Subgroups — C₃²×C₂²⋊(C₂²⋊C₉) #13049341

Order 1296.

910 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃³	C₃	1	1	yes	maximal, characteristic
2	C₃×C₂²⋊(C₂²⋊C₉)	C₃	1	12	yes	maximal, direct product factor
3	C₃²×C₂²⋊C₉	—	4	5	no	maximal
4	C₂³×C₃³	—	3	5	no	—
5	C₂⁴×C₃²	C₉	1	9	yes	complemented
6	C₂⁴×C₃²	C₃²	1	4	yes	—
7	C₂²⋊(C₂²⋊C₉)	C₃²	1	9	yes	direct product factor
8	C₂²×C₃³	—	3	10	no	—
9	C₂²×C₃³	A₄	1	5	yes	—
10	C₃×C₂²⋊C₉	—	4	60	no	—
11	C₃²×C₉	—	16	1	no	Sylow
12	C₂³×C₃²	—	3	45	no	—
13	C₂³×C₃²	—	3	20	no	—
14	C₂×C₃³	—	3	5	no	—
15	C₂⁴×C₃	C₃×C₉	1	12	yes	complemented
16	C₂⁴×C₃	C₃³	1	1	yes	characteristic
17	C₂²×C₃²	—	3	40	no	—
18	C₂²×C₃²	—	3	90	no	—
19	C₂²×C₃²	C₂²⋊C₉	1	45	yes	complemented
20	C₂²×C₃²	C₃×A₄	1	20	yes	—
21	C₂²⋊C₉	—	4	45	no	—
22	C₃³	C₂²⋊A₄	1	1	yes	characteristic
23	C₃×C₉	—	16	12	no	—
24	C₂³×C₃	—	3	60	no	—
25	C₂³×C₃	—	3	5	no	—
26	C₂×C₃²	—	3	20	no	—
27	C₂×C₃²	—	3	45	no	—
28	C₂⁴	C₃²×C₉	1	1	yes	characteristic, complemented, Sylow
29	C₂²×C₃	—	3	10	no	—
30	C₂²×C₃	—	3	120	no	—
31	C₂²×C₃	C₃×C₂²⋊C₉	1	60	yes	complemented
32	C₂²×C₃	C₃²×A₄	1	5	yes	—
33	C₃²	C₂²⋊(C₂²⋊C₉)	1	9	yes	direct product factor
34	C₃²	C₃×C₂²⋊A₄	1	4	yes	—
35	C₉	—	16	9	no	—
36	C₂³	—	3	5	no	—
37	C₂×C₃	—	3	5	no	—
38	C₂×C₃	—	3	60	no	—
39	C₂²	—	3	10	no	—
40	C₂²	C₃²×C₂²⋊C₉	1	5	yes	complemented
41	C₃	C₃×C₂²⋊(C₂²⋊C₉)	1	12	yes	direct product factor
42	C₃	C₃²×C₂²⋊A₄	1	1	yes	characteristic
43	C₂	—	3	5	no	—

	subgroup	G/H
center, hypercenter	C₃³	C₂²⋊A₄
commutator, hypocenter	C₂⁴	C₃²×C₉
Frattini	C₃	C₃²×C₂²⋊A₄
Fitting, socle, prime radical	C₂⁴×C₃³	C₃
cosocle	C₂⁴×C₃	C₃³
LCS	G ▷ C₂⁴
UCS	C₁ ◁ C₃³

Complements

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

N	H ≅ G/N	type
2. C₃×C₂²⋊(C₂²⋊C₉)	C₃	direct (N × H)
5. C₂⁴×C₃²	C₉	semidirect
7. C₂²⋊(C₂²⋊C₉)	C₃²	direct (N × H)
15. C₂⁴×C₃	C₃×C₉	semidirect
19. C₂²×C₃²	C₂²⋊C₉	semidirect
28. C₂⁴	C₃²×C₉	semidirect
31. C₂²×C₃	C₃×C₂²⋊C₉	semidirect
33. C₃²	C₂²⋊(C₂²⋊C₉)	direct (N × H)
40. C₂²	C₃²×C₂²⋊C₉	semidirect
41. C₃	C₃×C₂²⋊(C₂²⋊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
C₂⁴×C₃³	3
C₃×C₂²⋊(C₂²⋊C₉)	3
C₃²×C₂²⋊C₉	4

Subgroups — C32×C22⋊(C22⋊C9) #13049341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₂²⋊(C₂²⋊C₉) #13049341