Subgroups — C₂×C₇×#3176 #13237896

Order 1792.

2098 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#540	C₂	1	2	yes	maximal, complemented
2	C₇×#3176	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₇×#499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#493	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#490	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#469	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#466	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#442	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₇×D₈	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#405	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₇×D₈	C₂²	1	2	yes	—
12	C₂²×C₇×D₈	C₂²	1	2	yes	—
13	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
15	C₇×#540	—	2	8	no	—
16	C₇×#540	C₂²	1	16	yes	complemented
17	C₂×C₇×#127	C₂²	1	2	yes	—
18	C₂×C₇×#125	C₂²	1	2	yes	—
19	C₂×C₇×#123	—	2	4	no	—
20	C₂×C₇×#121	—	2	4	no	—
21	C₂×C₇×#121	C₂²	1	4	yes	—
22	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
23	C₂×C₇×#117	C₂²	1	1	yes	characteristic
24	C₇×#499	C₂²	1	8	yes	complemented
25	C₇×#493	C₂²	1	8	yes	complemented
26	C₇×#490	C₂²	1	16	yes	complemented
27	C₇×#469	C₂²	1	16	yes	complemented
28	C₇×#466	C₂²	1	16	yes	complemented
29	C₇×#442	C₂²	1	16	yes	complemented
30	C₄×C₇×D₈	C₂²	1	16	yes	complemented
31	C₂×C₇×#107	C₂²	1	2	yes	—
32	C₂×C₇×#106	C₂²	1	2	yes	—
33	C₂×C₇×#102	C₂²	1	4	yes	—
34	C₂×C₇×#102	C₂²	1	4	yes	—
35	C₇×#405	C₂²	1	8	yes	complemented
36	C₂×C₇×#97	C₂²	1	1	yes	characteristic
37	C₂×C₇×#97	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
40	C₂×#3176	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂²×C₇×D₄	—	2	4	no	—
42	C₂²×C₇×D₄	—	2	4	no	—
43	C₂²×C₇×D₄	C₂³	1	4	yes	—
44	C₂³×C₄×C₇	—	2	4	no	—
45	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
46	C₂×C₇×D₈	—	2	8	no	—
47	C₂×C₇×D₈	—	2	8	no	—
48	C₂×C₇×D₈	C₂³	1	8	yes	—
49	C₂×C₇×D₈	C₂³	1	8	yes	—
50	C₂×C₇×M₁₆	—	2	4	no	—
51	C₂×C₇×M₁₆	C₂³	1	4	yes	—
52	C₂²×C₇×C₈	—	2	4	no	—
53	C₂²×C₇×C₈	C₂³	1	4	yes	—
54	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
58	C₇×#127	—	2	4	no	—
59	C₇×#127	C₂³	1	8	yes	—
60	C₇×#125	—	2	4	no	—
61	C₇×#125	C₂³	1	8	yes	—
62	C₇×#123	—	2	32	no	—
63	C₇×#121	—	2	8	no	—
64	C₇×#121	—	2	32	no	—
65	C₇×#121	C₂³	1	16	yes	—
66	C₄×C₇×D₄	—	2	8	no	—
67	C₄×C₇×D₄	C₂³	1	16	yes	—
68	C₇×#117	D₄	1	4	yes	—
69	C₇×#117	C₂³	1	4	yes	—
70	C₂×C₇×C₄⋊C₄	—	2	4	no	—
71	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
72	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
73	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
