Subgroups — C₃×#10597710 #14273136

Order 1872.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#6131	C₃	1	1	yes	maximal, characteristic, complemented
3	#10597710	C₃	1	3	yes	maximal, direct product factor
4	C₃²×Dic₁₃	—	4	1	no	maximal
5	C₃×Q₈×C₁₃	C₂×C₃	1	1	yes	characteristic
6	C₃×D₅₂	—	3	1	no	—
7	C₃×C₄×D₁₃	—	3	1	no	—
8	C₁₃×SL(2,𝔽₃)	C₂×C₃	1	3	yes	complemented
9	C₂×C₃²×C₁₃	—	4	1	no	—
10	#6131	C₃²	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×D₁₃	—	3	1	no	—
12	C₃×C₄×C₁₃	—	3	1	no	—
13	C₃×Dic₁₃	—	4	3	no	—
14	C₃×Dic₁₃	A₄	1	1	yes	characteristic
15	C₃×#41⋊C₃	—	13	1	no	maximal, Hall
16	C₃²×C₁₃	—	4	1	no	Hall
17	Q₈×C₁₃	C₂×C₃²	1	1	yes	characteristic
18	D₅₂	—	3	1	no	—
19	C₄×D₁₃	—	3	1	no	—
20	C₂×C₃×C₁₃	—	4	3	no	—
21	C₂×C₃×C₁₃	C₂×A₄	1	1	yes	characteristic
22	C₃×D₁₃	—	6	1	no	—
23	C₃×SL(2,𝔽₃)	D₁₃	1	1	yes	characteristic, complemented
24	C₂×D₁₃	—	3	1	no	—
25	C₄×C₁₃	—	3	1	no	—
26	Dic₁₃	C₃×A₄	1	1	yes	characteristic
27	C₃×#41	—	13	1	no	—
28	#41⋊C₃	—	13	3	no	—
29	C₃×C₁₃	—	4	3	no	—
30	C₃×C₁₃	#41⋊C₃	1	1	yes	characteristic, complemented
31	C₃²×C₄	—	52	1	no	—
32	C₂×C₁₃	C₂×C₃×A₄	1	1	yes	characteristic
33	D₁₃	—	6	1	no	—
34	C₃×Q₈	C₃×D₁₃	1	1	yes	characteristic
35	C₃×D₄	—	39	1	no	—
36	C₂×C₃×C₄	—	39	1	no	—
37	SL(2,𝔽₃)	C₃×D₁₃	1	3	yes	complemented
38	C₂×C₃²	—	4	1	no	—
39	#41	—	13	1	no	Sylow
40	C₁₃	C₃×#41⋊C₃	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₃	—	39	1	no	—
42	C₃×C₄	—	3	1	no	—
43	C₃×C₄	—	13	1	no	—
44	C₃×C₄	—	52	3	no	—
45	C₃²	—	4	1	no	Sylow
46	Q₈	C₃²×D₁₃	1	1	yes	characteristic
47	D₄	—	39	1	no	—
48	C₂×C₄	—	39	1	no	—
49	C₂×C₃	—	4	3	no	—
50	C₂×C₃	—	78	1	no	—
51	C₂×C₃	A₄×D₁₃	1	1	yes	characteristic
52	C₂²	—	39	1	no	—
53	C₄	—	3	1	no	—
54	C₄	—	13	1	no	—
55	C₃	—	4	3	no	—
56	C₃	#10597710	1	1	yes	characteristic, direct product factor
57	C₂	—	78	1	no	—
58	C₂	C₃×A₄×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	A₄×D₁₃
commutator, cosocle, hypocenter	Q₈×C₁₃	C₂×C₃²
Frattini	C₂	C₃×A₄×D₁₃
Fitting	C₃×Q₈×C₁₃	C₂×C₃
socle	C₂×C₃×C₁₃	C₂×A₄
LCS	G ▷ Q₈×C₁₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×SL(2,𝔽₃)	C₂	semidirect
2. C₃×#6131	C₃	semidirect
3. #10597710	C₃	direct (N × H)
8. C₁₃×SL(2,𝔽₃)	C₂×C₃	semidirect
10. #6131	C₃²	semidirect
23. C₃×SL(2,𝔽₃)	D₁₃	semidirect
30. C₃×C₁₃	#41⋊C₃	semidirect
37. SL(2,𝔽₃)	C₃×D₁₃	semidirect
40. C₁₃	C₃×#41⋊C₃	semidirect
56. C₃	#10597710	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₁₃×SL(2,𝔽₃)	2
C₃×#6131	3
#10597710	3
C₃²×Dic₁₃	4
C₃×#41⋊C₃	13

Subgroups — C3×#10597710 #14273136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10597710 #14273136