Subgroups — #11744166

Order 896.

1022 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#562	C₂	1	1	yes	maximal, characteristic, complemented
2	#90384	C₂	1	1	yes	maximal, characteristic, complemented
3	#90380	C₂	1	1	yes	maximal, characteristic, complemented
4	#90373	C₂	1	1	yes	maximal, characteristic, complemented
5	#90366	C₂	1	1	yes	maximal, characteristic, complemented
6	#90361	C₂	1	1	yes	maximal, characteristic, complemented
7	#90361	C₂	1	1	yes	maximal, characteristic, complemented
8	#90358	C₂	1	1	yes	maximal, characteristic, complemented
9	#90354	C₂	1	1	yes	maximal, characteristic, complemented
10	#90353	C₂	1	1	yes	maximal, characteristic, complemented
11	#90352	C₂	1	1	yes	maximal, characteristic, complemented
12	#90346	C₂	1	1	yes	maximal, characteristic, complemented
13	#90341	C₂	1	1	yes	maximal, characteristic, complemented
14	#90340	C₂	1	1	yes	maximal, characteristic, complemented
15	#90339	C₂	1	1	yes	maximal, characteristic, complemented
16	#90338	C₂	1	1	yes	maximal, characteristic, complemented
17	#90334	C₂	1	1	yes	maximal, characteristic, complemented
18	#90331	C₂	1	1	yes	maximal, characteristic, complemented
19	#90327	C₂	1	1	yes	maximal, characteristic, complemented
20	#90324	C₂	1	1	yes	maximal, characteristic, complemented
21	#90323	C₂	1	1	yes	maximal, characteristic, complemented
22	#90314	C₂	1	1	yes	maximal, characteristic, complemented
23	#90313	C₂	1	1	yes	maximal, characteristic, complemented
24	#90312	C₂	1	1	yes	maximal, characteristic, complemented
25	#90307	C₂	1	1	yes	maximal, characteristic, complemented
26	#90306	C₂	1	1	yes	maximal, characteristic, complemented
27	#90299	C₂	1	1	yes	maximal, characteristic, complemented
28	#90292	C₂	1	1	yes	maximal, characteristic, complemented
29	#90289	C₂	1	1	yes	maximal, characteristic, complemented
30	#90288	C₂	1	1	yes	maximal, characteristic, complemented
31	#90287	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×Q₈×D₇	C₂²	1	1	yes	characteristic
33	C₂×#1159	C₂²	1	1	yes	characteristic
34	C₂×#1159	C₂²	1	1	yes	characteristic
35	C₂×#1159	C₂²	1	1	yes	characteristic
36	C₂×#1157	C₂²	1	1	yes	characteristic
37	C₂²×Dic₁₄	C₂²	1	1	yes	characteristic
38	C₇×#125	C₂²	1	1	yes	characteristic
39	C₇×#124	C₂²	1	1	yes	characteristic
40	C₇×#124	C₂²	1	1	yes	characteristic
41	C₇×#123	C₂²	1	1	yes	characteristic
42	C₇×#123	C₂²	1	1	yes	characteristic
43	C₇×#123	C₂²	1	1	yes	characteristic
44	C₇×#123	C₂²	1	1	yes	characteristic
45	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
47	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
48	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
49	C₇×#121	C₂²	1	1	yes	characteristic
50	C₇×#121	C₂²	1	1	yes	characteristic
51	C₇×#121	C₂²	1	1	yes	characteristic
52	C₇×#121	C₂²	1	1	yes	characteristic
53	#6510	C₂²	1	1	yes	characteristic
54	#6510	C₂²	1	1	yes	characteristic
55	#6509	C₂²	1	1	yes	characteristic
56	Q₈×Dic₇	C₂²	1	1	yes	characteristic
57	#6507	C₂²	1	1	yes	characteristic
58	#6507	C₂²	1	1	yes	characteristic
59	#6507	C₂²	1	1	yes	characteristic
60	#6503	C₂²	1	1	yes	characteristic
61	#6502	C₂²	1	1	yes	characteristic
62	#6502	C₂²	1	1	yes	characteristic
63	#6502	C₂²	1	1	yes	characteristic
64	#6502	C₂²	1	1	yes	characteristic
65	#6502	C₂²	1	1	yes	characteristic
66	#6502	C₂²	1	1	yes	characteristic
67	#6502	C₂²	1	1	yes	characteristic
68	#6502	C₂²	1	1	yes	characteristic
69	#6502	C₂²	1	1	yes	characteristic
70	#6502	C₂²	1	1	yes	characteristic
71	#6501	C₂²	1	1	yes	characteristic
72	#6501	C₂²	1	1	yes	characteristic
73	#6501	C₂²	1	1	yes	characteristic
74	#6499	C₂²	1	1	yes	characteristic
75	#6499	C₂²	1	1	yes	characteristic
76	#6498	C₂²	1	1	yes	characteristic
77	#6498	C₂²	1	1	yes	characteristic
78	D₄×Dic₇	C₂²	1	1	yes	characteristic
79	D₄×Dic₇	C₂²	1	1	yes	characteristic
80	D₄×Dic₇	C₂²	1	1	yes	characteristic
81	#6493	C₂²	1	1	yes	characteristic
82	#6493	C₂²	1	1	yes	characteristic
83	#6492	C₂²	1	1	yes	characteristic
84	#6492	C₂²	1	1	yes	characteristic
85	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
88	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
