Subgroups — C₇×#10624904 #19100313

Order 5103.

622 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#6899	C₃	1	6	yes	maximal, complemented
2	C₇×#6898	C₃	1	3	yes	maximal, complemented
3	C₇×#6897	C₃	1	6	yes	maximal, complemented
4	C₇×#6896	C₃	1	3	yes	maximal, complemented
5	C₇×#6895	C₃	1	1	yes	maximal, characteristic, complemented
6	C₇×#6894	C₃	1	2	yes	maximal, complemented
7	C₇×#6894	C₃	1	2	yes	maximal, complemented
8	C₇×#6894	C₃	1	6	yes	maximal, complemented
9	C₇×#6893	C₃	1	1	yes	maximal, characteristic
10	C₇×C₉⋊H(3,𝔽₃)	C₃	1	2	yes	maximal
11	C₇×C₉×3₋¹⁺²	C₃	1	2	yes	maximal, complemented
12	C₇×C₉×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
13	C₇×#6887	C₃	1	1	yes	maximal, characteristic, complemented
14	C₇×#6887	C₃	1	3	yes	maximal, complemented
15	C₃×C₇×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
16	#10624904	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃×C₇×3₋¹⁺²	C₃²	1	2	yes	—
18	C₃×C₇×3₋¹⁺²	C₃²	1	6	yes	—
19	C₃×C₇×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
20	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
21	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
22	C₃²×C₇×C₉	C₃²	1	3	yes	—
23	C₃²×C₇×C₉	C₃²	1	2	yes	—
24	C₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
25	C₇×C₉⋊C₉	C₃²	1	2	yes	—
26	C₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
27	C₇×C₉⋊C₉	C₃²	1	2	yes	—
28	C₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
29	C₇×C₉⋊C₉	C₃²	1	2	yes	—
30	C₇×C₉⋊C₉	C₃²	1	6	yes	—
31	C₇×C₉⋊C₉	C₃²	1	6	yes	—
32	C₇×C₉⋊C₉	C₃²	1	6	yes	—
33	C₇×C₉⋊C₉	C₃²	1	3	yes	—
34	C₇×C₉⋊C₉	C₃²	1	6	yes	—
35	C₇×C₉⋊C₉	C₃²	1	6	yes	—
36	C₇×C₉⋊C₉	C₃²	1	6	yes	—
37	C₇×C₉⋊C₉	C₃²	1	6	yes	—
38	C₇×C₉⋊C₉	C₃²	1	6	yes	—
39	C₇×C₉⋊C₉	C₃²	1	6	yes	—
40	C₇×C₉⋊C₉	C₃²	1	6	yes	—
41	C₇×C₃²⋊C₉	C₃²	1	1	yes	characteristic
42	C₇×C₃²⋊C₉	C₃²	1	2	yes	—
43	C₇×C₃²⋊C₉	C₃²	1	6	yes	—
44	C₇×C₃²⋊C₉	C₃²	1	3	yes	—
45	C₇×C₃²⋊C₉	C₃²	1	1	yes	characteristic
46	C₇×C₃²⋊C₉	C₃²	1	3	yes	—
47	C₇×C₃²⋊C₉	C₃²	1	3	yes	—
48	C₇×C₃²⋊C₉	C₃²	1	2	yes	—
49	C₇×C₃²⋊C₉	C₃²	1	6	yes	—
50	C₇×C₃²⋊C₉	C₃²	1	6	yes	—
51	C₇×C₉²	C₃²	1	3	yes	—
52	C₇×C₉²	C₃²	1	6	yes	—
53	#6899	C₃×C₇	1	6	yes	complemented
54	#6898	C₃×C₇	1	3	yes	complemented
55	#6897	C₃×C₇	1	6	yes	complemented
56	#6896	C₃×C₇	1	3	yes	complemented
57	#6895	C₃×C₇	1	1	yes	characteristic, complemented
58	#6894	C₃×C₇	1	2	yes	complemented
59	#6894	C₃×C₇	1	2	yes	complemented
60	#6894	C₃×C₇	1	6	yes	complemented
61	#6893	C₃×C₇	1	1	yes	characteristic
