Subgroups — C₇×#34465 #13211681

Order 1792.

2160 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#552	C₂	1	1	yes	maximal, characteristic
2	C₇×#2383	C₂	1	2	yes	maximal, complemented
3	C₇×#2382	C₂	1	2	yes	maximal, complemented
4	C₇×#2370	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2360	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2359	C₂	1	2	yes	maximal
8	C₇×Q₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
10	C₇×#2346	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2344	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2343	C₂	1	2	yes	maximal, complemented
13	C₇×#2334	C₂	1	2	yes	maximal, complemented
14	C₇×#2330	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2330	C₂	1	2	yes	maximal, complemented
16	C₇×#2323	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2322	C₂	1	2	yes	maximal
18	C₇×#2320	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2317	C₂	1	2	yes	maximal, complemented
20	C₇×#2317	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₇×#389	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2290	C₂	1	1	yes	maximal, characteristic
24	C₇×#552	C₄	1	16	yes	complemented
25	C₂×C₇×#126	C₂²	1	2	yes	—
26	C₂×C₇×#125	C₂²	1	1	yes	characteristic
27	C₂×C₇×#125	C₂²	1	2	yes	—
28	C₂×C₇×#123	C₂²	1	2	yes	—
29	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
35	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₇×#117	C₂²	1	1	yes	characteristic
37	C₂×C₇×#117	C₂²	1	2	yes	—
38	C₂×C₇×#117	C₂²	1	2	yes	—
39	C₂×C₇×#117	C₂²	1	1	yes	characteristic
40	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
41	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
45	C₇×#391	C₂²	1	1	yes	characteristic
46	C₇×#391	C₂²	1	1	yes	characteristic
47	C₇×#389	C₂²	1	1	yes	characteristic
48	C₇×#389	C₂²	1	1	yes	characteristic
49	C₇×#389	C₂²	1	2	yes	—
50	C₇×#389	C₂²	1	1	yes	characteristic
51	C₇×#389	C₂²	1	1	yes	characteristic
52	C₇×#389	C₂²	1	2	yes	—
53	C₇×#389	C₂²	1	1	yes	characteristic
54	C₇×#389	C₂²	1	2	yes	—
55	C₇×#389	C₂²	1	2	yes	—
56	C₇×#389	C₂²	1	1	yes	characteristic
57	C₇×#389	C₂²	1	1	yes	characteristic
58	C₇×#389	C₂²	1	2	yes	—
59	C₇×#389	C₂²	1	2	yes	—
60	C₇×#389	C₂²	1	1	yes	characteristic
61	C₇×#389	C₂²	1	2	yes	—
62	C₇×#389	C₂²	1	2	yes	—
63	C₇×#389	C₂²	1	2	yes	—
64	C₇×#389	C₂²	1	2	yes	—
65	C₇×#389	C₂²	1	2	yes	—
66	C₇×#388	C₂²	1	1	yes	characteristic
67	C₇×#388	C₂²	1	1	yes	characteristic
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×#387	C₂²	1	1	yes	characteristic
73	C₇×#387	C₂²	1	1	yes	characteristic
74	C₇×#387	C₂²	1	2	yes	—
75	C₇×#387	C₂²	1	2	yes	—
76	C₇×#387	C₂²	1	2	yes	—
77	C₇×#387	C₂²	1	2	yes	—
78	C₇×#387	C₂²	1	2	yes	—
79	C₇×#387	C₂²	1	2	yes	—
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×#386	C₂²	1	1	yes	characteristic
87	C₇×#386	C₂²	1	1	yes	characteristic
88	C₇×#385	C₂²	1	1	yes	characteristic
89	C₇×#385	C₂²	1	1	yes	characteristic
90	C₇×#385	C₂²	1	2	yes	—
91	C₇×#385	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×#385	C₂²	1	2	yes	—
97	C₇×#384	C₂²	1	2	yes	—
98	C₇×#384	C₂²	1	2	yes	—
99	C₇×#384	C₂²	1	1	yes	characteristic
100	C₇×#383	C₂²	1	2	yes	—
101	C₇×#382	C₂²	1	2	yes	—
102	C₇×#382	C₂²	1	2	yes	—
103	C₇×#382	C₂²	1	2	yes	—
104	C₇×#381	C₂²	1	2	yes	—
105	C₇×#380	C₂²	1	1	yes	characteristic
106	C₇×#380	C₂²	1	1	yes	characteristic
107	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
109	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
113	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
