Subgroups — C₃×#10619584 #14517270

Order 1944.

644 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴×Q₈	C₃	1	1	yes	maximal, characteristic
2	C₃²×Q₈⋊C₉	C₃	1	3	yes	maximal, complemented
3	#10619584	C₃	1	9	yes	maximal, direct product factor
4	C₂×C₃×C₃²⋊C₉	—	4	1	no	maximal
5	C₃⁴×C₄	—	3	1	no	—
6	C₃×C₃²⋊C₉	—	4	1	no	Sylow
7	C₃³×Q₈	—	3	3	no	—
8	C₃³×Q₈	—	3	6	no	—
9	C₃³×Q₈	C₉	1	9	yes	complemented
10	C₃³×Q₈	C₃²	1	3	yes	—
11	C₃³×Q₈	C₃²	1	1	yes	characteristic
12	C₃×Q₈⋊C₉	—	3	9	no	—
13	C₃×Q₈⋊C₉	C₃²	1	9	yes	complemented
14	C₂×C₃⁴	A₄	1	1	yes	characteristic
15	C₂×C₃²×C₉	—	4	3	no	—
16	C₂×C₃²⋊C₉	—	4	9	no	—
17	C₃³×C₄	—	3	18	no	—
18	C₃³×C₄	—	3	9	no	—
19	C₃³×C₄	—	3	9	no	—
20	C₃³×C₄	—	3	3	no	—
21	C₃³×C₄	—	3	1	no	—
22	C₃⁴	SL(2,𝔽₃)	1	1	yes	characteristic
23	C₃²×C₉	—	4	3	no	—
24	C₃²⋊C₉	—	4	9	no	—
25	C₃²×Q₈	—	3	27	no	—
26	C₃²×Q₈	—	3	3	no	—
27	C₃²×Q₈	—	3	6	no	—
28	C₃²×Q₈	C₃×C₉	1	3	yes	—
29	C₃²×Q₈	C₃×C₉	1	9	yes	complemented
30	C₃²×Q₈	H(3,𝔽₃)	1	3	yes	—
31	C₃²×Q₈	3₋¹⁺²	1	6	yes	—
32	C₃²×Q₈	C₃³	1	1	yes	characteristic
33	Q₈⋊C₉	—	3	9	no	—
34	C₂×C₃³	—	3	6	no	—
35	C₂×C₃³	—	3	3	no	—
36	C₂×C₃³	C₂²⋊C₉	1	9	yes	—
37	C₂×C₃³	C₃×A₄	1	3	yes	—
38	C₂×C₃³	C₃×A₄	1	1	yes	characteristic
39	C₂×C₃×C₉	—	4	9	no	—
40	C₂×C₃×C₉	—	12	9	no	—
41	C₃²×C₄	—	3	81	no	—
42	C₃²×C₄	—	3	18	no	—
43	C₃²×C₄	—	3	9	no	—
44	C₃²×C₄	—	3	3	no	—
45	C₃²×C₄	—	3	9	no	—
46	C₃²×C₄	—	3	6	no	—
47	C₃²×C₄	—	3	3	no	—
48	C₃²×C₄	—	3	1	no	—
49	C₃³	—	3	6	no	—
50	C₃³	—	3	3	no	—
51	C₃³	Q₈⋊C₉	1	9	yes	complemented
52	C₃³	C₃×SL(2,𝔽₃)	1	3	yes	—
53	C₃³	C₃×SL(2,𝔽₃)	1	1	yes	characteristic
54	C₃×C₉	—	4	9	no	—
55	C₃×C₉	—	12	9	no	—
56	C₃×Q₈	—	3	9	no	—
57	C₃×Q₈	C₃²⋊C₉	1	9	yes	complemented
58	C₃×Q₈	C₃²×C₉	1	1	yes	characteristic
59	C₃×Q₈	C₃×H(3,𝔽₃)	1	1	yes	characteristic
60	C₃×Q₈	C₃×3₋¹⁺²	1	2	yes	—
61	C₂×C₃²	—	3	27	no	—
62	C₂×C₃²	—	3	6	no	—
63	C₂×C₃²	—	3	3	no	—
64	C₂×C₃²	C₃×C₂²⋊C₉	1	9	yes	—
65	C₂×C₃²	C₃×C₂²⋊C₉	1	3	yes	—
66	C₂×C₃²	#1094	1	6	yes	—
67	C₂×C₃²	C₂²⋊H(3,𝔽₃)	1	3	yes	—
68	C₂×C₃²	C₃²×A₄	1	1	yes	characteristic
69	C₂×C₉	—	12	9	no	—
70	C₃×C₄	—	3	27	no	—
71	C₃×C₄	—	3	9	no	—
72	C₃×C₄	—	3	1	no	—
73	C₃×C₄	—	3	2	no	—
74	C₃×C₄	—	3	1	no	—
75	C₃²	—	3	6	no	—
76	C₃²	—	3	3	no	—
77	C₃²	—	3	27	no	—
78	C₃²	C₃×Q₈⋊C₉	1	3	yes	—
79	C₃²	C₃×Q₈⋊C₉	1	9	yes	complemented
80	C₃²	#6204	1	6	yes	—
81	C₃²	Q₈⋊H(3,𝔽₃)	1	3	yes	—
82	C₃²	C₃²×SL(2,𝔽₃)	1	1	yes	characteristic
83	C₉	—	12	9	no	—
84	Q₈	C₃×C₃²⋊C₉	1	1	yes	characteristic, complemented, Sylow
85	C₂×C₃	—	3	9	no	—
86	C₂×C₃	C₃²⋊(C₂²⋊C₉)	1	9	yes	—
87	C₂×C₃	C₃²×C₂²⋊C₉	1	1	yes	characteristic
88	C₂×C₃	C₃×#1094	1	2	yes	—
89	C₂×C₃	C₃×C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
90	C₄	—	3	1	no	—
91	C₃	—	3	9	no	—
92	C₃	#10619584	1	9	yes	direct product factor
93	C₃	C₃²×Q₈⋊C₉	1	1	yes	characteristic
94	C₃	C₃×#6204	1	2	yes	—
95	C₃	C₃×Q₈⋊H(3,𝔽₃)	1	1	yes	characteristic
96	C₂	C₃×C₃²⋊(C₂²⋊C₉)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃³	C₃×A₄
commutator	C₃×Q₈	C₃²×C₉
Frattini	C₂×C₃²	C₃²×A₄
Fitting	C₃⁴×Q₈	C₃
prime radical, hypercenter	C₂×C₃⁴	A₄
cosocle	C₃²×Q₈	C₃³
hypocenter	Q₈	C₃×C₃²⋊C₉
LCS	G ▷ C₃×Q₈ ▷ Q₈
UCS	C₁ ◁ C₂×C₃³ ◁ C₂×C₃⁴

Complements

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

N	H ≅ G/N	type
2. C₃²×Q₈⋊C₉	C₃	semidirect
3. #10619584	C₃	direct (N × H)
9. C₃³×Q₈	C₉	semidirect
13. C₃×Q₈⋊C₉	C₃²	semidirect
29. C₃²×Q₈	C₃×C₉	semidirect
51. C₃³	Q₈⋊C₉	semidirect
57. C₃×Q₈	C₃²⋊C₉	semidirect
79. C₃²	C₃×Q₈⋊C₉	semidirect
84. Q₈	C₃×C₃²⋊C₉	semidirect
92. C₃	#10619584	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃⁴×Q₈	3
C₃²×Q₈⋊C₉	3
#10619584	3
C₂×C₃×C₃²⋊C₉	4

Subgroups — C3×#10619584 #14517270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10619584 #14517270