89	#6489	C₂²	1	1	yes	characteristic
90	#6487	C₂²	1	1	yes	characteristic
91	#6487	C₂²	1	1	yes	characteristic
92	C₂×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
93	C₂×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
94	C₂×C₄×Dic₇	C₂²	1	1	yes	characteristic
95	#6461	C₂²	1	1	yes	characteristic
96	#6461	C₂²	1	1	yes	characteristic
97	#6461	C₂²	1	1	yes	characteristic
98	#6460	C₂²	1	1	yes	characteristic
99	#6460	C₂²	1	1	yes	characteristic
100	#6460	C₂²	1	1	yes	characteristic
101	#6459	C₂²	1	1	yes	characteristic
102	#6459	C₂²	1	1	yes	characteristic
103	#6459	C₂²	1	1	yes	characteristic
104	#6459	C₂²	1	1	yes	characteristic
105	#6459	C₂²	1	1	yes	characteristic
106	#6459	C₂²	1	1	yes	characteristic
107	#6459	C₂²	1	1	yes	characteristic
108	#6458	C₂²	1	1	yes	characteristic
109	#6457	C₂²	1	1	yes	characteristic
110	#6457	C₂²	1	1	yes	characteristic
111	#6457	C₂²	1	1	yes	characteristic
112	#6456	C₂²	1	1	yes	characteristic
113	#6456	C₂²	1	1	yes	characteristic
114	#6455	C₂²	1	1	yes	characteristic
115	#6455	C₂²	1	1	yes	characteristic
116	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
117	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
118	#6453	C₂²	1	1	yes	characteristic
119	#6452	C₂²	1	1	yes	characteristic
120	#6452	C₂²	1	1	yes	characteristic
121	#6452	C₂²	1	1	yes	characteristic
122	#6452	C₂²	1	1	yes	characteristic
123	#6452	C₂²	1	1	yes	characteristic
124	#6452	C₂²	1	1	yes	characteristic
125	#6452	C₂²	1	1	yes	characteristic
126	#6451	C₂²	1	1	yes	characteristic
127	#6451	C₂²	1	1	yes	characteristic
128	#6451	C₂²	1	1	yes	characteristic
129	#6451	C₂²	1	1	yes	characteristic
130	#6451	C₂²	1	1	yes	characteristic
131	#6450	C₂²	1	1	yes	characteristic
132	#6450	C₂²	1	1	yes	characteristic
133	#6450	C₂²	1	1	yes	characteristic
134	#6450	C₂²	1	1	yes	characteristic
135	#6449	C₂²	1	1	yes	characteristic
136	#6449	C₂²	1	1	yes	characteristic
137	#6448	C₂²	1	1	yes	characteristic
138	#6448	C₂²	1	1	yes	characteristic
139	#6448	C₂²	1	1	yes	characteristic
140	#6448	C₂²	1	1	yes	characteristic
141	#6448	C₂²	1	1	yes	characteristic
142	#6448	C₂²	1	1	yes	characteristic
143	#6448	C₂²	1	1	yes	characteristic
144	#6448	C₂²	1	1	yes	characteristic
145	#6448	C₂²	1	1	yes	characteristic
146	#6447	C₂²	1	1	yes	characteristic
147	#6447	C₂²	1	1	yes	characteristic
148	#6447	C₂²	1	1	yes	characteristic
149	#6447	C₂²	1	1	yes	characteristic
150	#6447	C₂²	1	1	yes	characteristic
151	#6447	C₂²	1	1	yes	characteristic
152	#6447	C₂²	1	1	yes	characteristic
153	#6446	C₂²	1	1	yes	characteristic
154	#6446	C₂²	1	1	yes	characteristic
155	#6446	C₂²	1	1	yes	characteristic
156	#6446	C₂²	1	1	yes	characteristic
157	#6446	C₂²	1	1	yes	characteristic
158	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
159	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
160	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
161	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
162	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
163	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
164	#6442	C₂²	1	1	yes	characteristic
165	#6442	C₂²	1	1	yes	characteristic
166	#6442	C₂²	1	1	yes	characteristic
167	#6441	C₂²	1	1	yes	characteristic
168	#6441	C₂²	1	1	yes	characteristic
169	#6441	C₂²	1	1	yes	characteristic
170	#6441	C₂²	1	1	yes	characteristic
171	#6441	C₂²	1	1	yes	characteristic
172	#6441	C₂²	1	1	yes	characteristic
173	#6441	C₂²	1	1	yes	characteristic
174	#6441	C₂²	1	1	yes	characteristic
175	#6441	C₂²	1	1	yes	characteristic
176	#6441	C₂²	1	1	yes	characteristic
177	#6440	C₂²	1	1	yes	characteristic
178	#6440	C₂²	1	1	yes	characteristic
179	#6440	C₂²	1	1	yes	characteristic
180	#6440	C₂²	1	1	yes	characteristic
181	#6440	C₂²	1	1	yes	characteristic
182	#6440	C₂²	1	1	yes	characteristic
183	#6435	C₂²	1	1	yes	characteristic
184	#6435	C₂²	1	1	yes	characteristic
185	#6435	C₂²	1	1	yes	characteristic
186	#6432	C₂²	1	1	yes	characteristic
187	#3547	—	7	1	no	maximal, Sylow
188	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
189	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
190	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
