Subgroups — C₇×#34439 #13211655

Order 1792.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#536	C₂	1	1	yes	maximal, characteristic
2	C₇×#2378	C₂	1	2	yes	maximal, complemented
3	C₇×#2376	C₂	1	2	yes	maximal, complemented
4	C₇×#2374	C₂	1	2	yes	maximal, complemented
5	C₇×#2368	C₂	1	2	yes	maximal, complemented
6	C₇×#2367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2367	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2365	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2365	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2341	C₂	1	1	yes	maximal, characteristic
11	C₇×Q₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×Q₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2339	C₂	1	1	yes	maximal, characteristic
14	C₇×#2335	C₂	1	2	yes	maximal, complemented
15	C₇×#2335	C₂	1	2	yes	maximal, complemented
16	C₇×#2332	C₂	1	2	yes	maximal, complemented
17	C₇×#2329	C₂	1	2	yes	maximal, complemented
18	C₇×#2327	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2326	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2314	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₇×#124	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2298	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
25	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
26	C₇×#536	C₄	1	16	yes	complemented
27	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×#124	C₂²	1	1	yes	characteristic
30	C₂×C₇×#124	C₂²	1	1	yes	characteristic
31	C₂×C₇×#123	C₂²	1	2	yes	—
32	C₂×C₇×#123	C₂²	1	2	yes	—
33	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
34	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
35	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
43	C₂×C₇×#117	C₂²	1	1	yes	characteristic
44	C₇×#391	C₂²	1	1	yes	characteristic
45	C₇×#391	C₂²	1	1	yes	characteristic
46	C₇×#391	C₂²	1	1	yes	characteristic
47	C₇×#391	C₂²	1	1	yes	characteristic
48	C₇×#391	C₂²	1	1	yes	characteristic
49	C₇×#391	C₂²	1	1	yes	characteristic
50	C₇×#391	C₂²	1	2	yes	—
51	C₇×#391	C₂²	1	2	yes	—
52	C₇×#391	C₂²	1	2	yes	—
53	C₇×#391	C₂²	1	2	yes	—
54	C₇×#390	C₂²	1	1	yes	characteristic
55	C₇×#390	C₂²	1	1	yes	characteristic
56	C₇×#390	C₂²	1	2	yes	—
57	C₇×#390	C₂²	1	2	yes	—
58	C₇×#389	C₂²	1	2	yes	—
59	C₇×#389	C₂²	1	2	yes	—
60	C₇×#389	C₂²	1	2	yes	—
61	C₇×#389	C₂²	1	2	yes	—
62	C₇×#388	C₂²	1	1	yes	characteristic
63	C₇×#388	C₂²	1	1	yes	characteristic
64	C₇×#388	C₂²	1	1	yes	characteristic
65	C₇×#388	C₂²	1	1	yes	characteristic
66	C₇×#388	C₂²	1	2	yes	—
67	C₇×#388	C₂²	1	2	yes	—
68	C₇×#388	C₂²	1	2	yes	—
69	C₇×#388	C₂²	1	2	yes	—
70	C₇×#388	C₂²	1	2	yes	—
71	C₇×#388	C₂²	1	2	yes	—
72	C₇×#388	C₂²	1	2	yes	—
73	C₇×#388	C₂²	1	2	yes	—
74	C₇×#388	C₂²	1	2	yes	—
75	C₇×#388	C₂²	1	2	yes	—
76	C₇×#387	C₂²	1	1	yes	characteristic
77	C₇×#387	C₂²	1	1	yes	characteristic
78	C₇×#387	C₂²	1	1	yes	characteristic
79	C₇×#387	C₂²	1	1	yes	characteristic
80	C₇×#387	C₂²	1	2	yes	—
81	C₇×#387	C₂²	1	2	yes	—
82	C₇×#387	C₂²	1	2	yes	—
83	C₇×#387	C₂²	1	2	yes	—
84	C₇×#387	C₂²	1	2	yes	—
85	C₇×#387	C₂²	1	2	yes	—
86	C₇×#387	C₂²	1	2	yes	—
87	C₇×#387	C₂²	1	2	yes	—
88	C₇×#387	C₂²	1	2	yes	—
89	C₇×#387	C₂²	1	2	yes	—
90	C₇×#386	C₂²	1	2	yes	—
91	C₇×#386	C₂²	1	2	yes	—
92	C₇×#385	C₂²	1	2	yes	—
93	C₇×#385	C₂²	1	2	yes	—
94	C₇×#385	C₂²	1	2	yes	—
95	C₇×#385	C₂²	1	2	yes	—
96	C₇×#384	C₂²	1	1	yes	characteristic
97	C₇×#382	C₂²	1	1	yes	characteristic
98	C₇×#381	C₂²	1	2	yes	—
99	C₇×#380	C₂²	1	1	yes	characteristic
100	C₇×#380	C₂²	1	1	yes	characteristic
101	C₇×#380	C₂²	1	2	yes	—
102	C₇×#380	C₂²	1	2	yes	—
103	C₇×#380	C₂²	1	2	yes	—
104	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
107	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
108	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
111	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
