Subgroups — C₂×C₇×#1714 #13196821

Order 1792.

914 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#492	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇×#492	C₂	1	1	yes	maximal, characteristic
5	C₂×C₇×#487	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#486	C₂	1	1	yes	maximal, characteristic
7	C₇×#1714	C₂	1	8	yes	maximal, direct product factor
8	C₂×C₇×#322	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₇×SD₁₆	—	2	2	no	—
10	C₂²×C₇×SD₁₆	—	2	2	no	—
11	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₇×#127	C₂²	1	1	yes	characteristic
15	C₇×#500	—	2	2	no	—
16	C₇×#500	C₂²	1	4	yes	complemented
17	C₇×#498	—	2	2	no	—
18	C₇×#498	C₂²	1	4	yes	complemented
19	C₇×#492	—	2	2	no	—
20	C₇×#492	—	2	2	no	—
21	C₇×#492	C₂²	1	4	yes	—
22	C₇×#492	C₂²	1	4	yes	—
23	C₇×#487	—	2	2	no	—
24	C₇×#487	C₂²	1	4	yes	complemented
25	C₇×#486	—	2	2	no	—
26	C₇×#486	C₂²	1	4	yes	—
27	C₂×C₇×#107	—	2	2	no	—
28	C₂×C₇×#106	—	2	2	no	—
29	C₂×C₇×#103	—	2	2	no	—
30	C₂×C₇×#102	—	2	2	no	—
31	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
34	C₇×#322	C₂²	1	4	yes	complemented
35	C₂×#1714	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂²×C₇×Q₈	—	2	1	no	—
37	C₂²×C₇×Q₈	—	2	1	no	—
38	C₂²×C₇×Q₈	—	2	1	no	—
39	C₂²×C₇×D₄	—	2	1	no	—
40	C₂²×C₇×D₄	—	2	1	no	—
41	C₂²×C₇×D₄	—	2	1	no	—
42	C₂×C₇×SD₁₆	—	2	8	no	—
43	C₂×C₇×SD₁₆	—	2	8	no	—
44	C₂×C₇×SD₁₆	—	4	8	no	—
45	C₂×C₇×SD₁₆	—	4	8	no	—
46	C₂²×C₇×C₈	D₄	1	2	yes	—
47	C₂²×C₇×C₈	D₄	1	2	yes	—
48	C₂²×C₇×C₈	D₄	1	2	yes	—
49	C₇×C₄⋊Q₈	—	2	1	no	—
50	C₇×C₄⋊Q₈	—	2	1	no	—
51	C₇×C₄⋊Q₈	—	2	1	no	—
52	C₇×C₄⋊Q₈	—	2	1	no	—
53	C₇×C₄⋊Q₈	—	2	1	no	—
54	C₇×C₄⋊Q₈	—	2	1	no	—
55	C₇×C₄⋊Q₈	—	2	1	no	—
56	C₇×C₄⋊Q₈	—	2	1	no	—
57	C₇×C₄⋊Q₈	—	2	1	no	—
58	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
60	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
61	C₇×#127	—	2	1	no	—
62	C₇×#127	—	2	1	no	—
63	C₇×#127	—	2	1	no	—
64	C₇×#127	C₂³	1	2	yes	—
65	C₂×C₇×C₄⋊C₄	—	2	1	no	—
66	C₂×C₇×C₄⋊C₄	—	2	1	no	—
67	C₂×C₇×C₄⋊C₄	—	2	1	no	—
68	C₂×C₇×C₄⋊C₄	—	2	1	no	—
69	C₂×C₇×C₄⋊C₄	—	2	1	no	—
70	C₂×C₇×C₄⋊C₄	—	2	1	no	—
71	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
72	C₇×#107	—	2	8	no	—
73	C₇×#106	—	2	8	no	—
74	C₇×#103	—	2	8	no	—
75	C₇×#102	—	2	8	no	—
76	C₄×C₇×C₈	D₄	1	2	yes	—
77	C₄×C₇×C₈	D₄	1	2	yes	—
78	C₄×C₇×C₈	D₄	1	2	yes	—
79	C₄×C₇×C₈	C₂³	1	2	yes	—
80	C₄×C₇×C₈	C₂³	1	2	yes	—
81	C₄×C₇×C₈	C₂³	1	2	yes	—
82	C₂×#500	C₂×C₇	1	1	yes	characteristic, complemented
83	C₂×#498	C₂×C₇	1	1	yes	characteristic, complemented
84	C₂×#492	C₂×C₇	1	1	yes	characteristic
85	C₂×#492	C₂×C₇	1	1	yes	characteristic
86	C₂×#487	C₂×C₇	1	1	yes	characteristic, complemented
87	C₂×#486	C₂×C₇	1	1	yes	characteristic
88	#1714	C₂×C₇	1	8	yes	direct product factor
89	C₂×#322	C₂×C₇	1	1	yes	characteristic, complemented
90	C₂⁴×C₇	—	4	1	no	—
91	C₂×C₇×Q₈	—	2	2	no	—
92	C₂×C₇×Q₈	—	2	2	no	—
93	C₂×C₇×Q₈	—	2	2	no	—
