Subgroups — C₃×C₇×#6896 #19100282

Order 5103.

884 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×3₋¹⁺²	C₃	1	2	yes	maximal
2	C₇×#6896	C₃	1	27	yes	maximal, direct product factor
3	C₃×C₇×C₉⋊C₉	C₃	1	4	yes	maximal, complemented
4	C₃×C₇×C₉⋊C₉	C₃	1	4	yes	maximal, complemented
5	C₃×C₇×C₃²⋊C₉	C₃	1	2	yes	maximal
6	C₃×C₇×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃×#6896	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₃⁴×C₇	C₃²	1	1	yes	characteristic
9	C₃×C₇×3₋¹⁺²	—	3	18	no	—
10	C₃×C₇×3₋¹⁺²	C₃²	1	18	yes	—
11	C₃²×C₇×C₉	C₃²	1	2	yes	—
12	C₃²×C₇×C₉	C₃²	1	4	yes	—
13	C₃²×C₇×C₉	C₃²	1	4	yes	—
14	C₃²×C₇×C₉	C₃²	1	2	yes	—
15	C₇×C₉⋊C₉	C₃²	1	36	yes	complemented
16	C₇×C₉⋊C₉	C₃²	1	36	yes	complemented
17	C₇×C₃²⋊C₉	C₃²	1	18	yes	—
18	C₇×C₉²	C₃²	1	9	yes	complemented
19	C₃²×3₋¹⁺²	C₃×C₇	1	2	yes	—
20	#6896	C₃×C₇	1	27	yes	direct product factor
21	C₃×C₉⋊C₉	C₃×C₇	1	4	yes	complemented
22	C₃×C₉⋊C₉	C₃×C₇	1	4	yes	complemented
23	C₃×C₃²⋊C₉	C₃×C₇	1	2	yes	—
24	C₃×C₉²	C₃×C₇	1	1	yes	characteristic, complemented
25	C₃³×C₇	—	3	6	no	—
26	C₃³×C₇	—	3	6	no	—
27	C₃³×C₇	C₃³	1	3	yes	—
28	C₃³×C₇	C₃³	1	1	yes	characteristic
29	C₇×3₋¹⁺²	—	3	54	no	—
30	C₃×C₇×C₉	—	3	12	no	—
31	C₃×C₇×C₉	—	3	6	no	—
32	C₃×C₇×C₉	—	3	12	no	—
33	C₃×C₇×C₉	3₋¹⁺²	1	18	yes	complemented
34	C₃×C₇×C₉	C₃³	1	6	yes	—
35	C₃×C₇×C₉	C₃³	1	12	yes	—
36	C₃×C₇×C₉	C₃³	1	12	yes	—
37	C₃×C₇×C₉	C₃³	1	6	yes	—
38	C₃⁴	C₃²×C₇	1	1	yes	characteristic
39	C₃×3₋¹⁺²	—	3	18	no	—
40	C₃×3₋¹⁺²	C₃²×C₇	1	18	yes	—
41	C₃²×C₉	C₃²×C₇	1	4	yes	—
42	C₃²×C₉	C₃²×C₇	1	2	yes	—
43	C₃²×C₉	C₃²×C₇	1	4	yes	—
44	C₃²×C₉	C₃²×C₇	1	2	yes	—
45	C₉⋊C₉	C₃²×C₇	1	36	yes	complemented
46	C₉⋊C₉	C₃²×C₇	1	36	yes	complemented
47	C₃²⋊C₉	C₃²×C₇	1	18	yes	—
48	C₉²	C₃²×C₇	1	9	yes	complemented
49	C₃²×C₇	—	3	6	no	—
50	C₃²×C₇	—	3	6	no	—
51	C₃²×C₇	—	9	9	no	—
52	C₃²×C₇	C₃×3₋¹⁺²	1	6	yes	—
53	C₃²×C₇	#737	1	6	yes	—
54	C₃²×C₇	C₃⁴	1	1	yes	characteristic
55	C₇×C₉	—	3	12	no	—
56	C₇×C₉	—	3	6	no	—
57	C₇×C₉	—	3	12	no	—
58	C₇×C₉	C₃×3₋¹⁺²	1	18	yes	complemented
59	C₃³	—	3	6	no	—
60	C₃³	—	3	6	no	—
61	C₃³	C₃³×C₇	1	3	yes	—
62	C₃³	C₃³×C₇	1	1	yes	characteristic
63	3₋¹⁺²	—	3	54	no	—
64	C₃×C₉	—	3	12	no	—
65	C₃×C₉	—	3	6	no	—
66	C₃×C₉	—	3	12	no	—
67	C₃×C₉	C₇×3₋¹⁺²	1	18	yes	complemented
68	C₃×C₉	C₃³×C₇	1	6	yes	—
69	C₃×C₉	C₃³×C₇	1	12	yes	—
70	C₃×C₉	C₃³×C₇	1	12	yes	—
71	C₃×C₉	C₃³×C₇	1	6	yes	—
72	C₃×C₇	—	9	3	no	—
73	C₃×C₇	#6896	1	9	yes	direct product factor
74	C₃×C₇	C₃²×3₋¹⁺²	1	2	yes	—
75	C₃×C₇	C₃×#737	1	2	yes	—
76	C₃²	—	3	6	no	—
77	C₃²	—	3	6	no	—
78	C₃²	—	9	9	no	—
79	C₃²	C₃×C₇×3₋¹⁺²	1	6	yes	—
80	C₃²	C₇×#737	1	6	yes	—
81	C₃²	C₃⁴×C₇	1	1	yes	characteristic
82	C₉	—	3	12	no	—
83	C₉	—	3	6	no	—
84	C₉	—	3	12	no	—
85	C₉	C₃×C₇×3₋¹⁺²	1	18	yes	complemented
86	C₇	C₃×#6896	1	1	yes	characteristic, direct product factor, Sylow
87	C₃	—	9	3	no	—
88	C₃	C₇×#6896	1	9	yes	direct product factor
89	C₃	C₃²×C₇×3₋¹⁺²	1	2	yes	—
90	C₃	C₃×C₇×#737	1	2	yes	—