112	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
113	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
114	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
115	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
116	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₇×#376	C₂²	1	1	yes	characteristic
122	C₂×C₇×#95	C₂²	1	2	yes	—
123	C₄³×C₇	C₂²	1	1	yes	characteristic
124	#34439	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂×C₇×#41	—	4	2	no	—
126	C₂×C₇×#41	—	4	2	no	—
127	C₂×C₇×#41	C₂×C₄	1	8	yes	—
128	C₂²×C₇×Q₈	—	4	2	no	—
129	C₂²×C₇×Q₈	—	4	2	no	—
130	C₂²×C₇×Q₈	C₂×C₄	1	8	yes	complemented
131	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
132	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
133	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
134	C₂²×C₇×Q₈	C₂³	1	2	yes	—
135	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
136	C₂²×C₇×D₄	C₂³	1	2	yes	—
137	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₇	C₂³	1	2	yes	—
139	C₂³×C₄×C₇	C₂³	1	2	yes	—
140	C₂³×C₄×C₇	C₂³	1	2	yes	—
141	C₂³×C₄×C₇	C₂³	1	2	yes	—
142	C₇×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
143	C₇×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
144	C₇×#124	C₂×C₄	1	8	yes	—
145	C₇×#124	C₂×C₄	1	8	yes	—
146	C₇×#123	C₂×C₄	1	16	yes	complemented
147	C₇×#123	C₂×C₄	1	16	yes	complemented
148	C₇×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
149	C₇×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
150	C₄×C₇×Q₈	—	4	2	no	—
151	C₄×C₇×Q₈	—	4	2	no	—
152	C₄×C₇×Q₈	—	4	2	no	—
153	C₄×C₇×Q₈	—	4	2	no	—
154	C₄×C₇×Q₈	—	4	2	no	—
155	C₄×C₇×Q₈	—	4	2	no	—
156	C₄×C₇×D₄	—	4	2	no	—
157	C₄×C₇×D₄	—	4	2	no	—
158	C₇×#117	C₂×C₄	1	8	yes	complemented
159	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₇	C₂³	1	2	yes	—
208	C₂×C₄²×C₇	C₂³	1	2	yes	—
209	C₂×C₄²×C₇	C₂³	1	2	yes	—
210	C₂×C₄²×C₇	C₂³	1	2	yes	—
211	C₂×C₄²×C₇	C₂³	1	2	yes	—
212	C₂×C₄²×C₇	C₂³	1	2	yes	—
213	C₂×C₄²×C₇	C₂³	1	2	yes	—
214	C₂×C₄²×C₇	C₂³	1	2	yes	—
215	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
217	C₇×#95	C₂³	1	1	yes	characteristic
218	C₇×#95	C₂³	1	2	yes	—
219	C₇×#95	C₂³	1	2	yes	—
220	C₇×#95	C₂³	1	2	yes	—
221	C₇×#95	C₂³	1	1	yes	characteristic
222	C₇×#95	C₂³	1	1	yes	characteristic
223	C₇×#95	C₂³	1	1	yes	characteristic
224	C₇×#95	C₂³	1	1	yes	characteristic
225	C₇×#95	C₂³	1	1	yes	characteristic
226	C₇×#95	C₂³	1	2	yes	—
227	C₇×#95	C₂³	1	1	yes	characteristic
228	C₇×#95	C₂³	1	1	yes	characteristic
229	C₇×#95	C₂³	1	2	yes	—
230	C₇×#95	C₂³	1	1	yes	characteristic
231	C₇×#95	C₂³	1	2	yes	—
232	C₇×#95	C₂³	1	2	yes	—
233	C₇×#95	C₂³	1	2	yes	—
234	C₇×#95	C₂³	1	1	yes	characteristic
235	C₇×#95	C₂³	1	2	yes	—
236	C₇×#95	C₂³	1	2	yes	—
237	C₇×#95	C₂³	1	2	yes	—
238	C₇×#95	C₂³	1	2	yes	—
239	C₇×#95	C₂³	1	2	yes	—
240	C₇×#95	C₂³	1	2	yes	—
241	C₇×#95	C₂³	1	2	yes	—
242	C₇×#95	C₂³	1	2	yes	—
243	C₇×#95	C₂³	1	2	yes	—
244	C₇×#95	C₂³	1	2	yes	—
245	C₇×#95	C₂³	1	1	yes	characteristic
246	C₇×#95	C₂³	1	1	yes	characteristic
247	C₂×#536	C₂×C₇	1	1	yes	characteristic
248	#2378	C₂×C₇	1	2	yes	complemented
249	#2376	C₂×C₇	1	2	yes	complemented
250	#2374	C₂×C₇	1	2	yes	complemented
251	#2368	C₂×C₇	1	2	yes	complemented
252	#2367	C₂×C₇	1	1	yes	characteristic, complemented
253	#2367	C₂×C₇	1	1	yes	characteristic, complemented
254	#2365	C₂×C₇	1	1	yes	characteristic, complemented
255	#2365	C₂×C₇	1	1	yes	characteristic, complemented
256	#2341	C₂×C₇	1	1	yes	characteristic
257	Q₈×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
258	Q₈×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
259	#2339	C₂×C₇	1	1	yes	characteristic
260	#2335	C₂×C₇	1	2	yes	complemented
261	#2335	C₂×C₇	1	2	yes	complemented
262	#2332	C₂×C₇	1	2	yes	complemented
263	#2329	C₂×C₇	1	2	yes	complemented
264	#2327	C₂×C₇	1	1	yes	characteristic, complemented
