Subgroups — C₂×C₃×C₄×Dic₃ #64045

Order 288.

243 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂²×C₃×C₄	D₃
commutator, hypocenter	C₃	C₂×C₃×C₄²
Frattini	C₂²	C₂²×C₃×D₃
Fitting	C₂²×C₃²×C₄	C₂
socle, prime radical	C₂³×C₃²	C₂²
cosocle	C₂²×C₃	C₂³×C₃
LCS	G ▷ C₃
UCS	C₁ ◁ C₂²×C₃×C₄

Complements

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

N	H ≅ G/N	type
3. C₃×C₄×Dic₃	C₂	direct (N × H)
5. C₂×C₄×Dic₃	C₃	direct (N × H)
7. C₂×C₃²×C₄	C₄	semidirect
9. C₂×C₃×Dic₃	C₄	direct (N × H)
17. C₄×Dic₃	C₂×C₃	direct (N × H)
21. C₃²×C₄	C₂×C₄	semidirect
22. C₃×Dic₃	C₂×C₄	direct (N × H)
31. C₂×C₃×C₄	Dic₃	direct (N × H)
32. C₂×C₃×C₄	C₃×C₄	semidirect
35. C₂×Dic₃	C₃×C₄	direct (N × H)
37. C₂×C₃²	C₄²	semidirect
54. C₃×C₄	C₂×Dic₃	direct (N × H)
55. C₃×C₄	C₂×C₃×C₄	semidirect
56. Dic₃	C₂×C₃×C₄	direct (N × H)
57. C₃²	C₂×C₄²	semidirect
61. C₂×C₄	C₃×Dic₃	direct (N × H)
66. C₂×C₃	C₄×Dic₃	direct (N × H)
67. C₂×C₃	C₃×C₄²	semidirect
76. C₄	C₂×C₃×Dic₃	direct (N × H)
78. C₃	C₂×C₄×Dic₃	direct (N × H)
79. C₃	C₂×C₃×C₄²	semidirect
80. C₂	C₃×C₄×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
C₂²×C₃²×C₄	2
C₂²×C₃×Dic₃	2
C₃×C₄×Dic₃	2
C₂×C₃×C₄²	3
C₂×C₄×Dic₃	3

Subgroups — C2×C3×C4×Dic3 #64045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄×Dic₃ #64045