Subgroups — C₂×D₃×#15668332 #46829429

Order 34596.

748 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#15668332	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×#15668332	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₃×C₃₁²	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂²×#15668332	—	3	1	no	maximal
5	C₃×#15668332	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×C₃₁²	C₂×C₃	1	2	yes	complemented
7	C₂×#15668332	—	2	1	no	—
8	C₂×#15668332	—	3	2	no	—
9	C₂×#15668332	D₃	1	1	yes	characteristic, direct product factor
10	C₂×C₃×C₃₁²	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂²×C₃₁²	—	3	1	no	Hall
12	C₃×C₃₁²	C₂²×C₃	1	1	yes	characteristic, complemented
13	#15668332	—	2	1	no	—
14	#15668332	C₂×D₃	1	1	yes	characteristic, direct product factor
15	C₂×C₃₁²	—	3	2	no	—
16	C₂×C₃₁²	C₃×D₃	1	1	yes	characteristic, complemented
17	C₂×D₃×C₃₁⋊C₃	—	31	32	no	maximal
18	C₃₁²	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃×C₃₁⋊C₃	—	31	32	no	—
20	D₃×C₃₁⋊C₃	—	31	64	no	—
21	C₂×D₃×C₃₁	C₃₁⋊C₃	1	32	yes	complemented
22	C₂²×C₃₁⋊C₃	—	93	32	no	—
23	C₃×C₃₁⋊C₃	—	31	32	no	—
24	C₂×C₃×C₃₁	C₂×C₃₁⋊C₃	1	32	yes	complemented
25	D₃×C₃₁	C₂×C₃₁⋊C₃	1	64	yes	complemented
26	C₂×C₃₁⋊C₃	—	31	32	no	—
27	C₂×C₃₁⋊C₃	—	62	32	no	—
28	C₂×C₃₁⋊C₃	—	93	64	no	—
29	C₂²×C₃₁	—	3	32	no	—
30	C₃×C₃₁	C₂²×C₃₁⋊C₃	1	32	yes	complemented
31	C₃₁⋊C₃	—	31	32	no	—
32	C₃₁⋊C₃	—	62	32	no	—
33	C₂×C₃₁	—	3	64	no	—
34	C₂×C₃₁	D₃×C₃₁⋊C₃	1	32	yes	complemented
35	C₂×C₃×D₃	—	961	1	no	Hall
36	C₃₁	C₂×D₃×C₃₁⋊C₃	1	32	yes	complemented
37	C₂×C₃²	—	961	1	no	—
38	C₃×D₃	—	961	2	no	—
39	C₂²×C₃	—	2883	1	no	—
40	C₂×D₃	#15668332	1	1	yes	characteristic, direct product factor
41	C₃²	—	961	1	no	Sylow
42	C₂×C₃	—	2883	2	no	—
43	C₂×C₃	—	1922	1	no	—
44	C₂×C₃	—	961	1	no	—
45	C₂×C₃	C₂×#15668332	1	1	yes	characteristic, complemented
46	D₃	C₂×#15668332	1	2	yes	direct product factor
47	C₂²	—	3	1	no	Sylow
48	C₃	—	1922	1	no	—
49	C₃	—	961	1	no	—
50	C₃	C₂²×#15668332	1	1	yes	characteristic, complemented
51	C₂	—	3	2	no	—
52	C₂	D₃×#15668332	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₃×#15668332
commutator, cosocle, hypocenter	C₃×C₃₁²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₃₁²	C₂×C₃
LCS	G ▷ C₃×C₃₁²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#15668332	C₂	semidirect
2. D₃×#15668332	C₂	direct (N × H)
3. C₂×D₃×C₃₁²	C₃	semidirect
5. C₃×#15668332	C₂²	semidirect
6. D₃×C₃₁²	C₂×C₃	semidirect
9. C₂×#15668332	D₃	direct (N × H)
10. C₂×C₃×C₃₁²	C₂×C₃	semidirect
12. C₃×C₃₁²	C₂²×C₃	semidirect
14. #15668332	C₂×D₃	direct (N × H)
16. C₂×C₃₁²	C₃×D₃	semidirect
18. C₃₁²	C₂×C₃×D₃	semidirect
21. C₂×D₃×C₃₁	C₃₁⋊C₃	semidirect
24. C₂×C₃×C₃₁	C₂×C₃₁⋊C₃	semidirect
25. D₃×C₃₁	C₂×C₃₁⋊C₃	semidirect
30. C₃×C₃₁	C₂²×C₃₁⋊C₃	semidirect
34. C₂×C₃₁	D₃×C₃₁⋊C₃	semidirect
36. C₃₁	C₂×D₃×C₃₁⋊C₃	semidirect
40. C₂×D₃	#15668332	direct (N × H)
45. C₂×C₃	C₂×#15668332	semidirect
46. D₃	C₂×#15668332	direct (N × H)
50. C₃	C₂²×#15668332	semidirect
52. C₂	D₃×#15668332	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×C₃×#15668332	2
D₃×#15668332	2
C₂×D₃×C₃₁²	3
C₂²×#15668332	3
C₂×D₃×C₃₁⋊C₃	31

Subgroups — C2×D3×#15668332 #46829429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×#15668332 #46829429