265	#2326	C₂×C₇	1	1	yes	characteristic, complemented
266	#2314	C₂×C₇	1	1	yes	characteristic, complemented
267	C₄×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
268	C₄×#124	C₂×C₇	1	1	yes	characteristic, complemented
269	#2298	C₂×C₇	1	1	yes	characteristic, complemented
270	C₂⁴×C₇	C₂⁴	1	2	yes	—
271	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
272	C₇×#41	—	4	16	no	—
273	C₂×C₇×Q₈	—	2	2	no	—
274	C₂×C₇×Q₈	—	2	2	no	—
275	C₂×C₇×Q₈	—	2	2	no	—
276	C₂×C₇×Q₈	—	2	2	no	—
277	C₂×C₇×Q₈	—	2	2	no	—
278	C₂×C₇×Q₈	—	2	2	no	—
279	C₂×C₇×Q₈	—	4	2	no	—
280	C₂×C₇×Q₈	—	4	2	no	—
281	C₂×C₇×Q₈	—	4	16	no	—
282	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
283	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
284	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
285	C₂×C₇×Q₈	C₂²×C₄	1	8	yes	—
286	C₂×C₇×D₄	—	2	2	no	—
287	C₂×C₇×D₄	—	2	2	no	—
288	C₂×C₇×D₄	—	4	2	no	—
289	C₂×C₇×D₄	—	4	2	no	—
290	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
291	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
292	C₂²×C₄×C₇	—	2	2	no	—
293	C₂²×C₄×C₇	—	2	2	no	—
294	C₂²×C₄×C₇	—	2	4	no	—
295	C₂²×C₄×C₇	—	4	2	no	—
296	C₂²×C₄×C₇	—	4	2	no	—
297	C₂²×C₄×C₇	—	4	2	no	—
298	C₂²×C₄×C₇	—	4	2	no	—
299	C₂²×C₄×C₇	—	4	2	no	—
300	C₂²×C₄×C₇	—	4	2	no	—
301	C₂²×C₄×C₇	—	4	2	no	—
302	C₂²×C₄×C₇	—	4	2	no	—
303	C₂²×C₄×C₇	—	4	2	no	—
304	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
305	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
306	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
307	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
328	C₇×C₄⋊C₄	—	2	2	no	—
329	C₇×C₄⋊C₄	—	2	2	no	—
330	C₇×C₄⋊C₄	—	2	2	no	—
331	C₇×C₄⋊C₄	—	2	2	no	—
332	C₇×C₄⋊C₄	—	2	2	no	—
333	C₇×C₄⋊C₄	—	2	2	no	—
334	C₇×C₄⋊C₄	—	4	1	no	—
335	C₇×C₄⋊C₄	—	4	1	no	—
336	C₇×C₄⋊C₄	—	4	2	no	—
337	C₇×C₄⋊C₄	—	4	2	no	—
338	C₇×C₄⋊C₄	—	4	2	no	—
339	C₇×C₄⋊C₄	—	4	2	no	—
340	C₇×C₄⋊C₄	—	4	2	no	—
341	C₇×C₄⋊C₄	—	4	2	no	—
342	C₇×C₄⋊C₄	—	4	2	no	—
343	C₇×C₄⋊C₄	—	4	2	no	—
344	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
345	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
346	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
347	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
348	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
349	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
350	C₇×C₂²⋊C₄	—	2	2	no	—
351	C₇×C₂²⋊C₄	—	2	4	no	—
352	C₇×C₂²⋊C₄	—	2	2	no	—
353	C₇×C₂²⋊C₄	—	4	2	no	—
354	C₇×C₂²⋊C₄	—	4	2	no	—
355	C₇×C₂²⋊C₄	—	4	1	no	—
356	C₇×C₂²⋊C₄	—	4	2	no	—
357	C₇×C₂²⋊C₄	—	4	1	no	—
358	C₇×C₂²⋊C₄	—	4	2	no	—
359	C₇×C₂²⋊C₄	—	4	2	no	—
360	C₇×C₂²⋊C₄	—	4	2	no	—
361	C₇×C₂²⋊C₄	—	4	2	no	—
362	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
363	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
364	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
365	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
366	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
367	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
368	C₄²×C₇	—	2	2	no	—
369	C₄²×C₇	—	2	2	no	—
370	C₄²×C₇	—	2	2	no	—
371	C₄²×C₇	—	2	2	no	—
372	C₄²×C₇	—	2	2	no	—
373	C₄²×C₇	—	2	2	no	—
374	C₄²×C₇	—	4	2	no	—
375	C₄²×C₇	—	4	2	no	—
376	C₄²×C₇	—	4	1	no	—
377	C₄²×C₇	—	4	1	no	—
378	C₄²×C₇	—	4	2	no	—
379	C₄²×C₇	—	4	2	no	—
380	C₄²×C₇	—	4	2	no	—
381	C₄²×C₇	—	4	2	no	—
382	C₄²×C₇	—	4	2	no	—
383	C₄²×C₇	—	4	2	no	—
384	C₄²×C₇	C₂²×C₄	1	4	yes	—
385	C₄²×C₇	C₂²×C₄	1	4	yes	—
386	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
387	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
388	#536	C₄×C₇	1	16	yes	complemented
389	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
390	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
391	C₂×#124	C₂²×C₇	1	1	yes	characteristic
392	C₂×#124	C₂²×C₇	1	1	yes	characteristic