94	C₂×C₇×Q₈	—	4	1	no	—
95	C₂×C₇×Q₈	—	4	1	no	—
96	C₂×C₇×Q₈	—	4	1	no	—
97	C₂×C₇×Q₈	—	4	4	no	—
98	C₂×C₇×Q₈	—	4	4	no	—
99	C₂×C₇×Q₈	—	4	4	no	—
100	C₂×C₇×D₄	—	2	2	no	—
101	C₂×C₇×D₄	—	2	2	no	—
102	C₂×C₇×D₄	—	2	2	no	—
103	C₂×C₇×D₄	—	4	1	no	—
104	C₂×C₇×D₄	—	4	1	no	—
105	C₂×C₇×D₄	—	4	1	no	—
106	C₂×C₇×D₄	—	4	4	no	—
107	C₂×C₇×D₄	—	4	4	no	—
108	C₂×C₇×D₄	—	4	4	no	—
109	C₂²×C₄×C₇	—	4	1	no	—
110	C₂²×C₄×C₇	—	4	1	no	—
111	C₂²×C₄×C₇	—	4	1	no	—
112	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
115	C₇×SD₁₆	—	4	16	no	—
116	C₇×SD₁₆	—	4	16	no	—
117	C₂×C₇×C₈	—	2	4	no	—
118	C₂×C₇×C₈	—	2	4	no	—
119	C₂×C₇×C₈	SD₁₆	1	8	yes	complemented
120	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
121	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
122	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
123	C₇×C₄⋊C₄	—	2	2	no	—
124	C₇×C₄⋊C₄	—	2	2	no	—
125	C₇×C₄⋊C₄	—	2	2	no	—
126	C₇×C₄⋊C₄	—	2	2	no	—
127	C₇×C₄⋊C₄	—	2	2	no	—
128	C₇×C₄⋊C₄	—	2	2	no	—
129	C₇×C₄⋊C₄	—	4	1	no	—
130	C₇×C₄⋊C₄	—	4	1	no	—
131	C₇×C₄⋊C₄	—	4	1	no	—
132	C₇×C₄⋊C₄	—	4	1	no	—
133	C₇×C₄⋊C₄	—	4	1	no	—
134	C₇×C₄⋊C₄	—	4	1	no	—
135	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₇	C₂⁴	1	1	yes	characteristic
139	C₂²×SD₁₆	—	2	2	no	—
140	C₂²×SD₁₆	—	2	2	no	—
141	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
142	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
143	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
144	C₂×#127	C₂²×C₇	1	1	yes	characteristic
145	#500	—	2	2	no	—
146	#500	C₂²×C₇	1	4	yes	complemented
147	#498	—	2	2	no	—
148	#498	C₂²×C₇	1	4	yes	complemented
149	#492	—	2	2	no	—
150	#492	—	2	2	no	—
151	#492	C₂²×C₇	1	4	yes	—
152	#492	C₂²×C₇	1	4	yes	—
153	#487	—	2	2	no	—
154	#487	C₂²×C₇	1	4	yes	complemented
155	#486	—	2	2	no	—
156	#486	C₂²×C₇	1	4	yes	—
157	C₂×#107	—	2	2	no	—
158	C₂×#106	—	2	2	no	—
159	C₂×#103	—	2	2	no	—
160	C₂×#102	—	2	2	no	—
161	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
162	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
163	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
164	#322	C₂²×C₇	1	4	yes	complemented
165	C₂³×C₇	—	4	2	no	—
166	C₂³×C₇	—	8	2	no	—
167	C₂³×C₇	—	8	2	no	—
168	C₂³×C₇	—	8	2	no	—
169	C₂³×C₇	#127	1	1	yes	characteristic
170	C₇×Q₈	—	4	4	no	—
171	C₇×Q₈	—	4	4	no	—
172	C₇×Q₈	—	4	4	no	—
173	C₇×Q₈	—	8	2	no	—
174	C₇×Q₈	—	8	2	no	—
175	C₇×Q₈	—	8	2	no	—
176	C₇×D₄	—	4	4	no	—
177	C₇×D₄	—	4	4	no	—
178	C₇×D₄	—	4	4	no	—
179	C₇×D₄	—	8	2	no	—
180	C₇×D₄	—	8	2	no	—
181	C₇×D₄	—	8	2	no	—
182	C₂×C₄×C₇	—	4	2	no	—
183	C₂×C₄×C₇	—	4	2	no	—
184	C₂×C₄×C₇	—	4	2	no	—
185	C₂×C₄×C₇	—	8	2	no	—
186	C₂×C₄×C₇	—	8	2	no	—
187	C₂×C₄×C₇	—	8	2	no	—
188	C₂×C₄×C₇	#127	1	1	yes	characteristic
189	C₂×C₄×C₇	#127	1	1	yes	characteristic
190	C₂×C₄×C₇	#127	1	1	yes	characteristic
191	C₂×C₄×C₇	C₂×SD₁₆	1	4	yes	—
192	C₂×C₄×C₇	AGL(1,ℤ/8)	1	4	yes	—
193	C₂×C₄×C₇	#137	1	4	yes	—
