Subgroups — C₂×C₇×#1691 #13196350

Order 1792.

726 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#476	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×#461	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic
5	C₇×#1691	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₇×#335	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#332	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₇×SD₁₆	—	2	1	no	—
10	C₂²×C₇×M₁₆	—	2	1	no	—
11	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
14	C₇×#498	—	2	2	no	—
15	C₇×#498	C₂²	1	4	yes	complemented
16	C₇×#476	—	2	2	no	—
17	C₇×#476	C₂²	1	4	yes	—
18	C₇×#461	—	2	2	no	—
19	C₇×#461	C₂²	1	4	yes	—
20	C₇×#436	—	2	2	no	—
21	C₇×#436	C₂²	1	4	yes	—
22	C₂×C₇×#106	—	2	1	no	—
23	C₂×C₇×#106	—	2	1	no	—
24	C₂×C₇×#106	—	2	1	no	—
25	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₇×#103	—	2	1	no	—
29	C₂×C₇×#102	—	2	1	no	—
30	C₂×C₇×C₂²⋊C₈	—	2	1	no	—
31	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
32	C₇×#335	C₂²	1	4	yes	complemented
33	C₇×#333	C₂²	1	4	yes	complemented
34	C₇×#332	C₂²	1	4	yes	complemented
35	C₂×#1691	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×D₄	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₇	—	2	1	no	—
40	C₂×C₇×SD₁₆	—	2	4	no	—
41	C₂×C₇×SD₁₆	—	4	4	no	—
42	C₂×C₇×M₁₆	—	2	4	no	—
43	C₂×C₇×M₁₆	—	4	4	no	—
44	C₂²×C₇×C₈	—	2	1	no	—
45	C₂²×C₇×C₈	—	2	1	no	—
46	C₂²×C₇×C₈	—	2	1	no	—
47	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
48	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
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	C₂³	1	2	yes	—
56	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
57	C₄×C₇×D₄	—	2	1	no	—
58	C₄×C₇×D₄	—	2	1	no	—
59	C₄×C₇×D₄	D₄	1	2	yes	—
60	C₄×C₇×D₄	C₂³	1	2	yes	—
61	C₂×C₇×C₄⋊C₄	—	2	1	no	—
62	C₂×C₇×C₄⋊C₄	—	2	1	no	—
63	C₂×C₇×C₄⋊C₄	—	2	1	no	—
64	C₂×C₇×C₄⋊C₄	—	2	1	no	—
65	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
68	C₇×#106	—	2	4	no	—
69	C₇×#106	—	2	4	no	—
70	C₇×#106	—	2	4	no	—
71	C₇×C₄⋊C₈	—	2	1	no	—
72	C₇×C₄⋊C₈	—	2	1	no	—
73	C₇×C₄⋊C₈	—	2	1	no	—
74	C₇×C₄⋊C₈	C₂³	1	2	yes	—
75	C₇×C₄⋊C₈	C₂³	1	2	yes	—
76	C₇×C₄⋊C₈	C₂³	1	2	yes	—
77	C₇×#103	—	2	4	no	—
78	C₇×#102	—	2	4	no	—
79	C₇×C₂²⋊C₈	—	2	4	no	—
80	C₄×C₇×C₈	D₄	1	2	yes	—
81	C₄×C₇×C₈	C₂³	1	2	yes	—
82	C₂×#498	C₂×C₇	1	1	yes	characteristic, complemented
83	C₂×#476	C₂×C₇	1	1	yes	characteristic
84	C₂×#461	C₂×C₇	1	1	yes	characteristic
85	C₂×#436	C₂×C₇	1	1	yes	characteristic
86	#1691	C₂×C₇	1	8	yes	direct product factor
87	C₂×#335	C₂×C₇	1	1	yes	characteristic, complemented
88	C₂×#333	C₂×C₇	1	1	yes	characteristic, complemented
89	C₂×#332	C₂×C₇	1	1	yes	characteristic, complemented
90	C₂⁴×C₇	—	2	1	no	—
91	C₂×C₇×Q₈	—	2	2	no	—
92	C₂×C₇×Q₈	—	2	2	no	—
93	C₂×C₇×Q₈	—	4	1	no	—
94	C₂×C₇×Q₈	—	4	1	no	—
95	C₂×C₇×Q₈	—	4	2	no	—
96	C₂×C₇×Q₈	—	4	2	no	—
