Subgroups — C₃×Dic₃×C₃₁² #46829370

Order 34596.

476 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₃₁²	C₂	1	1	yes	maximal, characteristic
2	Dic₃×C₃₁²	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₄×C₃₁²	—	3	1	no	maximal
4	C₃²×C₃₁²	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₃₁²	—	2	1	no	—
6	C₂×C₃×C₃₁²	D₃	1	1	yes	characteristic
7	C₂×C₃×C₃₁²	C₂×C₃	1	1	yes	characteristic
8	C₄×C₃₁²	—	3	1	no	Hall
9	C₃×C₃₁²	—	2	1	no	—
10	C₃×C₃₁²	Dic₃	1	1	yes	characteristic, direct product factor
11	C₃×C₃₁²	C₃×C₄	1	1	yes	characteristic, complemented
12	C₂×C₃₁²	C₃×D₃	1	1	yes	characteristic
13	C₃×Dic₃×C₃₁	C₃₁	1	32	yes	maximal, direct product factor
14	C₃₁²	C₃×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
15	C₂×C₃²×C₃₁	C₂×C₃₁	1	32	yes	—
16	C₃×C₄×C₃₁	—	3	32	no	—
17	Dic₃×C₃₁	C₃×C₃₁	1	32	yes	direct product factor
18	C₃²×C₃₁	C₄×C₃₁	1	32	yes	complemented
19	C₂×C₃×C₃₁	—	2	32	no	—
20	C₂×C₃×C₃₁	D₃×C₃₁	1	32	yes	—
21	C₂×C₃×C₃₁	C₂×C₃×C₃₁	1	32	yes	—
22	C₄×C₃₁	—	3	32	no	—
23	C₃×C₃₁	—	2	32	no	—
24	C₃×C₃₁	Dic₃×C₃₁	1	32	yes	direct product factor
25	C₃×C₃₁	C₃×C₄×C₃₁	1	32	yes	complemented
26	C₂×C₃₁	C₃×D₃×C₃₁	1	32	yes	—
27	C₃×Dic₃	C₃₁²	1	1	yes	characteristic, direct product factor, Hall
28	C₃₁	C₃×Dic₃×C₃₁	1	32	yes	direct product factor
29	C₂×C₃²	C₂×C₃₁²	1	1	yes	characteristic
30	C₃×C₄	—	3	1	no	—
31	Dic₃	C₃×C₃₁²	1	1	yes	characteristic, direct product factor
32	C₃²	C₄×C₃₁²	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃	—	2	1	no	—
34	C₂×C₃	C₂×C₃×C₃₁²	1	1	yes	characteristic
35	C₂×C₃	D₃×C₃₁²	1	1	yes	characteristic
36	C₄	—	3	1	no	Sylow
37	C₃	—	2	1	no	—
38	C₃	C₃×C₄×C₃₁²	1	1	yes	characteristic, complemented
39	C₃	Dic₃×C₃₁²	1	1	yes	characteristic, direct product factor
40	C₂	C₃×D₃×C₃₁²	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₃₁²	D₃
commutator, hypocenter	C₃	C₃×C₄×C₃₁²
Frattini	C₂	C₃×D₃×C₃₁²
Fitting, socle, prime radical	C₂×C₃²×C₃₁²	C₂
cosocle	C₂×C₃	C₂×C₃×C₃₁²
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₃₁²

Complements

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

N	H ≅ G/N	type
2. Dic₃×C₃₁²	C₃	direct (N × H)
4. C₃²×C₃₁²	C₄	semidirect
10. C₃×C₃₁²	Dic₃	direct (N × H)
11. C₃×C₃₁²	C₃×C₄	semidirect
13. C₃×Dic₃×C₃₁	C₃₁	direct (N × H)
14. C₃₁²	C₃×Dic₃	direct (N × H)
17. Dic₃×C₃₁	C₃×C₃₁	direct (N × H)
18. C₃²×C₃₁	C₄×C₃₁	semidirect
24. C₃×C₃₁	Dic₃×C₃₁	direct (N × H)
25. C₃×C₃₁	C₃×C₄×C₃₁	semidirect
27. C₃×Dic₃	C₃₁²	direct (N × H)
28. C₃₁	C₃×Dic₃×C₃₁	direct (N × H)
31. Dic₃	C₃×C₃₁²	direct (N × H)
32. C₃²	C₄×C₃₁²	semidirect
38. C₃	C₃×C₄×C₃₁²	semidirect
39. C₃	Dic₃×C₃₁²	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₃₁²	2
Dic₃×C₃₁²	3
C₃×C₄×C₃₁²	3
C₃×Dic₃×C₃₁	31

Subgroups — C3×Dic3×C312 #46829370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Dic₃×C₃₁² #46829370