Subgroups — C₃×Dic₁₁₃₁ #28330910

Order 13572.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₃×C₂₉	C₂	1	1	yes	maximal, characteristic
2	Dic₁₁₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×Dic₃₇₇	—	3	1	no	maximal
4	C₃²×C₁₃×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₃×C₂₉	—	2	1	no	—
6	C₂×C₃×C₁₃×C₂₉	D₃	1	1	yes	characteristic
7	C₂×C₃×C₁₃×C₂₉	C₂×C₃	1	1	yes	characteristic
8	Dic₃₇₇	—	3	1	no	Hall
9	C₃×C₁₃×C₂₉	—	2	1	no	—
10	C₃×C₁₃×C₂₉	Dic₃	1	1	yes	characteristic, complemented
11	C₃×C₁₃×C₂₉	C₃×C₄	1	1	yes	characteristic, complemented
12	C₃×Dic₈₇	—	13	1	no	maximal, Hall
13	C₂×C₁₃×C₂₉	C₃×D₃	1	1	yes	characteristic
14	C₂×C₃²×C₂₉	D₁₃	1	1	yes	characteristic
15	C₃×Dic₃₉	—	29	1	no	maximal, Hall
16	C₁₃×C₂₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
17	Dic₈₇	—	13	1	no	—
18	C₃×Dic₂₉	—	39	1	no	—
19	C₃²×C₂₉	Dic₁₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃²×C₁₃	D₂₉	1	1	yes	characteristic
21	C₂×C₃×C₂₉	—	2	1	no	—
22	C₂×C₃×C₂₉	C₃×D₁₃	1	1	yes	characteristic
23	C₂×C₃×C₂₉	D₃₉	1	1	yes	characteristic
24	Dic₃₉	—	29	1	no	—
25	C₃×Dic₁₃	—	87	1	no	—
26	C₃²×C₁₃	Dic₂₉	1	1	yes	characteristic, complemented, Hall
27	Dic₂₉	—	39	1	no	Hall
28	C₃×C₂₉	—	2	1	no	—
29	C₃×C₂₉	C₃×Dic₁₃	1	1	yes	characteristic, complemented
30	C₃×C₂₉	Dic₃₉	1	1	yes	characteristic, complemented
31	C₂×C₃×C₁₃	—	2	1	no	—
32	C₂×C₃×C₁₃	C₃×D₂₉	1	1	yes	characteristic
33	C₂×C₃×C₁₃	D₈₇	1	1	yes	characteristic
34	C₂×C₂₉	C₃×D₃₉	1	1	yes	characteristic
35	Dic₁₃	—	87	1	no	Hall
36	C₃×C₁₃	—	2	1	no	—
37	C₃×C₁₃	C₃×Dic₂₉	1	1	yes	characteristic, complemented
38	C₃×C₁₃	Dic₈₇	1	1	yes	characteristic, complemented
39	C₃×Dic₃	—	377	1	no	Hall
40	C₂₉	C₃×Dic₃₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₁₃	C₃×D₈₇	1	1	yes	characteristic
42	C₂×C₃²	D₃₇₇	1	1	yes	characteristic
43	C₁₃	C₃×Dic₈₇	1	1	yes	characteristic, complemented, Sylow
44	C₃×C₄	—	1131	1	no	—
45	Dic₃	—	377	1	no	—
46	C₃²	Dic₃₇₇	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	—	2	1	no	—
48	C₂×C₃	C₃×D₃₇₇	1	1	yes	characteristic
49	C₂×C₃	D₁₁₃₁	1	1	yes	characteristic
50	C₄	—	1131	1	no	Sylow
51	C₃	—	2	1	no	—
52	C₃	C₃×Dic₃₇₇	1	1	yes	characteristic, complemented
53	C₃	Dic₁₁₃₁	1	1	yes	characteristic, direct product factor
54	C₂	C₃×D₁₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	D₁₁₃₁
commutator, hypocenter	C₃×C₁₃×C₂₉	C₃×C₄
Frattini	C₂	C₃×D₁₁₃₁
Fitting, socle, prime radical	C₂×C₃²×C₁₃×C₂₉	C₂
cosocle	C₂×C₃×C₁₃×C₂₉	C₂×C₃
LCS	G ▷ C₃×C₁₃×C₂₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. Dic₁₁₃₁	C₃	direct (N × H)
4. C₃²×C₁₃×C₂₉	C₄	semidirect
10. C₃×C₁₃×C₂₉	Dic₃	semidirect
11. C₃×C₁₃×C₂₉	C₃×C₄	semidirect
16. C₁₃×C₂₉	C₃×Dic₃	semidirect
19. C₃²×C₂₉	Dic₁₃	semidirect
26. C₃²×C₁₃	Dic₂₉	semidirect
29. C₃×C₂₉	C₃×Dic₁₃	semidirect
30. C₃×C₂₉	Dic₃₉	semidirect
37. C₃×C₁₃	C₃×Dic₂₉	semidirect
38. C₃×C₁₃	Dic₈₇	semidirect
40. C₂₉	C₃×Dic₃₉	semidirect
43. C₁₃	C₃×Dic₈₇	semidirect
46. C₃²	Dic₃₇₇	semidirect
52. C₃	C₃×Dic₃₇₇	semidirect
53. C₃	Dic₁₁₃₁	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×C₃²×C₁₃×C₂₉	2
Dic₁₁₃₁	3
C₃×Dic₃₇₇	3
C₃×Dic₈₇	13
C₃×Dic₃₉	29

Subgroups — C3×Dic1131 #28330910

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Dic₁₁₃₁ #28330910