Subgroups — C₂×C₇×#2851 #13213832

Order 1792.

3182 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄²×C₇	C₂	1	1	yes	maximal, characteristic
3	C₇×#2851	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#389	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#387	C₂	1	4	yes	maximal, complemented
6	C₂×C₇×#385	C₂	1	4	yes	maximal
7	C₂×C₇×#382	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#380	C₂	1	2	yes	maximal
9	C₂⁴×C₄×C₇	C₂²	1	2	yes	—
10	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
11	C₂×C₇×#125	—	2	8	no	—
12	C₂×C₇×#125	C₂²	1	8	yes	complemented
13	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂²×C₇×C₄⋊C₄	C₂²	1	4	yes	—
15	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂²×C₇×C₄⋊C₄	C₂²	1	4	yes	—
17	C₂²×C₇×C₂²⋊C₄	C₂²	1	4	yes	—
18	C₂²×C₄²×C₇	—	2	8	no	—
19	C₂²×C₄²×C₇	C₂²	1	2	yes	—
20	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₇	C₂²	1	8	yes	—
22	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
23	C₇×#389	C₂²	1	16	yes	complemented
24	C₇×#387	C₂²	1	32	yes	complemented
25	C₇×#385	C₂²	1	32	yes	—
26	C₇×#382	C₂²	1	8	yes	complemented
27	C₇×#380	C₂²	1	16	yes	—
28	C₂×C₇×#95	C₂²	1	4	yes	—
29	C₂×C₇×#95	C₂²	1	4	yes	—
30	C₂×C₇×#95	C₂²	1	4	yes	—
31	C₂×#2851	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂⁵×C₇	C₂³	1	1	yes	characteristic
33	C₂³×C₄×C₇	—	2	8	no	—
34	C₂³×C₄×C₇	—	2	8	no	—
35	C₂³×C₄×C₇	—	2	4	no	—
36	C₂³×C₄×C₇	—	2	8	no	—
37	C₂³×C₄×C₇	—	2	4	no	—
38	C₂³×C₄×C₇	Q₈	1	8	yes	—
39	C₂³×C₄×C₇	C₂³	1	8	yes	—
40	C₂³×C₄×C₇	C₂³	1	4	yes	—
41	C₂³×C₄×C₇	C₂³	1	4	yes	—
42	C₂³×C₄×C₇	C₂³	1	2	yes	—
43	C₂³×C₄×C₇	C₂³	1	4	yes	—
44	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₇	C₂³	1	2	yes	—
46	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
47	C₇×#125	—	2	32	no	—
48	C₂×C₇×C₄⋊C₄	—	2	16	no	—
49	C₂×C₇×C₄⋊C₄	—	2	8	no	—
50	C₂×C₇×C₄⋊C₄	—	2	16	no	—
51	C₂×C₇×C₄⋊C₄	—	2	8	no	—
52	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
53	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
54	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
55	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
56	C₂×C₇×C₂²⋊C₄	—	2	16	no	—
57	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
58	C₂×C₄²×C₇	—	2	8	no	—
59	C₂×C₄²×C₇	—	2	4	no	—
60	C₂×C₄²×C₇	—	2	32	no	—
61	C₂×C₄²×C₇	D₄	1	8	yes	—
62	C₂×C₄²×C₇	C₂³	1	8	yes	—
63	C₂×C₄²×C₇	C₂³	1	4	yes	—
64	C₂×C₄²×C₇	C₂³	1	4	yes	—
65	C₇×#95	C₂³	1	16	yes	—
66	C₇×#95	C₂³	1	16	yes	—
67	C₇×#95	C₂³	1	16	yes	—
68	C₂²×#125	C₂×C₇	1	1	yes	characteristic, complemented
69	C₂³×C₄²	C₂×C₇	1	1	yes	characteristic
70	#2851	C₂×C₇	1	16	yes	direct product factor
