Subgroups — #11744012

Order 896.

936 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	#90426	C₂	1	1	yes	maximal, characteristic, complemented
3	#90422	C₂	1	1	yes	maximal, characteristic, complemented
4	#90390	C₂	1	1	yes	maximal, characteristic, complemented
5	#90387	C₂	1	1	yes	maximal, characteristic, complemented
6	#90387	C₂	1	1	yes	maximal, characteristic, complemented
7	#90384	C₂	1	1	yes	maximal, characteristic, complemented
8	#90337	C₂	1	1	yes	maximal, characteristic, complemented
9	#90337	C₂	1	1	yes	maximal, characteristic, complemented
10	#90334	C₂	1	1	yes	maximal, characteristic, complemented
11	#90333	C₂	1	1	yes	maximal, characteristic, complemented
12	#90332	C₂	1	1	yes	maximal, characteristic, complemented
13	#90331	C₂	1	1	yes	maximal, characteristic, complemented
14	#90329	C₂	1	1	yes	maximal, characteristic, complemented
15	#90328	C₂	1	1	yes	maximal, characteristic, complemented
16	#90328	C₂	1	1	yes	maximal, characteristic, complemented
17	#90325	C₂	1	1	yes	maximal, characteristic, complemented
18	#90314	C₂	1	1	yes	maximal, characteristic, complemented
19	#90313	C₂	1	1	yes	maximal, characteristic, complemented
20	#90274	C₂	1	1	yes	maximal, characteristic, complemented
21	#90259	C₂	1	1	yes	maximal, characteristic, complemented
22	#90255	C₂	1	1	yes	maximal, characteristic, complemented
23	#90251	C₂	1	1	yes	maximal, characteristic
24	#90247	C₂	1	1	yes	maximal, characteristic, complemented
25	#90247	C₂	1	1	yes	maximal, characteristic, complemented
26	#90232	C₂	1	1	yes	maximal, characteristic, complemented
27	#90229	C₂	1	1	yes	maximal, characteristic, complemented
28	#90206	C₂	1	1	yes	maximal, characteristic, complemented
29	#90204	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#6461	C₂	1	1	yes	maximal, characteristic, complemented
31	#90202	C₂	1	1	yes	maximal, characteristic, complemented
32	C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₇×#125	C₂²	1	1	yes	characteristic, complemented
34	C₇×#125	C₂²	1	1	yes	characteristic, complemented
35	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
43	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
44	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
45	C₂×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	#6510	C₂²	1	1	yes	characteristic
48	#6510	C₂²	1	1	yes	characteristic
49	#6509	C₂²	1	1	yes	characteristic
50	#6509	C₂²	1	1	yes	characteristic
51	#6509	C₂²	1	1	yes	characteristic
52	#6509	C₂²	1	1	yes	characteristic
53	#6509	C₂²	1	1	yes	characteristic, complemented
54	Q₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
55	Q₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
56	#6507	C₂²	1	1	yes	characteristic, complemented
57	#6507	C₂²	1	1	yes	characteristic, complemented
58	#6507	C₂²	1	1	yes	characteristic, complemented
59	#6502	C₂²	1	1	yes	characteristic
60	#6500	C₂²	1	1	yes	characteristic
61	#6498	C₂²	1	1	yes	characteristic
62	#6498	C₂²	1	1	yes	characteristic
63	#6493	C₂²	1	1	yes	characteristic
64	#6492	C₂²	1	1	yes	characteristic
65	#6492	C₂²	1	1	yes	characteristic
66	#6492	C₂²	1	1	yes	characteristic
67	#6492	C₂²	1	1	yes	characteristic, complemented
68	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
70	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
71	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
72	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
73	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
74	C₂×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
75	C₂×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
76	C₂×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
77	#6489	C₂²	1	1	yes	characteristic, complemented
78	#6489	C₂²	1	1	yes	characteristic, complemented
79	C₂×C₄⋊Dic₇	C₂²	1	1	yes	characteristic
80	#6487	C₂²	1	1	yes	characteristic
81	#6487	C₂²	1	1	yes	characteristic
82	#6487	C₂²	1	1	yes	characteristic
83	#6487	C₂²	1	1	yes	characteristic, complemented
84	#6487	C₂²	1	1	yes	characteristic, complemented
85	C₂×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
86	C₂×C₄×Dic₇	C₂²	1	1	yes	characteristic
87	#6461	C₂²	1	1	yes	characteristic
88	#6461	C₂²	1	1	yes	characteristic
89	#6461	C₂²	1	1	yes	characteristic
