Subgroups — C₃²×C₃⋊D₂₁ #11765819

Order 1134.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴×C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₃⋊D₂₁	C₃	1	4	yes	maximal, direct product factor
3	C₃²×D₂₁	—	3	4	no	maximal
4	C₃³×C₇	—	2	16	no	—
5	C₃³×C₇	D₃	1	4	yes	complemented
6	C₃³×C₇	C₂×C₃	1	4	yes	complemented
7	C₃²×C₃⋊D₃	—	7	1	no	maximal, Hall
8	C₃⋊D₂₁	C₃²	1	1	yes	characteristic, direct product factor
9	C₃×D₂₁	—	3	16	no	—
10	C₃²×D₇	—	9	1	no	—
11	C₃⁴	D₇	1	1	yes	characteristic, complemented, Sylow
12	C₃²×C₇	—	2	24	no	—
13	C₃²×C₇	—	2	16	no	—
14	C₃²×C₇	—	2	16	no	—
15	C₃²×C₇	C₃×D₃	1	16	yes	complemented
16	C₃²×C₇	C₃⋊D₃	1	1	yes	characteristic, complemented
17	C₃²×C₇	C₂×C₃²	1	1	yes	characteristic, complemented
18	C₃×C₃⋊D₃	—	7	4	no	—
19	C₃²×D₃	—	21	4	no	—
20	D₂₁	—	3	4	no	—
21	C₃×D₇	—	9	4	no	—
22	C₃³	—	2	16	no	—
23	C₃³	C₃×D₇	1	4	yes	complemented
24	C₃³	D₂₁	1	4	yes	complemented
25	C₃×C₇	—	2	16	no	—
26	C₃×C₇	C₃²×D₃	1	4	yes	complemented
27	C₃×C₇	C₃×C₃⋊D₃	1	4	yes	complemented
28	C₂×C₃²	—	63	1	no	—
29	C₃⋊D₃	—	7	1	no	—
30	C₃×D₃	—	21	16	no	—
31	D₇	—	9	1	no	Hall
32	C₃²	—	2	24	no	—
33	C₃²	—	2	16	no	—
34	C₃²	—	2	16	no	—
35	C₃²	C₃²×D₇	1	1	yes	characteristic, complemented
36	C₃²	C₃×D₂₁	1	16	yes	complemented
37	C₃²	C₃⋊D₂₁	1	1	yes	characteristic, direct product factor
38	C₇	C₃²×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₃	—	63	4	no	—
40	D₃	—	21	4	no	—
41	C₃	—	2	16	no	—
42	C₃	C₃²×D₂₁	1	4	yes	complemented
43	C₃	C₃×C₃⋊D₂₁	1	4	yes	direct product factor
44	C₂	—	63	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²	C₃⋊D₂₁
commutator, cosocle, hypocenter	C₃²×C₇	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃⁴×C₇	C₂
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₃²

Complements

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

N	H ≅ G/N	type
1. C₃⁴×C₇	C₂	semidirect
2. C₃×C₃⋊D₂₁	C₃	direct (N × H)
5. C₃³×C₇	D₃	semidirect
6. C₃³×C₇	C₂×C₃	semidirect
8. C₃⋊D₂₁	C₃²	direct (N × H)
11. C₃⁴	D₇	semidirect
15. C₃²×C₇	C₃×D₃	semidirect
16. C₃²×C₇	C₃⋊D₃	semidirect
17. C₃²×C₇	C₂×C₃²	semidirect
23. C₃³	C₃×D₇	semidirect
24. C₃³	D₂₁	semidirect
26. C₃×C₇	C₃²×D₃	semidirect
27. C₃×C₇	C₃×C₃⋊D₃	semidirect
35. C₃²	C₃²×D₇	semidirect
36. C₃²	C₃×D₂₁	semidirect
37. C₃²	C₃⋊D₂₁	direct (N × H)
38. C₇	C₃²×C₃⋊D₃	semidirect
42. C₃	C₃²×D₂₁	semidirect
43. C₃	C₃×C₃⋊D₂₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃⁴×C₇	2
C₃×C₃⋊D₂₁	3
C₃²×D₂₁	3
C₃²×C₃⋊D₃	7

Subgroups — C32×C3⋊D21 #11765819

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₃⋊D₂₁ #11765819