71	C₂×#389	C₂×C₇	1	2	yes	complemented
72	C₂×#387	C₂×C₇	1	4	yes	complemented
73	C₂×#385	C₂×C₇	1	4	yes	—
74	C₂×#382	C₂×C₇	1	1	yes	characteristic, complemented
75	C₂×#380	C₂×C₇	1	2	yes	—
76	C₂⁴×C₇	—	2	2	no	—
77	C₂⁴×C₇	—	2	2	no	—
78	C₂⁴×C₇	—	2	4	no	—
79	C₂⁴×C₇	C₂×Q₈	1	4	yes	—
80	C₂⁴×C₇	#41	1	8	yes	—
81	C₂⁴×C₇	C₂⁴	1	2	yes	—
82	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
83	C₂²×C₄×C₇	—	2	64	no	—
84	C₂²×C₄×C₇	—	2	2	no	—
85	C₂²×C₄×C₇	—	2	4	no	—
86	C₂²×C₄×C₇	—	2	16	no	—
87	C₂²×C₄×C₇	—	2	2	no	—
88	C₂²×C₄×C₇	—	2	4	no	—
89	C₂²×C₄×C₇	—	2	4	no	—
90	C₂²×C₄×C₇	—	2	4	no	—
91	C₂²×C₄×C₇	—	2	32	no	—
92	C₂²×C₄×C₇	—	2	16	no	—
93	C₂²×C₄×C₇	—	2	8	no	—
94	C₂²×C₄×C₇	—	2	16	no	—
95	C₂²×C₄×C₇	—	2	8	no	—
96	C₂²×C₄×C₇	—	2	8	no	—
97	C₂²×C₄×C₇	—	2	8	no	—
98	C₂²×C₄×C₇	—	2	8	no	—
99	C₂²×C₄×C₇	—	2	8	no	—
100	C₂²×C₄×C₇	—	2	8	no	—
101	C₂²×C₄×C₇	—	2	8	no	—
102	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
103	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
105	C₂²×C₄×C₇	C₂×Q₈	1	16	yes	—
106	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
107	C₂²×C₄×C₇	#41	1	8	yes	—
108	C₂²×C₄×C₇	#41	1	4	yes	—
109	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
110	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
111	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
112	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
113	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
114	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
115	C₇×C₄⋊C₄	—	2	32	no	—
116	C₇×C₄⋊C₄	—	2	16	no	—
117	C₇×C₄⋊C₄	—	2	32	no	—
118	C₇×C₄⋊C₄	—	2	16	no	—
119	C₇×C₂²⋊C₄	—	2	32	no	—
120	C₄²×C₇	—	2	16	no	—
121	C₄²×C₇	—	2	8	no	—
122	C₄²×C₇	C₂×D₄	1	16	yes	—
123	C₂⁴×C₄	C₂²×C₇	1	2	yes	—
124	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
125	C₂×#125	—	2	8	no	—
126	C₂×#125	C₂²×C₇	1	8	yes	complemented
127	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
128	C₂²×C₄⋊C₄	C₂²×C₇	1	4	yes	—
129	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
130	C₂²×C₄⋊C₄	C₂²×C₇	1	4	yes	—
131	C₂²×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
132	C₂²×C₄²	—	2	8	no	—
133	C₂²×C₄²	C₂²×C₇	1	8	yes	—
134	C₂²×C₄²	C₂²×C₇	1	2	yes	—
135	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
136	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
137	#389	C₂²×C₇	1	16	yes	complemented
138	#387	C₂²×C₇	1	32	yes	complemented
139	#385	C₂²×C₇	1	32	yes	—
140	#382	C₂²×C₇	1	8	yes	complemented
141	#380	C₂²×C₇	1	16	yes	—
142	C₂×#95	C₂²×C₇	1	4	yes	—
143	C₂×#95	C₂²×C₇	1	4	yes	—
144	C₂×#95	C₂²×C₇	1	4	yes	—
145	C₂³×C₇	—	2	8	no	—
146	C₂³×C₇	—	2	16	no	—
147	C₂³×C₇	—	2	16	no	—
