Subgroups — C₂×C₇×#1281 #13185133

Order 1792.

678 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#431	C₂	1	2	yes	maximal
2	C₂²×C₇×#97	C₂	1	1	yes	maximal, characteristic
3	C₇×#1281	C₂	1	4	yes	maximal, direct product factor
4	C₂³×C₇×C₈	C₄	1	2	yes	—
5	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
6	C₇×#431	—	2	2	no	—
7	C₇×#431	—	2	2	no	—
8	C₇×#431	C₄	1	4	yes	—
9	C₇×#431	C₂²	1	4	yes	—
10	C₂×C₇×C₄⋊C₈	—	2	2	no	—
11	C₂×C₇×C₂²⋊C₈	C₄	1	4	yes	—
12	C₂×C₇×#97	—	2	2	no	—
13	C₂×C₇×#97	—	2	2	no	—
14	C₂×C₇×#97	C₄	1	2	yes	—
15	C₂×C₇×#97	C₂²	1	2	yes	—
16	C₂×C₄×C₇×C₈	—	2	2	no	—
17	C₂×#1281	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂³×C₄×C₇	C₂×C₄	1	2	yes	—
19	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₇×C₈	—	2	2	no	—
21	C₂²×C₇×C₈	—	2	2	no	—
22	C₂²×C₇×C₈	—	2	4	no	—
23	C₂²×C₇×C₈	—	2	4	no	—
24	C₂²×C₇×C₈	C₈	1	8	yes	complemented
25	C₂²×C₇×C₈	C₂×C₄	1	4	yes	—
26	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₇	D₄	1	2	yes	—
29	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
30	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
31	C₂×C₄²×C₇	D₄	1	2	yes	—
32	C₂×C₄²×C₇	Q₈	1	1	yes	characteristic
33	C₂×C₄²×C₇	Q₈	1	1	yes	characteristic
34	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
35	C₇×C₄⋊C₈	—	2	4	no	—
36	C₇×C₄⋊C₈	—	2	4	no	—
37	C₇×C₂²⋊C₈	—	2	4	no	—
38	C₇×C₂²⋊C₈	C₂×C₄	1	8	yes	—
39	C₇×#97	—	2	4	no	—
40	C₇×#97	—	2	4	no	—
41	C₄×C₇×C₈	—	2	4	no	—
42	C₄×C₇×C₈	—	2	4	no	—
43	C₂×#431	C₂×C₇	1	2	yes	—
44	C₂²×#97	C₂×C₇	1	1	yes	characteristic
45	#1281	C₂×C₇	1	4	yes	direct product factor
46	C₂⁴×C₇	C₄²	1	1	yes	characteristic
47	C₂²×C₄×C₇	—	4	4	no	—
48	C₂²×C₄×C₇	C₄²	1	2	yes	—
49	C₂²×C₄×C₇	C₄²	1	1	yes	characteristic
50	C₂²×C₄×C₇	C₂²⋊C₄	1	2	yes	—
51	C₂²×C₄×C₇	C₂²⋊C₄	1	2	yes	—
52	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
53	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₇	C₄⋊C₄	1	2	yes	—
55	C₂²×C₄×C₇	C₄⋊C₄	1	2	yes	—
56	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
57	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
58	C₂²×C₄×C₇	C₂×C₈	1	4	yes	—
59	C₂²×C₄×C₇	M₁₆	1	4	yes	—
60	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
61	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₇×C₈	—	2	8	no	—
63	C₂×C₇×C₈	—	2	8	no	—
64	C₂×C₇×C₈	—	2	4	no	—
65	C₂×C₇×C₈	—	2	4	no	—