194	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
197	C₇×C₈	—	2	4	no	—
198	C₇×C₈	—	2	4	no	—
199	C₇×C₈	C₂×SD₁₆	1	8	yes	complemented
200	C₂²×Q₈	—	2	1	no	—
201	C₂²×Q₈	—	2	1	no	—
202	C₂²×Q₈	—	2	1	no	—
203	C₂²×D₄	—	2	1	no	—
204	C₂²×D₄	—	2	1	no	—
205	C₂²×D₄	—	2	1	no	—
206	C₂×SD₁₆	—	2	8	no	—
207	C₂×SD₁₆	—	2	8	no	—
208	C₂×SD₁₆	—	4	8	no	—
209	C₂×SD₁₆	—	4	8	no	—
210	C₂²×C₈	C₇×D₄	1	2	yes	—
211	C₂²×C₈	C₇×D₄	1	2	yes	—
212	C₂²×C₈	C₇×D₄	1	2	yes	—
213	C₄⋊Q₈	—	2	1	no	—
214	C₄⋊Q₈	—	2	1	no	—
215	C₄⋊Q₈	—	2	1	no	—
216	C₄⋊Q₈	—	2	1	no	—
217	C₄⋊Q₈	—	2	1	no	—
218	C₄⋊Q₈	—	2	1	no	—
219	C₄⋊Q₈	—	2	1	no	—
220	C₄⋊Q₈	—	2	1	no	—
221	C₄⋊Q₈	—	2	1	no	—
222	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
223	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
224	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
225	#127	—	2	1	no	—
226	#127	—	2	1	no	—
227	#127	—	2	1	no	—
228	#127	C₂³×C₇	1	2	yes	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₄⋊C₄	—	2	1	no	—
231	C₂×C₄⋊C₄	—	2	1	no	—
232	C₂×C₄⋊C₄	—	2	1	no	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
236	#107	—	2	8	no	—
237	#106	—	2	8	no	—
238	#103	—	2	8	no	—
239	#102	—	2	8	no	—
240	C₄×C₈	C₇×D₄	1	2	yes	—
241	C₄×C₈	C₇×D₄	1	2	yes	—
242	C₄×C₈	C₇×D₄	1	2	yes	—
243	C₄×C₈	C₂³×C₇	1	2	yes	—
244	C₄×C₈	C₂³×C₇	1	2	yes	—
245	C₄×C₈	C₂³×C₇	1	2	yes	—
246	C₂²×C₇	—	8	2	no	—
247	C₂²×C₇	—	8	2	no	—
248	C₂²×C₇	—	8	2	no	—
249	C₂²×C₇	—	16	4	no	—
250	C₂²×C₇	#492	1	2	yes	—
251	C₂²×C₇	#496	1	2	yes	—
252	C₂²×C₇	#497	1	2	yes	—
253	C₂²×C₇	C₂×#127	1	1	yes	characteristic
254	C₄×C₇	—	8	2	no	—
255	C₄×C₇	—	8	2	no	—
256	C₄×C₇	—	8	2	no	—
257	C₄×C₇	#492	1	2	yes	—
258	C₄×C₇	#496	1	2	yes	—
259	C₄×C₇	#497	1	2	yes	—
260	C₄×C₇	C₂²×SD₁₆	1	2	yes	—
261	C₄×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
262	C₄×C₇	C₂×#137	1	2	yes	—
263	C₂⁴	—	4	1	no	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	4	1	no	—
268	C₂×Q₈	—	4	1	no	—
269	C₂×Q₈	—	4	1	no	—
270	C₂×Q₈	—	4	4	no	—
271	C₂×Q₈	—	4	4	no	—
272	C₂×Q₈	—	4	4	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	4	1	no	—
277	C₂×D₄	—	4	1	no	—
278	C₂×D₄	—	4	1	no	—
279	C₂×D₄	—	4	4	no	—
280	C₂×D₄	—	4	4	no	—
281	C₂×D₄	—	4	4	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
288	SD₁₆	—	4	16	no	—
289	SD₁₆	—	4	16	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	—	2	4	no	—
292	C₂×C₈	C₇×SD₁₆	1	8	yes	complemented
293	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
294	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
295	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	4	1	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
309	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
310	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
311	C₄²	C₂⁴×C₇	1	1	yes	characteristic
312	C₂×C₇	—	16	2	no	—
313	C₂×C₇	#1714	1	4	yes	direct product factor
314	C₂×C₇	C₂×#492	1	1	yes	characteristic
