Subgroups — C₂×C₇×#2863 #13213849

Order 1792.

2142 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×#2863	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₇×#391	C₂	1	3	yes	maximal
3	C₂×C₇×#389	C₂	1	3	yes	maximal
4	C₂×C₇×#387	C₂	1	6	yes	maximal
5	C₂×C₇×#383	C₂	1	2	yes	maximal
6	C₂×C₄³×C₇	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
8	C₂²×C₇×C₄⋊C₄	C₂²	1	6	yes	—
9	C₂²×C₇×C₄⋊C₄	C₂²	1	3	yes	—
10	C₂²×C₄²×C₇	C₂²	1	3	yes	—
11	C₂²×C₄²×C₇	C₂²	1	3	yes	—
12	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
13	C₇×#391	C₂²	1	24	yes	—
14	C₇×#389	C₂²	1	24	yes	—
15	C₇×#387	C₂²	1	48	yes	—
16	C₇×#383	C₂²	1	16	yes	—
17	C₂×C₇×#95	C₂²	1	6	yes	—
18	C₂×C₇×#95	C₂²	1	6	yes	—
19	C₂×C₇×#95	C₂²	1	6	yes	—
20	C₄³×C₇	C₂²	1	8	yes	—
21	C₂×#2863	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂²×C₇×Q₈	—	2	12	no	—
23	C₂²×C₇×Q₈	C₂³	1	4	yes	—
24	C₂³×C₄×C₇	C₂³	1	2	yes	—
25	C₂³×C₄×C₇	C₂³	1	6	yes	—
26	C₂³×C₄×C₇	C₂³	1	3	yes	—
27	C₂³×C₄×C₇	C₂³	1	3	yes	—
28	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
29	C₂×C₇×C₄⋊C₄	—	2	24	no	—
30	C₂×C₇×C₄⋊C₄	—	2	12	no	—
31	C₂×C₇×C₄⋊C₄	C₂³	1	24	yes	—
32	C₂×C₇×C₄⋊C₄	C₂³	1	12	yes	—
33	C₂×C₄²×C₇	—	2	12	no	—
34	C₂×C₄²×C₇	—	2	12	no	—
35	C₂×C₄²×C₇	Q₈	1	8	yes	complemented
36	C₂×C₄²×C₇	C₂³	1	12	yes	—
37	C₂×C₄²×C₇	C₂³	1	12	yes	—
38	C₂×C₄²×C₇	C₂³	1	4	yes	—
39	C₇×#95	C₂³	1	24	yes	—
40	C₇×#95	C₂³	1	24	yes	—
41	C₇×#95	C₂³	1	24	yes	—
42	#2863	C₂×C₇	1	16	yes	direct product factor
43	C₂×#391	C₂×C₇	1	3	yes	—
44	C₂×#389	C₂×C₇	1	3	yes	—
45	C₂×#387	C₂×C₇	1	6	yes	—
46	C₂×#383	C₂×C₇	1	2	yes	—
47	C₂×C₄³	C₂×C₇	1	1	yes	characteristic
48	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
49	C₂×C₇×Q₈	—	2	24	no	—
50	C₂×C₇×Q₈	—	4	16	no	—
51	C₂²×C₄×C₇	—	2	6	no	—
52	C₂²×C₄×C₇	—	2	6	no	—
53	C₂²×C₄×C₇	—	2	6	no	—
54	C₂²×C₄×C₇	—	2	6	no	—
55	C₂²×C₄×C₇	—	2	12	no	—
56	C₂²×C₄×C₇	—	2	24	no	—
57	C₂²×C₄×C₇	—	2	12	no	—
58	C₂²×C₄×C₇	C₂×Q₈	1	12	yes	—
59	C₂²×C₄×C₇	#41	1	12	yes	—
60	C₂²×C₄×C₇	#41	1	12	yes	—
61	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
62	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
63	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
64	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
65	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
66	C₇×C₄⋊C₄	—	2	48	no	—
