Subgroups — C₇×#10624877 #19100286

Order 5103.

662 conjugacy classes of subgroups.

The subgroup lattice has 174 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	2	yes	maximal, complemented
6	C₇×#6894	C₃	1	4	yes	maximal, complemented
7	C₇×#6893	C₃	1	1	yes	maximal, characteristic
8	C₇×C₉⋊H(3,𝔽₃)	C₃	1	2	yes	maximal
9	C₇×C₉×3₋¹⁺²	C₃	1	6	yes	maximal, complemented
10	C₇×C₉×3₋¹⁺²	C₃	1	2	yes	maximal, complemented
11	C₇×C₉×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
12	C₇×#6887	C₃	1	3	yes	maximal, complemented
13	C₃×C₇×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
14	#10624877	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₃×C₇×3₋¹⁺²	C₃²	1	6	yes	—
16	C₃×C₇×3₋¹⁺²	C₃²	1	2	yes	—
17	C₃×C₇×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
18	C₃²×C₇×C₉	C₃²	1	2	yes	—
19	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
20	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
21	C₃²×C₇×C₉	C₃²	1	3	yes	—
22	C₇×C₉⋊C₉	C₃²	1	12	yes	—
23	C₇×C₉⋊C₉	C₃²	1	6	yes	—
24	C₇×C₉⋊C₉	C₃²	1	12	yes	—
25	C₇×C₉⋊C₉	C₃²	1	12	yes	—
26	C₇×C₉⋊C₉	C₃²	1	12	yes	—
27	C₇×C₉⋊C₉	C₃²	1	6	yes	—
28	C₇×C₉⋊C₉	C₃²	1	6	yes	—
29	C₇×C₃²⋊C₉	C₃²	1	6	yes	—
30	C₇×C₃²⋊C₉	C₃²	1	3	yes	—
31	C₇×C₃²⋊C₉	C₃²	1	2	yes	—
32	C₇×C₃²⋊C₉	C₃²	1	3	yes	—
33	C₇×C₃²⋊C₉	C₃²	1	3	yes	—
34	C₇×C₃²⋊C₉	C₃²	1	4	yes	—
35	C₇×C₃²⋊C₉	C₃²	1	6	yes	—
36	C₇×C₃²⋊C₉	C₃²	1	6	yes	—
37	C₇×C₉²	C₃²	1	1	yes	characteristic
38	C₇×C₉²	C₃²	1	2	yes	—
39	C₇×C₉²	C₃²	1	1	yes	characteristic
40	C₇×C₉²	C₃²	1	2	yes	—
41	C₇×C₉²	C₃²	1	1	yes	characteristic
42	C₇×C₉²	C₃²	1	2	yes	—
43	C₇×C₉²	C₃²	1	6	yes	—
44	#6899	C₃×C₇	1	6	yes	complemented
45	#6898	C₃×C₇	1	3	yes	complemented
46	#6897	C₃×C₇	1	6	yes	complemented
47	#6896	C₃×C₇	1	3	yes	complemented
48	#6895	C₃×C₇	1	2	yes	complemented
49	#6894	C₃×C₇	1	4	yes	complemented
50	#6893	C₃×C₇	1	1	yes	characteristic
51	C₉⋊H(3,𝔽₃)	C₃×C₇	1	2	yes	—
52	C₉×3₋¹⁺²	C₃×C₇	1	6	yes	complemented
53	C₉×3₋¹⁺²	C₃×C₇	1	2	yes	complemented
54	C₉×H(3,𝔽₃)	C₃×C₇	1	1	yes	characteristic
55	#6887	C₃×C₇	1	3	yes	complemented
56	C₃×C₉²	C₃×C₇	1	1	yes	characteristic, complemented