315	C₂×C₇	C₂×#496	1	1	yes	characteristic
316	C₂×C₇	C₂×#497	1	1	yes	characteristic
317	C₂³	—	4	2	no	—
318	C₂³	—	8	2	no	—
319	C₂³	—	8	2	no	—
320	C₂³	—	8	2	no	—
321	C₂³	C₇×#127	1	1	yes	characteristic
322	Q₈	—	4	4	no	—
323	Q₈	—	4	4	no	—
324	Q₈	—	4	4	no	—
325	Q₈	—	8	2	no	—
326	Q₈	—	8	2	no	—
327	Q₈	—	8	2	no	—
328	D₄	—	4	4	no	—
329	D₄	—	4	4	no	—
330	D₄	—	4	4	no	—
331	D₄	—	8	2	no	—
332	D₄	—	8	2	no	—
333	D₄	—	8	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	8	2	no	—
338	C₂×C₄	—	8	2	no	—
339	C₂×C₄	—	8	2	no	—
340	C₂×C₄	C₇×#127	1	1	yes	characteristic
341	C₂×C₄	C₇×#127	1	1	yes	characteristic
342	C₂×C₄	C₇×#127	1	1	yes	characteristic
343	C₂×C₄	C₂×C₇×SD₁₆	1	4	yes	—
344	C₂×C₄	C₇×AGL(1,ℤ/8)	1	4	yes	—
345	C₂×C₄	C₇×#137	1	4	yes	—
346	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
347	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
348	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
349	C₈	—	2	4	no	—
350	C₈	—	2	4	no	—
351	C₈	C₂×C₇×SD₁₆	1	8	yes	complemented
352	C₇	C₂×#1714	1	1	yes	characteristic, direct product factor, Sylow
353	C₂²	—	8	2	no	—
354	C₂²	—	8	2	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	16	4	no	—
357	C₂²	C₇×#492	1	2	yes	—
358	C₂²	C₇×#496	1	2	yes	—
359	C₂²	C₇×#497	1	2	yes	—
360	C₂²	C₂×C₇×#127	1	1	yes	characteristic
361	C₄	—	8	2	no	—
362	C₄	—	8	2	no	—
363	C₄	—	8	2	no	—
364	C₄	C₇×#492	1	2	yes	—
365	C₄	C₇×#496	1	2	yes	—
366	C₄	C₇×#497	1	2	yes	—
367	C₄	C₂²×C₇×SD₁₆	1	2	yes	—
368	C₄	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
369	C₄	C₂×C₇×#137	1	2	yes	—
370	C₂	—	16	2	no	—
371	C₂	C₇×#1714	1	4	yes	direct product factor
372	C₂	C₂×C₇×#492	1	1	yes	characteristic
373	C₂	C₂×C₇×#496	1	1	yes	characteristic
374	C₂	C₂×C₇×#497	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₂×C₇×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#500	C₂	semidirect
2. C₂×C₇×#498	C₂	semidirect
5. C₂×C₇×#487	C₂	semidirect
7. C₇×#1714	C₂	direct (N × H)
8. C₂×C₇×#322	C₂	semidirect
16. C₇×#500	C₂²	semidirect
18. C₇×#498	C₂²	semidirect
24. C₇×#487	C₂²	semidirect
34. C₇×#322	C₂²	semidirect
35. C₂×#1714	C₇	direct (N × H)
82. C₂×#500	C₂×C₇	semidirect
83. C₂×#498	C₂×C₇	semidirect
86. C₂×#487	C₂×C₇	semidirect
88. #1714	C₂×C₇	direct (N × H)
89. C₂×#322	C₂×C₇	semidirect
119. C₂×C₇×C₈	SD₁₆	semidirect
146. #500	C₂²×C₇	semidirect
148. #498	C₂²×C₇	semidirect
154. #487	C₂²×C₇	semidirect
164. #322	C₂²×C₇	semidirect
199. C₇×C₈	C₂×SD₁₆	semidirect
292. C₂×C₈	C₇×SD₁₆	semidirect
313. C₂×C₇	#1714	direct (N × H)
351. C₈	C₂×C₇×SD₁₆	semidirect
352. C₇	C₂×#1714	direct (N × H)
371. C₂	C₇×#1714	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×#500	2
C₂×C₇×#498	2
C₂×C₇×#492	2
C₂×C₇×#487	2
C₂×C₇×#486	2
C₇×#1714	2
C₂×C₇×#322	2
C₂×#1714	7

Subgroups — C2×C7×#1714 #13196821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#1714 #13196821