191	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
192	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
193	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
194	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
195	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
196	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
197	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
198	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
199	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
212	C₂²×Dic₇	C₂³	1	1	yes	characteristic
213	C₂²×Dic₇	C₂³	1	1	yes	characteristic
214	C₂²×Dic₇	C₂³	1	1	yes	characteristic
215	C₂²×Dic₇	C₂³	1	1	yes	characteristic
216	C₂²×Dic₇	C₂³	1	1	yes	characteristic
217	C₂²×Dic₇	C₂³	1	1	yes	characteristic
218	C₂²×Dic₇	C₂³	1	1	yes	characteristic
219	C₂²×Dic₇	C₂³	1	1	yes	characteristic
220	Q₈×D₇	—	4	2	no	—
221	#1159	—	4	2	no	—
222	#1159	—	4	2	no	—
223	#1159	—	4	2	no	—
224	#1157	—	4	2	no	—
225	C₂×D₂₈	C₂³	1	1	yes	characteristic
226	C₂×D₂₈	C₂³	1	1	yes	characteristic
227	C₂×D₂₈	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
237	C₂×Dic₁₄	—	4	2	no	—
238	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
239	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
240	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
241	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
242	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
243	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
244	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
245	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
246	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
247	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
248	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
249	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
250	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
251	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
252	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
253	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
254	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
255	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
256	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
257	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
258	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
259	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
260	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
261	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
262	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
263	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
264	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
265	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
266	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
267	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
268	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
269	C₄²×C₇	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
274	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
275	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
276	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
277	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
282	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
283	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
284	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
285	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
287	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
293	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
294	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
295	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
297	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
298	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
299	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
300	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
301	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
