Subgroups — C₃×Q₈×#733 #14517852

Order 1944.

396 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×#733	C₂	1	3	yes	maximal
2	C₃×Q₈×3₋¹⁺²	C₃	1	3	yes	maximal
3	C₃²×Q₈×C₉	C₃	1	1	yes	maximal, characteristic
4	Q₈×#733	C₃	1	9	yes	maximal, direct product factor
5	C₂×C₃×#733	C₂²	1	1	yes	characteristic
6	C₃×C₄×3₋¹⁺²	C₂×C₃	1	9	yes	—
7	C₃²×C₄×C₉	C₂×C₃	1	3	yes	—
8	C₄×#733	C₂×C₃	1	27	yes	—
9	C₃×#733	Q₈	1	1	yes	characteristic, direct product factor, Sylow
10	C₃³×Q₈	C₃²	1	1	yes	characteristic
11	Q₈×3₋¹⁺²	—	3	6	no	—
12	Q₈×3₋¹⁺²	C₃²	1	9	yes	—
13	C₃×Q₈×C₉	—	3	2	no	—
14	C₃×Q₈×C₉	—	3	1	no	—
15	C₃×Q₈×C₉	—	3	3	no	—
16	C₃×Q₈×C₉	C₃²	1	3	yes	—
17	C₂×C₃×3₋¹⁺²	C₂²×C₃	1	3	yes	—
18	C₂×C₃²×C₉	C₂²×C₃	1	1	yes	characteristic
19	C₂×#733	C₂²×C₃	1	9	yes	—
20	C₃³×C₄	C₂×C₃²	1	3	yes	—
21	C₄×3₋¹⁺²	—	3	18	no	—
22	C₄×3₋¹⁺²	C₂×C₃²	1	27	yes	—
23	C₃×C₄×C₉	—	3	6	no	—
24	C₃×C₄×C₉	—	3	3	no	—
25	C₃×C₄×C₉	—	3	9	no	—
26	C₃×C₄×C₉	C₂×C₃²	1	9	yes	—
27	C₃×3₋¹⁺²	C₃×Q₈	1	3	yes	—
28	C₃²×C₉	C₃×Q₈	1	1	yes	characteristic
29	#733	C₃×Q₈	1	9	yes	direct product factor
30	C₃²×Q₈	—	3	3	no	—
31	C₃²×Q₈	H(3,𝔽₃)	1	2	yes	—
32	C₃²×Q₈	H(3,𝔽₃)	1	1	yes	characteristic
33	C₃²×Q₈	C₃³	1	1	yes	characteristic
34	Q₈×C₉	—	3	3	no	—
35	Q₈×C₉	—	3	9	no	—
36	C₂×C₃³	C₂²×C₃²	1	1	yes	characteristic
37	C₂×3₋¹⁺²	—	3	6	no	—
38	C₂×3₋¹⁺²	C₂²×C₃²	1	9	yes	—
39	C₂×C₃×C₉	—	3	2	no	—
40	C₂×C₃×C₉	—	3	1	no	—
41	C₂×C₃×C₉	—	3	3	no	—
42	C₂×C₃×C₉	C₂²×C₃²	1	3	yes	—
43	C₃²×C₄	—	3	9	no	—
44	C₃²×C₄	C₂×H(3,𝔽₃)	1	6	yes	—
45	C₃²×C₄	C₂×H(3,𝔽₃)	1	3	yes	—
46	C₃²×C₄	C₂×C₃³	1	3	yes	—
47	C₄×C₉	—	3	9	no	—
48	C₄×C₉	—	3	27	no	—
49	C₃³	C₃²×Q₈	1	1	yes	characteristic
50	3₋¹⁺²	—	3	6	no	—
51	3₋¹⁺²	C₃²×Q₈	1	9	yes	—
52	C₃×C₉	—	3	2	no	—
53	C₃×C₉	—	3	1	no	—
54	C₃×C₉	—	3	3	no	—
55	C₃×C₉	C₃²×Q₈	1	3	yes	—
56	C₃×Q₈	—	3	2	no	—
57	C₃×Q₈	—	3	1	no	—
58	C₃×Q₈	#733	1	3	yes	direct product factor
59	C₃×Q₈	C₃×H(3,𝔽₃)	1	1	yes	characteristic
60	C₂×C₃²	—	3	3	no	—
61	C₂×C₃²	C₂²×H(3,𝔽₃)	1	2	yes	—
62	C₂×C₃²	C₂²×H(3,𝔽₃)	1	1	yes	characteristic
63	C₂×C₃²	C₂²×C₃³	1	1	yes	characteristic
64	C₂×C₉	—	3	3	no	—
65	C₂×C₉	—	3	9	no	—
66	C₃×C₄	—	3	6	no	—
67	C₃×C₄	—	3	3	no	—
68	C₃×C₄	C₂×#733	1	9	yes	—
69	C₃×C₄	C₂×C₃×H(3,𝔽₃)	1	3	yes	—
70	C₃²	—	3	3	no	—
71	C₃²	Q₈×H(3,𝔽₃)	1	2	yes	—
72	C₃²	Q₈×H(3,𝔽₃)	1	1	yes	characteristic
73	C₃²	C₃³×Q₈	1	1	yes	characteristic
74	C₉	—	3	3	no	—
75	C₉	—	3	9	no	—
76	Q₈	C₃×#733	1	1	yes	characteristic, direct product factor, Sylow
77	C₂×C₃	—	3	2	no	—
78	C₂×C₃	—	3	1	no	—
79	C₂×C₃	C₂²×#733	1	3	yes	—
80	C₂×C₃	C₂²×C₃×H(3,𝔽₃)	1	1	yes	characteristic
81	C₄	C₂×C₃×#733	1	3	yes	—
82	C₃	—	3	2	no	—
83	C₃	—	3	1	no	—
84	C₃	Q₈×#733	1	3	yes	direct product factor
85	C₃	C₃×Q₈×H(3,𝔽₃)	1	1	yes	characteristic
86	C₂	C₂²×C₃×#733	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃²	C₂²×H(3,𝔽₃)
commutator, Frattini, cosocle	C₂×C₃²	C₂²×C₃³
prime radical	C₂×C₃³	C₂²×C₃²
LCS	G ▷ C₂×C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₂×C₃² ◁ C₃³×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
4. Q₈×#733	C₃	direct (N × H)
9. C₃×#733	Q₈	direct (N × H)
29. #733	C₃×Q₈	direct (N × H)
58. C₃×Q₈	#733	direct (N × H)
76. Q₈	C₃×#733	direct (N × H)
84. C₃	Q₈×#733	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄×#733	2
C₃×Q₈×3₋¹⁺²	3
C₃²×Q₈×C₉	3
Q₈×#733	3

Subgroups — C3×Q8×#733 #14517852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Q₈×#733 #14517852