Subgroups — Dic₃×#11925882 #28408220

Order 14508.

56 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
2	Dic₃×C₁₃×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
3	C₄×#11925882	—	3	1	no	maximal
4	C₃×#11925882	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×#11925882	—	2	1	no	—
6	C₂×#11925882	D₃	1	1	yes	characteristic
7	C₂×C₃×C₁₃×C₃₁	C₂×C₃	1	1	yes	characteristic
8	C₄×C₁₃×C₃₁	—	3	1	no	Hall
9	C₃×C₁₃×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented
10	#11925882	—	2	1	no	—
11	#11925882	Dic₃	1	1	yes	characteristic, direct product factor
12	Dic₃×C₃₁⋊C₃	—	13	1	no	maximal, Hall
13	C₂×C₁₃×C₃₁	C₃×D₃	1	1	yes	characteristic
14	C₂×C₃×C₃₁⋊C₃	—	13	1	no	—
15	Dic₃×C₁₃⋊C₃	—	31	1	no	maximal, Hall
16	C₁₃×C₃₁	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
17	Dic₃×C₃₁	C₁₃⋊C₃	1	1	yes	characteristic, complemented
18	C₄×C₃₁⋊C₃	—	39	1	no	—
19	C₃×C₃₁⋊C₃	—	13	1	no	Hall
20	C₂×C₃×C₁₃⋊C₃	—	31	1	no	—
21	C₂×C₃×C₃₁	C₂×C₁₃⋊C₃	1	1	yes	characteristic
22	C₂×C₃₁⋊C₃	—	13	1	no	—
23	C₂×C₃₁⋊C₃	—	26	1	no	—
24	Dic₃×C₁₃	C₃₁⋊C₃	1	1	yes	characteristic, complemented
25	C₄×C₁₃⋊C₃	—	93	1	no	—
26	C₄×C₃₁	—	3	1	no	Hall
27	C₃×C₁₃⋊C₃	—	31	1	no	Hall
28	C₃×C₃₁	C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented
29	C₃₁⋊C₃	—	13	1	no	—
30	C₃₁⋊C₃	—	26	1	no	—
31	C₂×C₃×C₁₃	C₂×C₃₁⋊C₃	1	1	yes	characteristic
32	C₂×C₁₃⋊C₃	—	31	1	no	—
33	C₂×C₁₃⋊C₃	—	62	1	no	—
34	C₂×C₃₁	D₃×C₁₃⋊C₃	1	1	yes	characteristic
35	C₄×C₁₃	—	3	1	no	Hall
36	C₃×C₁₃	C₄×C₃₁⋊C₃	1	1	yes	characteristic, complemented
37	C₁₃⋊C₃	—	31	1	no	—
38	C₁₃⋊C₃	—	62	1	no	—
39	C₃×Dic₃	—	403	1	no	Hall
40	C₃₁	Dic₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₁₃	D₃×C₃₁⋊C₃	1	1	yes	characteristic
42	C₂×C₃²	—	403	1	no	—
43	C₁₃	Dic₃×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
44	C₃×C₄	—	1209	1	no	—
45	Dic₃	#11925882	1	1	yes	characteristic, direct product factor
46	C₃²	—	403	1	no	Sylow
47	C₂×C₃	—	806	1	no	—
48	C₂×C₃	—	403	1	no	—
49	C₂×C₃	C₂×#11925882	1	1	yes	characteristic
50	C₄	—	3	1	no	Sylow
51	C₃	—	806	1	no	—
52	C₃	—	403	1	no	—
53	C₃	C₄×#11925882	1	1	yes	characteristic, complemented
54	C₂	D₃×#11925882	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×#11925882
commutator, hypocenter	C₃×C₁₃×C₃₁	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₁₃×C₃₁	C₂×C₃
prime radical	C₂×C₃×#11925882	C₂
LCS	G ▷ C₃×C₁₃×C₃₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. Dic₃×C₁₃×C₃₁	C₃	semidirect
4. C₃×#11925882	C₄	semidirect
9. C₃×C₁₃×C₃₁	C₃×C₄	semidirect
11. #11925882	Dic₃	direct (N × H)
16. C₁₃×C₃₁	C₃×Dic₃	semidirect
17. Dic₃×C₃₁	C₁₃⋊C₃	semidirect
24. Dic₃×C₁₃	C₃₁⋊C₃	semidirect
28. C₃×C₃₁	C₄×C₁₃⋊C₃	semidirect
36. C₃×C₁₃	C₄×C₃₁⋊C₃	semidirect
40. C₃₁	Dic₃×C₁₃⋊C₃	semidirect
43. C₁₃	Dic₃×C₃₁⋊C₃	semidirect
45. Dic₃	#11925882	direct (N × H)
53. C₃	C₄×#11925882	semidirect

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
Dic₃×C₁₃×C₃₁	3
C₄×#11925882	3
Dic₃×C₃₁⋊C₃	13
Dic₃×C₁₃⋊C₃	31

Subgroups — Dic3×#11925882 #28408220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃×#11925882 #28408220