Subgroups — C₂×C₃×#627 #89010

Order 432.

210 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×Dic₃	C₂	1	2	yes	maximal
3	C₃×#627	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃×Dic₆	—	3	2	no	maximal
5	C₂×#627	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂²×C₃³	C₂²	1	1	yes	characteristic
7	C₃×C₃⋊Dic₃	C₂²	1	2	yes	—
8	C₃²×Dic₃	C₂²	1	4	yes	—
9	C₂×C₃²×C₄	—	3	2	no	—
10	C₂×C₃⋊Dic₃	C₂×C₃	1	1	yes	characteristic
11	C₂×C₃×Dic₃	—	2	2	no	—
12	C₂×C₃×Dic₃	—	3	2	no	—
13	C₂×C₃×Dic₃	—	6	1	no	—
14	C₂×C₃×Dic₃	D₃	1	2	yes	—
15	C₂×C₃×Dic₃	C₂×C₃	1	2	yes	—
16	C₃×Dic₆	—	3	8	no	—
17	#627	C₂×C₃	1	4	yes	direct product factor
18	C₂×C₃³	Q₈	1	2	yes	complemented
19	C₂×C₃³	C₂³	1	1	yes	characteristic
20	C₂×C₃×Q₈	—	9	1	no	—
21	C₂×Dic₆	—	3	2	no	—
22	C₂²×C₃²	—	2	1	no	—
23	C₂²×C₃²	—	2	2	no	—
24	C₂²×C₃²	—	4	1	no	—
25	C₂²×C₃²	C₂×D₃	1	2	yes	—
26	C₂²×C₃²	C₂²×C₃	1	1	yes	characteristic
27	C₃²×C₄	—	3	4	no	—
28	C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
29	C₃×Dic₃	—	2	4	no	—
30	C₃×Dic₃	—	3	4	no	—
31	C₃×Dic₃	—	6	2	no	—
32	C₃×Dic₃	C₂×D₃	1	4	yes	—
33	C₃×Dic₃	C₂²×C₃	1	4	yes	—
34	C₃³	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
35	C₃×Q₈	—	9	4	no	—
36	C₂×C₃×C₄	—	3	2	no	—
37	C₂×C₃×C₄	—	3	2	no	—
38	C₂×C₃×C₄	—	6	2	no	—
39	C₂×C₃×C₄	—	9	1	no	—
40	C₂×Dic₃	—	3	2	no	—
41	C₂×Dic₃	—	6	1	no	—
42	C₂×Dic₃	C₃×D₃	1	2	yes	—
43	Dic₆	—	3	8	no	—
44	C₂×C₃²	—	2	2	no	—
45	C₂×C₃²	—	2	4	no	—
46	C₂×C₃²	—	2	1	no	—
47	C₂×C₃²	—	2	2	no	—
48	C₂×C₃²	—	4	2	no	—
49	C₂×C₃²	—	4	1	no	—
50	C₂×C₃²	Dic₆	1	4	yes	complemented
51	C₂×C₃²	C₃×Q₈	1	2	yes	complemented
52	C₂×C₃²	C₂²×D₃	1	2	yes	—
53	C₂×C₃²	C₂³×C₃	1	1	yes	characteristic
54	C₂×Q₈	—	9	1	no	Sylow
55	C₂²×C₃	—	2	1	no	—
56	C₂²×C₃	—	2	2	no	—
57	C₂²×C₃	—	4	1	no	—
58	C₂²×C₃	D₃²	1	1	yes	characteristic
59	C₂²×C₃	C₂×C₃×D₃	1	2	yes	—
60	C₃×C₄	—	3	4	no	—
61	C₃×C₄	—	3	4	no	—
62	C₃×C₄	—	6	4	no	—
63	C₃×C₄	—	9	2	no	—
64	Dic₃	—	3	4	no	—
65	Dic₃	—	6	2	no	—
66	Dic₃	C₂×C₃×D₃	1	4	yes	—
67	C₃²	—	2	1	no	—
68	C₃²	—	2	2	no	—
69	C₃²	—	4	1	no	—
70	C₃²	C₂×Dic₆	1	2	yes	complemented
71	C₃²	C₂×C₃×Q₈	1	1	yes	characteristic, complemented
72	Q₈	—	9	4	no	—
73	C₂×C₄	—	3	2	no	—
74	C₂×C₄	—	9	1	no	—
75	C₂×C₃	—	2	4	no	—
76	C₂×C₃	—	2	2	no	—
77	C₂×C₃	—	2	1	no	—
78	C₂×C₃	—	2	2	no	—
79	C₂×C₃	—	4	2	no	—
80	C₂×C₃	—	4	1	no	—
81	C₂×C₃	#627	1	2	yes	direct product factor
82	C₂×C₃	C₃×Dic₆	1	4	yes	complemented
83	C₂×C₃	C₂×D₃²	1	1	yes	characteristic
84	C₂×C₃	C₂²×C₃×D₃	1	2	yes	—
85	C₂²	C₃×D₃²	1	1	yes	characteristic
86	C₄	—	3	4	no	—
87	C₄	—	9	2	no	—
88	C₃	—	2	2	no	—
89	C₃	—	2	1	no	—
90	C₃	—	4	1	no	—
91	C₃	C₂×#627	1	1	yes	characteristic, direct product factor
92	C₃	C₂×C₃×Dic₆	1	2	yes	complemented
93	C₂	C₃×#627	1	2	yes	direct product factor
94	C₂	C₂×C₃×D₃²	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₃	D₃²
commutator, cosocle	C₂×C₃²	C₂³×C₃
Frattini	C₂	C₂×C₃×D₃²
Fitting, socle, prime radical	C₂²×C₃³	C₂²
hypocenter	C₃²	C₂×C₃×Q₈
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃

Complements

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

N	H ≅ G/N	type
3. C₃×#627	C₂	direct (N × H)
5. C₂×#627	C₃	direct (N × H)
17. #627	C₂×C₃	direct (N × H)
18. C₂×C₃³	Q₈	semidirect
34. C₃³	C₂×Q₈	semidirect
50. C₂×C₃²	Dic₆	semidirect
51. C₂×C₃²	C₃×Q₈	semidirect
70. C₃²	C₂×Dic₆	semidirect
71. C₃²	C₂×C₃×Q₈	semidirect
81. C₂×C₃	#627	direct (N × H)
82. C₂×C₃	C₃×Dic₆	semidirect
91. C₃	C₂×#627	direct (N × H)
92. C₃	C₂×C₃×Dic₆	semidirect
93. C₂	C₃×#627	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×C₃×C₃⋊Dic₃	2
C₂×C₃²×Dic₃	2
C₃×#627	2
C₂×C₃×Dic₆	3
C₂×#627	3

Subgroups — C2×C3×#627 #89010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#627 #89010