Subgroups — C₃×#10619576 #14517233

Order 1944.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×Q₈×C₉	C₃	1	1	yes	maximal, characteristic
2	C₃×#6204	C₃	1	3	yes	maximal
3	#10619576	C₃	1	9	yes	maximal, direct product factor
4	C₂×C₃×#733	—	4	1	no	maximal
5	C₃²×C₄×C₉	—	3	1	no	—
6	C₃×#733	—	4	1	no	Sylow
7	C₃³×Q₈	C₃²	1	1	yes	characteristic
8	C₃×Q₈×C₉	—	3	2	no	—
9	C₃×Q₈×C₉	—	3	1	no	—
10	C₃×Q₈×C₉	C₃²	1	3	yes	—
11	#6204	—	3	6	no	—
12	#6204	C₃²	1	9	yes	—
13	C₃×Q₈⋊C₉	—	3	3	no	—
14	C₂×C₃×3₋¹⁺²	—	4	3	no	—
15	C₂×C₃²×C₉	A₄	1	1	yes	characteristic
16	C₂×#733	—	4	9	no	—
17	C₃³×C₄	—	3	1	no	—
18	C₃×C₄×C₉	—	3	6	no	—
19	C₃×C₄×C₉	—	3	3	no	—
20	C₃×C₄×C₉	—	3	3	no	—
21	C₃×3₋¹⁺²	—	4	3	no	—
22	C₃²×C₉	SL(2,𝔽₃)	1	1	yes	characteristic
23	#733	—	4	9	no	—
24	C₃²×Q₈	—	3	3	no	—
25	C₃²×Q₈	H(3,𝔽₃)	1	2	yes	—
26	C₃²×Q₈	H(3,𝔽₃)	1	1	yes	characteristic
27	C₃²×Q₈	C₃³	1	1	yes	characteristic
28	Q₈×C₉	—	3	3	no	—
29	Q₈⋊C₉	—	3	9	no	—
30	C₂×C₃³	C₃×A₄	1	1	yes	characteristic
31	C₂×3₋¹⁺²	—	4	9	no	—
32	C₂×3₋¹⁺²	—	12	6	no	—
33	C₂×C₃×C₉	—	3	2	no	—
34	C₂×C₃×C₉	—	3	1	no	—
35	C₂×C₃×C₉	—	12	3	no	—
36	C₂×C₃×C₉	C₃×A₄	1	3	yes	—
37	C₃²×C₄	—	3	9	no	—
38	C₃²×C₄	—	3	2	no	—
39	C₃²×C₄	—	3	1	no	—
40	C₃²×C₄	—	3	1	no	—
41	C₄×C₉	—	3	9	no	—
42	C₃³	C₃×SL(2,𝔽₃)	1	1	yes	characteristic
43	3₋¹⁺²	—	4	9	no	—
44	3₋¹⁺²	—	12	6	no	—
45	C₃×C₉	—	3	2	no	—
46	C₃×C₉	—	3	1	no	—
47	C₃×C₉	—	12	3	no	—
48	C₃×C₉	C₃×SL(2,𝔽₃)	1	3	yes	—
49	C₃×Q₈	—	3	2	no	—
50	C₃×Q₈	—	3	1	no	—
51	C₃×Q₈	#733	1	3	yes	complemented
52	C₃×Q₈	C₃×H(3,𝔽₃)	1	1	yes	characteristic
53	C₂×C₃²	—	3	3	no	—
54	C₂×C₃²	C₂²⋊H(3,𝔽₃)	1	2	yes	—
55	C₂×C₃²	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
56	C₂×C₃²	C₃²×A₄	1	1	yes	characteristic
57	C₂×C₉	—	3	3	no	—
58	C₂×C₉	—	12	9	no	—
59	C₃×C₄	—	3	6	no	—
60	C₃×C₄	—	3	3	no	—
61	C₃×C₄	—	3	3	no	—
62	C₃×C₄	—	3	1	no	—
63	C₃²	—	3	3	no	—
64	C₃²	Q₈⋊H(3,𝔽₃)	1	2	yes	—
65	C₃²	Q₈⋊H(3,𝔽₃)	1	1	yes	characteristic
66	C₃²	C₃²×SL(2,𝔽₃)	1	1	yes	characteristic
67	C₉	—	3	3	no	—
68	C₉	—	12	9	no	—
69	Q₈	C₃×#733	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	3	2	no	—
71	C₂×C₃	—	3	1	no	—
72	C₂×C₃	#66359	1	3	yes	—
73	C₂×C₃	C₃×C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
74	C₄	—	3	1	no	—
75	C₃	—	3	2	no	—
76	C₃	—	3	1	no	—
77	C₃	#10619576	1	3	yes	direct product factor
78	C₃	C₃×Q₈⋊H(3,𝔽₃)	1	1	yes	characteristic
79	C₂	C₃×#66359	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃²	C₂²⋊H(3,𝔽₃)
commutator, cosocle	C₃²×Q₈	C₃³
Frattini	C₂×C₃²	C₃²×A₄
Fitting	C₃²×Q₈×C₉	C₃
prime radical	C₂×C₃³	C₃×A₄
hypercenter	C₂×C₃²×C₉	A₄
hypocenter	Q₈	C₃×#733
LCS	G ▷ C₃²×Q₈ ▷ C₃×Q₈ ▷ Q₈
UCS	C₁ ◁ C₂×C₃² ◁ C₂×C₃³ ◁ C₂×C₃²×C₉

Complements

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

N	H ≅ G/N	type
3. #10619576	C₃	direct (N × H)
51. C₃×Q₈	#733	semidirect
69. Q₈	C₃×#733	semidirect
77. C₃	#10619576	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×Q₈×C₉	3
C₃×#6204	3
#10619576	3
C₂×C₃×#733	4

Subgroups — C3×#10619576 #14517233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10619576 #14517233