90	#6461	C₂²	1	1	yes	characteristic
91	#6461	C₂²	1	1	yes	characteristic
92	#6461	C₂²	1	1	yes	characteristic
93	#6461	C₂²	1	1	yes	characteristic
94	#6461	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	#6461	C₂²	1	1	yes	characteristic
99	#6461	C₂²	1	1	yes	characteristic
100	#6461	C₂²	1	1	yes	characteristic
101	#6461	C₂²	1	1	yes	characteristic
102	#6461	C₂²	1	1	yes	characteristic, complemented
103	#6461	C₂²	1	1	yes	characteristic, complemented
104	#6461	C₂²	1	1	yes	characteristic, complemented
105	#6460	C₂²	1	1	yes	characteristic
106	#6460	C₂²	1	1	yes	characteristic
107	#6460	C₂²	1	1	yes	characteristic, complemented
108	#6459	C₂²	1	1	yes	characteristic
109	#6459	C₂²	1	1	yes	characteristic
110	#6459	C₂²	1	1	yes	characteristic
111	#6459	C₂²	1	1	yes	characteristic
112	#6459	C₂²	1	1	yes	characteristic
113	#6459	C₂²	1	1	yes	characteristic
114	#6459	C₂²	1	1	yes	characteristic, complemented
115	#6459	C₂²	1	1	yes	characteristic, complemented
116	#6459	C₂²	1	1	yes	characteristic, complemented
117	#6457	C₂²	1	1	yes	characteristic
118	#6457	C₂²	1	1	yes	characteristic
119	#6457	C₂²	1	1	yes	characteristic
120	#6457	C₂²	1	1	yes	characteristic
121	#6457	C₂²	1	1	yes	characteristic
122	#6456	C₂²	1	1	yes	characteristic
123	#6456	C₂²	1	1	yes	characteristic
124	#6455	C₂²	1	1	yes	characteristic
125	#6455	C₂²	1	1	yes	characteristic
126	#6455	C₂²	1	1	yes	characteristic, complemented
127	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
128	#6453	C₂²	1	1	yes	characteristic, complemented
129	#6453	C₂²	1	1	yes	characteristic, complemented
130	#6453	C₂²	1	1	yes	characteristic, complemented
131	#6452	C₂²	1	1	yes	characteristic, complemented
132	#6452	C₂²	1	1	yes	characteristic, complemented
133	#6452	C₂²	1	1	yes	characteristic, complemented
134	#6452	C₂²	1	1	yes	characteristic, complemented
135	#6452	C₂²	1	1	yes	characteristic, complemented
136	#6452	C₂²	1	1	yes	characteristic, complemented
137	#6452	C₂²	1	1	yes	characteristic, complemented
138	#6452	C₂²	1	1	yes	characteristic, complemented
139	#6452	C₂²	1	1	yes	characteristic, complemented
140	#6452	C₂²	1	1	yes	characteristic, complemented
141	#6452	C₂²	1	1	yes	characteristic, complemented
142	#6452	C₂²	1	1	yes	characteristic, complemented
143	#6451	C₂²	1	1	yes	characteristic, complemented
144	#6451	C₂²	1	1	yes	characteristic, complemented
145	#6451	C₂²	1	1	yes	characteristic, complemented
146	#6451	C₂²	1	1	yes	characteristic, complemented
147	#6450	C₂²	1	1	yes	characteristic, complemented
148	#6450	C₂²	1	1	yes	characteristic, complemented
149	#6450	C₂²	1	1	yes	characteristic, complemented
150	#6450	C₂²	1	1	yes	characteristic, complemented
151	#6449	C₂²	1	1	yes	characteristic
152	#6449	C₂²	1	1	yes	characteristic
153	#6448	C₂²	1	1	yes	characteristic
154	#6448	C₂²	1	1	yes	characteristic
155	#6448	C₂²	1	1	yes	characteristic
156	#6448	C₂²	1	1	yes	characteristic, complemented
157	#6447	C₂²	1	1	yes	characteristic
158	#6446	C₂²	1	1	yes	characteristic
159	#6446	C₂²	1	1	yes	characteristic
160	#6446	C₂²	1	1	yes	characteristic, complemented
161	#6445	C₂²	1	1	yes	characteristic
162	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
163	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
164	#6442	C₂²	1	1	yes	characteristic, complemented
165	#6442	C₂²	1	1	yes	characteristic, complemented
166	#6442	C₂²	1	1	yes	characteristic, complemented
167	#6442	C₂²	1	1	yes	characteristic, complemented
168	#6441	C₂²	1	1	yes	characteristic
169	#6441	C₂²	1	1	yes	characteristic
170	#6441	C₂²	1	1	yes	characteristic
171	#6440	C₂²	1	1	yes	characteristic
172	#6440	C₂²	1	1	yes	characteristic
173	#6440	C₂²	1	1	yes	characteristic
174	#6440	C₂²	1	1	yes	characteristic
175	#6439	C₂²	1	1	yes	characteristic
176	#6439	C₂²	1	1	yes	characteristic
177	#6439	C₂²	1	1	yes	characteristic
178	#6439	C₂²	1	1	yes	characteristic, complemented
179	#6438	C₂²	1	1	yes	characteristic
180	#6435	C₂²	1	1	yes	characteristic
181	#6435	C₂²	1	1	yes	characteristic
182	#6435	C₂²	1	1	yes	characteristic, complemented
183	#6433	C₂²	1	1	yes	characteristic, complemented
184	#6433	C₂²	1	1	yes	characteristic, complemented
185	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