97	C₂×C₇×Q₈	—	8	2	no	—
98	C₂×C₇×D₄	—	2	1	no	—
99	C₂×C₇×D₄	—	2	2	no	—
100	C₂×C₇×D₄	—	2	2	no	—
101	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₇	—	2	1	no	—
103	C₂²×C₄×C₇	—	2	2	no	—
104	C₂²×C₄×C₇	—	2	2	no	—
105	C₂²×C₄×C₇	—	4	2	no	—
106	C₂²×C₄×C₇	—	4	2	no	—
107	C₂²×C₄×C₇	—	4	1	no	—
108	C₂²×C₄×C₇	—	4	1	no	—
109	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₇	#41	1	1	yes	characteristic
112	C₇×SD₁₆	—	4	8	no	—
113	C₇×M₁₆	—	4	8	no	—
114	C₂×C₇×C₈	—	2	2	no	—
115	C₂×C₇×C₈	—	2	2	no	—
116	C₂×C₇×C₈	—	2	2	no	—
117	C₂×C₇×C₈	—	2	2	no	—
118	C₂×C₇×C₈	—	4	2	no	—
119	C₂×C₇×C₈	—	4	2	no	—
120	C₂×C₇×C₈	—	4	2	no	—
121	C₂×C₇×C₈	SD₁₆	1	4	yes	complemented
122	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
123	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
124	C₇×C₄⋊C₄	—	2	1	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	C₂×D₄	1	2	yes	—
134	C₇×C₂²⋊C₄	—	2	2	no	—
135	C₇×C₂²⋊C₄	—	2	2	no	—
136	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₇	#41	1	1	yes	characteristic
139	C₄²×C₇	C₂⁴	1	1	yes	characteristic
140	C₂²×SD₁₆	—	2	1	no	—
141	C₂²×M₁₆	—	2	1	no	—
142	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
143	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
144	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
145	#498	—	2	2	no	—
146	#498	C₂²×C₇	1	4	yes	complemented
147	#476	—	2	2	no	—
148	#476	C₂²×C₇	1	4	yes	—
149	#461	—	2	2	no	—
150	#461	C₂²×C₇	1	4	yes	—
151	#436	—	2	2	no	—
152	#436	C₂²×C₇	1	4	yes	—
153	C₂×#106	—	2	1	no	—
154	C₂×#106	—	2	1	no	—
155	C₂×#106	—	2	1	no	—
156	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
157	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
158	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
159	C₂×#103	—	2	1	no	—
160	C₂×#102	—	2	1	no	—
161	C₂×C₂²⋊C₈	—	2	1	no	—
162	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
163	#335	C₂²×C₇	1	4	yes	complemented
164	#333	C₂²×C₇	1	4	yes	complemented
165	#332	C₂²×C₇	1	4	yes	complemented
166	C₂³×C₇	—	2	2	no	—
167	C₂³×C₇	—	4	2	no	—
168	C₂³×C₇	—	4	2	no	—
169	C₂³×C₇	—	4	2	no	—
170	C₂³×C₇	#121	1	1	yes	characteristic
171	C₇×Q₈	—	4	2	no	—
172	C₇×Q₈	—	4	2	no	—
173	C₇×Q₈	—	8	2	no	—
174	C₇×Q₈	—	8	2	no	—
175	C₇×Q₈	—	8	2	no	—
176	C₇×D₄	—	2	2	no	—
177	C₇×D₄	—	2	2	no	—
178	C₇×D₄	—	4	2	no	—
179	C₂×C₄×C₇	—	2	2	no	—
180	C₂×C₄×C₇	—	2	2	no	—
181	C₂×C₄×C₇	—	4	2	no	—
182	C₂×C₄×C₇	—	4	2	no	—
183	C₂×C₄×C₇	—	4	2	no	—
184	C₂×C₄×C₇	—	4	4	no	—
185	C₂×C₄×C₇	—	4	2	no	—
186	C₂×C₄×C₇	—	4	2	no	—
187	C₂×C₄×C₇	—	8	2	no	—
188	C₂×C₄×C₇	—	8	2	no	—
189	C₂×C₄×C₇	#121	1	1	yes	characteristic
190	C₂×C₄×C₇	#121	1	1	yes	characteristic
191	C₂×C₄×C₇	#121	1	1	yes	characteristic
192	C₂×C₄×C₇	C₂×SD₁₆	1	2	yes	—
193	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
194	C₂×C₄×C₇	#137	1	2	yes	—
195	C₂×C₄×C₇	#137	1	2	yes	—