393	C₂×#123	C₂²×C₇	1	2	yes	—
394	C₂×#123	C₂²×C₇	1	2	yes	—
395	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
396	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
397	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
398	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
399	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
400	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
401	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
402	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
403	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
404	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
405	C₂×#117	C₂²×C₇	1	1	yes	characteristic
406	#391	C₂²×C₇	1	1	yes	characteristic
407	#391	C₂²×C₇	1	1	yes	characteristic
408	#391	C₂²×C₇	1	1	yes	characteristic
409	#391	C₂²×C₇	1	1	yes	characteristic
410	#391	C₂²×C₇	1	1	yes	characteristic
411	#391	C₂²×C₇	1	2	yes	—
412	#391	C₂²×C₇	1	2	yes	—
413	#391	C₂²×C₇	1	2	yes	—
414	#391	C₂²×C₇	1	2	yes	—
415	#391	C₂²×C₇	1	1	yes	characteristic
416	#390	C₂²×C₇	1	1	yes	characteristic
417	#390	C₂²×C₇	1	2	yes	—
418	#390	C₂²×C₇	1	2	yes	—
419	#390	C₂²×C₇	1	1	yes	characteristic
420	#389	C₂²×C₇	1	2	yes	—
421	#389	C₂²×C₇	1	2	yes	—
422	#389	C₂²×C₇	1	2	yes	—
423	#389	C₂²×C₇	1	2	yes	—
424	#388	C₂²×C₇	1	2	yes	—
425	#388	C₂²×C₇	1	2	yes	—
426	#388	C₂²×C₇	1	2	yes	—
427	#388	C₂²×C₇	1	2	yes	—
428	#388	C₂²×C₇	1	2	yes	—
429	#388	C₂²×C₇	1	2	yes	—
430	#388	C₂²×C₇	1	2	yes	—
431	#388	C₂²×C₇	1	1	yes	characteristic
432	#388	C₂²×C₇	1	1	yes	characteristic
433	#388	C₂²×C₇	1	2	yes	—
434	#388	C₂²×C₇	1	2	yes	—
435	#388	C₂²×C₇	1	1	yes	characteristic
436	#388	C₂²×C₇	1	1	yes	characteristic
437	#388	C₂²×C₇	1	2	yes	—
438	#387	C₂²×C₇	1	2	yes	—
439	#387	C₂²×C₇	1	2	yes	—
440	#387	C₂²×C₇	1	2	yes	—
441	#387	C₂²×C₇	1	2	yes	—
442	#387	C₂²×C₇	1	2	yes	—
443	#387	C₂²×C₇	1	2	yes	—
444	#387	C₂²×C₇	1	1	yes	characteristic
445	#387	C₂²×C₇	1	2	yes	—
446	#387	C₂²×C₇	1	1	yes	characteristic
447	#387	C₂²×C₇	1	2	yes	—
448	#387	C₂²×C₇	1	2	yes	—
449	#387	C₂²×C₇	1	2	yes	—
450	#387	C₂²×C₇	1	1	yes	characteristic
451	#387	C₂²×C₇	1	1	yes	characteristic
452	#386	C₂²×C₇	1	2	yes	—
453	#386	C₂²×C₇	1	2	yes	—
454	#385	C₂²×C₇	1	2	yes	—
455	#385	C₂²×C₇	1	2	yes	—
456	#385	C₂²×C₇	1	2	yes	—
457	#385	C₂²×C₇	1	2	yes	—
458	#384	C₂²×C₇	1	1	yes	characteristic
459	#382	C₂²×C₇	1	1	yes	characteristic
460	#381	C₂²×C₇	1	2	yes	—
461	#380	C₂²×C₇	1	1	yes	characteristic
462	#380	C₂²×C₇	1	1	yes	characteristic
463	#380	C₂²×C₇	1	2	yes	—
464	#380	C₂²×C₇	1	2	yes	—
465	#380	C₂²×C₇	1	2	yes	—
466	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
467	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
468	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
469	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
470	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
471	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
472	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
473	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
474	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
475	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
476	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
477	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
478	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
479	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
480	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
481	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
482	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
483	#376	C₂²×C₇	1	1	yes	characteristic
484	C₂×#95	C₂²×C₇	1	2	yes	—
485	C₄³	C₂²×C₇	1	1	yes	characteristic
486	C₂³×C₇	—	2	2	no	—
487	C₂³×C₇	—	2	2	no	—
488	C₂³×C₇	—	2	1	no	—
489	C₂³×C₇	—	2	1	no	—
490	C₂³×C₇	—	2	1	no	—
