Subgroups — C₃×#88038 #11928028

Order 1248.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#6090	C₂	1	1	yes	maximal, characteristic, complemented
4	#88038	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₄×D₁₃	C₄	1	1	yes	characteristic
6	C₃×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₃×#1055	C₄	1	1	yes	characteristic
8	C₈×D₁₃	C₂×C₃	1	1	yes	characteristic
9	C₁₃×C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
10	#6090	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₃×D₁₃	C₈	1	1	yes	characteristic
12	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₃×Dic₁₃	C₈	1	1	yes	characteristic
14	C₄×D₁₃	C₃×C₄	1	1	yes	characteristic
15	C₈×C₁₃	C₂²×C₃	1	1	yes	characteristic
16	#1055	C₃×C₄	1	1	yes	characteristic
17	C₃×M₃₂	—	13	1	no	maximal, Hall
18	C₂×C₃×C₁₃	C₂×C₈	1	1	yes	characteristic
19	C₃×D₁₃	—	2	1	no	—
20	C₂×D₁₃	C₃×C₈	1	1	yes	characteristic
21	C₄×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
22	Dic₁₃	C₃×C₈	1	1	yes	characteristic
23	C₂×C₃×C₈	—	13	1	no	—
24	C₃×C₁₆	—	13	1	no	—
25	C₃×C₁₆	D₁₃	1	1	yes	characteristic, complemented
26	C₃×C₁₃	M₃₂	1	1	yes	characteristic, complemented, Hall
27	M₃₂	—	13	1	no	Sylow
28	C₂×C₁₃	C₂×C₃×C₈	1	1	yes	characteristic
29	D₁₃	—	2	1	no	—
30	C₂×C₃×C₄	—	13	1	no	—
31	C₃×C₈	—	13	1	no	—
32	C₃×C₈	C₂×D₁₃	1	1	yes	characteristic
33	C₂×C₈	—	13	1	no	—
34	C₁₆	—	13	1	no	—
35	C₁₆	C₃×D₁₃	1	1	yes	characteristic, complemented
36	C₁₃	C₃×M₃₂	1	1	yes	characteristic, complemented, Sylow
37	C₂²×C₃	—	13	1	no	—
38	C₃×C₄	—	13	1	no	—
39	C₃×C₄	C₄×D₁₃	1	1	yes	characteristic
40	C₂×C₄	—	13	1	no	—
41	C₈	—	13	1	no	—
42	C₈	C₂×C₃×D₁₃	1	1	yes	characteristic
43	C₂×C₃	—	26	1	no	—
44	C₂×C₃	C₈×D₁₃	1	1	yes	characteristic
45	C₂²	—	13	1	no	—
46	C₄	—	13	1	no	—
47	C₄	C₃×C₄×D₁₃	1	1	yes	characteristic
48	C₃	#88038	1	1	yes	characteristic, direct product factor, Sylow
49	C₂	—	26	1	no	—
50	C₂	C₃×C₈×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₈	C₂×D₁₃
commutator	C₂×C₁₃	C₂×C₃×C₈
Frattini	C₈	C₂×C₃×D₁₃
Fitting	C₃×C₁₃×C₁₆	C₂
socle	C₂×C₃×C₁₃	C₂×C₈
prime radical	C₂×C₃×D₁₃	C₈
cosocle	C₈×C₁₃	C₂²×C₃
hypercenter	C₃×C₁₆	D₁₃
hypocenter	C₁₃	C₃×M₃₂
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₃×C₈ ◁ C₃×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₃×C₁₆	C₂	semidirect
3. C₃×#6090	C₂	semidirect
4. #88038	C₃	direct (N × H)
9. C₁₃×C₁₆	C₂×C₃	semidirect
10. #6090	C₂×C₃	semidirect
25. C₃×C₁₆	D₁₃	semidirect
26. C₃×C₁₃	M₃₂	semidirect
35. C₁₆	C₃×D₁₃	semidirect
36. C₁₃	C₃×M₃₂	semidirect
48. C₃	#88038	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×C₈×D₁₃	2
C₃×C₁₃×C₁₆	2
C₃×#6090	2
#88038	3
C₃×M₃₂	13

Subgroups — C3×#88038 #11928028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#88038 #11928028