Subgroups — C₇×#10624899 #19100308

Order 5103.

740 conjugacy classes of subgroups.

The subgroup lattice has 180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
2	C₇×#6899	C₃	1	9	yes	maximal, complemented
3	C₇×#6896	C₃	1	9	yes	maximal, complemented
4	C₇×#6894	C₃	1	6	yes	maximal, complemented
5	C₇×#6894	C₃	1	6	yes	maximal, complemented
6	C₇×#6891	C₃	1	1	yes	maximal, characteristic
7	C₇×#6891	C₃	1	1	yes	maximal, characteristic
8	C₇×C₉×3₋¹⁺²	C₃	1	3	yes	maximal, complemented
9	C₇×C₉×3₋¹⁺²	C₃	1	3	yes	maximal, complemented
10	C₃×C₇×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
11	#10624899	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₃⁴×C₇	C₃²	1	1	yes	characteristic
13	C₃×C₇×3₋¹⁺²	—	3	9	no	—
14	C₃×C₇×3₋¹⁺²	C₃²	1	3	yes	—
15	C₃×C₇×3₋¹⁺²	C₃²	1	2	yes	—
16	C₃×C₇×3₋¹⁺²	C₃²	1	3	yes	—
17	C₃×C₇×3₋¹⁺²	C₃²	1	3	yes	—
18	C₃×C₇×3₋¹⁺²	C₃²	1	3	yes	—
19	C₃×C₇×3₋¹⁺²	C₃²	1	1	yes	characteristic
20	C₃²×C₇×C₉	C₃²	1	3	yes	—
21	C₃²×C₇×C₉	C₃²	1	3	yes	—
22	C₇×C₉⋊C₉	C₃²	1	18	yes	complemented
23	C₇×C₉⋊C₉	C₃²	1	18	yes	complemented
24	C₇×C₉⋊C₉	C₃²	1	36	yes	complemented
25	C₇×C₃²⋊C₉	C₃²	1	1	yes	characteristic
26	C₇×C₃²⋊C₉	C₃²	1	2	yes	—
27	C₇×C₃²⋊C₉	C₃²	1	3	yes	—
28	C₇×C₃²⋊C₉	C₃²	1	3	yes	—
29	C₇×C₃²⋊C₉	C₃²	1	3	yes	—
30	C₇×C₃²⋊C₉	C₃²	1	3	yes	—
31	C₇×C₃²⋊C₉	C₃²	1	3	yes	—
32	C₇×C₃²⋊C₉	C₃²	1	3	yes	—
33	C₇×C₃²⋊C₉	C₃²	1	3	yes	—
34	C₇×C₃²⋊C₉	C₃²	1	3	yes	—
35	C₇×C₉²	C₃²	1	9	yes	complemented
36	C₃²×3₋¹⁺²	C₃×C₇	1	1	yes	characteristic
37	#6899	C₃×C₇	1	9	yes	complemented
38	#6896	C₃×C₇	1	9	yes	complemented
39	#6894	C₃×C₇	1	6	yes	complemented
40	#6894	C₃×C₇	1	6	yes	complemented
41	#6891	C₃×C₇	1	1	yes	characteristic
42	#6891	C₃×C₇	1	1	yes	characteristic
43	C₉×3₋¹⁺²	C₃×C₇	1	3	yes	complemented
44	C₉×3₋¹⁺²	C₃×C₇	1	3	yes	complemented
45	C₃×C₃²⋊C₉	C₃×C₇	1	1	yes	characteristic
46	C₃³×C₇	—	3	3	no	—
47	C₃³×C₇	—	3	3	no	—
48	C₃³×C₇	—	9	1	no	—
49	C₃³×C₇	—	9	1	no	—
50	C₃³×C₇	C₃³	1	1	yes	characteristic
51	C₃³×C₇	C₃³	1	1	yes	characteristic
52	C₃³×C₇	C₃³	1	1	yes	characteristic
53	C₃³×C₇	C₃³	1	1	yes	characteristic
54	C₇×3₋¹⁺²	—	3	6	no	—
55	C₇×3₋¹⁺²	—	3	9	no	—
56	C₇×3₋¹⁺²	—	3	9	no	—
57	C₇×3₋¹⁺²	—	3	9	no	—
58	C₇×3₋¹⁺²	—	9	3	no	—
59	C₇×3₋¹⁺²	3₋¹⁺²	1	9	yes	complemented
60	C₃×C₇×C₉	—	3	9	no	—
61	C₃×C₇×C₉	—	9	3	no	—
62	C₃×C₇×C₉	C₃³	1	3	yes	—
63	C₃×C₇×C₉	C₃³	1	9	yes	—
64	C₃×C₇×C₉	C₃³	1	9	yes	—
65	C₃×C₇×C₉	C₃³	1	6	yes	—
66	C₃×C₇×C₉	C₃³	1	6	yes	—
67	C₃×C₇×C₉	C₃³	1	3	yes	—
68	C₃⁴	C₃²×C₇	1	1	yes	characteristic
69	C₃×3₋¹⁺²	—	3	9	no	—
70	C₃×3₋¹⁺²	C₃²×C₇	1	2	yes	—
71	C₃×3₋¹⁺²	C₃²×C₇	1	3	yes	—
72	C₃×3₋¹⁺²	C₃²×C₇	1	3	yes	—
73	C₃×3₋¹⁺²	C₃²×C₇	1	3	yes	—
74	C₃×3₋¹⁺²	C₃²×C₇	1	3	yes	—
75	C₃×3₋¹⁺²	C₃²×C₇	1	1	yes	characteristic
76	C₃²×C₉	C₃²×C₇	1	3	yes	—
