Subgroups — C₃×AGL(1,ℤ/8) #976

Order 96.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×SD₁₆	C₂	1	2	yes	maximal, complemented
4	C₃×D₈	C₂	1	2	yes	maximal, complemented
5	C₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	AGL(1,ℤ/8)	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂³×C₃	—	2	1	no	—
8	C₃×Q₈	C₂²	1	1	yes	characteristic, complemented
9	C₃×D₄	—	2	1	no	—
10	C₃×D₄	—	2	1	no	—
11	C₃×D₄	C₂²	1	2	yes	—
12	C₃×D₄	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₃×C₄	—	2	1	no	—
14	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
15	C₃×C₈	C₂²	1	2	yes	complemented
16	#41	C₂×C₃	1	1	yes	characteristic, complemented
17	C₂×D₄	C₂×C₃	1	1	yes	characteristic, complemented
18	SD₁₆	C₂×C₃	1	2	yes	complemented
19	D₈	C₂×C₃	1	2	yes	complemented
20	M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
21	C₂²×C₃	—	2	1	no	—
22	C₂²×C₃	—	2	2	no	—
23	C₂²×C₃	—	4	2	no	—
24	C₂²×C₃	D₄	1	1	yes	characteristic
25	C₃×C₄	—	2	1	no	—
26	C₃×C₄	D₄	1	1	yes	characteristic
27	C₃×C₄	C₂³	1	1	yes	characteristic
28	C₂³	—	2	1	no	—
29	Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
30	D₄	—	2	1	no	—
31	D₄	—	2	1	no	—
32	D₄	C₂²×C₃	1	2	yes	—
33	D₄	C₂²×C₃	1	1	yes	characteristic, complemented
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	C₂²×C₃	1	1	yes	characteristic
36	C₈	C₂²×C₃	1	2	yes	complemented
37	C₂×C₃	—	2	1	no	—
38	C₂×C₃	—	4	1	no	—
39	C₂×C₃	—	4	2	no	—
40	C₂×C₃	C₂×D₄	1	1	yes	characteristic
41	C₂²	—	2	1	no	—
42	C₂²	—	2	2	no	—
43	C₂²	—	4	2	no	—
44	C₂²	C₃×D₄	1	1	yes	characteristic
45	C₄	—	2	1	no	—
46	C₄	C₃×D₄	1	1	yes	characteristic
47	C₄	C₂³×C₃	1	1	yes	characteristic
48	C₃	AGL(1,ℤ/8)	1	1	yes	characteristic, direct product factor, Sylow
49	C₂	—	2	1	no	—
50	C₂	—	4	2	no	—
51	C₂	—	4	1	no	—
52	C₂	C₂×C₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	C₂×D₄
commutator, Frattini, cosocle	C₄	C₂³×C₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#41	C₂	semidirect
2. C₂×C₃×D₄	C₂	semidirect
3. C₃×SD₁₆	C₂	semidirect
4. C₃×D₈	C₂	semidirect
5. C₃×M₁₆	C₂	semidirect
6. AGL(1,ℤ/8)	C₃	direct (N × H)
8. C₃×Q₈	C₂²	semidirect
12. C₃×D₄	C₂²	semidirect
15. C₃×C₈	C₂²	semidirect
16. #41	C₂×C₃	semidirect
17. C₂×D₄	C₂×C₃	semidirect
18. SD₁₆	C₂×C₃	semidirect
19. D₈	C₂×C₃	semidirect
20. M₁₆	C₂×C₃	semidirect
29. Q₈	C₂²×C₃	semidirect
33. D₄	C₂²×C₃	semidirect
36. C₈	C₂²×C₃	semidirect
48. C₃	AGL(1,ℤ/8)	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×#41	2
C₂×C₃×D₄	2
C₃×SD₁₆	2
C₃×D₈	2
C₃×M₁₆	2
AGL(1,ℤ/8)	3

Subgroups — C3×AGL(1,ℤ/8) #976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×AGL(1,ℤ/8) #976