Subgroups — C₇×#10624901 #19100310

Order 5103.

718 conjugacy classes of subgroups.

The subgroup lattice has 210 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	6	yes	maximal, complemented
5	C₇×#6896	C₃	1	3	yes	maximal, complemented
6	C₇×#6895	C₃	1	2	yes	maximal, complemented
7	C₇×#6894	C₃	1	2	yes	maximal, complemented
8	C₇×#6894	C₃	1	1	yes	maximal, characteristic, complemented
9	C₇×#6894	C₃	1	6	yes	maximal, complemented
10	C₇×C₉⋊H(3,𝔽₃)	C₃	1	2	yes	maximal
11	C₇×C₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
12	C₇×C₉×3₋¹⁺²	C₃	1	2	yes	maximal, complemented
13	C₇×C₉×3₋¹⁺²	C₃	1	3	yes	maximal, complemented
14	C₇×C₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic, complemented
15	C₃×C₇×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
16	#10624901	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₇×#737	—	3	9	no	—
18	C₃×C₇×3₋¹⁺²	C₃²	1	3	yes	—
19	C₃×C₇×3₋¹⁺²	C₃²	1	1	yes	characteristic
20	C₃×C₇×3₋¹⁺²	C₃²	1	3	yes	—
21	C₃×C₇×3₋¹⁺²	C₃²	1	3	yes	—
22	C₃×C₇×3₋¹⁺²	C₃²	1	6	yes	—
23	C₃×C₇×3₋¹⁺²	C₃²	1	1	yes	characteristic
24	C₃×C₇×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
25	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
26	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
27	C₃²×C₇×C₉	C₃²	1	3	yes	—
28	C₃²×C₇×C₉	C₃²	1	2	yes	—
29	C₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
30	C₇×C₉⋊C₉	C₃²	1	2	yes	—
31	C₇×C₉⋊C₉	C₃²	1	2	yes	—
32	C₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
33	C₇×C₉⋊C₉	C₃²	1	2	yes	—
34	C₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
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	3	yes	—
41	C₇×C₉⋊C₉	C₃²	1	6	yes	—
42	C₇×C₉⋊C₉	C₃²	1	6	yes	—
43	C₇×C₉⋊C₉	C₃²	1	6	yes	—
44	C₇×C₉⋊C₉	C₃²	1	6	yes	—
45	C₇×C₉⋊C₉	C₃²	1	6	yes	—
46	C₇×C₃²⋊C₉	C₃²	1	2	yes	—
47	C₇×C₃²⋊C₉	C₃²	1	2	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×C₃²⋊C₉	C₃²	1	6	yes	—
52	C₇×C₉²	C₃²	1	6	yes	—
53	C₇×C₉²	C₃²	1	3	yes	—
54	C₃×#737	C₃×C₇	1	1	yes	characteristic
55	#6900	C₃×C₇	1	3	yes	complemented
56	#6899	C₃×C₇	1	6	yes	complemented
57	#6896	C₃×C₇	1	6	yes	complemented
58	#6896	C₃×C₇	1	3	yes	complemented
59	#6895	C₃×C₇	1	2	yes	complemented
60	#6894	C₃×C₇	1	2	yes	complemented
61	#6894	C₃×C₇	1	1	yes	characteristic, complemented
62	#6894	C₃×C₇	1	6	yes	complemented
63	C₉⋊H(3,𝔽₃)	C₃×C₇	1	2	yes	—
64	C₉⋊H(3,𝔽₃)	C₃×C₇	1	1	yes	characteristic
65	C₉×3₋¹⁺²	C₃×C₇	1	2	yes	complemented
66	C₉×3₋¹⁺²	C₃×C₇	1	3	yes	complemented
67	C₉×3₋¹⁺²	C₃×C₇	1	1	yes	characteristic, complemented
68	C₃×C₉⋊C₉	C₃×C₇	1	1	yes	characteristic, complemented