187	#3564	—	7	1	no	maximal, Sylow
188	C₂³×D₇	C₂³	1	1	yes	characteristic
189	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
190	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
191	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
192	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
193	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
194	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
195	C₂²×C₄×C₇	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	C₂×C₂²⋊D₇	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	C₂²×Dic₇	C₂³	1	1	yes	characteristic
204	C₂²×Dic₇	C₂³	1	1	yes	characteristic
205	C₂²×Dic₇	C₂³	1	1	yes	characteristic
206	C₂×D₂₈	C₂³	1	1	yes	characteristic
207	C₂×D₂₈	C₂³	1	1	yes	characteristic
208	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
209	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
210	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
211	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
212	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
213	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
214	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
215	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
216	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
217	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
218	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
219	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
220	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
221	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
222	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
223	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
224	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
225	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
226	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
227	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
228	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
229	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
230	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
231	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
232	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
233	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
234	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
235	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
236	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
237	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
238	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
239	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
240	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
241	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
242	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
243	C₄²×C₇	C₂³	1	1	yes	characteristic
244	C₄²×C₇	C₂³	1	1	yes	characteristic
245	C₄²×C₇	C₂³	1	1	yes	characteristic
246	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
247	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
248	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
249	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
250	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
251	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
252	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
253	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
254	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
255	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
256	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
257	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
258	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
259	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
260	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
261	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
262	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
263	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
264	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
265	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
266	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