491	C₂³×C₇	—	2	2	no	—
492	C₂³×C₇	—	2	1	no	—
493	C₂³×C₇	—	2	2	no	—
494	C₂³×C₇	—	2	1	no	—
495	C₂³×C₇	—	2	1	no	—
496	C₂³×C₇	—	2	2	no	—
497	C₂³×C₇	—	2	2	no	—
498	C₂³×C₇	C₂³×C₄	1	4	yes	—
499	C₂³×C₇	C₂³×C₄	1	2	yes	—
500	C₂³×C₇	C₂⁵	1	1	yes	characteristic
501	C₇×Q₈	—	2	8	no	—
502	C₇×Q₈	—	2	8	no	—
503	C₇×Q₈	—	2	8	no	—
504	C₇×Q₈	—	4	8	no	—
505	C₇×D₄	—	2	8	no	—
506	C₇×D₄	—	4	8	no	—
507	C₂×C₄×C₇	—	2	1	no	—
508	C₂×C₄×C₇	—	2	1	no	—
509	C₂×C₄×C₇	—	2	2	no	—
510	C₂×C₄×C₇	—	2	2	no	—
511	C₂×C₄×C₇	—	2	2	no	—
512	C₂×C₄×C₇	—	2	2	no	—
513	C₂×C₄×C₇	—	2	2	no	—
514	C₂×C₄×C₇	—	2	2	no	—
515	C₂×C₄×C₇	—	2	1	no	—
516	C₂×C₄×C₇	—	2	1	no	—
517	C₂×C₄×C₇	—	2	1	no	—
518	C₂×C₄×C₇	—	2	1	no	—
519	C₂×C₄×C₇	—	2	1	no	—
520	C₂×C₄×C₇	—	2	1	no	—
521	C₂×C₄×C₇	—	2	1	no	—
522	C₂×C₄×C₇	—	2	1	no	—
523	C₂×C₄×C₇	—	2	1	no	—
524	C₂×C₄×C₇	—	2	1	no	—
525	C₂×C₄×C₇	—	2	1	no	—
526	C₂×C₄×C₇	—	2	1	no	—
527	C₂×C₄×C₇	—	2	8	no	—
528	C₂×C₄×C₇	—	2	1	no	—
529	C₂×C₄×C₇	—	2	1	no	—
530	C₂×C₄×C₇	—	2	1	no	—
531	C₂×C₄×C₇	—	2	1	no	—
532	C₂×C₄×C₇	—	2	1	no	—
533	C₂×C₄×C₇	—	2	1	no	—
534	C₂×C₄×C₇	—	2	2	no	—
535	C₂×C₄×C₇	—	2	2	no	—
536	C₂×C₄×C₇	—	2	2	no	—
537	C₂×C₄×C₇	—	2	2	no	—
538	C₂×C₄×C₇	—	2	1	no	—
539	C₂×C₄×C₇	—	2	1	no	—
540	C₂×C₄×C₇	—	2	1	no	—
541	C₂×C₄×C₇	—	2	2	no	—
542	C₂×C₄×C₇	—	2	1	no	—
543	C₂×C₄×C₇	—	2	1	no	—
544	C₂×C₄×C₇	—	2	2	no	—
545	C₂×C₄×C₇	—	2	2	no	—
546	C₂×C₄×C₇	—	2	1	no	—
547	C₂×C₄×C₇	—	2	1	no	—
548	C₂×C₄×C₇	—	2	1	no	—
549	C₂×C₄×C₇	—	2	2	no	—
550	C₂×C₄×C₇	—	2	2	no	—
551	C₂×C₄×C₇	—	2	2	no	—
552	C₂×C₄×C₇	—	2	1	no	—
553	C₂×C₄×C₇	—	2	1	no	—
554	C₂×C₄×C₇	—	2	2	no	—
555	C₂×C₄×C₇	—	2	2	no	—
556	C₂×C₄×C₇	—	2	1	no	—
557	C₂×C₄×C₇	—	2	1	no	—
558	C₂×C₄×C₇	—	4	8	no	—
559	C₂×C₄×C₇	—	4	8	no	—
560	C₂×C₄×C₇	—	8	4	no	—
561	C₂×C₄×C₇	—	8	4	no	—
562	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
563	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
564	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
565	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
566	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
567	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
568	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
569	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
570	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
571	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
572	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
573	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
574	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
575	C₂×#41	—	4	2	no	—
576	C₂×#41	—	4	2	no	—
577	C₂×#41	C₂×C₄×C₇	1	8	yes	—
578	C₂²×Q₈	—	4	2	no	—
579	C₂²×Q₈	—	4	2	no	—
580	C₂²×Q₈	C₂×C₄×C₇	1	8	yes	complemented
581	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
582	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
583	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
584	C₂²×Q₈	C₂³×C₇	1	2	yes	—
585	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
586	C₂²×D₄	C₂³×C₇	1	2	yes	—
587	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
588	C₂³×C₄	C₂³×C₇	1	2	yes	—
589	C₂³×C₄	C₂³×C₇	1	2	yes	—
590	C₂³×C₄	C₂³×C₇	1	2	yes	—
591	C₂³×C₄	C₂³×C₇	1	2	yes	—
592	C₄⋊Q₈	C₂×C₄×C₇	1	8	yes	complemented
593	C₄⋊Q₈	C₂×C₄×C₇	1	8	yes	complemented
594	#124	C₂×C₄×C₇	1	8	yes	—
595	#124	C₂×C₄×C₇	1	8	yes	—
596	#123	C₂×C₄×C₇	1	16	yes	complemented
597	#123	C₂×C₄×C₇	1	16	yes	complemented
598	C₂²⋊Q₈	C₂×C₄×C₇	1	16	yes	complemented
599	C₂²⋊Q₈	C₂×C₄×C₇	1	16	yes	complemented
600	C₄×Q₈	—	4	2	no	—
601	C₄×Q₈	—	4	2	no	—
602	C₄×Q₈	—	4	2	no	—
603	C₄×Q₈	—	4	2	no	—
604	C₄×Q₈	—	4	2	no	—
605	C₄×Q₈	—	4	2	no	—
606	C₄×D₄	—	4	2	no	—
607	C₄×D₄	—	4	2	no	—
608	#117	C₂×C₄×C₇	1	8	yes	complemented
609	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
632	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
