Subgroups — #13091300

Order 1458.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624839	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊#4185	C₃	1	1	yes	maximal, characteristic, complemented
3	#92294	—	3	1	no	maximal
4	#92191	—	3	3	no	maximal
5	C₃×#732	—	2	1	no	—
6	C₃×#732	C₂×C₃	1	1	yes	characteristic
7	#6887	D₃	1	1	yes	characteristic, complemented
8	#6879	—	2	3	no	—
9	#6879	D₃	1	3	yes	complemented
10	C₃⋊((C₃⋊D₃)⋊C₃)	—	9	1	no	—
11	C₃×C₃⋊D₉	—	3	1	no	—
12	#4185	—	3	3	no	—
13	#4185	—	9	2	no	—
14	D₉⋊C₉	—	9	2	no	—
15	(C₃⋊D₃)⋊C₉	—	9	1	no	—
16	C₉×D₉	—	9	1	no	—
17	C₃×H(3,𝔽₃)	—	3	1	no	—
18	C₃×H(3,𝔽₃)	—	6	1	no	—
19	C₃²×C₉	C₃×D₃	1	1	yes	characteristic
20	#732	—	2	3	no	—
21	#732	—	3	2	no	—
22	#732	—	6	2	no	—
23	#732	C₃×D₃	1	3	yes	—
24	C₉⋊C₉	—	3	2	no	—
25	C₃²⋊C₉	—	3	1	no	—
26	C₉²	—	2	1	no	—
27	C₉²	C₃⋊D₃	1	1	yes	characteristic, complemented
28	C₃⋊(C₃⋊D₃)	—	9	1	no	—
29	C₃×C₃⋊D₃	—	9	1	no	—
30	C₃⋊D₉	—	3	1	no	—
31	(C₃⋊D₃)⋊C₃	—	27	3	no	—
32	D₃×C₉	—	27	1	no	—
33	C₃×D₉	—	9	2	no	—
34	C₃×D₉	—	9	1	no	—
35	C₃³	—	9	1	no	—
36	C₃³	—	18	1	no	—
37	C₃³	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
38	H(3,𝔽₃)	—	3	3	no	—
39	H(3,𝔽₃)	—	6	3	no	—
40	H(3,𝔽₃)	—	18	1	no	—
41	H(3,𝔽₃)	—	18	1	no	—
42	H(3,𝔽₃)	—	18	1	no	—
43	C₃×C₉	—	3	1	no	—
44	C₃×C₉	—	3	1	no	—
45	C₃×C₉	—	6	1	no	—
46	C₃×C₉	—	6	1	no	—
47	C₃×C₉	(C₃⋊D₃)⋊C₃	1	2	yes	—
48	C₃×C₉	C₃×C₃⋊D₃	1	1	yes	characteristic
49	C₃⋊D₃	—	9	1	no	—
50	C₃⋊D₃	—	27	3	no	—
51	C₃⋊D₃	—	81	3	no	—
52	C₃×D₃	—	27	1	no	—
53	C₃×D₃	—	81	1	no	—
54	C₂×C₉	—	81	1	no	—
55	D₉	—	9	2	no	—
56	D₉	—	9	1	no	—
57	C₃²	—	2	1	no	—
58	C₃²	—	9	1	no	—
59	C₃²	—	9	3	no	—
60	C₃²	—	18	3	no	—
61	C₃²	—	27	3	no	—
62	C₃²	—	54	3	no	—
63	C₃²	#4178	1	1	yes	characteristic
64	C₃²	C₃⋊((C₃⋊D₃)⋊C₃)	1	1	yes	characteristic
65	C₉	—	3	2	no	—
66	C₉	—	3	1	no	—
67	C₉	—	9	1	no	—
68	C₉	—	18	1	no	—
69	C₂×C₃	—	81	1	no	—
70	D₃	—	27	1	no	—
71	D₃	—	81	1	no	—
72	D₃	—	243	3	no	—
73	C₃	—	3	1	no	—
74	C₃	—	3	1	no	—
75	C₃	—	6	1	no	—
76	C₃	—	27	3	no	—
77	C₃	—	54	3	no	—
78	C₃	C₃⋊#4178	1	1	yes	characteristic
79	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃×#732	C₂×C₃
Frattini	C₃×C₉	C₃×C₃⋊D₃
Fitting	#10624839	C₂
socle	C₃	C₃⋊#4178
LCS	G ▷ C₃×#732
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #10624839	C₂	semidirect
2. C₃⋊#4185	C₃	semidirect
7. #6887	D₃	semidirect
9. #6879	D₃	semidirect
27. C₉²	C₃⋊D₃	semidirect

Maximal subgroups

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

subgroup	index
#10624839	2
C₃⋊#4185	3
#92294	3
#92191	3