267	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
268	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
269	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
270	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
271	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
272	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
273	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
274	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
275	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
276	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
277	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
278	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
279	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
280	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
281	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
282	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
283	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
284	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
285	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
286	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
287	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
288	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
289	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
290	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
291	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
292	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
293	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
294	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
295	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
296	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
297	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
298	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
299	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
300	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
301	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
302	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
303	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
304	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
305	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
306	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
307	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
308	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
309	Dic₇⋊C₄	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	C₄×Dic₇	C₂³	1	1	yes	characteristic
329	C₄×Dic₇	C₂³	1	1	yes	characteristic
330	C₄×Dic₇	C₂³	1	1	yes	characteristic
331	C₄×Dic₇	C₂³	1	1	yes	characteristic
332	C₄×Dic₇	C₂³	1	1	yes	characteristic
333	C₄×Dic₇	C₂³	1	1	yes	characteristic
334	C₄×Dic₇	C₂³	1	1	yes	characteristic
335	C₄×Dic₇	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	#563	—	7	1	no	—
344	#563	—	7	1	no	—
345	#563	—	7	1	no	—
346	#563	—	7	1	no	—
347	#556	—	7	1	no	—
348	#556	—	7	1	no	—
349	#554	—	7	1	no	—
350	#554	D₇	1	1	yes	characteristic, complemented
351	#552	—	7	1	no	—
352	#552	—	7	1	no	—
353	#552	—	7	1	no	—
354	#552	—	7	1	no	—
355	#551	—	7	1	no	—
356	#551	—	7	1	no	—
357	#551	—	7	1	no	—
358	#551	—	7	1	no	—
359	#544	—	7	1	no	—
360	#543	—	7	1	no	—
361	#542	—	7	1	no	—
362	#542	—	7	1	no	—
363	#541	—	7	1	no	—
364	#541	—	7	1	no	—
365	#541	—	7	1	no	—
366	#541	—	7	1	no	—
367	#539	—	7	1	no	—
368	#539	—	7	1	no	—
369	#539	—	7	1	no	—
370	#538	—	7	1	no	—
371	#533	—	7	1	no	—
372	#529	—	7	1	no	—
373	C₂×#126	—	7	1	no	—
374	C₂³×C₇	C₂⁴	1	1	yes	characteristic
375	C₂³×C₇	C₂⁴	1	1	yes	characteristic
376	C₂²×D₇	—	2	2	no	—
377	C₂²×D₇	—	4	1	no	—
378	C₂²×D₇	—	4	1	no	—
379	C₂²×D₇	C₂⁴	1	1	yes	characteristic
380	C₂²×D₇	C₂⁴	1	1	yes	characteristic
381	C₂²×D₇	C₂⁴	1	1	yes	characteristic
382	C₇×Q₈	—	4	1	no	—
383	C₇×Q₈	—	4	1	no	—
384	C₇×Q₈	—	4	1	no	—
385	C₇×D₄	—	2	2	no	—
386	C₂×C₄×C₇	—	4	1	no	—
387	C₂×C₄×C₇	—	4	1	no	—
388	C₂×C₄×C₇	—	4	1	no	—
389	C₂×C₄×C₇	—	4	1	no	—
390	C₂×C₄×C₇	—	4	1	no	—
391	C₂×C₄×C₇	—	4	1	no	—
392	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
393	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
394	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