114	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
115	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
116	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
117	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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	C₇×#376	C₂²	1	2	yes	—
123	C₂×C₇×#95	C₂²	1	2	yes	—
124	#34465	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
126	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₇	C₂³	1	2	yes	—
130	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₇	C₂³	1	2	yes	—
133	C₂³×C₄×C₇	C₂³	1	2	yes	—
134	C₇×#126	C₂×C₄	1	16	yes	complemented
135	C₇×#125	C₂×C₄	1	16	yes	complemented
136	C₇×#125	C₂×C₄	1	8	yes	complemented
137	C₇×#123	C₂×C₄	1	16	yes	—
138	C₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
139	C₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
140	C₄×C₇×Q₈	—	4	2	no	—
141	C₄×C₇×Q₈	—	4	2	no	—
142	C₄×C₇×Q₈	C₂×C₄	1	8	yes	complemented
143	C₄×C₇×D₄	—	4	4	no	—
144	C₄×C₇×D₄	C₂×C₄	1	8	yes	—
145	C₇×#117	—	4	2	no	—
146	C₇×#117	—	4	4	no	—
147	C₇×#117	C₂×C₄	1	8	yes	complemented
148	C₇×#117	C₂×C₄	1	16	yes	complemented
149	C₂×C₇×C₄⋊C₄	—	4	2	no	—
150	C₂×C₇×C₄⋊C₄	—	4	2	no	—
151	C₂×C₇×C₄⋊C₄	—	4	4	no	—
152	C₂×C₇×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
153	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
167	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
179	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₇×C₄⋊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	1	yes	characteristic
188	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
196	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₇	—	4	2	no	—
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	2	yes	—
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	2	yes	—
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	1	yes	characteristic
214	C₂×C₄²×C₇	C₂³	1	2	yes	—
215	C₇×#95	C₂³	1	2	yes	—
216	C₇×#95	C₂³	1	2	yes	—
217	C₇×#95	C₂³	1	2	yes	—
218	C₇×#95	C₂³	1	2	yes	—
219	C₇×#95	C₂³	1	1	yes	characteristic
220	C₇×#95	C₂³	1	2	yes	—
221	C₇×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
227	C₇×#95	C₂³	1	2	yes	—
228	C₇×#95	C₂³	1	2	yes	—
229	C₇×#95	C₂³	1	2	yes	—
230	C₇×#95	C₂³	1	2	yes	—
231	C₇×#95	C₂³	1	2	yes	—
232	C₇×#95	C₂³	1	1	yes	characteristic
233	C₇×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
244	C₂×#552	C₂×C₇	1	1	yes	characteristic
245	#2383	C₂×C₇	1	2	yes	complemented
246	#2382	C₂×C₇	1	2	yes	complemented
247	#2370	C₂×C₇	1	1	yes	characteristic, complemented
248	#2360	C₂×C₇	1	1	yes	characteristic, complemented
249	#2360	C₂×C₇	1	1	yes	characteristic, complemented
250	#2359	C₂×C₇	1	2	yes	—
251	Q₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
252	D₄×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic
253	#2346	C₂×C₇	1	1	yes	characteristic, complemented
254	#2344	C₂×C₇	1	1	yes	characteristic, complemented
255	#2343	C₂×C₇	1	2	yes	complemented
256	#2334	C₂×C₇	1	2	yes	complemented
257	#2330	C₂×C₇	1	1	yes	characteristic, complemented
258	#2330	C₂×C₇	1	2	yes	complemented
259	#2323	C₂×C₇	1	1	yes	characteristic, complemented
260	#2322	C₂×C₇	1	2	yes	—
261	#2320	C₂×C₇	1	1	yes	characteristic, complemented
262	#2317	C₂×C₇	1	2	yes	complemented
263	#2317	C₂×C₇	1	1	yes	characteristic, complemented
264	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
265	C₂×#389	C₂×C₇	1	1	yes	characteristic, complemented
266	#2290	C₂×C₇	1	1	yes	characteristic