66	C₂×C₇×C₈	—	2	8	no	—
67	C₂×C₇×C₈	—	4	8	no	—
68	C₂×C₇×C₈	C₂×C₈	1	8	yes	complemented
69	C₄²×C₇	C₂²⋊C₄	1	2	yes	—
70	C₄²×C₇	C₂²⋊C₄	1	2	yes	—
71	C₄²×C₇	C₂²⋊C₄	1	2	yes	—
72	C₄²×C₇	C₄⋊C₄	1	1	yes	characteristic
73	C₄²×C₇	C₄⋊C₄	1	1	yes	characteristic
74	C₄²×C₇	C₄⋊C₄	1	2	yes	—
75	C₄²×C₇	C₄⋊C₄	1	2	yes	—
76	C₄²×C₇	C₂×D₄	1	2	yes	—
77	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₇	C₂×Q₈	1	1	yes	characteristic
79	C₂³×C₈	C₄×C₇	1	2	yes	—
80	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
81	#431	—	2	2	no	—
82	#431	—	2	2	no	—
83	#431	C₄×C₇	1	4	yes	—
84	#431	C₂²×C₇	1	4	yes	—
85	C₂×C₄⋊C₈	—	2	2	no	—
86	C₂×C₂²⋊C₈	C₄×C₇	1	4	yes	—
87	C₂×#97	—	2	2	no	—
88	C₂×#97	—	2	2	no	—
89	C₂×#97	C₄×C₇	1	2	yes	—
90	C₂×#97	C₂²×C₇	1	2	yes	—
91	C₂×C₄×C₈	—	2	2	no	—
92	C₂³×C₇	—	2	4	no	—
93	C₂³×C₇	#95	1	1	yes	characteristic
94	C₂³×C₇	#95	1	1	yes	characteristic
95	C₂³×C₇	C₄×C₈	1	2	yes	—
96	C₂³×C₇	#97	1	2	yes	—
97	C₂³×C₇	C₂×C₄²	1	1	yes	characteristic
98	C₂×C₄×C₇	—	2	4	no	—
99	C₂×C₄×C₇	—	2	4	no	—
100	C₂×C₄×C₇	—	4	2	no	—
101	C₂×C₄×C₇	—	4	2	no	—
102	C₂×C₄×C₇	—	4	2	no	—
103	C₂×C₄×C₇	—	4	2	no	—
104	C₂×C₄×C₇	#95	1	2	yes	—
105	C₂×C₄×C₇	#95	1	2	yes	—
106	C₂×C₄×C₇	#95	1	1	yes	characteristic
107	C₂×C₄×C₇	#95	1	1	yes	characteristic
108	C₂×C₄×C₇	C₄×C₈	1	2	yes	—
109	C₂×C₄×C₇	#97	1	2	yes	—
110	C₂×C₄×C₇	C₂²⋊C₈	1	4	yes	—
111	C₂×C₄×C₇	C₂²⋊C₈	1	4	yes	—
112	C₂×C₄×C₇	C₄⋊C₈	1	4	yes	—
113	C₂×C₄×C₇	C₄⋊C₈	1	4	yes	—
114	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
115	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
116	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
117	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₄×C₇	C₂²×C₈	1	2	yes	—
119	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
120	C₇×C₈	—	2	8	no	—
121	C₇×C₈	—	4	8	no	—
122	C₂³×C₄	C₂×C₄×C₇	1	2	yes	—
123	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
124	C₂²×C₈	—	2	2	no	—
125	C₂²×C₈	—	2	2	no	—
126	C₂²×C₈	—	2	4	no	—
127	C₂²×C₈	—	2	4	no	—
128	C₂²×C₈	C₇×C₈	1	8	yes	complemented
129	C₂²×C₈	C₂×C₄×C₇	1	4	yes	—
130	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
131	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
132	C₂×C₄²	C₇×D₄	1	2	yes	—
133	C₂×C₄²	C₇×D₄	1	2	yes	—
134	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
