Subgroups — C₈×C₂²⋊(C₁₃⋊C₃) #11928756

Order 1248.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂²⋊(C₁₃⋊C₃)	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₂²⋊(C₁₃⋊C₃)	C₄	1	1	yes	characteristic
4	C₈×C₁₃⋊C₃	—	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	C₂²⋊(C₁₃⋊C₃)	C₈	1	1	yes	characteristic, direct product factor
9	C₄×C₁₃⋊C₃	—	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, complemented
15	C₈×A₄	—	13	1	no	maximal, Hall
16	C₂×C₁₃⋊C₃	—	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	—	13	1	no	—
23	C₁₃⋊C₃	—	4	1	no	Hall
24	C₂²×C₈	C₁₃⋊C₃	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	—	13	1	no	—
29	C₃×C₈	—	52	1	no	—
30	C₂²×C₄	C₂×C₁₃⋊C₃	1	1	yes	characteristic
31	C₂×C₈	—	3	1	no	—
32	C₂×C₈	—	3	1	no	—
33	C₁₃	C₈×A₄	1	1	yes	characteristic, complemented, Sylow
34	A₄	—	13	1	no	—
35	C₃×C₄	—	52	1	no	—
36	C₂³	C₄×C₁₃⋊C₃	1	1	yes	characteristic
37	C₂×C₄	—	3	1	no	—
38	C₂×C₄	—	3	1	no	—
39	C₈	—	3	1	no	—
40	C₈	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
41	C₂×C₃	—	52	1	no	—
42	C₂²	—	3	1	no	—
43	C₂²	—	3	1	no	—
44	C₂²	C₈×C₁₃⋊C₃	1	1	yes	characteristic, complemented
45	C₄	—	3	1	no	—
46	C₄	C₂×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic
47	C₃	—	52	1	no	Sylow
48	C₂	—	3	1	no	—
49	C₂	—	3	1	no	—
50	C₂	C₄×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic

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

Complements

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

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

Maximal subgroups

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

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

Subgroups — C8×C22⋊(C13⋊C3) #11928756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₂²⋊(C₁₃⋊C₃) #11928756