Subgroups — C₃×#157⋊D₃ #10620201

Order 648.

166 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#1113	C₂	1	2	yes	maximal, complemented
2	C₃²×#157	C₂	1	1	yes	maximal, characteristic, complemented
3	#157⋊D₃	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃×GO⁺(4,𝔽₂)	—	3	1	no	maximal
5	C₃²×C₃⋊D₃	—	2	2	no	—
6	C₃²×C₃⋊D₃	C₂²	1	1	yes	characteristic
7	#1113	C₂×C₃	1	2	yes	complemented
8	C₃×D₃²	—	3	2	no	—
9	C₃×D₃²	—	6	2	no	—
10	C₃×#157	—	2	1	no	—
11	C₃×#157	D₃	1	1	yes	characteristic, complemented
12	C₃×#157	C₂×C₃	1	1	yes	characteristic, complemented
13	C₃⁴	D₄	1	1	yes	characteristic, complemented, Sylow
14	GO⁺(4,𝔽₂)	—	3	1	no	—
15	C₃×D₁₂	—	9	1	no	maximal
16	C₃×C₃⋊D₃	—	2	2	no	—
17	C₃×C₃⋊D₃	—	2	2	no	—
18	C₃×C₃⋊D₃	—	2	1	no	—
19	C₃×C₃⋊D₃	—	4	2	no	—
20	C₃×C₃⋊D₃	C₂×D₃	1	1	yes	characteristic
21	C₃×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
22	C₃²×D₃	—	6	2	no	—
23	C₃²×D₃	—	6	2	no	—
24	C₃²×D₃	—	6	2	no	—
25	C₃²×D₃	—	12	2	no	—
26	C₂×C₃×D₃	—	9	2	no	—
27	C₂×C₃×D₃	—	18	2	no	—
28	D₃²	—	3	2	no	—
29	D₃²	—	6	2	no	—
30	#157	C₃×D₃	1	1	yes	characteristic, complemented
31	C₃²×C₄	—	9	1	no	—
32	C₃³	—	2	2	no	—
33	C₃³	—	2	1	no	—
34	C₃³	—	4	2	no	—
35	C₃³	—	4	2	no	—
36	C₃³	—	8	2	no	—
37	C₃³	D₁₂	1	1	yes	characteristic, complemented
38	C₃³	C₃×D₄	1	1	yes	characteristic, complemented
39	C₃×D₄	—	27	1	no	—
40	D₁₂	—	9	1	no	—
41	C₂×C₃²	—	9	1	no	—
42	C₂×C₃²	—	18	2	no	—
43	C₃⋊D₃	—	2	2	no	—
44	C₃⋊D₃	C₂×C₃×D₃	1	1	yes	characteristic
45	C₃×D₃	—	6	2	no	—
46	C₃×D₃	—	6	2	no	—
47	C₃×D₃	—	6	2	no	—
48	C₃×D₃	—	6	2	no	—
49	C₃×D₃	—	6	2	no	—
50	C₃×D₃	—	6	2	no	—
51	C₃×D₃	—	12	2	no	—
52	C₃×D₃	—	12	2	no	—
53	C₃×D₃	—	12	2	no	—
54	C₃×D₃	—	12	2	no	—
55	C₃×D₃	—	12	2	no	—
56	C₃×D₃	—	12	4	no	—
57	C₂²×C₃	—	27	2	no	—
58	C₂×D₃	—	9	2	no	—
59	C₂×D₃	—	18	2	no	—
60	C₃×C₄	—	9	1	no	—
61	C₃×C₄	—	9	1	no	—
62	C₃×C₄	—	18	1	no	—
63	C₃²	—	2	2	no	—
64	C₃²	—	2	2	no	—
65	C₃²	—	4	2	no	—
66	C₃²	—	4	2	no	—
67	C₃²	—	4	2	no	—
68	C₃²	—	4	4	no	—
69	C₃²	—	4	2	no	—
70	C₃²	—	4	2	no	—
71	C₃²	—	8	2	no	—
72	C₃²	—	8	2	no	—
73	C₃²	—	8	4	no	—
74	C₃²	C₃×D₁₂	1	1	yes	characteristic, complemented
75	C₃²	GO⁺(4,𝔽₂)	1	1	yes	characteristic, complemented
76	D₄	—	27	1	no	Sylow
77	C₂×C₃	—	9	1	no	—
78	C₂×C₃	—	9	1	no	—
79	C₂×C₃	—	18	1	no	—
80	C₂×C₃	—	18	2	no	—
81	C₂×C₃	—	18	2	no	—
82	C₂×C₃	—	36	2	no	—
83	D₃	—	6	2	no	—
84	D₃	—	6	2	no	—
85	D₃	—	6	2	no	—
86	D₃	—	12	2	no	—
87	C₂²	—	27	2	no	—
88	C₄	—	9	1	no	—
89	C₃	—	2	2	no	—
90	C₃	—	2	1	no	—
91	C₃	—	4	2	no	—
92	C₃	—	4	2	no	—
93	C₃	—	8	2	no	—
94	C₃	C₃×GO⁺(4,𝔽₂)	1	1	yes	characteristic, complemented
95	C₃	#157⋊D₃	1	1	yes	characteristic, direct product factor
96	C₂	—	9	1	no	—
97	C₂	—	18	2	no	—

	subgroup	G/H
center, hypercenter	C₃	#157⋊D₃
commutator, cosocle	C₃×C₃⋊D₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃⁴	D₄
hypocenter	C₃³	C₃×D₄
LCS	G ▷ C₃×C₃⋊D₃ ▷ C₃³
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×#1113	C₂	semidirect
2. C₃²×#157	C₂	semidirect
3. #157⋊D₃	C₃	direct (N × H)
7. #1113	C₂×C₃	semidirect
11. C₃×#157	D₃	semidirect
12. C₃×#157	C₂×C₃	semidirect
13. C₃⁴	D₄	semidirect
30. #157	C₃×D₃	semidirect
37. C₃³	D₁₂	semidirect
38. C₃³	C₃×D₄	semidirect
74. C₃²	C₃×D₁₂	semidirect
75. C₃²	GO⁺(4,𝔽₂)	semidirect
94. C₃	C₃×GO⁺(4,𝔽₂)	semidirect
95. C₃	#157⋊D₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#1113	2
C₃²×#157	2
#157⋊D₃	3
C₃×GO⁺(4,𝔽₂)	3
C₃×D₁₂	9

Subgroups — C3×#157⋊D3 #10620201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#157⋊D₃ #10620201