Subgroups — C₃×C₄⋊(C₃⋊Dic₃) #88842

Order 432.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₃⋊Dic₃	C₂	1	2	yes	maximal
3	C₄⋊(C₃⋊Dic₃)	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃×C₄⋊Dic₃	—	3	4	no	maximal
5	C₂²×C₃³	C₂²	1	1	yes	characteristic
6	C₃³×C₄	C₄	1	2	yes	complemented
7	C₃×C₃⋊Dic₃	—	2	2	no	—
8	C₂×C₃²×C₄	—	2	4	no	—
9	C₂×C₃²×C₄	D₃	1	4	yes	—
10	C₂×C₃²×C₄	C₂×C₃	1	1	yes	characteristic
11	C₂×C₃⋊Dic₃	C₂×C₃	1	2	yes	—
12	C₂×C₃×Dic₃	—	3	8	no	—
13	C₂×C₃³	C₂×C₄	1	1	yes	characteristic
14	C₂×C₃³	D₄	1	1	yes	characteristic
15	C₂×C₃³	Q₈	1	1	yes	characteristic
16	C₃×C₄⋊C₄	—	9	1	no	—
17	C₄⋊Dic₃	—	3	4	no	—
18	C₂²×C₃²	—	2	4	no	—
19	C₂²×C₃²	C₂×D₃	1	4	yes	—
20	C₂²×C₃²	C₂²×C₃	1	1	yes	characteristic
21	C₃²×C₄	—	2	8	no	—
22	C₃²×C₄	Dic₃	1	8	yes	complemented
23	C₃²×C₄	C₃×C₄	1	2	yes	complemented
24	C₃⋊Dic₃	—	2	2	no	—
25	C₃×Dic₃	—	6	8	no	—
26	C₃³	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃×C₄	—	2	4	no	—
28	C₂×C₃×C₄	—	9	2	no	—
29	C₂×C₃×C₄	C₃×D₃	1	4	yes	—
30	C₂×C₃×C₄	C₃⋊D₃	1	1	yes	characteristic
31	C₂×Dic₃	—	3	8	no	—
32	C₂×C₃²	—	2	4	no	—
33	C₂×C₃²	—	2	4	no	—
34	C₂×C₃²	—	2	4	no	—
35	C₂×C₃²	Dic₆	1	4	yes	—
36	C₂×C₃²	D₁₂	1	4	yes	—
37	C₂×C₃²	C₂×Dic₃	1	4	yes	—
38	C₂×C₃²	C₂×C₃×C₄	1	1	yes	characteristic
39	C₂×C₃²	C₃×D₄	1	1	yes	characteristic
40	C₂×C₃²	C₃×Q₈	1	1	yes	characteristic
41	C₄⋊C₄	—	9	1	no	Sylow
42	C₂²×C₃	—	2	4	no	—
43	C₂²×C₃	C₂×C₃×D₃	1	4	yes	—
44	C₂²×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
45	C₃×C₄	—	2	8	no	—
46	C₃×C₄	—	18	2	no	—
47	C₃×C₄	C₃×Dic₃	1	8	yes	complemented
48	C₃×C₄	C₃⋊Dic₃	1	2	yes	complemented
49	Dic₃	—	6	8	no	—
50	C₃²	—	2	4	no	—
51	C₃²	C₄⋊Dic₃	1	4	yes	complemented
52	C₃²	C₃×C₄⋊C₄	1	1	yes	characteristic, complemented
53	C₂×C₄	—	9	2	no	—
54	C₂×C₄	C₃×C₃⋊D₃	1	1	yes	characteristic
55	C₂×C₃	—	2	4	no	—
56	C₂×C₃	—	2	4	no	—
57	C₂×C₃	—	2	4	no	—
58	C₂×C₃	C₃×Dic₆	1	4	yes	—
59	C₂×C₃	C₃×D₁₂	1	4	yes	—
60	C₂×C₃	C₂×C₃×Dic₃	1	4	yes	—
61	C₂×C₃	#634	1	1	yes	characteristic
62	C₂×C₃	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
63	C₂×C₃	C₂×C₃⋊Dic₃	1	1	yes	characteristic
64	C₂²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
65	C₄	—	18	2	no	—
66	C₄	C₃×C₃⋊Dic₃	1	2	yes	complemented
67	C₃	—	2	4	no	—
68	C₃	C₃×C₄⋊Dic₃	1	4	yes	complemented
69	C₃	C₄⋊(C₃⋊Dic₃)	1	1	yes	characteristic, direct product factor
70	C₂	C₃×#634	1	1	yes	characteristic
71	C₂	C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
72	C₂	C₂×C₃×C₃⋊Dic₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₄⋊(C₃⋊Dic₃)	C₃	direct (N × H)
6. C₃³×C₄	C₄	semidirect
22. C₃²×C₄	Dic₃	semidirect
23. C₃²×C₄	C₃×C₄	semidirect
26. C₃³	C₄⋊C₄	semidirect
47. C₃×C₄	C₃×Dic₃	semidirect
48. C₃×C₄	C₃⋊Dic₃	semidirect
51. C₃²	C₄⋊Dic₃	semidirect
52. C₃²	C₃×C₄⋊C₄	semidirect
66. C₄	C₃×C₃⋊Dic₃	semidirect
68. C₃	C₃×C₄⋊Dic₃	semidirect
69. C₃	C₄⋊(C₃⋊Dic₃)	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×C₃³×C₄	2
C₂×C₃×C₃⋊Dic₃	2
C₄⋊(C₃⋊Dic₃)	3
C₃×C₄⋊Dic₃	3

Subgroups — C3×C4⋊(C3⋊Dic3) #88842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄⋊(C₃⋊Dic₃) #88842