Subgroups — C₂×D₃×C₈ #899

Order 96.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₈	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₈	—	3	1	no	maximal, Sylow
6	C₂²×D₃	C₄	1	1	yes	characteristic
7	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
8	C₂×Dic₃	C₄	1	1	yes	characteristic
9	C₄×D₃	C₄	1	2	yes	—
10	C₄×D₃	C₂²	1	2	yes	—
11	C₃×C₈	C₂²	1	2	yes	complemented
12	C₃⋊C₈	C₂²	1	2	yes	complemented
13	C₂²×C₄	—	3	1	no	—
14	C₂×C₈	—	3	1	no	—
15	C₂×C₈	—	3	4	no	—
16	C₂×C₈	D₃	1	1	yes	characteristic, direct product factor
17	C₂²×C₃	C₂×C₄	1	1	yes	characteristic
18	C₂×D₃	C₈	1	4	yes	direct product factor
19	C₂×D₃	C₂×C₄	1	2	yes	—
20	C₃×C₄	C₂×C₄	1	1	yes	characteristic
21	C₃×C₄	C₂³	1	1	yes	characteristic
22	Dic₃	C₂×C₄	1	2	yes	—
23	C₂³	—	3	1	no	—
24	C₂×C₄	—	3	1	no	—
25	C₂×C₄	—	3	2	no	—
26	C₂×C₄	—	3	2	no	—
27	C₂×C₄	C₂×D₃	1	1	yes	characteristic
28	C₈	—	3	2	no	—
29	C₈	C₂×D₃	1	2	yes	direct product factor
30	C₂×C₃	C₂×C₈	1	2	yes	complemented
31	C₂×C₃	C₂²×C₄	1	1	yes	characteristic
32	D₃	C₂×C₈	1	4	yes	direct product factor
33	C₂²	—	3	4	no	—
34	C₂²	—	3	2	no	—
35	C₂²	C₄×D₃	1	1	yes	characteristic
36	C₄	—	3	2	no	—
37	C₄	C₄×D₃	1	1	yes	characteristic
38	C₄	C₂²×D₃	1	1	yes	characteristic
39	C₃	C₂²×C₈	1	1	yes	characteristic, complemented, Sylow
40	C₂	—	3	4	no	—
41	C₂	D₃×C₈	1	2	yes	direct product factor
42	C₂	C₂×C₄×D₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₈	D₃
commutator, hypocenter	C₃	C₂²×C₈
Frattini	C₄	C₂²×D₃
Fitting	C₂×C₃×C₈	C₂
socle	C₂²×C₃	C₂×C₄
prime radical	C₂²×D₃	C₄
cosocle	C₃×C₄	C₂³
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₈	C₂	semidirect
3. C₂×C₃⋊C₈	C₂	semidirect
4. D₃×C₈	C₂	direct (N × H)
11. C₃×C₈	C₂²	semidirect
12. C₃⋊C₈	C₂²	semidirect
16. C₂×C₈	D₃	direct (N × H)
18. C₂×D₃	C₈	direct (N × H)
29. C₈	C₂×D₃	direct (N × H)
30. C₂×C₃	C₂×C₈	semidirect
32. D₃	C₂×C₈	direct (N × H)
39. C₃	C₂²×C₈	semidirect
41. C₂	D₃×C₈	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×C₄×D₃	2
C₂×C₃×C₈	2
C₂×C₃⋊C₈	2
D₃×C₈	2
C₂²×C₈	3

Subgroups — C2×D3×C8 #899

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×C₈ #899