Subgroups — C₇×#17967 #13195183

Order 1792.

594 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3172	C₂	1	1	yes	maximal, characteristic
2	C₇×#2966	C₂	1	1	yes	maximal, characteristic
3	C₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1591	C₂	1	2	yes	maximal, complemented
5	C₇×#1590	C₂	1	2	yes	maximal, complemented
6	C₇×#1579	C₂	1	2	yes	maximal, complemented
7	C₇×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₇×#1569	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1497	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1495	C₂	1	1	yes	maximal, characteristic
11	C₇×C₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#533	C₂²	1	1	yes	characteristic
13	C₇×#529	C₂²	1	1	yes	characteristic
14	C₇×#501	C₄	1	1	yes	characteristic
15	C₇×#497	C₄	1	1	yes	characteristic
16	C₇×#491	C₄	1	1	yes	characteristic
17	C₇×#489	C₄	1	1	yes	characteristic
18	C₇×#470	C₄	1	2	yes	—
19	C₇×#468	C₄	1	2	yes	—
20	C₇×#446	—	2	1	no	—
21	C₇×#446	C₂²	1	2	yes	—
22	C₇×#446	C₂²	1	1	yes	characteristic
23	C₇×C₈×Q₈	—	2	1	no	—
24	C₇×C₈×Q₈	C₂²	1	2	yes	—
25	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
26	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
27	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
28	C₇×#436	C₂²	1	1	yes	characteristic
29	C₇×#435	—	2	1	no	—
30	C₇×C₈×D₄	—	2	1	no	—
31	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
32	C₇×#433	—	2	1	no	—
33	C₇×#432	C₂²	1	1	yes	characteristic
34	C₇×#431	C₂²	1	1	yes	characteristic
35	C₇×#424	—	2	1	no	—
36	C₇×#423	C₂²	1	1	yes	characteristic
37	C₇×#405	—	2	1	no	—
38	C₇×#405	—	2	1	no	—
39	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
41	C₇×#335	C₂²	1	2	yes	—
42	C₇×#334	C₂²	1	2	yes	—
43	C₇×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₇×Q₈⋊C₈	C₂²	1	2	yes	—
45	C₇×Q₈⋊C₈	C₂²	1	2	yes	—
46	C₇×D₄⋊C₈	C₂²	1	2	yes	—
47	C₇×#322	C₂²	1	2	yes	—
48	C₇×C₈²	C₂²	1	2	yes	—
49	#17967	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₇×Q₁₆	C₂×C₄	1	2	yes	—
51	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	—
52	C₂×C₇×M₁₆	—	2	1	no	—
53	C₂×C₇×M₁₆	—	2	1	no	—
54	C₂×C₇×M₁₆	C₂×C₄	1	2	yes	—
55	C₂²×C₇×C₈	—	2	1	no	—
56	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
57	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
58	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
59	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
60	C₇×#126	—	2	1	no	—
61	C₇×#125	—	2	1	no	—
62	C₇×#125	C₂×C₄	1	1	yes	characteristic
63	C₇×#124	C₂×C₄	1	1	yes	characteristic
64	C₇×#123	—	2	1	no	—
65	C₇×C₂²⋊Q₈	—	2	1	no	—
66	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
67	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
68	C₇×#121	C₂×C₄	1	1	yes	characteristic
69	C₄×C₇×Q₈	—	2	1	no	—
70	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
71	C₄×C₇×Q₈	C₂³	1	2	yes	—
72	C₄×C₇×D₄	—	2	1	no	—
73	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
74	C₇×#117	—	2	1	no	—
75	C₇×#117	—	2	1	no	—
76	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
77	C₇×#107	C₂×C₄	1	2	yes	—
78	C₇×#106	C₂×C₄	1	2	yes	—
79	C₇×C₄⋊C₈	—	2	2	no	—
80	C₇×C₄⋊C₈	—	2	2	no	—
81	C₇×C₄⋊C₈	—	2	1	no	—
82	C₇×C₄⋊C₈	—	2	1	no	—
83	C₇×C₄⋊C₈	—	2	1	no	—
84	C₇×C₄⋊C₈	—	2	1	no	—
85	C₇×C₄⋊C₈	C₂³	1	2	yes	—
86	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₇×#103	C₂×C₄	1	2	yes	—
89	C₇×#103	C₂×C₄	1	2	yes	—
90	C₇×#103	C₂×C₄	1	2	yes	—
91	C₇×#102	C₂×C₄	1	2	yes	—
92	C₇×C₂²⋊C₈	—	2	1	no	—
93	C₇×C₂²⋊C₈	—	2	1	no	—
94	C₇×C₂²⋊C₈	—	2	1	no	—
95	C₇×C₂²⋊C₈	—	2	1	no	—
96	C₇×#97	—	2	1	no	—