74	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
75	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
76	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
78	C₇×#107	C₂³	1	8	yes	—
79	C₇×#106	C₂³	1	8	yes	—
80	C₇×#102	C₂³	1	16	yes	—
81	C₇×#102	C₂³	1	16	yes	—
82	C₇×#97	C₂³	1	4	yes	—
83	C₇×#97	C₂³	1	4	yes	—
84	C₄×C₇×C₈	C₂³	1	4	yes	—
85	C₄×C₇×C₈	C₂³	1	4	yes	—
86	C₂×#540	C₂×C₇	1	2	yes	complemented
87	#3176	C₂×C₇	1	16	yes	direct product factor
88	C₂×#499	C₂×C₇	1	1	yes	characteristic, complemented
89	C₂×#493	C₂×C₇	1	1	yes	characteristic, complemented
90	C₂×#490	C₂×C₇	1	2	yes	complemented
91	C₂×#469	C₂×C₇	1	2	yes	complemented
92	C₂×#466	C₂×C₇	1	2	yes	complemented
93	C₂×#442	C₂×C₇	1	2	yes	complemented
94	C₂×C₄×D₈	C₂×C₇	1	2	yes	complemented
95	C₂×#405	C₂×C₇	1	1	yes	characteristic, complemented
96	C₂⁴×C₇	—	2	4	no	—
97	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
98	C₂×C₇×D₄	—	2	16	no	—
99	C₂×C₇×D₄	—	2	4	no	—
100	C₂×C₇×D₄	—	2	16	no	—
101	C₂×C₇×D₄	—	2	8	no	—
102	C₂×C₇×D₄	—	2	8	no	—
103	C₂×C₇×D₄	—	8	8	no	—
104	C₂×C₇×D₄	—	8	8	no	—
105	C₂×C₇×D₄	C₂⁴	1	8	yes	—
106	C₂²×C₄×C₇	—	2	2	no	—
107	C₂²×C₄×C₇	—	2	2	no	—
108	C₂²×C₄×C₇	—	2	4	no	—
109	C₂²×C₄×C₇	—	2	16	no	—
110	C₂²×C₄×C₇	—	8	8	no	—
111	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
116	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
117	C₇×D₈	—	2	16	no	—
118	C₇×D₈	—	2	16	no	—
119	C₇×M₁₆	—	2	8	no	—
120	C₂×C₇×C₈	—	2	2	no	—
121	C₂×C₇×C₈	—	2	2	no	—
122	C₂×C₇×C₈	—	2	8	no	—
123	C₂×C₇×C₈	#41	1	4	yes	—
124	C₂×C₇×C₈	#41	1	4	yes	—
125	C₂×C₇×C₈	C₂⁴	1	2	yes	—
126	C₂×C₇×C₈	C₂⁴	1	2	yes	—
127	C₂×C₇×C₈	C₂⁴	1	2	yes	—
128	C₂×C₇×C₈	C₂⁴	1	2	yes	—
129	C₇×C₄⋊C₄	—	2	16	no	—
130	C₇×C₄⋊C₄	—	2	4	no	—
131	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
132	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
133	C₇×C₂²⋊C₄	—	2	16	no	—
134	C₇×C₂²⋊C₄	—	2	16	no	—
135	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
136	C₄²×C₇	C₂×D₄	1	2	yes	—
137	C₄²×C₇	C₂×D₄	1	2	yes	—
138	C₄²×C₇	C₂⁴	1	2	yes	—
139	C₄²×C₇	C₂⁴	1	2	yes	—
140	C₂²×D₈	C₂²×C₇	1	2	yes	—
141	C₂²×D₈	C₂²×C₇	1	2	yes	—
142	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
143	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
144	#540	—	2	8	no	—
145	#540	C₂²×C₇	1	16	yes	complemented
146	C₂×#127	C₂²×C₇	1	2	yes	—
147	C₂×#125	C₂²×C₇	1	2	yes	—
148	C₂×#123	—	2	4	no	—
149	C₂×#121	—	2	4	no	—
150	C₂×#121	C₂²×C₇	1	4	yes	—
151	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
152	C₂×#117	C₂²×C₇	1	1	yes	characteristic
153	#499	C₂²×C₇	1	8	yes	complemented
154	#493	C₂²×C₇	1	8	yes	complemented
155	#490	C₂²×C₇	1	16	yes	complemented
