Subgroups — C₂×C₃⋊#14559026 #28408317

Order 14508.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#11925882	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊#14559026	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃₁×D₃₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×#14559026	—	3	1	no	maximal
5	C₃×#11925882	C₂²	1	1	yes	characteristic, complemented, Hall
6	#14559026	—	3	2	no	—
7	C₃₁×D₃₉	C₂×C₃	1	2	yes	complemented
8	C₂×#11925882	—	2	1	no	—
9	C₂×#11925882	D₃	1	1	yes	characteristic, complemented
10	C₂×C₃×C₁₃×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×D₁₃×C₃₁	—	3	1	no	Hall
12	C₃×C₁₃×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented
13	#11925882	—	2	1	no	—
14	#11925882	C₂×D₃	1	1	yes	characteristic, complemented
15	C₂×D₃×C₃₁⋊C₃	—	13	1	no	maximal, Hall
16	C₂×C₁₃×C₃₁	C₃×D₃	1	1	yes	characteristic, complemented
17	D₁₃×C₃₁	—	3	2	no	—
18	C₂×C₃×C₃₁⋊C₃	—	26	1	no	—
19	D₃×C₃₁⋊C₃	—	13	2	no	—
20	C₂×C₃⋊(D₁₃⋊C₃)	—	31	1	no	maximal, Hall
21	C₁₃×C₃₁	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
22	C₂×D₃×C₃₁	—	13	1	no	—
23	C₂²×C₃₁⋊C₃	—	39	1	no	—
24	C₃×C₃₁⋊C₃	—	26	1	no	Hall
25	C₂×C₃×C₁₃⋊C₃	—	31	1	no	—
26	C₃⋊(D₁₃⋊C₃)	—	31	2	no	—
27	C₂×C₃×C₃₁	D₁₃⋊C₃	1	1	yes	characteristic, complemented
28	D₃×C₃₁	—	13	2	no	—
29	C₂×C₃₁⋊C₃	—	26	1	no	—
30	C₂×C₃₁⋊C₃	—	26	1	no	—
31	C₂×C₃₁⋊C₃	—	39	2	no	—
32	C₂×D₃₉	C₃₁⋊C₃	1	1	yes	characteristic, complemented
33	C₂×D₁₃⋊C₃	—	93	1	no	—
34	C₂²×C₃₁	—	39	1	no	Hall
35	C₃×C₁₃⋊C₃	—	31	1	no	Hall
36	C₃×C₃₁	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
37	C₃₁⋊C₃	—	26	1	no	—
38	C₃₁⋊C₃	—	26	1	no	—
39	C₂×C₃×C₁₃	C₂×C₃₁⋊C₃	1	1	yes	characteristic, complemented
40	D₃₉	C₂×C₃₁⋊C₃	1	2	yes	complemented
41	C₂×C₁₃⋊C₃	—	31	1	no	—
42	C₂×C₁₃⋊C₃	—	62	1	no	—
43	D₁₃⋊C₃	—	93	2	no	—
44	C₂×C₃₁	—	39	2	no	—
45	C₂×C₃₁	C₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented
46	C₂×D₁₃	—	3	1	no	Hall
47	C₃×C₁₃	C₂²×C₃₁⋊C₃	1	1	yes	characteristic, complemented
48	C₁₃⋊C₃	—	31	1	no	—
49	C₁₃⋊C₃	—	62	1	no	—
50	C₂×C₃×D₃	—	403	1	no	Hall
51	C₃₁	C₂×C₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₁₃	D₃×C₃₁⋊C₃	1	1	yes	characteristic, complemented
53	D₁₃	—	3	2	no	—
54	C₂×C₃²	—	806	1	no	—
55	C₃×D₃	—	403	2	no	—
56	C₁₃	C₂×D₃×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₃	—	1209	1	no	—
58	C₂×D₃	—	13	1	no	—
59	C₃²	—	806	1	no	Sylow
60	C₂×C₃	—	806	1	no	—
61	C₂×C₃	—	806	1	no	—
62	C₂×C₃	—	1209	2	no	—
63	C₂×C₃	#14559026	1	1	yes	characteristic, complemented
64	D₃	—	13	2	no	—
65	C₂²	—	39	1	no	Sylow
66	C₃	—	806	1	no	—
67	C₃	—	806	1	no	—
68	C₃	C₂×#14559026	1	1	yes	characteristic, complemented
69	C₂	—	39	2	no	—
70	C₂	C₃⋊#14559026	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊#14559026
commutator, cosocle, hypocenter	C₃×C₁₃×C₃₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₃₁	C₂×C₃
LCS	G ▷ C₃×C₁₃×C₃₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#11925882	C₂	semidirect
2. C₃⋊#14559026	C₂	direct (N × H)
3. C₂×C₃₁×D₃₉	C₃	semidirect
5. C₃×#11925882	C₂²	semidirect
7. C₃₁×D₃₉	C₂×C₃	semidirect
9. C₂×#11925882	D₃	semidirect
10. C₂×C₃×C₁₃×C₃₁	C₂×C₃	semidirect
12. C₃×C₁₃×C₃₁	C₂²×C₃	semidirect
14. #11925882	C₂×D₃	semidirect
16. C₂×C₁₃×C₃₁	C₃×D₃	semidirect
21. C₁₃×C₃₁	C₂×C₃×D₃	semidirect
27. C₂×C₃×C₃₁	D₁₃⋊C₃	semidirect
32. C₂×D₃₉	C₃₁⋊C₃	semidirect
36. C₃×C₃₁	C₂×D₁₃⋊C₃	semidirect
39. C₂×C₃×C₁₃	C₂×C₃₁⋊C₃	semidirect
40. D₃₉	C₂×C₃₁⋊C₃	semidirect
45. C₂×C₃₁	C₃⋊(D₁₃⋊C₃)	semidirect
47. C₃×C₁₃	C₂²×C₃₁⋊C₃	semidirect
51. C₃₁	C₂×C₃⋊(D₁₃⋊C₃)	semidirect
52. C₂×C₁₃	D₃×C₃₁⋊C₃	semidirect
56. C₁₃	C₂×D₃×C₃₁⋊C₃	semidirect
63. C₂×C₃	#14559026	semidirect
68. C₃	C₂×#14559026	semidirect
70. C₂	C₃⋊#14559026	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×#11925882	2
C₃⋊#14559026	2
C₂×C₃₁×D₃₉	3
C₂×#14559026	3
C₂×D₃×C₃₁⋊C₃	13
C₂×C₃⋊(D₁₃⋊C₃)	31

Subgroups — C2×C3⋊#14559026 #28408317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊#14559026 #28408317