135	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
136	C₂×C₄²	C₇×Q₈	1	1	yes	characteristic
137	C₂×C₄²	C₇×Q₈	1	1	yes	characteristic
138	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
139	C₄⋊C₈	—	2	4	no	—
140	C₄⋊C₈	—	2	4	no	—
141	C₂²⋊C₈	—	2	4	no	—
142	C₂²⋊C₈	C₂×C₄×C₇	1	8	yes	—
143	#97	—	2	4	no	—
144	#97	—	2	4	no	—
145	C₄×C₈	—	2	4	no	—
146	C₄×C₈	—	2	4	no	—
147	C₂²×C₇	—	2	4	no	—
148	C₂²×C₇	—	2	4	no	—
149	C₂²×C₇	—	2	2	no	—
150	C₂²×C₇	—	2	2	no	—
151	C₂²×C₇	#336	1	2	yes	—
152	C₂²×C₇	#336	1	2	yes	—
153	C₂²×C₇	#344	1	4	yes	—
154	C₂²×C₇	C₂×#95	1	1	yes	characteristic
155	C₂²×C₇	C₂×C₄×C₈	1	1	yes	characteristic
156	C₂²×C₇	C₂×#97	1	1	yes	characteristic
157	C₄×C₇	—	2	2	no	—
158	C₄×C₇	—	2	2	no	—
159	C₄×C₇	—	2	2	no	—
160	C₄×C₇	—	2	2	no	—
161	C₄×C₇	#336	1	2	yes	—
162	C₄×C₇	#336	1	2	yes	—
163	C₄×C₇	C₂×C₂²⋊C₈	1	2	yes	—
164	C₄×C₇	C₂×C₄⋊C₈	1	2	yes	—
165	C₂⁴	C₄²×C₇	1	1	yes	characteristic
166	C₂²×C₄	—	4	4	no	—
167	C₂²×C₄	C₄²×C₇	1	2	yes	—
168	C₂²×C₄	C₄²×C₇	1	1	yes	characteristic
169	C₂²×C₄	C₇×C₂²⋊C₄	1	2	yes	—
170	C₂²×C₄	C₇×C₂²⋊C₄	1	2	yes	—
171	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
172	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
173	C₂²×C₄	C₇×C₄⋊C₄	1	2	yes	—
174	C₂²×C₄	C₇×C₄⋊C₄	1	2	yes	—
175	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
176	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
177	C₂²×C₄	C₂×C₇×C₈	1	4	yes	—
178	C₂²×C₄	C₇×M₁₆	1	4	yes	—
179	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
180	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
181	C₂×C₈	—	2	8	no	—
182	C₂×C₈	—	2	8	no	—
183	C₂×C₈	—	2	4	no	—
184	C₂×C₈	—	2	4	no	—
185	C₂×C₈	—	2	8	no	—
186	C₂×C₈	—	4	8	no	—
187	C₂×C₈	C₂×C₇×C₈	1	8	yes	complemented
188	C₄²	C₇×C₂²⋊C₄	1	2	yes	—
189	C₄²	C₇×C₂²⋊C₄	1	2	yes	—
190	C₄²	C₇×C₂²⋊C₄	1	2	yes	—
191	C₄²	C₇×C₄⋊C₄	1	1	yes	characteristic
192	C₄²	C₇×C₄⋊C₄	1	1	yes	characteristic
193	C₄²	C₇×C₄⋊C₄	1	2	yes	—
194	C₄²	C₇×C₄⋊C₄	1	2	yes	—
195	C₄²	C₂×C₇×D₄	1	2	yes	—
196	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
197	C₄²	C₂×C₇×Q₈	1	1	yes	characteristic
198	C₂×C₇	—	2	2	no	—
199	C₂×C₇	—	2	1	no	—
200	C₂×C₇	—	2	1	no	—
201	C₂×C₇	#1281	1	4	yes	direct product factor
202	C₂×C₇	C₂×#336	1	1	yes	characteristic
203	C₂×C₇	C₂×#344	1	2	yes	—
204	C₂³	—	2	4	no	—
205	C₂³	C₇×#95	1	1	yes	characteristic