395	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
396	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
397	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
398	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	C₂²⋊D₇	—	2	2	no	—
406	C₂²⋊D₇	—	4	1	no	—
407	C₂²⋊D₇	—	4	1	no	—
408	C₂²⋊D₇	—	4	1	no	—
409	C₂×Dic₇	—	2	2	no	—
410	C₂×Dic₇	—	2	2	no	—
411	C₂×Dic₇	—	4	1	no	—
412	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
413	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
414	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
415	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
416	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
417	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
418	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
419	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
420	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
421	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
422	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
423	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
424	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
425	D₂₈	—	4	1	no	—
426	D₂₈	—	4	1	no	—
427	C₄×D₇	—	4	1	no	—
428	C₄×D₇	—	4	1	no	—
429	C₄×D₇	—	4	1	no	—
430	C₄×D₇	—	4	1	no	—
431	C₄×D₇	—	4	1	no	—
432	C₄×D₇	—	4	1	no	—
433	C₄×D₇	—	4	1	no	—
434	Dic₁₄	—	4	1	no	—
435	Dic₁₄	—	4	1	no	—
436	Dic₁₄	—	4	1	no	—
437	Dic₁₄	—	4	1	no	—
438	Dic₁₄	—	4	1	no	—
439	Dic₁₄	—	4	1	no	—
440	C₄⋊Q₈	—	7	1	no	—
441	C₄⋊Q₈	—	7	1	no	—
442	C₄⋊Q₈	—	7	1	no	—
443	C₄⋊Q₈	—	7	1	no	—
444	C₄⋊Q₈	—	7	1	no	—
445	C₄⋊Q₈	—	7	1	no	—
446	C₄⋊Q₈	—	7	1	no	—
447	C₄⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
448	#126	—	7	1	no	—
449	#126	—	7	1	no	—
450	#126	—	7	1	no	—
451	#126	—	7	1	no	—
452	#126	—	7	1	no	—
453	#126	—	7	1	no	—
454	#126	—	7	1	no	—
455	#126	—	7	1	no	—
456	#126	—	7	1	no	—
457	#126	—	7	1	no	—
458	#126	—	7	1	no	—
459	#126	—	7	1	no	—
460	#126	—	7	1	no	—
461	#126	—	7	1	no	—
462	#126	—	7	1	no	—
463	#126	—	7	1	no	—
464	#126	—	7	1	no	—
465	#126	—	7	1	no	—
466	#126	—	7	1	no	—
467	#126	—	7	1	no	—
468	#126	—	7	1	no	—
469	#126	—	7	1	no	—
470	#126	—	7	1	no	—
471	#126	—	7	1	no	—
472	#126	—	7	1	no	—
473	#126	—	7	1	no	—
474	#125	—	7	1	no	—
475	#125	—	7	1	no	—
476	#125	—	7	1	no	—
477	#125	—	7	1	no	—
478	#125	—	7	1	no	—
479	#125	—	7	1	no	—
480	#125	—	7	1	no	—
481	#125	—	7	1	no	—
482	#125	—	7	1	no	—
483	#125	—	7	1	no	—
484	#125	—	7	1	no	—
485	#125	—	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	C₂×D₇	1	1	yes	characteristic, complemented
492	#125	C₂×D₇	1	1	yes	characteristic, complemented
493	#124	—	7	1	no	—
494	#124	—	7	1	no	—
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	#123	—	7	1	no	—
501	#123	—	7	1	no	—
502	#123	—	7	1	no	—
503	#123	—	7	1	no	—
504	#123	—	7	1	no	—
505	#123	—	7	1	no	—
506	#123	—	7	1	no	—
507	#123	—	7	1	no	—
508	#123	—	7	1	no	—
509	#123	—	7	1	no	—
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	C₂²⋊Q₈	—	7	1	no	—
517	C₂²⋊Q₈	—	7	1	no	—
518	C₂²⋊Q₈	—	7	1	no	—
519	C₂²⋊Q₈	—	7	1	no	—
520	C₂²⋊Q₈	—	7	1	no	—
521	C₂²⋊Q₈	—	7	1	no	—
522	C₂²⋊Q₈	—	7	1	no	—
523	C₂²⋊Q₈	—	7	1	no	—
524	C₂²⋊Q₈	—	7	1	no	—
525	C₂²⋊Q₈	—	7	1	no	—
526	C₂²⋊Q₈	—	7	1	no	—
527	C₂²⋊Q₈	—	7	1	no	—
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	C₂×D₇	1	1	yes	characteristic
542	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic
543	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic
544	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
545	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
546	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
547	#121	—	7	1	no	—
548	#121	—	7	1	no	—
549	#121	—	7	1	no	—
550	#120	—	7	1	no	—
551	#120	—	7	1	no	—
552	C₄×Q₈	—	7	1	no	—
553	C₄×Q₈	—	7	1	no	—
554	C₄×Q₈	—	7	1	no	—
555	C₄×Q₈	—	7	1	no	—
556	C₄×Q₈	—	7	1	no	—
557	C₄×Q₈	—	7	1	no	—
558	C₄×Q₈	—	7	1	no	—
559	C₄×Q₈	—	7	1	no	—
560	C₄×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
561	C₄×D₄	—	7	1	no	—
562	C₄×D₄	—	7	1	no	—
563	C₄×D₄	—	7	1	no	—
564	C₄×D₄	—	7	1	no	—
565	C₄×D₄	—	7	1	no	—
566	C₄×D₄	—	7	1	no	—
567	C₄×D₄	—	7	1	no	—
568	C₄×D₄	—	7	1	no	—
569	C₄×D₄	C₂×D₇	1	1	yes	characteristic
570	C₄×D₄	C₂×D₇	1	1	yes	characteristic
