Subgroups — #14516732

Order 1944.

241 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11757605	C₂	1	1	yes	maximal, characteristic
2	#10620126	—	3	1	no	maximal
3	C₂×C₃²⋊H(3,𝔽₃)	C₄	1	1	yes	characteristic
4	C₃⋊(C₃⋊(C₃⋊Dic₃))	D₃	1	1	yes	characteristic
5	C₃⋊((C₃⋊Dic₃)⋊C₃)	—	6	2	no	—
6	C₃²⋊H(3,𝔽₃)	C₈	1	1	yes	characteristic, complemented, Sylow
7	C₃⋊#622	—	9	1	no	maximal
8	C₂×C₃⁴	Dic₃	1	1	yes	characteristic
9	C₂×C₃×H(3,𝔽₃)	—	2	2	no	—
10	C₂×C₃×H(3,𝔽₃)	—	4	2	no	—
11	C₃⋊(C₃⋊Dic₃)	—	6	2	no	—
12	C₃⋊(C₃⋊Dic₃)	—	18	6	no	—
13	C₃×C₃⋊Dic₃	—	9	1	no	—
14	(C₃⋊Dic₃)⋊C₃	—	18	6	no	—
15	C₃⁴	C₃⋊C₈	1	1	yes	characteristic, complemented
16	C₃×H(3,𝔽₃)	—	2	2	no	—
17	C₃×H(3,𝔽₃)	—	4	2	no	—
18	#622	—	27	1	no	—
19	#622	—	27	9	no	—
20	C₂×C₃³	—	2	2	no	—
21	C₂×C₃³	—	4	2	no	—
22	C₂×C₃³	—	6	6	no	—
23	C₂×C₃³	#157	1	1	yes	characteristic
24	C₂×H(3,𝔽₃)	—	6	6	no	—
25	C₂×H(3,𝔽₃)	—	12	6	no	—
26	C₃⋊Dic₃	—	9	1	no	—
27	C₃⋊Dic₃	—	18	6	no	—
28	C₃⋊Dic₃	—	27	9	no	—
29	C₃⋊Dic₃	—	54	6	no	—
30	C₃⋊Dic₃	—	54	9	no	—
31	C₃×Dic₃	—	54	2	no	—
32	C₃³	—	2	2	no	—
33	C₃³	—	4	2	no	—
34	C₃³	—	6	6	no	—
35	C₃³	#622	1	1	yes	characteristic, complemented
36	H(3,𝔽₃)	—	6	6	no	—
37	H(3,𝔽₃)	—	12	6	no	—
38	C₃⋊C₈	—	81	1	no	—
39	C₂×C₃²	—	2	6	no	—
40	C₂×C₃²	—	3	9	no	—
41	C₂×C₃²	—	6	6	no	—
42	C₂×C₃²	—	6	2	no	—
43	C₂×C₃²	—	6	9	no	—
44	C₂×C₃²	—	12	2	no	—
45	C₂×C₃²	—	12	6	no	—
46	C₂×C₃²	C₃⋊#157	1	1	yes	characteristic
47	C₃×C₄	—	81	1	no	—
48	Dic₃	—	54	2	no	—
49	Dic₃	—	162	6	no	—
50	C₃²	—	2	6	no	—
51	C₃²	—	3	9	no	—
52	C₃²	—	6	6	no	—
53	C₃²	—	6	2	no	—
54	C₃²	—	6	9	no	—
55	C₃²	—	12	2	no	—
56	C₃²	—	12	6	no	—
57	C₃²	C₃⋊#622	1	1	yes	characteristic
58	C₈	—	243	1	no	Sylow
59	C₂×C₃	—	2	2	no	—
60	C₂×C₃	—	6	6	no	—
61	C₂×C₃	—	9	1	no	—
62	C₂×C₃	—	36	2	no	—
63	C₄	—	81	1	no	—
64	C₃	—	2	2	no	—
65	C₃	—	6	6	no	—
66	C₃	—	9	1	no	—
67	C₃	—	36	2	no	—
68	C₂	#11757689	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	#11757689
commutator, hypocenter	C₃²⋊H(3,𝔽₃)	C₈
Frattini, socle	C₂×C₃²	C₃⋊#157
Fitting, prime radical	C₂×C₃²⋊H(3,𝔽₃)	C₄
cosocle	#11757605	C₂
LCS	G ▷ C₃²⋊H(3,𝔽₃)
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
6. C₃²⋊H(3,𝔽₃)	C₈	semidirect
15. C₃⁴	C₃⋊C₈	semidirect
35. C₃³	#622	semidirect

Maximal subgroups

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

subgroup	index
#11757605	2
#10620126	3
C₃⋊#622	9