Subgroups — C₈×A₄×C₁₃ #11928748

Order 1248.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×A₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×A₄×C₁₃	C₄	1	1	yes	characteristic
4	C₃×C₈×C₁₃	—	4	1	no	maximal
5	C₂²×C₄×C₁₃	C₂×C₃	1	1	yes	characteristic
6	C₂×C₈×C₁₃	—	3	1	no	—
7	C₂×C₈×C₁₃	—	3	1	no	—
8	A₄×C₁₃	C₈	1	1	yes	characteristic, direct product factor
9	C₃×C₄×C₁₃	—	4	1	no	—
10	C₂³×C₁₃	C₃×C₄	1	1	yes	characteristic
11	C₂×C₄×C₁₃	—	3	1	no	—
12	C₂×C₄×C₁₃	—	3	1	no	—
13	C₈×C₁₃	—	3	1	no	—
14	C₈×C₁₃	A₄	1	1	yes	characteristic, direct product factor
15	C₈×A₄	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₃×C₁₃	—	4	1	no	—
17	C₂²×C₁₃	—	3	1	no	—
18	C₂²×C₁₃	—	3	1	no	—
19	C₂²×C₁₃	C₃×C₈	1	1	yes	characteristic, complemented
20	C₄×C₁₃	—	3	1	no	—
21	C₄×C₁₃	C₂×A₄	1	1	yes	characteristic
22	C₄×A₄	C₂×C₁₃	1	1	yes	characteristic
23	C₃×C₁₃	—	4	1	no	Hall
24	C₂²×C₈	C₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₁₃	—	3	1	no	—
26	C₂×C₁₃	—	3	1	no	—
27	C₂×C₁₃	C₄×A₄	1	1	yes	characteristic
28	C₂×A₄	C₄×C₁₃	1	1	yes	characteristic
29	C₃×C₈	—	4	1	no	—
30	C₂²×C₄	C₂×C₃×C₁₃	1	1	yes	characteristic
31	C₂×C₈	—	3	1	no	—
32	C₂×C₈	—	3	1	no	—
33	C₁₃	C₈×A₄	1	1	yes	characteristic, direct product factor, Sylow
34	A₄	C₈×C₁₃	1	1	yes	characteristic, direct product factor
35	C₃×C₄	—	4	1	no	—
36	C₂³	C₃×C₄×C₁₃	1	1	yes	characteristic
37	C₂×C₄	—	3	1	no	—
38	C₂×C₄	—	3	1	no	—
39	C₈	—	3	1	no	—
40	C₈	A₄×C₁₃	1	1	yes	characteristic, direct product factor
41	C₂×C₃	—	4	1	no	—
42	C₂²	—	3	1	no	—
43	C₂²	—	3	1	no	—
44	C₂²	C₃×C₈×C₁₃	1	1	yes	characteristic, complemented
45	C₄	—	3	1	no	—
46	C₄	C₂×A₄×C₁₃	1	1	yes	characteristic
47	C₃	—	4	1	no	Sylow
48	C₂	—	3	1	no	—
49	C₂	—	3	1	no	—
50	C₂	C₄×A₄×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₈×C₁₃	A₄
commutator, hypocenter	C₂²	C₃×C₈×C₁₃
Frattini	C₄	C₂×A₄×C₁₃
Fitting	C₂²×C₈×C₁₃	C₃
socle	C₂³×C₁₃	C₃×C₄
prime radical	C₂×A₄×C₁₃	C₄
cosocle	C₂²×C₄	C₂×C₃×C₁₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₈×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₂²×C₈×C₁₃	C₃	semidirect
8. A₄×C₁₃	C₈	direct (N × H)
14. C₈×C₁₃	A₄	direct (N × H)
15. C₈×A₄	C₁₃	direct (N × H)
19. C₂²×C₁₃	C₃×C₈	semidirect
24. C₂²×C₈	C₃×C₁₃	semidirect
33. C₁₃	C₈×A₄	direct (N × H)
34. A₄	C₈×C₁₃	direct (N × H)
40. C₈	A₄×C₁₃	direct (N × H)
44. C₂²	C₃×C₈×C₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×A₄×C₁₃	2
C₂²×C₈×C₁₃	3
C₃×C₈×C₁₃	4
C₈×A₄	13

Subgroups — C8×A4×C13 #11928748

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×A₄×C₁₃ #11928748