267	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
268	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
269	C₂×C₇×Q₈	—	2	2	no	—
270	C₂×C₇×Q₈	—	2	2	no	—
271	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
272	C₂×C₇×D₄	—	2	2	no	—
273	C₂×C₇×D₄	—	2	2	no	—
274	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
275	C₂²×C₄×C₇	—	2	4	no	—
276	C₂²×C₄×C₇	—	2	4	no	—
277	C₂²×C₄×C₇	—	2	2	no	—
278	C₂²×C₄×C₇	—	2	2	no	—
279	C₂²×C₄×C₇	—	2	2	no	—
280	C₂²×C₄×C₇	—	2	2	no	—
281	C₂²×C₄×C₇	—	2	2	no	—
282	C₂²×C₄×C₇	—	2	2	no	—
283	C₂²×C₄×C₇	—	2	4	no	—
284	C₂²×C₄×C₇	—	2	2	no	—
285	C₂²×C₄×C₇	—	4	1	no	—
286	C₂²×C₄×C₇	—	4	1	no	—
287	C₂²×C₄×C₇	—	4	1	no	—
288	C₂²×C₄×C₇	—	4	2	no	—
289	C₂²×C₄×C₇	—	4	2	no	—
290	C₂²×C₄×C₇	—	4	2	no	—
291	C₂²×C₄×C₇	—	4	2	no	—
292	C₂²×C₄×C₇	—	4	2	no	—
293	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
294	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
295	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
296	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
317	C₇×C₄⋊C₄	—	2	2	no	—
318	C₇×C₄⋊C₄	—	2	2	no	—
319	C₇×C₄⋊C₄	—	2	2	no	—
320	C₇×C₄⋊C₄	—	2	2	no	—
321	C₇×C₄⋊C₄	—	2	2	no	—
322	C₇×C₄⋊C₄	—	4	2	no	—
323	C₇×C₄⋊C₄	—	4	2	no	—
324	C₇×C₄⋊C₄	—	4	2	no	—
325	C₇×C₄⋊C₄	—	4	2	no	—
326	C₇×C₄⋊C₄	—	4	2	no	—
327	C₇×C₄⋊C₄	—	4	2	no	—
328	C₇×C₄⋊C₄	—	4	2	no	—
329	C₇×C₄⋊C₄	—	4	2	no	—
330	C₇×C₄⋊C₄	—	4	2	no	—
331	C₇×C₄⋊C₄	—	4	1	no	—
332	C₇×C₄⋊C₄	—	4	1	no	—
333	C₇×C₄⋊C₄	—	4	1	no	—
334	C₇×C₄⋊C₄	—	4	2	no	—
335	C₇×C₄⋊C₄	—	4	2	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	C₂²×C₄	1	4	yes	—
340	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
341	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
342	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
343	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
344	C₇×C₄⋊C₄	C₂²×C₄	1	8	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×C₂²⋊C₄	—	2	2	no	—
350	C₇×C₂²⋊C₄	—	2	4	no	—
351	C₇×C₂²⋊C₄	—	2	2	no	—
352	C₇×C₂²⋊C₄	—	2	2	no	—
353	C₇×C₂²⋊C₄	—	4	1	no	—
354	C₇×C₂²⋊C₄	—	4	1	no	—
355	C₇×C₂²⋊C₄	—	4	1	no	—
356	C₇×C₂²⋊C₄	—	4	2	no	—
357	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
358	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
359	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
360	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
361	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
362	C₄²×C₇	—	2	2	no	—
363	C₄²×C₇	—	2	2	no	—
364	C₄²×C₇	—	2	2	no	—
365	C₄²×C₇	—	2	4	no	—
366	C₄²×C₇	—	2	2	no	—
367	C₄²×C₇	—	4	1	no	—
368	C₄²×C₇	—	4	1	no	—
369	C₄²×C₇	—	4	2	no	—
370	C₄²×C₇	—	4	2	no	—
371	C₄²×C₇	—	4	2	no	—
372	C₄²×C₇	—	4	2	no	—
373	C₄²×C₇	—	4	2	no	—
374	C₄²×C₇	—	4	2	no	—
375	C₄²×C₇	C₂²×C₄	1	8	yes	—
376	C₄²×C₇	C₂²×C₄	1	8	yes	—
377	C₄²×C₇	C₂²×C₄	1	4	yes	—
378	#552	C₄×C₇	1	16	yes	complemented
379	C₂×#126	C₂²×C₇	1	2	yes	—
380	C₂×#125	C₂²×C₇	1	1	yes	characteristic
381	C₂×#125	C₂²×C₇	1	2	yes	—
382	C₂×#123	C₂²×C₇	1	2	yes	—
383	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
384	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
385	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
386	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
387	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
388	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
389	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
390	C₂×#117	C₂²×C₇	1	1	yes	characteristic
391	C₂×#117	C₂²×C₇	1	2	yes	—
392	C₂×#117	C₂²×C₇	1	2	yes	—