57	C₃³×C₇	C₃³	1	3	yes	—
58	C₃³×C₇	C₃³	1	1	yes	characteristic
59	C₇×3₋¹⁺²	—	3	6	no	—
60	C₇×3₋¹⁺²	—	3	18	no	—
61	C₇×H(3,𝔽₃)	—	3	3	no	—
62	C₃×C₇×C₉	—	3	3	no	—
63	C₃×C₇×C₉	—	3	3	no	—
64	C₃×C₇×C₉	—	3	9	no	—
65	C₃×C₇×C₉	—	3	6	no	—
66	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
67	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
68	C₃×C₇×C₉	C₃³	1	2	yes	—
69	C₃×C₇×C₉	C₃³	1	2	yes	—
70	C₃×C₇×C₉	C₃³	1	2	yes	—
71	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
72	C₃×C₇×C₉	C₃³	1	12	yes	—
73	C₃×C₇×C₉	C₃³	1	6	yes	—
74	C₃×C₇×C₉	C₃³	1	6	yes	—
75	C₃×C₇×C₉	C₃³	1	2	yes	—
76	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
77	C₃×3₋¹⁺²	C₃²×C₇	1	6	yes	—
78	C₃×3₋¹⁺²	C₃²×C₇	1	2	yes	—
79	C₃×H(3,𝔽₃)	C₃²×C₇	1	1	yes	characteristic
80	C₃²×C₉	C₃²×C₇	1	1	yes	characteristic
81	C₃²×C₉	C₃²×C₇	1	2	yes	—
82	C₃²×C₉	C₃²×C₇	1	1	yes	characteristic
83	C₃²×C₉	C₃²×C₇	1	3	yes	—
84	C₉⋊C₉	C₃²×C₇	1	12	yes	—
85	C₉⋊C₉	C₃²×C₇	1	6	yes	—
86	C₉⋊C₉	C₃²×C₇	1	12	yes	—
87	C₉⋊C₉	C₃²×C₇	1	12	yes	—
88	C₉⋊C₉	C₃²×C₇	1	12	yes	—
89	C₉⋊C₉	C₃²×C₇	1	6	yes	—
90	C₉⋊C₉	C₃²×C₇	1	6	yes	—
91	C₃²⋊C₉	C₃²×C₇	1	6	yes	—
92	C₃²⋊C₉	C₃²×C₇	1	3	yes	—
93	C₃²⋊C₉	C₃²×C₇	1	2	yes	—
94	C₃²⋊C₉	C₃²×C₇	1	3	yes	—
95	C₃²⋊C₉	C₃²×C₇	1	3	yes	—
96	C₃²⋊C₉	C₃²×C₇	1	4	yes	—
97	C₃²⋊C₉	C₃²×C₇	1	6	yes	—
98	C₃²⋊C₉	C₃²×C₇	1	6	yes	—
99	C₉²	C₃²×C₇	1	1	yes	characteristic
100	C₉²	C₃²×C₇	1	2	yes	—
101	C₉²	C₃²×C₇	1	1	yes	characteristic
102	C₉²	C₃²×C₇	1	2	yes	—
103	C₉²	C₃²×C₇	1	1	yes	characteristic
104	C₉²	C₃²×C₇	1	2	yes	—
105	C₉²	C₃²×C₇	1	6	yes	—
106	C₃²×C₇	—	3	1	no	—
107	C₃²×C₇	—	3	2	no	—
108	C₃²×C₇	—	3	3	no	—
109	C₃²×C₇	—	3	3	no	—
110	C₃²×C₇	—	3	6	no	—
111	C₃²×C₇	#737	1	3	yes	—
112	C₃²×C₇	C₃⁴	1	1	yes	characteristic
113	C₇×C₉	—	3	1	no	—
114	C₇×C₉	—	3	2	no	—
115	C₇×C₉	—	3	1	no	—
116	C₇×C₉	—	3	1	no	—
117	C₇×C₉	—	3	2	no	—
118	C₇×C₉	—	3	2	no	—
119	C₇×C₉	—	3	6	no	—
120	C₇×C₉	—	3	6	no	—
121	C₇×C₉	—	3	12	no	—
122	C₇×C₉	#737	1	3	yes	—
123	C₇×C₉	#737	1	6	yes	—
124	C₃³	C₃³×C₇	1	3	yes	—
125	C₃³	C₃³×C₇	1	1	yes	characteristic
126	3₋¹⁺²	—	3	6	no	—
127	3₋¹⁺²	—	3	18	no	—
