Subgroups — C₃×#3754 #88845

Order 432.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×D₄	C₂	1	1	yes	maximal, characteristic
2	C₃×#634	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	#3754	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃×#214	—	3	4	no	maximal
6	C₂²×C₃³	—	2	1	no	—
7	C₃³×C₄	C₂²	1	1	yes	characteristic
8	C₃×C₃⋊Dic₃	—	2	1	no	—
9	C₃²×D₄	—	2	4	no	—
10	C₃²×D₄	D₃	1	4	yes	—
11	C₃²×D₄	C₂×C₃	1	1	yes	characteristic
12	#634	C₂×C₃	1	1	yes	characteristic, complemented
13	C₃×Dic₆	—	3	4	no	—
14	C₃⋊(C₃⋊C₈)	C₂×C₃	1	1	yes	characteristic, complemented
15	C₃×C₃⋊C₈	—	3	4	no	—
16	C₂×C₃³	—	4	1	no	—
17	C₂×C₃³	D₄	1	1	yes	characteristic
18	C₃×SD₁₆	—	9	1	no	—
19	#214	—	3	4	no	—
20	C₂²×C₃²	—	2	8	no	—
21	C₂²×C₃²	—	2	4	no	—
22	C₂²×C₃²	—	2	1	no	—
23	C₃²×C₄	—	2	4	no	—
24	C₃²×C₄	C₂×D₃	1	4	yes	—
25	C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
26	C₃⋊Dic₃	—	2	1	no	—
27	C₃×Dic₃	—	6	4	no	—
28	C₃³	SD₁₆	1	1	yes	characteristic, complemented, Sylow
29	C₃×Q₈	—	9	1	no	—
30	C₃×D₄	—	2	4	no	—
31	C₃×D₄	C₃×D₃	1	4	yes	—
32	C₃×D₄	C₃⋊D₃	1	1	yes	characteristic
33	Dic₆	—	3	4	no	—
34	C₃×C₈	—	9	1	no	—
35	C₃⋊C₈	—	3	4	no	—
36	C₂×C₃²	—	2	4	no	—
37	C₂×C₃²	—	4	8	no	—
38	C₂×C₃²	—	4	4	no	—
39	C₂×C₃²	—	4	1	no	—
40	C₂×C₃²	#67	1	4	yes	—
41	C₂×C₃²	C₃×D₄	1	1	yes	characteristic
42	SD₁₆	—	9	1	no	Sylow
43	C₂²×C₃	—	2	8	no	—
44	C₂²×C₃	—	2	4	no	—
45	C₂²×C₃	—	2	1	no	—
46	C₃×C₄	—	2	4	no	—
47	C₃×C₄	—	18	1	no	—
48	C₃×C₄	C₂×C₃×D₃	1	4	yes	—
49	C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
50	Dic₃	—	6	4	no	—
51	C₃²	—	2	4	no	—
52	C₃²	#214	1	4	yes	complemented
53	C₃²	C₃×SD₁₆	1	1	yes	characteristic, complemented
54	Q₈	—	9	1	no	—
55	D₄	C₃×C₃⋊D₃	1	1	yes	characteristic
56	C₈	—	9	1	no	—
57	C₂×C₃	—	2	4	no	—
58	C₂×C₃	—	4	8	no	—
59	C₂×C₃	—	4	4	no	—
60	C₂×C₃	—	4	1	no	—
61	C₂×C₃	C₃×#67	1	4	yes	—
62	C₂×C₃	#638	1	1	yes	characteristic
63	C₂²	—	2	1	no	—
64	C₄	—	18	1	no	—
65	C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
66	C₃	—	2	4	no	—
67	C₃	C₃×#214	1	4	yes	complemented
68	C₃	#3754	1	1	yes	characteristic, direct product factor
69	C₂	—	4	1	no	—
70	C₂	C₃×#638	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	#638
commutator, cosocle	C₃²×C₄	C₂²×C₃
Frattini	C₄	C₂×C₃×C₃⋊D₃
Fitting, prime radical	C₃³×D₄	C₂
socle	C₂×C₃³	D₄
hypercenter	C₃×D₄	C₃⋊D₃
hypocenter	C₃²	C₃×SD₁₆
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×D₄

Complements

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

N	H ≅ G/N	type
2. C₃×#634	C₂	semidirect
3. C₃×C₃⋊(C₃⋊C₈)	C₂	semidirect
4. #3754	C₃	direct (N × H)
12. #634	C₂×C₃	semidirect
14. C₃⋊(C₃⋊C₈)	C₂×C₃	semidirect
28. C₃³	SD₁₆	semidirect
52. C₃²	#214	semidirect
53. C₃²	C₃×SD₁₆	semidirect
67. C₃	C₃×#214	semidirect
68. C₃	#3754	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×D₄	2
C₃×#634	2
C₃×C₃⋊(C₃⋊C₈)	2
#3754	3
C₃×#214	3

Subgroups — C3×#3754 #88845

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3754 #88845