393	C₂×#117	C₂²×C₇	1	1	yes	characteristic
394	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
395	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
396	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
397	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
398	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
399	#391	C₂²×C₇	1	1	yes	characteristic
400	#391	C₂²×C₇	1	1	yes	characteristic
401	#389	C₂²×C₇	1	1	yes	characteristic
402	#389	C₂²×C₇	1	2	yes	—
403	#389	C₂²×C₇	1	2	yes	—
404	#389	C₂²×C₇	1	1	yes	characteristic
405	#389	C₂²×C₇	1	1	yes	characteristic
406	#389	C₂²×C₇	1	1	yes	characteristic
407	#389	C₂²×C₇	1	2	yes	—
408	#389	C₂²×C₇	1	2	yes	—
409	#389	C₂²×C₇	1	1	yes	characteristic
410	#389	C₂²×C₇	1	2	yes	—
411	#389	C₂²×C₇	1	2	yes	—
412	#389	C₂²×C₇	1	1	yes	characteristic
413	#389	C₂²×C₇	1	2	yes	—
414	#389	C₂²×C₇	1	2	yes	—
415	#389	C₂²×C₇	1	2	yes	—
416	#389	C₂²×C₇	1	2	yes	—
417	#389	C₂²×C₇	1	1	yes	characteristic
418	#389	C₂²×C₇	1	1	yes	characteristic
419	#389	C₂²×C₇	1	2	yes	—
420	#388	C₂²×C₇	1	2	yes	—
421	#388	C₂²×C₇	1	2	yes	—
422	#388	C₂²×C₇	1	2	yes	—
423	#388	C₂²×C₇	1	1	yes	characteristic
424	#388	C₂²×C₇	1	2	yes	—
425	#388	C₂²×C₇	1	1	yes	characteristic
426	#387	C₂²×C₇	1	2	yes	—
427	#387	C₂²×C₇	1	2	yes	—
428	#387	C₂²×C₇	1	2	yes	—
429	#387	C₂²×C₇	1	2	yes	—
430	#387	C₂²×C₇	1	1	yes	characteristic
431	#387	C₂²×C₇	1	2	yes	—
432	#387	C₂²×C₇	1	2	yes	—
433	#387	C₂²×C₇	1	2	yes	—
434	#387	C₂²×C₇	1	2	yes	—
435	#387	C₂²×C₇	1	2	yes	—
436	#387	C₂²×C₇	1	2	yes	—
437	#387	C₂²×C₇	1	2	yes	—
438	#387	C₂²×C₇	1	1	yes	characteristic
439	#387	C₂²×C₇	1	2	yes	—
440	#386	C₂²×C₇	1	1	yes	characteristic
441	#386	C₂²×C₇	1	1	yes	characteristic
442	#385	C₂²×C₇	1	1	yes	characteristic
443	#385	C₂²×C₇	1	2	yes	—
444	#385	C₂²×C₇	1	2	yes	—
445	#385	C₂²×C₇	1	2	yes	—
446	#385	C₂²×C₇	1	2	yes	—
447	#385	C₂²×C₇	1	2	yes	—
448	#385	C₂²×C₇	1	2	yes	—
449	#385	C₂²×C₇	1	2	yes	—
450	#385	C₂²×C₇	1	1	yes	characteristic
451	#384	C₂²×C₇	1	2	yes	—
452	#384	C₂²×C₇	1	2	yes	—
453	#384	C₂²×C₇	1	1	yes	characteristic
454	#383	C₂²×C₇	1	2	yes	—
455	#382	C₂²×C₇	1	2	yes	—
456	#382	C₂²×C₇	1	2	yes	—
457	#382	C₂²×C₇	1	2	yes	—
458	#381	C₂²×C₇	1	2	yes	—
459	#380	C₂²×C₇	1	1	yes	characteristic
460	#380	C₂²×C₇	1	1	yes	characteristic
461	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
462	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
463	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
464	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
465	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
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×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
471	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
472	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
473	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
474	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
475	#376	C₂²×C₇	1	1	yes	characteristic
476	#376	C₂²×C₇	1	2	yes	—
477	C₂×#95	C₂²×C₇	1	2	yes	—
478	C₂³×C₇	—	2	1	no	—
479	C₂³×C₇	—	2	1	no	—
480	C₂³×C₇	—	2	1	no	—
481	C₂³×C₇	—	2	1	no	—
482	C₂³×C₇	—	2	1	no	—
483	C₂³×C₇	—	2	1	no	—
484	C₂³×C₇	—	2	1	no	—
485	C₂³×C₇	—	2	1	no	—
486	C₂³×C₇	—	2	1	no	—
487	C₂³×C₇	—	2	1	no	—
488	C₂³×C₇	C₂³×C₄	1	2	yes	—
489	C₂³×C₇	C₂³×C₄	1	2	yes	—
490	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
491	C₂³×C₇	2₋¹⁺⁴	1	2	yes	—
492	C₂³×C₇	C₂⁵	1	1	yes	characteristic
493	C₇×Q₈	—	2	8	no	—
494	C₇×D₄	—	2	8	no	—