69	C₃³×C₇	C₃³	1	3	yes	—
70	C₃³×C₇	C₃³	1	1	yes	characteristic
71	C₇×3₋¹⁺²	—	3	3	no	—
72	C₇×3₋¹⁺²	—	3	9	no	—
73	C₇×3₋¹⁺²	—	3	9	no	—
74	C₇×3₋¹⁺²	—	3	9	no	—
75	C₇×3₋¹⁺²	—	9	6	no	—
76	C₇×3₋¹⁺²	3₋¹⁺²	1	9	yes	complemented
77	C₇×H(3,𝔽₃)	—	3	3	no	—
78	C₃×C₇×C₉	—	3	3	no	—
79	C₃×C₇×C₉	—	3	9	no	—
80	C₃×C₇×C₉	—	3	3	no	—
81	C₃×C₇×C₉	—	9	2	no	—
82	C₃×C₇×C₉	C₃³	1	2	yes	—
83	C₃×C₇×C₉	C₃³	1	6	yes	—
84	C₃×C₇×C₉	C₃³	1	6	yes	—
85	C₃×C₇×C₉	C₃³	1	6	yes	—
86	C₃×C₇×C₉	C₃³	1	2	yes	—
87	C₃×C₇×C₉	C₃³	1	2	yes	—
88	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
89	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
90	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
91	C₃×C₇×C₉	C₃³	1	3	yes	—
92	C₃×C₇×C₉	C₃³	1	2	yes	—
93	C₃×C₇×C₉	C₃³	1	3	yes	—
94	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
95	#737	—	3	9	no	—
96	C₃×3₋¹⁺²	C₃²×C₇	1	1	yes	characteristic
97	C₃×3₋¹⁺²	C₃²×C₇	1	3	yes	—
98	C₃×3₋¹⁺²	C₃²×C₇	1	3	yes	—
99	C₃×3₋¹⁺²	C₃²×C₇	1	3	yes	—
100	C₃×3₋¹⁺²	C₃²×C₇	1	6	yes	—
101	C₃×3₋¹⁺²	C₃²×C₇	1	1	yes	characteristic
102	C₃×H(3,𝔽₃)	C₃²×C₇	1	1	yes	characteristic
103	C₃²×C₉	C₃²×C₇	1	1	yes	characteristic
104	C₃²×C₉	C₃²×C₇	1	3	yes	—
105	C₃²×C₉	C₃²×C₇	1	1	yes	characteristic
106	C₃²×C₉	C₃²×C₇	1	2	yes	—
107	C₉⋊C₉	C₃²×C₇	1	1	yes	characteristic
108	C₉⋊C₉	C₃²×C₇	1	2	yes	—
109	C₉⋊C₉	C₃²×C₇	1	2	yes	—
110	C₉⋊C₉	C₃²×C₇	1	1	yes	characteristic
111	C₉⋊C₉	C₃²×C₇	1	2	yes	—
112	C₉⋊C₉	C₃²×C₇	1	1	yes	characteristic
113	C₉⋊C₉	C₃²×C₇	1	6	yes	—
114	C₉⋊C₉	C₃²×C₇	1	6	yes	—
115	C₉⋊C₉	C₃²×C₇	1	6	yes	—
116	C₉⋊C₉	C₃²×C₇	1	6	yes	—
117	C₉⋊C₉	C₃²×C₇	1	6	yes	—
118	C₉⋊C₉	C₃²×C₇	1	3	yes	—
119	C₉⋊C₉	C₃²×C₇	1	6	yes	—
120	C₉⋊C₉	C₃²×C₇	1	6	yes	—
121	C₉⋊C₉	C₃²×C₇	1	6	yes	—
122	C₉⋊C₉	C₃²×C₇	1	6	yes	—
123	C₉⋊C₉	C₃²×C₇	1	6	yes	—
124	C₃²⋊C₉	C₃²×C₇	1	2	yes	—
125	C₃²⋊C₉	C₃²×C₇	1	2	yes	—
126	C₃²⋊C₉	C₃²×C₇	1	2	yes	—
127	C₃²⋊C₉	C₃²×C₇	1	6	yes	—
128	C₃²⋊C₉	C₃²×C₇	1	6	yes	—
129	C₃²⋊C₉	C₃²×C₇	1	6	yes	—
130	C₉²	C₃²×C₇	1	6	yes	—
131	C₉²	C₃²×C₇	1	3	yes	—
132	C₃²×C₇	—	3	1	no	—
133	C₃²×C₇	—	3	2	no	—
134	C₃²×C₇	—	3	3	no	—
135	C₃²×C₇	—	3	3	no	—
136	C₃²×C₇	—	3	6	no	—
137	C₃²×C₇	C₃×3₋¹⁺²	1	3	yes	—
138	C₃²×C₇	C₃⁴	1	1	yes	characteristic
139	C₇×C₉	—	3	1	no	—
140	C₇×C₉	—	3	1	no	—
141	C₇×C₉	—	3	1	no	—
142	C₇×C₉	—	3	3	no	—
143	C₇×C₉	—	3	2	no	—
144	C₇×C₉	—	3	6	no	—
145	C₇×C₉	—	3	2	no	—
146	C₇×C₉	—	3	2	no	—
147	C₇×C₉	—	3	2	no	—
148	C₇×C₉	—	3	6	no	—
149	C₇×C₉	—	3	6	no	—
150	C₇×C₉	C₃×3₋¹⁺²	1	9	yes	—
151	C₇×C₉	#737	1	3	yes	complemented
152	C₃³	C₃³×C₇	1	3	yes	—
153	C₃³	C₃³×C₇	1	1	yes	characteristic
154	3₋¹⁺²	—	3	3	no	—
