Subgroups — C₂×C₃×C₃⋊C₈ #3731

Order 144.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
2. C₃×C₃⋊C₈	C₂	direct (N × H)
4. C₂×C₃⋊C₈	C₃	direct (N × H)
12. C₃⋊C₈	C₂×C₃	direct (N × H)
13. C₂×C₃²	C₈	semidirect
25. C₃²	C₂×C₈	semidirect
30. C₂×C₃	C₃⋊C₈	direct (N × H)
31. C₂×C₃	C₃×C₈	semidirect
38. C₃	C₂×C₃⋊C₈	direct (N × H)
39. C₃	C₂×C₃×C₈	semidirect
40. C₂	C₃×C₃⋊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×C₃²×C₄	2
C₃×C₃⋊C₈	2
C₂×C₃×C₈	3
C₂×C₃⋊C₈	3

Subgroups — C2×C3×C3⋊C8 #3731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₃⋊C₈ #3731