Subgroups — D₄×C₃⋊Dic₃ #64143

Order 288.

282 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃⋊Dic₃	C₂	1	2	yes	maximal, complemented
3	#3757	C₂	1	2	yes	maximal, complemented
4	C₄⋊(C₃⋊Dic₃)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×Dic₃	—	3	4	no	maximal
7	C₂³×C₃²	C₂²	1	2	yes	—
8	C₃²×D₄	C₄	1	4	yes	complemented
9	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
10	C₂×C₃⋊Dic₃	—	2	4	no	—
11	C₂×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
12	C₂×C₃⋊Dic₃	C₂²	1	2	yes	—
13	C₂×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
14	C₂×C₃×D₄	D₃	1	4	yes	—
15	C₂²×Dic₃	—	3	8	no	—
16	#217	—	3	8	no	—
17	C₄⋊Dic₃	—	3	4	no	—
18	C₄×Dic₃	—	3	4	no	—
19	C₂²×C₃²	—	2	2	no	—
20	C₂²×C₃²	—	2	2	no	—
21	C₂²×C₃²	C₂×C₄	1	4	yes	complemented
22	C₂²×C₃²	C₂³	1	1	yes	characteristic
23	C₃²×C₄	C₂×C₄	1	2	yes	complemented
24	C₃⋊Dic₃	—	2	2	no	—
25	C₃⋊Dic₃	—	2	1	no	—
26	C₃⋊Dic₃	D₄	1	2	yes	direct product factor
27	C₄×D₄	—	9	1	no	Sylow
28	C₂³×C₃	C₂×D₃	1	8	yes	—
29	C₃×D₄	Dic₃	1	16	yes	complemented
30	C₂×C₃×C₄	C₂×D₃	1	4	yes	—
31	C₂×Dic₃	—	3	4	no	—
32	C₂×Dic₃	—	3	4	no	—
33	C₂×Dic₃	—	3	8	no	—
34	C₂×Dic₃	—	6	16	no	—
35	C₂×C₃²	—	2	4	no	—
36	C₂×C₃²	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₃²	C₂×D₄	1	1	yes	characteristic
38	C₂×C₃²	#41	1	1	yes	characteristic
39	C₂×D₄	C₃⋊D₃	1	1	yes	characteristic
40	C₂²×C₄	—	9	2	no	—
41	C₄⋊C₄	—	9	1	no	—
42	C₂²⋊C₄	—	9	2	no	—
43	C₄²	—	9	1	no	—
44	C₂²×C₃	—	2	8	no	—
45	C₂²×C₃	—	2	8	no	—
46	C₂²×C₃	C₂×Dic₃	1	16	yes	complemented
47	C₂²×C₃	C₂²×D₃	1	4	yes	—
48	C₃×C₄	C₂×Dic₃	1	8	yes	complemented
49	Dic₃	—	3	8	no	—
50	Dic₃	—	6	8	no	—
51	Dic₃	—	6	4	no	—
52	C₃²	C₄×D₄	1	1	yes	characteristic, complemented, Sylow
53	C₂³	C₂×C₃⋊D₃	1	2	yes	—
54	D₄	C₃⋊Dic₃	1	4	yes	direct product factor
55	C₂×C₄	—	9	1	no	—
56	C₂×C₄	—	9	1	no	—
57	C₂×C₄	—	9	2	no	—
58	C₂×C₄	—	18	4	no	—
59	C₂×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
60	C₂×C₃	—	2	16	no	—
61	C₂×C₃	D₃×D₄	1	4	yes	—
62	C₂×C₃	#237	1	4	yes	—
63	C₂×C₃	C₂²×Dic₃	1	4	yes	—
64	C₂²	—	2	2	no	—
65	C₂²	—	2	2	no	—
66	C₂²	C₂×C₃⋊Dic₃	1	4	yes	complemented
67	C₂²	C₂²×C₃⋊D₃	1	1	yes	characteristic
68	C₄	—	9	2	no	—
69	C₄	—	18	2	no	—
70	C₄	—	18	1	no	—
71	C₄	C₂×C₃⋊Dic₃	1	2	yes	complemented
72	C₃	D₄×Dic₃	1	4	yes	complemented
73	C₂	—	2	4	no	—
74	C₂	D₄×C₃⋊D₃	1	1	yes	characteristic
75	C₂	#3830	1	1	yes	characteristic
76	C₂	C₂²×C₃⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×C₃⋊D₃
commutator	C₂×C₃²	C₂²×C₄
Fitting, prime radical	C₂×C₃²×D₄	C₂
socle, cosocle	C₂²×C₃²	C₂³
hypercenter	C₂×D₄	C₃⋊D₃
hypocenter	C₃²	C₄×D₄
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃⋊Dic₃	C₂	semidirect
3. #3757	C₂	semidirect
4. C₄⋊(C₃⋊Dic₃)	C₂	semidirect
5. C₄×C₃⋊Dic₃	C₂	semidirect
8. C₃²×D₄	C₄	semidirect
21. C₂²×C₃²	C₂×C₄	semidirect
23. C₃²×C₄	C₂×C₄	semidirect
26. C₃⋊Dic₃	D₄	direct (N × H)
29. C₃×D₄	Dic₃	semidirect
46. C₂²×C₃	C₂×Dic₃	semidirect
48. C₃×C₄	C₂×Dic₃	semidirect
52. C₃²	C₄×D₄	semidirect
54. D₄	C₃⋊Dic₃	direct (N × H)
66. C₂²	C₂×C₃⋊Dic₃	semidirect
71. C₄	C₂×C₃⋊Dic₃	semidirect
72. C₃	D₄×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×D₄	2
C₂²×C₃⋊Dic₃	2
#3757	2
C₄⋊(C₃⋊Dic₃)	2
C₄×C₃⋊Dic₃	2
D₄×Dic₃	3

Subgroups — D4×C3⋊Dic3 #64143

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₃⋊Dic₃ #64143