62	C₉⋊H(3,𝔽₃)	C₃×C₇	1	2	yes	—
63	C₉×3₋¹⁺²	C₃×C₇	1	2	yes	complemented
64	C₉×H(3,𝔽₃)	C₃×C₇	1	1	yes	characteristic
65	#6887	C₃×C₇	1	1	yes	characteristic, complemented
66	#6887	C₃×C₇	1	3	yes	complemented
67	C₃×C₉⋊C₉	C₃×C₇	1	1	yes	characteristic, complemented
68	C₃³×C₇	C₃³	1	3	yes	—
69	C₃³×C₇	C₃³	1	1	yes	characteristic
70	C₇×3₋¹⁺²	—	3	6	no	—
71	C₇×3₋¹⁺²	—	9	6	no	—
72	C₇×H(3,𝔽₃)	—	3	3	no	—
73	C₃×C₇×C₉	—	3	3	no	—
74	C₃×C₇×C₉	—	3	3	no	—
75	C₃×C₇×C₉	—	3	9	no	—
76	C₃×C₇×C₉	—	9	2	no	—
77	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
78	C₃×C₇×C₉	C₃³	1	3	yes	—
79	C₃×C₇×C₉	C₃³	1	2	yes	—
80	C₃×C₇×C₉	C₃³	1	6	yes	—
81	C₃×C₇×C₉	C₃³	1	6	yes	—
82	C₃×C₇×C₉	C₃³	1	6	yes	—
83	C₃×C₇×C₉	C₃³	1	3	yes	—
84	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
85	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
86	C₃×C₇×C₉	C₃³	1	2	yes	—
87	C₃×C₇×C₉	C₃³	1	2	yes	—
88	C₃×C₇×C₉	C₃³	1	2	yes	—
89	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
90	C₃×3₋¹⁺²	C₃²×C₇	1	2	yes	—
91	C₃×3₋¹⁺²	C₃²×C₇	1	6	yes	—
92	C₃×H(3,𝔽₃)	C₃²×C₇	1	1	yes	characteristic
93	C₃²×C₉	C₃²×C₇	1	1	yes	characteristic
94	C₃²×C₉	C₃²×C₇	1	1	yes	characteristic
95	C₃²×C₉	C₃²×C₇	1	3	yes	—
96	C₃²×C₉	C₃²×C₇	1	2	yes	—
97	C₉⋊C₉	C₃²×C₇	1	1	yes	characteristic
98	C₉⋊C₉	C₃²×C₇	1	2	yes	—
99	C₉⋊C₉	C₃²×C₇	1	1	yes	characteristic
100	C₉⋊C₉	C₃²×C₇	1	2	yes	—
101	C₉⋊C₉	C₃²×C₇	1	1	yes	characteristic
102	C₉⋊C₉	C₃²×C₇	1	2	yes	—
103	C₉⋊C₉	C₃²×C₇	1	6	yes	—
104	C₉⋊C₉	C₃²×C₇	1	6	yes	—
105	C₉⋊C₉	C₃²×C₇	1	6	yes	—
106	C₉⋊C₉	C₃²×C₇	1	3	yes	—
107	C₉⋊C₉	C₃²×C₇	1	6	yes	—
108	C₉⋊C₉	C₃²×C₇	1	6	yes	—
109	C₉⋊C₉	C₃²×C₇	1	6	yes	—
110	C₉⋊C₉	C₃²×C₇	1	6	yes	—
111	C₉⋊C₉	C₃²×C₇	1	6	yes	—
112	C₉⋊C₉	C₃²×C₇	1	6	yes	—
113	C₉⋊C₉	C₃²×C₇	1	6	yes	—
114	C₃²⋊C₉	C₃²×C₇	1	1	yes	characteristic
115	C₃²⋊C₉	C₃²×C₇	1	2	yes	—
116	C₃²⋊C₉	C₃²×C₇	1	6	yes	—
117	C₃²⋊C₉	C₃²×C₇	1	3	yes	—
118	C₃²⋊C₉	C₃²×C₇	1	1	yes	characteristic
119	C₃²⋊C₉	C₃²×C₇	1	3	yes	—
120	C₃²⋊C₉	C₃²×C₇	1	3	yes	—
121	C₃²⋊C₉	C₃²×C₇	1	2	yes	—
122	C₃²⋊C₉	C₃²×C₇	1	6	yes	—
123	C₃²⋊C₉	C₃²×C₇	1	6	yes	—
124	C₉²	C₃²×C₇	1	3	yes	—
125	C₉²	C₃²×C₇	1	6	yes	—
126	C₃²×C₇	—	3	1	no	—
127	C₃²×C₇	—	3	2	no	—
128	C₃²×C₇	—	3	3	no	—
129	C₃²×C₇	—	3	3	no	—
130	C₃²×C₇	—	3	6	no	—
131	C₃²×C₇	#737	1	3	yes	—
132	C₃²×C₇	C₃⁴	1	1	yes	characteristic
133	C₇×C₉	—	3	1	no	—
134	C₇×C₉	—	3	2	no	—
135	C₇×C₉	—	3	3	no	—
136	C₇×C₉	—	3	1	no	—
137	C₇×C₉	—	3	1	no	—
138	C₇×C₉	—	3	3	no	—
139	C₇×C₉	—	3	6	no	—
140	C₇×C₉	—	3	2	no	—
141	C₇×C₉	—	3	2	no	—