302	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
303	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
304	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
305	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
306	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
307	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
308	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
309	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
310	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
311	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
312	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
313	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
314	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
315	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
316	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
317	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
318	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
319	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
320	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
321	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
322	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
323	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
324	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
325	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
326	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
327	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
328	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
329	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
330	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
331	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
332	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
333	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
334	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
335	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
336	C₄×Dic₇	C₂³	1	1	yes	characteristic
337	C₄×Dic₇	C₂³	1	1	yes	characteristic
338	C₄×Dic₇	C₂³	1	1	yes	characteristic
339	C₄×Dic₇	C₂³	1	1	yes	characteristic
340	C₄×Dic₇	C₂³	1	1	yes	characteristic
341	C₄×Dic₇	C₂³	1	1	yes	characteristic
342	C₄×Dic₇	C₂³	1	1	yes	characteristic
343	C₄×Dic₇	C₂³	1	1	yes	characteristic
344	C₄×Dic₇	C₂³	1	1	yes	characteristic
345	C₄×Dic₇	C₂³	1	1	yes	characteristic
346	C₄×Dic₇	C₂³	1	1	yes	characteristic
347	C₄×Dic₇	C₂³	1	1	yes	characteristic
348	C₄×Dic₇	C₂³	1	1	yes	characteristic
349	#562	—	7	1	no	—
350	#562	—	7	1	no	—
351	#562	—	7	1	no	—
352	#562	D₇	1	1	yes	characteristic, complemented
353	#555	—	7	1	no	—
354	#555	—	7	1	no	—
355	#555	—	7	1	no	—
356	#554	—	7	1	no	—
357	#553	—	7	1	no	—
358	#553	—	7	1	no	—
359	#552	—	7	1	no	—
360	#552	—	7	1	no	—
361	D₄×Q₈	—	7	1	no	—
362	#548	—	7	1	no	—
363	#548	—	7	1	no	—
364	#547	—	7	1	no	—
365	#544	—	7	1	no	—
366	#544	—	7	1	no	—
367	#542	—	7	1	no	—
368	#542	—	7	1	no	—
369	#542	—	7	1	no	—
370	#542	—	7	1	no	—
371	#540	—	7	1	no	—
372	#540	—	7	1	no	—
373	#537	—	7	1	no	—
374	#537	—	7	1	no	—
375	#536	—	7	1	no	—
376	#536	—	7	1	no	—
377	#533	—	7	1	no	—
378	#532	—	7	1	no	—
379	#529	—	7	1	no	—
380	C₂³×C₇	C₂⁴	1	1	yes	characteristic
381	C₂³×C₇	C₂⁴	1	1	yes	characteristic
382	C₂³×C₇	C₂⁴	1	1	yes	characteristic
383	C₂³×C₇	C₂⁴	1	1	yes	characteristic
384	C₂²×D₇	C₂⁴	1	1	yes	characteristic
385	C₂²×D₇	C₂⁴	1	1	yes	characteristic
386	C₂²×D₇	C₂⁴	1	1	yes	characteristic
387	C₇×Q₈	—	4	1	no	—
388	C₇×Q₈	—	4	1	no	—
389	C₇×D₄	—	4	1	no	—
390	C₇×D₄	—	4	1	no	—
391	C₇×D₄	—	4	1	no	—
392	C₇×D₄	—	4	1	no	—
393	C₇×D₄	—	4	1	no	—
394	C₇×D₄	—	4	1	no	—
395	C₂×C₄×C₇	—	4	1	no	—
396	C₂×C₄×C₇	—	4	1	no	—
397	C₂×C₄×C₇	—	4	1	no	—
398	C₂×C₄×C₇	—	4	1	no	—
399	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
400	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
401	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
402	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
403	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
404	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