156	#469	C₂²×C₇	1	16	yes	complemented
157	#466	C₂²×C₇	1	16	yes	complemented
158	#442	C₂²×C₇	1	16	yes	complemented
159	C₄×D₈	C₂²×C₇	1	16	yes	complemented
160	C₂×#107	C₂²×C₇	1	2	yes	—
161	C₂×#106	C₂²×C₇	1	2	yes	—
162	C₂×#102	C₂²×C₇	1	4	yes	—
163	C₂×#102	C₂²×C₇	1	4	yes	—
164	#405	C₂²×C₇	1	8	yes	complemented
165	C₂×#97	C₂²×C₇	1	1	yes	characteristic
166	C₂×#97	C₂²×C₇	1	1	yes	characteristic
167	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
168	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
169	C₂³×C₇	—	2	2	no	—
170	C₂³×C₇	—	2	4	no	—
171	C₂³×C₇	—	2	8	no	—
172	C₂³×C₇	—	4	8	no	—
173	C₂³×C₇	—	4	8	no	—
174	C₂³×C₇	—	4	8	no	—
175	C₂³×C₇	C₂²×D₄	1	2	yes	—
176	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
177	C₇×D₄	—	2	8	no	—
178	C₇×D₄	—	2	8	no	—
179	C₇×D₄	—	4	8	no	—
180	C₇×D₄	—	8	16	no	—
181	C₇×D₄	—	8	16	no	—
182	C₂×C₄×C₇	—	2	2	no	—
183	C₂×C₄×C₇	—	2	4	no	—
184	C₂×C₄×C₇	—	2	4	no	—
185	C₂×C₄×C₇	—	2	4	no	—
186	C₂×C₄×C₇	—	2	2	no	—
187	C₂×C₄×C₇	—	2	2	no	—
188	C₂×C₄×C₇	—	2	8	no	—
189	C₂×C₄×C₇	—	4	8	no	—
190	C₂×C₄×C₇	—	8	16	no	—
191	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
192	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
193	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₇	C₂×#41	1	2	yes	—
196	C₂×C₄×C₇	C₂×#41	1	2	yes	—
197	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
198	C₇×C₈	—	2	2	no	—
199	C₇×C₈	—	2	2	no	—
200	C₇×C₈	C₂×#41	1	4	yes	—
201	C₇×C₈	C₂×#41	1	4	yes	—
202	C₂²×D₄	—	2	4	no	—
203	C₂²×D₄	—	2	4	no	—
204	C₂²×D₄	C₂³×C₇	1	4	yes	—
205	C₂³×C₄	—	2	4	no	—
206	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
207	C₂×D₈	—	2	8	no	—
208	C₂×D₈	—	2	8	no	—
209	C₂×D₈	C₂³×C₇	1	8	yes	—
210	C₂×D₈	C₂³×C₇	1	8	yes	—
211	C₂×M₁₆	—	2	4	no	—
212	C₂×M₁₆	C₂³×C₇	1	4	yes	—
213	C₂²×C₈	—	2	4	no	—
214	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
215	C₂²×C₈	C₂³×C₇	1	4	yes	—
216	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
217	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
218	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
219	#127	—	2	4	no	—
220	#127	C₂³×C₇	1	8	yes	—
221	#125	—	2	4	no	—
222	#125	C₂³×C₇	1	8	yes	—
223	#123	—	2	32	no	—
224	#121	—	2	8	no	—
225	#121	—	2	32	no	—
226	#121	C₂³×C₇	1	16	yes	—
227	C₄×D₄	—	2	8	no	—
228	C₄×D₄	C₂³×C₇	1	16	yes	—
229	#117	C₇×D₄	1	4	yes	—
230	#117	C₂³×C₇	1	4	yes	—
231	C₂×C₄⋊C₄	—	2	4	no	—
232	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
233	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
234	C₂×C₂²⋊C₄	—	2	4	no	—
235	C₂×C₂²⋊C₄	—	2	4	no	—
236	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
237	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