206	C₂³	C₇×#95	1	1	yes	characteristic
207	C₂³	C₄×C₇×C₈	1	2	yes	—
208	C₂³	C₇×#97	1	2	yes	—
209	C₂³	C₂×C₄²×C₇	1	1	yes	characteristic
210	C₂×C₄	—	2	4	no	—
211	C₂×C₄	—	2	4	no	—
212	C₂×C₄	—	4	2	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	C₇×#95	1	2	yes	—
217	C₂×C₄	C₇×#95	1	2	yes	—
218	C₂×C₄	C₇×#95	1	1	yes	characteristic
219	C₂×C₄	C₇×#95	1	1	yes	characteristic
220	C₂×C₄	C₄×C₇×C₈	1	2	yes	—
221	C₂×C₄	C₇×#97	1	2	yes	—
222	C₂×C₄	C₇×C₂²⋊C₈	1	4	yes	—
223	C₂×C₄	C₇×C₂²⋊C₈	1	4	yes	—
224	C₂×C₄	C₇×C₄⋊C₈	1	4	yes	—
225	C₂×C₄	C₇×C₄⋊C₈	1	4	yes	—
226	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
227	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
229	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
230	C₂×C₄	C₂²×C₇×C₈	1	2	yes	—
231	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
232	C₈	—	2	8	no	—
233	C₈	—	4	8	no	—
234	C₇	C₂×#1281	1	1	yes	characteristic, direct product factor, Sylow
235	C₂²	—	2	2	no	—
236	C₂²	—	2	2	no	—
237	C₂²	—	2	4	no	—
238	C₂²	—	2	4	no	—
239	C₂²	C₇×#336	1	2	yes	—
240	C₂²	C₇×#336	1	2	yes	—
241	C₂²	C₇×#344	1	4	yes	—
242	C₂²	C₂×C₇×#95	1	1	yes	characteristic
243	C₂²	C₂×C₄×C₇×C₈	1	1	yes	characteristic
244	C₂²	C₂×C₇×#97	1	1	yes	characteristic
245	C₄	—	2	2	no	—
246	C₄	—	2	2	no	—
247	C₄	—	2	2	no	—
248	C₄	—	2	2	no	—
249	C₄	C₇×#336	1	2	yes	—
250	C₄	C₇×#336	1	2	yes	—
251	C₄	C₂×C₇×C₂²⋊C₈	1	2	yes	—
252	C₄	C₂×C₇×C₄⋊C₈	1	2	yes	—
253	C₂	—	2	2	no	—
254	C₂	—	2	1	no	—
255	C₂	—	2	1	no	—
256	C₂	C₇×#1281	1	4	yes	direct product factor
257	C₂	C₂×C₇×#336	1	1	yes	characteristic
258	C₂	C₂×C₇×#344	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₇	C₂²⋊C₄
commutator	C₂²	C₂×C₄×C₇×C₈
Frattini, cosocle	C₂×C₄²	C₂³×C₇
socle	C₂³×C₇	#95
prime radical	C₂⁴×C₇	C₄²
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×#1281	C₂	direct (N × H)
17. C₂×#1281	C₇	direct (N × H)
24. C₂²×C₇×C₈	C₈	semidirect
45. #1281	C₂×C₇	direct (N × H)
68. C₂×C₇×C₈	C₂×C₈	semidirect
128. C₂²×C₈	C₇×C₈	semidirect
187. C₂×C₈	C₂×C₇×C₈	semidirect
201. C₂×C₇	#1281	direct (N × H)
234. C₇	C₂×#1281	direct (N × H)
256. C₂	C₇×#1281	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×#431	2
C₂²×C₇×#97	2
C₇×#1281	2
C₂×#1281	7

Subgroups — C2×C7×#1281 #13185133

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#1281 #13185133