Subgroups — C₃×#88240 #11929175

Order 1248.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6131	C₂	1	1	yes	maximal, characteristic
2	C₃×#6118	C₂	1	3	yes	maximal, complemented
3	C₃×D₁₃⋊C₈	C₂	1	3	yes	maximal, complemented
4	#88240	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×Q₈×C₁₃	C₄	1	1	yes	characteristic
6	C₃×D₅₂	C₄	1	3	yes	—
7	C₃×C₄×D₁₃	C₂²	1	3	yes	—
8	C₃×#1057	C₂²	1	1	yes	characteristic
9	C₃×#1057	C₂²	1	3	yes	—
10	#6131	C₂×C₃	1	1	yes	characteristic
11	#6118	C₂×C₃	1	3	yes	complemented
12	D₁₃⋊C₈	C₂×C₃	1	3	yes	complemented
13	C₂×C₃×D₁₃	C₂×C₄	1	3	yes	—
14	C₃×C₄×C₁₃	C₂×C₄	1	3	yes	—
15	C₃×Dic₁₃	C₂³	1	1	yes	characteristic
16	Q₈×C₁₃	C₃×C₄	1	1	yes	characteristic
17	D₅₂	C₃×C₄	1	3	yes	—
18	C₄×D₁₃	C₂²×C₃	1	3	yes	—
19	#1057	C₂²×C₃	1	1	yes	characteristic
20	#1057	C₂²×C₃	1	3	yes	—
21	C₃×#131	—	13	1	no	maximal, Hall
22	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
23	C₃×D₁₃	—	2	3	no	—
24	C₂×D₁₃	C₂×C₃×C₄	1	3	yes	—
25	C₄×C₁₃	C₂×C₃×C₄	1	3	yes	—
26	Dic₁₃	C₂³×C₃	1	1	yes	characteristic
27	C₃×#41	—	13	1	no	—
28	C₃×M₁₆	—	13	3	no	—
29	C₂×C₃×C₈	—	13	3	no	—
30	C₃×C₁₃	#131	1	1	yes	characteristic, complemented, Hall
31	#131	—	13	1	no	Sylow
32	C₂×C₁₃	C₂²×C₃×C₄	1	1	yes	characteristic
33	D₁₃	—	2	3	no	—
34	C₃×Q₈	#261	1	1	yes	characteristic
35	C₃×D₄	—	13	3	no	—
36	C₂×C₃×C₄	—	13	3	no	—
37	C₃×C₈	—	13	1	no	—
38	C₃×C₈	—	13	3	no	—
39	#41	—	13	1	no	—
40	M₁₆	—	13	3	no	—
41	C₂×C₈	—	13	3	no	—
42	C₁₃	C₃×#131	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₃	—	13	3	no	—
44	C₃×C₄	—	13	1	no	—
45	C₃×C₄	C₂×#261	1	3	yes	—
46	Q₈	C₃×#261	1	1	yes	characteristic
47	D₄	—	13	3	no	—
48	C₂×C₄	—	13	3	no	—
49	C₈	—	13	1	no	—
50	C₈	—	13	3	no	—
51	C₂×C₃	—	26	3	no	—
52	C₂×C₃	C₂²×#261	1	1	yes	characteristic
53	C₂²	—	13	3	no	—
54	C₄	—	13	1	no	—
55	C₄	C₂×C₃×#261	1	3	yes	—
56	C₃	#88240	1	1	yes	characteristic, direct product factor, Sylow
57	C₂	—	26	3	no	—
58	C₂	C₂²×C₃×#261	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂²×#261
commutator	C₂×C₁₃	C₂²×C₃×C₄
Frattini	C₂	C₂²×C₃×#261
Fitting	C₃×Q₈×C₁₃	C₄
socle	C₂×C₃×C₁₃	C₂²×C₄
prime radical	C₃×#6131	C₂
cosocle	Dic₁₃	C₂³×C₃
hypercenter	C₃×Q₈	#261
hypocenter	C₁₃	C₃×#131
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₃ ◁ C₃×Q₈

Complements

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

N	H ≅ G/N	type
2. C₃×#6118	C₂	semidirect
3. C₃×D₁₃⋊C₈	C₂	semidirect
4. #88240	C₃	direct (N × H)
11. #6118	C₂×C₃	semidirect
12. D₁₃⋊C₈	C₂×C₃	semidirect
30. C₃×C₁₃	#131	semidirect
42. C₁₃	C₃×#131	semidirect
56. C₃	#88240	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×#6131	2
C₃×#6118	2
C₃×D₁₃⋊C₈	2
#88240	3
C₃×#131	13

Subgroups — C3×#88240 #11929175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#88240 #11929175