128	H(3,𝔽₃)	—	3	3	no	—
129	C₃×C₉	—	3	3	no	—
130	C₃×C₉	—	3	3	no	—
131	C₃×C₉	—	3	9	no	—
132	C₃×C₉	—	3	6	no	—
133	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
134	C₃×C₉	C₃³×C₇	1	2	yes	—
135	C₃×C₉	C₃³×C₇	1	2	yes	—
136	C₃×C₉	C₃³×C₇	1	2	yes	—
137	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
138	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
139	C₃×C₉	C₃³×C₇	1	12	yes	—
140	C₃×C₉	C₃³×C₇	1	6	yes	—
141	C₃×C₉	C₃³×C₇	1	6	yes	—
142	C₃×C₉	C₃³×C₇	1	2	yes	—
143	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
144	C₃×C₇	—	3	3	no	—
145	C₃×C₇	—	9	3	no	—
146	C₃×C₇	C₃×#737	1	1	yes	characteristic
147	C₃×C₇	C₃×#737	1	1	yes	characteristic
148	C₃×C₇	C₃×#737	1	2	yes	—
149	C₃²	—	3	1	no	—
150	C₃²	—	3	2	no	—
151	C₃²	—	3	3	no	—
152	C₃²	—	3	3	no	—
153	C₃²	—	3	6	no	—
154	C₃²	C₇×#737	1	3	yes	—
155	C₃²	C₃⁴×C₇	1	1	yes	characteristic
156	C₉	—	3	1	no	—
157	C₉	—	3	2	no	—
158	C₉	—	3	1	no	—
159	C₉	—	3	1	no	—
160	C₉	—	3	2	no	—
161	C₉	—	3	2	no	—
162	C₉	—	3	6	no	—
163	C₉	—	3	6	no	—
164	C₉	—	3	12	no	—
165	C₉	C₇×#737	1	3	yes	—
166	C₉	C₇×#737	1	6	yes	—
167	C₇	#10624877	1	1	yes	characteristic, direct product factor, Sylow
168	C₃	—	3	3	no	—
169	C₃	—	9	3	no	—
170	C₃	C₃×C₇×#737	1	1	yes	characteristic
171	C₃	C₃×C₇×#737	1	1	yes	characteristic
172	C₃	C₃×C₇×#737	1	2	yes	—

	subgroup	G/H
center	C₃×C₇×C₉	C₃³
commutator, Frattini	C₃²	C₃⁴×C₇
socle	C₃²×C₇	C₃⁴
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃×C₇×C₉ ◁ 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
9. C₇×C₉×3₋¹⁺²	C₃	semidirect
10. C₇×C₉×3₋¹⁺²	C₃	semidirect
12. C₇×#6887	C₃	semidirect
13. C₃×C₇×C₉²	C₃	semidirect
14. #10624877	C₇	direct (N × H)
44. #6899	C₃×C₇	semidirect
45. #6898	C₃×C₇	semidirect
46. #6897	C₃×C₇	semidirect
47. #6896	C₃×C₇	semidirect
48. #6895	C₃×C₇	semidirect
49. #6894	C₃×C₇	semidirect
52. C₉×3₋¹⁺²	C₃×C₇	semidirect
53. C₉×3₋¹⁺²	C₃×C₇	semidirect
55. #6887	C₃×C₇	semidirect
56. C₃×C₉²	C₃×C₇	semidirect
167. C₇	#10624877	direct (N × H)

Subgroups — C7×#10624877 #19100286

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624877 #19100286