238	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
239	#107	C₂³×C₇	1	8	yes	—
240	#106	C₂³×C₇	1	8	yes	—
241	#102	C₂³×C₇	1	16	yes	—
242	#102	C₂³×C₇	1	16	yes	—
243	#97	C₂³×C₇	1	4	yes	—
244	#97	C₂³×C₇	1	4	yes	—
245	C₄×C₈	C₂³×C₇	1	4	yes	—
246	C₄×C₈	C₂³×C₇	1	4	yes	—
247	C₂²×C₇	—	2	2	no	—
248	C₂²×C₇	—	2	4	no	—
249	C₂²×C₇	—	4	4	no	—
250	C₂²×C₇	—	4	8	no	—
251	C₂²×C₇	—	4	8	no	—
252	C₂²×C₇	—	4	8	no	—
253	C₂²×C₇	—	8	16	no	—
254	C₂²×C₇	#532	1	2	yes	—
255	C₂²×C₇	#576	1	4	yes	—
256	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
257	C₄×C₇	—	2	2	no	—
258	C₄×C₇	—	2	4	no	—
259	C₄×C₇	—	2	4	no	—
260	C₄×C₇	—	4	8	no	—
261	C₄×C₇	#532	1	2	yes	—
262	C₄×C₇	C₂²×#41	1	1	yes	characteristic
263	C₄×C₇	C₂²×#41	1	1	yes	characteristic
264	C₂⁴	—	2	4	no	—
265	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
266	C₂×D₄	—	2	16	no	—
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	2	16	no	—
269	C₂×D₄	—	2	8	no	—
270	C₂×D₄	—	2	8	no	—
271	C₂×D₄	—	8	8	no	—
272	C₂×D₄	—	8	8	no	—
273	C₂×D₄	C₂⁴×C₇	1	8	yes	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	16	no	—
278	C₂²×C₄	—	8	8	no	—
279	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
280	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
281	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
283	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
284	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
285	D₈	—	2	16	no	—
286	D₈	—	2	16	no	—
287	M₁₆	—	2	8	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	8	no	—
291	C₂×C₈	C₇×#41	1	4	yes	—
292	C₂×C₈	C₇×#41	1	4	yes	—
293	C₂×C₈	C₂⁴×C₇	1	2	yes	—
294	C₂×C₈	C₂⁴×C₇	1	2	yes	—
295	C₂×C₈	C₂⁴×C₇	1	2	yes	—
296	C₂×C₈	C₂⁴×C₇	1	2	yes	—
297	C₄⋊C₄	—	2	16	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
300	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
301	C₂²⋊C₄	—	2	16	no	—
302	C₂²⋊C₄	—	2	16	no	—
303	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
304	C₄²	C₂×C₇×D₄	1	2	yes	—
305	C₄²	C₂×C₇×D₄	1	2	yes	—
306	C₄²	C₂⁴×C₇	1	2	yes	—
307	C₄²	C₂⁴×C₇	1	2	yes	—
308	C₂×C₇	—	4	2	no	—
309	C₂×C₇	—	8	8	no	—
310	C₂×C₇	#3176	1	4	yes	direct product factor
311	C₂×C₇	C₂×#532	1	1	yes	characteristic
312	C₂×C₇	C₂×#576	1	2	yes	—
313	C₂³	—	2	2	no	—
314	C₂³	—	2	4	no	—
315	C₂³	—	2	8	no	—
316	C₂³	—	4	8	no	—
317	C₂³	—	4	8	no	—
318	C₂³	—	4	8	no	—
319	C₂³	C₂²×C₇×D₄	1	2	yes	—
320	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
321	D₄	—	2	8	no	—
322	D₄	—	2	8	no	—
323	D₄	—	4	8	no	—
324	D₄	—	8	16	no	—
325	D₄	—	8	16	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	4	8	no	—
334	C₂×C₄	—	8	16	no	—
335	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