571	C₄×D₄	C₂×D₇	1	1	yes	characteristic
572	#117	—	7	1	no	—
573	#117	—	7	1	no	—
574	#117	—	7	1	no	—
575	#117	—	7	1	no	—
576	#117	—	7	1	no	—
577	#117	—	7	1	no	—
578	#117	—	7	1	no	—
579	#117	—	7	1	no	—
580	#117	—	7	1	no	—
581	#117	—	7	1	no	—
582	#117	—	7	1	no	—
583	#117	—	7	1	no	—
584	C₂×C₄⋊C₄	—	7	1	no	—
585	C₂×C₄⋊C₄	—	7	1	no	—
586	C₂×C₄⋊C₄	—	7	1	no	—
587	C₂×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
589	C₂×C₂²⋊C₄	—	7	1	no	—
590	C₂×C₂²⋊C₄	—	7	1	no	—
591	C₂×C₂²⋊C₄	—	7	1	no	—
592	C₂×C₂²⋊C₄	—	7	1	no	—
593	C₂×C₂²⋊C₄	—	7	1	no	—
594	C₂×C₄²	—	7	1	no	—
595	C₂²×C₇	—	2	1	no	—
596	C₂²×C₇	—	2	1	no	—
597	C₂²×C₇	—	2	1	no	—
598	C₂²×C₇	—	2	1	no	—
599	C₂²×C₇	—	2	1	no	—
600	C₂²×C₇	2₋¹⁺⁴	1	2	yes	—
601	C₂²×C₇	C₂⁵	1	1	yes	characteristic
602	C₂×D₇	—	2	1	no	—
603	C₂×D₇	—	2	1	no	—
604	C₂×D₇	—	2	1	no	—
605	C₂×D₇	—	2	1	no	—
606	C₂×D₇	—	2	1	no	—
607	C₂×D₇	—	2	1	no	—
608	C₂×D₇	—	2	1	no	—
609	C₂×D₇	—	2	1	no	—
610	C₂×D₇	—	2	1	no	—
611	C₂×D₇	—	8	2	no	—
612	C₄×C₇	—	2	1	no	—
613	C₄×C₇	—	2	1	no	—
614	C₄×C₇	—	2	1	no	—
615	C₄×C₇	—	2	1	no	—
616	C₄×C₇	—	2	1	no	—
617	C₄×C₇	—	2	1	no	—
618	C₄×C₇	—	2	1	no	—
619	C₄×C₇	—	2	1	no	—
620	C₄×C₇	—	2	1	no	—
621	C₄×C₇	—	2	1	no	—
622	C₄×C₇	—	2	1	no	—
623	C₄×C₇	—	2	1	no	—
624	C₄×C₇	—	2	1	no	—
625	Dic₇	—	2	1	no	—
626	Dic₇	—	2	1	no	—
627	Dic₇	—	2	1	no	—
628	Dic₇	—	2	1	no	—
629	Dic₇	—	2	1	no	—
630	Dic₇	—	2	1	no	—
631	Dic₇	—	2	1	no	—
632	Dic₇	—	2	1	no	—
633	Dic₇	—	2	1	no	—
634	Dic₇	—	2	1	no	—
635	Dic₇	—	2	1	no	—
636	Dic₇	—	2	1	no	—
637	Dic₇	—	2	1	no	—
638	C₂⁴	—	7	1	no	—
639	C₂×Q₈	—	7	1	no	—
640	C₂×Q₈	—	7	1	no	—
641	C₂×Q₈	—	7	1	no	—
642	C₂×Q₈	—	7	1	no	—
643	C₂×Q₈	—	7	1	no	—
644	C₂×Q₈	—	7	1	no	—
645	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
646	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
647	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
648	C₂×D₄	—	7	1	no	—
649	C₂×D₄	—	7	1	no	—
650	C₂×D₄	—	7	1	no	—
651	C₂×D₄	—	7	1	no	—
652	C₂×D₄	—	7	1	no	—
653	C₂×D₄	—	7	1	no	—
654	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
655	C₂²×C₄	—	7	1	no	—
656	C₂²×C₄	—	7	1	no	—
657	C₂²×C₄	—	7	1	no	—
658	C₂²×C₄	—	7	1	no	—
659	C₂²×C₄	—	7	1	no	—
660	C₂²×C₄	—	7	1	no	—
661	C₂²×C₄	—	7	1	no	—
662	C₂²×C₄	—	7	1	no	—
663	C₂²×C₄	—	7	1	no	—
664	C₂²×C₄	—	7	1	no	—
665	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
666	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
667	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
668	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
669	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
670	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
671	C₄⋊C₄	—	7	1	no	—
672	C₄⋊C₄	—	7	1	no	—
673	C₄⋊C₄	—	7	1	no	—
674	C₄⋊C₄	—	7	1	no	—
675	C₄⋊C₄	—	7	1	no	—
676	C₄⋊C₄	—	7	1	no	—
677	C₄⋊C₄	—	7	1	no	—
678	C₄⋊C₄	—	7	1	no	—
679	C₄⋊C₄	—	7	1	no	—
680	C₄⋊C₄	—	7	1	no	—
681	C₄⋊C₄	—	7	1	no	—
682	C₄⋊C₄	—	7	1	no	—
683	C₄⋊C₄	—	7	1	no	—
684	C₄⋊C₄	—	7	1	no	—
685	C₄⋊C₄	—	7	1	no	—
686	C₄⋊C₄	—	7	1	no	—
687	C₄⋊C₄	—	7	1	no	—
688	C₄⋊C₄	—	7	1	no	—
689	C₄⋊C₄	—	7	1	no	—
690	C₄⋊C₄	—	7	1	no	—
691	C₄⋊C₄	—	7	1	no	—
692	C₄⋊C₄	—	7	1	no	—
693	C₄⋊C₄	—	7	1	no	—
694	C₄⋊C₄	—	7	1	no	—
695	C₄⋊C₄	—	7	1	no	—
696	C₄⋊C₄	—	7	1	no	—
697	C₄⋊C₄	—	7	1	no	—
698	C₄⋊C₄	—	7	1	no	—
699	C₄⋊C₄	—	7	1	no	—
700	C₄⋊C₄	—	7	1	no	—
701	C₄⋊C₄	—	7	1	no	—
702	C₄⋊C₄	—	7	1	no	—
703	C₄⋊C₄	—	7	1	no	—
704	C₄⋊C₄	—	7	1	no	—
705	C₄⋊C₄	—	7	1	no	—
706	C₄⋊C₄	—	7	1	no	—
707	C₄⋊C₄	—	7	1	no	—
708	C₄⋊C₄	—	7	1	no	—
709	C₄⋊C₄	—	7	1	no	—
710	C₄⋊C₄	—	7	1	no	—
711	C₄⋊C₄	—	7	1	no	—
712	C₄⋊C₄	—	7	1	no	—
713	C₄⋊C₄	—	7	1	no	—
714	C₄⋊C₄	—	7	1	no	—
715	C₄⋊C₄	—	7	1	no	—
716	C₄⋊C₄	—	7	1	no	—
717	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
718	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
719	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
720	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
721	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
722	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
723	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
724	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
725	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
726	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
727	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
