Subgroups — C₂×C₇×#1685 #13196346

Order 1792.

842 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#474	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#459	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1685	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₇×#335	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#331	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₇×SD₁₆	—	2	1	no	—
10	C₂²×C₇×SD₁₆	—	2	1	no	—
11	C₂²×C₇×D₈	—	2	1	no	—
12	C₂²×C₇×M₁₆	—	2	1	no	—
13	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₇×#127	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
16	C₇×#492	—	2	2	no	—
17	C₇×#492	C₂²	1	4	yes	complemented
18	C₇×#474	—	2	2	no	—
19	C₇×#474	C₂²	1	4	yes	complemented
20	C₇×#459	—	2	2	no	—
21	C₇×#459	C₂²	1	4	yes	—
22	C₇×#436	—	2	2	no	—
23	C₇×#436	C₂²	1	4	yes	complemented
24	C₂×C₇×#107	—	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×#102	—	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×#332	C₂²	1	4	yes	complemented
34	C₇×#331	C₂²	1	4	yes	complemented
35	C₂×#1685	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂²×C₇×Q₈	—	2	1	no	—
37	C₂²×C₇×D₄	—	2	1	no	—
38	C₂²×C₇×D₄	—	2	1	no	—
39	C₂²×C₇×D₄	—	2	1	no	—
40	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₇	—	2	1	no	—
42	C₂×C₇×SD₁₆	—	2	4	no	—
43	C₂×C₇×SD₁₆	—	2	4	no	—
44	C₂×C₇×SD₁₆	—	4	4	no	—
45	C₂×C₇×SD₁₆	—	4	4	no	—
46	C₂×C₇×D₈	—	2	4	no	—
47	C₂×C₇×D₈	—	4	4	no	—
48	C₂×C₇×M₁₆	—	2	4	no	—
49	C₂×C₇×M₁₆	—	4	4	no	—
50	C₂²×C₇×C₈	—	2	1	no	—
51	C₂²×C₇×C₈	—	2	1	no	—
52	C₂²×C₇×C₈	—	2	1	no	—
53	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
54	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
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×#127	—	2	1	no	—
60	C₇×#127	—	2	1	no	—
61	C₇×#127	—	2	1	no	—
62	C₇×#127	C₂³	1	2	yes	—
63	C₄×C₇×D₄	—	2	1	no	—
64	C₄×C₇×D₄	—	2	1	no	—
65	C₄×C₇×D₄	D₄	1	2	yes	—
66	C₄×C₇×D₄	C₂³	1	2	yes	—
67	C₂×C₇×C₄⋊C₄	—	2	1	no	—
68	C₂×C₇×C₄⋊C₄	—	2	1	no	—
69	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
70	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
72	C₇×#107	—	2	4	no	—
73	C₇×C₄⋊C₈	—	2	1	no	—
74	C₇×C₄⋊C₈	—	2	1	no	—
75	C₇×C₄⋊C₈	—	2	1	no	—
76	C₇×C₄⋊C₈	C₂³	1	2	yes	—
77	C₇×C₄⋊C₈	C₂³	1	2	yes	—
78	C₇×C₄⋊C₈	C₂³	1	2	yes	—
79	C₇×#102	—	2	4	no	—
80	C₇×#102	—	2	4	no	—
81	C₇×C₂²⋊C₈	—	2	4	no	—
82	C₄×C₇×C₈	D₄	1	2	yes	—
83	C₄×C₇×C₈	C₂³	1	2	yes	—
84	C₂×#492	C₂×C₇	1	1	yes	characteristic, complemented
85	C₂×#474	C₂×C₇	1	1	yes	characteristic, complemented
86	C₂×#459	C₂×C₇	1	1	yes	characteristic
87	C₂×#436	C₂×C₇	1	1	yes	characteristic, complemented
88	#1685	C₂×C₇	1	8	yes	direct product factor
89	C₂×#335	C₂×C₇	1	1	yes	characteristic, complemented
90	C₂×#332	C₂×C₇	1	1	yes	characteristic, complemented
91	C₂×#331	C₂×C₇	1	1	yes	characteristic, complemented
92	C₂⁴×C₇	—	2	1	no	—
93	C₂⁴×C₇	—	4	1	no	—
94	C₂×C₇×Q₈	—	2	2	no	—
95	C₂×C₇×Q₈	—	4	1	no	—
96	C₂×C₇×Q₈	—	4	2	no	—
97	C₂×C₇×Q₈	—	4	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	—	2	2	no	—
102	C₂×C₇×D₄	—	2	2	no	—
103	C₂×C₇×D₄	—	2	2	no	—
104	C₂×C₇×D₄	—	4	1	no	—
105	C₂×C₇×D₄	—	4	1	no	—
106	C₂×C₇×D₄	—	4	1	no	—
107	C₂×C₇×D₄	—	4	2	no	—
108	C₂×C₇×D₄	—	4	2	no	—
109	C₂×C₇×D₄	—	4	2	no	—