405	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
406	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
407	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
408	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
409	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
410	C₂²⋊D₇	—	2	2	no	—
411	C₂²⋊D₇	—	2	2	no	—
412	C₂²⋊D₇	—	2	2	no	—
413	C₂²⋊D₇	—	4	1	no	—
414	C₂²⋊D₇	—	4	1	no	—
415	C₂²⋊D₇	—	4	1	no	—
416	C₂²⋊D₇	—	4	1	no	—
417	C₂²⋊D₇	—	4	1	no	—
418	C₂²⋊D₇	—	4	1	no	—
419	C₂²⋊D₇	—	4	1	no	—
420	C₂²⋊D₇	—	4	1	no	—
421	C₂²⋊D₇	—	4	1	no	—
422	C₂×Dic₇	—	2	2	no	—
423	C₂×Dic₇	—	2	2	no	—
424	C₂×Dic₇	—	2	2	no	—
425	C₂×Dic₇	—	2	2	no	—
426	C₂×Dic₇	—	2	2	no	—
427	C₂×Dic₇	—	4	1	no	—
428	C₂×Dic₇	—	4	1	no	—
429	C₂×Dic₇	—	4	1	no	—
430	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
431	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
432	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
433	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
434	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
435	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
436	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
437	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
438	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
439	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
440	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
441	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
442	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
443	D₂₈	—	4	1	no	—
444	D₂₈	—	4	1	no	—
445	D₂₈	—	4	1	no	—
446	C₄×D₇	—	2	2	no	—
447	C₄×D₇	—	2	2	no	—
448	C₄×D₇	—	2	2	no	—
449	C₄×D₇	—	4	1	no	—
450	C₄×D₇	—	4	1	no	—
451	C₄×D₇	—	4	1	no	—
452	C₄×D₇	—	4	1	no	—
453	C₄×D₇	—	4	1	no	—
454	C₄×D₇	—	4	1	no	—
455	Dic₁₄	—	2	2	no	—
456	Dic₁₄	—	2	2	no	—
457	Dic₁₄	—	2	2	no	—
458	Dic₁₄	—	4	1	no	—
459	Dic₁₄	—	4	1	no	—
460	Dic₁₄	—	4	1	no	—
461	Dic₁₄	—	4	1	no	—
462	Dic₁₄	—	4	1	no	—
463	Dic₁₄	—	4	1	no	—
464	C₂×#41	—	7	1	no	—
465	C₂×#41	—	7	1	no	—
466	C₂×#41	—	7	1	no	—
467	C₂×#41	—	7	1	no	—
468	C₂²×Q₈	—	7	1	no	—
469	C₂²×Q₈	—	7	1	no	—
470	C₄⋊Q₈	—	7	1	no	—
471	C₄⋊Q₈	—	7	1	no	—
472	C₄⋊Q₈	—	7	1	no	—
473	C₄⋊Q₈	—	7	1	no	—
474	C₄⋊Q₈	—	7	1	no	—
475	C₄⋊Q₈	—	7	1	no	—
476	C₄⋊Q₈	—	7	1	no	—
477	C₄⋊Q₈	—	7	1	no	—
478	C₄⋊Q₈	—	7	1	no	—
479	#127	—	7	1	no	—
480	#126	—	7	1	no	—
481	#126	—	7	1	no	—
482	#126	—	7	1	no	—
483	#126	—	7	1	no	—
484	#126	—	7	1	no	—
485	#126	—	7	1	no	—
486	#125	—	7	1	no	—
487	#125	—	7	1	no	—
488	#125	—	7	1	no	—
489	#125	—	7	1	no	—
490	#125	—	7	1	no	—
491	#125	—	7	1	no	—
492	#125	—	7	1	no	—
493	#125	—	7	1	no	—
494	#125	C₂×D₇	1	1	yes	characteristic
495	#124	—	7	1	no	—
496	#124	—	7	1	no	—
497	#124	—	7	1	no	—
498	#124	—	7	1	no	—
499	#124	—	7	1	no	—
500	#124	—	7	1	no	—
501	#124	—	7	1	no	—
502	#124	—	7	1	no	—
503	#124	—	7	1	no	—
504	#124	—	7	1	no	—
505	#124	—	7	1	no	—
506	#124	—	7	1	no	—
507	#124	—	7	1	no	—
508	#124	C₂×D₇	1	1	yes	characteristic
509	#124	C₂×D₇	1	1	yes	characteristic
510	#123	—	7	1	no	—
511	#123	—	7	1	no	—
512	#123	—	7	1	no	—
513	#123	—	7	1	no	—
514	#123	—	7	1	no	—
515	#123	—	7	1	no	—
516	#123	—	7	1	no	—
517	#123	—	7	1	no	—
518	#123	—	7	1	no	—
519	#123	—	7	1	no	—
520	#123	—	7	1	no	—
521	#123	—	7	1	no	—
522	#123	—	7	1	no	—
523	#123	—	7	1	no	—
524	#123	C₂×D₇	1	1	yes	characteristic
525	#123	C₂×D₇	1	1	yes	characteristic
526	#123	C₂×D₇	1	1	yes	characteristic
527	#123	C₂×D₇	1	1	yes	characteristic
528	C₂²⋊Q₈	—	7	1	no	—
529	C₂²⋊Q₈	—	7	1	no	—
530	C₂²⋊Q₈	—	7	1	no	—
531	C₂²⋊Q₈	—	7	1	no	—
532	C₂²⋊Q₈	—	7	1	no	—
533	C₂²⋊Q₈	—	7	1	no	—
534	C₂²⋊Q₈	—	7	1	no	—
535	C₂²⋊Q₈	—	7	1	no	—
536	C₂²⋊Q₈	—	7	1	no	—
537	C₂²⋊Q₈	—	7	1	no	—
538	C₂²⋊Q₈	—	7	1	no	—
539	C₂²⋊Q₈	—	7	1	no	—
540	C₂²⋊Q₈	—	7	1	no	—
541	C₂²⋊Q₈	—	7	1	no	—
542	C₂²⋊Q₈	—	7	1	no	—
543	C₂²⋊Q₈	—	7	1	no	—
544	C₂²⋊Q₈	—	7	1	no	—
545	C₂²⋊Q₈	—	7	1	no	—
546	C₂²⋊Q₈	—	7	1	no	—
547	C₂²⋊Q₈	—	7	1	no	—
548	C₂²⋊Q₈	—	7	1	no	—
549	C₂²⋊Q₈	—	7	1	no	—
550	C₂²⋊Q₈	—	7	1	no	—
551	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic
552	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic
553	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic
554	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic
555	#121	—	7	1	no	—
556	#121	—	7	1	no	—
557	#121	—	7	1	no	—
558	#121	—	7	1	no	—
559	#121	—	7	1	no	—
560	#121	—	7	1	no	—
561	#121	—	7	1	no	—
562	#121	—	7	1	no	—
563	#121	—	7	1	no	—
564	#121	—	7	1	no	—
565	#121	—	7	1	no	—
566	#121	—	7	1	no	—
567	#121	—	7	1	no	—
568	#121	—	7	1	no	—
569	#121	—	7	1	no	—
570	#121	—	7	1	no	—
571	#121	—	7	1	no	—
572	#121	—	7	1	no	—
573	#121	—	7	1	no	—
574	#121	—	7	1	no	—
575	#121	—	7	1	no	—
576	#121	—	7	1	no	—
577	#121	—	7	1	no	—
578	#121	C₂×D₇	1	1	yes	characteristic
579	#121	C₂×D₇	1	1	yes	characteristic
580	#121	C₂×D₇	1	1	yes	characteristic
581	#121	C₂×D₇	1	1	yes	characteristic
582	C₄×Q₈	—	7	1	no	—
583	C₄×Q₈	—	7	1	no	—
584	C₄×Q₈	—	7	1	no	—
585	C₄×Q₈	—	7	1	no	—
586	C₄×Q₈	—	7	1	no	—
587	C₄×D₄	—	7	1	no	—
588	C₄×D₄	—	7	1	no	—
589	C₄×D₄	—	7	1	no	—
590	C₄×D₄	—	7	1	no	—
591	C₄×D₄	—	7	1	no	—
592	C₄×D₄	—	7	1	no	—
593	C₄×D₄	—	7	1	no	—
594	C₄×D₄	—	7	1	no	—
595	C₄×D₄	—	7	1	no	—
596	C₄×D₄	—	7	1	no	—
597	C₄×D₄	—	7	1	no	—
598	C₄×D₄	—	7	1	no	—
599	C₄×D₄	—	7	1	no	—
600	C₄×D₄	—	7	1	no	—
601	C₄×D₄	—	7	1	no	—
602	#117	—	7	1	no	—
603	#117	—	7	1	no	—
604	#117	—	7	1	no	—
605	#117	—	7	1	no	—
606	#117	—	7	1	no	—
607	#117	—	7	1	no	—
608	#117	—	7	1	no	—
609	#117	—	7	1	no	—
610	#117	—	7	1	no	—
611	#117	—	7	1	no	—
612	#117	—	7	1	no	—
613	#117	—	7	1	no	—
614	C₂×C₄⋊C₄	—	7	1	no	—
615	C₂×C₄⋊C₄	—	7	1	no	—
616	C₂×C₄⋊C₄	—	7	1	no	—
617	C₂×C₄⋊C₄	—	7	1	no	—
618	C₂×C₄²	—	7	1	no	—
619	C₂²×C₇	—	2	1	no	—
620	C₂²×C₇	—	2	1	no	—
621	C₂²×C₇	—	2	1	no	—
622	C₂²×C₇	—	2	1	no	—
623	C₂²×C₇	—	2	1	no	—
624	C₂²×C₇	—	2	1	no	—
625	C₂²×C₇	—	2	1	no	—
626	C₂²×C₇	—	2	1	no	—
627	C₂²×C₇	—	2	1	no	—
628	C₂²×C₇	—	2	1	no	—
629	C₂²×C₇	—	2	1	no	—
630	C₂²×C₇	—	2	1	no	—
631	C₂²×C₇	C₂⁵	1	1	yes	characteristic
632	C₂×D₇	—	2	1	no	—
633	C₂×D₇	—	2	1	no	—
634	C₂×D₇	—	2	1	no	—
635	C₂×D₇	—	2	1	no	—
636	C₂×D₇	—	2	1	no	—
637	C₂×D₇	—	2	1	no	—
638	C₂×D₇	—	2	1	no	—
639	C₂×D₇	—	2	1	no	—
640	C₂×D₇	—	2	1	no	—
641	C₄×C₇	—	2	1	no	—
642	C₄×C₇	—	2	1	no	—
643	C₄×C₇	—	2	1	no	—
644	C₄×C₇	—	2	1	no	—
645	C₄×C₇	—	2	1	no	—
646	C₄×C₇	—	2	1	no	—
647	C₄×C₇	—	2	1	no	—
648	C₄×C₇	—	2	1	no	—
649	C₄×C₇	—	2	1	no	—
650	C₄×C₇	—	2	1	no	—
651	C₄×C₇	—	2	1	no	—
652	Dic₇	—	2	1	no	—
653	Dic₇	—	2	1	no	—
654	Dic₇	—	2	1	no	—
655	Dic₇	—	2	1	no	—
656	Dic₇	—	2	1	no	—
657	Dic₇	—	2	1	no	—
658	Dic₇	—	2	1	no	—
659	Dic₇	—	2	1	no	—
660	Dic₇	—	2	1	no	—
661	Dic₇	—	2	1	no	—
662	Dic₇	—	2	1	no	—
663	Dic₇	H(5,𝔽₂)	1	2	yes	—
664	Dic₇	2₋¹⁺⁴	1	2	yes	—
665	#41	—	28	2	no	—
666	#41	—	28	2	no	—
667	#41	—	28	2	no	—
668	#41	—	28	2	no	—
669	C₂×Q₈	—	7	1	no	—
670	C₂×Q₈	—	7	1	no	—
671	C₂×Q₈	—	7	1	no	—
672	C₂×Q₈	—	7	1	no	—
673	C₂×Q₈	—	7	1	no	—
674	C₂×Q₈	—	7	1	no	—
675	C₂×Q₈	—	7	1	no	—
676	C₂×Q₈	—	7	1	no	—
677	C₂×Q₈	—	7	1	no	—
678	C₂×Q₈	—	28	2	no	—
679	C₂×Q₈	—	28	2	no	—
680	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
681	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
682	C₂×D₄	—	7	1	no	—
683	C₂×D₄	—	7	1	no	—
684	C₂×D₄	—	7	1	no	—
685	C₂×D₄	—	7	1	no	—
686	C₂×D₄	—	7	1	no	—
687	C₂×D₄	—	7	1	no	—
688	C₂×D₄	—	7	1	no	—
689	C₂×D₄	—	7	1	no	—
690	C₂×D₄	—	7	1	no	—
691	C₂×D₄	—	7	1	no	—
692	C₂×D₄	—	7	1	no	—
693	C₂×D₄	—	7	1	no	—
694	C₂×D₄	—	7	1	no	—
695	C₂×D₄	—	7	1	no	—
696	C₂×D₄	—	7	1	no	—
697	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
698	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
699	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
700	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
701	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
702	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
703	C₂²×C₄	—	7	1	no	—
704	C₂²×C₄	—	7	1	no	—
705	C₂²×C₄	—	7	1	no	—
706	C₂²×C₄	—	7	1	no	—
707	C₂²×C₄	—	7	1	no	—
708	C₂²×C₄	—	7	1	no	—
709	C₂²×C₄	—	7	1	no	—
710	C₂²×C₄	—	7	1	no	—
711	C₂²×C₄	—	7	1	no	—
712	C₂²×C₄	—	7	1	no	—
713	C₂²×C₄	—	7	1	no	—
714	C₂²×C₄	—	7	1	no	—
715	C₂²×C₄	—	7	1	no	—
716	C₂²×C₄	—	7	1	no	—
717	C₂²×C₄	—	7	1	no	—
718	C₂²×C₄	—	7	1	no	—
719	C₂²×C₄	—	7	1	no	—
720	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
721	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