97	C₇×#97	—	2	2	no	—
98	C₇×#97	—	2	1	no	—
99	C₇×#97	C₂×C₄	1	1	yes	characteristic
100	C₇×#97	C₂×C₄	1	1	yes	characteristic
101	C₄×C₇×C₈	—	2	1	no	—
102	C₄×C₇×C₈	—	2	2	no	—
103	C₄×C₇×C₈	D₄	1	1	yes	characteristic
104	C₄×C₇×C₈	D₄	1	1	yes	characteristic
105	C₄×C₇×C₈	C₂³	1	2	yes	—
106	C₄×C₇×C₈	C₂³	1	2	yes	—
107	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
108	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
109	#3172	C₂×C₇	1	1	yes	characteristic
110	#2966	C₂×C₇	1	1	yes	characteristic
111	#2960	C₂×C₇	1	1	yes	characteristic, complemented
112	#1591	C₂×C₇	1	2	yes	complemented
113	#1590	C₂×C₇	1	2	yes	complemented
114	#1579	C₂×C₇	1	2	yes	complemented
115	SD₁₆⋊C₈	C₂×C₇	1	2	yes	complemented
116	#1569	C₂×C₇	1	1	yes	characteristic, complemented
117	#1497	C₂×C₇	1	1	yes	characteristic, complemented
118	#1495	C₂×C₇	1	1	yes	characteristic
119	C₈×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
120	C₂×C₇×Q₈	—	2	1	no	—
121	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
123	C₂×C₇×D₄	—	2	1	no	—
124	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₇	—	2	1	no	—
126	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇	#41	1	1	yes	characteristic
129	C₇×Q₁₆	—	2	4	no	—
130	C₇×SD₁₆	—	2	4	no	—
131	C₇×M₁₆	—	2	4	no	—
132	C₇×M₁₆	—	4	2	no	—
133	C₇×M₁₆	—	4	2	no	—
134	C₂×C₇×C₈	—	2	2	no	—
135	C₂×C₇×C₈	—	2	1	no	—
136	C₂×C₇×C₈	—	2	2	no	—
137	C₂×C₇×C₈	—	2	1	no	—
138	C₂×C₇×C₈	—	2	2	no	—
139	C₂×C₇×C₈	—	4	1	no	—
140	C₂×C₇×C₈	—	4	2	no	—
141	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
142	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
143	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
144	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
145	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
146	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
147	C₇×C₄⋊C₄	—	2	1	no	—
148	C₇×C₄⋊C₄	—	2	1	no	—
149	C₇×C₄⋊C₄	—	2	1	no	—
150	C₇×C₄⋊C₄	—	2	1	no	—
151	C₇×C₄⋊C₄	—	2	1	no	—
152	C₇×C₄⋊C₄	—	2	1	no	—
153	C₇×C₄⋊C₄	—	2	2	no	—
154	C₇×C₄⋊C₄	—	2	2	no	—
155	C₇×C₄⋊C₄	—	2	1	no	—
156	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
157	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
158	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
159	C₇×C₂²⋊C₄	—	2	2	no	—
160	C₇×C₂²⋊C₄	—	2	1	no	—
161	C₇×C₂²⋊C₄	—	2	1	no	—
162	C₇×C₂²⋊C₄	—	2	1	no	—
163	C₇×C₂²⋊C₄	—	2	1	no	—
164	C₇×C₂²⋊C₄	—	2	1	no	—
165	C₄²×C₇	—	2	1	no	—
166	C₄²×C₇	—	2	2	no	—
167	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₇	#41	1	1	yes	characteristic
170	C₄²×C₇	C₂⁴	1	1	yes	characteristic
171	#533	C₂²×C₇	1	1	yes	characteristic
172	#529	C₂²×C₇	1	1	yes	characteristic
173	#501	C₄×C₇	1	1	yes	characteristic
174	#497	C₄×C₇	1	1	yes	characteristic
175	#491	C₄×C₇	1	1	yes	characteristic
176	#489	C₄×C₇	1	1	yes	characteristic
177	#470	C₄×C₇	1	2	yes	—
178	#468	C₄×C₇	1	2	yes	—
179	#446	—	2	1	no	—
180	#446	C₂²×C₇	1	2	yes	—
181	#446	C₂²×C₇	1	1	yes	characteristic
182	C₈×Q₈	—	2	1	no	—
183	C₈×Q₈	C₂²×C₇	1	2	yes	—
184	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
185	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
186	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
187	#436	C₂²×C₇	1	1	yes	characteristic
188	#435	—	2	1	no	—
189	C₈×D₄	—	2	1	no	—
190	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
191	#433	—	2	1	no	—
192	#432	C₂²×C₇	1	1	yes	characteristic
193	#431	C₂²×C₇	1	1	yes	characteristic
194	#424	—	2	1	no	—
195	#423	C₂²×C₇	1	1	yes	characteristic
196	#405	—	2	1	no	—
