Subgroups — C₂×C₃×C₄⋊Dic₃ #64048

Order 288.

211 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×C₄⋊C₄	—	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	—	2	4	no	—
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×C₄⋊C₄	—	3	4	no	—
17	C₄⋊Dic₃	C₂×C₃	1	4	yes	direct product factor
18	C₂²×C₃²	C₂×C₄	1	2	yes	—
19	C₂²×C₃²	D₄	1	2	yes	—
20	C₂²×C₃²	Q₈	1	2	yes	—
21	C₂²×C₃²	C₂³	1	1	yes	characteristic
22	C₃²×C₄	C₂×C₄	1	4	yes	complemented
23	C₃×Dic₃	—	2	4	no	—
24	C₂×C₄⋊C₄	—	3	1	no	Sylow
25	C₂³×C₃	—	2	1	no	—
26	C₂³×C₃	C₂×D₃	1	1	yes	characteristic
27	C₂³×C₃	C₂²×C₃	1	1	yes	characteristic
28	C₂×C₃×C₄	—	2	4	no	—
29	C₂×C₃×C₄	—	2	2	no	—
30	C₂×C₃×C₄	—	3	4	no	—
31	C₂×C₃×C₄	—	6	4	no	—
32	C₂×C₃×C₄	Dic₃	1	4	yes	complemented
33	C₂×C₃×C₄	C₃×C₄	1	4	yes	complemented
34	C₂×C₃×C₄	C₂×D₃	1	2	yes	—
35	C₂×C₃×C₄	C₂²×C₃	1	2	yes	—
36	C₂×Dic₃	—	2	4	no	—
37	C₂×Dic₃	C₂²×C₃	1	4	yes	—
38	C₂×C₃²	C₄⋊C₄	1	4	yes	complemented
39	C₂×C₃²	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₃²	C₂×D₄	1	1	yes	characteristic
41	C₂×C₃²	C₂×Q₈	1	1	yes	characteristic
42	C₂²×C₄	—	3	2	no	—
43	C₂²×C₄	C₃×D₃	1	1	yes	characteristic
44	C₄⋊C₄	—	3	4	no	—
45	C₂²×C₃	—	2	2	no	—
46	C₂²×C₃	—	2	2	no	—
47	C₂²×C₃	—	2	2	no	—
48	C₂²×C₃	—	2	1	no	—
49	C₂²×C₃	Dic₆	1	2	yes	—
50	C₂²×C₃	D₁₂	1	2	yes	—
51	C₂²×C₃	C₂×Dic₃	1	2	yes	—
52	C₂²×C₃	C₂×C₃×C₄	1	2	yes	—
53	C₂²×C₃	C₃×D₄	1	2	yes	—
54	C₂²×C₃	C₃×Q₈	1	2	yes	—
55	C₂²×C₃	C₂²×D₃	1	1	yes	characteristic
56	C₂²×C₃	C₂³×C₃	1	1	yes	characteristic
57	C₃×C₄	—	2	4	no	—
58	C₃×C₄	—	6	4	no	—
59	C₃×C₄	C₂×Dic₃	1	4	yes	complemented
60	C₃×C₄	C₂×C₃×C₄	1	4	yes	complemented
61	Dic₃	—	2	4	no	—
62	C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
63	C₂³	C₂×C₃×D₃	1	1	yes	characteristic
64	C₂×C₄	—	3	4	no	—
65	C₂×C₄	—	6	4	no	—
66	C₂×C₄	C₃×Dic₃	1	4	yes	complemented
67	C₂×C₄	C₂×C₃×D₃	1	2	yes	—
68	C₂×C₃	—	2	4	no	—
69	C₂×C₃	—	2	1	no	—
70	C₂×C₃	—	2	1	no	—
71	C₂×C₃	—	2	1	no	—
72	C₂×C₃	C₄⋊Dic₃	1	4	yes	direct product factor
73	C₂×C₃	C₃×C₄⋊C₄	1	4	yes	complemented
74	C₂×C₃	C₂×Dic₆	1	1	yes	characteristic
75	C₂×C₃	C₂×D₁₂	1	1	yes	characteristic
76	C₂×C₃	C₂²×Dic₃	1	1	yes	characteristic
77	C₂×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
78	C₂×C₃	C₂×C₃×D₄	1	1	yes	characteristic
79	C₂×C₃	C₂×C₃×Q₈	1	1	yes	characteristic
80	C₂²	C₃×Dic₆	1	2	yes	—
81	C₂²	C₃×D₁₂	1	2	yes	—
82	C₂²	C₂×C₃×Dic₃	1	2	yes	—
83	C₂²	C₂²×C₃×D₃	1	1	yes	characteristic
84	C₄	—	6	4	no	—
85	C₄	C₂×C₃×Dic₃	1	4	yes	complemented
86	C₃	—	2	1	no	—
87	C₃	C₂×C₄⋊Dic₃	1	1	yes	characteristic, direct product factor
88	C₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic, complemented
89	C₂	C₃×C₄⋊Dic₃	1	4	yes	direct product factor
90	C₂	C₂×C₃×Dic₆	1	1	yes	characteristic
91	C₂	C₂×C₃×D₁₂	1	1	yes	characteristic
92	C₂	C₂²×C₃×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×D₃
commutator	C₂×C₃	C₂²×C₃×C₄
Frattini	C₂²	C₂²×C₃×D₃
Fitting	C₂²×C₃²×C₄	C₂
socle, prime radical	C₂³×C₃²	C₂²
cosocle	C₂²×C₃	C₂³×C₃
hypercenter	C₂²×C₃×C₄	D₃
hypocenter	C₃	C₂×C₃×C₄⋊C₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ 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
17. C₄⋊Dic₃	C₂×C₃	direct (N × H)
22. C₃²×C₄	C₂×C₄	semidirect
32. C₂×C₃×C₄	Dic₃	semidirect
33. C₂×C₃×C₄	C₃×C₄	semidirect
38. C₂×C₃²	C₄⋊C₄	semidirect
59. C₃×C₄	C₂×Dic₃	semidirect
60. C₃×C₄	C₂×C₃×C₄	semidirect
62. C₃²	C₂×C₄⋊C₄	semidirect
66. C₂×C₄	C₃×Dic₃	semidirect
72. C₂×C₃	C₄⋊Dic₃	direct (N × H)
73. C₂×C₃	C₃×C₄⋊C₄	semidirect
85. C₄	C₂×C₃×Dic₃	semidirect
87. C₃	C₂×C₄⋊Dic₃	direct (N × H)
88. C₃	C₂×C₃×C₄⋊C₄	semidirect
89. 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×C₄⋊C₄	3
C₂×C₄⋊Dic₃	3

Subgroups — C2×C3×C4⋊Dic3 #64048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄⋊Dic₃ #64048