148	C₂³×C₇	—	2	8	no	—
149	C₂³×C₇	—	2	2	no	—
150	C₂³×C₇	—	2	2	no	—
151	C₂³×C₇	—	2	4	no	—
152	C₂³×C₇	#125	1	16	yes	complemented
153	C₂³×C₇	C₂²×D₄	1	2	yes	—
154	C₂³×C₇	C₂²×Q₈	1	4	yes	—
155	C₂³×C₇	C₂²×Q₈	1	2	yes	—
156	C₂³×C₇	C₂×#41	1	8	yes	—
157	C₂³×C₇	C₂×#41	1	2	yes	—
158	C₂³×C₇	C₂×#41	1	4	yes	—
159	C₂³×C₇	C₂×#41	1	4	yes	—
160	C₂³×C₇	C₂⁵	1	1	yes	characteristic
161	C₂×C₄×C₇	—	2	64	no	—
162	C₂×C₄×C₇	—	2	8	no	—
163	C₂×C₄×C₇	—	2	16	no	—
164	C₂×C₄×C₇	—	2	16	no	—
165	C₂×C₄×C₇	—	2	2	no	—
166	C₂×C₄×C₇	—	2	4	no	—
167	C₂×C₄×C₇	—	2	2	no	—
168	C₂×C₄×C₇	—	2	4	no	—
169	C₂×C₄×C₇	—	2	4	no	—
170	C₂×C₄×C₇	—	2	4	no	—
171	C₂×C₄×C₇	—	2	32	no	—
172	C₂×C₄×C₇	—	2	8	no	—
173	C₂×C₄×C₇	—	2	8	no	—
174	C₂×C₄×C₇	—	2	8	no	—
175	C₂×C₄×C₇	—	2	8	no	—
176	C₂×C₄×C₇	—	2	8	no	—
177	C₂×C₄×C₇	—	2	8	no	—
178	C₂×C₄×C₇	—	4	16	no	—
179	C₂×C₄×C₇	—	4	16	no	—
180	C₂×C₄×C₇	C₂²⋊Q₈	1	16	yes	—
181	C₂×C₄×C₇	C₂²×D₄	1	8	yes	—
182	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
183	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
184	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
185	C₂×C₄×C₇	C₂×#41	1	8	yes	—
186	C₂×C₄×C₇	C₂×#41	1	4	yes	—
187	C₂⁵	C₂³×C₇	1	1	yes	characteristic
188	C₂³×C₄	—	2	8	no	—
189	C₂³×C₄	—	2	8	no	—
190	C₂³×C₄	—	2	4	no	—
191	C₂³×C₄	—	2	8	no	—
192	C₂³×C₄	—	2	4	no	—
193	C₂³×C₄	C₇×Q₈	1	8	yes	—
194	C₂³×C₄	C₂³×C₇	1	4	yes	—
195	C₂³×C₄	C₂³×C₇	1	4	yes	—
196	C₂³×C₄	C₂³×C₇	1	8	yes	—
197	C₂³×C₄	C₂³×C₇	1	2	yes	—
198	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
199	C₂³×C₄	C₂³×C₇	1	4	yes	—
200	C₂³×C₄	C₂³×C₇	1	2	yes	—
201	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
202	#125	—	2	32	no	—
203	C₂×C₄⋊C₄	—	2	16	no	—
204	C₂×C₄⋊C₄	—	2	8	no	—
205	C₂×C₄⋊C₄	—	2	16	no	—
206	C₂×C₄⋊C₄	—	2	8	no	—
207	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
208	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
209	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
210	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
211	C₂×C₂²⋊C₄	—	2	16	no	—
212	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
213	C₂×C₄²	—	2	8	no	—
214	C₂×C₄²	—	2	4	no	—
215	C₂×C₄²	—	2	32	no	—
216	C₂×C₄²	C₇×D₄	1	8	yes	—
217	C₂×C₄²	C₂³×C₇	1	8	yes	—
218	C₂×C₄²	C₂³×C₇	1	4	yes	—
219	C₂×C₄²	C₂³×C₇	1	4	yes	—
220	#95	C₂³×C₇	1	16	yes	—
221	#95	C₂³×C₇	1	16	yes	—
222	#95	C₂³×C₇	1	16	yes	—
223	C₂²×C₇	—	2	32	no	—
224	C₂²×C₇	—	2	4	no	—
225	C₂²×C₇	—	2	8	no	—
226	C₂²×C₇	—	2	8	no	—
227	C₂²×C₇	—	2	4	no	—
228	C₂²×C₇	C₂×C₂²⋊Q₈	1	4	yes	—
229	C₂²×C₇	#525	1	8	yes	—
230	C₂²×C₇	C₂×#125	1	4	yes	—
231	C₂²×C₇	C₂×#125	1	8	yes	complemented
232	C₂²×C₇	#529	1	8	yes	—