336	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
337	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
338	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
339	C₂×C₄	C₂×C₇×#41	1	2	yes	—
340	C₂×C₄	C₂×C₇×#41	1	2	yes	—
341	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
342	C₈	—	2	2	no	—
343	C₈	—	2	2	no	—
344	C₈	C₂×C₇×#41	1	4	yes	—
345	C₈	C₂×C₇×#41	1	4	yes	—
346	C₇	C₂×#3176	1	1	yes	characteristic, direct product factor, Sylow
347	C₂²	—	2	4	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	4	4	no	—
350	C₂²	—	4	8	no	—
351	C₂²	—	4	8	no	—
352	C₂²	—	4	8	no	—
353	C₂²	—	8	16	no	—
354	C₂²	C₇×#532	1	2	yes	—
355	C₂²	C₇×#576	1	4	yes	—
356	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
357	C₄	—	2	4	no	—
358	C₄	—	2	4	no	—
359	C₄	—	2	2	no	—
360	C₄	—	4	8	no	—
361	C₄	C₇×#532	1	2	yes	—
362	C₄	C₂²×C₇×#41	1	1	yes	characteristic
363	C₄	C₂²×C₇×#41	1	1	yes	characteristic
364	C₂	—	4	2	no	—
365	C₂	—	8	8	no	—
366	C₂	C₇×#3176	1	4	yes	direct product factor
367	C₂	C₂×C₇×#532	1	1	yes	characteristic
368	C₂	C₂×C₇×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#540	C₂	semidirect
2. C₇×#3176	C₂	direct (N × H)
3. C₂×C₇×#499	C₂	semidirect
4. C₂×C₇×#493	C₂	semidirect
5. C₂×C₇×#490	C₂	semidirect
6. C₂×C₇×#469	C₂	semidirect
7. C₂×C₇×#466	C₂	semidirect
8. C₂×C₇×#442	C₂	semidirect
9. C₂×C₄×C₇×D₈	C₂	semidirect
10. C₂×C₇×#405	C₂	semidirect
16. C₇×#540	C₂²	semidirect
24. C₇×#499	C₂²	semidirect
25. C₇×#493	C₂²	semidirect
26. C₇×#490	C₂²	semidirect
27. C₇×#469	C₂²	semidirect
28. C₇×#466	C₂²	semidirect
29. C₇×#442	C₂²	semidirect
30. C₄×C₇×D₈	C₂²	semidirect
35. C₇×#405	C₂²	semidirect
40. C₂×#3176	C₇	direct (N × H)
86. C₂×#540	C₂×C₇	semidirect
87. #3176	C₂×C₇	direct (N × H)
88. C₂×#499	C₂×C₇	semidirect
89. C₂×#493	C₂×C₇	semidirect
90. C₂×#490	C₂×C₇	semidirect
91. C₂×#469	C₂×C₇	semidirect
92. C₂×#466	C₂×C₇	semidirect
93. C₂×#442	C₂×C₇	semidirect
94. C₂×C₄×D₈	C₂×C₇	semidirect
95. C₂×#405	C₂×C₇	semidirect
145. #540	C₂²×C₇	semidirect
153. #499	C₂²×C₇	semidirect
154. #493	C₂²×C₇	semidirect
155. #490	C₂²×C₇	semidirect
156. #469	C₂²×C₇	semidirect
157. #466	C₂²×C₇	semidirect
158. #442	C₂²×C₇	semidirect
159. C₄×D₈	C₂²×C₇	semidirect
164. #405	C₂²×C₇	semidirect
310. C₂×C₇	#3176	direct (N × H)
346. C₇	C₂×#3176	direct (N × H)
366. C₂	C₇×#3176	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×#540	2
C₇×#3176	2
C₂×C₇×#499	2
C₂×C₇×#493	2
C₂×C₇×#490	2
C₂×C₇×#469	2
C₂×C₇×#466	2
C₂×C₇×#442	2
C₂×C₄×C₇×D₈	2
C₂×C₇×#405	2
C₂×#3176	7

Subgroups — C2×C7×#3176 #13237896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3176 #13237896