495	C₂×C₄×C₇	—	2	16	no	—
496	C₂×C₄×C₇	—	2	1	no	—
497	C₂×C₄×C₇	—	2	1	no	—
498	C₂×C₄×C₇	—	2	2	no	—
499	C₂×C₄×C₇	—	2	1	no	—
500	C₂×C₄×C₇	—	2	2	no	—
501	C₂×C₄×C₇	—	2	1	no	—
502	C₂×C₄×C₇	—	2	2	no	—
503	C₂×C₄×C₇	—	2	2	no	—
504	C₂×C₄×C₇	—	2	1	no	—
505	C₂×C₄×C₇	—	2	2	no	—
506	C₂×C₄×C₇	—	2	2	no	—
507	C₂×C₄×C₇	—	2	1	no	—
508	C₂×C₄×C₇	—	2	1	no	—
509	C₂×C₄×C₇	—	2	1	no	—
510	C₂×C₄×C₇	—	2	1	no	—
511	C₂×C₄×C₇	—	2	2	no	—
512	C₂×C₄×C₇	—	2	2	no	—
513	C₂×C₄×C₇	—	2	1	no	—
514	C₂×C₄×C₇	—	2	8	no	—
515	C₂×C₄×C₇	—	2	8	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	2	no	—
522	C₂×C₄×C₇	—	2	1	no	—
523	C₂×C₄×C₇	—	2	1	no	—
524	C₂×C₄×C₇	—	2	2	no	—
525	C₂×C₄×C₇	—	2	2	no	—
526	C₂×C₄×C₇	—	2	2	no	—
527	C₂×C₄×C₇	—	2	2	no	—
528	C₂×C₄×C₇	—	2	2	no	—
529	C₂×C₄×C₇	—	2	2	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	2	no	—
534	C₂×C₄×C₇	—	2	1	no	—
535	C₂×C₄×C₇	—	2	1	no	—
536	C₂×C₄×C₇	—	2	1	no	—
537	C₂×C₄×C₇	—	2	1	no	—
538	C₂×C₄×C₇	—	2	1	no	—
539	C₂×C₄×C₇	—	2	2	no	—
540	C₂×C₄×C₇	—	2	1	no	—
541	C₂×C₄×C₇	—	2	1	no	—
542	C₂×C₄×C₇	—	2	1	no	—
543	C₂×C₄×C₇	—	2	2	no	—
544	C₂×C₄×C₇	—	2	1	no	—
545	C₂×C₄×C₇	—	2	1	no	—
546	C₂×C₄×C₇	—	2	1	no	—
547	C₂×C₄×C₇	—	2	2	no	—
548	C₂×C₄×C₇	—	2	2	no	—
549	C₂×C₄×C₇	—	4	4	no	—
550	C₂×C₄×C₇	—	4	4	no	—
551	C₂×C₄×C₇	—	8	4	no	—
552	C₂×C₄×C₇	—	8	4	no	—
553	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
554	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
555	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
556	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
557	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
558	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
559	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
560	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
561	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
562	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
563	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
564	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
565	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
566	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
567	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
568	C₂³×C₄	C₂³×C₇	1	2	yes	—
569	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
570	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
571	C₂³×C₄	C₂³×C₇	1	2	yes	—
572	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
573	C₂³×C₄	C₂³×C₇	1	2	yes	—
574	#126	C₂×C₄×C₇	1	16	yes	complemented
575	#125	C₂×C₄×C₇	1	16	yes	complemented
576	#125	C₂×C₄×C₇	1	8	yes	complemented
577	#123	C₂×C₄×C₇	1	16	yes	—
578	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	complemented
579	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	complemented
580	C₄×Q₈	—	4	2	no	—
581	C₄×Q₈	—	4	2	no	—
582	C₄×Q₈	C₂×C₄×C₇	1	8	yes	complemented
583	C₄×D₄	—	4	4	no	—
584	C₄×D₄	C₂×C₄×C₇	1	8	yes	—
585	#117	—	4	2	no	—
586	#117	—	4	4	no	—
587	#117	C₂×C₄×C₇	1	8	yes	complemented
588	#117	C₂×C₄×C₇	1	16	yes	complemented
589	C₂×C₄⋊C₄	—	4	2	no	—
590	C₂×C₄⋊C₄	—	4	2	no	—
591	C₂×C₄⋊C₄	—	4	4	no	—
592	C₂×C₄⋊C₄	C₂×C₄×C₇	1	8	yes	complemented
593	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
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	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
628	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
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	1	yes	characteristic
637	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