155	3₋¹⁺²	—	3	9	no	—
156	3₋¹⁺²	—	3	9	no	—
157	3₋¹⁺²	—	3	9	no	—
158	3₋¹⁺²	—	9	6	no	—
159	3₋¹⁺²	C₇×3₋¹⁺²	1	9	yes	complemented
160	H(3,𝔽₃)	—	3	3	no	—
161	C₃×C₉	—	3	3	no	—
162	C₃×C₉	—	3	9	no	—
163	C₃×C₉	—	3	3	no	—
164	C₃×C₉	—	9	2	no	—
165	C₃×C₉	C₃³×C₇	1	2	yes	—
166	C₃×C₉	C₃³×C₇	1	6	yes	—
167	C₃×C₉	C₃³×C₇	1	6	yes	—
168	C₃×C₉	C₃³×C₇	1	6	yes	—
169	C₃×C₉	C₃³×C₇	1	2	yes	—
170	C₃×C₉	C₃³×C₇	1	2	yes	—
171	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
172	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
173	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
174	C₃×C₉	C₃³×C₇	1	3	yes	—
175	C₃×C₉	C₃³×C₇	1	2	yes	—
176	C₃×C₉	C₃³×C₇	1	3	yes	—
177	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
178	C₃×C₇	—	3	3	no	—
179	C₃×C₇	—	9	3	no	—
180	C₃×C₇	C₃²×3₋¹⁺²	1	1	yes	characteristic
181	C₃×C₇	C₃×#737	1	1	yes	characteristic
182	C₃×C₇	3₋¹⁺⁴	1	2	yes	—
183	C₃²	—	3	1	no	—
184	C₃²	—	3	2	no	—
185	C₃²	—	3	3	no	—
186	C₃²	—	3	3	no	—
187	C₃²	—	3	6	no	—
188	C₃²	C₃×C₇×3₋¹⁺²	1	3	yes	—
189	C₃²	C₃⁴×C₇	1	1	yes	characteristic
190	C₉	—	3	1	no	—
191	C₉	—	3	1	no	—
192	C₉	—	3	1	no	—
193	C₉	—	3	3	no	—
194	C₉	—	3	2	no	—
195	C₉	—	3	6	no	—
196	C₉	—	3	2	no	—
197	C₉	—	3	2	no	—
198	C₉	—	3	2	no	—
199	C₉	—	3	6	no	—
200	C₉	—	3	6	no	—
201	C₉	C₃×C₇×3₋¹⁺²	1	9	yes	—
202	C₉	C₇×#737	1	3	yes	complemented
203	C₇	#10624901	1	1	yes	characteristic, direct product factor, Sylow
204	C₃	—	3	3	no	—
205	C₃	—	9	3	no	—
206	C₃	C₃²×C₇×3₋¹⁺²	1	1	yes	characteristic
207	C₃	C₃×C₇×#737	1	1	yes	characteristic
208	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
2. C₇×#6900	C₃	semidirect
3. C₇×#6899	C₃	semidirect
4. C₇×#6896	C₃	semidirect
5. C₇×#6896	C₃	semidirect
6. C₇×#6895	C₃	semidirect
7. C₇×#6894	C₃	semidirect
8. C₇×#6894	C₃	semidirect
9. C₇×#6894	C₃	semidirect
12. C₇×C₉×3₋¹⁺²	C₃	semidirect
13. C₇×C₉×3₋¹⁺²	C₃	semidirect
14. C₇×C₉×3₋¹⁺²	C₃	semidirect
15. C₃×C₇×C₉⋊C₉	C₃	semidirect
16. #10624901	C₇	direct (N × H)
55. #6900	C₃×C₇	semidirect
56. #6899	C₃×C₇	semidirect
57. #6896	C₃×C₇	semidirect
58. #6896	C₃×C₇	semidirect
59. #6895	C₃×C₇	semidirect
60. #6894	C₃×C₇	semidirect
61. #6894	C₃×C₇	semidirect
62. #6894	C₃×C₇	semidirect
65. C₉×3₋¹⁺²	C₃×C₇	semidirect
66. C₉×3₋¹⁺²	C₃×C₇	semidirect
67. C₉×3₋¹⁺²	C₃×C₇	semidirect
68. C₃×C₉⋊C₉	C₃×C₇	semidirect
76. C₇×3₋¹⁺²	3₋¹⁺²	semidirect
151. C₇×C₉	#737	semidirect
159. 3₋¹⁺²	C₇×3₋¹⁺²	semidirect
202. C₉	C₇×#737	semidirect
203. C₇	#10624901	direct (N × H)

Subgroups — C7×#10624901 #19100310

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624901 #19100310