233	C₂²×C₇	#533	1	4	yes	—
234	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
235	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
236	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
237	C₂²×C₇	C₂²×#41	1	2	yes	—
238	C₂²×C₇	C₂²×#41	1	2	yes	—
239	C₄×C₇	—	2	4	no	—
240	C₄×C₇	—	2	8	no	—
241	C₄×C₇	—	2	8	no	—
242	C₄×C₇	—	4	8	no	—
243	C₄×C₇	—	4	8	no	—
244	C₄×C₇	C₂×C₂²⋊Q₈	1	8	yes	—
245	C₂⁴	—	2	2	no	—
246	C₂⁴	—	2	2	no	—
247	C₂⁴	—	2	4	no	—
248	C₂⁴	C₂×C₇×Q₈	1	4	yes	—
249	C₂⁴	C₇×#41	1	8	yes	—
250	C₂⁴	C₂⁴×C₇	1	2	yes	—
251	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
252	C₂²×C₄	—	2	64	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	16	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	32	no	—
261	C₂²×C₄	—	2	16	no	—
262	C₂²×C₄	—	2	8	no	—
263	C₂²×C₄	—	2	16	no	—
264	C₂²×C₄	—	2	8	no	—
265	C₂²×C₄	—	2	8	no	—
266	C₂²×C₄	—	2	8	no	—
267	C₂²×C₄	—	2	8	no	—
268	C₂²×C₄	—	2	8	no	—
269	C₂²×C₄	—	2	8	no	—
270	C₂²×C₄	—	2	8	no	—
271	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
272	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
273	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
274	C₂²×C₄	C₂×C₇×Q₈	1	16	yes	—
275	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
276	C₂²×C₄	C₇×#41	1	8	yes	—
277	C₂²×C₄	C₇×#41	1	4	yes	—
278	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
279	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
280	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
281	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
282	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
283	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
284	C₄⋊C₄	—	2	32	no	—
285	C₄⋊C₄	—	2	16	no	—
286	C₄⋊C₄	—	2	32	no	—
287	C₄⋊C₄	—	2	16	no	—
288	C₂²⋊C₄	—	2	32	no	—
289	C₄²	—	2	16	no	—
290	C₄²	—	2	8	no	—
291	C₄²	C₂×C₇×D₄	1	16	yes	—
292	C₂×C₇	—	2	8	no	—
293	C₂×C₇	#2851	1	8	yes	direct product factor
294	C₂×C₇	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
295	C₂×C₇	C₂×#525	1	2	yes	—
296	C₂×C₇	C₂²×#125	1	1	yes	characteristic
297	C₂×C₇	C₂×#529	1	2	yes	—
298	C₂×C₇	C₂×#533	1	1	yes	characteristic
299	C₂³	—	2	2	no	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	4	no	—
302	C₂³	—	2	8	no	—
303	C₂³	—	2	16	no	—
304	C₂³	—	2	16	no	—
305	C₂³	—	2	8	no	—
306	C₂³	C₇×#125	1	16	yes	complemented
307	C₂³	C₂²×C₇×D₄	1	2	yes	—
308	C₂³	C₂²×C₇×Q₈	1	4	yes	—
309	C₂³	C₂²×C₇×Q₈	1	2	yes	—
310	C₂³	C₂×C₇×#41	1	8	yes	—
311	C₂³	C₂×C₇×#41	1	2	yes	—
312	C₂³	C₂×C₇×#41	1	4	yes	—
313	C₂³	C₂×C₇×#41	1	4	yes	—
314	C₂³	C₂⁵×C₇	1	1	yes	characteristic
315	C₂×C₄	—	2	64	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	8	no	—
