Subgroups — C₃×#10619575 #14517231

Order 1944.

302 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, complemented
2	C₃×Q₈⋊H(3,𝔽₃)	C₃	1	3	yes	maximal, complemented
3	#10619575	C₃	1	9	yes	maximal, direct product factor
4	C₂×C₃×#732	—	4	1	no	maximal
5	C₃²×C₄×C₉	—	3	1	no	—
6	C₃×#732	—	4	1	no	Sylow
7	C₃³×Q₈	C₃²	1	1	yes	characteristic
8	C₃²×SL(2,𝔽₃)	—	3	3	no	—
9	C₃×Q₈×C₉	—	3	2	no	—
10	C₃×Q₈×C₉	—	3	1	no	—
11	C₃×Q₈×C₉	C₃²	1	3	yes	complemented
12	Q₈⋊H(3,𝔽₃)	—	3	6	no	—
13	Q₈⋊H(3,𝔽₃)	C₃²	1	9	yes	complemented
14	C₂×C₃×H(3,𝔽₃)	—	4	3	no	—
15	C₂×C₃²×C₉	A₄	1	1	yes	characteristic
16	C₂×#732	—	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×H(3,𝔽₃)	—	4	3	no	—
22	C₃²×C₉	SL(2,𝔽₃)	1	1	yes	characteristic, complemented
23	#732	—	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	C₃×SL(2,𝔽₃)	—	3	9	no	—
29	C₃×SL(2,𝔽₃)	—	9	9	no	—
30	Q₈×C₉	—	3	3	no	—
31	C₂×C₃³	—	12	3	no	—
32	C₂×C₃³	C₃×A₄	1	1	yes	characteristic
33	C₂×H(3,𝔽₃)	—	4	9	no	—
34	C₂×H(3,𝔽₃)	—	12	6	no	—
35	C₂×C₃×C₉	—	3	2	no	—
36	C₂×C₃×C₉	—	3	1	no	—
37	C₂×C₃×C₉	C₃×A₄	1	3	yes	—
38	C₃²×C₄	—	3	9	no	—
39	C₃²×C₄	—	3	2	no	—
40	C₃²×C₄	—	3	1	no	—
41	C₃²×C₄	—	3	1	no	—
42	C₄×C₉	—	3	9	no	—
43	C₃³	—	12	3	no	—
44	C₃³	C₃×SL(2,𝔽₃)	1	1	yes	characteristic
45	H(3,𝔽₃)	—	4	9	no	—
46	H(3,𝔽₃)	—	12	6	no	—
47	C₃×C₉	—	3	2	no	—
48	C₃×C₉	—	3	1	no	—
49	C₃×C₉	C₃×SL(2,𝔽₃)	1	3	yes	complemented
50	C₃×Q₈	—	3	2	no	—
51	C₃×Q₈	—	3	1	no	—
52	C₃×Q₈	#732	1	3	yes	complemented
53	C₃×Q₈	C₃×H(3,𝔽₃)	1	1	yes	characteristic
54	SL(2,𝔽₃)	—	9	9	no	—
55	C₂×C₃²	—	3	3	no	—
56	C₂×C₃²	—	12	9	no	—
57	C₂×C₃²	—	36	9	no	—
58	C₂×C₃²	C₂²⋊H(3,𝔽₃)	1	2	yes	—
59	C₂×C₃²	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
60	C₂×C₃²	C₃²×A₄	1	1	yes	characteristic
61	C₂×C₉	—	3	3	no	—
62	C₃×C₄	—	3	6	no	—
63	C₃×C₄	—	3	3	no	—
64	C₃×C₄	—	3	3	no	—
65	C₃×C₄	—	3	1	no	—
66	C₃²	—	3	3	no	—
67	C₃²	—	12	9	no	—
68	C₃²	—	36	9	no	—
69	C₃²	Q₈⋊H(3,𝔽₃)	1	2	yes	—
70	C₃²	Q₈⋊H(3,𝔽₃)	1	1	yes	characteristic
71	C₃²	C₃²×SL(2,𝔽₃)	1	1	yes	characteristic
72	C₉	—	3	3	no	—
73	Q₈	C₃×#732	1	1	yes	characteristic, complemented, Sylow
74	C₂×C₃	—	3	2	no	—
75	C₂×C₃	—	3	1	no	—
76	C₂×C₃	—	36	9	no	—
77	C₂×C₃	#66358	1	3	yes	—
78	C₂×C₃	C₃×C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
79	C₄	—	3	1	no	—
80	C₃	—	3	2	no	—
81	C₃	—	3	1	no	—
82	C₃	—	36	9	no	—
83	C₃	#10619575	1	3	yes	direct product factor
84	C₃	C₃×Q₈⋊H(3,𝔽₃)	1	1	yes	characteristic
85	C₂	C₃×#66358	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
hypercenter	C₂×C₃²×C₉	A₄
hypocenter	Q₈	C₃×#732
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
1. C₃²×Q₈×C₉	C₃	semidirect
2. C₃×Q₈⋊H(3,𝔽₃)	C₃	semidirect
3. #10619575	C₃	direct (N × H)
11. C₃×Q₈×C₉	C₃²	semidirect
13. Q₈⋊H(3,𝔽₃)	C₃²	semidirect
22. C₃²×C₉	SL(2,𝔽₃)	semidirect
49. C₃×C₉	C₃×SL(2,𝔽₃)	semidirect
52. C₃×Q₈	#732	semidirect
73. Q₈	C₃×#732	semidirect
83. C₃	#10619575	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×Q₈⋊H(3,𝔽₃)	3
#10619575	3
C₂×C₃×#732	4

Subgroups — C3×#10619575 #14517231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10619575 #14517231