197	#405	—	2	1	no	—
198	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
199	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
200	#335	C₂²×C₇	1	2	yes	—
201	#334	C₂²×C₇	1	2	yes	—
202	Q₈⋊C₈	C₂²×C₇	1	2	yes	—
203	Q₈⋊C₈	C₂²×C₇	1	2	yes	—
204	Q₈⋊C₈	C₂²×C₇	1	2	yes	—
205	D₄⋊C₈	C₂²×C₇	1	2	yes	—
206	#322	C₂²×C₇	1	2	yes	—
207	C₈²	C₂²×C₇	1	2	yes	—
208	C₂³×C₇	—	2	1	no	—
209	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
210	C₇×Q₈	—	2	2	no	—
211	C₇×Q₈	—	2	2	no	—
212	C₇×Q₈	—	2	2	no	—
213	C₇×Q₈	—	4	2	no	—
214	C₇×D₄	—	2	2	no	—
215	C₇×D₄	—	4	2	no	—
216	C₂×C₄×C₇	—	2	2	no	—
217	C₂×C₄×C₇	—	2	1	no	—
218	C₂×C₄×C₇	—	2	1	no	—
219	C₂×C₄×C₇	—	2	1	no	—
220	C₂×C₄×C₇	—	2	2	no	—
221	C₂×C₄×C₇	—	2	1	no	—
222	C₂×C₄×C₇	—	2	2	no	—
223	C₂×C₄×C₇	—	2	1	no	—
224	C₂×C₄×C₇	—	4	1	no	—
225	C₂×C₄×C₇	—	4	1	no	—
226	C₂×C₄×C₇	—	4	1	no	—
227	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
233	C₇×C₈	—	2	2	no	—
234	C₇×C₈	—	2	1	no	—
235	C₇×C₈	—	2	1	no	—
236	C₇×C₈	—	2	1	no	—
237	C₇×C₈	—	4	2	no	—
238	C₇×C₈	—	4	1	no	—
239	C₇×C₈	—	4	1	no	—
240	C₇×C₈	—	4	2	no	—
241	C₇×C₈	#131	1	4	yes	—
242	C₇×C₈	#137	1	2	yes	—
243	C₂×Q₁₆	C₂×C₄×C₇	1	2	yes	—
244	C₂×SD₁₆	C₂×C₄×C₇	1	2	yes	—
245	C₂×M₁₆	—	2	1	no	—
246	C₂×M₁₆	—	2	1	no	—
247	C₂×M₁₆	C₂×C₄×C₇	1	2	yes	—
248	C₂²×C₈	—	2	1	no	—
249	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
250	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
251	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
252	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
253	#126	—	2	1	no	—
254	#125	—	2	1	no	—
255	#125	C₂×C₄×C₇	1	1	yes	characteristic
256	#124	C₂×C₄×C₇	1	1	yes	characteristic
257	#123	—	2	1	no	—
258	C₂²⋊Q₈	—	2	1	no	—
259	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
260	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
261	#121	C₂×C₄×C₇	1	1	yes	characteristic
262	C₄×Q₈	—	2	1	no	—
263	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
264	C₄×Q₈	C₂³×C₇	1	2	yes	—
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
267	#117	—	2	1	no	—
268	#117	—	2	1	no	—
269	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
270	#107	C₂×C₄×C₇	1	2	yes	—
271	#106	C₂×C₄×C₇	1	2	yes	—
272	C₄⋊C₈	—	2	2	no	—
273	C₄⋊C₈	—	2	2	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	C₂³×C₇	1	2	yes	—
279	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
280	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
281	#103	C₂×C₄×C₇	1	2	yes	—
282	#103	C₂×C₄×C₇	1	2	yes	—
283	#103	C₂×C₄×C₇	1	2	yes	—
284	#102	C₂×C₄×C₇	1	2	yes	—
285	C₂²⋊C₈	—	2	1	no	—
286	C₂²⋊C₈	—	2	1	no	—
287	C₂²⋊C₈	—	2	1	no	—
288	C₂²⋊C₈	—	2	1	no	—
289	#97	—	2	1	no	—
290	#97	—	2	2	no	—
291	#97	—	2	1	no	—
292	#97	C₂×C₄×C₇	1	1	yes	characteristic
293	#97	C₂×C₄×C₇	1	1	yes	characteristic
294	C₄×C₈	—	2	1	no	—
295	C₄×C₈	—	2	2	no	—
296	C₄×C₈	C₇×D₄	1	1	yes	characteristic
297	C₄×C₈	C₇×D₄	1	1	yes	characteristic
298	C₄×C₈	C₂³×C₇	1	2	yes	—
299	C₄×C₈	C₂³×C₇	1	2	yes	—
300	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
301	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
302	C₂²×C₇	—	2	1	no	—
303	C₂²×C₇	—	2	1	no	—
304	C₂²×C₇	—	2	1	no	—
305	C₂²×C₇	—	4	1	no	—
306	C₂²×C₇	—	4	1	no	—
307	C₂²×C₇	—	4	1	no	—
308	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
309	C₄×C₇	—	2	1	no	—
310	C₄×C₇	—	2	1	no	—
311	C₄×C₇	—	2	1	no	—
312	C₄×C₇	—	2	1	no	—
313	C₄×C₇	—	4	1	no	—
314	C₄×C₇	—	4	2	no	—
315	C₄×C₇	—	4	1	no	—
316	C₄×C₇	—	4	1	no	—
317	C₄×C₇	—	4	2	no	—
318	C₄×C₇	C₂×#131	1	2	yes	—
319	C₄×C₇	C₂×#137	1	1	yes	characteristic