323	C₂×C₄	—	2	16	no	—
324	C₂×C₄	—	2	16	no	—
325	C₂×C₄	—	2	32	no	—
326	C₂×C₄	—	2	8	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	4	16	no	—
333	C₂×C₄	—	4	16	no	—
334	C₂×C₄	C₇×C₂²⋊Q₈	1	16	yes	—
335	C₂×C₄	C₂²×C₇×D₄	1	8	yes	—
336	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
337	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
338	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
339	C₂×C₄	C₂×C₇×#41	1	8	yes	—
340	C₂×C₄	C₂×C₇×#41	1	4	yes	—
341	C₇	C₂×#2851	1	1	yes	characteristic, direct product factor, Sylow
342	C₂²	—	2	4	no	—
343	C₂²	—	2	8	no	—
344	C₂²	—	2	8	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	2	32	no	—
347	C₂²	C₂×C₇×C₂²⋊Q₈	1	4	yes	—
348	C₂²	C₇×#525	1	8	yes	—
349	C₂²	C₂×C₇×#125	1	4	yes	—
350	C₂²	C₂×C₇×#125	1	8	yes	complemented
351	C₂²	C₇×#529	1	8	yes	—
352	C₂²	C₇×#533	1	4	yes	—
353	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
354	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
355	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
356	C₂²	C₂²×C₇×#41	1	2	yes	—
357	C₂²	C₂²×C₇×#41	1	2	yes	—
358	C₄	—	2	4	no	—
359	C₄	—	2	8	no	—
360	C₄	—	2	8	no	—
361	C₄	—	4	8	no	—
362	C₄	—	4	8	no	—
363	C₄	C₂×C₇×C₂²⋊Q₈	1	8	yes	—
364	C₂	—	2	8	no	—
365	C₂	C₇×#2851	1	8	yes	direct product factor
366	C₂	C₂²×C₇×C₂²⋊Q₈	1	1	yes	characteristic
367	C₂	C₂×C₇×#525	1	2	yes	—
368	C₂	C₂²×C₇×#125	1	1	yes	characteristic
369	C₂	C₂×C₇×#529	1	2	yes	—
370	C₂	C₂×C₇×#533	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂⁵×C₇	C₂³
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. C₂²×C₇×#125	C₂	semidirect
3. C₇×#2851	C₂	direct (N × H)
4. C₂×C₇×#389	C₂	semidirect
5. C₂×C₇×#387	C₂	semidirect
7. C₂×C₇×#382	C₂	semidirect
12. C₂×C₇×#125	C₂²	semidirect
23. C₇×#389	C₂²	semidirect
24. C₇×#387	C₂²	semidirect
26. C₇×#382	C₂²	semidirect
31. C₂×#2851	C₇	direct (N × H)
68. C₂²×#125	C₂×C₇	semidirect
70. #2851	C₂×C₇	direct (N × H)
71. C₂×#389	C₂×C₇	semidirect
72. C₂×#387	C₂×C₇	semidirect
74. C₂×#382	C₂×C₇	semidirect
126. C₂×#125	C₂²×C₇	semidirect
137. #389	C₂²×C₇	semidirect
138. #387	C₂²×C₇	semidirect
140. #382	C₂²×C₇	semidirect
152. C₂³×C₇	#125	semidirect
231. C₂²×C₇	C₂×#125	semidirect
293. C₂×C₇	#2851	direct (N × H)
306. C₂³	C₇×#125	semidirect
341. C₇	C₂×#2851	direct (N × H)
350. C₂²	C₂×C₇×#125	semidirect
365. C₂	C₇×#2851	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₇×#125	2
C₂³×C₄²×C₇	2
C₇×#2851	2
C₂×C₇×#389	2
C₂×C₇×#387	2
C₂×C₇×#385	2
C₂×C₇×#382	2
C₂×C₇×#380	2
C₂×#2851	7

Subgroups — C2×C7×#2851 #13213832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2851 #13213832