C₄×C₉	C₂×C₃	1	6	yes	direct product factor
11	C₃×C₉	C₂×C₄	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃×C₄	C₉	1	3	yes	direct product factor
13	C₂×C₃×C₄	C₃²	1	1	yes	characteristic
14	C₂×C₃²	C₃×C₄	1	2	yes	—
15	C₂×C₃²	C₂²×C₃	1	1	yes	characteristic
16	C₂×C₉	C₃×C₄	1	6	yes	direct product factor
17	C₂×C₉	C₂²×C₃	1	3	yes	—
18	C₂²×C₃	C₂×C₉	1	3	yes	—
19	C₂²×C₃	C₂×C₃²	1	1	yes	characteristic
20	C₃×C₄	C₂×C₉	1	6	yes	direct product factor
21	C₃×C₄	C₂×C₃²	1	2	yes	—
22	C₃²	C₂×C₃×C₄	1	1	yes	characteristic
23	C₉	C₂×C₃×C₄	1	3	yes	direct product factor
24	C₂×C₄	C₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₃	C₄×C₉	1	6	yes	direct product factor
26	C₂×C₃	C₂²×C₉	1	3	yes	—
27	C₂×C₃	C₃²×C₄	1	2	yes	—
28	C₂×C₃	C₂²×C₃²	1	1	yes	characteristic
29	C₂²	C₂×C₃×C₉	1	1	yes	characteristic
30	C₄	C₂×C₃×C₉	1	2	yes	direct product factor
31	C₃	C₂×C₄×C₉	1	3	yes	direct product factor
32	C₃	C₂×C₃²×C₄	1	1	yes	characteristic
33	C₂	C₃×C₄×C₉	1	2	yes	direct product factor
34	C₂	C₂²×C₃×C₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂²×C₃²
socle, prime radical	C₂²×C₃²	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₉	C₂	direct (N × H)
4. C₂×C₄×C₉	C₃	direct (N × H)
5. C₂×C₃×C₉	C₄	direct (N × H)
10. C₄×C₉	C₂×C₃	direct (N × H)
11. C₃×C₉	C₂×C₄	direct (N × H)
12. C₂×C₃×C₄	C₉	direct (N × H)
16. C₂×C₉	C₃×C₄	direct (N × H)
20. C₃×C₄	C₂×C₉	direct (N × H)
23. C₉	C₂×C₃×C₄	direct (N × H)
24. C₂×C₄	C₃×C₉	direct (N × H)
25. C₂×C₃	C₄×C₉	direct (N × H)
30. C₄	C₂×C₃×C₉	direct (N × H)
31. C₃	C₂×C₄×C₉	direct (N × H)
33. C₂	C₃×C₄×C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₉	2
C₃×C₄×C₉	2
C₂×C₃²×C₄	3
C₂×C₄×C₉	3

Subgroups — C2×C3×C4×C9 #6236

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄×C₉ #6236