722	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
723	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
724	C₄⋊C₄	—	7	1	no	—
725	C₄⋊C₄	—	7	1	no	—
726	C₄⋊C₄	—	7	1	no	—
727	C₄⋊C₄	—	7	1	no	—
728	C₄⋊C₄	—	7	1	no	—
729	C₄⋊C₄	—	7	1	no	—
730	C₄⋊C₄	—	7	1	no	—
731	C₄⋊C₄	—	7	1	no	—
732	C₄⋊C₄	—	7	1	no	—
733	C₄⋊C₄	—	7	1	no	—
734	C₄⋊C₄	—	7	1	no	—
735	C₄⋊C₄	—	7	1	no	—
736	C₄⋊C₄	—	7	1	no	—
737	C₄⋊C₄	—	7	1	no	—
738	C₄⋊C₄	—	7	1	no	—
739	C₄⋊C₄	—	7	1	no	—
740	C₄⋊C₄	—	7	1	no	—
741	C₄⋊C₄	—	7	1	no	—
742	C₄⋊C₄	—	7	1	no	—
743	C₄⋊C₄	—	7	1	no	—
744	C₄⋊C₄	—	7	1	no	—
745	C₄⋊C₄	—	7	1	no	—
746	C₄⋊C₄	—	7	1	no	—
747	C₄⋊C₄	—	7	1	no	—
748	C₄⋊C₄	—	7	1	no	—
749	C₄⋊C₄	—	7	1	no	—
750	C₄⋊C₄	—	7	1	no	—
751	C₄⋊C₄	—	7	1	no	—
752	C₄⋊C₄	—	7	1	no	—
753	C₄⋊C₄	—	7	1	no	—
754	C₄⋊C₄	—	7	1	no	—
755	C₄⋊C₄	—	7	1	no	—
756	C₄⋊C₄	—	7	1	no	—
757	C₄⋊C₄	—	7	1	no	—
758	C₄⋊C₄	—	7	1	no	—
759	C₄⋊C₄	—	7	1	no	—
760	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
761	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
762	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
763	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
764	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
765	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
766	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
767	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
768	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
769	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
770	C₂²⋊C₄	—	7	1	no	—
771	C₂²⋊C₄	—	7	1	no	—
772	C₂²⋊C₄	—	7	1	no	—
773	C₂²⋊C₄	—	7	1	no	—
774	C₂²⋊C₄	—	7	1	no	—
775	C₂²⋊C₄	—	7	1	no	—
776	C₂²⋊C₄	—	7	1	no	—
777	C₂²⋊C₄	—	7	1	no	—
778	C₂²⋊C₄	—	7	1	no	—
779	C₂²⋊C₄	—	7	1	no	—
780	C₂²⋊C₄	—	7	1	no	—
781	C₂²⋊C₄	—	7	1	no	—
782	C₂²⋊C₄	—	7	1	no	—
783	C₂²⋊C₄	—	7	1	no	—
784	C₂²⋊C₄	—	7	1	no	—
785	C₂²⋊C₄	—	7	1	no	—
786	C₂²⋊C₄	—	7	1	no	—
787	C₂²⋊C₄	—	7	1	no	—
788	C₂²⋊C₄	—	7	1	no	—
789	C₂²⋊C₄	—	7	1	no	—
790	C₂²⋊C₄	—	7	1	no	—
791	C₂²⋊C₄	—	7	1	no	—
792	C₂²⋊C₄	—	7	1	no	—
793	C₂²⋊C₄	—	7	1	no	—
794	C₂²⋊C₄	—	7	1	no	—
795	C₂²⋊C₄	—	7	1	no	—
796	C₂²⋊C₄	—	7	1	no	—
797	C₂²⋊C₄	—	7	1	no	—
798	C₂²⋊C₄	—	7	1	no	—
799	C₂²⋊C₄	—	7	1	no	—
800	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
801	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
802	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
803	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
804	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
805	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
806	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
807	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
808	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
809	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
810	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
811	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
812	C₄²	—	7	1	no	—
813	C₄²	—	7	1	no	—
814	C₄²	—	7	1	no	—
815	C₄²	—	7	1	no	—
816	C₄²	—	7	1	no	—
817	C₄²	—	7	1	no	—
818	C₄²	—	7	1	no	—
819	C₄²	—	7	1	no	—
820	C₄²	—	7	1	no	—
821	C₄²	—	7	1	no	—
822	C₄²	—	7	1	no	—
823	C₄²	—	7	1	no	—
824	C₄²	—	7	1	no	—
825	C₄²	C₂²×D₇	1	1	yes	characteristic
826	C₂×C₇	—	4	1	no	—
827	C₂×C₇	—	4	1	no	—
828	C₂×C₇	—	4	1	no	—
829	C₂×C₇	—	4	1	no	—
830	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
831	C₂×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
832	C₂×C₇	#585	1	1	yes	characteristic
833	D₇	—	4	1	no	—
834	D₇	—	4	1	no	—
835	D₇	—	4	1	no	—
836	C₂³	—	7	1	no	—
837	C₂³	—	7	1	no	—
838	C₂³	—	7	1	no	—
839	C₂³	C₂³×D₇	1	1	yes	characteristic
840	C₂³	C₂³×D₇	1	1	yes	characteristic
841	C₂³	C₂³×D₇	1	1	yes	characteristic
842	C₂³	C₂³×D₇	1	1	yes	characteristic
843	Q₈	—	4	1	no	—
844	Q₈	—	4	1	no	—
845	Q₈	—	14	2	no	—
846	Q₈	—	14	2	no	—
847	Q₈	—	14	2	no	—
848	Q₈	—	28	1	no	—
849	Q₈	—	28	1	no	—
850	Q₈	—	28	1	no	—
851	Q₈	—	28	1	no	—
852	Q₈	—	28	1	no	—
853	Q₈	—	28	1	no	—
854	D₄	—	4	1	no	—
855	D₄	—	4	1	no	—
856	D₄	—	4	1	no	—
857	D₄	—	4	1	no	—
858	D₄	—	4	1	no	—
859	D₄	—	4	1	no	—
860	D₄	—	14	2	no	—
861	D₄	—	14	2	no	—
862	D₄	—	14	2	no	—
863	D₄	—	28	1	no	—