77	C₃²×C₉	C₃²×C₇	1	3	yes	—
78	C₉⋊C₉	C₃²×C₇	1	18	yes	complemented
79	C₉⋊C₉	C₃²×C₇	1	18	yes	complemented
80	C₉⋊C₉	C₃²×C₇	1	36	yes	complemented
81	C₃²⋊C₉	C₃²×C₇	1	1	yes	characteristic
82	C₃²⋊C₉	C₃²×C₇	1	2	yes	—
83	C₃²⋊C₉	C₃²×C₇	1	3	yes	—
84	C₃²⋊C₉	C₃²×C₇	1	3	yes	—
85	C₃²⋊C₉	C₃²×C₇	1	3	yes	—
86	C₃²⋊C₉	C₃²×C₇	1	3	yes	—
87	C₃²⋊C₉	C₃²×C₇	1	3	yes	—
88	C₃²⋊C₉	C₃²×C₇	1	3	yes	—
89	C₃²⋊C₉	C₃²×C₇	1	3	yes	—
90	C₃²⋊C₉	C₃²×C₇	1	3	yes	—
91	C₉²	C₃²×C₇	1	9	yes	complemented
92	C₃²×C₇	—	3	1	no	—
93	C₃²×C₇	—	3	1	no	—
94	C₃²×C₇	—	3	1	no	—
95	C₃²×C₇	—	3	1	no	—
96	C₃²×C₇	—	3	1	no	—
97	C₃²×C₇	—	3	1	no	—
98	C₃²×C₇	—	3	1	no	—
99	C₃²×C₇	—	3	1	no	—
100	C₃²×C₇	—	3	1	no	—
101	C₃²×C₇	—	3	1	no	—
102	C₃²×C₇	—	3	1	no	—
103	C₃²×C₇	—	3	1	no	—
104	C₃²×C₇	—	3	1	no	—
105	C₃²×C₇	—	3	1	no	—
106	C₃²×C₇	—	9	9	no	—
107	C₃²×C₇	C₃×3₋¹⁺²	1	3	yes	—
108	C₃²×C₇	#737	1	3	yes	—
109	C₃²×C₇	C₃⁴	1	1	yes	characteristic
110	C₇×C₉	—	3	6	no	—
111	C₇×C₉	—	3	9	no	—
112	C₇×C₉	—	3	3	no	—
113	C₇×C₉	—	3	6	no	—
114	C₇×C₉	—	3	9	no	—
115	C₇×C₉	C₃×3₋¹⁺²	1	9	yes	—
116	C₃³	—	3	3	no	—
117	C₃³	—	3	3	no	—
118	C₃³	—	9	1	no	—
119	C₃³	—	9	1	no	—
120	C₃³	C₃³×C₇	1	1	yes	characteristic
121	C₃³	C₃³×C₇	1	1	yes	characteristic
122	C₃³	C₃³×C₇	1	1	yes	characteristic
123	C₃³	C₃³×C₇	1	1	yes	characteristic
124	3₋¹⁺²	—	3	6	no	—
125	3₋¹⁺²	—	3	9	no	—
126	3₋¹⁺²	—	3	9	no	—
127	3₋¹⁺²	—	3	9	no	—
128	3₋¹⁺²	—	9	3	no	—
129	3₋¹⁺²	C₇×3₋¹⁺²	1	9	yes	complemented
130	C₃×C₉	—	3	9	no	—
131	C₃×C₉	—	9	3	no	—
132	C₃×C₉	C₃³×C₇	1	3	yes	—
133	C₃×C₉	C₃³×C₇	1	9	yes	—
134	C₃×C₉	C₃³×C₇	1	9	yes	—
135	C₃×C₉	C₃³×C₇	1	6	yes	—
136	C₃×C₉	C₃³×C₇	1	6	yes	—
137	C₃×C₉	C₃³×C₇	1	3	yes	—
138	C₃×C₇	—	3	3	no	—
139	C₃×C₇	—	3	3	no	—
140	C₃×C₇	—	9	1	no	—
141	C₃×C₇	—	9	1	no	—
142	C₃×C₇	C₃²×3₋¹⁺²	1	1	yes	characteristic
143	C₃×C₇	C₃×#737	1	1	yes	characteristic
144	C₃×C₇	3₋¹⁺⁴	1	1	yes	characteristic
145	C₃×C₇	3₋¹⁺⁴	1	1	yes	characteristic
146	C₃²	—	3	1	no	—
147	C₃²	—	3	1	no	—
148	C₃²	—	3	1	no	—
149	C₃²	—	3	1	no	—
150	C₃²	—	3	1	no	—
151	C₃²	—	3	1	no	—
152	C₃²	—	3	1	no	—
153	C₃²	—	3	1	no	—
154	C₃²	—	3	1	no	—
155	C₃²	—	3	1	no	—
156	C₃²	—	3	1	no	—
157	C₃²	—	3	1	no	—
158	C₃²	—	3	1	no	—
159	C₃²	—	3	1	no	—
160	C₃²	—	9	9	no	—
161	C₃²	C₃×C₇×3₋¹⁺²	1	3	yes	—
162	C₃²	C₇×#737	1	3	yes	—
163	C₃²	C₃⁴×C₇	1	1	yes	characteristic
164	C₉	—	3	6	no	—
165	C₉	—	3	9	no	—
166	C₉	—	3	3	no	—
167	C₉	—	3	6	no	—
168	C₉	—	3	9	no	—
169	C₉	C₃×C₇×3₋¹⁺²	1	9	yes	—
170	C₇	#10624899	1	1	yes	characteristic, direct product factor, Sylow
171	C₃	—	3	3	no	—
172	C₃	—	3	3	no	—
173	C₃	—	9	1	no	—
174	C₃	—	9	1	no	—
175	C₃	C₃²×C₇×3₋¹⁺²	1	1	yes	characteristic
176	C₃	C₃×C₇×#737	1	1	yes	characteristic
177	C₃	C₇×3₋¹⁺⁴	1	1	yes	characteristic
178	C₃	C₇×3₋¹⁺⁴	1	1	yes	characteristic