110	C₂×C₇×D₄	—	4	2	no	—
111	C₂×C₇×D₄	—	8	2	no	—
112	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₇	—	2	1	no	—
114	C₂²×C₄×C₇	—	2	2	no	—
115	C₂²×C₄×C₇	—	2	2	no	—
116	C₂²×C₄×C₇	—	4	2	no	—
117	C₂²×C₄×C₇	—	4	2	no	—
118	C₂²×C₄×C₇	—	4	1	no	—
119	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₇	#41	1	1	yes	characteristic
122	C₇×SD₁₆	—	4	8	no	—
123	C₇×SD₁₆	—	4	8	no	—
124	C₇×D₈	—	4	8	no	—
125	C₇×M₁₆	—	4	8	no	—
126	C₂×C₇×C₈	—	2	2	no	—
127	C₂×C₇×C₈	—	2	2	no	—
128	C₂×C₇×C₈	—	2	2	no	—
129	C₂×C₇×C₈	—	2	2	no	—
130	C₂×C₇×C₈	—	4	2	no	—
131	C₂×C₇×C₈	—	4	2	no	—
132	C₂×C₇×C₈	—	4	2	no	—
133	C₂×C₇×C₈	D₈	1	4	yes	complemented
134	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
135	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
136	C₇×C₄⋊C₄	—	2	1	no	—
137	C₇×C₄⋊C₄	—	2	2	no	—
138	C₇×C₄⋊C₄	—	2	2	no	—
139	C₇×C₄⋊C₄	—	4	1	no	—
140	C₇×C₄⋊C₄	—	4	1	no	—
141	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
142	C₇×C₂²⋊C₄	—	2	2	no	—
143	C₇×C₂²⋊C₄	—	2	2	no	—
144	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₇	#41	1	1	yes	characteristic
147	C₄²×C₇	C₂⁴	1	1	yes	characteristic
148	C₂²×SD₁₆	—	2	1	no	—
149	C₂²×SD₁₆	—	2	1	no	—
150	C₂²×D₈	—	2	1	no	—
151	C₂²×M₁₆	—	2	1	no	—
152	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
153	C₂×#127	C₂²×C₇	1	1	yes	characteristic
154	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
155	#492	—	2	2	no	—
156	#492	C₂²×C₇	1	4	yes	complemented
157	#474	—	2	2	no	—
158	#474	C₂²×C₇	1	4	yes	complemented
159	#459	—	2	2	no	—
160	#459	C₂²×C₇	1	4	yes	—
161	#436	—	2	2	no	—
162	#436	C₂²×C₇	1	4	yes	complemented
163	C₂×#107	—	2	1	no	—
164	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
165	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
166	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
167	C₂×#102	—	2	1	no	—
168	C₂×#102	—	2	1	no	—
169	C₂×C₂²⋊C₈	—	2	1	no	—
170	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
171	#335	C₂²×C₇	1	4	yes	complemented
172	#332	C₂²×C₇	1	4	yes	complemented
173	#331	C₂²×C₇	1	4	yes	complemented
174	C₂³×C₇	—	2	2	no	—
175	C₂³×C₇	—	4	2	no	—
176	C₂³×C₇	—	4	2	no	—
177	C₂³×C₇	—	4	2	no	—
178	C₂³×C₇	—	4	2	no	—
179	C₂³×C₇	—	8	2	no	—
180	C₂³×C₇	—	8	2	no	—
181	C₂³×C₇	—	8	2	no	—
182	C₂³×C₇	#121	1	1	yes	characteristic
183	C₇×Q₈	—	4	2	no	—
184	C₇×Q₈	—	4	2	no	—
185	C₇×Q₈	—	8	2	no	—
186	C₇×D₄	—	2	2	no	—
187	C₇×D₄	—	2	2	no	—
188	C₇×D₄	—	4	2	no	—
189	C₇×D₄	—	4	2	no	—
190	C₇×D₄	—	4	2	no	—
191	C₇×D₄	—	4	2	no	—
192	C₇×D₄	—	4	2	no	—
193	C₇×D₄	—	8	2	no	—
194	C₇×D₄	—	8	2	no	—
195	C₇×D₄	—	8	2	no	—
196	C₇×D₄	—	8	2	no	—
197	C₂×C₄×C₇	—	2	2	no	—
198	C₂×C₄×C₇	—	2	2	no	—
199	C₂×C₄×C₇	—	4	2	no	—
200	C₂×C₄×C₇	—	4	2	no	—
201	C₂×C₄×C₇	—	4	2	no	—
202	C₂×C₄×C₇	—	4	4	no	—
203	C₂×C₄×C₇	—	4	2	no	—
204	C₂×C₄×C₇	—	8	2	no	—
205	C₂×C₄×C₇	#121	1	1	yes	characteristic
206	C₂×C₄×C₇	#121	1	1	yes	characteristic
207	C₂×C₄×C₇	#121	1	1	yes	characteristic
208	C₂×C₄×C₇	C₂×D₈	1	2	yes	—
209	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
210	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
211	C₂×C₄×C₇	#137	1	2	yes	—
212	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
215	C₇×C₈	—	2	2	no	—
216	C₇×C₈	—	4	2	no	—
217	C₇×C₈	—	4	2	no	—
