Subgroups — C₂×C₃⋊#19153449 #46829420

Order 34596.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#15668333	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊#19153449	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃₁×D₉₃	—	3	1	no	maximal
4	C₂×#19153449	—	3	3	no	maximal
5	C₃×#15668333	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃₁×D₉₃	—	3	2	no	—
7	C₂×#15668333	D₃	1	3	yes	complemented
8	#19153449	—	3	6	no	—
9	C₂×C₃×C₃₁²	D₃	1	1	yes	characteristic, complemented
10	C₂×C₃₁×D₃₁	—	9	1	no	Hall
11	C₃×C₃₁²	C₂×D₃	1	1	yes	characteristic, complemented
12	#15668333	C₂×D₃	1	3	yes	complemented
13	C₂×C₃₁²	C₃⋊D₃	1	1	yes	characteristic, complemented
14	C₃₁×D₃₁	—	9	2	no	—
15	C₃₁²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃×C₃₁⋊C₃	—	62	1	no	—
17	C₂×D₉₃	—	3	1	no	—
18	C₂×D₃×C₃₁	—	93	1	no	—
19	C₃×C₃₁⋊C₃	—	62	1	no	—
20	C₂×C₃×C₃₁	—	2	1	no	—
21	C₂×C₃×C₃₁	—	3	1	no	—
22	C₂×C₃×C₃₁	—	3	1	no	—
23	C₂×C₃×C₃₁	—	6	4	no	—
24	D₉₃	—	3	2	no	—
25	D₃×C₃₁	—	93	2	no	—
26	C₂×C₃₁⋊C₃	—	62	3	no	—
27	C₂²×C₃₁	—	279	1	no	—
28	C₂×D₃₁	—	9	1	no	—
29	C₃×C₃₁	—	2	1	no	—
30	C₃×C₃₁	—	3	1	no	—
31	C₃×C₃₁	—	3	1	no	—
32	C₃×C₃₁	—	6	4	no	—
33	C₃₁⋊C₃	—	62	3	no	—
34	C₂×C₃₁	—	2	1	no	—
35	C₂×C₃₁	—	3	1	no	—
36	C₂×C₃₁	—	3	1	no	—
37	C₂×C₃₁	—	6	4	no	—
38	C₂×C₃₁	—	279	2	no	—
39	D₃₁	—	9	2	no	—
40	C₂×C₃⋊D₃	—	961	1	no	maximal, Hall
41	C₃₁	—	2	1	no	—
42	C₃₁	—	3	1	no	—
43	C₃₁	—	3	1	no	—
44	C₃₁	—	6	4	no	—
45	C₂×C₃²	—	961	1	no	—
46	C₃⋊D₃	—	961	2	no	—
47	C₂×D₃	—	2883	3	no	—
48	C₂×D₃	—	93	1	no	—
49	C₃²	—	961	1	no	Sylow
50	C₂×C₃	—	961	3	no	—
51	C₂×C₃	#19153449	1	1	yes	characteristic, complemented
52	D₃	—	2883	6	no	—
53	D₃	—	93	2	no	—
54	C₂²	—	279	1	no	Sylow
55	C₃	—	961	3	no	—
56	C₃	C₂×#19153449	1	1	yes	characteristic, complemented
57	C₂	—	279	2	no	—
58	C₂	C₃⋊#19153449	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊#19153449
commutator, cosocle, hypocenter	C₃×#15668333	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₃₁²	D₃
LCS	G ▷ C₃×#15668333
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#15668333	C₂	semidirect
2. C₃⋊#19153449	C₂	direct (N × H)
5. C₃×#15668333	C₂²	semidirect
7. C₂×#15668333	D₃	semidirect
9. C₂×C₃×C₃₁²	D₃	semidirect
11. C₃×C₃₁²	C₂×D₃	semidirect
12. #15668333	C₂×D₃	semidirect
13. C₂×C₃₁²	C₃⋊D₃	semidirect
15. C₃₁²	C₂×C₃⋊D₃	semidirect
51. C₂×C₃	#19153449	semidirect
56. C₃	C₂×#19153449	semidirect
58. C₂	C₃⋊#19153449	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×#15668333	2
C₃⋊#19153449	2
C₂×C₃₁×D₉₃	3
C₂×#19153449	3
C₂×C₃⋊D₃	961

Subgroups — C2×C3⋊#19153449 #46829420

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊#19153449 #46829420