196	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
199	C₇×C₈	—	2	2	no	—
200	C₇×C₈	—	4	2	no	—
201	C₇×C₈	—	4	2	no	—
202	C₇×C₈	—	4	2	no	—
203	C₇×C₈	C₂×SD₁₆	1	4	yes	complemented
204	C₂²×Q₈	—	2	1	no	—
205	C₂²×Q₈	—	2	1	no	—
206	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
207	C₂³×C₄	—	2	1	no	—
208	C₂×SD₁₆	—	2	4	no	—
209	C₂×SD₁₆	—	4	4	no	—
210	C₂×M₁₆	—	2	4	no	—
211	C₂×M₁₆	—	4	4	no	—
212	C₂²×C₈	—	2	1	no	—
213	C₂²×C₈	—	2	1	no	—
214	C₂²×C₈	—	2	1	no	—
215	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
216	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
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	—	2	1	no	—
223	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
224	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
225	C₄×D₄	—	2	1	no	—
226	C₄×D₄	—	2	1	no	—
227	C₄×D₄	C₇×D₄	1	2	yes	—
228	C₄×D₄	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	C₇×D₄	1	1	yes	characteristic
234	C₂×C₂²⋊C₄	—	2	1	no	—
235	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
236	#106	—	2	4	no	—
237	#106	—	2	4	no	—
238	#106	—	2	4	no	—
239	C₄⋊C₈	—	2	1	no	—
240	C₄⋊C₈	—	2	1	no	—
241	C₄⋊C₈	—	2	1	no	—
242	C₄⋊C₈	C₂³×C₇	1	2	yes	—
243	C₄⋊C₈	C₂³×C₇	1	2	yes	—
244	C₄⋊C₈	C₂³×C₇	1	2	yes	—
245	#103	—	2	4	no	—
246	#102	—	2	4	no	—
247	C₂²⋊C₈	—	2	4	no	—
248	C₄×C₈	C₇×D₄	1	2	yes	—
249	C₄×C₈	C₂³×C₇	1	2	yes	—
250	C₂²×C₇	—	4	2	no	—
251	C₂²×C₇	—	4	2	no	—
252	C₂²×C₇	—	4	2	no	—
253	C₂²×C₇	—	8	4	no	—
254	C₂²×C₇	#461	1	2	yes	—
255	C₂²×C₇	#468	1	2	yes	—
256	C₂²×C₇	#471	1	2	yes	—
257	C₂²×C₇	C₂×#121	1	1	yes	characteristic
258	C₄×C₇	—	2	1	no	—
259	C₄×C₇	—	2	1	no	—
260	C₄×C₇	—	4	2	no	—
261	C₄×C₇	—	8	2	no	—
262	C₄×C₇	—	8	2	no	—
263	C₄×C₇	#461	1	2	yes	—
264	C₄×C₇	#468	1	2	yes	—
265	C₄×C₇	C₂²×SD₁₆	1	1	yes	characteristic
266	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
267	C₄×C₇	C₂×#137	1	1	yes	characteristic
268	C₄×C₇	C₂×#137	1	1	yes	characteristic
269	C₂⁴	—	2	1	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	4	1	no	—
273	C₂×Q₈	—	4	1	no	—
274	C₂×Q₈	—	4	2	no	—
275	C₂×Q₈	—	4	2	no	—
276	C₂×Q₈	—	8	2	no	—
277	C₂×D₄	—	2	1	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
290	C₂²×C₄	C₇×#41	1	1	yes	characteristic
291	SD₁₆	—	4	8	no	—
292	M₁₆	—	4	8	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	4	2	no	—
298	C₂×C₈	—	4	2	no	—
299	C₂×C₈	—	4	2	no	—
300	C₂×C₈	C₇×SD₁₆	1	4	yes	complemented
301	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
302	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
316	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
317	C₄²	C₇×#41	1	1	yes	characteristic
318	C₄²	C₂⁴×C₇	1	1	yes	characteristic
319	C₂×C₇	—	8	2	no	—
320	C₂×C₇	#1691	1	4	yes	direct product factor
321	C₂×C₇	C₂×#461	1	1	yes	characteristic
322	C₂×C₇	C₂×#468	1	1	yes	characteristic
323	C₂×C₇	C₂×#471	1	1	yes	characteristic
