Subgroups — C₂×A₄×C₃⋊D₃ #89117

Order 432.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	A₄×C₃⋊D₃	C₂	1	2	yes	maximal, direct product factor
3	C₂³×C₃⋊D₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃×A₄	—	3	4	no	maximal
5	C₂×C₃×C₃⋊D₃	—	4	1	no	maximal
6	C₃²×A₄	C₂²	1	1	yes	characteristic, complemented
7	C₂³×C₃²	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂²×C₃⋊D₃	—	3	1	no	—
9	C₂²×C₃⋊D₃	—	3	1	no	—
10	C₂²×C₃⋊D₃	—	3	2	no	—
11	C₂²×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
12	C₂×C₃×A₄	—	2	4	no	—
13	C₂×C₃×A₄	D₃	1	4	yes	complemented
14	D₃×A₄	—	3	8	no	—
15	C₂×C₃³	—	4	1	no	—
16	C₃×C₃⋊D₃	—	4	2	no	—
17	C₂³×D₃	—	3	4	no	—
18	C₂²×A₄	—	9	1	no	—
19	C₂²×C₃²	—	3	1	no	—
20	C₂²×C₃²	—	3	1	no	—
21	C₂²×C₃²	C₂²×C₃	1	1	yes	characteristic, complemented
22	C₂×C₃⋊D₃	—	3	2	no	—
23	C₂×C₃⋊D₃	—	3	1	no	—
24	C₂×C₃⋊D₃	—	3	2	no	—
25	C₂×C₃⋊D₃	—	3	2	no	—
26	C₂×C₃⋊D₃	—	3	2	no	—
27	C₂×C₃⋊D₃	A₄	1	1	yes	characteristic, direct product factor
28	C₂×C₃×D₃	—	12	4	no	—
29	C₃×A₄	—	2	4	no	—
30	C₃×A₄	C₂×D₃	1	4	yes	complemented
31	C₃³	—	4	1	no	Sylow
32	C₂³×C₃	C₃×D₃	1	4	yes	complemented
33	C₂²×D₃	—	3	8	no	—
34	C₂²×D₃	—	9	4	no	—
35	C₂²×D₃	—	9	8	no	—
36	C₂²×D₃	—	9	4	no	—
37	C₂×A₄	—	2	4	no	—
38	C₂×A₄	—	9	2	no	—
39	C₂×A₄	C₃⋊D₃	1	1	yes	characteristic, direct product factor
40	C₂×C₃²	—	3	1	no	—
41	C₂×C₃²	—	3	1	no	—
42	C₂×C₃²	—	4	4	no	—
43	C₂×C₃²	—	8	4	no	—
44	C₂×C₃²	C₂×A₄	1	1	yes	characteristic, complemented
45	C₃⋊D₃	—	3	2	no	—
46	C₃⋊D₃	C₂×A₄	1	2	yes	direct product factor
47	C₃×D₃	—	12	8	no	—
48	C₂⁴	—	9	1	no	Sylow
49	C₂²×C₃	—	3	4	no	—
50	C₂²×C₃	—	3	4	no	—
51	C₂²×C₃	—	36	1	no	—
52	C₂²×C₃	C₂×C₃×D₃	1	4	yes	complemented
53	C₂×D₃	—	3	4	no	—
54	C₂×D₃	—	9	8	no	—
55	C₂×D₃	—	9	8	no	—
56	C₂×D₃	—	9	8	no	—
57	C₂×D₃	—	9	4	no	—
58	C₂×D₃	—	9	8	no	—
59	A₄	—	2	4	no	—
60	A₄	C₂×C₃⋊D₃	1	1	yes	characteristic, direct product factor
61	C₃²	—	4	4	no	—
62	C₃²	—	8	4	no	—
63	C₃²	C₂²×A₄	1	1	yes	characteristic, complemented
64	C₂³	—	9	2	no	—
65	C₂³	—	27	1	no	—
66	C₂³	—	27	2	no	—
67	C₂³	—	27	1	no	—
68	C₂³	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
69	C₂×C₃	—	3	4	no	—
70	C₂×C₃	—	3	4	no	—
71	C₂×C₃	—	4	1	no	—
72	C₂×C₃	—	8	4	no	—
73	C₂×C₃	—	36	2	no	—
74	C₂×C₃	D₃×A₄	1	4	yes	complemented
75	D₃	—	3	8	no	—
76	D₃	—	9	8	no	—
77	C₂²	—	3	1	no	—
78	C₂²	—	3	1	no	—
79	C₂²	—	9	1	no	—
80	C₂²	—	27	2	no	—
81	C₂²	—	27	2	no	—
82	C₂²	—	27	2	no	—
83	C₂²	—	27	2	no	—
84	C₂²	—	27	1	no	—
85	C₂²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
86	C₃	—	4	1	no	—
87	C₃	—	8	4	no	—
88	C₃	C₂×D₃×A₄	1	4	yes	complemented
89	C₂	—	3	1	no	—
90	C₂	—	3	1	no	—
91	C₂	—	9	2	no	—
92	C₂	—	27	2	no	—
93	C₂	A₄×C₃⋊D₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	A₄×C₃⋊D₃
commutator, cosocle, hypocenter	C₂²×C₃²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂³×C₃²	C₂×C₃
LCS	G ▷ C₂²×C₃²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×A₄	C₂	semidirect
2. A₄×C₃⋊D₃	C₂	direct (N × H)
3. C₂³×C₃⋊D₃	C₃	semidirect
6. C₃²×A₄	C₂²	semidirect
7. C₂³×C₃²	C₂×C₃	semidirect
11. C₂²×C₃⋊D₃	C₂×C₃	semidirect
13. C₂×C₃×A₄	D₃	semidirect
21. C₂²×C₃²	C₂²×C₃	semidirect
27. C₂×C₃⋊D₃	A₄	direct (N × H)
30. C₃×A₄	C₂×D₃	semidirect
32. C₂³×C₃	C₃×D₃	semidirect
39. C₂×A₄	C₃⋊D₃	direct (N × H)
44. C₂×C₃²	C₂×A₄	semidirect
46. C₃⋊D₃	C₂×A₄	direct (N × H)
52. C₂²×C₃	C₂×C₃×D₃	semidirect
60. A₄	C₂×C₃⋊D₃	direct (N × H)
63. C₃²	C₂²×A₄	semidirect
68. C₂³	C₃×C₃⋊D₃	semidirect
74. C₂×C₃	D₃×A₄	semidirect
85. C₂²	C₂×C₃×C₃⋊D₃	semidirect
88. C₃	C₂×D₃×A₄	semidirect
93. C₂	A₄×C₃⋊D₃	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×C₃²×A₄	2
A₄×C₃⋊D₃	2
C₂³×C₃⋊D₃	3
C₂×D₃×A₄	3
C₂×C₃×C₃⋊D₃	4

Subgroups — C2×A4×C3⋊D3 #89117

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×A₄×C₃⋊D₃ #89117