142	C₇×C₉	—	3	2	no	—
143	C₇×C₉	—	3	6	no	—
144	C₇×C₉	—	3	6	no	—
145	C₇×C₉	#737	1	3	yes	—
146	C₃³	C₃³×C₇	1	3	yes	—
147	C₃³	C₃³×C₇	1	1	yes	characteristic
148	3₋¹⁺²	—	3	6	no	—
149	3₋¹⁺²	—	9	6	no	—
150	H(3,𝔽₃)	—	3	3	no	—
151	C₃×C₉	—	3	3	no	—
152	C₃×C₉	—	3	3	no	—
153	C₃×C₉	—	3	9	no	—
154	C₃×C₉	—	9	2	no	—
155	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
156	C₃×C₉	C₃³×C₇	1	3	yes	—
157	C₃×C₉	C₃³×C₇	1	2	yes	—
158	C₃×C₉	C₃³×C₇	1	6	yes	—
159	C₃×C₉	C₃³×C₇	1	6	yes	—
160	C₃×C₉	C₃³×C₇	1	6	yes	—
161	C₃×C₉	C₃³×C₇	1	3	yes	—
162	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
163	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
164	C₃×C₉	C₃³×C₇	1	2	yes	—
165	C₃×C₉	C₃³×C₇	1	2	yes	—
166	C₃×C₉	C₃³×C₇	1	2	yes	—
167	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
168	C₃×C₇	—	3	3	no	—
169	C₃×C₇	—	9	3	no	—
170	C₃×C₇	C₃×#737	1	1	yes	characteristic
171	C₃×C₇	C₃×#737	1	1	yes	characteristic
172	C₃×C₇	3₋¹⁺⁴	1	2	yes	—
173	C₃²	—	3	1	no	—
174	C₃²	—	3	2	no	—
175	C₃²	—	3	3	no	—
176	C₃²	—	3	3	no	—
177	C₃²	—	3	6	no	—
178	C₃²	C₇×#737	1	3	yes	—
179	C₃²	C₃⁴×C₇	1	1	yes	characteristic
180	C₉	—	3	1	no	—
181	C₉	—	3	2	no	—
182	C₉	—	3	3	no	—
183	C₉	—	3	1	no	—
184	C₉	—	3	1	no	—
185	C₉	—	3	3	no	—
186	C₉	—	3	6	no	—
187	C₉	—	3	2	no	—
188	C₉	—	3	2	no	—
189	C₉	—	3	2	no	—
190	C₉	—	3	6	no	—
191	C₉	—	3	6	no	—
192	C₉	C₇×#737	1	3	yes	—
193	C₇	#10624904	1	1	yes	characteristic, direct product factor, Sylow
194	C₃	—	3	3	no	—
195	C₃	—	9	3	no	—
196	C₃	C₃×C₇×#737	1	1	yes	characteristic
197	C₃	C₃×C₇×#737	1	1	yes	characteristic
198	C₃	C₇×3₋¹⁺⁴	1	2	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
1. C₇×#6899	C₃	semidirect
2. C₇×#6898	C₃	semidirect
3. C₇×#6897	C₃	semidirect
4. C₇×#6896	C₃	semidirect
5. C₇×#6895	C₃	semidirect
6. C₇×#6894	C₃	semidirect
7. C₇×#6894	C₃	semidirect
8. C₇×#6894	C₃	semidirect
11. C₇×C₉×3₋¹⁺²	C₃	semidirect
13. C₇×#6887	C₃	semidirect
14. C₇×#6887	C₃	semidirect
15. C₃×C₇×C₉⋊C₉	C₃	semidirect
16. #10624904	C₇	direct (N × H)
53. #6899	C₃×C₇	semidirect
54. #6898	C₃×C₇	semidirect
55. #6897	C₃×C₇	semidirect
56. #6896	C₃×C₇	semidirect
57. #6895	C₃×C₇	semidirect
58. #6894	C₃×C₇	semidirect
59. #6894	C₃×C₇	semidirect
60. #6894	C₃×C₇	semidirect
63. C₉×3₋¹⁺²	C₃×C₇	semidirect
65. #6887	C₃×C₇	semidirect
66. #6887	C₃×C₇	semidirect
67. C₃×C₉⋊C₉	C₃×C₇	semidirect
193. C₇	#10624904	direct (N × H)

Subgroups — C7×#10624904 #19100313

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624904 #19100313