634	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
638	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
640	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
644	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
645	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
649	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₇	1	2	yes	—
656	C₂×C₄²	C₂³×C₇	1	2	yes	—
657	C₂×C₄²	C₂³×C₇	1	2	yes	—
658	C₂×C₄²	C₂³×C₇	1	2	yes	—
659	C₂×C₄²	C₂³×C₇	1	2	yes	—
660	C₂×C₄²	C₂³×C₇	1	2	yes	—
661	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₇	1	2	yes	—
664	C₂×C₄²	C₂³×C₇	1	2	yes	—
665	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
666	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
667	#95	C₂³×C₇	1	1	yes	characteristic
668	#95	C₂³×C₇	1	2	yes	—
669	#95	C₂³×C₇	1	2	yes	—
670	#95	C₂³×C₇	1	2	yes	—
671	#95	C₂³×C₇	1	1	yes	characteristic
672	#95	C₂³×C₇	1	1	yes	characteristic
673	#95	C₂³×C₇	1	1	yes	characteristic
674	#95	C₂³×C₇	1	1	yes	characteristic
675	#95	C₂³×C₇	1	1	yes	characteristic
676	#95	C₂³×C₇	1	2	yes	—
677	#95	C₂³×C₇	1	1	yes	characteristic
678	#95	C₂³×C₇	1	1	yes	characteristic
679	#95	C₂³×C₇	1	2	yes	—
680	#95	C₂³×C₇	1	2	yes	—
681	#95	C₂³×C₇	1	1	yes	characteristic
682	#95	C₂³×C₇	1	2	yes	—
683	#95	C₂³×C₇	1	2	yes	—
684	#95	C₂³×C₇	1	1	yes	characteristic
685	#95	C₂³×C₇	1	2	yes	—
686	#95	C₂³×C₇	1	2	yes	—
687	#95	C₂³×C₇	1	2	yes	—
688	#95	C₂³×C₇	1	2	yes	—
689	#95	C₂³×C₇	1	2	yes	—
690	#95	C₂³×C₇	1	2	yes	—
691	#95	C₂³×C₇	1	2	yes	—
692	#95	C₂³×C₇	1	2	yes	—
693	#95	C₂³×C₇	1	2	yes	—
694	#95	C₂³×C₇	1	2	yes	—
695	#95	C₂³×C₇	1	1	yes	characteristic
696	#95	C₂³×C₇	1	1	yes	characteristic
697	C₂²×C₇	—	2	2	no	—
698	C₂²×C₇	—	2	4	no	—
699	C₂²×C₇	—	2	2	no	—
700	C₂²×C₇	—	2	2	no	—
701	C₂²×C₇	—	2	4	no	—
702	C₂²×C₇	—	2	4	no	—
703	C₂²×C₇	—	4	2	no	—
704	C₂²×C₇	—	4	1	no	—
705	C₂²×C₇	—	4	2	no	—
706	C₂²×C₇	—	4	1	no	—
707	C₂²×C₇	—	4	2	no	—
708	C₂²×C₇	—	4	1	no	—
709	C₂²×C₇	—	4	2	no	—
710	C₂²×C₇	—	4	1	no	—
711	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
712	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
713	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
714	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
715	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
716	C₂²×C₇	#585	1	1	yes	characteristic
717	C₂²×C₇	#585	1	1	yes	characteristic
718	C₄×C₇	—	2	2	no	—
719	C₄×C₇	—	2	4	no	—
720	C₄×C₇	—	2	4	no	—
721	C₄×C₇	—	2	4	no	—
722	C₄×C₇	—	2	2	no	—
723	C₄×C₇	—	2	2	no	—
724	C₄×C₇	—	2	2	no	—
725	C₄×C₇	—	2	2	no	—
726	C₄×C₇	—	2	2	no	—
727	C₄×C₇	—	2	2	no	—
728	C₄×C₇	—	4	1	no	—
729	C₄×C₇	—	4	1	no	—
730	C₄×C₇	—	4	1	no	—
731	C₄×C₇	—	4	2	no	—
732	C₄×C₇	—	4	1	no	—
733	C₄×C₇	—	4	2	no	—
734	C₄×C₇	—	4	1	no	—
735	C₄×C₇	—	4	2	no	—
736	C₄×C₇	—	4	2	no	—
737	C₄×C₇	—	4	1	no	—
738	C₄×C₇	#518	1	4	yes	—
739	C₂⁴	C₂⁴×C₇	1	2	yes	—
740	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
741	#41	—	4	16	no	—
742	C₂×Q₈	—	2	2	no	—
743	C₂×Q₈	—	2	2	no	—
744	C₂×Q₈	—	2	2	no	—
745	C₂×Q₈	—	2	2	no	—
746	C₂×Q₈	—	2	2	no	—
747	C₂×Q₈	—	2	2	no	—
748	C₂×Q₈	—	4	2	no	—
749	C₂×Q₈	—	4	2	no	—
750	C₂×Q₈	—	4	16	no	—
751	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
752	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
753	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
754	C₂×Q₈	C₂²×C₄×C₇	1	8	yes	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	4	2	no	—
758	C₂×D₄	—	4	2	no	—
759	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
760	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	4	no	—
764	C₂²×C₄	—	4	2	no	—
765	C₂²×C₄	—	4	2	no	—
766	C₂²×C₄	—	4	2	no	—
767	C₂²×C₄	—	4	2	no	—
768	C₂²×C₄	—	4	2	no	—
769	C₂²×C₄	—	4	2	no	—
770	C₂²×C₄	—	4	2	no	—
771	C₂²×C₄	—	4	2	no	—
772	C₂²×C₄	—	4	2	no	—
773	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
