Subgroups — C₂²×C₃×#11925881 #28408367

Order 14508.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#11925881	C₂	1	3	yes	maximal, direct product factor
2	C₂²×#11925881	C₃	1	3	yes	maximal, direct product factor
3	C₂²×C₃×C₁₃×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×#11925881	C₂²	1	1	yes	characteristic, direct product factor, Hall
5	C₂×#11925881	C₂×C₃	1	9	yes	direct product factor
6	C₂×C₃×C₁₃×C₃₁	C₂×C₃	1	3	yes	complemented
7	C₂²×C₁₃×C₃₁	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₃×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented
9	#11925881	C₂²×C₃	1	3	yes	direct product factor
10	C₂²×C₃×C₃₁⋊C₃	—	13	1	no	maximal, Hall
11	C₂×C₁₃×C₃₁	C₂×C₃²	1	3	yes	complemented
12	C₂×C₃×C₃₁⋊C₃	—	13	3	no	—
13	C₂²×C₃×C₁₃⋊C₃	—	31	1	no	maximal, Hall
14	C₁₃×C₃₁	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
15	C₂²×C₃×C₃₁	C₁₃⋊C₃	1	1	yes	characteristic, complemented
16	C₂²×C₃₁⋊C₃	—	13	3	no	—
17	C₃×C₃₁⋊C₃	—	13	1	no	Hall
18	C₂×C₃×C₁₃⋊C₃	—	31	3	no	—
19	C₂×C₃×C₃₁	C₂×C₁₃⋊C₃	1	3	yes	complemented
20	C₂×C₃₁⋊C₃	—	13	9	no	—
21	C₂²×C₃×C₁₃	C₃₁⋊C₃	1	1	yes	characteristic, complemented
22	C₂²×C₁₃⋊C₃	—	31	3	no	—
23	C₂²×C₃₁	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
24	C₃×C₁₃⋊C₃	—	31	1	no	Hall
25	C₃×C₃₁	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, complemented
26	C₃₁⋊C₃	—	13	3	no	—
27	C₂×C₃×C₁₃	C₂×C₃₁⋊C₃	1	3	yes	complemented
28	C₂×C₁₃⋊C₃	—	31	9	no	—
29	C₂×C₃₁	C₂×C₃×C₁₃⋊C₃	1	3	yes	complemented
30	C₂²×C₁₃	C₃×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
31	C₃×C₁₃	C₂²×C₃₁⋊C₃	1	1	yes	characteristic, complemented
32	C₁₃⋊C₃	—	31	3	no	—
33	C₂²×C₃²	—	403	1	no	Hall
34	C₃₁	C₂²×C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₁₃	C₂×C₃×C₃₁⋊C₃	1	3	yes	complemented
36	C₂×C₃²	—	403	3	no	—
37	C₁₃	C₂²×C₃×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₃	—	403	3	no	—
39	C₂²×C₃	#11925881	1	1	yes	characteristic, direct product factor
40	C₃²	—	403	1	no	Sylow
41	C₂×C₃	—	403	9	no	—
42	C₂×C₃	C₂×#11925881	1	3	yes	direct product factor
43	C₂²	C₃×#11925881	1	1	yes	characteristic, direct product factor, Sylow
44	C₃	—	403	3	no	—
45	C₃	C₂²×#11925881	1	1	yes	characteristic, direct product factor
46	C₂	C₂×C₃×#11925881	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃	#11925881
commutator, cosocle, hypocenter	C₁₃×C₃₁	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₃×C₃₁	C₃
LCS	G ▷ C₁₃×C₃₁
UCS	C₁ ◁ C₂²×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#11925881	C₂	direct (N × H)
2. C₂²×#11925881	C₃	direct (N × H)
3. C₂²×C₃×C₁₃×C₃₁	C₃	semidirect
4. C₃×#11925881	C₂²	direct (N × H)
5. C₂×#11925881	C₂×C₃	direct (N × H)
6. C₂×C₃×C₁₃×C₃₁	C₂×C₃	semidirect
7. C₂²×C₁₃×C₃₁	C₃²	semidirect
8. C₃×C₁₃×C₃₁	C₂²×C₃	semidirect
9. #11925881	C₂²×C₃	direct (N × H)
11. C₂×C₁₃×C₃₁	C₂×C₃²	semidirect
14. C₁₃×C₃₁	C₂²×C₃²	semidirect
15. C₂²×C₃×C₃₁	C₁₃⋊C₃	semidirect
19. C₂×C₃×C₃₁	C₂×C₁₃⋊C₃	semidirect
21. C₂²×C₃×C₁₃	C₃₁⋊C₃	semidirect
23. C₂²×C₃₁	C₃×C₁₃⋊C₃	semidirect
25. C₃×C₃₁	C₂²×C₁₃⋊C₃	semidirect
27. C₂×C₃×C₁₃	C₂×C₃₁⋊C₃	semidirect
29. C₂×C₃₁	C₂×C₃×C₁₃⋊C₃	semidirect
30. C₂²×C₁₃	C₃×C₃₁⋊C₃	semidirect
31. C₃×C₁₃	C₂²×C₃₁⋊C₃	semidirect
34. C₃₁	C₂²×C₃×C₁₃⋊C₃	semidirect
35. C₂×C₁₃	C₂×C₃×C₃₁⋊C₃	semidirect
37. C₁₃	C₂²×C₃×C₃₁⋊C₃	semidirect
39. C₂²×C₃	#11925881	direct (N × H)
42. C₂×C₃	C₂×#11925881	direct (N × H)
43. C₂²	C₃×#11925881	direct (N × H)
45. C₃	C₂²×#11925881	direct (N × H)
46. C₂	C₂×C₃×#11925881	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×#11925881	2
C₂²×#11925881	3
C₂²×C₃×C₁₃×C₃₁	3
C₂²×C₃×C₃₁⋊C₃	13
C₂²×C₃×C₁₃⋊C₃	31

Subgroups — C22×C3×#11925881 #28408367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#11925881 #28408367