Subgroups — C₃²×#6229 #14518914

Order 1944.

1332 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic
2	C₃²×#1084	C₂	1	2	yes	maximal
3	C₃³×Dic₆	—	3	4	no	maximal
4	C₃×#6229	C₃	1	4	yes	maximal, direct product factor
5	C₂×C₃²×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
6	C₃⁴×C₄	D₃	1	4	yes	—
7	C₃³×Dic₃	—	3	8	no	—
8	C₃×C₄×H(3,𝔽₃)	—	2	16	no	—
9	C₃×C₄×H(3,𝔽₃)	C₂×C₃	1	4	yes	—
10	C₃×#1084	C₂×C₃	1	8	yes	—
11	C₃²×H(3,𝔽₃)	Q₈	1	1	yes	characteristic, complemented, Sylow
12	C₃³×Q₈	—	9	1	no	—
13	C₃²×Dic₆	—	3	36	no	—
14	C₃²×Dic₆	—	3	16	no	—
15	#6229	C₃²	1	1	yes	characteristic, direct product factor
16	C₂×C₃⁴	C₂×D₃	1	4	yes	—
17	C₂×C₃×H(3,𝔽₃)	—	2	16	no	—
18	C₂×C₃×H(3,𝔽₃)	C₂²×C₃	1	4	yes	—
19	C₃³×C₄	—	2	16	no	—
20	C₃³×C₄	—	3	36	no	—
21	C₃³×C₄	—	9	2	no	—
22	C₃³×C₄	C₃×D₃	1	16	yes	—
23	C₃³×C₄	C₃⋊D₃	1	1	yes	characteristic
24	C₃²×Dic₃	—	3	72	no	—
25	C₃²×Dic₃	—	3	32	no	—
26	C₄×H(3,𝔽₃)	—	2	24	no	—
27	C₄×H(3,𝔽₃)	—	2	16	no	—
28	C₄×H(3,𝔽₃)	C₂×C₃²	1	1	yes	characteristic
29	#1084	C₂×C₃²	1	2	yes	—
30	C₃⁴	Dic₆	1	4	yes	complemented
31	C₃×H(3,𝔽₃)	—	2	16	no	—
32	C₃×H(3,𝔽₃)	C₃×Q₈	1	4	yes	complemented
33	C₃²×Q₈	—	9	9	no	—
34	C₃²×Q₈	—	9	4	no	—
35	C₃×Dic₆	—	3	48	no	—
36	C₃×Dic₆	—	3	4	no	—
37	C₂×C₃³	—	2	16	no	—
38	C₂×C₃³	—	3	36	no	—
39	C₂×C₃³	C₂×C₃×D₃	1	16	yes	—
40	C₂×C₃³	C₂×C₃⋊D₃	1	1	yes	characteristic
41	C₂×H(3,𝔽₃)	—	2	24	no	—
42	C₂×H(3,𝔽₃)	—	2	16	no	—
43	C₂×H(3,𝔽₃)	C₂²×C₃²	1	1	yes	characteristic
44	C₃²×C₄	—	2	16	no	—
45	C₃²×C₄	—	3	48	no	—
46	C₃²×C₄	—	6	48	no	—
47	C₃²×C₄	—	9	18	no	—
48	C₃²×C₄	—	9	8	no	—
49	C₃²×C₄	#272	1	9	yes	—
50	C₃²×C₄	C₃²×D₃	1	4	yes	—
51	C₃²×C₄	C₃×C₃⋊D₃	1	4	yes	—
52	C₃×Dic₃	—	3	96	no	—
53	C₃×Dic₃	—	3	8	no	—
54	C₃³	—	2	16	no	—
55	C₃³	—	3	36	no	—
56	C₃³	C₃×Dic₆	1	16	yes	complemented
57	C₃³	#634	1	1	yes	characteristic
58	H(3,𝔽₃)	—	2	24	no	—
59	H(3,𝔽₃)	—	2	16	no	—
60	H(3,𝔽₃)	C₃²×Q₈	1	1	yes	characteristic, complemented
61	C₃×Q₈	—	9	12	no	—
62	C₃×Q₈	—	9	1	no	—
63	Dic₆	—	3	4	no	—
64	C₂×C₃²	—	2	16	no	—
65	C₂×C₃²	—	3	48	no	—
66	C₂×C₃²	—	6	48	no	—
67	C₂×C₃²	C₂×#272	1	9	yes	—
68	C₂×C₃²	C₂×C₃²×D₃	1	4	yes	—
69	C₂×C₃²	C₂×C₃×C₃⋊D₃	1	4	yes	—
70	C₃×C₄	—	3	4	no	—
71	C₃×C₄	—	6	16	no	—
72	C₃×C₄	—	9	24	no	—
73	C₃×C₄	—	9	2	no	—
74	C₃×C₄	C₃×#272	1	12	yes	—
75	C₃×C₄	C₃²×C₃⋊D₃	1	1	yes	characteristic
76	Dic₃	—	3	8	no	—
77	C₃²	—	2	16	no	—
78	C₃²	—	3	48	no	—
79	C₃²	—	6	48	no	—
80	C₃²	#6229	1	9	yes	direct product factor
81	C₃²	C₃²×Dic₆	1	4	yes	complemented
82	C₃²	C₃×#634	1	4	yes	—
83	Q₈	—	9	1	no	Sylow
84	C₂×C₃	—	3	4	no	—
85	C₂×C₃	—	6	16	no	—
86	C₂×C₃	C₂×C₃×#272	1	12	yes	—
87	C₂×C₃	C₂×C₃²×C₃⋊D₃	1	1	yes	characteristic
88	C₄	—	9	2	no	—
89	C₄	C₃²×#272	1	1	yes	characteristic
90	C₃	—	3	4	no	—
91	C₃	—	6	16	no	—
92	C₃	C₃×#6229	1	12	yes	direct product factor
93	C₃	C₃²×#634	1	1	yes	characteristic
94	C₂	C₂×C₃²×#272	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃³	C₂×C₃⋊D₃
commutator, cosocle	C₂×H(3,𝔽₃)	C₂²×C₃²
Frattini	C₂×C₃	C₂×C₃²×C₃⋊D₃
Fitting	C₃²×C₄×H(3,𝔽₃)	C₂
prime radical	C₂×C₃²×H(3,𝔽₃)	C₂²
hypercenter	C₃³×C₄	C₃⋊D₃
hypocenter	H(3,𝔽₃)	C₃²×Q₈
LCS	G ▷ C₂×H(3,𝔽₃) ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₃³ ◁ C₃³×C₄

Complements

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

N	H ≅ G/N	type
4. C₃×#6229	C₃	direct (N × H)
11. C₃²×H(3,𝔽₃)	Q₈	semidirect
15. #6229	C₃²	direct (N × H)
30. C₃⁴	Dic₆	semidirect
32. C₃×H(3,𝔽₃)	C₃×Q₈	semidirect
56. C₃³	C₃×Dic₆	semidirect
60. H(3,𝔽₃)	C₃²×Q₈	semidirect
80. C₃²	#6229	direct (N × H)
81. C₃²	C₃²×Dic₆	semidirect
92. C₃	C₃×#6229	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×C₄×H(3,𝔽₃)	2
C₃²×#1084	2
C₃³×Dic₆	3
C₃×#6229	3

Subgroups — C32×#6229 #14518914

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#6229 #14518914