218	C₇×C₈	—	4	2	no	—
219	C₇×C₈	C₂×D₈	1	4	yes	complemented
220	C₂²×Q₈	—	2	1	no	—
221	C₂²×D₄	—	2	1	no	—
222	C₂²×D₄	—	2	1	no	—
223	C₂²×D₄	—	2	1	no	—
224	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
225	C₂³×C₄	—	2	1	no	—
226	C₂×SD₁₆	—	2	4	no	—
227	C₂×SD₁₆	—	2	4	no	—
228	C₂×SD₁₆	—	4	4	no	—
229	C₂×SD₁₆	—	4	4	no	—
230	C₂×D₈	—	2	4	no	—
231	C₂×D₈	—	4	4	no	—
232	C₂×M₁₆	—	2	4	no	—
233	C₂×M₁₆	—	4	4	no	—
234	C₂²×C₈	—	2	1	no	—
235	C₂²×C₈	—	2	1	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
238	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
239	C₄⋊Q₈	—	2	1	no	—
240	C₄⋊Q₈	—	2	1	no	—
241	C₄⋊Q₈	—	2	1	no	—
242	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
243	#127	—	2	1	no	—
244	#127	—	2	1	no	—
245	#127	—	2	1	no	—
246	#127	C₂³×C₇	1	2	yes	—
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	C₇×D₄	1	2	yes	—
250	C₄×D₄	C₂³×C₇	1	2	yes	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
256	#107	—	2	4	no	—
257	C₄⋊C₈	—	2	1	no	—
258	C₄⋊C₈	—	2	1	no	—
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	C₂³×C₇	1	2	yes	—
261	C₄⋊C₈	C₂³×C₇	1	2	yes	—
262	C₄⋊C₈	C₂³×C₇	1	2	yes	—
263	#102	—	2	4	no	—
264	#102	—	2	4	no	—
265	C₂²⋊C₈	—	2	4	no	—
266	C₄×C₈	C₇×D₄	1	2	yes	—
267	C₄×C₈	C₂³×C₇	1	2	yes	—
268	C₂²×C₇	—	4	2	no	—
269	C₂²×C₇	—	4	2	no	—
270	C₂²×C₇	—	4	2	no	—
271	C₂²×C₇	—	8	4	no	—
272	C₂²×C₇	—	8	2	no	—
273	C₂²×C₇	—	8	2	no	—
274	C₂²×C₇	—	8	2	no	—
275	C₂²×C₇	—	16	4	no	—
276	C₂²×C₇	#459	1	2	yes	—
277	C₂²×C₇	#468	1	2	yes	—
278	C₂²×C₇	#471	1	2	yes	—
279	C₂²×C₇	C₂×#121	1	1	yes	characteristic
280	C₄×C₇	—	2	1	no	—
281	C₄×C₇	—	2	1	no	—
282	C₄×C₇	—	4	2	no	—
283	C₄×C₇	—	8	2	no	—
284	C₄×C₇	#459	1	2	yes	—
285	C₄×C₇	#468	1	2	yes	—
286	C₄×C₇	C₂²×D₈	1	1	yes	characteristic
287	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
288	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
289	C₄×C₇	C₂×#137	1	1	yes	characteristic
290	C₂⁴	—	2	1	no	—
291	C₂⁴	—	4	1	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	4	1	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×Q₈	—	4	2	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂×D₄	—	8	2	no	—
310	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	4	2	no	—
315	C₂²×C₄	—	4	2	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
318	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
319	C₂²×C₄	C₇×#41	1	1	yes	characteristic
320	SD₁₆	—	4	8	no	—
321	SD₁₆	—	4	8	no	—
322	D₈	—	4	8	no	—
323	M₁₆	—	4	8	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	4	2	no	—
329	C₂×C₈	—	4	2	no	—
330	C₂×C₈	—	4	2	no	—
331	C₂×C₈	C₇×D₈	1	4	yes	complemented
332	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
333	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
340	C₂²⋊C₄	—	2	2	no	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
343	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
344	C₄²	C₇×#41	1	1	yes	characteristic
345	C₄²	C₂⁴×C₇	1	1	yes	characteristic
346	C₂×C₇	—	8	2	no	—
347	C₂×C₇	—	16	2	no	—
348	C₂×C₇	#1685	1	4	yes	direct product factor
349	C₂×C₇	C₂×#459	1	1	yes	characteristic
350	C₂×C₇	C₂×#468	1	1	yes	characteristic
351	C₂×C₇	C₂×#471	1	1	yes	characteristic
352	C₂³	—	2	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	8	2	no	—