	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×#6899	C₃	semidirect
3. C₇×#6896	C₃	semidirect
4. C₇×#6894	C₃	semidirect
5. C₇×#6894	C₃	semidirect
8. C₇×C₉×3₋¹⁺²	C₃	semidirect
9. C₇×C₉×3₋¹⁺²	C₃	semidirect
11. #10624899	C₇	direct (N × H)
22. C₇×C₉⋊C₉	C₃²	semidirect
23. C₇×C₉⋊C₉	C₃²	semidirect
24. C₇×C₉⋊C₉	C₃²	semidirect
35. C₇×C₉²	C₃²	semidirect
37. #6899	C₃×C₇	semidirect
38. #6896	C₃×C₇	semidirect
39. #6894	C₃×C₇	semidirect
40. #6894	C₃×C₇	semidirect
43. C₉×3₋¹⁺²	C₃×C₇	semidirect
44. C₉×3₋¹⁺²	C₃×C₇	semidirect
59. C₇×3₋¹⁺²	3₋¹⁺²	semidirect
78. C₉⋊C₉	C₃²×C₇	semidirect
79. C₉⋊C₉	C₃²×C₇	semidirect
80. C₉⋊C₉	C₃²×C₇	semidirect
91. C₉²	C₃²×C₇	semidirect
129. 3₋¹⁺²	C₇×3₋¹⁺²	semidirect
170. C₇	#10624899	direct (N × H)

Subgroups — C7×#10624899 #19100308

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624899 #19100308