Subgroups — C₃×#88130 #11928766

Order 1248.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#6103	C₂	1	3	yes	maximal
3	C₃×#6101	C₂	1	3	yes	maximal, complemented
4	#88130	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×D₁₃	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄×C₁₃	C₂²	1	3	yes	—
7	C₂×C₃×Dic₁₃	C₂²	1	3	yes	—
8	C₄²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
9	#6103	C₂×C₃	1	3	yes	—
10	#6101	C₂×C₃	1	3	yes	complemented
11	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
12	C₂×C₃×D₁₃	—	2	3	no	—
13	C₃×C₄×C₁₃	—	2	3	no	—
14	C₃×Dic₁₃	—	2	3	no	—
15	C₂²×D₁₃	C₂²×C₃	1	1	yes	characteristic
16	C₂×C₄×C₁₃	C₂²×C₃	1	3	yes	—
17	C₂×Dic₁₃	C₂²×C₃	1	3	yes	—
18	C₃×#126	—	13	1	no	maximal, Hall
19	C₂×C₃×C₁₃	#41	1	3	yes	—
20	C₃×D₁₃	—	4	1	no	—
21	C₂²×C₁₃	C₂³×C₃	1	1	yes	characteristic
22	C₂×D₁₃	—	2	3	no	—
23	C₄×C₁₃	—	2	3	no	—
24	Dic₁₃	—	2	3	no	—
25	C₃×C₄⋊C₄	—	13	3	no	—
26	C₃×C₂²⋊C₄	—	13	3	no	—
27	C₃×C₄²	D₁₃	1	1	yes	characteristic, complemented
28	C₃×C₁₃	#126	1	1	yes	characteristic, complemented, Hall
29	#126	—	13	1	no	Sylow
30	C₂×C₁₃	C₃×#41	1	3	yes	—
31	D₁₃	—	4	1	no	—
32	C₂³×C₃	—	13	1	no	—
33	C₂×C₃×C₄	—	13	3	no	—
34	C₂×C₃×C₄	C₂×D₁₃	1	3	yes	—
35	C₄⋊C₄	—	13	3	no	—
36	C₂²⋊C₄	—	13	3	no	—
37	C₄²	C₃×D₁₃	1	1	yes	characteristic, complemented
38	C₁₃	C₃×#126	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₃	—	26	3	no	—
40	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
41	C₃×C₄	—	2	3	no	—
42	C₃×C₄	—	26	3	no	—
43	C₂³	—	13	1	no	—
44	C₂×C₄	—	13	3	no	—
45	C₂×C₄	C₂×C₃×D₁₃	1	3	yes	—
46	C₂×C₃	—	52	1	no	—
47	C₂×C₃	#6127	1	3	yes	—
48	C₂²	—	26	3	no	—
49	C₂²	C₂²×C₃×D₁₃	1	1	yes	characteristic
50	C₄	—	2	3	no	—
51	C₄	—	26	3	no	—
52	C₃	#88130	1	1	yes	characteristic, direct product factor, Sylow
53	C₂	—	52	1	no	—
54	C₂	C₃×#6127	1	3	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂²×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂³×C₃
Frattini	C₂²	C₂²×C₃×D₁₃
Fitting	C₃×C₄²×C₁₃	C₂
socle	C₂²×C₃×C₁₃	C₂³
prime radical	C₂²×C₃×D₁₃	C₂²
hypercenter	C₃×C₄²	D₁₃
hypocenter	C₁₃	C₃×#126
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄²

Complements

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

N	H ≅ G/N	type
1. C₃×C₄²×C₁₃	C₂	semidirect
3. C₃×#6101	C₂	semidirect
4. #88130	C₃	direct (N × H)
8. C₄²×C₁₃	C₂×C₃	semidirect
10. #6101	C₂×C₃	semidirect
27. C₃×C₄²	D₁₃	semidirect
28. C₃×C₁₃	#126	semidirect
37. C₄²	C₃×D₁₃	semidirect
38. C₁₃	C₃×#126	semidirect
52. C₃	#88130	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×C₄²×C₁₃	2
C₃×#6103	2
C₃×#6101	2
#88130	3
C₃×#126	13

Subgroups — C3×#88130 #11928766

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#88130 #11928766