320	C₄×C₇	#575	1	1	yes	characteristic
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
323	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
328	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
329	C₂²×C₄	C₇×#41	1	1	yes	characteristic
330	Q₁₆	—	2	4	no	—
331	SD₁₆	—	2	4	no	—
332	M₁₆	—	2	4	no	—
333	M₁₆	—	4	2	no	—
334	M₁₆	—	4	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	2	no	—
342	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
343	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
344	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
345	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
346	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
347	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
358	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
359	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
360	C₂²⋊C₄	—	2	2	no	—
361	C₂²⋊C₄	—	2	1	no	—
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	2	1	no	—
364	C₂²⋊C₄	—	2	1	no	—
365	C₂²⋊C₄	—	2	1	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	2	no	—
368	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
369	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
370	C₄²	C₇×#41	1	1	yes	characteristic
371	C₄²	C₂⁴×C₇	1	1	yes	characteristic
372	C₂×C₇	—	4	1	no	—
373	C₂×C₇	—	8	1	no	—
374	C₂×C₇	#2931	1	1	yes	characteristic
375	C₂×C₇	C₄×#137	1	1	yes	characteristic
376	C₂×C₇	#2955	1	1	yes	characteristic
377	C₂³	—	2	1	no	—
378	C₂³	C₄×C₇×D₄	1	1	yes	characteristic
379	Q₈	—	2	2	no	—
380	Q₈	—	2	2	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	4	2	no	—
383	D₄	—	2	2	no	—
384	D₄	—	4	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
397	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
398	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
399	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
401	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	2	1	no	—
406	C₈	—	4	2	no	—
407	C₈	—	4	1	no	—
408	C₈	—	4	1	no	—
409	C₈	—	4	2	no	—
410	C₈	C₇×#131	1	4	yes	—
411	C₈	C₇×#137	1	2	yes	—
412	C₇	#17967	1	1	yes	characteristic, direct product factor, Sylow
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	1	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	2	no	—
429	C₄	C₂×C₇×#131	1	2	yes	—
430	C₄	C₂×C₇×#137	1	1	yes	characteristic
431	C₄	C₇×#575	1	1	yes	characteristic
432	C₂	—	4	1	no	—
433	C₂	—	8	1	no	—
434	C₂	C₇×#2931	1	1	yes	characteristic
435	C₂	C₄×C₇×#137	1	1	yes	characteristic
436	C₂	C₇×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₄²	C₂⁴×C₇
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₇×#121	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₄×C₇×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×#2960	C₂	semidirect
4. C₇×#1591	C₂	semidirect
5. C₇×#1590	C₂	semidirect
6. C₇×#1579	C₂	semidirect
7. C₇×SD₁₆⋊C₈	C₂	semidirect
8. C₇×#1569	C₂	semidirect
9. C₇×#1497	C₂	semidirect
11. C₇×C₈×M₁₆	C₂	semidirect
49. #17967	C₇	direct (N × H)
111. #2960	C₂×C₇	semidirect
112. #1591	C₂×C₇	semidirect
113. #1590	C₂×C₇	semidirect
114. #1579	C₂×C₇	semidirect
115. SD₁₆⋊C₈	C₂×C₇	semidirect
116. #1569	C₂×C₇	semidirect
117. #1497	C₂×C₇	semidirect
119. C₈×M₁₆	C₂×C₇	semidirect
412. C₇	#17967	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3172	2
C₇×#2966	2
C₇×#2960	2
C₇×#1591	2
C₇×#1590	2
C₇×#1579	2
C₇×SD₁₆⋊C₈	2
C₇×#1569	2
C₇×#1497	2
C₇×#1495	2
C₇×C₈×M₁₆	2
#17967	7

Subgroups — C7×#17967 #13195183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#17967 #13195183