324	C₂³	—	2	2	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	2	no	—
328	C₂³	C₇×#121	1	1	yes	characteristic
329	Q₈	—	4	2	no	—
330	Q₈	—	4	2	no	—
331	Q₈	—	8	2	no	—
332	Q₈	—	8	2	no	—
333	Q₈	—	8	2	no	—
334	D₄	—	2	2	no	—
335	D₄	—	2	2	no	—
336	D₄	—	4	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	8	2	no	—
346	C₂×C₄	—	8	2	no	—
347	C₂×C₄	C₇×#121	1	1	yes	characteristic
348	C₂×C₄	C₇×#121	1	1	yes	characteristic
349	C₂×C₄	C₇×#121	1	1	yes	characteristic
350	C₂×C₄	C₂×C₇×SD₁₆	1	2	yes	—
351	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
352	C₂×C₄	C₇×#137	1	2	yes	—
353	C₂×C₄	C₇×#137	1	2	yes	—
354	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
355	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
356	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
357	C₈	—	2	2	no	—
358	C₈	—	4	2	no	—
359	C₈	—	4	2	no	—
360	C₈	—	4	2	no	—
361	C₈	C₂×C₇×SD₁₆	1	4	yes	complemented
362	C₇	C₂×#1691	1	1	yes	characteristic, direct product factor, Sylow
363	C₂²	—	4	2	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	8	4	no	—
367	C₂²	C₇×#461	1	2	yes	—
368	C₂²	C₇×#468	1	2	yes	—
369	C₂²	C₇×#471	1	2	yes	—
370	C₂²	C₂×C₇×#121	1	1	yes	characteristic
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	4	2	no	—
374	C₄	—	8	2	no	—
375	C₄	—	8	2	no	—
376	C₄	C₇×#461	1	2	yes	—
377	C₄	C₇×#468	1	2	yes	—
378	C₄	C₂²×C₇×SD₁₆	1	1	yes	characteristic
379	C₄	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
380	C₄	C₂×C₇×#137	1	1	yes	characteristic
381	C₄	C₂×C₇×#137	1	1	yes	characteristic
382	C₂	—	8	2	no	—
383	C₂	C₇×#1691	1	4	yes	direct product factor
384	C₂	C₂×C₇×#461	1	1	yes	characteristic
385	C₂	C₂×C₇×#468	1	1	yes	characteristic
386	C₂	C₂×C₇×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₂²×C₇×D₄	D₄
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×#498	C₂	semidirect
5. C₇×#1691	C₂	direct (N × H)
6. C₂×C₇×#335	C₂	semidirect
7. C₂×C₇×#333	C₂	semidirect
8. C₂×C₇×#332	C₂	semidirect
15. C₇×#498	C₂²	semidirect
32. C₇×#335	C₂²	semidirect
33. C₇×#333	C₂²	semidirect
34. C₇×#332	C₂²	semidirect
35. C₂×#1691	C₇	direct (N × H)
82. C₂×#498	C₂×C₇	semidirect
86. #1691	C₂×C₇	direct (N × H)
87. C₂×#335	C₂×C₇	semidirect
88. C₂×#333	C₂×C₇	semidirect
89. C₂×#332	C₂×C₇	semidirect
121. C₂×C₇×C₈	SD₁₆	semidirect
146. #498	C₂²×C₇	semidirect
163. #335	C₂²×C₇	semidirect
164. #333	C₂²×C₇	semidirect
165. #332	C₂²×C₇	semidirect
203. C₇×C₈	C₂×SD₁₆	semidirect
300. C₂×C₈	C₇×SD₁₆	semidirect
320. C₂×C₇	#1691	direct (N × H)
361. C₈	C₂×C₇×SD₁₆	semidirect
362. C₇	C₂×#1691	direct (N × H)
383. C₂	C₇×#1691	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×#498	2
C₂×C₇×#476	2
C₂×C₇×#461	2
C₂×C₇×#436	2
C₇×#1691	2
C₂×C₇×#335	2
C₂×C₇×#333	2
C₂×C₇×#332	2
C₂×#1691	7

Subgroups — C2×C7×#1691 #13196350

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#1691 #13196350