358	C₂³	—	8	2	no	—
359	C₂³	—	8	2	no	—
360	C₂³	C₇×#121	1	1	yes	characteristic
361	Q₈	—	4	2	no	—
362	Q₈	—	4	2	no	—
363	Q₈	—	8	2	no	—
364	D₄	—	2	2	no	—
365	D₄	—	2	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	4	2	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	8	2	no	—
372	D₄	—	8	2	no	—
373	D₄	—	8	2	no	—
374	D₄	—	8	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	8	2	no	—
383	C₂×C₄	C₇×#121	1	1	yes	characteristic
384	C₂×C₄	C₇×#121	1	1	yes	characteristic
385	C₂×C₄	C₇×#121	1	1	yes	characteristic
386	C₂×C₄	C₂×C₇×D₈	1	2	yes	—
387	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
388	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
389	C₂×C₄	C₇×#137	1	2	yes	—
390	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
391	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
392	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
393	C₈	—	2	2	no	—
394	C₈	—	4	2	no	—
395	C₈	—	4	2	no	—
396	C₈	—	4	2	no	—
397	C₈	C₂×C₇×D₈	1	4	yes	complemented
398	C₇	C₂×#1685	1	1	yes	characteristic, direct product factor, Sylow
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	8	4	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	16	4	no	—
407	C₂²	C₇×#459	1	2	yes	—
408	C₂²	C₇×#468	1	2	yes	—
409	C₂²	C₇×#471	1	2	yes	—
410	C₂²	C₂×C₇×#121	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	4	2	no	—
414	C₄	—	8	2	no	—
415	C₄	C₇×#459	1	2	yes	—
416	C₄	C₇×#468	1	2	yes	—
417	C₄	C₂²×C₇×D₈	1	1	yes	characteristic
418	C₄	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
419	C₄	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
420	C₄	C₂×C₇×#137	1	1	yes	characteristic
421	C₂	—	8	2	no	—
422	C₂	—	16	2	no	—
423	C₂	C₇×#1685	1	4	yes	direct product factor
424	C₂	C₂×C₇×#459	1	1	yes	characteristic
425	C₂	C₂×C₇×#468	1	1	yes	characteristic
426	C₂	C₂×C₇×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₂×C₇×#459	C₂
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×#492	C₂	semidirect
2. C₂×C₇×#474	C₂	semidirect
4. C₂×C₇×#436	C₂	semidirect
5. C₇×#1685	C₂	direct (N × H)
6. C₂×C₇×#335	C₂	semidirect
7. C₂×C₇×#332	C₂	semidirect
8. C₂×C₇×#331	C₂	semidirect
17. C₇×#492	C₂²	semidirect
19. C₇×#474	C₂²	semidirect
23. C₇×#436	C₂²	semidirect
32. C₇×#335	C₂²	semidirect
33. C₇×#332	C₂²	semidirect
34. C₇×#331	C₂²	semidirect
35. C₂×#1685	C₇	direct (N × H)
84. C₂×#492	C₂×C₇	semidirect
85. C₂×#474	C₂×C₇	semidirect
87. C₂×#436	C₂×C₇	semidirect
88. #1685	C₂×C₇	direct (N × H)
89. C₂×#335	C₂×C₇	semidirect
90. C₂×#332	C₂×C₇	semidirect
91. C₂×#331	C₂×C₇	semidirect
133. C₂×C₇×C₈	D₈	semidirect
156. #492	C₂²×C₇	semidirect
158. #474	C₂²×C₇	semidirect
162. #436	C₂²×C₇	semidirect
171. #335	C₂²×C₇	semidirect
172. #332	C₂²×C₇	semidirect
173. #331	C₂²×C₇	semidirect
219. C₇×C₈	C₂×D₈	semidirect
331. C₂×C₈	C₇×D₈	semidirect
348. C₂×C₇	#1685	direct (N × H)
397. C₈	C₂×C₇×D₈	semidirect
398. C₇	C₂×#1685	direct (N × H)
423. C₂	C₇×#1685	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×#492	2
C₂×C₇×#474	2
C₂×C₇×#459	2
C₂×C₇×#436	2
C₇×#1685	2
C₂×C₇×#335	2
C₂×C₇×#332	2
C₂×C₇×#331	2
C₂×#1685	7

Subgroups — C2×C7×#1685 #13196346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#1685 #13196346