67	C₇×C₄⋊C₄	—	2	24	no	—
68	C₄²×C₇	—	2	24	no	—
69	C₄²×C₇	—	2	24	no	—
70	C₄²×C₇	C₂×Q₈	1	16	yes	complemented
71	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
72	C₂²×C₄⋊C₄	C₂²×C₇	1	6	yes	—
73	C₂²×C₄⋊C₄	C₂²×C₇	1	3	yes	—
74	C₂²×C₄²	C₂²×C₇	1	3	yes	—
75	C₂²×C₄²	C₂²×C₇	1	3	yes	—
76	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
77	#391	C₂²×C₇	1	24	yes	—
78	#389	C₂²×C₇	1	24	yes	—
79	#387	C₂²×C₇	1	48	yes	—
80	#383	C₂²×C₇	1	16	yes	—
81	C₂×#95	C₂²×C₇	1	6	yes	—
82	C₂×#95	C₂²×C₇	1	6	yes	—
83	C₂×#95	C₂²×C₇	1	6	yes	—
84	C₄³	C₂²×C₇	1	8	yes	—
85	C₂³×C₇	C₂²×Q₈	1	2	yes	—
86	C₂³×C₇	C₂×#41	1	6	yes	—
87	C₂³×C₇	C₂×#41	1	6	yes	—
88	C₂³×C₇	C₂⁵	1	1	yes	characteristic
89	C₇×Q₈	—	4	16	no	—
90	C₂×C₄×C₇	—	2	24	no	—
91	C₂×C₄×C₇	—	2	24	no	—
92	C₂×C₄×C₇	—	2	6	no	—
93	C₂×C₄×C₇	—	2	6	no	—
94	C₂×C₄×C₇	—	2	6	no	—
95	C₂×C₄×C₇	—	2	6	no	—
96	C₂×C₄×C₇	—	2	12	no	—
97	C₂×C₄×C₇	—	2	24	no	—
98	C₂×C₄×C₇	—	2	12	no	—
99	C₂×C₄×C₇	—	4	8	no	—
100	C₂×C₄×C₇	—	4	24	no	—
101	C₂×C₄×C₇	#126	1	16	yes	—
102	C₂×C₄×C₇	C₂²×Q₈	1	12	yes	—
103	C₂×C₄×C₇	C₂×#41	1	12	yes	—
104	C₂×C₄×C₇	C₂×#41	1	12	yes	—
105	C₂²×Q₈	—	2	12	no	—
106	C₂²×Q₈	C₂³×C₇	1	4	yes	—
107	C₂³×C₄	C₂³×C₇	1	6	yes	—
108	C₂³×C₄	C₂³×C₇	1	2	yes	—
109	C₂³×C₄	C₂³×C₇	1	3	yes	—
110	C₂³×C₄	C₂³×C₇	1	3	yes	—
111	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
112	C₂×C₄⋊C₄	—	2	24	no	—
113	C₂×C₄⋊C₄	—	2	12	no	—
114	C₂×C₄⋊C₄	C₂³×C₇	1	24	yes	—
115	C₂×C₄⋊C₄	C₂³×C₇	1	12	yes	—
116	C₂×C₄²	—	2	12	no	—
117	C₂×C₄²	—	2	12	no	—
118	C₂×C₄²	C₇×Q₈	1	8	yes	complemented
119	C₂×C₄²	C₂³×C₇	1	12	yes	—
120	C₂×C₄²	C₂³×C₇	1	12	yes	—
121	C₂×C₄²	C₂³×C₇	1	4	yes	—
122	#95	C₂³×C₇	1	24	yes	—
123	#95	C₂³×C₇	1	24	yes	—
124	#95	C₂³×C₇	1	24	yes	—
125	C₂²×C₇	C₂×#126	1	4	yes	—
126	C₂²×C₇	#529	1	12	yes	—
127	C₂²×C₇	#533	1	12	yes	—
128	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
129	C₂²×C₇	C₂²×#41	1	3	yes	—
130	C₂²×C₇	C₂²×#41	1	3	yes	—
131	C₄×C₇	—	2	12	no	—
132	C₄×C₇	—	2	12	no	—
133	C₄×C₇	—	4	4	no	—
134	C₄×C₇	—	4	12	no	—
135	C₄×C₇	C₂×#126	1	8	yes	—
136	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
137	C₂×Q₈	—	2	24	no	—
138	C₂×Q₈	—	4	16	no	—
139	C₂²×C₄	—	2	6	no	—
140	C₂²×C₄	—	2	6	no	—
141	C₂²×C₄	—	2	6	no	—
142	C₂²×C₄	—	2	6	no	—
143	C₂²×C₄	—	2	12	no	—
144	C₂²×C₄	—	2	24	no	—
145	C₂²×C₄	—	2	12	no	—
