Subgroups — C₃×Q₈×#732 #14517851

Order 1944.

504 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×#732	C₂	1	3	yes	maximal
2	C₃×Q₈×H(3,𝔽₃)	C₃	1	3	yes	maximal, complemented
3	C₃²×Q₈×C₉	C₃	1	1	yes	maximal, characteristic, complemented
4	Q₈×#732	C₃	1	9	yes	maximal, direct product factor
5	C₂×C₃×#732	C₂²	1	1	yes	characteristic
6	C₃×C₄×H(3,𝔽₃)	C₂×C₃	1	9	yes	—
7	C₃²×C₄×C₉	C₂×C₃	1	3	yes	—
8	C₄×#732	C₂×C₃	1	27	yes	—
9	C₃×#732	Q₈	1	1	yes	characteristic, direct product factor, Sylow
10	C₃³×Q₈	—	3	3	no	—
11	C₃³×Q₈	C₃²	1	1	yes	characteristic
12	Q₈×H(3,𝔽₃)	—	3	6	no	—
13	Q₈×H(3,𝔽₃)	C₃²	1	9	yes	complemented
14	C₃×Q₈×C₉	—	3	2	no	—
15	C₃×Q₈×C₉	—	3	1	no	—
16	C₃×Q₈×C₉	C₃²	1	3	yes	complemented
17	C₂×C₃×H(3,𝔽₃)	C₂²×C₃	1	3	yes	—
18	C₂×C₃²×C₉	C₂²×C₃	1	1	yes	characteristic
19	C₂×#732	C₂²×C₃	1	9	yes	—
20	C₃³×C₄	—	3	9	no	—
21	C₃³×C₄	C₂×C₃²	1	3	yes	—
22	C₄×H(3,𝔽₃)	—	3	18	no	—
23	C₄×H(3,𝔽₃)	C₂×C₃²	1	27	yes	—
24	C₃×C₄×C₉	—	3	6	no	—
25	C₃×C₄×C₉	—	3	3	no	—
26	C₃×C₄×C₉	C₂×C₃²	1	9	yes	—
27	C₃×H(3,𝔽₃)	C₃×Q₈	1	3	yes	complemented
28	C₃²×C₉	C₃×Q₈	1	1	yes	characteristic, complemented
29	#732	C₃×Q₈	1	9	yes	direct product factor
30	C₃²×Q₈	—	3	3	no	—
31	C₃²×Q₈	—	3	9	no	—
32	C₃²×Q₈	—	9	9	no	—
33	C₃²×Q₈	H(3,𝔽₃)	1	2	yes	—
34	C₃²×Q₈	H(3,𝔽₃)	1	1	yes	characteristic
35	C₃²×Q₈	C₃³	1	1	yes	characteristic
36	Q₈×C₉	—	3	3	no	—
37	C₂×C₃³	—	3	3	no	—
38	C₂×C₃³	C₂²×C₃²	1	1	yes	characteristic
39	C₂×H(3,𝔽₃)	—	3	6	no	—
40	C₂×H(3,𝔽₃)	C₂²×C₃²	1	9	yes	—
41	C₂×C₃×C₉	—	3	2	no	—
42	C₂×C₃×C₉	—	3	1	no	—
43	C₂×C₃×C₉	C₂²×C₃²	1	3	yes	—
44	C₃²×C₄	—	3	9	no	—
45	C₃²×C₄	—	3	27	no	—
46	C₃²×C₄	—	9	27	no	—
47	C₃²×C₄	C₂×H(3,𝔽₃)	1	6	yes	—
48	C₃²×C₄	C₂×H(3,𝔽₃)	1	3	yes	—
49	C₃²×C₄	C₂×C₃³	1	3	yes	—
50	C₄×C₉	—	3	9	no	—
51	C₃³	—	3	3	no	—
52	C₃³	C₃²×Q₈	1	1	yes	characteristic
53	H(3,𝔽₃)	—	3	6	no	—
54	H(3,𝔽₃)	C₃²×Q₈	1	9	yes	complemented
55	C₃×C₉	—	3	2	no	—
56	C₃×C₉	—	3	1	no	—
57	C₃×C₉	C₃²×Q₈	1	3	yes	complemented
58	C₃×Q₈	—	3	2	no	—
59	C₃×Q₈	—	3	1	no	—
60	C₃×Q₈	—	9	9	no	—
61	C₃×Q₈	#732	1	3	yes	direct product factor
62	C₃×Q₈	C₃×H(3,𝔽₃)	1	1	yes	characteristic
63	C₂×C₃²	—	3	3	no	—
64	C₂×C₃²	—	3	9	no	—
65	C₂×C₃²	—	9	9	no	—
66	C₂×C₃²	C₂²×H(3,𝔽₃)	1	2	yes	—
67	C₂×C₃²	C₂²×H(3,𝔽₃)	1	1	yes	characteristic
68	C₂×C₃²	C₂²×C₃³	1	1	yes	characteristic
69	C₂×C₉	—	3	3	no	—
70	C₃×C₄	—	3	6	no	—
71	C₃×C₄	—	3	3	no	—
72	C₃×C₄	—	9	27	no	—
73	C₃×C₄	C₂×#732	1	9	yes	—
74	C₃×C₄	C₂×C₃×H(3,𝔽₃)	1	3	yes	—
75	C₃²	—	3	3	no	—
76	C₃²	—	3	9	no	—
77	C₃²	—	9	9	no	—
78	C₃²	Q₈×H(3,𝔽₃)	1	2	yes	—
79	C₃²	Q₈×H(3,𝔽₃)	1	1	yes	characteristic
80	C₃²	C₃³×Q₈	1	1	yes	characteristic
81	C₉	—	3	3	no	—
82	Q₈	C₃×#732	1	1	yes	characteristic, direct product factor, Sylow
83	C₂×C₃	—	3	2	no	—
84	C₂×C₃	—	3	1	no	—
85	C₂×C₃	—	9	9	no	—
86	C₂×C₃	C₂²×#732	1	3	yes	—
87	C₂×C₃	C₂²×C₃×H(3,𝔽₃)	1	1	yes	characteristic
88	C₄	C₂×C₃×#732	1	3	yes	—
89	C₃	—	3	2	no	—
90	C₃	—	3	1	no	—
91	C₃	—	9	9	no	—
92	C₃	Q₈×#732	1	3	yes	direct product factor
93	C₃	C₃×Q₈×H(3,𝔽₃)	1	1	yes	characteristic
94	C₂	C₂²×C₃×#732	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×C₃×#732	C₂²
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
2. C₃×Q₈×H(3,𝔽₃)	C₃	semidirect
3. C₃²×Q₈×C₉	C₃	semidirect
4. Q₈×#732	C₃	direct (N × H)
9. C₃×#732	Q₈	direct (N × H)
13. Q₈×H(3,𝔽₃)	C₃²	semidirect
16. C₃×Q₈×C₉	C₃²	semidirect
27. C₃×H(3,𝔽₃)	C₃×Q₈	semidirect
28. C₃²×C₉	C₃×Q₈	semidirect
29. #732	C₃×Q₈	direct (N × H)
54. H(3,𝔽₃)	C₃²×Q₈	semidirect
57. C₃×C₉	C₃²×Q₈	semidirect
61. C₃×Q₈	#732	direct (N × H)
82. Q₈	C₃×#732	direct (N × H)
92. C₃	Q₈×#732	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×#732	2
C₃×Q₈×H(3,𝔽₃)	3
C₃²×Q₈×C₉	3
Q₈×#732	3

Subgroups — C3×Q8×#732 #14517851

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Q₈×#732 #14517851