864	D₄	—	28	1	no	—
865	D₄	—	28	1	no	—
866	D₄	—	28	1	no	—
867	D₄	—	28	1	no	—
868	D₄	—	28	1	no	—
869	D₄	—	28	1	no	—
870	D₄	—	28	1	no	—
871	D₄	—	28	1	no	—
872	D₄	—	28	1	no	—
873	D₄	—	28	1	no	—
874	D₄	—	28	1	no	—
875	C₂×C₄	—	4	1	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	7	1	no	—
880	C₂×C₄	—	7	1	no	—
881	C₂×C₄	—	7	1	no	—
882	C₂×C₄	—	7	1	no	—
883	C₂×C₄	—	7	1	no	—
884	C₂×C₄	—	7	1	no	—
885	C₂×C₄	—	7	1	no	—
886	C₂×C₄	—	7	1	no	—
887	C₂×C₄	—	7	1	no	—
888	C₂×C₄	—	7	1	no	—
889	C₂×C₄	—	7	1	no	—
890	C₂×C₄	—	7	1	no	—
891	C₂×C₄	—	7	1	no	—
892	C₂×C₄	—	14	2	no	—
893	C₂×C₄	—	14	2	no	—
894	C₂×C₄	—	14	2	no	—
895	C₂×C₄	—	14	2	no	—
896	C₂×C₄	—	14	2	no	—
897	C₂×C₄	—	14	2	no	—
898	C₂×C₄	—	14	2	no	—
899	C₂×C₄	—	14	2	no	—
900	C₂×C₄	—	28	1	no	—
901	C₂×C₄	—	28	1	no	—
902	C₂×C₄	—	28	1	no	—
903	C₂×C₄	—	28	1	no	—
904	C₂×C₄	—	28	1	no	—
905	C₂×C₄	—	28	1	no	—
906	C₂×C₄	—	28	1	no	—
907	C₂×C₄	—	28	1	no	—
908	C₂×C₄	—	28	1	no	—
909	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
910	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
911	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
912	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
913	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
914	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
915	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
916	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
917	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
918	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
919	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
920	C₇	#3547	1	1	yes	characteristic, complemented, Sylow
921	C₂²	—	2	1	no	—
922	C₂²	—	2	1	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	2	1	no	—
930	C₂²	—	2	1	no	—
931	C₂²	—	2	1	no	—
932	C₂²	—	2	1	no	—
933	C₂²	—	14	1	no	—
934	C₂²	—	14	1	no	—
935	C₂²	—	14	1	no	—
936	C₂²	—	14	1	no	—
937	C₂²	—	14	1	no	—
938	C₂²	—	14	1	no	—
939	C₂²	—	14	1	no	—
940	C₂²	—	14	1	no	—
941	C₂²	—	14	1	no	—
942	C₂²	C₂⁴×D₇	1	1	yes	characteristic
943	C₄	—	2	1	no	—
944	C₄	—	2	1	no	—
945	C₄	—	2	1	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	1	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	7	2	no	—
955	C₄	—	7	2	no	—
956	C₄	—	14	1	no	—
957	C₄	—	14	1	no	—
958	C₄	—	14	1	no	—
959	C₄	—	14	1	no	—
960	C₄	—	14	1	no	—
961	C₄	—	14	1	no	—
962	C₄	—	14	1	no	—
963	C₄	—	14	1	no	—
964	C₄	—	14	1	no	—
965	C₄	—	14	1	no	—
966	C₄	—	14	1	no	—
967	C₂	—	4	1	no	—
968	C₂	—	4	1	no	—
969	C₂	—	4	1	no	—
970	C₂	—	4	1	no	—
971	C₂	—	28	1	no	—
972	C₂	—	28	1	no	—
973	C₂	—	28	1	no	—
974	C₂	D₇×H(5,𝔽₂)	1	1	yes	characteristic
975	C₂	#90618	1	1	yes	characteristic
976	C₂	D₇×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#562	C₂
hypercenter	#562	D₇
hypocenter	C₇	#3547
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #562

Complements

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

N	H ≅ G/N	type
1. C₇×#562	C₂	semidirect
2. #90384	C₂	semidirect
3. #90380	C₂	semidirect
4. #90373	C₂	semidirect
5. #90366	C₂	semidirect
6. #90361	C₂	semidirect
7. #90361	C₂	semidirect
8. #90358	C₂	semidirect
9. #90354	C₂	semidirect
10. #90353	C₂	semidirect
11. #90352	C₂	semidirect
12. #90346	C₂	semidirect
13. #90341	C₂	semidirect
14. #90340	C₂	semidirect
15. #90339	C₂	semidirect
16. #90338	C₂	semidirect
17. #90334	C₂	semidirect
18. #90331	C₂	semidirect
19. #90327	C₂	semidirect
20. #90324	C₂	semidirect
21. #90323	C₂	semidirect
22. #90314	C₂	semidirect
23. #90313	C₂	semidirect
24. #90312	C₂	semidirect
25. #90307	C₂	semidirect
26. #90306	C₂	semidirect
27. #90299	C₂	semidirect
28. #90292	C₂	semidirect
29. #90289	C₂	semidirect
30. #90288	C₂	semidirect
31. #90287	C₂	semidirect
352. #562	D₇	semidirect
920. C₇	#3547	semidirect

Maximal subgroups

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

subgroup	index
C₇×#562	2
#90384	2
#90380	2
#90373	2
#90366	2
#90361	2
#90358	2
#90354	2
#90353	2
#90352	2
#90346	2
#90341	2
#90340	2
#90339	2
#90338	2
#90334	2
#90331	2
#90327	2
#90324	2
#90323	2
#90314	2
#90313	2
#90312	2
#90307	2
#90306	2
#90299	2
#90292	2
#90289	2
#90288	2
#90287	2
#3547	7