146	C₂²×C₄	C₂×C₇×Q₈	1	12	yes	—
147	C₂²×C₄	C₇×#41	1	12	yes	—
148	C₂²×C₄	C₇×#41	1	12	yes	—
149	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
150	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
151	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
152	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
153	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
154	C₄⋊C₄	—	2	48	no	—
155	C₄⋊C₄	—	2	24	no	—
156	C₄²	—	2	24	no	—
157	C₄²	—	2	24	no	—
158	C₄²	C₂×C₇×Q₈	1	16	yes	complemented
159	C₂×C₇	#2863	1	8	yes	direct product factor
160	C₂×C₇	C₂²×#126	1	1	yes	characteristic
161	C₂×C₇	C₂×#529	1	3	yes	—
162	C₂×C₇	C₂×#533	1	3	yes	—
163	C₂³	C₂²×C₇×Q₈	1	2	yes	—
164	C₂³	C₂×C₇×#41	1	6	yes	—
165	C₂³	C₂×C₇×#41	1	6	yes	—
166	C₂³	C₂⁵×C₇	1	1	yes	characteristic
167	Q₈	—	4	16	no	—
168	C₂×C₄	—	2	6	no	—
169	C₂×C₄	—	2	6	no	—
170	C₂×C₄	—	2	6	no	—
171	C₂×C₄	—	2	6	no	—
172	C₂×C₄	—	2	24	no	—
173	C₂×C₄	—	2	24	no	—
174	C₂×C₄	—	2	12	no	—
175	C₂×C₄	—	2	24	no	—
176	C₂×C₄	—	2	12	no	—
177	C₂×C₄	—	4	8	no	—
178	C₂×C₄	—	4	24	no	—
179	C₂×C₄	C₇×#126	1	16	yes	—
180	C₂×C₄	C₂²×C₇×Q₈	1	12	yes	—
181	C₂×C₄	C₂×C₇×#41	1	12	yes	—
182	C₂×C₄	C₂×C₇×#41	1	12	yes	—
183	C₇	C₂×#2863	1	1	yes	characteristic, direct product factor, Sylow
184	C₂²	C₂×C₇×#126	1	4	yes	—
185	C₂²	C₇×#529	1	12	yes	—
186	C₂²	C₇×#533	1	12	yes	—
187	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
188	C₂²	C₂²×C₇×#41	1	3	yes	—
189	C₂²	C₂²×C₇×#41	1	3	yes	—
190	C₄	—	2	12	no	—
191	C₄	—	2	12	no	—
192	C₄	—	4	4	no	—
193	C₄	—	4	12	no	—
194	C₄	C₂×C₇×#126	1	8	yes	—
195	C₂	C₇×#2863	1	8	yes	direct product factor
196	C₂	C₂²×C₇×#126	1	1	yes	characteristic
197	C₂	C₂×C₇×#529	1	3	yes	—
198	C₂	C₂×C₇×#533	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#2863	C₂	direct (N × H)
21. C₂×#2863	C₇	direct (N × H)
35. C₂×C₄²×C₇	Q₈	semidirect
42. #2863	C₂×C₇	direct (N × H)
70. C₄²×C₇	C₂×Q₈	semidirect
118. C₂×C₄²	C₇×Q₈	semidirect
158. C₄²	C₂×C₇×Q₈	semidirect
159. C₂×C₇	#2863	direct (N × H)
183. C₇	C₂×#2863	direct (N × H)
195. C₂	C₇×#2863	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇×#2863	2
C₂×C₇×#391	2
C₂×C₇×#389	2
C₂×C₇×#387	2
C₂×C₇×#383	2
C₂×C₄³×C₇	2
C₂×#2863	7

Subgroups — C2×C7×#2863 #13213849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2863 #13213849