Subgroups — #14519084

Order 1944.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758052	C₂	1	1	yes	maximal, characteristic
2	#92404	C₄	1	1	yes	characteristic
3	H(5,𝔽₃)	C₈	1	1	yes	characteristic, complemented, Sylow
4	#6249	—	9	2	no	maximal
5	C₃⋊#272	—	12	2	no	—
6	C₃⋊#272	—	12	4	no	—
7	C₃⋊#272	—	12	4	no	—
8	C₃×#157	—	18	2	no	—
9	#1088	—	9	2	no	—
10	#1088	—	18	2	no	—
11	C₃×H(3,𝔽₃)	—	4	4	no	—
12	C₃×H(3,𝔽₃)	—	4	2	no	—
13	C₃×H(3,𝔽₃)	—	4	4	no	—
14	C₃×C₃⋊D₃	—	18	2	no	—
15	C₃×C₃⋊D₃	—	36	2	no	—
16	C₃×C₃⋊D₃	—	36	2	no	—
17	C₃×C₃⋊D₃	—	36	1	no	—
18	C₃×C₃⋊D₃	—	36	4	no	—
19	#272	—	9	2	no	—
20	#272	—	18	2	no	—
21	#272	—	36	8	no	—
22	#272	—	36	8	no	—
23	#272	—	36	1	no	—
24	#272	—	36	4	no	—
25	#157	—	18	2	no	—
26	C₃³	—	2	2	no	—
27	C₃³	—	4	1	no	—
28	C₃³	—	4	2	no	—
29	C₃³	—	4	2	no	—
30	C₃³	—	4	4	no	—
31	H(3,𝔽₃)	—	2	2	no	—
32	H(3,𝔽₃)	—	4	4	no	—
33	H(3,𝔽₃)	—	4	8	no	—
34	H(3,𝔽₃)	—	4	8	no	—
35	H(3,𝔽₃)	—	4	1	no	—
36	H(3,𝔽₃)	AGL(1,𝔽₉)	1	2	yes	—
37	C₃⋊C₈	—	81	1	no	—
38	C₃⋊D₃	—	18	2	no	—
39	C₃⋊D₃	—	36	2	no	—
40	C₃⋊D₃	—	36	1	no	—
41	C₃⋊D₃	—	36	2	no	—
42	C₃⋊D₃	—	36	4	no	—
43	C₃×D₃	—	108	2	no	—
44	C₃×D₃	—	108	4	no	—
45	C₃×D₃	—	108	4	no	—
46	C₃×C₄	—	81	1	no	—
47	C₃²	—	4	4	no	—
48	C₃²	—	4	2	no	—
49	C₃²	—	4	4	no	—
50	C₃²	—	18	2	no	—
51	C₃²	—	36	4	no	—
52	C₃²	—	36	2	no	—
53	C₃²	—	36	1	no	—
54	C₃²	—	36	2	no	—
55	C₈	—	243	1	no	Sylow
56	C₂×C₃	—	81	1	no	—
57	D₃	—	108	4	no	—
58	D₃	—	108	4	no	—
59	D₃	—	108	2	no	—
60	C₄	—	81	1	no	—
61	C₃	—	12	4	no	—
62	C₃	—	12	4	no	—
63	C₃	—	12	2	no	—
64	C₃	#10620193	1	1	yes	characteristic
65	C₂	—	81	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	H(5,𝔽₃)	C₈
Frattini, socle	C₃	#10620193
prime radical	#92404	C₄
cosocle	#11758052	C₂
LCS	G ▷ H(5,𝔽₃)
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. H(5,𝔽₃)	C₈	semidirect

Maximal subgroups

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

subgroup	index
#11758052	2
#6249	9