774	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
775	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
776	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
778	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
780	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
781	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
786	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
792	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
794	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	4	2	no	—
804	C₄⋊C₄	—	4	2	no	—
805	C₄⋊C₄	—	4	2	no	—
806	C₄⋊C₄	—	4	2	no	—
807	C₄⋊C₄	—	4	2	no	—
808	C₄⋊C₄	—	4	2	no	—
809	C₄⋊C₄	—	4	1	no	—
810	C₄⋊C₄	—	4	1	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	—	4	2	no	—
813	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
814	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
815	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
816	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
817	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
818	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	4	2	no	—
823	C₂²⋊C₄	—	4	2	no	—
824	C₂²⋊C₄	—	4	2	no	—
825	C₂²⋊C₄	—	4	2	no	—
826	C₂²⋊C₄	—	4	1	no	—
827	C₂²⋊C₄	—	4	2	no	—
828	C₂²⋊C₄	—	4	1	no	—
829	C₂²⋊C₄	—	4	2	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
832	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
833	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
834	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
835	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
836	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	2	no	—
840	C₄²	—	2	2	no	—
841	C₄²	—	2	2	no	—
842	C₄²	—	2	2	no	—
843	C₄²	—	4	2	no	—
844	C₄²	—	4	2	no	—
845	C₄²	—	4	2	no	—
846	C₄²	—	4	2	no	—
847	C₄²	—	4	2	no	—
848	C₄²	—	4	2	no	—
849	C₄²	—	4	2	no	—
850	C₄²	—	4	2	no	—
851	C₄²	—	4	1	no	—
852	C₄²	—	4	1	no	—
853	C₄²	C₂²×C₄×C₇	1	4	yes	—
854	C₄²	C₂²×C₄×C₇	1	4	yes	—
855	C₂×C₇	—	4	2	no	—
856	C₂×C₇	—	4	4	no	—
857	C₂×C₇	C₂×#518	1	1	yes	characteristic
858	C₂×C₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
859	C₂×C₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
860	C₂×C₇	#3552	1	1	yes	characteristic
861	C₂×C₇	#3554	1	1	yes	characteristic
862	C₂×C₇	#3561	1	1	yes	characteristic
863	C₂×C₇	#3562	1	1	yes	characteristic
864	C₂³	—	2	2	no	—
865	C₂³	—	2	2	no	—
866	C₂³	—	2	1	no	—
867	C₂³	—	2	1	no	—
868	C₂³	—	2	1	no	—
869	C₂³	—	2	1	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	1	no	—
873	C₂³	—	2	1	no	—
874	C₂³	—	2	2	no	—
875	C₂³	—	2	2	no	—
876	C₂³	C₂³×C₄×C₇	1	4	yes	—
877	C₂³	C₂³×C₄×C₇	1	2	yes	—
878	C₂³	C₂⁵×C₇	1	1	yes	characteristic
879	Q₈	—	2	8	no	—
880	Q₈	—	2	8	no	—
881	Q₈	—	2	8	no	—
882	Q₈	—	4	8	no	—
883	D₄	—	2	8	no	—
884	D₄	—	4	8	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	8	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	4	8	no	—
937	C₂×C₄	—	4	8	no	—
938	C₂×C₄	—	8	4	no	—
939	C₂×C₄	—	8	4	no	—
940	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
941	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
942	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
943	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
944	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
945	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
946	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
947	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
948	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
949	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
950	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
951	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
952	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
953	C₇	#34439	1	1	yes	characteristic, direct product factor, Sylow
954	C₂²	—	2	2	no	—