638	C₂×C₄²	—	4	2	no	—
639	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
640	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
641	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₇	1	2	yes	—
644	C₂×C₄²	C₂³×C₇	1	2	yes	—
645	C₂×C₄²	C₂³×C₇	1	2	yes	—
646	C₂×C₄²	C₂³×C₇	1	2	yes	—
647	C₂×C₄²	C₂³×C₇	1	2	yes	—
648	C₂×C₄²	C₂³×C₇	1	2	yes	—
649	C₂×C₄²	C₂³×C₇	1	2	yes	—
650	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₇	1	2	yes	—
653	C₂×C₄²	C₂³×C₇	1	2	yes	—
654	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
655	#95	C₂³×C₇	1	2	yes	—
656	#95	C₂³×C₇	1	2	yes	—
657	#95	C₂³×C₇	1	2	yes	—
658	#95	C₂³×C₇	1	2	yes	—
659	#95	C₂³×C₇	1	1	yes	characteristic
660	#95	C₂³×C₇	1	2	yes	—
661	#95	C₂³×C₇	1	2	yes	—
662	#95	C₂³×C₇	1	1	yes	characteristic
663	#95	C₂³×C₇	1	1	yes	characteristic
664	#95	C₂³×C₇	1	1	yes	characteristic
665	#95	C₂³×C₇	1	1	yes	characteristic
666	#95	C₂³×C₇	1	1	yes	characteristic
667	#95	C₂³×C₇	1	2	yes	—
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	2	yes	—
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	2	yes	—
676	#95	C₂³×C₇	1	2	yes	—
677	#95	C₂³×C₇	1	2	yes	—
678	#95	C₂³×C₇	1	2	yes	—
679	#95	C₂³×C₇	1	2	yes	—
680	#95	C₂³×C₇	1	2	yes	—
681	#95	C₂³×C₇	1	2	yes	—
682	#95	C₂³×C₇	1	2	yes	—
683	#95	C₂³×C₇	1	1	yes	characteristic
684	C₂²×C₇	—	2	2	no	—
685	C₂²×C₇	—	2	2	no	—
686	C₂²×C₇	—	2	2	no	—
687	C₂²×C₇	—	2	2	no	—
688	C₂²×C₇	—	2	2	no	—
689	C₂²×C₇	—	2	2	no	—
690	C₂²×C₇	—	2	2	no	—
691	C₂²×C₇	—	2	2	no	—
692	C₂²×C₇	—	2	2	no	—
693	C₂²×C₇	—	4	1	no	—
694	C₂²×C₇	—	4	1	no	—
695	C₂²×C₇	—	4	1	no	—
696	C₂²×C₇	—	4	1	no	—
697	C₂²×C₇	#520	1	4	yes	—
698	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
699	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
700	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
701	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
702	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
703	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
704	C₂²×C₇	#585	1	1	yes	characteristic
705	C₄×C₇	—	2	4	no	—
706	C₄×C₇	—	2	4	no	—
707	C₄×C₇	—	2	2	no	—
708	C₄×C₇	—	2	2	no	—
709	C₄×C₇	—	2	2	no	—
710	C₄×C₇	—	2	4	no	—
711	C₄×C₇	—	2	4	no	—
712	C₄×C₇	—	2	2	no	—
713	C₄×C₇	—	2	2	no	—
714	C₄×C₇	—	4	1	no	—
715	C₄×C₇	—	4	1	no	—
716	C₄×C₇	—	4	1	no	—
717	C₄×C₇	—	4	1	no	—
718	C₄×C₇	—	4	1	no	—
719	C₄×C₇	—	4	2	no	—
720	C₄×C₇	—	4	2	no	—
721	C₄×C₇	—	4	2	no	—
722	C₄×C₇	—	4	2	no	—
723	C₄×C₇	—	4	1	no	—
724	C₄×C₇	—	4	1	no	—
725	C₄×C₇	#520	1	4	yes	—
726	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
727	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
728	C₂×Q₈	—	2	2	no	—
729	C₂×Q₈	—	2	2	no	—
730	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
734	C₂²×C₄	—	2	4	no	—
735	C₂²×C₄	—	2	4	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	4	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	4	1	no	—
745	C₂²×C₄	—	4	1	no	—
746	C₂²×C₄	—	4	1	no	—
747	C₂²×C₄	—	4	2	no	—
748	C₂²×C₄	—	4	2	no	—
749	C₂²×C₄	—	4	2	no	—
750	C₂²×C₄	—	4	2	no	—
751	C₂²×C₄	—	4	2	no	—
752	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
753	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
754	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
755	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
765	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	—	4	2	no	—
783	C₄⋊C₄	—	4	2	no	—
784	C₄⋊C₄	—	4	2	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₄⋊C₄	—	4	2	no	—
787	C₄⋊C₄	—	4	1	no	—
