Subgroups — C₈×C₃⋊Dic₃ #63640

Order 288.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₃	—	3	4	no	maximal
5	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
6	C₂×C₃⋊Dic₃	C₄	1	2	yes	—
7	C₃²×C₈	C₄	1	2	yes	complemented
8	C₃⋊(C₃⋊C₈)	C₄	1	2	yes	complemented
9	C₂×C₃×C₈	D₃	1	4	yes	—
10	C₄×Dic₃	—	3	4	no	—
11	C₂×C₃⋊C₈	—	3	4	no	—
12	C₂²×C₃²	C₂×C₄	1	1	yes	characteristic
13	C₃²×C₄	C₂×C₄	1	1	yes	characteristic
14	C₃²×C₄	C₂×C₄	1	1	yes	characteristic
15	C₃⋊Dic₃	C₈	1	4	yes	direct product factor
16	C₄×C₈	—	9	1	no	Sylow
17	C₂×C₃×C₄	C₂×D₃	1	4	yes	—
18	C₂×Dic₃	—	3	8	no	—
19	C₃×C₈	Dic₃	1	8	yes	complemented
20	C₃⋊C₈	—	3	8	no	—
21	C₂×C₃²	C₄²	1	1	yes	characteristic
22	C₂×C₃²	C₂×C₈	1	2	yes	—
23	C₂×C₈	—	9	1	no	—
24	C₂×C₈	C₃⋊D₃	1	1	yes	characteristic
25	C₄²	—	9	1	no	—
26	C₂²×C₃	C₄×D₃	1	4	yes	—
27	C₃×C₄	C₄×D₃	1	4	yes	—
28	C₃×C₄	C₂×Dic₃	1	4	yes	—
29	Dic₃	—	3	16	no	—
30	C₃²	C₄×C₈	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₄	—	9	2	no	—
32	C₂×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
33	C₈	—	9	2	no	—
34	C₈	C₃⋊Dic₃	1	2	yes	direct product factor
35	C₂×C₃	D₃×C₈	1	8	yes	—
36	C₂×C₃	C₄×Dic₃	1	4	yes	—
37	C₂²	C₄×C₃⋊D₃	1	1	yes	characteristic
38	C₄	—	9	4	no	—
39	C₄	C₄×C₃⋊D₃	1	1	yes	characteristic
40	C₄	C₂×C₃⋊Dic₃	1	1	yes	characteristic
41	C₃	C₈×Dic₃	1	4	yes	complemented
42	C₂	C₈×C₃⋊D₃	1	2	yes	—
43	C₂	C₄×C₃⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₈	C₃⋊D₃
commutator, hypocenter	C₃²	C₄×C₈
Frattini	C₂×C₄	C₂×C₃⋊D₃
Fitting	C₂×C₃²×C₈	C₂
socle, prime radical	C₂²×C₃²	C₂×C₄
cosocle	C₂×C₃²×C₄	C₂²
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
7. C₃²×C₈	C₄	semidirect
8. C₃⋊(C₃⋊C₈)	C₄	semidirect
15. C₃⋊Dic₃	C₈	direct (N × H)
19. C₃×C₈	Dic₃	semidirect
30. C₃²	C₄×C₈	semidirect
34. C₈	C₃⋊Dic₃	direct (N × H)
41. C₃	C₈×Dic₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₈	2
C₄×C₃⋊Dic₃	2
C₂×C₃⋊(C₃⋊C₈)	2
C₈×Dic₃	3

Subgroups — C8×C3⋊Dic3 #63640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₃⋊Dic₃ #63640