955	C₂²	—	2	4	no	—
956	C₂²	—	2	2	no	—
957	C₂²	—	2	2	no	—
958	C₂²	—	2	4	no	—
959	C₂²	—	2	4	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	1	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	1	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	1	no	—
966	C₂²	—	4	2	no	—
967	C₂²	—	4	1	no	—
968	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
969	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
970	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
971	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
972	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
973	C₂²	C₇×#585	1	1	yes	characteristic
974	C₂²	C₇×#585	1	1	yes	characteristic
975	C₄	—	2	2	no	—
976	C₄	—	2	2	no	—
977	C₄	—	2	4	no	—
978	C₄	—	2	4	no	—
979	C₄	—	2	4	no	—
980	C₄	—	2	2	no	—
981	C₄	—	2	2	no	—
982	C₄	—	2	2	no	—
983	C₄	—	2	2	no	—
984	C₄	—	2	2	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	1	no	—
987	C₄	—	4	1	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	1	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	1	no	—
992	C₄	—	4	1	no	—
993	C₄	—	4	1	no	—
994	C₄	—	4	2	no	—
995	C₄	C₇×#518	1	4	yes	—
996	C₂	—	4	2	no	—
997	C₂	—	4	4	no	—
998	C₂	C₂×C₇×#518	1	1	yes	characteristic
999	C₂	C₄×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1000	C₂	C₄×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1001	C₂	C₇×#3552	1	1	yes	characteristic
1002	C₂	C₇×#3554	1	1	yes	characteristic
1003	C₂	C₇×#3561	1	1	yes	characteristic
1004	C₂	C₇×#3562	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₇
Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂²×C₇×#41	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2378	C₂	semidirect
3. C₇×#2376	C₂	semidirect
4. C₇×#2374	C₂	semidirect
5. C₇×#2368	C₂	semidirect
6. C₇×#2367	C₂	semidirect
7. C₇×#2367	C₂	semidirect
8. C₇×#2365	C₂	semidirect
9. C₇×#2365	C₂	semidirect
11. C₇×Q₈×C₂²⋊C₄	C₂	semidirect
12. C₇×Q₈×C₂²⋊C₄	C₂	semidirect
14. C₇×#2335	C₂	semidirect
15. C₇×#2335	C₂	semidirect
16. C₇×#2332	C₂	semidirect
17. C₇×#2329	C₂	semidirect
18. C₇×#2327	C₂	semidirect
19. C₇×#2326	C₂	semidirect
20. C₇×#2314	C₂	semidirect
21. C₄×C₇×C₄⋊Q₈	C₂	semidirect
22. C₄×C₇×#124	C₂	semidirect
23. C₇×#2298	C₂	semidirect
26. C₇×#536	C₄	semidirect
124. #34439	C₇	direct (N × H)
130. C₂²×C₇×Q₈	C₂×C₄	semidirect
142. C₇×C₄⋊Q₈	C₂×C₄	semidirect
143. C₇×C₄⋊Q₈	C₂×C₄	semidirect
146. C₇×#123	C₂×C₄	semidirect
147. C₇×#123	C₂×C₄	semidirect
148. C₇×C₂²⋊Q₈	C₂×C₄	semidirect
149. C₇×C₂²⋊Q₈	C₂×C₄	semidirect
158. C₇×#117	C₂×C₄	semidirect
248. #2378	C₂×C₇	semidirect
249. #2376	C₂×C₇	semidirect
250. #2374	C₂×C₇	semidirect
251. #2368	C₂×C₇	semidirect
252. #2367	C₂×C₇	semidirect
253. #2367	C₂×C₇	semidirect
254. #2365	C₂×C₇	semidirect
255. #2365	C₂×C₇	semidirect
257. Q₈×C₂²⋊C₄	C₂×C₇	semidirect
258. Q₈×C₂²⋊C₄	C₂×C₇	semidirect
260. #2335	C₂×C₇	semidirect
261. #2335	C₂×C₇	semidirect
262. #2332	C₂×C₇	semidirect
263. #2329	C₂×C₇	semidirect
264. #2327	C₂×C₇	semidirect
265. #2326	C₂×C₇	semidirect
266. #2314	C₂×C₇	semidirect
267. C₄×C₄⋊Q₈	C₂×C₇	semidirect
268. C₄×#124	C₂×C₇	semidirect
269. #2298	C₂×C₇	semidirect
388. #536	C₄×C₇	semidirect
580. C₂²×Q₈	C₂×C₄×C₇	semidirect
592. C₄⋊Q₈	C₂×C₄×C₇	semidirect
593. C₄⋊Q₈	C₂×C₄×C₇	semidirect
596. #123	C₂×C₄×C₇	semidirect
597. #123	C₂×C₄×C₇	semidirect
598. C₂²⋊Q₈	C₂×C₄×C₇	semidirect
599. C₂²⋊Q₈	C₂×C₄×C₇	semidirect
608. #117	C₂×C₄×C₇	semidirect
953. C₇	#34439	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×#536	2
C₇×#2378	2
C₇×#2376	2
C₇×#2374	2
C₇×#2368	2
C₇×#2367	2
C₇×#2365	2
C₇×#2341	2
C₇×Q₈×C₂²⋊C₄	2
C₇×#2339	2
C₇×#2335	2
C₇×#2332	2
C₇×#2329	2
C₇×#2327	2
C₇×#2326	2
C₇×#2314	2
C₄×C₇×C₄⋊Q₈	2
C₄×C₇×#124	2
C₇×#2298	2
#34439	7

Subgroups — C7×#34439 #13211655

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34439 #13211655