788	C₄⋊C₄	—	4	1	no	—
789	C₄⋊C₄	—	4	2	no	—
790	C₄⋊C₄	—	4	2	no	—
791	C₄⋊C₄	—	4	2	no	—
792	C₄⋊C₄	—	4	2	no	—
793	C₄⋊C₄	—	4	2	no	—
794	C₄⋊C₄	—	4	2	no	—
795	C₄⋊C₄	—	4	2	no	—
796	C₄⋊C₄	—	4	2	no	—
797	C₄⋊C₄	—	4	1	no	—
798	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
799	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
800	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
801	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
802	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
803	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
804	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
805	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
806	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
807	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	4	1	no	—
813	C₂²⋊C₄	—	4	1	no	—
814	C₂²⋊C₄	—	4	2	no	—
815	C₂²⋊C₄	—	4	1	no	—
816	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
817	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
818	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
819	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
820	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	—	2	2	no	—
824	C₄²	—	2	4	no	—
825	C₄²	—	2	2	no	—
826	C₄²	—	4	1	no	—
827	C₄²	—	4	1	no	—
828	C₄²	—	4	2	no	—
829	C₄²	—	4	2	no	—
830	C₄²	—	4	2	no	—
831	C₄²	—	4	2	no	—
832	C₄²	—	4	2	no	—
833	C₄²	—	4	2	no	—
834	C₄²	C₂²×C₄×C₇	1	8	yes	—
835	C₄²	C₂²×C₄×C₇	1	8	yes	—
836	C₄²	C₂²×C₄×C₇	1	4	yes	—
837	C₂×C₇	—	2	4	no	—
838	C₂×C₇	—	4	2	no	—
839	C₂×C₇	C₂×#520	1	1	yes	characteristic
840	C₂×C₇	C₂×#520	1	1	yes	characteristic
841	C₂×C₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
842	C₂×C₇	#3538	1	1	yes	characteristic
843	C₂×C₇	#3542	1	1	yes	characteristic
844	C₂×C₇	#3544	1	1	yes	characteristic
845	C₂×C₇	#3563	1	1	yes	characteristic
846	C₂³	—	2	1	no	—
847	C₂³	—	2	1	no	—
848	C₂³	—	2	1	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	1	no	—
854	C₂³	—	2	1	no	—
855	C₂³	—	2	1	no	—
856	C₂³	C₂³×C₄×C₇	1	2	yes	—
857	C₂³	C₂³×C₄×C₇	1	2	yes	—
858	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
859	C₂³	C₇×2₋¹⁺⁴	1	2	yes	—
860	C₂³	C₂⁵×C₇	1	1	yes	characteristic
861	Q₈	—	2	8	no	—
862	D₄	—	2	8	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	16	no	—
882	C₂×C₄	—	2	8	no	—
883	C₂×C₄	—	2	8	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	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	2	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	4	4	no	—
918	C₂×C₄	—	4	4	no	—
919	C₂×C₄	—	8	4	no	—
920	C₂×C₄	—	8	4	no	—
921	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
922	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
923	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
924	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
925	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
926	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
927	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
928	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
929	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
930	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
931	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
932	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
933	C₇	#34465	1	1	yes	characteristic, direct product factor, Sylow
934	C₂²	—	2	2	no	—
935	C₂²	—	2	2	no	—
936	C₂²	—	2	2	no	—
937	C₂²	—	2	2	no	—
938	C₂²	—	2	2	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	4	1	no	—