	subgroup	G/H
center, socle	C₃³×C₇	C₃³
commutator, Frattini	C₃²	C₃⁴×C₇
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#6896	C₃	direct (N × H)
3. C₃×C₇×C₉⋊C₉	C₃	semidirect
4. C₃×C₇×C₉⋊C₉	C₃	semidirect
6. C₃×C₇×C₉²	C₃	semidirect
7. C₃×#6896	C₇	direct (N × H)
15. C₇×C₉⋊C₉	C₃²	semidirect
16. C₇×C₉⋊C₉	C₃²	semidirect
18. C₇×C₉²	C₃²	semidirect
20. #6896	C₃×C₇	direct (N × H)
21. C₃×C₉⋊C₉	C₃×C₇	semidirect
22. C₃×C₉⋊C₉	C₃×C₇	semidirect
24. C₃×C₉²	C₃×C₇	semidirect
33. C₃×C₇×C₉	3₋¹⁺²	semidirect
45. C₉⋊C₉	C₃²×C₇	semidirect
46. C₉⋊C₉	C₃²×C₇	semidirect
48. C₉²	C₃²×C₇	semidirect
58. C₇×C₉	C₃×3₋¹⁺²	semidirect
67. C₃×C₉	C₇×3₋¹⁺²	semidirect
73. C₃×C₇	#6896	direct (N × H)
85. C₉	C₃×C₇×3₋¹⁺²	semidirect
86. C₇	C₃×#6896	direct (N × H)
88. C₃	C₇×#6896	direct (N × H)

Subgroups — C3×C7×#6896 #19100282

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₇×#6896 #19100282