728	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
729	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
730	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
731	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
732	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
733	C₂²⋊C₄	—	7	1	no	—
734	C₂²⋊C₄	—	7	1	no	—
735	C₂²⋊C₄	—	7	1	no	—
736	C₂²⋊C₄	—	7	1	no	—
737	C₂²⋊C₄	—	7	1	no	—
738	C₂²⋊C₄	—	7	1	no	—
739	C₂²⋊C₄	—	7	1	no	—
740	C₂²⋊C₄	—	7	1	no	—
741	C₂²⋊C₄	—	7	1	no	—
742	C₂²⋊C₄	—	7	1	no	—
743	C₂²⋊C₄	—	7	1	no	—
744	C₂²⋊C₄	—	7	1	no	—
745	C₂²⋊C₄	—	7	1	no	—
746	C₂²⋊C₄	—	7	1	no	—
747	C₂²⋊C₄	—	7	1	no	—
748	C₂²⋊C₄	—	7	1	no	—
749	C₂²⋊C₄	—	7	1	no	—
750	C₂²⋊C₄	—	7	1	no	—
751	C₂²⋊C₄	—	7	1	no	—
752	C₂²⋊C₄	—	7	1	no	—
753	C₂²⋊C₄	—	7	1	no	—
754	C₂²⋊C₄	—	7	1	no	—
755	C₂²⋊C₄	—	7	1	no	—
756	C₂²⋊C₄	—	7	1	no	—
757	C₂²⋊C₄	—	7	1	no	—
758	C₂²⋊C₄	—	7	1	no	—
759	C₂²⋊C₄	—	7	1	no	—
760	C₂²⋊C₄	—	7	1	no	—
761	C₂²⋊C₄	—	7	1	no	—
762	C₂²⋊C₄	—	7	1	no	—
763	C₂²⋊C₄	—	7	1	no	—
764	C₂²⋊C₄	—	7	1	no	—
765	C₂²⋊C₄	—	7	1	no	—
766	C₂²⋊C₄	—	7	1	no	—
767	C₂²⋊C₄	—	7	1	no	—
768	C₂²⋊C₄	—	7	1	no	—
769	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
770	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
771	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
772	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
773	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
774	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
775	C₄²	—	7	1	no	—
776	C₄²	—	7	1	no	—
777	C₄²	—	7	1	no	—
778	C₄²	—	7	1	no	—
779	C₄²	—	7	1	no	—
780	C₄²	—	7	1	no	—
781	C₄²	—	7	1	no	—
782	C₄²	—	7	1	no	—
783	C₄²	—	7	1	no	—
784	C₄²	—	7	1	no	—
785	C₄²	—	7	1	no	—
786	C₄²	—	7	1	no	—
787	C₄²	—	7	1	no	—
788	C₄²	—	7	1	no	—
789	C₄²	—	7	1	no	—
790	C₄²	C₂²×D₇	1	1	yes	characteristic
791	C₄²	C₂²×D₇	1	1	yes	characteristic
792	C₄²	C₂²×D₇	1	1	yes	characteristic
793	C₂×C₇	—	2	2	no	—
794	C₂×C₇	—	4	1	no	—
795	C₂×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
796	C₂×C₇	#585	1	1	yes	characteristic
797	C₂×C₇	#585	1	1	yes	characteristic
798	D₇	—	4	1	no	—
799	D₇	—	4	1	no	—
800	D₇	—	4	1	no	—
801	C₂³	—	7	1	no	—
802	C₂³	—	7	1	no	—
803	C₂³	—	7	1	no	—
804	C₂³	—	14	2	no	—
805	C₂³	—	28	1	no	—
806	C₂³	—	28	1	no	—
807	C₂³	C₂³×D₇	1	1	yes	characteristic
808	C₂³	C₂³×D₇	1	1	yes	characteristic
809	Q₈	—	4	1	no	—
810	Q₈	—	4	1	no	—
811	Q₈	—	4	1	no	—
812	Q₈	—	28	1	no	—
813	Q₈	—	28	1	no	—
814	Q₈	—	28	1	no	—
815	Q₈	—	28	1	no	—
816	Q₈	—	28	1	no	—
817	Q₈	—	28	1	no	—
818	D₄	—	2	2	no	—
819	D₄	—	14	2	no	—
820	D₄	—	28	1	no	—
821	D₄	—	28	1	no	—
822	D₄	—	28	1	no	—
823	D₄	—	28	1	no	—
824	D₄	—	28	1	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	1	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	7	1	no	—
832	C₂×C₄	—	7	1	no	—
833	C₂×C₄	—	7	1	no	—
834	C₂×C₄	—	7	1	no	—
835	C₂×C₄	—	7	1	no	—
836	C₂×C₄	—	7	1	no	—
837	C₂×C₄	—	7	1	no	—
838	C₂×C₄	—	7	1	no	—
839	C₂×C₄	—	7	1	no	—
840	C₂×C₄	—	7	1	no	—
841	C₂×C₄	—	7	1	no	—
842	C₂×C₄	—	7	1	no	—
843	C₂×C₄	—	7	1	no	—
844	C₂×C₄	—	14	2	no	—
845	C₂×C₄	—	14	2	no	—
846	C₂×C₄	—	28	1	no	—
847	C₂×C₄	—	28	1	no	—
848	C₂×C₄	—	28	1	no	—
849	C₂×C₄	—	28	1	no	—
850	C₂×C₄	—	28	1	no	—
851	C₂×C₄	—	28	1	no	—
852	C₂×C₄	—	28	1	no	—
853	C₂×C₄	—	28	1	no	—
854	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
855	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
856	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
857	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
858	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
859	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
860	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
861	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
862	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
863	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
864	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
865	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
866	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
867	C₇	#3564	1	1	yes	characteristic, complemented, Sylow
868	C₂²	—	2	1	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	2	1	no	—
872	C₂²	—	2	1	no	—
873	C₂²	—	14	1	no	—
874	C₂²	—	14	1	no	—
875	C₂²	—	14	1	no	—