944	C₂²	—	4	1	no	—
945	C₂²	—	4	1	no	—
946	C₂²	—	4	1	no	—
947	C₂²	C₇×#520	1	4	yes	—
948	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
949	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
950	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
951	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
952	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
953	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
954	C₂²	C₇×#585	1	1	yes	characteristic
955	C₄	—	2	4	no	—
956	C₄	—	2	4	no	—
957	C₄	—	2	2	no	—
958	C₄	—	2	2	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	4	no	—
961	C₄	—	2	4	no	—
962	C₄	—	2	2	no	—
963	C₄	—	2	2	no	—
964	C₄	—	4	1	no	—
965	C₄	—	4	1	no	—
966	C₄	—	4	1	no	—
967	C₄	—	4	1	no	—
968	C₄	—	4	1	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	2	no	—
972	C₄	—	4	1	no	—
973	C₄	—	4	2	no	—
974	C₄	—	4	1	no	—
975	C₄	C₇×#520	1	4	yes	—
976	C₂	—	2	4	no	—
977	C₂	—	4	2	no	—
978	C₂	C₂×C₇×#520	1	1	yes	characteristic
979	C₂	C₂×C₇×#520	1	1	yes	characteristic
980	C₂	C₄×C₇×2₋¹⁺⁴	1	1	yes	characteristic
981	C₂	C₇×#3538	1	1	yes	characteristic
982	C₂	C₇×#3542	1	1	yes	characteristic
983	C₂	C₇×#3544	1	1	yes	characteristic
984	C₂	C₇×#3563	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×D₄	C₂³
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×#2383	C₂	semidirect
3. C₇×#2382	C₂	semidirect
4. C₇×#2370	C₂	semidirect
5. C₇×#2360	C₂	semidirect
6. C₇×#2360	C₂	semidirect
8. C₇×Q₈×C₄⋊C₄	C₂	semidirect
10. C₇×#2346	C₂	semidirect
11. C₇×#2344	C₂	semidirect
12. C₇×#2343	C₂	semidirect
13. C₇×#2334	C₂	semidirect
14. C₇×#2330	C₂	semidirect
15. C₇×#2330	C₂	semidirect
16. C₇×#2323	C₂	semidirect
18. C₇×#2320	C₂	semidirect
19. C₇×#2317	C₂	semidirect
20. C₇×#2317	C₂	semidirect
21. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
22. C₂×C₇×#389	C₂	semidirect
24. C₇×#552	C₄	semidirect
124. #34465	C₇	direct (N × H)
134. C₇×#126	C₂×C₄	semidirect
135. C₇×#125	C₂×C₄	semidirect
136. C₇×#125	C₂×C₄	semidirect
138. C₇×C₂²⋊Q₈	C₂×C₄	semidirect
139. C₇×C₂²⋊Q₈	C₂×C₄	semidirect
142. C₄×C₇×Q₈	C₂×C₄	semidirect
147. C₇×#117	C₂×C₄	semidirect
148. C₇×#117	C₂×C₄	semidirect
152. C₂×C₇×C₄⋊C₄	C₂×C₄	semidirect
245. #2383	C₂×C₇	semidirect
246. #2382	C₂×C₇	semidirect
247. #2370	C₂×C₇	semidirect
248. #2360	C₂×C₇	semidirect
249. #2360	C₂×C₇	semidirect
251. Q₈×C₄⋊C₄	C₂×C₇	semidirect
253. #2346	C₂×C₇	semidirect
254. #2344	C₂×C₇	semidirect
255. #2343	C₂×C₇	semidirect
256. #2334	C₂×C₇	semidirect
257. #2330	C₂×C₇	semidirect
258. #2330	C₂×C₇	semidirect
259. #2323	C₂×C₇	semidirect
261. #2320	C₂×C₇	semidirect
262. #2317	C₂×C₇	semidirect
263. #2317	C₂×C₇	semidirect
264. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
265. C₂×#389	C₂×C₇	semidirect
378. #552	C₄×C₇	semidirect
574. #126	C₂×C₄×C₇	semidirect
575. #125	C₂×C₄×C₇	semidirect
576. #125	C₂×C₄×C₇	semidirect
578. C₂²⋊Q₈	C₂×C₄×C₇	semidirect
579. C₂²⋊Q₈	C₂×C₄×C₇	semidirect
582. C₄×Q₈	C₂×C₄×C₇	semidirect
587. #117	C₂×C₄×C₇	semidirect
588. #117	C₂×C₄×C₇	semidirect
592. C₂×C₄⋊C₄	C₂×C₄×C₇	semidirect
933. C₇	#34465	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×#552	2
C₇×#2383	2
C₇×#2382	2
C₇×#2370	2
C₇×#2360	2
C₇×#2359	2
C₇×Q₈×C₄⋊C₄	2
C₇×D₄×C₄⋊C₄	2
C₇×#2346	2
C₇×#2344	2
C₇×#2343	2
C₇×#2334	2
C₇×#2330	2
C₇×#2323	2
C₇×#2322	2
C₇×#2320	2
C₇×#2317	2
C₄×C₇×C₂²⋊Q₈	2
C₂×C₇×#389	2
C₇×#2290	2
#34465	7

Subgroups — C7×#34465 #13211681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34465 #13211681