Subgroups — D₃×#634 #89013

Order 432.

276 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6308	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#634	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₄×D₃	C₂	1	1	yes	maximal, characteristic
4	#6293	C₂	1	2	yes	maximal, complemented
5	D₃×C₃⋊Dic₃	C₂	1	2	yes	maximal
6	C₂×#634	—	3	1	no	maximal
7	D₃×Dic₆	—	3	4	no	maximal
8	C₂×C₃²×D₃	C₂²	1	1	yes	characteristic
9	C₃³×C₄	C₂²	1	1	yes	characteristic
10	C₃⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
11	C₃×C₃⋊Dic₃	C₂²	1	2	yes	—
12	C₃²×Dic₃	C₂²	1	1	yes	characteristic
13	C₂×C₃²×C₄	—	3	1	no	—
14	C₂×C₃⋊Dic₃	—	3	2	no	—
15	#634	—	3	1	no	—
16	#634	—	3	2	no	—
17	#634	—	3	4	no	—
18	#634	—	6	4	no	—
19	#634	D₃	1	1	yes	characteristic, direct product factor
20	C₃×C₄×D₃	D₃	1	4	yes	—
21	C₃×Dic₆	—	3	4	no	—
22	#627	—	3	8	no	—
23	D₃×Dic₃	—	3	8	no	—
24	C₂×C₃³	C₂³	1	1	yes	characteristic
25	C₃²×D₃	Q₈	1	2	yes	complemented
26	D₃×Q₈	—	9	1	no	—
27	C₂×Dic₆	—	9	4	no	—
28	C₂²×C₃²	—	3	1	no	—
29	C₂×C₃×D₃	C₂×D₃	1	4	yes	—
30	C₃²×C₄	—	2	4	no	—
31	C₃²×C₄	—	3	1	no	—
32	C₃²×C₄	C₂×D₃	1	4	yes	—
33	C₃²×C₄	C₂×D₃	1	1	yes	characteristic
34	C₃⋊Dic₃	—	3	2	no	—
35	C₃⋊Dic₃	—	3	8	no	—
36	C₃⋊Dic₃	—	6	8	no	—
37	C₃⋊Dic₃	C₂×D₃	1	2	yes	—
38	C₃×Dic₃	—	3	8	no	—
39	C₃×Dic₃	C₂×D₃	1	4	yes	—
40	C₃³	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
41	C₃×Q₈	—	9	1	no	—
42	C₂×C₃×C₄	—	3	4	no	—
43	C₂×Dic₃	—	9	8	no	—
44	C₄×D₃	—	9	2	no	—
45	C₄×D₃	C₃⋊D₃	1	1	yes	characteristic
46	Dic₆	—	3	4	no	—
47	Dic₆	—	9	8	no	—
48	Dic₆	—	9	4	no	—
49	Dic₆	—	9	1	no	—
50	Dic₆	—	9	2	no	—
51	Dic₆	—	18	4	no	—
52	C₂×C₃²	—	2	4	no	—
53	C₂×C₃²	—	3	2	no	—
54	C₂×C₃²	C₂²×D₃	1	4	yes	—
55	C₂×C₃²	C₂²×D₃	1	1	yes	characteristic
56	C₃×D₃	Dic₆	1	8	yes	complemented
57	C₂×Q₈	—	27	1	no	Sylow
58	C₂²×C₃	—	3	4	no	—
59	C₂×D₃	C₂×C₃⋊D₃	1	1	yes	characteristic
60	C₃×C₄	—	2	4	no	—
61	C₃×C₄	—	3	4	no	—
62	C₃×C₄	—	9	2	no	—
63	C₃×C₄	D₃²	1	4	yes	—
64	C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
65	Dic₃	—	3	8	no	—
66	Dic₃	—	9	8	no	—
67	Dic₃	—	9	2	no	—
68	Dic₃	—	18	8	no	—
69	Dic₃	C₂×C₃⋊D₃	1	1	yes	characteristic
70	C₃²	—	2	4	no	—
71	C₃²	C₂×Dic₆	1	4	yes	complemented
72	C₃²	D₃×Q₈	1	1	yes	characteristic, complemented
73	Q₈	—	9	1	no	—
74	Q₈	—	27	2	no	—
75	Q₈	—	27	1	no	—
76	C₂×C₄	—	3	1	no	—
77	C₂×C₄	—	27	2	no	—
78	C₂×C₃	—	2	4	no	—
79	C₂×C₃	—	3	8	no	—
80	C₂×C₃	C₂×D₃²	1	4	yes	—
81	C₂×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
82	D₃	#634	1	2	yes	direct product factor
83	C₂²	—	3	1	no	—
84	C₄	—	3	1	no	—
85	C₄	—	9	2	no	—
86	C₄	—	27	2	no	—
87	C₄	D₃×C₃⋊D₃	1	1	yes	characteristic
88	C₃	—	2	4	no	—
89	C₃	D₃×Dic₆	1	4	yes	complemented
90	C₃	C₂×#634	1	1	yes	characteristic, complemented
91	C₂	—	3	2	no	—
92	C₂	C₂×D₃×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×D₃×C₃⋊D₃
commutator, socle, cosocle	C₂×C₃³	C₂³
Fitting	C₃³×C₄	C₂²
prime radical	C₂×C₃²×D₃	C₂²
hypercenter	C₄	D₃×C₃⋊D₃
hypocenter	C₃³	C₂×Q₈
LCS	G ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
1. #6308	C₂	semidirect
2. C₃×#634	C₂	semidirect
4. #6293	C₂	semidirect
19. #634	D₃	direct (N × H)
25. C₃²×D₃	Q₈	semidirect
40. C₃³	C₂×Q₈	semidirect
56. C₃×D₃	Dic₆	semidirect
71. C₃²	C₂×Dic₆	semidirect
72. C₃²	D₃×Q₈	semidirect
82. D₃	#634	direct (N × H)
89. C₃	D₃×Dic₆	semidirect
90. C₃	C₂×#634	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#6308	2
C₃×#634	2
C₃²×C₄×D₃	2
#6293	2
D₃×C₃⋊Dic₃	2
C₂×#634	3
D₃×Dic₆	3

Subgroups — D3×#634 #89013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#634 #89013