876	C₂²	—	14	1	no	—
877	C₂²	—	14	1	no	—
878	C₂²	—	14	1	no	—
879	C₂²	—	14	1	no	—
880	C₂²	—	14	1	no	—
881	C₂²	—	14	1	no	—
882	C₂²	—	56	2	no	—
883	C₂²	#6551	1	2	yes	—
884	C₂²	C₂⁴×D₇	1	1	yes	characteristic
885	C₄	—	2	1	no	—
886	C₄	—	2	1	no	—
887	C₄	—	2	1	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	1	no	—
890	C₄	—	2	1	no	—
891	C₄	—	2	1	no	—
892	C₄	—	2	1	no	—
893	C₄	—	2	1	no	—
894	C₄	—	2	1	no	—
895	C₄	—	2	1	no	—
896	C₄	—	2	1	no	—
897	C₄	—	2	1	no	—
898	C₄	—	14	1	no	—
899	C₄	—	14	1	no	—
900	C₄	—	14	1	no	—
901	C₄	—	14	1	no	—
902	C₄	—	14	1	no	—
903	C₄	—	14	1	no	—
904	C₄	—	14	1	no	—
905	C₄	—	14	1	no	—
906	C₄	—	14	1	no	—
907	C₄	—	14	1	no	—
908	C₄	—	14	1	no	—
909	C₄	—	14	1	no	—
910	C₄	—	14	1	no	—
911	C₂	—	2	2	no	—
912	C₂	—	4	1	no	—
913	C₂	—	28	1	no	—
914	C₂	—	28	1	no	—
915	C₂	—	28	1	no	—
916	C₂	C₂×#6551	1	1	yes	characteristic
917	C₂	#90616	1	1	yes	characteristic
918	C₂	#90618	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#554	C₂
prime radical	#90251	C₂
hypercenter	#554	D₇
hypocenter	C₇	#3564
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. C₇×#554	C₂	semidirect
2. #90426	C₂	semidirect
3. #90422	C₂	semidirect
4. #90390	C₂	semidirect
5. #90387	C₂	semidirect
6. #90387	C₂	semidirect
7. #90384	C₂	semidirect
8. #90337	C₂	semidirect
9. #90337	C₂	semidirect
10. #90334	C₂	semidirect
11. #90333	C₂	semidirect
12. #90332	C₂	semidirect
13. #90331	C₂	semidirect
14. #90329	C₂	semidirect
15. #90328	C₂	semidirect
16. #90328	C₂	semidirect
17. #90325	C₂	semidirect
18. #90314	C₂	semidirect
19. #90313	C₂	semidirect
20. #90274	C₂	semidirect
21. #90259	C₂	semidirect
22. #90255	C₂	semidirect
24. #90247	C₂	semidirect
25. #90247	C₂	semidirect
26. #90232	C₂	semidirect
27. #90229	C₂	semidirect
28. #90206	C₂	semidirect
29. #90204	C₂	semidirect
30. C₂×#6461	C₂	semidirect
31. #90202	C₂	semidirect
32. C₇×C₄⋊Q₈	C₂²	semidirect
33. C₇×#125	C₂²	semidirect
34. C₇×#125	C₂²	semidirect
38. C₇×C₂²⋊Q₈	C₂²	semidirect
39. C₇×C₂²⋊Q₈	C₂²	semidirect
40. C₇×C₂²⋊Q₈	C₂²	semidirect
41. C₄×C₇×Q₈	C₂²	semidirect
46. C₂×C₇×C₄⋊C₄	C₂²	semidirect
53. #6509	C₂²	semidirect
54. Q₈×Dic₇	C₂²	semidirect
55. Q₈×Dic₇	C₂²	semidirect
56. #6507	C₂²	semidirect
57. #6507	C₂²	semidirect
58. #6507	C₂²	semidirect
67. #6492	C₂²	semidirect
73. C₄×C₂²⋊D₇	C₂²	semidirect
77. #6489	C₂²	semidirect
78. #6489	C₂²	semidirect
83. #6487	C₂²	semidirect
84. #6487	C₂²	semidirect
102. #6461	C₂²	semidirect
103. #6461	C₂²	semidirect
104. #6461	C₂²	semidirect
107. #6460	C₂²	semidirect
114. #6459	C₂²	semidirect
115. #6459	C₂²	semidirect
116. #6459	C₂²	semidirect
126. #6455	C₂²	semidirect
127. D₇×C₄⋊C₄	C₂²	semidirect
128. #6453	C₂²	semidirect
129. #6453	C₂²	semidirect
130. #6453	C₂²	semidirect
131. #6452	C₂²	semidirect
132. #6452	C₂²	semidirect
133. #6452	C₂²	semidirect
134. #6452	C₂²	semidirect
135. #6452	C₂²	semidirect
136. #6452	C₂²	semidirect
137. #6452	C₂²	semidirect
138. #6452	C₂²	semidirect
139. #6452	C₂²	semidirect
140. #6452	C₂²	semidirect
141. #6452	C₂²	semidirect
142. #6452	C₂²	semidirect
143. #6451	C₂²	semidirect
144. #6451	C₂²	semidirect
145. #6451	C₂²	semidirect
146. #6451	C₂²	semidirect
147. #6450	C₂²	semidirect
148. #6450	C₂²	semidirect
149. #6450	C₂²	semidirect
150. #6450	C₂²	semidirect
156. #6448	C₂²	semidirect
160. #6446	C₂²	semidirect
164. #6442	C₂²	semidirect
165. #6442	C₂²	semidirect
166. #6442	C₂²	semidirect
167. #6442	C₂²	semidirect
178. #6439	C₂²	semidirect
182. #6435	C₂²	semidirect
183. #6433	C₂²	semidirect
184. #6433	C₂²	semidirect
185. C₄×Dic₁₄	C₂²	semidirect
186. C₄×Dic₁₄	C₂²	semidirect
350. #554	D₇	semidirect
447. C₄⋊Q₈	C₂×D₇	semidirect
491. #125	C₂×D₇	semidirect
492. #125	C₂×D₇	semidirect
544. C₂²⋊Q₈	C₂×D₇	semidirect
545. C₂²⋊Q₈	C₂×D₇	semidirect
546. C₂²⋊Q₈	C₂×D₇	semidirect
560. C₄×Q₈	C₂×D₇	semidirect
588. C₂×C₄⋊C₄	C₂×D₇	semidirect
867. C₇	#3564	semidirect

Maximal subgroups

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

subgroup	index
C₇×#554	2
#90426	2
#90422	2
#90390	2
#90387	2
#90384	2
#90337	2
#90334	2
#90333	2
#90332	2
#90331	2
#90329	2
#90328	2
#90325	2
#90314	2
#90313	2
#90274	2
#90259	2
#90255	2
#90251	2
#90247	2
#90232	2
#90229	2
#90206	2
#90204	2
C₂×#6461	2
#90202	2
#3564	7