Subgroups — C₃×#88106 #11928343

Order 1248.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#1055	C₂	1	1	yes	maximal, characteristic
2	C₃×#6092	C₂	1	2	yes	maximal, complemented
3	#88106	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₄×C₁₃	C₄	1	1	yes	characteristic
5	C₃×#1055	C₄	1	1	yes	characteristic
6	C₃×#1055	C₂²	1	1	yes	characteristic
7	C₂×#1055	C₂×C₃	1	1	yes	characteristic
8	#6092	C₂×C₃	1	2	yes	complemented
9	C₂²×C₃×C₁₃	C₈	1	1	yes	characteristic
10	C₃×C₄×C₁₃	C₈	1	1	yes	characteristic
11	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₃	C₃×C₄	1	1	yes	characteristic
13	#1055	C₃×C₄	1	1	yes	characteristic
14	#1055	C₂²×C₃	1	1	yes	characteristic
15	C₃×M₃₂	—	13	1	no	maximal, Hall
16	C₂×C₃×C₁₃	—	2	1	no	—
17	C₂×C₃×C₁₃	C₂×C₈	1	1	yes	characteristic
18	C₂²×C₁₃	C₃×C₈	1	1	yes	characteristic
19	C₄×C₁₃	C₃×C₈	1	1	yes	characteristic
20	C₄×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
21	C₂×C₃×C₈	—	13	1	no	—
22	C₃×C₁₆	—	13	2	no	—
23	C₃×C₁₃	M₃₂	1	1	yes	characteristic, complemented, Hall
24	M₃₂	—	13	1	no	Sylow
25	C₂×C₁₃	—	2	1	no	—
26	C₂×C₁₃	C₂×C₃×C₈	1	1	yes	characteristic
27	C₂×C₃×C₄	#261	1	1	yes	characteristic
28	C₃×C₈	—	13	1	no	—
29	C₃×C₈	—	13	1	no	—
30	C₂×C₈	—	13	1	no	—
31	C₁₆	—	13	2	no	—
32	C₁₃	C₃×M₃₂	1	1	yes	characteristic, complemented, Sylow
33	C₂²×C₃	#1057	1	1	yes	characteristic
34	C₃×C₄	#1057	1	1	yes	characteristic
35	C₃×C₄	C₂×#261	1	1	yes	characteristic
36	C₂×C₄	C₃×#261	1	1	yes	characteristic
37	C₈	—	13	1	no	—
38	C₈	—	13	1	no	—
39	C₂×C₃	—	2	1	no	—
40	C₂×C₃	C₂×#1057	1	1	yes	characteristic
41	C₂²	C₃×#1057	1	1	yes	characteristic
42	C₄	C₃×#1057	1	1	yes	characteristic
43	C₄	C₂×C₃×#261	1	1	yes	characteristic
44	C₃	#88106	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	2	1	no	—
46	C₂	C₂×C₃×#1057	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂×#261
commutator	C₂×C₁₃	C₂×C₃×C₈
Frattini	C₄	C₂×C₃×#261
Fitting	C₂×C₃×C₄×C₁₃	C₄
socle	C₂×C₃×C₁₃	C₂×C₈
prime radical	C₂²×C₃×C₁₃	C₈
cosocle	#1055	C₂²×C₃
hypercenter	C₂×C₃×C₄	#261
hypocenter	C₁₃	C₃×M₃₂
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₄

Complements

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

N	H ≅ G/N	type
2. C₃×#6092	C₂	semidirect
3. #88106	C₃	direct (N × H)
8. #6092	C₂×C₃	semidirect
23. C₃×C₁₃	M₃₂	semidirect
32. C₁₃	C₃×M₃₂	semidirect
44. C₃	#88106	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×C₃×#1055	2
C₃×#6092	2
#88106	3
C₃×M₃₂	13

Subgroups — C3×#88106 #11928343

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#88106 #11928343