Subgroups — C₇×#10624887 #19100296

Order 5103.

698 conjugacy classes of subgroups.

The subgroup lattice has 142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×#737	C₃	1	1	yes	maximal, characteristic
2	C₇×#6900	C₃	1	3	yes	maximal, complemented
3	C₇×#6899	C₃	1	6	yes	maximal, complemented
4	C₇×#6896	C₃	1	9	yes	maximal, complemented
5	C₇×#6894	C₃	1	6	yes	maximal, complemented
6	C₇×#6894	C₃	1	9	yes	maximal, complemented
7	C₇×C₉⋊H(3,𝔽₃)	C₃	1	3	yes	maximal
8	C₇×#6887	C₃	1	1	yes	maximal, characteristic, complemented
9	C₇×#6887	C₃	1	1	yes	maximal, characteristic, complemented
10	C₃×C₇×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
11	#10624887	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₇×#737	—	3	9	no	—
13	C₃×C₇×3₋¹⁺²	C₃²	1	2	yes	—
14	C₃×C₇×3₋¹⁺²	C₃²	1	3	yes	—
15	C₃×C₇×3₋¹⁺²	C₃²	1	3	yes	—
16	C₃×C₇×3₋¹⁺²	C₃²	1	9	yes	—
17	C₃×C₇×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
18	C₃²×C₇×C₉	C₃²	1	3	yes	—
19	C₃²×C₇×C₉	C₃²	1	3	yes	—
20	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
21	C₇×C₉⋊C₉	C₃²	1	3	yes	—
22	C₇×C₉⋊C₉	C₃²	1	3	yes	—
23	C₇×C₉⋊C₉	C₃²	1	2	yes	—
24	C₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
25	C₇×C₉⋊C₉	C₃²	1	3	yes	—
26	C₇×C₉⋊C₉	C₃²	1	3	yes	—
27	C₇×C₉⋊C₉	C₃²	1	3	yes	—
28	C₇×C₉⋊C₉	C₃²	1	3	yes	—
29	C₇×C₉⋊C₉	C₃²	1	36	yes	—
30	C₇×C₉⋊C₉	C₃²	1	18	yes	—
31	C₇×C₃²⋊C₉	C₃²	1	3	yes	—
32	C₇×C₃²⋊C₉	C₃²	1	3	yes	—
33	C₇×C₃²⋊C₉	C₃²	1	18	yes	—
34	C₇×C₉²	C₃²	1	3	yes	—
35	C₇×C₉²	C₃²	1	3	yes	—
36	C₃×#737	C₃×C₇	1	1	yes	characteristic
37	#6900	C₃×C₇	1	3	yes	complemented
38	#6899	C₃×C₇	1	6	yes	complemented
39	#6896	C₃×C₇	1	9	yes	complemented
40	#6894	C₃×C₇	1	6	yes	complemented
41	#6894	C₃×C₇	1	9	yes	complemented
42	C₉⋊H(3,𝔽₃)	C₃×C₇	1	3	yes	—
43	#6887	C₃×C₇	1	1	yes	characteristic, complemented
44	#6887	C₃×C₇	1	1	yes	characteristic, complemented
45	C₃×C₉⋊C₉	C₃×C₇	1	1	yes	characteristic, complemented
46	C₃³×C₇	C₃³	1	3	yes	—
47	C₃³×C₇	C₃³	1	1	yes	characteristic
48	C₇×3₋¹⁺²	—	3	6	no	—
49	C₇×3₋¹⁺²	—	3	9	no	—
50	C₇×3₋¹⁺²	—	3	9	no	—
51	C₇×3₋¹⁺²	—	9	9	no	—
52	C₇×H(3,𝔽₃)	—	3	3	no	—
53	C₃×C₇×C₉	—	3	9	no	—
54	C₃×C₇×C₉	—	9	3	no	—
55	C₃×C₇×C₉	3₋¹⁺²	1	9	yes	complemented
56	C₃×C₇×C₉	C₃³	1	9	yes	—
57	C₃×C₇×C₉	C₃³	1	9	yes	—
58	C₃×C₇×C₉	C₃³	1	6	yes	—
59	C₃×C₇×C₉	C₃³	1	6	yes	—
60	C₃×C₇×C₉	C₃³	1	3	yes	—
61	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
62	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
63	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
64	#737	—	3	9	no	—
65	C₃×3₋¹⁺²	C₃²×C₇	1	2	yes	—
66	C₃×3₋¹⁺²	C₃²×C₇	1	3	yes	—
67	C₃×3₋¹⁺²	C₃²×C₇	1	3	yes	—
68	C₃×3₋¹⁺²	C₃²×C₇	1	9	yes	—
69	C₃×H(3,𝔽₃)	C₃²×C₇	1	1	yes	characteristic
70	C₃²×C₉	C₃²×C₇	1	3	yes	—
71	C₃²×C₉	C₃²×C₇	1	3	yes	—
72	C₃²×C₉	C₃²×C₇	1	1	yes	characteristic
73	C₉⋊C₉	C₃²×C₇	1	3	yes	—
74	C₉⋊C₉	C₃²×C₇	1	3	yes	—
75	C₉⋊C₉	C₃²×C₇	1	2	yes	—
76	C₉⋊C₉	C₃²×C₇	1	1	yes	characteristic
77	C₉⋊C₉	C₃²×C₇	1	3	yes	—
78	C₉⋊C₉	C₃²×C₇	1	3	yes	—
79	C₉⋊C₉	C₃²×C₇	1	3	yes	—
80	C₉⋊C₉	C₃²×C₇	1	3	yes	—
81	C₉⋊C₉	C₃²×C₇	1	36	yes	—
82	C₉⋊C₉	C₃²×C₇	1	18	yes	—
83	C₃²⋊C₉	C₃²×C₇	1	3	yes	—
84	C₃²⋊C₉	C₃²×C₇	1	3	yes	—
85	C₃²⋊C₉	C₃²×C₇	1	18	yes	—
86	C₉²	C₃²×C₇	1	3	yes	—
87	C₉²	C₃²×C₇	1	3	yes	—
88	C₃²×C₇	—	3	3	no	—
89	C₃²×C₇	—	3	3	no	—
90	C₃²×C₇	—	3	9	no	—
91	C₃²×C₇	C₃×3₋¹⁺²	1	3	yes	—
92	C₃²×C₇	C₃⁴	1	1	yes	characteristic
93	C₇×C₉	—	3	6	no	—
94	C₇×C₉	—	3	6	no	—
95	C₇×C₉	—	3	3	no	—
96	C₇×C₉	—	3	9	no	—
97	C₇×C₉	—	3	9	no	—
98	C₇×C₉	C₃×3₋¹⁺²	1	3	yes	—
99	C₇×C₉	C₃×3₋¹⁺²	1	3	yes	—
100	C₇×C₉	C₃×3₋¹⁺²	1	3	yes	—
101	C₃³	C₃³×C₇	1	3	yes	—
102	C₃³	C₃³×C₇	1	1	yes	characteristic
103	3₋¹⁺²	—	3	6	no	—
104	3₋¹⁺²	—	3	9	no	—
105	3₋¹⁺²	—	3	9	no	—
106	3₋¹⁺²	—	9	9	no	—
107	H(3,𝔽₃)	—	3	3	no	—
108	C₃×C₉	—	3	9	no	—
109	C₃×C₉	—	9	3	no	—
110	C₃×C₉	C₇×3₋¹⁺²	1	9	yes	complemented
111	C₃×C₉	C₃³×C₇	1	9	yes	—
112	C₃×C₉	C₃³×C₇	1	9	yes	—
113	C₃×C₉	C₃³×C₇	1	6	yes	—
114	C₃×C₉	C₃³×C₇	1	6	yes	—
115	C₃×C₉	C₃³×C₇	1	3	yes	—
116	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
117	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
118	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
119	C₃×C₇	—	3	3	no	—
120	C₃×C₇	—	9	3	no	—
121	C₃×C₇	C₃²×3₋¹⁺²	1	1	yes	characteristic
122	C₃×C₇	3₋¹⁺⁴	1	3	yes	—
123	C₃²	—	3	3	no	—
124	C₃²	—	3	3	no	—
125	C₃²	—	3	9	no	—
126	C₃²	C₃×C₇×3₋¹⁺²	1	3	yes	—
127	C₃²	C₃⁴×C₇	1	1	yes	characteristic
128	C₉	—	3	6	no	—
129	C₉	—	3	6	no	—
130	C₉	—	3	3	no	—
131	C₉	—	3	9	no	—
132	C₉	—	3	9	no	—
133	C₉	C₃×C₇×3₋¹⁺²	1	3	yes	—
134	C₉	C₃×C₇×3₋¹⁺²	1	3	yes	—
135	C₉	C₃×C₇×3₋¹⁺²	1	3	yes	—
136	C₇	#10624887	1	1	yes	characteristic, direct product factor, Sylow
137	C₃	—	3	3	no	—
138	C₃	—	9	3	no	—
139	C₃	C₃²×C₇×3₋¹⁺²	1	1	yes	characteristic
140	C₃	C₇×3₋¹⁺⁴	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₇×#6900	C₃	semidirect
3. C₇×#6899	C₃	semidirect
4. C₇×#6896	C₃	semidirect
5. C₇×#6894	C₃	semidirect
6. C₇×#6894	C₃	semidirect
8. C₇×#6887	C₃	semidirect
9. C₇×#6887	C₃	semidirect
10. C₃×C₇×C₉⋊C₉	C₃	semidirect
11. #10624887	C₇	direct (N × H)
37. #6900	C₃×C₇	semidirect
38. #6899	C₃×C₇	semidirect
39. #6896	C₃×C₇	semidirect
40. #6894	C₃×C₇	semidirect
41. #6894	C₃×C₇	semidirect
43. #6887	C₃×C₇	semidirect
44. #6887	C₃×C₇	semidirect
45. C₃×C₉⋊C₉	C₃×C₇	semidirect
55. C₃×C₇×C₉	3₋¹⁺²	semidirect
110. C₃×C₉	C₇×3₋¹⁺²	semidirect
136. C₇	#10624887	direct (N × H)

Subgroups — C7×#10624887 #19100296

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624887 #19100296